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"using Plots, ComplexPhasePortrait, ApproxFun, SingularIntegralEquations, DifferentialEquations\n",
"gr();"
]
},
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"# M3M6: Methods of Mathematical Physics\n",
"\n",
"$$\n",
"\\def\\dashint{{\\int\\!\\!\\!\\!\\!\\!-\\,}}\n",
"\\def\\infdashint{\\dashint_{\\!\\!\\!-\\infty}^{\\,\\infty}}\n",
"\\def\\D{\\,{\\rm d}}\n",
"\\def\\E{{\\rm e}}\n",
"\\def\\dx{\\D x}\n",
"\\def\\dt{\\D t}\n",
"\\def\\dz{\\D z}\n",
"\\def\\C{{\\mathbb C}}\n",
"\\def\\R{{\\mathbb R}}\n",
"\\def\\CC{{\\cal C}}\n",
"\\def\\HH{{\\cal H}}\n",
"\\def\\I{{\\rm i}}\n",
"\\def\\qqqquad{\\qquad\\qquad}\n",
"\\def\\qqfor{\\qquad\\hbox{for}\\qquad}\n",
"\\def\\qqwhere{\\qquad\\hbox{where}\\qquad}\n",
"\\def\\Res_#1{\\underset{#1}{\\rm Res}}\\,\n",
"\\def\\sech{{\\rm sech}\\,}\n",
"\\def\\acos{\\,{\\rm acos}\\,}\n",
"\\def\\vc#1{{\\mathbf #1}}\n",
"\\def\\ip<#1,#2>{\\left\\langle#1,#2\\right\\rangle}\n",
"\\def\\norm#1{\\left\\|#1\\right\\|}\n",
"$$\n",
"\n",
"Dr. Sheehan Olver\n",
"<br>\n",
"s.olver@imperial.ac.uk\n",
"\n",
"<br>\n",
"Website: https://github.com/dlfivefifty/M3M6LectureNotes\n",
"\n",
"# Chapter 3: Orthogonal Polynomials\n",
"\n",
"We now introduce orthogonal polynomials (OPs). These are ___fundamental___ for computational mathematics, with applications in\n",
"1. Function approximation\n",
"2. Quadrature (calculating integrals)\n",
"2. Solving differential equations\n",
"3. Spectral analysis of Schrödinger operators\n",
"\n",
"We will investigate the properties of _general_ OPs:\n",
"\n",
"1. Construction via Gram–Schmidt \n",
"2. Three-term recurrence relationships\n",
"3. Gaussian quadrature\n",
"3. Relationship with Cauchy and logarithmic transforms\n",
"\n",
"We will also investigate the properties of _classical_ OPs:\n",
"\n",
"1. Explicit formulae\n",
"3. Rodriguez formulae\n",
"2. Ordinary differential equations\n",
"2. Derivatives\n",
"\n",
"A good reference is [Digital Library of Mathematical Functions, Chapter 18](http://dlmf.nist.gov/18).\n",
"\n",
"\n",
"\n",
"# Lecture 14: Constructing orthogonal polynomials\n",
"\n",
"\n",
"This lecture we do the following:\n",
"1. Definition of orthogonal polynomials\n",
"2. Definition of classical orthogonal polynomials\n",
" - Hermite, Laguerre, and Jacobi polynomials\n",
" - Legendre, Chebyshev, and ultraspherical polynomials\n",
" - Explicit construction for Chebyshev polynomials\n",
"2. Construction of orthogonal polynomials via Gram–Schmidt process \n",
"3. Function approximation with orthogonal polynomials \n",
"\n",
"\n",
"## Definition of orthogonal polynomials\n",
"\n",
"Let $p_0(x),p_1(x),p_2(x),…$ be a sequence of polynomials such that $p_n(x)$ is exactly degree $n$, that is,\n",
"$$\n",
"p_n(x) = k_n x^n + O(x^{n-1})\n",
"$$\n",
"where $k_n \\neq 0$.\n",
"\n",
"Let $w(x)$ be a continuous weight function on a (possibly infinite) interval $(a,b)$: that is $w(x) \\geq 0$ for all $a < x < b$. This induces an inner product\n",
"$$\n",
"\\ip<f,g> := \\int_a^b f(x) g(x) w(x) \\dx\n",
"$$\n",
"We say that $\\{p_0, p_1,\\ldots\\}$ are _orthogonal with respect to the weight $w$_ if \n",
"$$\n",
"\\ip<p_n,p_m> = 0\\qqfor n \\neq m.\n",
"$$\n",
"Because $w$ is continuous, we have\n",
"$$\n",
"\\norm{p_n}^2 = \\ip<p_n,p_n> > 0 .\n",
"$$\n",
"\n",
"Orthogonal polymomials are not unique: we can multiply each $p_n$ by a different nonzero constant $\\tilde p_n(x) = c_n p_n(x)$, and $\\tilde p_n$ will be orthogonal w.r.t. $w$. However, if we specify $k_n$, this is sufficient to uniquely define them:\n",
"\n",
"**Proposition (Uniqueness of OPs I)** Given a non-zero $k_n$, there is a unique polynomial $p_n$ orthogonal w.r.t. $w$ to all lower degree polynomials.\n",
"\n",
"**Proof** Suppose $r_n(x) = k_n x^n + O(x^{n-1})$ is another OP w.r.t. $w$. We want to show $p_n - r_n$ is zero. But this is a polynomial of degree $<n$, hence\n",
"$$\n",
"p_n(x) - r_n(x) = \\sum_{k=0}^{n-1} c_k p_k(x)\n",
"$$\n",
"But we have for $k \\leq n-1$\n",
"$$\n",
"\\ip<p_k,p_k> c_k = \\ip<p_n - r_n, p_k> = \\ip<p_n,p_k> - \\ip<r_n, p_k> = 0 - 0 = 0\n",
"$$\n",
"which shows all $c_k$ are zero.\n",
"\n",
"**Corollary (Uniqueness of OPs I)** If $q_n$ and $p_n$ are orthogonal w.r.t. $w$ to all lower degree polynomials, then $q_n(x) = C p_n(x)$ for some constant $C$. \n",
"\n",
"### Monic orthogonal polynomials\n",
"\n",
"If $k_n = 1$, that is, \n",
"$$\n",
"p_n(x) = x^n + O(x^{n-1})\n",
"$$\n",
"then we refer to the orthogonal polymomials as monic.\n",
"\n",
"Monic OPs are unique as we have specified $k_n$.\n",
"\n",
"\n",
"### Orthonormal polynomials\n",
"\n",
"If $\\norm{p_n} = 1$, then we refer to the orthogonal polynomials as orthonormal w.r.t. $w$. We will usually use $q_n$ when they are orthonormal. Note it's not unique: we can multiply by $\\pm 1$ without changing the norm.\n",
"\n",
"\n",
"**Remark** The classical OPs are __not__ monic or orthonormal (apart from one case). Many people make the mistake of using orthonormal polynomials for computations. But there is a good reason to use classical OPs: their properties result in rational formulae, whereas orthonormal polynomials require square roots. This makes a big performance difference.\n"
]
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"## Definition of classical orthogonal polynomials\n",
"\n",
"Classical orthogonal polynomials are orthogonal with respect to the following three weights:\n",
"\n",
"\n",
"| Name | Interval $(a,b)$ |Weight function $w(x)$ | Standard polynomial | highest order coefficient $k_n$ |\n",
"|:-------------|:------------- |:----------------------|:-----|:-----|\n",
"| Hermite |$(-\\infty,\\infty)$ | $\\E^{-x^2}$ | $H_n(x)$ | $2^n$ |\n",
"| Laguerre | $(0,\\infty)$ | $x^\\alpha \\E^{-x}$ | $L_n^{(\\alpha)}(x)$ | See [Table 18.3.1](http://dlmf.nist.gov/18.3) |\n",
"| Jacobi | $(-1,1)$ | $(1-x)^{\\alpha} (1+x)^\\beta$ | $P_n^{(\\alpha,\\beta)}(x)$ | See [Table 18.3.1](http://dlmf.nist.gov/18.3) |\n",
"\n",
"\n",
"Note out of convention the parameters for Jacobi polynomials are in the \"wrong\" order.\n",
"\n",
"We can actually construct these polynomials in Julia: first consider Hermite:"
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" 937.322,773.539 939.82,773.539 942.318,773.539 944.816,773.539 947.314,773.539 949.812,773.539 952.31,773.539 954.808,773.539 957.306,773.539 959.805,773.539 \n",
" 962.303,773.539 964.801,773.539 967.299,773.539 969.797,773.539 972.295,773.539 974.793,773.539 977.291,773.539 979.789,773.539 982.287,773.539 984.785,773.539 \n",
" 987.283,773.539 989.781,773.539 992.28,773.539 994.778,773.539 997.276,773.539 999.774,773.539 1002.27,773.539 1004.77,773.539 1007.27,773.539 1009.77,773.539 \n",
" 1012.26,773.539 1014.76,773.539 1017.26,773.539 1019.76,773.539 1022.26,773.539 1024.75,773.539 1027.25,773.539 1029.75,773.539 1032.25,773.539 1034.75,773.539 \n",
" 1037.25,773.539 1039.74,773.539 1042.24,773.539 1044.74,773.539 1047.24,773.539 1049.74,773.539 1052.23,773.539 1054.73,773.539 1057.23,773.539 1059.73,773.539 \n",
" 1062.23,773.539 1064.72,773.539 1067.22,773.539 1069.72,773.539 1072.22,773.539 1074.72,773.539 1077.21,773.539 1079.71,773.539 1082.21,773.539 1084.71,773.539 \n",
" 1087.21,773.539 1089.7,773.539 1092.2,773.539 1094.7,773.539 1097.2,773.539 1099.7,773.539 1102.2,773.539 1104.69,773.539 1107.19,773.539 1109.69,773.539 \n",
" 1112.19,773.539 1114.69,773.539 1117.18,773.539 1119.68,773.539 1122.18,773.539 1124.68,773.539 1127.18,773.539 1129.67,773.539 1132.17,773.539 1134.67,773.539 \n",
" 1137.17,773.539 1139.67,773.539 1142.16,773.539 1144.66,773.539 1147.16,773.539 1149.66,773.539 1152.16,773.539 1154.65,773.539 1157.15,773.539 1159.65,773.539 \n",
" 1162.15,773.539 1164.65,773.539 1167.15,773.539 1169.64,773.539 1172.14,773.539 1174.64,773.539 1177.14,773.539 1179.64,773.539 1182.13,773.539 1184.63,773.539 \n",
" 1187.13,773.539 1189.63,773.539 1192.13,773.539 1194.62,773.539 1197.12,773.539 1199.62,773.539 1202.12,773.539 1204.62,773.539 1207.11,773.539 1209.61,773.539 \n",
" 1212.11,773.539 1214.61,773.539 1217.11,773.539 1219.61,773.539 1222.1,773.539 1224.6,773.539 1227.1,773.539 1229.6,773.539 1232.1,773.539 1234.59,773.539 \n",
" 1237.09,773.539 1239.59,773.539 1242.09,773.539 1244.59,773.539 1247.08,773.539 1249.58,773.539 1252.08,773.539 1254.58,773.539 1257.08,773.539 1259.57,773.539 \n",
" 1262.07,773.539 1264.57,773.539 1267.07,773.539 1269.57,773.539 1272.06,773.539 1274.56,773.539 1277.06,773.539 1279.56,773.539 1282.06,773.539 1284.56,773.539 \n",
" 1287.05,773.539 1289.55,773.539 1292.05,773.539 1294.55,773.539 1297.05,773.539 1299.54,773.539 1302.04,773.539 1304.54,773.539 1307.04,773.539 1309.54,773.539 \n",
" 1312.03,773.539 1314.53,773.539 1317.03,773.539 1319.53,773.539 1322.03,773.539 1324.52,773.539 1327.02,773.539 1329.52,773.539 1332.02,773.539 1334.52,773.539 \n",
" 1337.02,773.539 1339.51,773.539 1342.01,773.539 1344.51,773.539 1347.01,773.539 1349.51,773.539 1352,773.539 1354.5,773.539 1357,773.539 1359.5,773.539 \n",
" 1362,773.539 1364.49,773.539 1366.99,773.539 1369.49,773.539 1371.99,773.539 1374.49,773.539 1376.98,773.539 1379.48,773.539 1381.98,773.539 1384.48,773.539 \n",
" 1386.98,773.539 1389.47,773.539 1391.97,773.539 1394.47,773.539 1396.97,773.539 1399.47,773.539 1401.97,773.539 1404.46,773.539 1406.96,773.539 1409.46,773.539 \n",
" 1411.96,773.539 1414.46,773.539 1416.95,773.539 1419.45,773.539 1421.95,773.539 1424.45,773.539 1426.95,773.539 1429.44,773.539 1431.94,773.539 1434.44,773.539 \n",
" 1436.94,773.539 1439.44,773.539 1441.93,773.539 1444.43,773.539 1446.93,773.539 1449.43,773.539 1451.93,773.539 1454.42,773.539 1456.92,773.539 1459.42,773.539 \n",
" 1461.92,773.539 1464.42,773.539 1466.92,773.539 1469.41,773.539 1471.91,773.539 1474.41,773.539 1476.91,773.539 1479.41,773.539 1481.9,773.539 1484.4,773.539 \n",
" 1486.9,773.539 1489.4,773.539 1491.9,773.539 1494.39,773.539 1496.89,773.539 1499.39,773.539 1501.89,773.539 1504.39,773.539 1506.88,773.539 1509.38,773.539 \n",
" 1511.88,773.539 1514.38,773.539 1516.88,773.539 1519.38,773.539 1521.87,773.539 1524.37,773.539 1526.87,773.539 1529.37,773.539 1531.87,773.539 1534.36,773.539 \n",
" 1536.86,773.539 1539.36,773.539 1541.86,773.539 1544.36,773.539 1546.85,773.539 1549.35,773.539 1551.85,773.539 1554.35,773.539 1556.85,773.539 1559.34,773.539 \n",
" 1561.84,773.539 1564.34,773.539 1566.84,773.539 1569.34,773.539 1571.83,773.539 1574.33,773.539 1576.83,773.539 1579.33,773.539 1581.83,773.539 1584.33,773.539 \n",
" 1586.82,773.539 1589.32,773.539 1591.82,773.539 1594.32,773.539 1596.82,773.539 1599.31,773.539 1601.81,773.539 1604.31,773.539 1606.81,773.539 1609.31,773.539 \n",
" 1611.8,773.539 1614.3,773.539 1616.8,773.539 1619.3,773.539 1621.8,773.539 1624.29,773.539 1626.79,773.539 1629.29,773.539 1631.79,773.539 1634.29,773.539 \n",
" 1636.79,773.539 1639.28,773.539 1641.78,773.539 1644.28,773.539 1646.78,773.539 1649.28,773.539 1651.77,773.539 1654.27,773.539 1656.77,773.539 1659.27,773.539 \n",
" 1661.77,773.539 1664.26,773.539 1666.76,773.539 1669.26,773.539 1671.76,773.539 1674.26,773.539 1676.75,773.539 1679.25,773.539 1681.75,773.539 1684.25,773.539 \n",
" 1686.75,773.539 1689.24,773.539 1691.74,773.539 1694.24,773.539 1696.74,773.539 1699.24,773.539 1701.74,773.539 1704.23,773.539 1706.73,773.539 1709.23,773.539 \n",
" 1711.73,773.539 1714.23,773.539 1716.72,773.539 1719.22,773.539 1721.72,773.539 1724.22,773.539 1726.72,773.539 1729.21,773.539 1731.71,773.539 1734.21,773.539 \n",
" 1736.71,773.539 1739.21,773.539 1741.7,773.539 1744.2,773.539 1746.7,773.539 1749.2,773.539 1751.7,773.539 1754.19,773.539 1756.69,773.539 1759.19,773.539 \n",
" 1761.69,773.539 1764.19,773.539 1766.69,773.539 1769.18,773.539 1771.68,773.539 1774.18,773.539 1776.68,773.539 1779.18,773.539 1781.67,773.539 1784.17,773.539 \n",
" 1786.67,773.539 1789.17,773.539 1791.67,773.539 1794.16,773.539 1796.66,773.539 1799.16,773.539 1801.66,773.539 1804.16,773.539 1806.65,773.539 1809.15,773.539 \n",
" 1811.65,773.539 1814.15,773.539 1816.65,773.539 1819.15,773.539 1821.64,773.539 1824.14,773.539 1826.64,773.539 1829.14,773.539 1831.64,773.539 1834.13,773.539 \n",
" 1836.63,773.539 1839.13,773.539 1841.63,773.539 1844.13,773.539 1846.62,773.539 1849.12,773.539 1851.62,773.539 1854.12,773.539 1856.62,773.539 1859.11,773.539 \n",
" 1861.61,773.539 1864.11,773.539 1866.61,773.539 1869.11,773.539 1871.6,773.539 1874.1,773.539 1876.6,773.539 1879.1,773.539 1881.6,773.539 1884.1,773.539 \n",
" 1886.59,773.539 1889.09,773.539 1891.59,773.539 1894.09,773.539 1896.59,773.539 1899.08,773.539 1901.58,773.539 1904.08,773.539 1906.58,773.539 1909.08,773.539 \n",
" 1911.57,773.539 1914.07,773.539 1916.57,773.539 1919.07,773.539 1921.57,773.539 1924.06,773.539 1926.56,773.539 1929.06,773.539 1931.56,773.539 1934.06,773.539 \n",
" 1936.56,773.539 1939.05,773.539 1941.55,773.539 1944.05,773.539 1946.55,773.539 1949.05,773.539 1951.54,773.539 1954.04,773.539 1956.54,773.539 1959.04,773.539 \n",
" 1961.54,773.539 1964.03,773.539 1966.53,773.539 1969.03,773.539 1971.53,773.539 1974.03,773.539 1976.52,773.539 1979.02,773.539 1981.52,773.539 1984.02,773.539 \n",
" 1986.52,773.539 1989.01,773.539 1991.51,773.539 1994.01,773.539 1996.51,773.539 1999.01,773.539 2001.51,773.539 2004,773.539 2006.5,773.539 2009,773.539 \n",
" 2011.5,773.539 2014,773.539 2016.49,773.539 2018.99,773.539 2021.49,773.539 2023.99,773.539 2026.49,773.539 2028.98,773.539 2031.48,773.539 2033.98,773.539 \n",
" 2036.48,773.539 2038.98,773.539 2041.47,773.539 2043.97,773.539 2046.47,773.539 2048.97,773.539 2051.47,773.539 2053.96,773.539 2056.46,773.539 2058.96,773.539 \n",
" 2061.46,773.539 2063.96,773.539 2066.46,773.539 2068.95,773.539 2071.45,773.539 2073.95,773.539 2076.45,773.539 2078.95,773.539 2081.44,773.539 2083.94,773.539 \n",
" 2086.44,773.539 2088.94,773.539 2091.44,773.539 2093.93,773.539 2096.43,773.539 2098.93,773.539 2101.43,773.539 2103.93,773.539 2106.42,773.539 2108.92,773.539 \n",
" 2111.42,773.539 2113.92,773.539 2116.42,773.539 2118.92,773.539 2121.41,773.539 2123.91,773.539 2126.41,773.539 2128.91,773.539 2131.41,773.539 2133.9,773.539 \n",
" 2136.4,773.539 2138.9,773.539 2141.4,773.539 2143.9,773.539 2146.39,773.539 2148.89,773.539 2151.39,773.539 2153.89,773.539 2156.39,773.539 2158.88,773.539 \n",
" 2161.38,773.539 2163.88,773.539 2166.38,773.539 2168.88,773.539 2171.37,773.539 2173.87,773.539 2176.37,773.539 2178.87,773.539 2181.37,773.539 2183.87,773.539 \n",
" 2186.36,773.539 2188.86,773.539 2191.36,773.539 2193.86,773.539 2196.36,773.539 2198.85,773.539 2201.35,773.539 2203.85,773.539 2206.35,773.539 2208.85,773.539 \n",
" 2211.34,773.539 2213.84,773.539 2216.34,773.539 2218.84,773.539 2221.34,773.539 2223.83,773.539 2226.33,773.539 2228.83,773.539 2231.33,773.539 2233.83,773.539 \n",
" 2236.33,773.539 2238.82,773.539 2241.32,773.539 2243.82,773.539 2246.32,773.539 2248.82,773.539 2251.31,773.539 2253.81,773.539 2256.31,773.539 2258.81,773.539 \n",
" 2261.31,773.539 \n",
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" 1187.13,776.452 1189.63,776.415 1192.13,776.379 1194.62,776.342 1197.12,776.306 1199.62,776.27 1202.12,776.233 1204.62,776.197 1207.11,776.16 1209.61,776.124 \n",
" 1212.11,776.088 1214.61,776.051 1217.11,776.015 1219.61,775.978 1222.1,775.942 1224.6,775.905 1227.1,775.869 1229.6,775.833 1232.1,775.796 1234.59,775.76 \n",
" 1237.09,775.723 1239.59,775.687 1242.09,775.651 1244.59,775.614 1247.08,775.578 1249.58,775.541 1252.08,775.505 1254.58,775.469 1257.08,775.432 1259.57,775.396 \n",
" 1262.07,775.359 1264.57,775.323 1267.07,775.287 1269.57,775.25 1272.06,775.214 1274.56,775.177 1277.06,775.141 1279.56,775.105 1282.06,775.068 1284.56,775.032 \n",
" 1287.05,774.995 1289.55,774.959 1292.05,774.923 1294.55,774.886 1297.05,774.85 1299.54,774.813 1302.04,774.777 1304.54,774.741 1307.04,774.704 1309.54,774.668 \n",
" 1312.03,774.631 1314.53,774.595 1317.03,774.558 1319.53,774.522 1322.03,774.486 1324.52,774.449 1327.02,774.413 1329.52,774.376 1332.02,774.34 1334.52,774.304 \n",
" 1337.02,774.267 1339.51,774.231 1342.01,774.194 1344.51,774.158 1347.01,774.122 1349.51,774.085 1352,774.049 1354.5,774.012 1357,773.976 1359.5,773.94 \n",
" 1362,773.903 1364.49,773.867 1366.99,773.83 1369.49,773.794 1371.99,773.758 1374.49,773.721 1376.98,773.685 1379.48,773.648 1381.98,773.612 1384.48,773.576 \n",
" 1386.98,773.539 1389.47,773.503 1391.97,773.466 1394.47,773.43 1396.97,773.393 1399.47,773.357 1401.97,773.321 1404.46,773.284 1406.96,773.248 1409.46,773.211 \n",
" 1411.96,773.175 1414.46,773.139 1416.95,773.102 1419.45,773.066 1421.95,773.029 1424.45,772.993 1426.95,772.957 1429.44,772.92 1431.94,772.884 1434.44,772.847 \n",
" 1436.94,772.811 1439.44,772.775 1441.93,772.738 1444.43,772.702 1446.93,772.665 1449.43,772.629 1451.93,772.593 1454.42,772.556 1456.92,772.52 1459.42,772.483 \n",
" 1461.92,772.447 1464.42,772.411 1466.92,772.374 1469.41,772.338 1471.91,772.301 1474.41,772.265 1476.91,772.229 1479.41,772.192 1481.9,772.156 1484.4,772.119 \n",
" 1486.9,772.083 1489.4,772.046 1491.9,772.01 1494.39,771.974 1496.89,771.937 1499.39,771.901 1501.89,771.864 1504.39,771.828 1506.88,771.792 1509.38,771.755 \n",
" 1511.88,771.719 1514.38,771.682 1516.88,771.646 1519.38,771.61 1521.87,771.573 1524.37,771.537 1526.87,771.5 1529.37,771.464 1531.87,771.428 1534.36,771.391 \n",
" 1536.86,771.355 1539.36,771.318 1541.86,771.282 1544.36,771.246 1546.85,771.209 1549.35,771.173 1551.85,771.136 1554.35,771.1 1556.85,771.064 1559.34,771.027 \n",
" 1561.84,770.991 1564.34,770.954 1566.84,770.918 1569.34,770.882 1571.83,770.845 1574.33,770.809 1576.83,770.772 1579.33,770.736 1581.83,770.699 1584.33,770.663 \n",
" 1586.82,770.627 1589.32,770.59 1591.82,770.554 1594.32,770.517 1596.82,770.481 1599.31,770.445 1601.81,770.408 1604.31,770.372 1606.81,770.335 1609.31,770.299 \n",
" 1611.8,770.263 1614.3,770.226 1616.8,770.19 1619.3,770.153 1621.8,770.117 1624.29,770.081 1626.79,770.044 1629.29,770.008 1631.79,769.971 1634.29,769.935 \n",
" 1636.79,769.899 1639.28,769.862 1641.78,769.826 1644.28,769.789 1646.78,769.753 1649.28,769.717 1651.77,769.68 1654.27,769.644 1656.77,769.607 1659.27,769.571 \n",
" 1661.77,769.534 1664.26,769.498 1666.76,769.462 1669.26,769.425 1671.76,769.389 1674.26,769.352 1676.75,769.316 1679.25,769.28 1681.75,769.243 1684.25,769.207 \n",
" 1686.75,769.17 1689.24,769.134 1691.74,769.098 1694.24,769.061 1696.74,769.025 1699.24,768.988 1701.74,768.952 1704.23,768.916 1706.73,768.879 1709.23,768.843 \n",
" 1711.73,768.806 1714.23,768.77 1716.72,768.734 1719.22,768.697 1721.72,768.661 1724.22,768.624 1726.72,768.588 1729.21,768.552 1731.71,768.515 1734.21,768.479 \n",
" 1736.71,768.442 1739.21,768.406 1741.7,768.37 1744.2,768.333 1746.7,768.297 1749.2,768.26 1751.7,768.224 1754.19,768.187 1756.69,768.151 1759.19,768.115 \n",
" 1761.69,768.078 1764.19,768.042 1766.69,768.005 1769.18,767.969 1771.68,767.933 1774.18,767.896 1776.68,767.86 1779.18,767.823 1781.67,767.787 1784.17,767.751 \n",
" 1786.67,767.714 1789.17,767.678 1791.67,767.641 1794.16,767.605 1796.66,767.569 1799.16,767.532 1801.66,767.496 1804.16,767.459 1806.65,767.423 1809.15,767.387 \n",
" 1811.65,767.35 1814.15,767.314 1816.65,767.277 1819.15,767.241 1821.64,767.205 1824.14,767.168 1826.64,767.132 1829.14,767.095 1831.64,767.059 1834.13,767.022 \n",
" 1836.63,766.986 1839.13,766.95 1841.63,766.913 1844.13,766.877 1846.62,766.84 1849.12,766.804 1851.62,766.768 1854.12,766.731 1856.62,766.695 1859.11,766.658 \n",
" 1861.61,766.622 1864.11,766.586 1866.61,766.549 1869.11,766.513 1871.6,766.476 1874.1,766.44 1876.6,766.404 1879.1,766.367 1881.6,766.331 1884.1,766.294 \n",
" 1886.59,766.258 1889.09,766.222 1891.59,766.185 1894.09,766.149 1896.59,766.112 1899.08,766.076 1901.58,766.04 1904.08,766.003 1906.58,765.967 1909.08,765.93 \n",
" 1911.57,765.894 1914.07,765.858 1916.57,765.821 1919.07,765.785 1921.57,765.748 1924.06,765.712 1926.56,765.675 1929.06,765.639 1931.56,765.603 1934.06,765.566 \n",
" 1936.56,765.53 1939.05,765.493 1941.55,765.457 1944.05,765.421 1946.55,765.384 1949.05,765.348 1951.54,765.311 1954.04,765.275 1956.54,765.239 1959.04,765.202 \n",
" 1961.54,765.166 1964.03,765.129 1966.53,765.093 1969.03,765.057 1971.53,765.02 1974.03,764.984 1976.52,764.947 1979.02,764.911 1981.52,764.875 1984.02,764.838 \n",
" 1986.52,764.802 1989.01,764.765 1991.51,764.729 1994.01,764.693 1996.51,764.656 1999.01,764.62 2001.51,764.583 2004,764.547 2006.5,764.51 2009,764.474 \n",
" 2011.5,764.438 2014,764.401 2016.49,764.365 2018.99,764.328 2021.49,764.292 2023.99,764.256 2026.49,764.219 2028.98,764.183 2031.48,764.146 2033.98,764.11 \n",
" 2036.48,764.074 2038.98,764.037 2041.47,764.001 2043.97,763.964 2046.47,763.928 2048.97,763.892 2051.47,763.855 2053.96,763.819 2056.46,763.782 2058.96,763.746 \n",
" 2061.46,763.71 2063.96,763.673 2066.46,763.637 2068.95,763.6 2071.45,763.564 2073.95,763.528 2076.45,763.491 2078.95,763.455 2081.44,763.418 2083.94,763.382 \n",
" 2086.44,763.346 2088.94,763.309 2091.44,763.273 2093.93,763.236 2096.43,763.2 2098.93,763.163 2101.43,763.127 2103.93,763.091 2106.42,763.054 2108.92,763.018 \n",
" 2111.42,762.981 2113.92,762.945 2116.42,762.909 2118.92,762.872 2121.41,762.836 2123.91,762.799 2126.41,762.763 2128.91,762.727 2131.41,762.69 2133.9,762.654 \n",
" 2136.4,762.617 2138.9,762.581 2141.4,762.545 2143.9,762.508 2146.39,762.472 2148.89,762.435 2151.39,762.399 2153.89,762.363 2156.39,762.326 2158.88,762.29 \n",
" 2161.38,762.253 2163.88,762.217 2166.38,762.181 2168.88,762.144 2171.37,762.108 2173.87,762.071 2176.37,762.035 2178.87,761.998 2181.37,761.962 2183.87,761.926 \n",
" 2186.36,761.889 2188.86,761.853 2191.36,761.816 2193.86,761.78 2196.36,761.744 2198.85,761.707 2201.35,761.671 2203.85,761.634 2206.35,761.598 2208.85,761.562 \n",
" 2211.34,761.525 2213.84,761.489 2216.34,761.452 2218.84,761.416 2221.34,761.38 2223.83,761.343 2226.33,761.307 2228.83,761.27 2231.33,761.234 2233.83,761.198 \n",
" 2236.33,761.161 2238.82,761.125 2241.32,761.088 2243.82,761.052 2246.32,761.016 2248.82,760.979 2251.31,760.943 2253.81,760.906 2256.31,760.87 2258.81,760.834 \n",
" 2261.31,760.797 \n",
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" 1162.15,777.835 1164.65,777.893 1167.15,777.949 1169.64,778.003 1172.14,778.056 1174.64,778.108 1177.14,778.158 1179.64,778.207 1182.13,778.254 1184.63,778.3 \n",
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" 1237.09,778.927 1239.59,778.941 1242.09,778.953 1244.59,778.964 1247.08,778.974 1249.58,778.982 1252.08,778.988 1254.58,778.993 1257.08,778.997 1259.57,778.999 \n",
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" 1362,777.835 1364.49,777.776 1366.99,777.716 1369.49,777.654 1371.99,777.59 1374.49,777.526 1376.98,777.459 1379.48,777.392 1381.98,777.322 1384.48,777.252 \n",
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" 1461.92,774.34 1464.42,774.223 1466.92,774.104 1469.41,773.984 1471.91,773.862 1474.41,773.739 1476.91,773.615 1479.41,773.489 1481.9,773.361 1484.4,773.233 \n",
" 1486.9,773.102 1489.4,772.97 1491.9,772.837 1494.39,772.703 1496.89,772.566 1499.39,772.429 1501.89,772.29 1504.39,772.149 1506.88,772.007 1509.38,771.864 \n",
" 1511.88,771.719 1514.38,771.572 1516.88,771.425 1519.38,771.275 1521.87,771.125 1524.37,770.973 1526.87,770.819 1529.37,770.664 1531.87,770.507 1534.36,770.349 \n",
" 1536.86,770.19 1539.36,770.029 1541.86,769.867 1544.36,769.703 1546.85,769.537 1549.35,769.371 1551.85,769.202 1554.35,769.033 1556.85,768.862 1559.34,768.689 \n",
" 1561.84,768.515 1564.34,768.34 1566.84,768.163 1569.34,767.984 1571.83,767.804 1574.33,767.623 1576.83,767.44 1579.33,767.256 1581.83,767.071 1584.33,766.883 \n",
" 1586.82,766.695 1589.32,766.505 1591.82,766.313 1594.32,766.12 1596.82,765.926 1599.31,765.73 1601.81,765.533 1604.31,765.334 1606.81,765.134 1609.31,764.932 \n",
" 1611.8,764.729 1614.3,764.524 1616.8,764.318 1619.3,764.111 1621.8,763.902 1624.29,763.691 1626.79,763.479 1629.29,763.266 1631.79,763.051 1634.29,762.835 \n",
" 1636.79,762.617 1639.28,762.398 1641.78,762.178 1644.28,761.956 1646.78,761.732 1649.28,761.507 1651.77,761.281 1654.27,761.053 1656.77,760.823 1659.27,760.593 \n",
" 1661.77,760.36 1664.26,760.127 1666.76,759.891 1669.26,759.655 1671.76,759.417 1674.26,759.177 1676.75,758.936 1679.25,758.694 1681.75,758.45 1684.25,758.204 \n",
" 1686.75,757.957 1689.24,757.709 1691.74,757.459 1694.24,757.208 1696.74,756.956 1699.24,756.701 1701.74,756.446 1704.23,756.189 1706.73,755.93 1709.23,755.67 \n",
" 1711.73,755.409 1714.23,755.146 1716.72,754.882 1719.22,754.616 1721.72,754.349 1724.22,754.08 1726.72,753.81 1729.21,753.539 1731.71,753.265 1734.21,752.991 \n",
" 1736.71,752.715 1739.21,752.438 1741.7,752.159 1744.2,751.878 1746.7,751.597 1749.2,751.313 1751.7,751.029 1754.19,750.743 1756.69,750.455 1759.19,750.166 \n",
" 1761.69,749.875 1764.19,749.583 1766.69,749.29 1769.18,748.995 1771.68,748.699 1774.18,748.401 1776.68,748.102 1779.18,747.801 1781.67,747.499 1784.17,747.195 \n",
" 1786.67,746.89 1789.17,746.584 1791.67,746.276 1794.16,745.966 1796.66,745.655 1799.16,745.343 1801.66,745.029 1804.16,744.714 1806.65,744.397 1809.15,744.079 \n",
" 1811.65,743.759 1814.15,743.438 1816.65,743.116 1819.15,742.792 1821.64,742.466 1824.14,742.139 1826.64,741.811 1829.14,741.481 1831.64,741.15 1834.13,740.817 \n",
" 1836.63,740.483 1839.13,740.147 1841.63,739.81 1844.13,739.471 1846.62,739.131 1849.12,738.79 1851.62,738.447 1854.12,738.102 1856.62,737.757 1859.11,737.409 \n",
" 1861.61,737.061 1864.11,736.71 1866.61,736.359 1869.11,736.006 1871.6,735.651 1874.1,735.295 1876.6,734.937 1879.1,734.578 1881.6,734.218 1884.1,733.856 \n",
" 1886.59,733.493 1889.09,733.128 1891.59,732.762 1894.09,732.394 1896.59,732.025 1899.08,731.654 1901.58,731.282 1904.08,730.909 1906.58,730.534 1909.08,730.157 \n",
" 1911.57,729.779 1914.07,729.4 1916.57,729.019 1919.07,728.637 1921.57,728.253 1924.06,727.868 1926.56,727.481 1929.06,727.093 1931.56,726.704 1934.06,726.313 \n",
" 1936.56,725.92 1939.05,725.526 1941.55,725.131 1944.05,724.734 1946.55,724.336 1949.05,723.936 1951.54,723.535 1954.04,723.132 1956.54,722.728 1959.04,722.323 \n",
" 1961.54,721.916 1964.03,721.507 1966.53,721.097 1969.03,720.686 1971.53,720.273 1974.03,719.859 1976.52,719.443 1979.02,719.026 1981.52,718.607 1984.02,718.187 \n",
" 1986.52,717.765 1989.01,717.342 1991.51,716.918 1994.01,716.492 1996.51,716.065 1999.01,715.636 2001.51,715.205 2004,714.774 2006.5,714.34 2009,713.906 \n",
" 2011.5,713.47 2014,713.032 2016.49,712.593 2018.99,712.152 2021.49,711.71 2023.99,711.267 2026.49,710.822 2028.98,710.376 2031.48,709.928 2033.98,709.479 \n",
" 2036.48,709.028 2038.98,708.576 2041.47,708.122 2043.97,707.667 2046.47,707.211 2048.97,706.753 2051.47,706.293 2053.96,705.832 2056.46,705.37 2058.96,704.906 \n",
" 2061.46,704.441 2063.96,703.974 2066.46,703.506 2068.95,703.036 2071.45,702.565 2073.95,702.093 2076.45,701.619 2078.95,701.143 2081.44,700.666 2083.94,700.188 \n",
" 2086.44,699.708 2088.94,699.227 2091.44,698.744 2093.93,698.26 2096.43,697.774 2098.93,697.287 2101.43,696.799 2103.93,696.309 2106.42,695.817 2108.92,695.324 \n",
" 2111.42,694.83 2113.92,694.334 2116.42,693.837 2118.92,693.338 2121.41,692.838 2123.91,692.336 2126.41,691.833 2128.91,691.328 2131.41,690.822 2133.9,690.315 \n",
" 2136.4,689.806 2138.9,689.295 2141.4,688.784 2143.9,688.27 2146.39,687.755 2148.89,687.239 2151.39,686.722 2153.89,686.202 2156.39,685.682 2158.88,685.16 \n",
" 2161.38,684.636 2163.88,684.111 2166.38,683.585 2168.88,683.057 2171.37,682.528 2173.87,681.997 2176.37,681.465 2178.87,680.931 2181.37,680.396 2183.87,679.859 \n",
" 2186.36,679.321 2188.86,678.781 2191.36,678.24 2193.86,677.698 2196.36,677.154 2198.85,676.609 2201.35,676.062 2203.85,675.514 2206.35,674.964 2208.85,674.413 \n",
" 2211.34,673.86 2213.84,673.306 2216.34,672.75 2218.84,672.193 2221.34,671.635 2223.83,671.075 2226.33,670.514 2228.83,669.951 2231.33,669.387 2233.83,668.821 \n",
" 2236.33,668.254 2238.82,667.685 2241.32,667.115 2243.82,666.543 2246.32,665.97 2248.82,665.396 2251.31,664.82 2253.81,664.242 2256.31,663.664 2258.81,663.083 \n",
" 2261.31,662.502 \n",
" \"/>\n",
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" 287.82,1553.99 290.318,1547.58 292.816,1541.21 295.314,1534.87 297.812,1528.56 300.311,1522.28 302.809,1516.04 305.307,1509.84 307.805,1503.66 310.303,1497.52 \n",
" 312.801,1491.42 315.299,1485.34 317.797,1479.3 320.295,1473.3 322.793,1467.32 325.291,1461.38 327.789,1455.47 330.288,1449.6 332.786,1443.75 335.284,1437.94 \n",
" 337.782,1432.16 340.28,1426.42 342.778,1420.7 345.276,1415.02 347.774,1409.37 350.272,1403.75 352.77,1398.17 355.268,1392.61 357.766,1387.09 360.265,1381.6 \n",
" 362.763,1376.14 365.261,1370.71 367.759,1365.32 370.257,1359.95 372.755,1354.62 375.253,1349.32 377.751,1344.04 380.249,1338.8 382.747,1333.59 385.245,1328.41 \n",
" 387.743,1323.27 390.242,1318.15 392.74,1313.06 395.238,1308 397.736,1302.98 400.234,1297.98 402.732,1293.01 405.23,1288.08 407.728,1283.17 410.226,1278.3 \n",
" 412.724,1273.45 415.222,1268.63 417.72,1263.84 420.219,1259.09 422.717,1254.36 425.215,1249.66 427.713,1244.99 430.211,1240.35 432.709,1235.74 435.207,1231.16 \n",
" 437.705,1226.6 440.203,1222.08 442.701,1217.58 445.199,1213.11 447.697,1208.68 450.196,1204.26 452.694,1199.88 455.192,1195.53 457.69,1191.2 460.188,1186.91 \n",
" 462.686,1182.64 465.184,1178.4 467.682,1174.18 470.18,1170 472.678,1165.84 475.176,1161.71 477.674,1157.61 480.173,1153.53 482.671,1149.48 485.169,1145.46 \n",
" 487.667,1141.47 490.165,1137.5 492.663,1133.56 495.161,1129.65 497.659,1125.77 500.157,1121.91 502.655,1118.08 505.153,1114.27 507.651,1110.49 510.15,1106.74 \n",
" 512.648,1103.01 515.146,1099.31 517.644,1095.64 520.142,1091.99 522.64,1088.37 525.138,1084.77 527.636,1081.2 530.134,1077.65 532.632,1074.14 535.13,1070.64 \n",
" 537.628,1067.17 540.127,1063.73 542.625,1060.31 545.123,1056.92 547.621,1053.55 550.119,1050.21 552.617,1046.89 555.115,1043.6 557.613,1040.33 560.111,1037.09 \n",
" 562.609,1033.87 565.107,1030.68 567.605,1027.51 570.104,1024.36 572.602,1021.24 575.1,1018.14 577.598,1015.07 580.096,1012.02 582.594,1008.99 585.092,1005.99 \n",
" 587.59,1003.01 590.088,1000.06 592.586,997.126 595.084,994.219 597.582,991.334 600.081,988.473 602.579,985.635 605.077,982.821 607.575,980.029 610.073,977.26 \n",
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" 687.513,902.299 690.012,900.216 692.51,898.154 695.008,896.111 697.506,894.088 700.004,892.085 702.502,890.102 705,888.138 707.498,886.194 709.996,884.269 \n",
" 712.494,882.363 714.992,880.477 717.49,878.61 719.989,876.761 722.487,874.932 724.985,873.122 727.483,871.33 729.981,869.557 732.479,867.803 734.977,866.067 \n",
" 737.475,864.35 739.973,862.651 742.471,860.97 744.969,859.307 747.467,857.663 749.966,856.036 752.464,854.428 754.962,852.837 757.46,851.264 759.958,849.709 \n",
" 762.456,848.171 764.954,846.651 767.452,845.148 769.95,843.662 772.448,842.194 774.946,840.742 777.444,839.308 779.943,837.891 782.441,836.49 784.939,835.107 \n",
" 787.437,833.74 789.935,832.389 792.433,831.055 794.931,829.738 797.429,828.437 799.927,827.152 802.425,825.883 804.923,824.631 807.421,823.394 809.92,822.173 \n",
" 812.418,820.969 814.916,819.779 817.414,818.606 819.912,817.448 822.41,816.305 824.908,815.178 827.406,814.066 829.904,812.97 832.402,811.888 834.9,810.822 \n",
" 837.398,809.77 839.897,808.733 842.395,807.711 844.893,806.704 847.391,805.712 849.889,804.733 852.387,803.77 854.885,802.82 857.383,801.885 859.881,800.964 \n",
" 862.379,800.057 864.877,799.164 867.375,798.285 869.874,797.42 872.372,796.568 874.87,795.73 877.368,794.906 879.866,794.095 882.364,793.297 884.862,792.513 \n",
" 887.36,791.742 889.858,790.984 892.356,790.239 894.854,789.507 897.352,788.788 899.851,788.081 902.349,787.388 904.847,786.706 907.345,786.038 909.843,785.381 \n",
" 912.341,784.738 914.839,784.106 917.337,783.486 919.835,782.879 922.333,782.283 924.831,781.699 927.329,781.128 929.828,780.567 932.326,780.019 934.824,779.482 \n",
" 937.322,778.956 939.82,778.442 942.318,777.939 944.816,777.447 947.314,776.967 949.812,776.497 952.31,776.038 954.808,775.59 957.306,775.153 959.805,774.727 \n",
" 962.303,774.311 964.801,773.905 967.299,773.51 969.797,773.126 972.295,772.751 974.793,772.387 977.291,772.033 979.789,771.688 982.287,771.354 984.785,771.029 \n",
" 987.283,770.714 989.781,770.409 992.28,770.113 994.778,769.826 997.276,769.549 999.774,769.281 1002.27,769.023 1004.77,768.773 1007.27,768.533 1009.77,768.301 \n",
" 1012.26,768.078 1014.76,767.864 1017.26,767.659 1019.76,767.462 1022.26,767.273 1024.75,767.093 1027.25,766.922 1029.75,766.758 1032.25,766.603 1034.75,766.456 \n",
" 1037.25,766.316 1039.74,766.185 1042.24,766.061 1044.74,765.945 1047.24,765.836 1049.74,765.736 1052.23,765.642 1054.73,765.556 1057.23,765.477 1059.73,765.405 \n",
" 1062.23,765.341 1064.72,765.283 1067.22,765.232 1069.72,765.188 1072.22,765.151 1074.72,765.12 1077.21,765.096 1079.71,765.079 1082.21,765.067 1084.71,765.063 \n",
" 1087.21,765.064 1089.7,765.071 1092.2,765.085 1094.7,765.104 1097.2,765.129 1099.7,765.16 1102.2,765.197 1104.69,765.239 1107.19,765.287 1109.69,765.34 \n",
" 1112.19,765.399 1114.69,765.463 1117.18,765.531 1119.68,765.605 1122.18,765.684 1124.68,765.768 1127.18,765.857 1129.67,765.95 1132.17,766.048 1134.67,766.151 \n",
" 1137.17,766.258 1139.67,766.369 1142.16,766.485 1144.66,766.605 1147.16,766.729 1149.66,766.857 1152.16,766.989 1154.65,767.125 1157.15,767.264 1159.65,767.407 \n",
" 1162.15,767.554 1164.65,767.704 1167.15,767.858 1169.64,768.015 1172.14,768.175 1174.64,768.339 1177.14,768.505 1179.64,768.674 1182.13,768.847 1184.63,769.022 \n",
" 1187.13,769.2 1189.63,769.38 1192.13,769.563 1194.62,769.748 1197.12,769.936 1199.62,770.126 1202.12,770.318 1204.62,770.513 1207.11,770.709 1209.61,770.907 \n",
" 1212.11,771.107 1214.61,771.309 1217.11,771.513 1219.61,771.718 1222.1,771.924 1224.6,772.132 1227.1,772.341 1229.6,772.552 1232.1,772.763 1234.59,772.976 \n",
" 1237.09,773.19 1239.59,773.404 1242.09,773.619 1244.59,773.835 1247.08,774.052 1249.58,774.269 1252.08,774.487 1254.58,774.704 1257.08,774.923 1259.57,775.141 \n",
" 1262.07,775.359 1264.57,775.578 1267.07,775.796 1269.57,776.014 1272.06,776.232 1274.56,776.45 1277.06,776.667 1279.56,776.883 1282.06,777.099 1284.56,777.315 \n",
" 1287.05,777.529 1289.55,777.743 1292.05,777.955 1294.55,778.167 1297.05,778.378 1299.54,778.587 1302.04,778.795 1304.54,779.001 1307.04,779.206 1309.54,779.41 \n",
" 1312.03,779.612 1314.53,779.812 1317.03,780.01 1319.53,780.206 1322.03,780.401 1324.52,780.593 1327.02,780.783 1329.52,780.971 1332.02,781.156 1334.52,781.339 \n",
" 1337.02,781.519 1339.51,781.697 1342.01,781.872 1344.51,782.044 1347.01,782.214 1349.51,782.38 1352,782.544 1354.5,782.704 1357,782.861 1359.5,783.015 \n",
" 1362,783.165 1364.49,783.312 1366.99,783.455 1369.49,783.594 1371.99,783.73 1374.49,783.862 1376.98,783.99 1379.48,784.114 1381.98,784.234 1384.48,784.349 \n",
" 1386.98,784.461 1389.47,784.568 1391.97,784.67 1394.47,784.768 1396.97,784.862 1399.47,784.951 1401.97,785.034 1404.46,785.113 1406.96,785.187 1409.46,785.256 \n",
" 1411.96,785.32 1414.46,785.379 1416.95,785.432 1419.45,785.48 1421.95,785.522 1424.45,785.558 1426.95,785.589 1429.44,785.615 1431.94,785.634 1434.44,785.648 \n",
" 1436.94,785.655 1439.44,785.656 1441.93,785.651 1444.43,785.64 1446.93,785.623 1449.43,785.599 1451.93,785.568 1454.42,785.531 1456.92,785.487 1459.42,785.436 \n",
" 1461.92,785.378 1464.42,785.314 1466.92,785.242 1469.41,785.163 1471.91,785.077 1474.41,784.983 1476.91,784.882 1479.41,784.774 1481.9,784.658 1484.4,784.534 \n",
" 1486.9,784.403 1489.4,784.263 1491.9,784.116 1494.39,783.961 1496.89,783.797 1499.39,783.625 1501.89,783.445 1504.39,783.257 1506.88,783.06 1509.38,782.855 \n",
" 1511.88,782.641 1514.38,782.418 1516.88,782.186 1519.38,781.946 1521.87,781.696 1524.37,781.437 1526.87,781.17 1529.37,780.892 1531.87,780.606 1534.36,780.31 \n",
" 1536.86,780.005 1539.36,779.69 1541.86,779.365 1544.36,779.031 1546.85,778.686 1549.35,778.332 1551.85,777.968 1554.35,777.593 1556.85,777.208 1559.34,776.813 \n",
" 1561.84,776.408 1564.34,775.992 1566.84,775.565 1569.34,775.128 1571.83,774.68 1574.33,774.222 1576.83,773.752 1579.33,773.271 1581.83,772.78 1584.33,772.277 \n",
" 1586.82,771.763 1589.32,771.237 1591.82,770.7 1594.32,770.151 1596.82,769.591 1599.31,769.019 1601.81,768.436 1604.31,767.84 1606.81,767.233 1609.31,766.613 \n",
" 1611.8,765.981 1614.3,765.337 1616.8,764.681 1619.3,764.012 1621.8,763.331 1624.29,762.637 1626.79,761.931 1629.29,761.212 1631.79,760.48 1634.29,759.735 \n",
" 1636.79,758.977 1639.28,758.206 1641.78,757.421 1644.28,756.624 1646.78,755.813 1649.28,754.989 1651.77,754.151 1654.27,753.299 1656.77,752.434 1659.27,751.555 \n",
" 1661.77,750.662 1664.26,749.755 1666.76,748.834 1669.26,747.899 1671.76,746.949 1674.26,745.985 1676.75,745.007 1679.25,744.015 1681.75,743.007 1684.25,741.985 \n",
" 1686.75,740.949 1689.24,739.897 1691.74,738.831 1694.24,737.749 1696.74,736.652 1699.24,735.541 1701.74,734.413 1704.23,733.271 1706.73,732.113 1709.23,730.939 \n",
" 1711.73,729.75 1714.23,728.545 1716.72,727.325 1719.22,726.088 1721.72,724.835 1724.22,723.567 1726.72,722.282 1729.21,720.981 1731.71,719.663 1734.21,718.33 \n",
" 1736.71,716.979 1739.21,715.612 1741.7,714.228 1744.2,712.828 1746.7,711.411 1749.2,709.976 1751.7,708.525 1754.19,707.057 1756.69,705.571 1759.19,704.068 \n",
" 1761.69,702.548 1764.19,701.01 1766.69,699.455 1769.18,697.882 1771.68,696.291 1774.18,694.682 1776.68,693.056 1779.18,691.411 1781.67,689.749 1784.17,688.068 \n",
" 1786.67,686.369 1789.17,684.652 1791.67,682.916 1794.16,681.162 1796.66,679.389 1799.16,677.597 1801.66,675.787 1804.16,673.958 1806.65,672.109 1809.15,670.242 \n",
" 1811.65,668.356 1814.15,666.45 1816.65,664.525 1819.15,662.581 1821.64,660.617 1824.14,658.633 1826.64,656.63 1829.14,654.608 1831.64,652.565 1834.13,650.502 \n",
" 1836.63,648.42 1839.13,646.317 1841.63,644.194 1844.13,642.051 1846.62,639.888 1849.12,637.704 1851.62,635.499 1854.12,633.274 1856.62,631.028 1859.11,628.762 \n",
" 1861.61,626.474 1864.11,624.166 1866.61,621.836 1869.11,619.486 1871.6,617.114 1874.1,614.721 1876.6,612.306 1879.1,609.87 1881.6,607.412 1884.1,604.933 \n",
" 1886.59,602.432 1889.09,599.909 1891.59,597.364 1894.09,594.797 1896.59,592.208 1899.08,589.597 1901.58,586.964 1904.08,584.308 1906.58,581.63 1909.08,578.929 \n",
" 1911.57,576.205 1914.07,573.459 1916.57,570.69 1919.07,567.898 1921.57,565.083 1924.06,562.246 1926.56,559.384 1929.06,556.5 1931.56,553.592 1934.06,550.661 \n",
" 1936.56,547.707 1939.05,544.729 1941.55,541.727 1944.05,538.701 1946.55,535.652 1949.05,532.578 1951.54,529.481 1954.04,526.36 1956.54,523.214 1959.04,520.044 \n",
" 1961.54,516.849 1964.03,513.63 1966.53,510.387 1969.03,507.119 1971.53,503.826 1974.03,500.509 1976.52,497.166 1979.02,493.799 1981.52,490.406 1984.02,486.988 \n",
" 1986.52,483.545 1989.01,480.077 1991.51,476.583 1994.01,473.064 1996.51,469.519 1999.01,465.949 2001.51,462.352 2004,458.73 2006.5,455.082 2009,451.408 \n",
" 2011.5,447.708 2014,443.981 2016.49,440.228 2018.99,436.449 2021.49,432.643 2023.99,428.811 2026.49,424.952 2028.98,421.067 2031.48,417.154 2033.98,413.215 \n",
" 2036.48,409.248 2038.98,405.255 2041.47,401.234 2043.97,397.187 2046.47,393.111 2048.97,389.009 2051.47,384.879 2053.96,380.721 2056.46,376.535 2058.96,372.322 \n",
" 2061.46,368.081 2063.96,363.812 2066.46,359.515 2068.95,355.189 2071.45,350.836 2073.95,346.454 2076.45,342.044 2078.95,337.605 2081.44,333.138 2083.94,328.642 \n",
" 2086.44,324.117 2088.94,319.564 2091.44,314.981 2093.93,310.37 2096.43,305.729 2098.93,301.06 2101.43,296.361 2103.93,291.632 2106.42,286.875 2108.92,282.087 \n",
" 2111.42,277.27 2113.92,272.424 2116.42,267.547 2118.92,262.641 2121.41,257.705 2123.91,252.738 2126.41,247.742 2128.91,242.715 2131.41,237.658 2133.9,232.571 \n",
" 2136.4,227.453 2138.9,222.304 2141.4,217.125 2143.9,211.915 2146.39,206.674 2148.89,201.402 2151.39,196.1 2153.89,190.766 2156.39,185.401 2158.88,180.005 \n",
" 2161.38,174.577 2163.88,169.118 2166.38,163.627 2168.88,158.105 2171.37,152.551 2173.87,146.965 2176.37,141.347 2178.87,135.698 2181.37,130.016 2183.87,124.302 \n",
" 2186.36,118.556 2188.86,112.777 2191.36,106.966 2193.86,101.123 2196.36,95.2469 2198.85,89.3383 2201.35,83.3968 2203.85,77.4225 2206.35,71.4153 2208.85,65.3751 \n",
" 2211.34,59.3017 2213.84,53.1951 2216.34,47.0553 2218.84,40.882 2221.34,34.6753 2223.83,28.4351 2226.33,22.1612 2228.83,15.8535 2231.33,9.51211 2233.83,3.13678 \n",
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" 687.513,400.697 690.012,410.769 692.51,420.675 695.008,430.417 697.506,439.996 700.004,449.414 702.502,458.673 705,467.773 707.498,476.718 709.996,485.507 \n",
" 712.494,494.144 714.992,502.629 717.49,510.963 719.989,519.149 722.487,527.188 724.985,535.081 727.483,542.83 729.981,550.437 732.479,557.902 734.977,565.228 \n",
" 737.475,572.416 739.973,579.467 742.471,586.383 744.969,593.166 747.467,599.815 749.966,606.335 752.464,612.724 754.962,618.986 757.46,625.121 759.958,631.131 \n",
" 762.456,637.018 764.954,642.781 767.452,648.425 769.95,653.948 772.448,659.353 774.946,664.642 777.444,669.815 779.943,674.874 782.441,679.821 784.939,684.656 \n",
" 787.437,689.381 789.935,693.997 792.433,698.506 794.931,702.909 797.429,707.207 799.927,711.402 802.425,715.494 804.923,719.486 807.421,723.378 809.92,727.172 \n",
" 812.418,730.869 814.916,734.47 817.414,737.976 819.912,741.39 822.41,744.711 824.908,747.941 827.406,751.082 829.904,754.135 832.402,757.1 834.9,759.98 \n",
" 837.398,762.775 839.897,765.486 842.395,768.115 844.893,770.663 847.391,773.13 849.889,775.519 852.387,777.831 854.885,780.065 857.383,782.225 859.881,784.31 \n",
" 862.379,786.322 864.877,788.262 867.375,790.131 869.874,791.93 872.372,793.661 874.87,795.324 877.368,796.921 879.866,798.452 882.364,799.919 884.862,801.322 \n",
" 887.36,802.664 889.858,803.944 892.356,805.164 894.854,806.325 897.352,807.428 899.851,808.474 902.349,809.464 904.847,810.399 907.345,811.28 909.843,812.108 \n",
" 912.341,812.884 914.839,813.608 917.337,814.283 919.835,814.909 922.333,815.487 924.831,816.017 927.329,816.501 929.828,816.94 932.326,817.335 934.824,817.686 \n",
" 937.322,817.995 939.82,818.262 942.318,818.488 944.816,818.675 947.314,818.823 949.812,818.933 952.31,819.005 954.808,819.041 957.306,819.042 959.805,819.009 \n",
" 962.303,818.941 964.801,818.841 967.299,818.709 969.797,818.546 972.295,818.352 974.793,818.129 977.291,817.877 979.789,817.597 982.287,817.29 984.785,816.956 \n",
" 987.283,816.597 989.781,816.213 992.28,815.805 994.778,815.374 997.276,814.92 999.774,814.444 1002.27,813.948 1004.77,813.431 1007.27,812.894 1009.77,812.339 \n",
" 1012.26,811.765 1014.76,811.174 1017.26,810.566 1019.76,809.942 1022.26,809.303 1024.75,808.649 1027.25,807.98 1029.75,807.299 1032.25,806.604 1034.75,805.898 \n",
" 1037.25,805.18 1039.74,804.451 1042.24,803.712 1044.74,802.964 1047.24,802.206 1049.74,801.44 1052.23,800.667 1054.73,799.886 1057.23,799.098 1059.73,798.305 \n",
" 1062.23,797.506 1064.72,796.702 1067.22,795.894 1069.72,795.082 1072.22,794.266 1074.72,793.449 1077.21,792.628 1079.71,791.807 1082.21,790.984 1084.71,790.16 \n",
" 1087.21,789.336 1089.7,788.513 1092.2,787.69 1094.7,786.869 1097.2,786.05 1099.7,785.232 1102.2,784.418 1104.69,783.607 1107.19,782.799 1109.69,781.995 \n",
" 1112.19,781.196 1114.69,780.402 1117.18,779.613 1119.68,778.829 1122.18,778.052 1124.68,777.281 1127.18,776.518 1129.67,775.761 1132.17,775.012 1134.67,774.272 \n",
" 1137.17,773.539 1139.67,772.815 1142.16,772.101 1144.66,771.396 1147.16,770.7 1149.66,770.015 1152.16,769.34 1154.65,768.676 1157.15,768.022 1159.65,767.381 \n",
" 1162.15,766.75 1164.65,766.132 1167.15,765.525 1169.64,764.932 1172.14,764.35 1174.64,763.782 1177.14,763.227 1179.64,762.686 1182.13,762.158 1184.63,761.644 \n",
" 1187.13,761.144 1189.63,760.658 1192.13,760.187 1194.62,759.731 1197.12,759.289 1199.62,758.863 1202.12,758.452 1204.62,758.057 1207.11,757.677 1209.61,757.312 \n",
" 1212.11,756.964 1214.61,756.632 1217.11,756.316 1219.61,756.017 1222.1,755.734 1224.6,755.467 1227.1,755.217 1229.6,754.984 1232.1,754.768 1234.59,754.569 \n",
" 1237.09,754.387 1239.59,754.222 1242.09,754.074 1244.59,753.943 1247.08,753.83 1249.58,753.734 1252.08,753.656 1254.58,753.595 1257.08,753.551 1259.57,753.525 \n",
" 1262.07,753.516 1264.57,753.525 1267.07,753.551 1269.57,753.595 1272.06,753.656 1274.56,753.734 1277.06,753.83 1279.56,753.943 1282.06,754.074 1284.56,754.222 \n",
" 1287.05,754.387 1289.55,754.569 1292.05,754.768 1294.55,754.984 1297.05,755.217 1299.54,755.467 1302.04,755.734 1304.54,756.017 1307.04,756.316 1309.54,756.632 \n",
" 1312.03,756.964 1314.53,757.312 1317.03,757.677 1319.53,758.057 1322.03,758.452 1324.52,758.863 1327.02,759.289 1329.52,759.731 1332.02,760.187 1334.52,760.658 \n",
" 1337.02,761.144 1339.51,761.644 1342.01,762.158 1344.51,762.686 1347.01,763.227 1349.51,763.782 1352,764.35 1354.5,764.932 1357,765.525 1359.5,766.132 \n",
" 1362,766.75 1364.49,767.381 1366.99,768.022 1369.49,768.676 1371.99,769.34 1374.49,770.015 1376.98,770.7 1379.48,771.396 1381.98,772.101 1384.48,772.815 \n",
" 1386.98,773.539 1389.47,774.272 1391.97,775.012 1394.47,775.761 1396.97,776.518 1399.47,777.281 1401.97,778.052 1404.46,778.829 1406.96,779.613 1409.46,780.402 \n",
" 1411.96,781.196 1414.46,781.995 1416.95,782.799 1419.45,783.607 1421.95,784.418 1424.45,785.232 1426.95,786.05 1429.44,786.869 1431.94,787.69 1434.44,788.513 \n",
" 1436.94,789.336 1439.44,790.16 1441.93,790.984 1444.43,791.807 1446.93,792.628 1449.43,793.449 1451.93,794.266 1454.42,795.082 1456.92,795.894 1459.42,796.702 \n",
" 1461.92,797.506 1464.42,798.305 1466.92,799.098 1469.41,799.886 1471.91,800.667 1474.41,801.44 1476.91,802.206 1479.41,802.964 1481.9,803.712 1484.4,804.451 \n",
" 1486.9,805.18 1489.4,805.898 1491.9,806.604 1494.39,807.299 1496.89,807.98 1499.39,808.649 1501.89,809.303 1504.39,809.942 1506.88,810.566 1509.38,811.174 \n",
" 1511.88,811.765 1514.38,812.339 1516.88,812.894 1519.38,813.431 1521.87,813.948 1524.37,814.444 1526.87,814.92 1529.37,815.374 1531.87,815.805 1534.36,816.213 \n",
" 1536.86,816.597 1539.36,816.956 1541.86,817.29 1544.36,817.597 1546.85,817.877 1549.35,818.129 1551.85,818.352 1554.35,818.546 1556.85,818.709 1559.34,818.841 \n",
" 1561.84,818.941 1564.34,819.009 1566.84,819.042 1569.34,819.041 1571.83,819.005 1574.33,818.933 1576.83,818.823 1579.33,818.675 1581.83,818.488 1584.33,818.262 \n",
" 1586.82,817.995 1589.32,817.686 1591.82,817.335 1594.32,816.94 1596.82,816.501 1599.31,816.017 1601.81,815.487 1604.31,814.909 1606.81,814.283 1609.31,813.608 \n",
" 1611.8,812.884 1614.3,812.108 1616.8,811.28 1619.3,810.399 1621.8,809.464 1624.29,808.474 1626.79,807.428 1629.29,806.325 1631.79,805.164 1634.29,803.944 \n",
" 1636.79,802.664 1639.28,801.322 1641.78,799.919 1644.28,798.452 1646.78,796.921 1649.28,795.324 1651.77,793.661 1654.27,791.93 1656.77,790.131 1659.27,788.262 \n",
" 1661.77,786.322 1664.26,784.31 1666.76,782.225 1669.26,780.065 1671.76,777.831 1674.26,775.519 1676.75,773.13 1679.25,770.663 1681.75,768.115 1684.25,765.486 \n",
" 1686.75,762.775 1689.24,759.98 1691.74,757.1 1694.24,754.135 1696.74,751.082 1699.24,747.941 1701.74,744.711 1704.23,741.39 1706.73,737.976 1709.23,734.47 \n",
" 1711.73,730.869 1714.23,727.172 1716.72,723.378 1719.22,719.486 1721.72,715.494 1724.22,711.402 1726.72,707.207 1729.21,702.909 1731.71,698.506 1734.21,693.997 \n",
" 1736.71,689.381 1739.21,684.656 1741.7,679.821 1744.2,674.874 1746.7,669.815 1749.2,664.642 1751.7,659.353 1754.19,653.948 1756.69,648.425 1759.19,642.781 \n",
" 1761.69,637.018 1764.19,631.131 1766.69,625.121 1769.18,618.986 1771.68,612.724 1774.18,606.335 1776.68,599.815 1779.18,593.166 1781.67,586.383 1784.17,579.467 \n",
" 1786.67,572.416 1789.17,565.228 1791.67,557.902 1794.16,550.437 1796.66,542.83 1799.16,535.081 1801.66,527.188 1804.16,519.149 1806.65,510.963 1809.15,502.629 \n",
" 1811.65,494.144 1814.15,485.507 1816.65,476.718 1819.15,467.773 1821.64,458.673 1824.14,449.414 1826.64,439.996 1829.14,430.417 1831.64,420.675 1834.13,410.769 \n",
" 1836.63,400.697 1839.13,390.458 1841.63,380.05 1844.13,369.471 1846.62,358.72 1849.12,347.795 1851.62,336.695 1854.12,325.417 1856.62,313.961 1859.11,302.324 \n",
" 1861.61,290.505 1864.11,278.502 1866.61,266.313 1869.11,253.937 1871.6,241.373 1874.1,228.617 1876.6,215.67 1879.1,202.528 1881.6,189.191 1884.1,175.656 \n",
" 1886.59,161.922 1889.09,147.987 1891.59,133.85 1894.09,119.507 1896.59,104.959 1899.08,90.2027 1901.58,75.2365 1904.08,60.0588 1906.58,44.6677 1909.08,29.0614 \n",
" 1911.57,13.2382 1914.07,-2.80383 1916.57,-19.0665 1919.07,-35.5515 1921.57,-52.2608 1924.06,-69.1963 1926.56,-86.3597 1929.06,-103.753 1931.56,-121.378 1934.06,-139.236 \n",
" 1936.56,-157.33 1939.05,-175.661 1941.55,-194.232 1944.05,-213.043 1946.55,-232.098 1949.05,-251.397 1951.54,-270.943 1954.04,-290.738 1956.54,-310.784 1959.04,-331.082 \n",
" 1961.54,-351.635 1964.03,-372.444 1966.53,-393.512 1969.03,-414.841 1971.53,-436.431 1974.03,-458.287 1976.52,-480.408 1979.02,-502.798 1981.52,-525.459 1984.02,-548.391 \n",
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"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"H₀ = Fun(Hermite(), [1])\n",
"H₁ = Fun(Hermite(), [0,1])\n",
"H₂ = Fun(Hermite(), [0,0,1])\n",
"H₃ = Fun(Hermite(), [0,0,0,1])\n",
"H₄ = Fun(Hermite(), [0,0,0,0,1])\n",
"H₅ = Fun(Hermite(), [0,0,0,0,0,1])\n",
"\n",
"xx = -4:0.01:4\n",
"plot(xx, H₀.(xx); label=\"H_0\", ylims=(-400,400))\n",
"plot!(xx, H₁.(xx); label=\"H_1\", ylims=(-400,400))\n",
"plot!(xx, H₂.(xx); label=\"H_2\", ylims=(-400,400))\n",
"plot!(xx, H₃.(xx); label=\"H_3\", ylims=(-400,400))\n",
"plot!(xx, H₄.(xx); label=\"H_4\", ylims=(-400,400))\n",
"plot!(xx, H₅.(xx); label=\"H_5\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We verify their orthogonality:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sum(H₂ * H₅ * w) = 0.0\n",
"sum(H₅ * H₅ * w) = 6806.222787477181\n"
]
}
],
"source": [
"w = Fun(GaussWeight(), [1.0])\n",
"\n",
"@show sum(H₂*H₅*w) # means integrate\n",
"@show sum(H₅*H₅*w);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now Jacobi:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
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"source": [
"α,β = 0.1,0.2\n",
"P₀ = Fun(Jacobi(β,α), [1])\n",
"P₁ = Fun(Jacobi(β,α), [0,1])\n",
"P₂ = Fun(Jacobi(β,α), [0,0,1])\n",
"P₃ = Fun(Jacobi(β,α), [0,0,0,1])\n",
"P₄ = Fun(Jacobi(β,α), [0,0,0,0,1])\n",
"P₅ = Fun(Jacobi(β,α), [0,0,0,0,0,1])\n",
"\n",
"xx = -1:0.01:1\n",
"plot( xx, P₀.(xx); label=\"P_0^($α,$β)\", ylims=(-2,2))\n",
"plot!(xx, P₁.(xx); label=\"P_1^($α,$β)\")\n",
"plot!(xx, P₂.(xx); label=\"P_2^($α,$β)\")\n",
"plot!(xx, P₃.(xx); label=\"P_3^($α,$β)\")\n",
"plot!(xx, P₄.(xx); label=\"P_4^($α,$β)\")\n",
"plot!(xx, P₅.(xx); label=\"P_5^($α,$β)\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sum(P₂ * P₅ * w) = 2.1250362580715887e-17\n",
"sum(P₅ * P₅ * w) = 0.2171335824839316\n"
]
}
],
"source": [
"w = Fun(JacobiWeight(β,α), [1.0])\n",
"@show sum(P₂*P₅*w) # means integrate\n",
"@show sum(P₅*P₅*w);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Legendre, Chebyshev, and ultraspherical polynomials\n",
"\n",
"There are special families of Jacobi weights with their own name. \n",
"\n",
"| Name | Jacobi parameters |Weight function $w(x)$ | Standard polynomial | highest order coefficient $k_n$ |\n",
"|:-------------|:------------- |:----------------------|:-----|:------|\n",
"| Jacobi | $\\alpha,\\beta$ | $(1-x)^{\\alpha} (1+x)^\\beta$ | $P_n^{(\\alpha,\\beta)}(x)$ | See [Table 18.3.1](http://dlmf.nist.gov/18.3) | \n",
"| Legendre | $0,0$ | $1$ | $P_n(x)$ | $2^n(1/2)_n/n!$ | \n",
"| Chebyshev (first kind) | $-{1 \\over 2},-{1 \\over 2}$ | $1 \\over \\sqrt{1-x^2}$ | $T_n(x)$ | $1 (n=0), 2^{n-1} (n \\neq 0)$ |\n",
"| Chebyshev (second kind) | ${1 \\over 2},{1 \\over 2}$ | $\\sqrt{1-x^2}$ | $U_n(x)$ | $2^n$\n",
"| Ultraspherical | $\\lambda-{1 \\over 2},\\lambda-{1 \\over 2}$ | $(1-x^2)^{\\lambda - 1/2}, \\lambda \\neq 0$ | $C_n^{(\\lambda)}(x)$ | $2^n(\\lambda)_n/n!$ |\n",
"\n",
"Note that other than Legendre, these polynomials have a different normalization than $P_n^{(\\alpha,\\beta)}$:\n"
]
},
{
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"T₂ = Fun(Chebyshev(), [0.0,0,1])\n",
"P₂ = Fun(Jacobi(-1/2,-1/2), [0.0,0,1])\n",
"plot(T₂; label=\"T_2\", title=\"T_2 is C*P_2 for some C\")\n",
"plot!(P₂; label=\"P_2\") "
]
},
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"source": [
"But because they are orthogonal w.r.t. the same weight, they must be a constant multiple of each-other."
]
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"### Explicit construction of Chebyshev polynomials (first kind and second kind)\n",
"\n",
"Chebyshev polynomials are pretty much the only OPs with _simple_ closed form expressions.\n",
"\n",
"**Proposition (Chebyshev first kind formula)** \n",
"$$T_n(x) = \\cos n \\acos x$$\n",
"or in other words,\n",
"$$\n",
"T_n(\\cos \\theta) = \\cos n \\theta\n",
"$$\n",
"\n",
"**Proof** We first show that they are orthogonal w.r.t. $1/\\sqrt{1-x^2}$. Too easy: do $x = \\cos \\theta$, $\\dx = -\\sin \\theta$ to get (for $n \\neq m$)\n",
"$$\n",
" \\int_{-1}^1 {\\cos n \\acos x \\cos m \\acos x \\dx \\over \\sqrt{1-x^2}} = -\\int_\\pi^0 \\cos n \\theta \\cos m \\theta \\D \\theta = \\int_0^\\pi {\\E^{\\I (-n-m)\\theta} + \\E^{\\I (n-m)\\theta} + \\E^{\\I (m-n)\\theta} + \\E^{\\I (n+m)\\theta} \\over 4} \\D \\theta =0\n",
"$$\n",
"\n",
"We then need to show it has the right highest order term $k_n$. Note that $k_0 = k_1 = 1$. Using $z = \\E^{\\I \\theta}$ we see that $\\cos n \\theta$ has a simple recurrence for $n=2,3,\\ldots$:\n",
"$$\n",
"\\cos n \\theta = {z^n + z^{-n} \\over 2} = 2 {z + z^{-1} \\over 2} {z^{n-1} + z^{1-n} \\over 2}- {z^{n-2} + z^{2-n} \\over 2} = 2 \\cos \\theta \\cos (n-1)\\theta - \\cos(n-2)\\theta \n",
"$$\n",
"thus \n",
"$$\n",
"\\cos n \\acos x = 2 x \\cos(n-1) \\acos x - \\cos(n-2) \\acos x\n",
"$$\n",
"It follows that \n",
"$$\n",
"k_n = 2 x k_{n-1} = 2^{n-1} k_1 = 2^{n-1}\n",
"$$\n",
"By uniqueness we have $T_n(x) \\cos n \\acos x$.\n",
"\n",
"⬛️\n",
"\n",
"\n",
"\n",
"**Proposition (Chebyshev second kind formula)** \n",
"$$U_n(x) = {\\sin (n+1) \\acos x \\over \\sin \\acos x}$$\n",
"or in other words,\n",
"$$\n",
"U_n(\\cos \\theta) = {\\sin (n+1) \\theta \\over \\sin \\theta}\n",
"$$\n",
"\n"
]
},
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"source": [
"## Gram–Schmidt algorithm\n",
"\n",
"In general we don't have nice formulae. But we can always construct them via Gram–Schmidt:\n",
"\n",
"**Proposition (Gram–Schmidt)** Define\n",
"\\begin{align*}\n",
"p_0(x) = 1 \\\\\n",
"q_0(x) = {1 \\over \\norm{p_0}}\\\\\n",
"p_{n+1}(x) = x q_n(x) - \\sum_{k=0}^n \\ip<x q_n, q_k> q_k(x)\\\\\n",
"q_{n+1}(x) = {p_{n+1}(x) \\over \\norm{p_n}}\n",
"\\end{align*}\n",
"Then $q_0(x), q_1(x), \\ldots$ are orthonormal w.r.t. $w$.\n",
"\n",
"**Proof** By linearity we have\n",
"$$\n",
"\\ip<p_{n+1}, q_j> = \\ip<x q_n - \\sum_{k=0}^n \\ip<x q_n, q_k> q_k, q_j> = \\ip<x q_n, q_j> - \\ip<x q_n, q_j> \\ip<q_j,q_j> = 0\n",
"$$\n",
"Thus $p_{n+1}$ is orthogonal to all lower degree polynomials. So is $q_{n+1}$, since it is a constant multiple of $p_{n+1}$.\n",
"\n",
"⬛️\n",
"\n",
"Let's make our own family:"
]
},
{
"cell_type": "code",
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"metadata": {},
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"source": [
"x = Fun()\n",
"w = exp(x)\n",
"ip = (f,g) -> sum(f*g*w)\n",
"nrm = f -> sqrt(ip(f,f))\n",
"n = 10\n",
"q = Array{Fun}(undef,n)\n",
"p = Array{Fun}(undef,n)\n",
"p[1] = Fun(1, -1 .. 1 )\n",
"q[1] = p[1]/nrm(p[1])\n",
"\n",
"for k=1:n-1\n",
" p[k+1] = x*q[k] \n",
" for j=1:k\n",
" p[k+1] -= ip(p[k+1],q[j])*q[j]\n",
" end\n",
" q[k+1] = p[k+1]/nrm(p[k+1])\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
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{
"data": {
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"2.338624086051233e-16"
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"source": [
"sum(q[2]*q[4]*w)"
]
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{
"cell_type": "code",
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"source": [
"p = plot(; legend=false)\n",
"for k=1:10\n",
" plot!(q[k])\n",
"end\n",
"p"
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"\n",
"## Function approximation with orthogonal polynomials\n",
"\n",
"A basic usage of orthogonal polynomials is for polynomial approximation. Suppose $f(x)$ is a degree $n-1$ polynomial. Since $\\{p_0(x),\\ldots,p_{n-1}(x)\\}$ span all degree $n-1$ polynomials, we know that\n",
"$$\n",
"f(x) = \\sum_{k=0}^{n-1} f_k p_k(x)\n",
"$$\n",
"where\n",
"$$\n",
"f_k = {\\ip<f, p_k> \\over \\ip<p_k,p_k>}\n",
"$$\n",
"\n",
"Here, we demonstrate this with Chebyshev polynomials:"
]
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{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"(f₀, f₁, f₂, f₃) = (1.5, 1.7499999999999998, 0.5, 0.25000000000000006)\n",
"f₀ * 1 + f₁ * x + f₂ * cos(2 * acos(x)) + f₃ * cos(3 * acos(x)) = 1.111\n",
"1 + x + x ^ 2 + x ^ 3 = 1.111\n"
]
}
],
"source": [
"f = Fun(x -> 1 + x + x^2 + x^3, Chebyshev())\n",
"f₀, f₁, f₂, f₃ = f.coefficients\n",
"@show f₀, f₁, f₂, f₃\n",
"\n",
"x = 0.1\n",
"@show f₀*1 + f₁*x + f₂*cos(2acos(x)) + f₃*cos(3acos(x))\n",
"@show 1 + x + x^2 + x^3;"
]
},
{
"cell_type": "code",
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"source": [
"plot(Fun(exp))\n",
"plot!(Fun(t-> exp(cos(t)), -pi .. pi))"
]
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"0.5"
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"source": [
"x = Fun()\n",
"ip = (f,g) -> sum(f*g/sqrt(1-x^2))\n",
"\n",
"T₂ = cos.(2 .* acos.(x))\n",
"ip(T₂,f)/ip(T₂,T₂) # gives back f₂"
]
},
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"Of course, if $p_k$ are othernormal than we don't need the denominator.\n",
"\n",
"This can be extended to function approximation Provided the sum converges absolutely and uniformly in $x$, we can write\n",
"$$\n",
"f(x) = \\sum_{k=0}^\\infty f_k p_k(x).\n",
"$$\n",
"In practice, we can approximate smooth functions by a finite truncation:\n",
"$$\n",
"f(x) \\approx f_n(x) = \\sum_{k=0}^{n-1} f_k p_k(x)\n",
"$$\n",
"\n",
"Here we see that $\\E^x$ can be approximated by a Chebyshev approximation using 14 coefficients and is accurate to 16 digits:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f.coefficients = [1.26607, 1.13032, 0.271495, 0.0443368, 0.00547424, 0.000542926, 4.49773e-5, 3.19844e-6, 1.99212e-7, 1.10368e-8, 5.5059e-10, 2.49796e-11, 1.03911e-12, 3.98969e-14]\n",
"ncoefficients(f) = 14\n",
"f(0.1) = 1.1051709180756477\n",
"exp(0.1) = 1.1051709180756477\n"
]
}
],
"source": [
"f = Fun(x -> exp(x), Chebyshev())\n",
"@show f.coefficients\n",
"@show ncoefficients(f)\n",
"\n",
"@show f(0.1) # equivalent to f.coefficients'*[cos(k*acos(x)) for k=0:ncoefficients(f)-1]\n",
"@show exp(0.1);"
]
},
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"The accuracy of this approximation is typically dictated by the smoothness of $f$: the more times we can differentiate, the faster it converges. For analytic functions, it's dictated by the domain of analyticity, just like Laurent/Fourier series. In the case above, $\\E^x$ is entire hence we get faster than exponential convergence.\n",
"\n",
"\n",
"Chebyshev expansions work even when Taylor series do not. For example, the following function has poles at $\\pm {\\I \\over 5}$, which means the radius of convergence for the Taylor series is $ |x| < {1 \\over 5}$, but Chebyshev polynomials continue to work on $[-1,1]$:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ncoefficients(f) = 189\n"
]
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},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = Fun( x -> 1/(25x^2 + 1), Chebyshev())\n",
"@show ncoefficients(f)\n",
"plot(f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This can be explained for Chebyshev expansion by noting that it is cosine expansion / Fourier expansion of an even function:\n",
"$$\n",
"f(x) = \\sum_{k=0}^\\infty f_k T_k(x) \\Leftrightarrow f(\\cos \\theta) = \\sum_{k=0}^\\infty f_k \\cos k \\theta\n",
"$$\n",
"From Lecture 4 we saw that Fourier coefficients decay exponentially (thence the approximation converges exponentially fast) uf $f\\left({z + z^{-1} \\over 2}\\right)$ is analytic in an ellipse. In the case of $f(x) = {1 \\over 25 x^2 + 1}$, we find that \n",
"$$\n",
"f(z) = {4 z^2 \\over 25 + 54 z^2 + 25 z^4}\n",
"$$\n",
"which has poles at \n",
"$\n",
"\\pm 0.8198040\\I,\\pm1.2198\\I:\n",
"$"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"400×400 Array{RGB{Float64},2} with eltype RGB{Float64}:\n",
" RGB{Float64}(0.617696,1.0,0.0) … RGB{Float64}(0.617696,0.0,1.0)\n",
" RGB{Float64}(0.617696,1.0,0.0) RGB{Float64}(0.617696,0.0,1.0)\n",
" RGB{Float64}(0.627713,1.0,0.0) RGB{Float64}(0.627713,0.0,1.0)\n",
" RGB{Float64}(0.63773,1.0,0.0) RGB{Float64}(0.63773,0.0,1.0) \n",
" RGB{Float64}(0.63773,1.0,0.0) RGB{Float64}(0.63773,0.0,1.0) \n",
" RGB{Float64}(0.647746,1.0,0.0) … RGB{Float64}(0.647746,0.0,1.0)\n",
" RGB{Float64}(0.647746,1.0,0.0) RGB{Float64}(0.647746,0.0,1.0)\n",
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" RGB{Float64}(0.66778,1.0,0.0) RGB{Float64}(0.66778,0.0,1.0) \n",
" RGB{Float64}(0.66778,1.0,0.0) … RGB{Float64}(0.66778,0.0,1.0) \n",
" RGB{Float64}(0.677796,1.0,0.0) RGB{Float64}(0.677796,0.0,1.0)\n",
" RGB{Float64}(0.677796,1.0,0.0) RGB{Float64}(0.677796,0.0,1.0)\n",
" ⋮ ⋱ \n",
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" RGB{Float64}(0.66778,0.0,1.0) RGB{Float64}(0.66778,1.0,0.0) \n",
" RGB{Float64}(0.66778,0.0,1.0) … RGB{Float64}(0.66778,1.0,0.0) \n",
" RGB{Float64}(0.657763,0.0,1.0) RGB{Float64}(0.657763,1.0,0.0)\n",
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" RGB{Float64}(0.647746,0.0,1.0) RGB{Float64}(0.647746,1.0,0.0)\n",
" RGB{Float64}(0.647746,0.0,1.0) RGB{Float64}(0.647746,1.0,0.0)\n",
" RGB{Float64}(0.63773,0.0,1.0) … RGB{Float64}(0.63773,1.0,0.0) \n",
" RGB{Float64}(0.63773,0.0,1.0) RGB{Float64}(0.63773,1.0,0.0) \n",
" RGB{Float64}(0.627713,0.0,1.0) RGB{Float64}(0.627713,1.0,0.0)\n",
" RGB{Float64}(0.617696,0.0,1.0) RGB{Float64}(0.617696,1.0,0.0)\n",
" RGB{Float64}(0.617696,0.0,1.0) RGB{Float64}(0.617696,1.0,0.0)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = x -> 1/(25x^2 + 1)\n",
"portrait(-3..3, -3..3, z -> f((z+1/z)/2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hence we predict a rate of decay of about $1.2198^{-k}$:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
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"source": [
"f = Fun( x -> 1/(25x^2 + 1), Chebyshev())\n",
"plot(abs.(f.coefficients) .+ 1E-40; yscale=:log10, label=\"Chebyshev coefficients\")\n",
"plot!( 1.2198.^(-(0:ncoefficients(f))); label=\"R^(-k)\")"
]
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"source": [
"\n",
"### Weighted approximation\n",
"\n",
"Sometimes, we want to incorporate the weight into the approximation. This is typically one of two forms, depending on the application: \n",
"$$\n",
"f(x) = w(x) \\sum_{k=0}^\\infty f_k p_k(x)\n",
"$$\n",
"or\n",
"$$\n",
" f(x) = \\sqrt{w(x)} \\sum_{k=0}^\\infty f_k p_k(x)\n",
"$$\n",
"\n",
"This is often the case with Hermite polynomials: on the real line polynomial approximation is unnatural unless the function approximated is a polynomial as otherwise the behaviour at ∞ is inconsistent, so what we really want is weighted approximation. Thus we can either use\n",
"$$\n",
"f(x) = \\E^{-x^2}\\sum_{k=0}^\\infty f_k H_k(x)\n",
"$$\n",
"or\n",
"$$\n",
"f(x) = \\E^{-x^2/2}\\sum_{k=0}^\\infty f_k H_k(x)\n",
"$$\n",
"Depending on your problem, getting this wrong can be disasterous:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.109999999999997"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"f = Fun(x -> 1+x +x^2, Hermite())\n",
"f(0.10)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
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" 1071.62,741.508 1072.88,741.207 1074.15,740.904 1075.41,740.6 1076.68,740.294 1077.94,739.985 1079.21,739.675 1080.47,739.363 1081.73,739.049 1083,738.734 \n",
" 1084.26,738.416 1085.53,738.097 1086.79,737.776 1088.06,737.453 1089.32,737.129 1090.59,736.803 1091.85,736.475 1093.12,736.145 1094.38,735.814 1095.65,735.481 \n",
" 1096.91,735.147 1098.18,734.811 1099.44,734.473 1100.71,734.134 1101.97,733.793 1103.24,733.451 1104.5,733.108 1105.77,732.763 1107.03,732.417 1108.3,732.07 \n",
" 1109.56,731.721 1110.83,731.371 1112.09,731.02 1113.36,730.668 1114.62,730.314 1115.89,729.96 1117.15,729.604 1118.41,729.248 1119.68,728.891 1120.94,728.533 \n",
" 1122.21,728.174 1123.47,727.814 1124.74,727.453 1126,727.092 1127.27,726.731 1128.53,726.369 1129.8,726.006 1131.06,725.643 1132.33,725.279 1133.59,724.916 \n",
" 1134.86,724.552 1136.12,724.188 1137.39,723.824 1138.65,723.46 1139.92,723.096 1141.18,722.732 1142.45,722.369 1143.71,722.005 1144.98,721.642 1146.24,721.28 \n",
" 1147.51,720.918 1148.77,720.557 1150.04,720.197 1151.3,719.837 1152.56,719.478 1153.83,719.121 1155.09,718.764 1156.36,718.408 1157.62,718.054 1158.89,717.701 \n",
" 1160.15,717.35 1161.42,717 1162.68,716.652 1163.95,716.306 1165.21,715.961 1166.48,715.619 1167.74,715.278 1169.01,714.94 1170.27,714.604 1171.54,714.27 \n",
" 1172.8,713.939 1174.07,713.611 1175.33,713.285 1176.6,712.962 1177.86,712.642 1179.13,712.325 1180.39,712.011 1181.66,711.7 1182.92,711.393 1184.19,711.089 \n",
" 1185.45,710.789 1186.72,710.492 1187.98,710.2 1189.24,709.911 1190.51,709.626 1191.77,709.345 1193.04,709.069 1194.3,708.797 1195.57,708.529 1196.83,708.266 \n",
" 1198.1,708.008 1199.36,707.755 1200.63,707.506 1201.89,707.263 1203.16,707.024 1204.42,706.791 1205.69,706.563 1206.95,706.34 1208.22,706.123 1209.48,705.912 \n",
" 1210.75,705.706 1212.01,705.506 1213.28,705.312 1214.54,705.124 1215.81,704.941 1217.07,704.765 1218.34,704.596 1219.6,704.432 1220.87,704.275 1222.13,704.124 \n",
" 1223.39,703.98 1224.66,703.843 1225.92,703.712 1227.19,703.587 1228.45,703.47 1229.72,703.359 1230.98,703.256 1232.25,703.159 1233.51,703.069 1234.78,702.986 \n",
" 1236.04,702.91 1237.31,702.842 1238.57,702.78 1239.84,702.726 1241.1,702.679 1242.37,702.639 1243.63,702.606 1244.9,702.581 1246.16,702.562 1247.43,702.552 \n",
" 1248.69,702.548 1249.96,702.552 1251.22,702.562 1252.49,702.581 1253.75,702.606 1255.02,702.639 1256.28,702.679 1257.55,702.726 1258.81,702.78 1260.07,702.842 \n",
" 1261.34,702.91 1262.6,702.986 1263.87,703.069 1265.13,703.159 1266.4,703.256 1267.66,703.359 1268.93,703.47 1270.19,703.587 1271.46,703.712 1272.72,703.843 \n",
" 1273.99,703.98 1275.25,704.124 1276.52,704.275 1277.78,704.432 1279.05,704.596 1280.31,704.765 1281.58,704.941 1282.84,705.124 1284.11,705.312 1285.37,705.506 \n",
" 1286.64,705.706 1287.9,705.912 1289.17,706.123 1290.43,706.34 1291.7,706.563 1292.96,706.791 1294.22,707.024 1295.49,707.263 1296.75,707.506 1298.02,707.755 \n",
" 1299.28,708.008 1300.55,708.266 1301.81,708.529 1303.08,708.797 1304.34,709.069 1305.61,709.345 1306.87,709.626 1308.14,709.911 1309.4,710.2 1310.67,710.492 \n",
" 1311.93,710.789 1313.2,711.089 1314.46,711.393 1315.73,711.7 1316.99,712.011 1318.26,712.325 1319.52,712.642 1320.79,712.962 1322.05,713.285 1323.32,713.611 \n",
" 1324.58,713.939 1325.85,714.27 1327.11,714.604 1328.38,714.94 1329.64,715.278 1330.9,715.619 1332.17,715.961 1333.43,716.306 1334.7,716.652 1335.96,717 \n",
" 1337.23,717.35 1338.49,717.701 1339.76,718.054 1341.02,718.408 1342.29,718.764 1343.55,719.121 1344.82,719.478 1346.08,719.837 1347.35,720.197 1348.61,720.557 \n",
" 1349.88,720.918 1351.14,721.28 1352.41,721.642 1353.67,722.005 1354.94,722.369 1356.2,722.732 1357.47,723.096 1358.73,723.46 1360,723.824 1361.26,724.188 \n",
" 1362.53,724.552 1363.79,724.916 1365.05,725.279 1366.32,725.643 1367.58,726.006 1368.85,726.369 1370.11,726.731 1371.38,727.092 1372.64,727.453 1373.91,727.814 \n",
" 1375.17,728.174 1376.44,728.533 1377.7,728.891 1378.97,729.248 1380.23,729.604 1381.5,729.96 1382.76,730.314 1384.03,730.668 1385.29,731.02 1386.56,731.371 \n",
" 1387.82,731.721 1389.09,732.07 1390.35,732.417 1391.62,732.763 1392.88,733.108 1394.15,733.451 1395.41,733.793 1396.68,734.134 1397.94,734.473 1399.21,734.811 \n",
" 1400.47,735.147 1401.73,735.481 1403,735.814 1404.26,736.145 1405.53,736.475 1406.79,736.803 1408.06,737.129 1409.32,737.453 1410.59,737.776 1411.85,738.097 \n",
" 1413.12,738.416 1414.38,738.734 1415.65,739.049 1416.91,739.363 1418.18,739.675 1419.44,739.985 1420.71,740.294 1421.97,740.6 1423.24,740.904 1424.5,741.207 \n",
" 1425.77,741.508 1427.03,741.806 1428.3,742.103 1429.56,742.398 1430.83,742.691 1432.09,742.982 1433.36,743.271 1434.62,743.558 1435.88,743.843 1437.15,744.126 \n",
" 1438.41,744.408 1439.68,744.687 1440.94,744.964 1442.21,745.239 1443.47,745.512 1444.74,745.784 1446,746.053 1447.27,746.32 1448.53,746.585 1449.8,746.849 \n",
" 1451.06,747.11 1452.33,747.37 1453.59,747.627 1454.86,747.882 1456.12,748.136 1457.39,748.387 1458.65,748.637 1459.92,748.884 1461.18,749.13 1462.45,749.374 \n",
" 1463.71,749.616 1464.98,749.855 1466.24,750.093 1467.51,750.329 1468.77,750.563 1470.04,750.796 1471.3,751.026 1472.56,751.254 1473.83,751.481 1475.09,751.706 \n",
" 1476.36,751.928 1477.62,752.149 1478.89,752.368 1480.15,752.586 1481.42,752.801 1482.68,753.014 1483.95,753.226 1485.21,753.436 1486.48,753.644 1487.74,753.851 \n",
" 1489.01,754.055 1490.27,754.258 1491.54,754.459 1492.8,754.659 1494.07,754.856 1495.33,755.052 1496.6,755.246 1497.86,755.439 1499.13,755.629 1500.39,755.819 \n",
" 1501.66,756.006 1502.92,756.192 1504.19,756.376 1505.45,756.558 1506.71,756.739 1507.98,756.918 1509.24,757.096 1510.51,757.272 1511.77,757.446 1513.04,757.619 \n",
" 1514.3,757.79 1515.57,757.96 1516.83,758.128 1518.1,758.295 1519.36,758.46 1520.63,758.624 1521.89,758.786 1523.16,758.946 1524.42,759.106 1525.69,759.263 \n",
" 1526.95,759.42 1528.22,759.574 1529.48,759.728 1530.75,759.88 1532.01,760.03 1533.28,760.179 1534.54,760.327 1535.81,760.474 1537.07,760.619 1538.34,760.762 \n",
" 1539.6,760.905 1540.87,761.046 1542.13,761.185 1543.39,761.324 1544.66,761.461 1545.92,761.597 1547.19,761.731 1548.45,761.864 1549.72,761.996 1550.98,762.127 \n",
" 1552.25,762.257 1553.51,762.385 1554.78,762.512 1556.04,762.638 1557.31,762.762 1558.57,762.886 1559.84,763.008 1561.1,763.129 1562.37,763.249 1563.63,763.368 \n",
" 1564.9,763.486 1566.16,763.603 1567.43,763.718 1568.69,763.832 1569.96,763.946 1571.22,764.058 1572.49,764.169 1573.75,764.279 1575.02,764.388 1576.28,764.496 \n",
" 1577.54,764.603 1578.81,764.709 1580.07,764.814 1581.34,764.917 1582.6,765.02 1583.87,765.122 1585.13,765.223 1586.4,765.323 1587.66,765.422 1588.93,765.52 \n",
" 1590.19,765.617 1591.46,765.713 1592.72,765.808 1593.99,765.902 1595.25,765.996 1596.52,766.088 1597.78,766.179 1599.05,766.27 1600.31,766.36 1601.58,766.449 \n",
" 1602.84,766.537 1604.11,766.624 1605.37,766.71 1606.64,766.796 1607.9,766.88 1609.17,766.964 1610.43,767.047 1611.7,767.129 1612.96,767.211 1614.22,767.291 \n",
" 1615.49,767.371 1616.75,767.45 1618.02,767.528 1619.28,767.606 1620.55,767.682 1621.81,767.758 1623.08,767.834 1624.34,767.908 1625.61,767.982 1626.87,768.055 \n",
" 1628.14,768.127 1629.4,768.199 1630.67,768.27 1631.93,768.34 1633.2,768.409 1634.46,768.478 1635.73,768.546 1636.99,768.614 1638.26,768.681 1639.52,768.747 \n",
" 1640.79,768.812 1642.05,768.877 1643.32,768.942 1644.58,769.005 1645.85,769.068 1647.11,769.131 1648.37,769.192 1649.64,769.253 1650.9,769.314 1652.17,769.374 \n",
" 1653.43,769.433 1654.7,769.492 1655.96,769.55 1657.23,769.608 1658.49,769.665 1659.76,769.721 1661.02,769.777 1662.29,769.833 1663.55,769.888 1664.82,769.942 \n",
" 1666.08,769.996 1667.35,770.049 1668.61,770.102 1669.88,770.154 1671.14,770.205 1672.41,770.257 1673.67,770.307 1674.94,770.357 1676.2,770.407 1677.47,770.456 \n",
" 1678.73,770.505 1680,770.553 1681.26,770.601 1682.53,770.648 1683.79,770.695 1685.05,770.741 1686.32,770.787 1687.58,770.832 1688.85,770.877 1690.11,770.922 \n",
" 1691.38,770.966 1692.64,771.01 1693.91,771.053 1695.17,771.096 1696.44,771.138 1697.7,771.18 1698.97,771.221 1700.23,771.263 1701.5,771.303 1702.76,771.344 \n",
" 1704.03,771.383 1705.29,771.423 1706.56,771.462 1707.82,771.501 1709.09,771.539 1710.35,771.577 1711.62,771.615 1712.88,771.652 1714.15,771.689 1715.41,771.725 \n",
" 1716.68,771.761 1717.94,771.797 1719.2,771.832 1720.47,771.868 1721.73,771.902 1723,771.937 1724.26,771.971 1725.53,772.004 1726.79,772.038 1728.06,772.071 \n",
" 1729.32,772.103 1730.59,772.136 1731.85,772.168 1733.12,772.199 1734.38,772.231 1735.65,772.262 1736.91,772.293 1738.18,772.323 1739.44,772.353 1740.71,772.383 \n",
" 1741.97,772.413 1743.24,772.442 1744.5,772.471 1745.77,772.5 1747.03,772.528 1748.3,772.557 1749.56,772.584 1750.83,772.612 1752.09,772.639 1753.36,772.666 \n",
" 1754.62,772.693 1755.88,772.72 1757.15,772.746 1758.41,772.772 1759.68,772.798 1760.94,772.823 1762.21,772.848 1763.47,772.873 1764.74,772.898 1766,772.922 \n",
" 1767.27,772.947 1768.53,772.971 1769.8,772.994 1771.06,773.018 1772.33,773.041 1773.59,773.064 1774.86,773.087 1776.12,773.11 1777.39,773.132 1778.65,773.154 \n",
" 1779.92,773.176 1781.18,773.198 1782.45,773.219 1783.71,773.241 1784.98,773.262 1786.24,773.283 1787.51,773.303 1788.77,773.324 1790.03,773.344 1791.3,773.364 \n",
" 1792.56,773.384 1793.83,773.404 1795.09,773.423 1796.36,773.442 1797.62,773.461 1798.89,773.48 1800.15,773.499 1801.42,773.517 1802.68,773.536 1803.95,773.554 \n",
" 1805.21,773.572 1806.48,773.59 1807.74,773.607 1809.01,773.625 1810.27,773.642 1811.54,773.659 1812.8,773.676 1814.07,773.693 1815.33,773.709 1816.6,773.726 \n",
" 1817.86,773.742 1819.13,773.758 1820.39,773.774 1821.66,773.79 1822.92,773.805 1824.19,773.821 1825.45,773.836 1826.71,773.851 1827.98,773.866 1829.24,773.881 \n",
" 1830.51,773.896 1831.77,773.91 1833.04,773.925 1834.3,773.939 1835.57,773.953 1836.83,773.967 1838.1,773.981 1839.36,773.995 1840.63,774.008 1841.89,774.022 \n",
" 1843.16,774.035 1844.42,774.048 1845.69,774.061 1846.95,774.074 1848.22,774.087 1849.48,774.1 1850.75,774.112 1852.01,774.125 1853.28,774.137 1854.54,774.149 \n",
" 1855.81,774.161 1857.07,774.173 1858.34,774.185 1859.6,774.196 1860.86,774.208 1862.13,774.219 1863.39,774.231 1864.66,774.242 1865.92,774.253 1867.19,774.264 \n",
" 1868.45,774.275 1869.72,774.286 1870.98,774.297 1872.25,774.307 1873.51,774.318 1874.78,774.328 1876.04,774.338 1877.31,774.348 1878.57,774.358 1879.84,774.368 \n",
" 1881.1,774.378 1882.37,774.388 1883.63,774.398 1884.9,774.407 1886.16,774.417 1887.43,774.426 1888.69,774.435 1889.96,774.445 1891.22,774.454 1892.49,774.463 \n",
" 1893.75,774.472 1895.02,774.48 1896.28,774.489 1897.54,774.498 1898.81,774.506 1900.07,774.515 1901.34,774.523 1902.6,774.532 1903.87,774.54 1905.13,774.548 \n",
" 1906.4,774.556 1907.66,774.564 1908.93,774.572 1910.19,774.58 1911.46,774.588 1912.72,774.595 1913.99,774.603 1915.25,774.61 1916.52,774.618 1917.78,774.625 \n",
" 1919.05,774.633 1920.31,774.64 1921.58,774.647 1922.84,774.654 1924.11,774.661 1925.37,774.668 1926.64,774.675 1927.9,774.682 1929.17,774.688 1930.43,774.695 \n",
" 1931.69,774.702 1932.96,774.708 1934.22,774.715 1935.49,774.721 1936.75,774.727 1938.02,774.734 1939.28,774.74 1940.55,774.746 1941.81,774.752 1943.08,774.758 \n",
" 1944.34,774.764 1945.61,774.77 1946.87,774.776 1948.14,774.782 1949.4,774.788 1950.67,774.793 1951.93,774.799 1953.2,774.805 1954.46,774.81 1955.73,774.816 \n",
" 1956.99,774.821 1958.26,774.826 1959.52,774.832 1960.79,774.837 1962.05,774.842 1963.32,774.847 1964.58,774.852 1965.85,774.857 1967.11,774.862 1968.37,774.867 \n",
" 1969.64,774.872 1970.9,774.877 1972.17,774.882 1973.43,774.887 1974.7,774.891 1975.96,774.896 1977.23,774.901 1978.49,774.905 1979.76,774.91 1981.02,774.914 \n",
" 1982.29,774.919 1983.55,774.923 1984.82,774.927 1986.08,774.932 1987.35,774.936 1988.61,774.94 1989.88,774.944 1991.14,774.948 1992.41,774.952 1993.67,774.956 \n",
" 1994.94,774.96 1996.2,774.964 1997.47,774.968 1998.73,774.972 2000,774.976 2001.26,774.98 2002.52,774.984 2003.79,774.987 2005.05,774.991 2006.32,774.995 \n",
" 2007.58,774.998 2008.85,775.002 2010.11,775.006 2011.38,775.009 2012.64,775.013 2013.91,775.016 2015.17,775.019 2016.44,775.023 2017.7,775.026 2018.97,775.03 \n",
" 2020.23,775.033 2021.5,775.036 2022.76,775.039 2024.03,775.042 2025.29,775.046 2026.56,775.049 2027.82,775.052 2029.09,775.055 2030.35,775.058 2031.62,775.061 \n",
" 2032.88,775.064 2034.15,775.067 2035.41,775.07 2036.68,775.073 2037.94,775.075 2039.2,775.078 2040.47,775.081 2041.73,775.084 2043,775.087 2044.26,775.089 \n",
" 2045.53,775.092 2046.79,775.095 2048.06,775.097 2049.32,775.1 2050.59,775.102 2051.85,775.105 2053.12,775.108 2054.38,775.11 2055.65,775.113 2056.91,775.115 \n",
" 2058.18,775.117 2059.44,775.12 2060.71,775.122 2061.97,775.125 2063.24,775.127 2064.5,775.129 2065.77,775.132 2067.03,775.134 2068.3,775.136 2069.56,775.138 \n",
" 2070.83,775.14 2072.09,775.143 2073.35,775.145 2074.62,775.147 2075.88,775.149 2077.15,775.151 2078.41,775.153 2079.68,775.155 2080.94,775.157 2082.21,775.159 \n",
" 2083.47,775.161 2084.74,775.163 2086,775.165 2087.27,775.167 2088.53,775.169 2089.8,775.171 2091.06,775.173 2092.33,775.175 2093.59,775.177 2094.86,775.178 \n",
" 2096.12,775.18 2097.39,775.182 2098.65,775.184 2099.92,775.185 2101.18,775.187 2102.45,775.189 2103.71,775.191 2104.98,775.192 2106.24,775.194 2107.51,775.196 \n",
" 2108.77,775.197 2110.03,775.199 2111.3,775.2 2112.56,775.202 2113.83,775.204 2115.09,775.205 2116.36,775.207 2117.62,775.208 2118.89,775.21 2120.15,775.211 \n",
" 2121.42,775.213 2122.68,775.214 2123.95,775.216 2125.21,775.217 2126.48,775.218 2127.74,775.22 2129.01,775.221 2130.27,775.223 2131.54,775.224 2132.8,775.225 \n",
" 2134.07,775.227 2135.33,775.228 2136.6,775.229 2137.86,775.231 2139.13,775.232 2140.39,775.233 2141.66,775.234 2142.92,775.236 2144.18,775.237 2145.45,775.238 \n",
" 2146.71,775.239 2147.98,775.24 2149.24,775.242 2150.51,775.243 2151.77,775.244 2153.04,775.245 2154.3,775.246 2155.57,775.247 2156.83,775.248 2158.1,775.25 \n",
" 2159.36,775.251 2160.63,775.252 2161.89,775.253 2163.16,775.254 2164.42,775.255 2165.69,775.256 2166.95,775.257 2168.22,775.258 2169.48,775.259 2170.75,775.26 \n",
" 2172.01,775.261 2173.28,775.262 2174.54,775.263 2175.81,775.264 2177.07,775.265 2178.34,775.266 2179.6,775.267 2180.86,775.268 2182.13,775.269 2183.39,775.27 \n",
" 2184.66,775.27 2185.92,775.271 2187.19,775.272 2188.45,775.273 2189.72,775.274 2190.98,775.275 2192.25,775.276 2193.51,775.276 2194.78,775.277 2196.04,775.278 \n",
" 2197.31,775.279 2198.57,775.28 2199.84,775.28 2201.1,775.281 2202.37,775.282 2203.63,775.283 2204.9,775.284 2206.16,775.284 2207.43,775.285 2208.69,775.286 \n",
" 2209.96,775.287 2211.22,775.287 2212.49,775.288 2213.75,775.289 2215.01,775.289 2216.28,775.29 2217.54,775.291 2218.81,775.291 2220.07,775.292 2221.34,775.293 \n",
" 2222.6,775.293 2223.87,775.294 2225.13,775.295 2226.4,775.295 2227.66,775.296 2228.93,775.297 2230.19,775.297 2231.46,775.298 2232.72,775.299 2233.99,775.299 \n",
" 2235.25,775.3 2236.52,775.3 2237.78,775.301 2239.05,775.302 2240.31,775.302 2241.58,775.303 2242.84,775.303 2244.11,775.304 2245.37,775.304 2246.64,775.305 \n",
" 2247.9,775.305 2249.17,775.306 2250.43,775.306 2251.69,775.307 2252.96,775.308 2254.22,775.308 2255.49,775.309 2256.75,775.309 2258.02,775.31 2259.28,775.31 \n",
" 2260.55,775.311 \n",
" \"/>\n",
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" 1362.53,724.552 1363.79,724.916 1365.05,725.279 1366.32,725.643 1367.58,726.006 1368.85,726.369 1370.11,726.731 1371.38,727.092 1372.64,727.453 1373.91,727.814 \n",
" 1375.17,728.174 1376.44,728.533 1377.7,728.891 1378.97,729.248 1380.23,729.604 1381.5,729.96 1382.76,730.314 1384.03,730.668 1385.29,731.02 1386.56,731.371 \n",
" 1387.82,731.721 1389.09,732.07 1390.35,732.417 1391.62,732.763 1392.88,733.108 1394.15,733.451 1395.41,733.793 1396.68,734.134 1397.94,734.473 1399.21,734.811 \n",
" 1400.47,735.147 1401.73,735.481 1403,735.814 1404.26,736.145 1405.53,736.475 1406.79,736.803 1408.06,737.129 1409.32,737.453 1410.59,737.776 1411.85,738.097 \n",
" 1413.12,738.416 1414.38,738.734 1415.65,739.049 1416.91,739.363 1418.18,739.675 1419.44,739.985 1420.71,740.294 1421.97,740.6 1423.24,740.904 1424.5,741.207 \n",
" 1425.77,741.508 1427.03,741.806 1428.3,742.103 1429.56,742.398 1430.83,742.691 1432.09,742.982 1433.36,743.271 1434.62,743.558 1435.88,743.843 1437.15,744.126 \n",
" 1438.41,744.407 1439.68,744.687 1440.94,744.964 1442.21,745.239 1443.47,745.512 1444.74,745.784 1446,746.053 1447.27,746.32 1448.53,746.585 1449.8,746.849 \n",
" 1451.06,747.11 1452.33,747.37 1453.59,747.627 1454.86,747.882 1456.12,748.136 1457.39,748.387 1458.65,748.637 1459.92,748.885 1461.18,749.13 1462.45,749.374 \n",
" 1463.71,749.616 1464.98,749.856 1466.24,750.094 1467.51,750.33 1468.77,750.564 1470.04,750.796 1471.3,751.026 1472.56,751.255 1473.83,751.481 1475.09,751.706 \n",
" 1476.36,751.928 1477.62,752.149 1478.89,752.368 1480.15,752.586 1481.42,752.801 1482.68,753.015 1483.95,753.226 1485.21,753.436 1486.48,753.644 1487.74,753.851 \n",
" 1489.01,754.055 1490.27,754.258 1491.54,754.459 1492.8,754.658 1494.07,754.856 1495.33,755.052 1496.6,755.246 1497.86,755.438 1499.13,755.629 1500.39,755.818 \n",
" 1501.66,756.006 1502.92,756.191 1504.19,756.376 1505.45,756.558 1506.71,756.739 1507.98,756.918 1509.24,757.096 1510.51,757.272 1511.77,757.446 1513.04,757.619 \n",
" 1514.3,757.79 1515.57,757.96 1516.83,758.128 1518.1,758.295 1519.36,758.46 1520.63,758.624 1521.89,758.786 1523.16,758.946 1524.42,759.106 1525.69,759.263 \n",
" 1526.95,759.42 1528.22,759.575 1529.48,759.728 1530.75,759.88 1532.01,760.031 1533.28,760.18 1534.54,760.328 1535.81,760.474 1537.07,760.619 1538.34,760.763 \n",
" 1539.6,760.905 1540.87,761.046 1542.13,761.186 1543.39,761.324 1544.66,761.461 1545.92,761.597 1547.19,761.732 1548.45,761.865 1549.72,761.997 1550.98,762.128 \n",
" 1552.25,762.257 1553.51,762.385 1554.78,762.512 1556.04,762.638 1557.31,762.763 1558.57,762.886 1559.84,763.009 1561.1,763.13 1562.37,763.25 1563.63,763.368 \n",
" 1564.9,763.486 1566.16,763.602 1567.43,763.718 1568.69,763.832 1569.96,763.945 1571.22,764.057 1572.49,764.168 1573.75,764.278 1575.02,764.387 1576.28,764.495 \n",
" 1577.54,764.602 1578.81,764.708 1580.07,764.813 1581.34,764.916 1582.6,765.019 1583.87,765.121 1585.13,765.222 1586.4,765.322 1587.66,765.421 1588.93,765.519 \n",
" 1590.19,765.616 1591.46,765.712 1592.72,765.807 1593.99,765.901 1595.25,765.995 1596.52,766.087 1597.78,766.179 1599.05,766.269 1600.31,766.359 1601.58,766.448 \n",
" 1602.84,766.536 1604.11,766.624 1605.37,766.71 1606.64,766.796 1607.9,766.881 1609.17,766.965 1610.43,767.048 1611.7,767.13 1612.96,767.212 1614.22,767.292 \n",
" 1615.49,767.372 1616.75,767.452 1618.02,767.53 1619.28,767.608 1620.55,767.684 1621.81,767.761 1623.08,767.836 1624.34,767.911 1625.61,767.984 1626.87,768.058 \n",
" 1628.14,768.13 1629.4,768.202 1630.67,768.272 1631.93,768.343 1633.2,768.412 1634.46,768.481 1635.73,768.549 1636.99,768.616 1638.26,768.683 1639.52,768.749 \n",
" 1640.79,768.814 1642.05,768.879 1643.32,768.943 1644.58,769.006 1645.85,769.068 1647.11,769.13 1648.37,769.192 1649.64,769.252 1650.9,769.313 1652.17,769.372 \n",
" 1653.43,769.431 1654.7,769.489 1655.96,769.547 1657.23,769.604 1658.49,769.661 1659.76,769.717 1661.02,769.772 1662.29,769.827 1663.55,769.882 1664.82,769.936 \n",
" 1666.08,769.989 1667.35,770.042 1668.61,770.095 1669.88,770.147 1671.14,770.198 1672.41,770.249 1673.67,770.3 1674.94,770.35 1676.2,770.4 1677.47,770.45 \n",
" 1678.73,770.499 1680,770.548 1681.26,770.596 1682.53,770.644 1683.79,770.692 1685.05,770.739 1686.32,770.786 1687.58,770.832 1688.85,770.878 1690.11,770.924 \n",
" 1691.38,770.969 1692.64,771.014 1693.91,771.059 1695.17,771.103 1696.44,771.146 1697.7,771.19 1698.97,771.233 1700.23,771.275 1701.5,771.317 1702.76,771.359 \n",
" 1704.03,771.4 1705.29,771.441 1706.56,771.481 1707.82,771.52 1709.09,771.559 1710.35,771.598 1711.62,771.636 1712.88,771.673 1714.15,771.71 1715.41,771.747 \n",
" 1716.68,771.782 1717.94,771.817 1719.2,771.852 1720.47,771.886 1721.73,771.919 1723,771.952 1724.26,771.984 1725.53,772.015 1726.79,772.046 1728.06,772.076 \n",
" 1729.32,772.105 1730.59,772.134 1731.85,772.163 1733.12,772.19 1734.38,772.218 1735.65,772.245 1736.91,772.271 1738.18,772.297 1739.44,772.322 1740.71,772.348 \n",
" 1741.97,772.373 1743.24,772.397 1744.5,772.422 1745.77,772.447 1747.03,772.471 1748.3,772.495 1749.56,772.52 1750.83,772.544 1752.09,772.569 1753.36,772.594 \n",
" 1754.62,772.62 1755.88,772.645 1757.15,772.672 1758.41,772.698 1759.68,772.726 1760.94,772.754 1762.21,772.782 1763.47,772.812 1764.74,772.842 1766,772.873 \n",
" 1767.27,772.904 1768.53,772.937 1769.8,772.97 1771.06,773.004 1772.33,773.039 1773.59,773.074 1774.86,773.111 1776.12,773.148 1777.39,773.185 1778.65,773.223 \n",
" 1779.92,773.261 1781.18,773.3 1782.45,773.339 1783.71,773.378 1784.98,773.416 1786.24,773.454 1787.51,773.492 1788.77,773.529 1790.03,773.565 1791.3,773.6 \n",
" 1792.56,773.634 1793.83,773.665 1795.09,773.695 1796.36,773.723 1797.62,773.749 1798.89,773.771 1800.15,773.791 1801.42,773.808 1802.68,773.821 1803.95,773.831 \n",
" 1805.21,773.837 1806.48,773.839 1807.74,773.837 1809.01,773.83 1810.27,773.819 1811.54,773.804 1812.8,773.783 1814.07,773.759 1815.33,773.729 1816.6,773.695 \n",
" 1817.86,773.657 1819.13,773.614 1820.39,773.568 1821.66,773.518 1822.92,773.464 1824.19,773.408 1825.45,773.349 1826.71,773.289 1827.98,773.227 1829.24,773.165 \n",
" 1830.51,773.103 1831.77,773.042 1833.04,772.983 1834.3,772.926 1835.57,772.874 1836.83,772.827 1838.1,772.786 1839.36,772.752 1840.63,772.727 1841.89,772.711 \n",
" 1843.16,772.706 1844.42,772.713 1845.69,772.734 1846.95,772.769 1848.22,772.819 1849.48,772.887 1850.75,772.972 1852.01,773.076 1853.28,773.201 1854.54,773.345 \n",
" 1855.81,773.511 1857.07,773.698 1858.34,773.907 1859.6,774.139 1860.86,774.392 1862.13,774.667 1863.39,774.963 1864.66,775.279 1865.92,775.614 1867.19,775.967 \n",
" 1868.45,776.335 1869.72,776.718 1870.98,777.112 1872.25,777.514 1873.51,777.921 1874.78,778.33 1876.04,778.738 1877.31,779.138 1878.57,779.528 1879.84,779.901 \n",
" 1881.1,780.253 1882.37,780.577 1883.63,780.868 1884.9,781.12 1886.16,781.326 1887.43,781.479 1888.69,781.572 1889.96,781.599 1891.22,781.552 1892.49,781.424 \n",
" 1893.75,781.209 1895.02,780.899 1896.28,780.489 1897.54,779.971 1898.81,779.341 1900.07,778.593 1901.34,777.722 1902.6,776.725 1903.87,775.599 1905.13,774.342 \n",
" 1906.4,772.953 1907.66,771.433 1908.93,769.783 1910.19,768.007 1911.46,766.11 1912.72,764.098 1913.99,761.981 1915.25,759.769 1916.52,757.475 1917.78,755.113 \n",
" 1919.05,752.701 1920.31,750.258 1921.58,747.807 1922.84,745.372 1924.11,742.98 1925.37,740.661 1926.64,738.446 1927.9,736.37 1929.17,734.47 1930.43,732.784 \n",
" 1931.69,731.355 1932.96,730.226 1934.22,729.44 1935.49,729.045 1936.75,729.088 1938.02,729.617 1939.28,730.682 1940.55,732.332 1941.81,734.614 1943.08,737.576 \n",
" 1944.34,741.264 1945.61,745.722 1946.87,750.991 1948.14,757.108 1949.4,764.105 1950.67,772.011 1951.93,780.846 1953.2,790.626 1954.46,801.356 1955.73,813.036 \n",
" 1956.99,825.651 1958.26,839.18 1959.52,853.587 1960.79,868.824 1962.05,884.83 1963.32,901.526 1964.58,918.822 1965.85,936.605 1967.11,954.75 1968.37,973.11 \n",
" 1969.64,991.519 1970.9,1009.79 1972.17,1027.72 1973.43,1045.09 1974.7,1061.64 1975.96,1077.11 1977.23,1091.2 1978.49,1103.61 1979.76,1114.02 1981.02,1122.07 \n",
" 1982.29,1127.39 1983.55,1129.62 1984.82,1128.34 1986.08,1123.17 1987.35,1113.67 1988.61,1099.44 1989.88,1080.04 1991.14,1055.05 1992.41,1024.06 1993.67,986.665 \n",
" 1994.94,942.466 1996.2,891.098 1997.47,832.221 1998.73,765.529 2000,690.758 2001.26,607.696 2002.52,516.186 2003.79,416.141 2005.05,307.548 2006.32,190.482 \n",
" 2007.58,65.1103 2008.85,-68.2914 2010.11,-209.333 2011.38,-357.497 2012.64,-512.13 2013.91,-672.429 2015.17,-837.435 2016.44,-1006.02 2017.7,-1176.87 2018.97,-1348.51 \n",
" 2020.23,-1519.23 2021.5,-1687.14 2022.76,-1850.14 2024.03,-2005.91 2025.29,-2151.89 2026.56,-2285.33 2027.82,-2403.24 2029.09,-2502.39 2030.35,-2579.36 2031.62,-2630.49 \n",
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" 2045.53,-276.179 2046.79,321.488 2048.06,1002.49 2049.32,1770.66 2050.59,2629.46 2051.85,3581.88 2053.12,4630.34 2054.38,5776.58 2055.65,7021.62 2056.91,8365.55 \n",
" 2058.18,9807.48 2059.44,11345.4 2060.71,12976.1 2061.97,14694.9 2063.24,16495.6 2064.5,18370.5 2065.77,20309.8 2067.03,22302 2068.3,24333.4 2069.56,26387.9 \n",
" 2070.83,28447.3 2072.09,30490.8 2073.35,32494.6 2074.62,34432.5 2075.88,36275.2 2077.15,37990.4 2078.41,39542.7 2079.68,40893.6 2080.94,42001.4 2082.21,42820.8 \n",
" 2083.47,43303.8 2084.74,43398.8 2086,43051.3 2087.27,42203.6 2088.53,40795.4 2089.8,38763.5 2091.06,36042.4 2092.33,32564.9 2093.59,28261.6 2094.86,23062.3 \n",
" 2096.12,16896.1 2097.39,9691.99 2098.65,1379.78 2099.92,-8109.31 2101.18,-18841.6 2102.45,-30880.1 2103.71,-44283.1 2104.98,-59103.3 2106.24,-75386.4 2107.51,-93169.2 \n",
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" 2134.07,-681700 2135.33,-698141 2136.6,-709507 2137.86,-714929 2139.13,-713470 2140.39,-704126 2141.66,-685827 2142.92,-657433 2144.18,-617742 2145.45,-565486 \n",
" 2146.71,-499341 2147.98,-417926 2149.24,-319811 2150.51,-203523 2151.77,-67557.1 2153.04,89615.7 2154.3,269536 2155.57,473743 2156.83,703757 2158.1,961061 \n",
" 2159.36,1.24708e+06 2160.63,1.56317e+06 2161.89,1.91057e+06 2163.16,2.29039e+06 2164.42,2.70357e+06 2165.69,3.15085e+06 2166.95,3.63274e+06 2168.22,4.14946e+06 2169.48,4.70091e+06 2170.75,5.28662e+06 \n",
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" 2184.66,1.33024e+07 2185.92,1.40424e+07 2187.19,1.47472e+07 2188.45,1.54038e+07 2189.72,1.59977e+07 2190.98,1.65128e+07 2192.25,1.69311e+07 2193.51,1.72331e+07 2194.78,1.73971e+07 2196.04,1.73995e+07 \n",
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},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# nonsense trying to approximating sech(x) by a degree 50 polynomial:\n",
"f = Fun(x -> sech(x), Hermite(), 51)\n",
"xx = -8:0.01:8\n",
"plot(xx, sech.(xx); ylims=(-10,10), label=\"sech x\")\n",
"plot!(xx, f.(xx); label=\"f\")"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
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" 1046.32,747.11 1047.58,746.849 1048.85,746.585 1050.11,746.32 1051.38,746.053 1052.64,745.784 1053.91,745.512 1055.17,745.239 1056.44,744.964 1057.7,744.687 \n",
" 1058.97,744.408 1060.23,744.126 1061.5,743.843 1062.76,743.558 1064.03,743.271 1065.29,742.982 1066.56,742.691 1067.82,742.398 1069.09,742.103 1070.35,741.806 \n",
" 1071.62,741.508 1072.88,741.207 1074.15,740.904 1075.41,740.6 1076.68,740.294 1077.94,739.985 1079.21,739.675 1080.47,739.363 1081.73,739.049 1083,738.734 \n",
" 1084.26,738.416 1085.53,738.097 1086.79,737.776 1088.06,737.453 1089.32,737.129 1090.59,736.803 1091.85,736.475 1093.12,736.145 1094.38,735.814 1095.65,735.481 \n",
" 1096.91,735.147 1098.18,734.811 1099.44,734.473 1100.71,734.134 1101.97,733.793 1103.24,733.451 1104.5,733.108 1105.77,732.763 1107.03,732.417 1108.3,732.07 \n",
" 1109.56,731.721 1110.83,731.371 1112.09,731.02 1113.36,730.668 1114.62,730.314 1115.89,729.96 1117.15,729.604 1118.41,729.248 1119.68,728.891 1120.94,728.533 \n",
" 1122.21,728.174 1123.47,727.814 1124.74,727.453 1126,727.092 1127.27,726.731 1128.53,726.369 1129.8,726.006 1131.06,725.643 1132.33,725.279 1133.59,724.916 \n",
" 1134.86,724.552 1136.12,724.188 1137.39,723.824 1138.65,723.46 1139.92,723.096 1141.18,722.732 1142.45,722.369 1143.71,722.005 1144.98,721.642 1146.24,721.28 \n",
" 1147.51,720.918 1148.77,720.557 1150.04,720.197 1151.3,719.837 1152.56,719.478 1153.83,719.121 1155.09,718.764 1156.36,718.408 1157.62,718.054 1158.89,717.701 \n",
" 1160.15,717.35 1161.42,717 1162.68,716.652 1163.95,716.306 1165.21,715.961 1166.48,715.619 1167.74,715.278 1169.01,714.94 1170.27,714.604 1171.54,714.27 \n",
" 1172.8,713.939 1174.07,713.611 1175.33,713.285 1176.6,712.962 1177.86,712.642 1179.13,712.325 1180.39,712.011 1181.66,711.7 1182.92,711.393 1184.19,711.089 \n",
" 1185.45,710.789 1186.72,710.492 1187.98,710.2 1189.24,709.911 1190.51,709.626 1191.77,709.345 1193.04,709.069 1194.3,708.797 1195.57,708.529 1196.83,708.266 \n",
" 1198.1,708.008 1199.36,707.755 1200.63,707.506 1201.89,707.263 1203.16,707.024 1204.42,706.791 1205.69,706.563 1206.95,706.34 1208.22,706.123 1209.48,705.912 \n",
" 1210.75,705.706 1212.01,705.506 1213.28,705.312 1214.54,705.124 1215.81,704.941 1217.07,704.765 1218.34,704.596 1219.6,704.432 1220.87,704.275 1222.13,704.124 \n",
" 1223.39,703.98 1224.66,703.843 1225.92,703.712 1227.19,703.587 1228.45,703.47 1229.72,703.359 1230.98,703.256 1232.25,703.159 1233.51,703.069 1234.78,702.986 \n",
" 1236.04,702.91 1237.31,702.842 1238.57,702.78 1239.84,702.726 1241.1,702.679 1242.37,702.639 1243.63,702.606 1244.9,702.581 1246.16,702.562 1247.43,702.552 \n",
" 1248.69,702.548 1249.96,702.552 1251.22,702.562 1252.49,702.581 1253.75,702.606 1255.02,702.639 1256.28,702.679 1257.55,702.726 1258.81,702.78 1260.07,702.842 \n",
" 1261.34,702.91 1262.6,702.986 1263.87,703.069 1265.13,703.159 1266.4,703.256 1267.66,703.359 1268.93,703.47 1270.19,703.587 1271.46,703.712 1272.72,703.843 \n",
" 1273.99,703.98 1275.25,704.124 1276.52,704.275 1277.78,704.432 1279.05,704.596 1280.31,704.765 1281.58,704.941 1282.84,705.124 1284.11,705.312 1285.37,705.506 \n",
" 1286.64,705.706 1287.9,705.912 1289.17,706.123 1290.43,706.34 1291.7,706.563 1292.96,706.791 1294.22,707.024 1295.49,707.263 1296.75,707.506 1298.02,707.755 \n",
" 1299.28,708.008 1300.55,708.266 1301.81,708.529 1303.08,708.797 1304.34,709.069 1305.61,709.345 1306.87,709.626 1308.14,709.911 1309.4,710.2 1310.67,710.492 \n",
" 1311.93,710.789 1313.2,711.089 1314.46,711.393 1315.73,711.7 1316.99,712.011 1318.26,712.325 1319.52,712.642 1320.79,712.962 1322.05,713.285 1323.32,713.611 \n",
" 1324.58,713.939 1325.85,714.27 1327.11,714.604 1328.38,714.94 1329.64,715.278 1330.9,715.619 1332.17,715.961 1333.43,716.306 1334.7,716.652 1335.96,717 \n",
" 1337.23,717.35 1338.49,717.701 1339.76,718.054 1341.02,718.408 1342.29,718.764 1343.55,719.121 1344.82,719.478 1346.08,719.837 1347.35,720.197 1348.61,720.557 \n",
" 1349.88,720.918 1351.14,721.28 1352.41,721.642 1353.67,722.005 1354.94,722.369 1356.2,722.732 1357.47,723.096 1358.73,723.46 1360,723.824 1361.26,724.188 \n",
" 1362.53,724.552 1363.79,724.916 1365.05,725.279 1366.32,725.643 1367.58,726.006 1368.85,726.369 1370.11,726.731 1371.38,727.092 1372.64,727.453 1373.91,727.814 \n",
" 1375.17,728.174 1376.44,728.533 1377.7,728.891 1378.97,729.248 1380.23,729.604 1381.5,729.96 1382.76,730.314 1384.03,730.668 1385.29,731.02 1386.56,731.371 \n",
" 1387.82,731.721 1389.09,732.07 1390.35,732.417 1391.62,732.763 1392.88,733.108 1394.15,733.451 1395.41,733.793 1396.68,734.134 1397.94,734.473 1399.21,734.811 \n",
" 1400.47,735.147 1401.73,735.481 1403,735.814 1404.26,736.145 1405.53,736.475 1406.79,736.803 1408.06,737.129 1409.32,737.453 1410.59,737.776 1411.85,738.097 \n",
" 1413.12,738.416 1414.38,738.734 1415.65,739.049 1416.91,739.363 1418.18,739.675 1419.44,739.985 1420.71,740.294 1421.97,740.6 1423.24,740.904 1424.5,741.207 \n",
" 1425.77,741.508 1427.03,741.806 1428.3,742.103 1429.56,742.398 1430.83,742.691 1432.09,742.982 1433.36,743.271 1434.62,743.558 1435.88,743.843 1437.15,744.126 \n",
" 1438.41,744.408 1439.68,744.687 1440.94,744.964 1442.21,745.239 1443.47,745.512 1444.74,745.784 1446,746.053 1447.27,746.32 1448.53,746.585 1449.8,746.849 \n",
" 1451.06,747.11 1452.33,747.37 1453.59,747.627 1454.86,747.882 1456.12,748.136 1457.39,748.387 1458.65,748.637 1459.92,748.884 1461.18,749.13 1462.45,749.374 \n",
" 1463.71,749.616 1464.98,749.855 1466.24,750.093 1467.51,750.329 1468.77,750.563 1470.04,750.796 1471.3,751.026 1472.56,751.254 1473.83,751.481 1475.09,751.706 \n",
" 1476.36,751.928 1477.62,752.149 1478.89,752.368 1480.15,752.586 1481.42,752.801 1482.68,753.014 1483.95,753.226 1485.21,753.436 1486.48,753.644 1487.74,753.851 \n",
" 1489.01,754.055 1490.27,754.258 1491.54,754.459 1492.8,754.659 1494.07,754.856 1495.33,755.052 1496.6,755.246 1497.86,755.439 1499.13,755.629 1500.39,755.819 \n",
" 1501.66,756.006 1502.92,756.192 1504.19,756.376 1505.45,756.558 1506.71,756.739 1507.98,756.918 1509.24,757.096 1510.51,757.272 1511.77,757.446 1513.04,757.619 \n",
" 1514.3,757.79 1515.57,757.96 1516.83,758.128 1518.1,758.295 1519.36,758.46 1520.63,758.624 1521.89,758.786 1523.16,758.946 1524.42,759.106 1525.69,759.263 \n",
" 1526.95,759.42 1528.22,759.574 1529.48,759.728 1530.75,759.88 1532.01,760.03 1533.28,760.179 1534.54,760.327 1535.81,760.474 1537.07,760.619 1538.34,760.762 \n",
" 1539.6,760.905 1540.87,761.046 1542.13,761.185 1543.39,761.324 1544.66,761.461 1545.92,761.597 1547.19,761.731 1548.45,761.864 1549.72,761.996 1550.98,762.127 \n",
" 1552.25,762.257 1553.51,762.385 1554.78,762.512 1556.04,762.638 1557.31,762.762 1558.57,762.886 1559.84,763.008 1561.1,763.129 1562.37,763.249 1563.63,763.368 \n",
" 1564.9,763.486 1566.16,763.603 1567.43,763.718 1568.69,763.832 1569.96,763.946 1571.22,764.058 1572.49,764.169 1573.75,764.279 1575.02,764.388 1576.28,764.496 \n",
" 1577.54,764.603 1578.81,764.709 1580.07,764.814 1581.34,764.917 1582.6,765.02 1583.87,765.122 1585.13,765.223 1586.4,765.323 1587.66,765.422 1588.93,765.52 \n",
" 1590.19,765.617 1591.46,765.713 1592.72,765.808 1593.99,765.902 1595.25,765.996 1596.52,766.088 1597.78,766.179 1599.05,766.27 1600.31,766.36 1601.58,766.449 \n",
" 1602.84,766.537 1604.11,766.624 1605.37,766.71 1606.64,766.796 1607.9,766.88 1609.17,766.964 1610.43,767.047 1611.7,767.129 1612.96,767.211 1614.22,767.291 \n",
" 1615.49,767.371 1616.75,767.45 1618.02,767.528 1619.28,767.606 1620.55,767.682 1621.81,767.758 1623.08,767.834 1624.34,767.908 1625.61,767.982 1626.87,768.055 \n",
" 1628.14,768.127 1629.4,768.199 1630.67,768.27 1631.93,768.34 1633.2,768.409 1634.46,768.478 1635.73,768.546 1636.99,768.614 1638.26,768.681 1639.52,768.747 \n",
" 1640.79,768.812 1642.05,768.877 1643.32,768.942 1644.58,769.005 1645.85,769.068 1647.11,769.131 1648.37,769.192 1649.64,769.253 1650.9,769.314 1652.17,769.374 \n",
" 1653.43,769.433 1654.7,769.492 1655.96,769.55 1657.23,769.608 1658.49,769.665 1659.76,769.721 1661.02,769.777 1662.29,769.833 1663.55,769.888 1664.82,769.942 \n",
" 1666.08,769.996 1667.35,770.049 1668.61,770.102 1669.88,770.154 1671.14,770.205 1672.41,770.257 1673.67,770.307 1674.94,770.357 1676.2,770.407 1677.47,770.456 \n",
" 1678.73,770.505 1680,770.553 1681.26,770.601 1682.53,770.648 1683.79,770.695 1685.05,770.741 1686.32,770.787 1687.58,770.832 1688.85,770.877 1690.11,770.922 \n",
" 1691.38,770.966 1692.64,771.01 1693.91,771.053 1695.17,771.096 1696.44,771.138 1697.7,771.18 1698.97,771.221 1700.23,771.263 1701.5,771.303 1702.76,771.344 \n",
" 1704.03,771.383 1705.29,771.423 1706.56,771.462 1707.82,771.501 1709.09,771.539 1710.35,771.577 1711.62,771.615 1712.88,771.652 1714.15,771.689 1715.41,771.725 \n",
" 1716.68,771.761 1717.94,771.797 1719.2,771.832 1720.47,771.868 1721.73,771.902 1723,771.937 1724.26,771.971 1725.53,772.004 1726.79,772.038 1728.06,772.071 \n",
" 1729.32,772.103 1730.59,772.136 1731.85,772.168 1733.12,772.199 1734.38,772.231 1735.65,772.262 1736.91,772.293 1738.18,772.323 1739.44,772.353 1740.71,772.383 \n",
" 1741.97,772.413 1743.24,772.442 1744.5,772.471 1745.77,772.5 1747.03,772.528 1748.3,772.557 1749.56,772.584 1750.83,772.612 1752.09,772.639 1753.36,772.666 \n",
" 1754.62,772.693 1755.88,772.72 1757.15,772.746 1758.41,772.772 1759.68,772.798 1760.94,772.823 1762.21,772.848 1763.47,772.873 1764.74,772.898 1766,772.922 \n",
" 1767.27,772.947 1768.53,772.971 1769.8,772.994 1771.06,773.018 1772.33,773.041 1773.59,773.064 1774.86,773.087 1776.12,773.11 1777.39,773.132 1778.65,773.154 \n",
" 1779.92,773.176 1781.18,773.198 1782.45,773.219 1783.71,773.241 1784.98,773.262 1786.24,773.283 1787.51,773.303 1788.77,773.324 1790.03,773.344 1791.3,773.364 \n",
" 1792.56,773.384 1793.83,773.404 1795.09,773.423 1796.36,773.442 1797.62,773.461 1798.89,773.48 1800.15,773.499 1801.42,773.517 1802.68,773.536 1803.95,773.554 \n",
" 1805.21,773.572 1806.48,773.59 1807.74,773.607 1809.01,773.625 1810.27,773.642 1811.54,773.659 1812.8,773.676 1814.07,773.693 1815.33,773.709 1816.6,773.726 \n",
" 1817.86,773.742 1819.13,773.758 1820.39,773.774 1821.66,773.79 1822.92,773.805 1824.19,773.821 1825.45,773.836 1826.71,773.851 1827.98,773.866 1829.24,773.881 \n",
" 1830.51,773.896 1831.77,773.91 1833.04,773.925 1834.3,773.939 1835.57,773.953 1836.83,773.967 1838.1,773.981 1839.36,773.995 1840.63,774.008 1841.89,774.022 \n",
" 1843.16,774.035 1844.42,774.048 1845.69,774.061 1846.95,774.074 1848.22,774.087 1849.48,774.1 1850.75,774.112 1852.01,774.125 1853.28,774.137 1854.54,774.149 \n",
" 1855.81,774.161 1857.07,774.173 1858.34,774.185 1859.6,774.196 1860.86,774.208 1862.13,774.219 1863.39,774.231 1864.66,774.242 1865.92,774.253 1867.19,774.264 \n",
" 1868.45,774.275 1869.72,774.286 1870.98,774.297 1872.25,774.307 1873.51,774.318 1874.78,774.328 1876.04,774.338 1877.31,774.348 1878.57,774.358 1879.84,774.368 \n",
" 1881.1,774.378 1882.37,774.388 1883.63,774.398 1884.9,774.407 1886.16,774.417 1887.43,774.426 1888.69,774.435 1889.96,774.445 1891.22,774.454 1892.49,774.463 \n",
" 1893.75,774.472 1895.02,774.48 1896.28,774.489 1897.54,774.498 1898.81,774.506 1900.07,774.515 1901.34,774.523 1902.6,774.532 1903.87,774.54 1905.13,774.548 \n",
" 1906.4,774.556 1907.66,774.564 1908.93,774.572 1910.19,774.58 1911.46,774.588 1912.72,774.595 1913.99,774.603 1915.25,774.61 1916.52,774.618 1917.78,774.625 \n",
" 1919.05,774.633 1920.31,774.64 1921.58,774.647 1922.84,774.654 1924.11,774.661 1925.37,774.668 1926.64,774.675 1927.9,774.682 1929.17,774.688 1930.43,774.695 \n",
" 1931.69,774.702 1932.96,774.708 1934.22,774.715 1935.49,774.721 1936.75,774.727 1938.02,774.734 1939.28,774.74 1940.55,774.746 1941.81,774.752 1943.08,774.758 \n",
" 1944.34,774.764 1945.61,774.77 1946.87,774.776 1948.14,774.782 1949.4,774.788 1950.67,774.793 1951.93,774.799 1953.2,774.805 1954.46,774.81 1955.73,774.816 \n",
" 1956.99,774.821 1958.26,774.826 1959.52,774.832 1960.79,774.837 1962.05,774.842 1963.32,774.847 1964.58,774.852 1965.85,774.857 1967.11,774.862 1968.37,774.867 \n",
" 1969.64,774.872 1970.9,774.877 1972.17,774.882 1973.43,774.887 1974.7,774.891 1975.96,774.896 1977.23,774.901 1978.49,774.905 1979.76,774.91 1981.02,774.914 \n",
" 1982.29,774.919 1983.55,774.923 1984.82,774.927 1986.08,774.932 1987.35,774.936 1988.61,774.94 1989.88,774.944 1991.14,774.948 1992.41,774.952 1993.67,774.956 \n",
" 1994.94,774.96 1996.2,774.964 1997.47,774.968 1998.73,774.972 2000,774.976 2001.26,774.98 2002.52,774.984 2003.79,774.987 2005.05,774.991 2006.32,774.995 \n",
" 2007.58,774.998 2008.85,775.002 2010.11,775.006 2011.38,775.009 2012.64,775.013 2013.91,775.016 2015.17,775.019 2016.44,775.023 2017.7,775.026 2018.97,775.03 \n",
" 2020.23,775.033 2021.5,775.036 2022.76,775.039 2024.03,775.042 2025.29,775.046 2026.56,775.049 2027.82,775.052 2029.09,775.055 2030.35,775.058 2031.62,775.061 \n",
" 2032.88,775.064 2034.15,775.067 2035.41,775.07 2036.68,775.073 2037.94,775.075 2039.2,775.078 2040.47,775.081 2041.73,775.084 2043,775.087 2044.26,775.089 \n",
" 2045.53,775.092 2046.79,775.095 2048.06,775.097 2049.32,775.1 2050.59,775.102 2051.85,775.105 2053.12,775.108 2054.38,775.11 2055.65,775.113 2056.91,775.115 \n",
" 2058.18,775.117 2059.44,775.12 2060.71,775.122 2061.97,775.125 2063.24,775.127 2064.5,775.129 2065.77,775.132 2067.03,775.134 2068.3,775.136 2069.56,775.138 \n",
" 2070.83,775.14 2072.09,775.143 2073.35,775.145 2074.62,775.147 2075.88,775.149 2077.15,775.151 2078.41,775.153 2079.68,775.155 2080.94,775.157 2082.21,775.159 \n",
" 2083.47,775.161 2084.74,775.163 2086,775.165 2087.27,775.167 2088.53,775.169 2089.8,775.171 2091.06,775.173 2092.33,775.175 2093.59,775.177 2094.86,775.178 \n",
" 2096.12,775.18 2097.39,775.182 2098.65,775.184 2099.92,775.185 2101.18,775.187 2102.45,775.189 2103.71,775.191 2104.98,775.192 2106.24,775.194 2107.51,775.196 \n",
" 2108.77,775.197 2110.03,775.199 2111.3,775.2 2112.56,775.202 2113.83,775.204 2115.09,775.205 2116.36,775.207 2117.62,775.208 2118.89,775.21 2120.15,775.211 \n",
" 2121.42,775.213 2122.68,775.214 2123.95,775.216 2125.21,775.217 2126.48,775.218 2127.74,775.22 2129.01,775.221 2130.27,775.223 2131.54,775.224 2132.8,775.225 \n",
" 2134.07,775.227 2135.33,775.228 2136.6,775.229 2137.86,775.231 2139.13,775.232 2140.39,775.233 2141.66,775.234 2142.92,775.236 2144.18,775.237 2145.45,775.238 \n",
" 2146.71,775.239 2147.98,775.24 2149.24,775.242 2150.51,775.243 2151.77,775.244 2153.04,775.245 2154.3,775.246 2155.57,775.247 2156.83,775.248 2158.1,775.25 \n",
" 2159.36,775.251 2160.63,775.252 2161.89,775.253 2163.16,775.254 2164.42,775.255 2165.69,775.256 2166.95,775.257 2168.22,775.258 2169.48,775.259 2170.75,775.26 \n",
" 2172.01,775.261 2173.28,775.262 2174.54,775.263 2175.81,775.264 2177.07,775.265 2178.34,775.266 2179.6,775.267 2180.86,775.268 2182.13,775.269 2183.39,775.27 \n",
" 2184.66,775.27 2185.92,775.271 2187.19,775.272 2188.45,775.273 2189.72,775.274 2190.98,775.275 2192.25,775.276 2193.51,775.276 2194.78,775.277 2196.04,775.278 \n",
" 2197.31,775.279 2198.57,775.28 2199.84,775.28 2201.1,775.281 2202.37,775.282 2203.63,775.283 2204.9,775.284 2206.16,775.284 2207.43,775.285 2208.69,775.286 \n",
" 2209.96,775.287 2211.22,775.287 2212.49,775.288 2213.75,775.289 2215.01,775.289 2216.28,775.29 2217.54,775.291 2218.81,775.291 2220.07,775.292 2221.34,775.293 \n",
" 2222.6,775.293 2223.87,775.294 2225.13,775.295 2226.4,775.295 2227.66,775.296 2228.93,775.297 2230.19,775.297 2231.46,775.298 2232.72,775.299 2233.99,775.299 \n",
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" 1387.82,731.721 1389.09,732.07 1390.35,732.417 1391.62,732.763 1392.88,733.108 1394.15,733.451 1395.41,733.793 1396.68,734.134 1397.94,734.473 1399.21,734.811 \n",
" 1400.47,735.147 1401.73,735.481 1403,735.814 1404.26,736.145 1405.53,736.475 1406.79,736.803 1408.06,737.129 1409.32,737.453 1410.59,737.776 1411.85,738.097 \n",
" 1413.12,738.416 1414.38,738.734 1415.65,739.049 1416.91,739.363 1418.18,739.675 1419.44,739.985 1420.71,740.294 1421.97,740.6 1423.24,740.904 1424.5,741.207 \n",
" 1425.77,741.508 1427.03,741.806 1428.3,742.103 1429.56,742.398 1430.83,742.691 1432.09,742.982 1433.36,743.271 1434.62,743.558 1435.88,743.843 1437.15,744.126 \n",
" 1438.41,744.408 1439.68,744.687 1440.94,744.964 1442.21,745.239 1443.47,745.512 1444.74,745.784 1446,746.053 1447.27,746.32 1448.53,746.585 1449.8,746.849 \n",
" 1451.06,747.11 1452.33,747.37 1453.59,747.627 1454.86,747.882 1456.12,748.136 1457.39,748.387 1458.65,748.637 1459.92,748.884 1461.18,749.13 1462.45,749.374 \n",
" 1463.71,749.616 1464.98,749.855 1466.24,750.093 1467.51,750.329 1468.77,750.563 1470.04,750.796 1471.3,751.026 1472.56,751.254 1473.83,751.481 1475.09,751.706 \n",
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" 1526.95,759.42 1528.22,759.574 1529.48,759.728 1530.75,759.88 1532.01,760.03 1533.28,760.179 1534.54,760.327 1535.81,760.474 1537.07,760.619 1538.34,760.762 \n",
" 1539.6,760.905 1540.87,761.046 1542.13,761.185 1543.39,761.324 1544.66,761.461 1545.92,761.597 1547.19,761.731 1548.45,761.864 1549.72,761.996 1550.98,762.127 \n",
" 1552.25,762.257 1553.51,762.385 1554.78,762.512 1556.04,762.638 1557.31,762.762 1558.57,762.886 1559.84,763.008 1561.1,763.129 1562.37,763.249 1563.63,763.368 \n",
" 1564.9,763.486 1566.16,763.603 1567.43,763.718 1568.69,763.832 1569.96,763.946 1571.22,764.058 1572.49,764.169 1573.75,764.279 1575.02,764.388 1576.28,764.496 \n",
" 1577.54,764.603 1578.81,764.709 1580.07,764.814 1581.34,764.917 1582.6,765.02 1583.87,765.122 1585.13,765.223 1586.4,765.323 1587.66,765.422 1588.93,765.52 \n",
" 1590.19,765.617 1591.46,765.713 1592.72,765.808 1593.99,765.902 1595.25,765.996 1596.52,766.088 1597.78,766.179 1599.05,766.27 1600.31,766.36 1601.58,766.449 \n",
" 1602.84,766.537 1604.11,766.624 1605.37,766.71 1606.64,766.796 1607.9,766.88 1609.17,766.964 1610.43,767.047 1611.7,767.129 1612.96,767.211 1614.22,767.291 \n",
" 1615.49,767.371 1616.75,767.45 1618.02,767.528 1619.28,767.606 1620.55,767.682 1621.81,767.758 1623.08,767.834 1624.34,767.908 1625.61,767.982 1626.87,768.055 \n",
" 1628.14,768.127 1629.4,768.199 1630.67,768.27 1631.93,768.34 1633.2,768.409 1634.46,768.478 1635.73,768.546 1636.99,768.614 1638.26,768.681 1639.52,768.747 \n",
" 1640.79,768.812 1642.05,768.877 1643.32,768.942 1644.58,769.005 1645.85,769.068 1647.11,769.131 1648.37,769.192 1649.64,769.253 1650.9,769.314 1652.17,769.374 \n",
" 1653.43,769.433 1654.7,769.492 1655.96,769.55 1657.23,769.608 1658.49,769.665 1659.76,769.721 1661.02,769.777 1662.29,769.833 1663.55,769.888 1664.82,769.942 \n",
" 1666.08,769.996 1667.35,770.049 1668.61,770.102 1669.88,770.154 1671.14,770.205 1672.41,770.257 1673.67,770.307 1674.94,770.357 1676.2,770.407 1677.47,770.456 \n",
" 1678.73,770.505 1680,770.553 1681.26,770.601 1682.53,770.648 1683.79,770.695 1685.05,770.741 1686.32,770.787 1687.58,770.832 1688.85,770.877 1690.11,770.922 \n",
" 1691.38,770.966 1692.64,771.01 1693.91,771.053 1695.17,771.096 1696.44,771.138 1697.7,771.18 1698.97,771.221 1700.23,771.263 1701.5,771.303 1702.76,771.344 \n",
" 1704.03,771.383 1705.29,771.423 1706.56,771.462 1707.82,771.501 1709.09,771.539 1710.35,771.577 1711.62,771.615 1712.88,771.652 1714.15,771.689 1715.41,771.725 \n",
" 1716.68,771.761 1717.94,771.797 1719.2,771.832 1720.47,771.868 1721.73,771.902 1723,771.937 1724.26,771.971 1725.53,772.004 1726.79,772.038 1728.06,772.071 \n",
" 1729.32,772.103 1730.59,772.136 1731.85,772.168 1733.12,772.199 1734.38,772.231 1735.65,772.262 1736.91,772.293 1738.18,772.323 1739.44,772.353 1740.71,772.383 \n",
" 1741.97,772.413 1743.24,772.442 1744.5,772.471 1745.77,772.5 1747.03,772.528 1748.3,772.557 1749.56,772.584 1750.83,772.612 1752.09,772.639 1753.36,772.666 \n",
" 1754.62,772.693 1755.88,772.72 1757.15,772.746 1758.41,772.772 1759.68,772.798 1760.94,772.823 1762.21,772.848 1763.47,772.873 1764.74,772.898 1766,772.922 \n",
" 1767.27,772.947 1768.53,772.971 1769.8,772.994 1771.06,773.018 1772.33,773.041 1773.59,773.064 1774.86,773.087 1776.12,773.11 1777.39,773.132 1778.65,773.154 \n",
" 1779.92,773.176 1781.18,773.198 1782.45,773.219 1783.71,773.241 1784.98,773.262 1786.24,773.283 1787.51,773.303 1788.77,773.324 1790.03,773.344 1791.3,773.364 \n",
" 1792.56,773.384 1793.83,773.404 1795.09,773.423 1796.36,773.442 1797.62,773.461 1798.89,773.48 1800.15,773.499 1801.42,773.517 1802.68,773.536 1803.95,773.554 \n",
" 1805.21,773.572 1806.48,773.59 1807.74,773.607 1809.01,773.625 1810.27,773.642 1811.54,773.659 1812.8,773.676 1814.07,773.693 1815.33,773.709 1816.6,773.726 \n",
" 1817.86,773.742 1819.13,773.758 1820.39,773.774 1821.66,773.79 1822.92,773.805 1824.19,773.821 1825.45,773.836 1826.71,773.851 1827.98,773.866 1829.24,773.881 \n",
" 1830.51,773.896 1831.77,773.91 1833.04,773.925 1834.3,773.939 1835.57,773.953 1836.83,773.967 1838.1,773.981 1839.36,773.995 1840.63,774.008 1841.89,774.022 \n",
" 1843.16,774.035 1844.42,774.048 1845.69,774.061 1846.95,774.074 1848.22,774.087 1849.48,774.1 1850.75,774.112 1852.01,774.125 1853.28,774.137 1854.54,774.149 \n",
" 1855.81,774.161 1857.07,774.173 1858.34,774.185 1859.6,774.196 1860.86,774.208 1862.13,774.219 1863.39,774.231 1864.66,774.242 1865.92,774.253 1867.19,774.264 \n",
" 1868.45,774.275 1869.72,774.286 1870.98,774.297 1872.25,774.307 1873.51,774.318 1874.78,774.328 1876.04,774.338 1877.31,774.348 1878.57,774.358 1879.84,774.368 \n",
" 1881.1,774.378 1882.37,774.388 1883.63,774.398 1884.9,774.407 1886.16,774.417 1887.43,774.426 1888.69,774.435 1889.96,774.445 1891.22,774.454 1892.49,774.463 \n",
" 1893.75,774.472 1895.02,774.48 1896.28,774.489 1897.54,774.498 1898.81,774.506 1900.07,774.515 1901.34,774.523 1902.6,774.532 1903.87,774.54 1905.13,774.548 \n",
" 1906.4,774.556 1907.66,774.564 1908.93,774.572 1910.19,774.58 1911.46,774.588 1912.72,774.595 1913.99,774.603 1915.25,774.61 1916.52,774.618 1917.78,774.625 \n",
" 1919.05,774.633 1920.31,774.64 1921.58,774.647 1922.84,774.654 1924.11,774.661 1925.37,774.668 1926.64,774.675 1927.9,774.682 1929.17,774.688 1930.43,774.695 \n",
" 1931.69,774.702 1932.96,774.708 1934.22,774.715 1935.49,774.721 1936.75,774.727 1938.02,774.734 1939.28,774.74 1940.55,774.746 1941.81,774.752 1943.08,774.758 \n",
" 1944.34,774.764 1945.61,774.77 1946.87,774.776 1948.14,774.782 1949.4,774.788 1950.67,774.793 1951.93,774.799 1953.2,774.805 1954.46,774.81 1955.73,774.816 \n",
" 1956.99,774.821 1958.26,774.826 1959.52,774.832 1960.79,774.837 1962.05,774.842 1963.32,774.847 1964.58,774.852 1965.85,774.857 1967.11,774.862 1968.37,774.867 \n",
" 1969.64,774.872 1970.9,774.877 1972.17,774.882 1973.43,774.887 1974.7,774.891 1975.96,774.896 1977.23,774.901 1978.49,774.905 1979.76,774.91 1981.02,774.914 \n",
" 1982.29,774.919 1983.55,774.923 1984.82,774.927 1986.08,774.932 1987.35,774.936 1988.61,774.94 1989.88,774.944 1991.14,774.948 1992.41,774.952 1993.67,774.956 \n",
" 1994.94,774.96 1996.2,774.964 1997.47,774.968 1998.73,774.972 2000,774.976 2001.26,774.98 2002.52,774.984 2003.79,774.987 2005.05,774.991 2006.32,774.995 \n",
" 2007.58,774.998 2008.85,775.002 2010.11,775.006 2011.38,775.009 2012.64,775.013 2013.91,775.016 2015.17,775.019 2016.44,775.023 2017.7,775.026 2018.97,775.03 \n",
" 2020.23,775.033 2021.5,775.036 2022.76,775.039 2024.03,775.042 2025.29,775.046 2026.56,775.049 2027.82,775.052 2029.09,775.055 2030.35,775.058 2031.62,775.061 \n",
" 2032.88,775.064 2034.15,775.067 2035.41,775.07 2036.68,775.073 2037.94,775.075 2039.2,775.078 2040.47,775.081 2041.73,775.084 2043,775.087 2044.26,775.089 \n",
" 2045.53,775.092 2046.79,775.095 2048.06,775.097 2049.32,775.1 2050.59,775.102 2051.85,775.105 2053.12,775.108 2054.38,775.11 2055.65,775.113 2056.91,775.115 \n",
" 2058.18,775.117 2059.44,775.12 2060.71,775.122 2061.97,775.125 2063.24,775.127 2064.5,775.129 2065.77,775.132 2067.03,775.134 2068.3,775.136 2069.56,775.138 \n",
" 2070.83,775.14 2072.09,775.143 2073.35,775.145 2074.62,775.147 2075.88,775.149 2077.15,775.151 2078.41,775.153 2079.68,775.155 2080.94,775.157 2082.21,775.159 \n",
" 2083.47,775.161 2084.74,775.163 2086,775.165 2087.27,775.167 2088.53,775.169 2089.8,775.171 2091.06,775.173 2092.33,775.175 2093.59,775.177 2094.86,775.178 \n",
" 2096.12,775.18 2097.39,775.182 2098.65,775.184 2099.92,775.185 2101.18,775.187 2102.45,775.189 2103.71,775.191 2104.98,775.192 2106.24,775.194 2107.51,775.196 \n",
" 2108.77,775.197 2110.03,775.199 2111.3,775.2 2112.56,775.202 2113.83,775.204 2115.09,775.205 2116.36,775.207 2117.62,775.208 2118.89,775.21 2120.15,775.211 \n",
" 2121.42,775.213 2122.68,775.214 2123.95,775.216 2125.21,775.217 2126.48,775.218 2127.74,775.22 2129.01,775.221 2130.27,775.223 2131.54,775.224 2132.8,775.225 \n",
" 2134.07,775.227 2135.33,775.228 2136.6,775.229 2137.86,775.231 2139.13,775.232 2140.39,775.233 2141.66,775.234 2142.92,775.236 2144.18,775.237 2145.45,775.238 \n",
" 2146.71,775.239 2147.98,775.24 2149.24,775.242 2150.51,775.243 2151.77,775.244 2153.04,775.245 2154.3,775.246 2155.57,775.247 2156.83,775.248 2158.1,775.25 \n",
" 2159.36,775.251 2160.63,775.252 2161.89,775.253 2163.16,775.254 2164.42,775.255 2165.69,775.256 2166.95,775.257 2168.22,775.258 2169.48,775.259 2170.75,775.26 \n",
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},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# weighted by works sqrt(w(x)) = exp(-x^2/2)\n",
"f = Fun(x -> sech(x), GaussWeight(Hermite(),1/2),101)\n",
"\n",
"plot(xx, sech.(xx); ylims=(-10,10), label=\"sech x\")\n",
"plot!(xx, f.(xx); label=\"f\")"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
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"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1682.85, 1557.47)\" x=\"1682.85\" y=\"1557.47\">3</text>\n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 2032.35, 1557.47)\" x=\"2032.35\" y=\"1557.47\">6</text>\n",
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"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 101.318, 1328.1)\" x=\"101.318\" y=\"1328.1\">-</text>\n",
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"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 129.428, 1328.1)\" x=\"129.428\" y=\"1328.1\">5.0×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 277.969, 1300.69)\" x=\"277.969\" y=\"1300.69\">30</text>\n",
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"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 101.318, 1056.92)\" x=\"101.318\" y=\"1056.92\">-</text>\n",
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"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 129.428, 1056.92)\" x=\"129.428\" y=\"1056.92\">2.5×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 277.969, 1029.51)\" x=\"277.969\" y=\"1029.51\">30</text>\n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:end;\" transform=\"rotate(0, 321.457, 779.504)\" x=\"321.457\" y=\"779.504\">0</text>\n",
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"</g>\n",
"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 277.969, 487.135)\" x=\"277.969\" y=\"487.135\">30</text>\n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 129.428, 243.359)\" x=\"129.428\" y=\"243.359\">5.0×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip3201)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 277.969, 215.949)\" x=\"277.969\" y=\"215.949\">30</text>\n",
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" 564.473,762.004 565.638,762.004 566.803,762.004 567.968,762.004 569.133,762.004 570.298,762.004 571.463,762.004 572.628,762.004 573.793,762.004 574.958,762.004 \n",
" 576.123,762.004 577.288,762.004 578.453,762.004 579.618,762.004 580.783,762.004 581.948,762.004 583.113,762.004 584.278,762.004 585.443,762.004 586.608,762.004 \n",
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" 611.072,762.003 612.237,762.003 613.402,762.003 614.567,762.003 615.732,762.003 616.897,762.004 618.062,762.004 619.227,762.004 620.392,762.004 621.557,762.004 \n",
" 622.722,762.004 623.887,762.004 625.052,762.004 626.217,762.004 627.382,762.004 628.547,762.004 629.712,762.004 630.877,762.004 632.042,762.004 633.207,762.004 \n",
" 634.372,762.004 635.537,762.004 636.702,762.004 637.867,762.004 639.032,762.004 640.197,762.004 641.362,762.004 642.527,762.004 643.692,762.004 644.857,762.004 \n",
" 646.022,762.003 647.187,762.003 648.352,762.003 649.517,762.003 650.682,762.003 651.847,762.003 653.011,762.003 654.176,762.003 655.341,762.003 656.506,762.003 \n",
" 657.671,762.003 658.836,762.003 660.001,762.003 661.166,762.003 662.331,762.003 663.496,762.003 664.661,762.003 665.826,762.003 666.991,762.003 668.156,762.003 \n",
" 669.321,762.003 670.486,762.003 671.651,762.003 672.816,762.003 673.981,762.004 675.146,762.004 676.311,762.004 677.476,762.004 678.641,762.004 679.806,762.004 \n",
" 680.971,762.004 682.136,762.005 683.301,762.005 684.466,762.005 685.631,762.005 686.796,762.005 687.961,762.005 689.126,762.005 690.291,762.005 691.456,762.005 \n",
" 692.621,762.005 693.786,762.005 694.951,762.005 696.116,762.005 697.281,762.005 698.446,762.004 699.611,762.004 700.776,762.004 701.941,762.003 703.106,762.003 \n",
" 704.271,762.002 705.435,762.002 706.6,762.001 707.765,762.001 708.93,762 710.095,762 711.26,761.999 712.425,761.999 713.59,761.998 714.755,761.998 \n",
" 715.92,761.998 717.085,761.997 718.25,761.997 719.415,761.997 720.58,761.998 721.745,761.998 722.91,761.998 724.075,761.999 725.24,762 726.405,762.001 \n",
" 727.57,762.002 728.735,762.003 729.9,762.005 731.065,762.006 732.23,762.008 733.395,762.01 734.56,762.011 735.725,762.013 736.89,762.015 738.055,762.017 \n",
" 739.22,762.018 740.385,762.02 741.55,762.021 742.715,762.022 743.88,762.023 745.045,762.023 746.21,762.023 747.375,762.023 748.54,762.022 749.705,762.02 \n",
" 750.87,762.019 752.035,762.016 753.2,762.014 754.365,762.01 755.53,762.007 756.695,762.002 757.86,761.998 759.024,761.993 760.189,761.988 761.354,761.982 \n",
" 762.519,761.977 763.684,761.972 764.849,761.967 766.014,761.962 767.179,761.957 768.344,761.953 769.509,761.95 770.674,761.947 771.839,761.946 773.004,761.945 \n",
" 774.169,761.946 775.334,761.948 776.499,761.951 777.664,761.956 778.829,761.962 779.994,761.97 781.159,761.979 782.324,761.989 783.489,762.001 784.654,762.014 \n",
" 785.819,762.028 786.984,762.042 788.149,762.058 789.314,762.073 790.479,762.088 791.644,762.103 792.809,762.117 793.974,762.131 795.139,762.142 796.304,762.152 \n",
" 797.469,762.16 798.634,762.165 799.799,762.167 800.964,762.165 802.129,762.161 803.294,762.152 804.459,762.14 805.624,762.124 806.789,762.103 807.954,762.079 \n",
" 809.119,762.051 810.284,762.02 811.448,761.986 812.613,761.948 813.778,761.909 814.943,761.869 816.108,761.827 817.273,761.786 818.438,761.746 819.603,761.708 \n",
" 820.768,761.672 821.933,761.641 823.098,761.614 824.263,761.594 825.428,761.58 826.593,761.574 827.758,761.576 828.923,761.588 830.088,761.609 831.253,761.64 \n",
" 832.418,761.682 833.583,761.734 834.748,761.796 835.913,761.867 837.078,761.947 838.243,762.035 839.408,762.129 840.573,762.229 841.738,762.332 842.903,762.436 \n",
" 844.068,762.54 845.233,762.641 846.398,762.738 847.563,762.826 848.728,762.904 849.893,762.97 851.058,763.021 852.223,763.055 853.388,763.069 854.553,763.062 \n",
" 855.718,763.033 856.883,762.98 858.048,762.902 859.213,762.799 860.378,762.671 861.543,762.519 862.708,762.345 863.872,762.15 865.037,761.937 866.202,761.709 \n",
" 867.367,761.47 868.532,761.223 869.697,760.973 870.862,760.726 872.027,760.487 873.192,760.262 874.357,760.056 875.522,759.875 876.687,759.724 877.852,759.611 \n",
" 879.017,759.538 880.182,759.512 881.347,759.536 882.512,759.613 883.677,759.745 884.842,759.935 886.007,760.182 887.172,760.484 888.337,760.841 889.502,761.248 \n",
" 890.667,761.7 891.832,762.191 892.997,762.714 894.162,763.259 895.327,763.817 896.492,764.378 897.657,764.928 898.822,765.457 899.987,765.951 901.152,766.398 \n",
" 902.317,766.784 903.482,767.098 904.647,767.328 905.812,767.462 906.977,767.493 908.142,767.41 909.307,767.21 910.472,766.887 911.637,766.441 912.802,765.871 \n",
" 913.967,765.183 915.132,764.381 916.296,763.476 917.461,762.479 918.626,761.405 919.791,760.272 920.956,759.1 922.121,757.91 923.286,756.726 924.451,755.574 \n",
" 925.616,754.481 926.781,753.472 927.946,752.575 929.111,751.815 930.276,751.218 931.441,750.807 932.606,750.603 933.771,750.622 934.936,750.88 936.101,751.385 \n",
" 937.266,752.142 938.431,753.153 939.596,754.411 940.761,755.906 941.926,757.622 943.091,759.535 944.256,761.618 945.421,763.839 946.586,766.158 947.751,768.533 \n",
" 948.916,770.918 950.081,773.263 951.246,775.516 952.411,777.626 953.576,779.538 954.741,781.201 955.906,782.565 957.071,783.583 958.236,784.214 959.401,784.421 \n",
" 960.566,784.176 961.731,783.456 962.896,782.249 964.061,780.551 965.226,778.371 966.391,775.725 967.556,772.642 968.721,769.163 969.885,765.336 971.05,761.223 \n",
" 972.215,756.893 973.38,752.425 974.545,747.905 975.71,743.425 976.875,739.08 978.04,734.969 979.205,731.191 980.37,727.844 981.535,725.021 982.7,722.811 \n",
" 983.865,721.292 985.03,720.534 986.195,720.594 987.36,721.514 988.525,723.322 989.69,726.027 990.855,729.619 992.02,734.071 993.185,739.334 994.35,745.34 \n",
" 995.515,752.004 996.68,759.219 997.845,766.864 999.01,774.799 1000.17,782.875 1001.34,790.93 1002.5,798.794 1003.67,806.292 1004.83,813.251 1006,819.498 \n",
" 1007.16,824.866 1008.33,829.199 1009.49,832.358 1010.66,834.216 1011.82,834.674 1012.99,833.652 1014.15,831.101 1015.32,827 1016.48,821.361 1017.65,814.228 \n",
" 1018.81,805.679 1019.98,795.826 1021.14,784.814 1022.31,772.818 1023.47,760.043 1024.64,746.719 1025.8,733.1 1026.97,719.456 1028.13,706.07 1029.3,693.234 \n",
" 1030.46,681.24 1031.63,670.376 1032.79,660.92 1033.96,653.13 1035.12,647.242 1036.29,643.464 1037.45,641.965 1038.62,642.876 1039.78,646.282 1040.95,652.219 \n",
" 1042.11,660.671 1043.28,671.569 1044.44,684.789 1045.61,700.153 1046.77,717.429 1047.94,736.339 1049.1,756.553 1050.27,777.707 1051.43,799.396 1052.6,821.19 \n",
" 1053.76,842.641 1054.93,863.288 1056.09,882.668 1057.26,900.328 1058.42,915.833 1059.59,928.776 1060.75,938.788 1061.92,945.546 1063.08,948.787 1064.25,948.309 \n",
" 1065.41,943.98 1066.58,935.746 1067.74,923.632 1068.91,907.746 1070.07,888.281 1071.24,865.508 1072.4,839.783 1073.57,811.533 1074.73,781.255 1075.9,749.506 \n",
" 1077.06,716.894 1078.23,684.068 1079.39,651.702 1080.56,620.485 1081.72,591.105 1082.89,564.236 1084.05,540.522 1085.22,520.561 1086.38,504.894 1087.55,493.989 \n",
" 1088.71,488.228 1089.88,487.901 1091.04,493.189 1092.21,504.164 1093.37,520.779 1094.54,542.867 1095.7,570.143 1096.87,602.2 1098.03,638.521 1099.2,678.484 \n",
" 1100.36,721.368 1101.53,766.371 1102.69,812.623 1103.86,859.201 1105.02,905.146 1106.19,949.489 1107.35,991.26 1108.52,1029.52 1109.68,1063.38 1110.85,1092.01 \n",
" 1112.01,1114.66 1113.18,1130.71 1114.34,1139.65 1115.51,1141.09 1116.67,1134.8 1117.84,1120.71 1119,1098.91 1120.17,1069.64 1121.33,1033.33 1122.5,990.538 \n",
" 1123.66,941.999 1124.83,888.573 1125.99,831.246 1127.16,771.111 1128.32,709.348 1129.49,647.197 1130.65,585.937 1131.82,526.86 1132.98,471.24 1134.15,420.308 \n",
" 1135.31,375.225 1136.48,337.057 1137.64,306.746 1138.81,285.091 1139.97,272.726 1141.14,270.104 1142.3,277.483 1143.47,294.917 1144.63,322.25 1145.8,359.112 \n",
" 1146.96,404.931 1148.13,458.932 1149.29,520.153 1150.46,587.464 1151.62,659.584 1152.79,735.108 1153.95,812.535 1155.12,890.293 1156.28,966.78 1157.45,1040.39 \n",
" 1158.61,1109.55 1159.78,1172.75 1160.94,1228.59 1162.11,1275.79 1163.27,1313.24 1164.44,1340.01 1165.6,1355.39 1166.77,1358.89 1167.93,1350.25 1169.1,1329.5 \n",
" 1170.26,1296.87 1171.43,1252.9 1172.59,1198.34 1173.76,1134.17 1174.92,1061.6 1176.09,982.035 1177.25,897.031 1178.42,808.284 1179.58,717.587 1180.75,626.798 \n",
" 1181.91,537.793 1183.08,452.435 1184.24,372.529 1185.41,299.784 1186.57,235.774 1187.74,181.907 1188.9,139.39 1190.07,109.202 1191.23,92.0717 1192.4,88.4582 \n",
" 1193.56,98.5407 1194.73,122.212 1195.89,159.076 1197.06,208.459 1198.22,269.417 1199.39,340.758 1200.55,421.061 1201.72,508.711 1202.88,601.928 1204.05,698.806 \n",
" 1205.21,797.354 1206.38,895.534 1207.54,991.311 1208.71,1082.69 1209.87,1167.77 1211.04,1244.76 1212.2,1312.05 1213.37,1368.24 1214.53,1412.13 1215.7,1442.82 \n",
" 1216.86,1459.64 1218.03,1462.26 1219.19,1450.62 1220.36,1424.97 1221.52,1385.86 1222.69,1334.12 1223.85,1270.84 1225.02,1197.38 1226.18,1115.27 1227.35,1026.27 \n",
" 1228.51,932.235 1229.68,835.15 1230.84,737.047 1232.01,639.972 1233.17,545.944 1234.34,456.901 1235.5,374.671 1236.67,300.921 1237.83,237.13 1239,184.553 \n",
" 1240.16,144.199 1241.33,116.805 1242.49,102.827 1243.66,102.431 1244.82,115.487 1245.99,141.582 1247.15,180.025 1248.32,229.868 1249.48,289.927 1250.65,358.814 \n",
" 1251.81,434.966 1252.98,516.682 1254.14,602.165 1255.31,689.56 1256.47,776.997 1257.64,862.632 1258.8,944.688 1259.96,1021.49 1261.13,1091.52 1262.29,1153.42 \n",
" 1263.46,1206.02 1264.62,1248.41 1265.79,1279.89 1266.95,1300.03 1268.12,1308.65 1269.28,1305.82 1270.45,1291.89 1271.61,1267.42 1272.78,1233.2 1273.94,1190.21 \n",
" 1275.11,1139.63 1276.27,1082.76 1277.44,1020.99 1278.6,955.826 1279.77,888.775 1280.93,821.36 1282.1,755.067 1283.26,691.31 1284.43,631.405 1285.59,576.537 \n",
" 1286.76,527.736 1287.92,485.858 1289.09,451.568 1290.25,425.33 1291.42,407.4 1292.58,397.83 1293.75,396.467 1294.91,402.969 1296.08,416.814 1297.24,437.323 \n",
" 1298.41,463.68 1299.57,494.96 1300.74,530.152 1301.9,568.193 1303.07,607.993 1304.23,648.469 1305.4,688.571 1306.56,727.307 1307.73,763.774 1308.89,797.175 \n",
" 1310.06,826.835 1311.22,852.224 1312.39,872.957 1313.55,888.807 1314.72,899.702 1315.88,905.725 1317.05,907.102 1318.21,904.195 1319.38,897.482 1320.54,887.542 \n",
" 1321.71,875.032 1322.87,860.667 1324.04,845.189 1325.2,829.351 1326.37,813.885 1327.53,799.48 1328.7,786.763 1329.86,776.275 1331.03,768.457 1332.19,763.634 \n",
" 1333.36,762.004 1334.52,763.634 1335.69,768.457 1336.85,776.275 1338.02,786.763 1339.18,799.48 1340.35,813.885 1341.51,829.351 1342.68,845.189 1343.84,860.667 \n",
" 1345.01,875.032 1346.17,887.542 1347.34,897.482 1348.5,904.195 1349.67,907.102 1350.83,905.725 1352,899.702 1353.16,888.807 1354.33,872.957 1355.49,852.224 \n",
" 1356.66,826.835 1357.82,797.175 1358.99,763.774 1360.15,727.307 1361.32,688.571 1362.48,648.469 1363.65,607.993 1364.81,568.193 1365.98,530.152 1367.14,494.96 \n",
" 1368.31,463.68 1369.47,437.323 1370.64,416.814 1371.8,402.969 1372.97,396.467 1374.13,397.83 1375.3,407.4 1376.46,425.33 1377.63,451.568 1378.79,485.858 \n",
" 1379.96,527.736 1381.12,576.537 1382.29,631.405 1383.45,691.31 1384.62,755.067 1385.78,821.36 1386.95,888.775 1388.11,955.826 1389.28,1020.99 1390.44,1082.76 \n",
" 1391.61,1139.63 1392.77,1190.21 1393.94,1233.2 1395.1,1267.42 1396.27,1291.89 1397.43,1305.82 1398.6,1308.65 1399.76,1300.03 1400.93,1279.89 1402.09,1248.41 \n",
" 1403.26,1206.02 1404.42,1153.42 1405.59,1091.52 1406.75,1021.49 1407.92,944.688 1409.08,862.632 1410.25,776.997 1411.41,689.56 1412.58,602.165 1413.74,516.682 \n",
" 1414.91,434.966 1416.07,358.814 1417.24,289.927 1418.4,229.868 1419.57,180.025 1420.73,141.582 1421.9,115.487 1423.06,102.431 1424.23,102.827 1425.39,116.805 \n",
" 1426.56,144.199 1427.72,184.553 1428.89,237.13 1430.05,300.921 1431.22,374.671 1432.38,456.901 1433.55,545.944 1434.71,639.972 1435.88,737.047 1437.04,835.15 \n",
" 1438.21,932.235 1439.37,1026.27 1440.54,1115.27 1441.7,1197.38 1442.87,1270.84 1444.03,1334.12 1445.2,1385.86 1446.36,1424.97 1447.53,1450.62 1448.69,1462.26 \n",
" 1449.86,1459.64 1451.02,1442.82 1452.19,1412.13 1453.35,1368.24 1454.52,1312.05 1455.68,1244.76 1456.85,1167.77 1458.01,1082.69 1459.18,991.311 1460.34,895.534 \n",
" 1461.51,797.354 1462.67,698.806 1463.84,601.928 1465,508.711 1466.17,421.061 1467.33,340.758 1468.5,269.417 1469.66,208.459 1470.83,159.076 1471.99,122.212 \n",
" 1473.16,98.5407 1474.32,88.4582 1475.49,92.0717 1476.65,109.202 1477.82,139.39 1478.98,181.907 1480.15,235.774 1481.31,299.784 1482.48,372.529 1483.64,452.435 \n",
" 1484.81,537.793 1485.97,626.798 1487.14,717.587 1488.3,808.284 1489.47,897.031 1490.63,982.035 1491.8,1061.6 1492.96,1134.17 1494.13,1198.34 1495.29,1252.9 \n",
" 1496.46,1296.87 1497.62,1329.5 1498.79,1350.25 1499.95,1358.89 1501.12,1355.39 1502.28,1340.01 1503.45,1313.24 1504.61,1275.79 1505.78,1228.59 1506.94,1172.75 \n",
" 1508.11,1109.55 1509.27,1040.39 1510.44,966.78 1511.6,890.293 1512.77,812.535 1513.93,735.108 1515.1,659.584 1516.26,587.464 1517.43,520.153 1518.59,458.932 \n",
" 1519.76,404.931 1520.92,359.112 1522.09,322.25 1523.25,294.917 1524.41,277.483 1525.58,270.104 1526.74,272.726 1527.91,285.091 1529.07,306.746 1530.24,337.057 \n",
" 1531.4,375.225 1532.57,420.308 1533.73,471.24 1534.9,526.86 1536.06,585.937 1537.23,647.197 1538.39,709.348 1539.56,771.111 1540.72,831.246 1541.89,888.573 \n",
" 1543.05,941.999 1544.22,990.538 1545.38,1033.33 1546.55,1069.64 1547.71,1098.91 1548.88,1120.71 1550.04,1134.8 1551.21,1141.09 1552.37,1139.65 1553.54,1130.71 \n",
" 1554.7,1114.66 1555.87,1092.01 1557.03,1063.38 1558.2,1029.52 1559.36,991.26 1560.53,949.489 1561.69,905.146 1562.86,859.201 1564.02,812.623 1565.19,766.371 \n",
" 1566.35,721.368 1567.52,678.484 1568.68,638.521 1569.85,602.2 1571.01,570.143 1572.18,542.867 1573.34,520.779 1574.51,504.164 1575.67,493.189 1576.84,487.901 \n",
" 1578,488.228 1579.17,493.989 1580.33,504.894 1581.5,520.561 1582.66,540.522 1583.83,564.236 1584.99,591.105 1586.16,620.485 1587.32,651.702 1588.49,684.068 \n",
" 1589.65,716.894 1590.82,749.506 1591.98,781.255 1593.15,811.533 1594.31,839.783 1595.48,865.508 1596.64,888.281 1597.81,907.746 1598.97,923.632 1600.14,935.746 \n",
" 1601.3,943.98 1602.47,948.309 1603.63,948.787 1604.8,945.546 1605.96,938.788 1607.13,928.776 1608.29,915.833 1609.46,900.328 1610.62,882.668 1611.79,863.288 \n",
" 1612.95,842.641 1614.12,821.19 1615.28,799.396 1616.45,777.707 1617.61,756.553 1618.78,736.339 1619.94,717.429 1621.11,700.153 1622.27,684.789 1623.44,671.569 \n",
" 1624.6,660.671 1625.77,652.219 1626.93,646.282 1628.1,642.876 1629.26,641.965 1630.43,643.464 1631.59,647.242 1632.76,653.13 1633.92,660.92 1635.09,670.376 \n",
" 1636.25,681.24 1637.42,693.234 1638.58,706.07 1639.75,719.456 1640.91,733.1 1642.08,746.719 1643.24,760.043 1644.41,772.818 1645.57,784.814 1646.74,795.826 \n",
" 1647.9,805.679 1649.07,814.228 1650.23,821.361 1651.4,827 1652.56,831.101 1653.73,833.652 1654.89,834.674 1656.06,834.216 1657.22,832.358 1658.39,829.199 \n",
" 1659.55,824.866 1660.72,819.498 1661.88,813.251 1663.05,806.292 1664.21,798.794 1665.38,790.93 1666.54,782.875 1667.71,774.799 1668.87,766.864 1670.04,759.219 \n",
" 1671.2,752.004 1672.37,745.34 1673.53,739.334 1674.7,734.071 1675.86,729.619 1677.03,726.027 1678.19,723.322 1679.36,721.514 1680.52,720.594 1681.69,720.534 \n",
" 1682.85,721.292 1684.02,722.811 1685.18,725.021 1686.35,727.844 1687.51,731.191 1688.68,734.969 1689.84,739.08 1691.01,743.425 1692.17,747.905 1693.34,752.425 \n",
" 1694.5,756.893 1695.67,761.223 1696.83,765.336 1698,769.163 1699.16,772.642 1700.33,775.725 1701.49,778.371 1702.66,780.551 1703.82,782.249 1704.99,783.456 \n",
" 1706.15,784.176 1707.32,784.421 1708.48,784.214 1709.65,783.583 1710.81,782.565 1711.98,781.201 1713.14,779.538 1714.31,777.626 1715.47,775.516 1716.64,773.263 \n",
" 1717.8,770.918 1718.97,768.533 1720.13,766.158 1721.3,763.839 1722.46,761.618 1723.63,759.535 1724.79,757.622 1725.96,755.906 1727.12,754.411 1728.29,753.153 \n",
" 1729.45,752.142 1730.62,751.385 1731.78,750.88 1732.95,750.622 1734.11,750.603 1735.28,750.807 1736.44,751.218 1737.61,751.815 1738.77,752.575 1739.94,753.472 \n",
" 1741.1,754.481 1742.27,755.574 1743.43,756.726 1744.6,757.91 1745.76,759.1 1746.93,760.272 1748.09,761.405 1749.26,762.479 1750.42,763.476 1751.59,764.381 \n",
" 1752.75,765.183 1753.92,765.871 1755.08,766.441 1756.25,766.887 1757.41,767.21 1758.58,767.41 1759.74,767.493 1760.91,767.462 1762.07,767.328 1763.24,767.098 \n",
" 1764.4,766.784 1765.57,766.398 1766.73,765.951 1767.9,765.457 1769.06,764.928 1770.23,764.378 1771.39,763.817 1772.56,763.259 1773.72,762.714 1774.89,762.191 \n",
" 1776.05,761.7 1777.22,761.248 1778.38,760.841 1779.55,760.484 1780.71,760.182 1781.88,759.935 1783.04,759.745 1784.21,759.613 1785.37,759.536 1786.53,759.512 \n",
" 1787.7,759.538 1788.86,759.611 1790.03,759.724 1791.19,759.875 1792.36,760.056 1793.52,760.262 1794.69,760.487 1795.85,760.726 1797.02,760.973 1798.18,761.223 \n",
" 1799.35,761.47 1800.51,761.709 1801.68,761.937 1802.84,762.15 1804.01,762.345 1805.17,762.519 1806.34,762.671 1807.5,762.799 1808.67,762.902 1809.83,762.98 \n",
" 1811,763.033 1812.16,763.062 1813.33,763.069 1814.49,763.055 1815.66,763.021 1816.82,762.97 1817.99,762.904 1819.15,762.826 1820.32,762.738 1821.48,762.641 \n",
" 1822.65,762.54 1823.81,762.436 1824.98,762.332 1826.14,762.229 1827.31,762.129 1828.47,762.035 1829.64,761.947 1830.8,761.867 1831.97,761.796 1833.13,761.734 \n",
" 1834.3,761.682 1835.46,761.64 1836.63,761.609 1837.79,761.588 1838.96,761.576 1840.12,761.574 1841.29,761.58 1842.45,761.594 1843.62,761.614 1844.78,761.641 \n",
" 1845.95,761.672 1847.11,761.708 1848.28,761.746 1849.44,761.786 1850.61,761.827 1851.77,761.869 1852.94,761.909 1854.1,761.948 1855.27,761.986 1856.43,762.02 \n",
" 1857.6,762.051 1858.76,762.079 1859.93,762.103 1861.09,762.124 1862.26,762.14 1863.42,762.152 1864.59,762.161 1865.75,762.165 1866.92,762.167 1868.08,762.165 \n",
" 1869.25,762.16 1870.41,762.152 1871.58,762.142 1872.74,762.131 1873.91,762.117 1875.07,762.103 1876.24,762.088 1877.4,762.073 1878.57,762.058 1879.73,762.042 \n",
" 1880.9,762.028 1882.06,762.014 1883.23,762.001 1884.39,761.989 1885.56,761.979 1886.72,761.97 1887.89,761.962 1889.05,761.956 1890.22,761.951 1891.38,761.948 \n",
" 1892.55,761.946 1893.71,761.945 1894.88,761.946 1896.04,761.947 1897.21,761.95 1898.37,761.953 1899.54,761.957 1900.7,761.962 1901.87,761.967 1903.03,761.972 \n",
" 1904.2,761.977 1905.36,761.982 1906.53,761.988 1907.69,761.993 1908.86,761.998 1910.02,762.002 1911.19,762.007 1912.35,762.01 1913.52,762.014 1914.68,762.016 \n",
" 1915.85,762.019 1917.01,762.02 1918.18,762.022 1919.34,762.023 1920.51,762.023 1921.67,762.023 1922.84,762.023 1924,762.022 1925.17,762.021 1926.33,762.02 \n",
" 1927.5,762.018 1928.66,762.017 1929.83,762.015 1930.99,762.013 1932.16,762.011 1933.32,762.01 1934.49,762.008 1935.65,762.006 1936.82,762.005 1937.98,762.003 \n",
" 1939.15,762.002 1940.31,762.001 1941.48,762 1942.64,761.999 1943.81,761.998 1944.97,761.998 1946.14,761.998 1947.3,761.997 1948.47,761.997 1949.63,761.997 \n",
" 1950.8,761.998 1951.96,761.998 1953.13,761.998 1954.29,761.999 1955.46,761.999 1956.62,762 1957.79,762 1958.95,762.001 1960.12,762.001 1961.28,762.002 \n",
" 1962.45,762.002 1963.61,762.003 1964.78,762.003 1965.94,762.004 1967.11,762.004 1968.27,762.004 1969.44,762.005 1970.6,762.005 1971.77,762.005 1972.93,762.005 \n",
" 1974.1,762.005 1975.26,762.005 1976.43,762.005 1977.59,762.005 1978.76,762.005 1979.92,762.005 1981.09,762.005 1982.25,762.005 1983.42,762.005 1984.58,762.005 \n",
" 1985.75,762.004 1986.91,762.004 1988.08,762.004 1989.24,762.004 1990.41,762.004 1991.57,762.004 1992.74,762.004 1993.9,762.003 1995.07,762.003 1996.23,762.003 \n",
" 1997.4,762.003 1998.56,762.003 1999.73,762.003 2000.89,762.003 2002.06,762.003 2003.22,762.003 2004.39,762.003 2005.55,762.003 2006.72,762.003 2007.88,762.003 \n",
" 2009.05,762.003 2010.21,762.003 2011.38,762.003 2012.54,762.003 2013.71,762.003 2014.87,762.003 2016.04,762.003 2017.2,762.003 2018.37,762.003 2019.53,762.003 \n",
" 2020.7,762.003 2021.86,762.004 2023.03,762.004 2024.19,762.004 2025.36,762.004 2026.52,762.004 2027.69,762.004 2028.85,762.004 2030.02,762.004 2031.18,762.004 \n",
" 2032.35,762.004 2033.51,762.004 2034.68,762.004 2035.84,762.004 2037.01,762.004 2038.17,762.004 2039.34,762.004 2040.5,762.004 2041.67,762.004 2042.83,762.004 \n",
" 2044,762.004 2045.16,762.004 2046.33,762.004 2047.49,762.004 2048.66,762.004 2049.82,762.004 2050.98,762.003 2052.15,762.003 2053.31,762.003 2054.48,762.003 \n",
" 2055.64,762.003 2056.81,762.003 2057.97,762.003 2059.14,762.003 2060.3,762.003 2061.47,762.003 2062.63,762.003 2063.8,762.003 2064.96,762.003 2066.13,762.003 \n",
" 2067.29,762.003 2068.46,762.003 2069.62,762.003 2070.79,762.003 2071.95,762.003 2073.12,762.003 2074.28,762.003 2075.45,762.004 2076.61,762.004 2077.78,762.004 \n",
" 2078.94,762.004 2080.11,762.004 2081.27,762.004 2082.44,762.004 2083.6,762.004 2084.77,762.004 2085.93,762.004 2087.1,762.004 2088.26,762.004 2089.43,762.004 \n",
" 2090.59,762.004 2091.76,762.004 2092.92,762.004 2094.09,762.004 2095.25,762.004 2096.42,762.004 2097.58,762.004 2098.75,762.004 2099.91,762.004 2101.08,762.004 \n",
" 2102.24,762.004 2103.41,762.004 2104.57,762.004 2105.74,762.004 2106.9,762.004 2108.07,762.004 2109.23,762.004 2110.4,762.004 2111.56,762.004 2112.73,762.004 \n",
" 2113.89,762.004 2115.06,762.004 2116.22,762.004 2117.39,762.004 2118.55,762.004 2119.72,762.004 2120.88,762.004 2122.05,762.004 2123.21,762.004 2124.38,762.004 \n",
" 2125.54,762.004 2126.71,762.004 2127.87,762.004 2129.04,762.004 2130.2,762.004 2131.37,762.004 2132.53,762.004 2133.7,762.004 2134.86,762.004 2136.03,762.004 \n",
" 2137.19,762.004 2138.36,762.004 2139.52,762.004 2140.69,762.004 2141.85,762.004 2143.02,762.004 2144.18,762.004 2145.35,762.004 2146.51,762.004 2147.68,762.004 \n",
" 2148.84,762.004 2150.01,762.004 2151.17,762.004 2152.34,762.004 2153.5,762.004 2154.67,762.004 2155.83,762.004 2157,762.004 2158.16,762.004 2159.33,762.004 \n",
" 2160.49,762.004 2161.66,762.004 2162.82,762.004 2163.99,762.004 2165.15,762.004 2166.32,762.004 2167.48,762.004 2168.65,762.004 2169.81,762.004 2170.98,762.004 \n",
" 2172.14,762.004 2173.31,762.004 2174.47,762.004 2175.64,762.004 2176.8,762.004 2177.97,762.004 2179.13,762.004 2180.3,762.004 2181.46,762.004 2182.63,762.004 \n",
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],
"source": [
"# weighted by w(x) = exp(-x^2) breaks again\n",
"f = Fun(x -> sech(x), GaussWeight(Hermite()),101)\n",
"\n",
"plot(xx, sech.(xx); ylims=(-10,10), label=\"sech x\")\n",
"plot(xx, f.(xx); label=\"f\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that correctly weighted Hermite, that is, with $\\sqrt{w(x)} = \\E^{-x^2/2}$ look \"nice\":"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
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" 700.004,845.183 701.253,845.183 702.502,845.183 703.751,845.183 705,845.183 706.249,845.183 707.498,845.183 708.747,845.183 709.996,845.183 711.245,845.183 \n",
" 712.494,845.182 713.743,845.182 714.992,845.182 716.241,845.182 717.49,845.182 718.739,845.182 719.989,845.182 721.238,845.182 722.487,845.182 723.736,845.182 \n",
" 724.985,845.182 726.234,845.182 727.483,845.182 728.732,845.182 729.981,845.182 731.23,845.182 732.479,845.182 733.728,845.182 734.977,845.182 736.226,845.182 \n",
" 737.475,845.182 738.724,845.182 739.973,845.182 741.222,845.182 742.471,845.182 743.72,845.182 744.969,845.182 746.218,845.182 747.467,845.182 748.716,845.182 \n",
" 749.966,845.182 751.215,845.182 752.464,845.182 753.713,845.182 754.962,845.182 756.211,845.181 757.46,845.181 758.709,845.181 759.958,845.181 761.207,845.181 \n",
" 762.456,845.181 763.705,845.181 764.954,845.181 766.203,845.181 767.452,845.181 768.701,845.181 769.95,845.181 771.199,845.181 772.448,845.181 773.697,845.181 \n",
" 774.946,845.18 776.195,845.18 777.444,845.18 778.693,845.18 779.943,845.18 781.192,845.18 782.441,845.18 783.69,845.18 784.939,845.18 786.188,845.179 \n",
" 787.437,845.179 788.686,845.179 789.935,845.179 791.184,845.179 792.433,845.179 793.682,845.179 794.931,845.178 796.18,845.178 797.429,845.178 798.678,845.178 \n",
" 799.927,845.178 801.176,845.178 802.425,845.177 803.674,845.177 804.923,845.177 806.172,845.177 807.421,845.176 808.67,845.176 809.92,845.176 811.169,845.176 \n",
" 812.418,845.175 813.667,845.175 814.916,845.175 816.165,845.175 817.414,845.174 818.663,845.174 819.912,845.174 821.161,845.173 822.41,845.173 823.659,845.173 \n",
" 824.908,845.172 826.157,845.172 827.406,845.172 828.655,845.171 829.904,845.171 831.153,845.17 832.402,845.17 833.651,845.169 834.9,845.169 836.149,845.169 \n",
" 837.398,845.168 838.647,845.168 839.897,845.167 841.146,845.166 842.395,845.166 843.644,845.165 844.893,845.165 846.142,845.164 847.391,845.163 848.64,845.163 \n",
" 849.889,845.162 851.138,845.161 852.387,845.161 853.636,845.16 854.885,845.159 856.134,845.158 857.383,845.158 858.632,845.157 859.881,845.156 861.13,845.155 \n",
" 862.379,845.154 863.628,845.153 864.877,845.152 866.126,845.151 867.375,845.15 868.624,845.149 869.874,845.148 871.123,845.147 872.372,845.146 873.621,845.145 \n",
" 874.87,845.144 876.119,845.142 877.368,845.141 878.617,845.14 879.866,845.138 881.115,845.137 882.364,845.136 883.613,845.134 884.862,845.133 886.111,845.131 \n",
" 887.36,845.13 888.609,845.128 889.858,845.126 891.107,845.125 892.356,845.123 893.605,845.121 894.854,845.119 896.103,845.117 897.352,845.115 898.601,845.113 \n",
" 899.851,845.111 901.1,845.109 902.349,845.107 903.598,845.105 904.847,845.103 906.096,845.1 907.345,845.098 908.594,845.096 909.843,845.093 911.092,845.091 \n",
" 912.341,845.088 913.59,845.085 914.839,845.082 916.088,845.08 917.337,845.077 918.586,845.074 919.835,845.071 921.084,845.068 922.333,845.064 923.582,845.061 \n",
" 924.831,845.058 926.08,845.054 927.329,845.051 928.578,845.047 929.828,845.044 931.077,845.04 932.326,845.036 933.575,845.032 934.824,845.028 936.073,845.024 \n",
" 937.322,845.02 938.571,845.016 939.82,845.011 941.069,845.007 942.318,845.002 943.567,844.998 944.816,844.993 946.065,844.988 947.314,844.983 948.563,844.978 \n",
" 949.812,844.973 951.061,844.967 952.31,844.962 953.559,844.956 954.808,844.951 956.057,844.945 957.306,844.939 958.555,844.933 959.805,844.927 961.054,844.921 \n",
" 962.303,844.914 963.552,844.908 964.801,844.901 966.05,844.894 967.299,844.887 968.548,844.88 969.797,844.873 971.046,844.866 972.295,844.858 973.544,844.851 \n",
" 974.793,844.843 976.042,844.835 977.291,844.827 978.54,844.819 979.789,844.811 981.038,844.802 982.287,844.794 983.536,844.785 984.785,844.776 986.034,844.767 \n",
" 987.283,844.757 988.532,844.748 989.781,844.738 991.031,844.729 992.28,844.719 993.529,844.709 994.778,844.698 996.027,844.688 997.276,844.677 998.525,844.666 \n",
" 999.774,844.655 1001.02,844.644 1002.27,844.633 1003.52,844.621 1004.77,844.61 1006.02,844.598 1007.27,844.586 1008.52,844.573 1009.77,844.561 1011.02,844.548 \n",
" 1012.26,844.535 1013.51,844.522 1014.76,844.509 1016.01,844.496 1017.26,844.482 1018.51,844.468 1019.76,844.454 1021.01,844.44 1022.26,844.426 1023.51,844.411 \n",
" 1024.75,844.396 1026,844.381 1027.25,844.366 1028.5,844.35 1029.75,844.335 1031,844.319 1032.25,844.303 1033.5,844.286 1034.75,844.27 1036,844.253 \n",
" 1037.25,844.236 1038.49,844.219 1039.74,844.202 1040.99,844.184 1042.24,844.166 1043.49,844.148 1044.74,844.13 1045.99,844.112 1047.24,844.093 1048.49,844.074 \n",
" 1049.74,844.055 1050.98,844.036 1052.23,844.016 1053.48,843.997 1054.73,843.977 1055.98,843.957 1057.23,843.936 1058.48,843.916 1059.73,843.895 1060.98,843.874 \n",
" 1062.23,843.853 1063.47,843.831 1064.72,843.81 1065.97,843.788 1067.22,843.766 1068.47,843.744 1069.72,843.721 1070.97,843.699 1072.22,843.676 1073.47,843.653 \n",
" 1074.72,843.63 1075.97,843.606 1077.21,843.583 1078.46,843.559 1079.71,843.535 1080.96,843.511 1082.21,843.487 1083.46,843.462 1084.71,843.437 1085.96,843.413 \n",
" 1087.21,843.387 1088.46,843.362 1089.7,843.337 1090.95,843.311 1092.2,843.286 1093.45,843.26 1094.7,843.234 1095.95,843.207 1097.2,843.181 1098.45,843.155 \n",
" 1099.7,843.128 1100.95,843.101 1102.2,843.074 1103.44,843.047 1104.69,843.02 1105.94,842.993 1107.19,842.965 1108.44,842.938 1109.69,842.91 1110.94,842.882 \n",
" 1112.19,842.854 1113.44,842.826 1114.69,842.798 1115.93,842.77 1117.18,842.742 1118.43,842.713 1119.68,842.685 1120.93,842.657 1122.18,842.628 1123.43,842.599 \n",
" 1124.68,842.571 1125.93,842.542 1127.18,842.513 1128.43,842.484 1129.67,842.455 1130.92,842.426 1132.17,842.397 1133.42,842.368 1134.67,842.339 1135.92,842.31 \n",
" 1137.17,842.281 1138.42,842.252 1139.67,842.223 1140.92,842.194 1142.16,842.165 1143.41,842.136 1144.66,842.108 1145.91,842.079 1147.16,842.05 1148.41,842.021 \n",
" 1149.66,841.992 1150.91,841.964 1152.16,841.935 1153.41,841.906 1154.65,841.878 1155.9,841.85 1157.15,841.821 1158.4,841.793 1159.65,841.765 1160.9,841.737 \n",
" 1162.15,841.709 1163.4,841.681 1164.65,841.654 1165.9,841.626 1167.15,841.599 1168.39,841.572 1169.64,841.545 1170.89,841.518 1172.14,841.491 1173.39,841.465 \n",
" 1174.64,841.439 1175.89,841.413 1177.14,841.387 1178.39,841.361 1179.64,841.335 1180.88,841.31 1182.13,841.285 1183.38,841.26 1184.63,841.236 1185.88,841.211 \n",
" 1187.13,841.187 1188.38,841.163 1189.63,841.14 1190.88,841.116 1192.13,841.093 1193.38,841.071 1194.62,841.048 1195.87,841.026 1197.12,841.004 1198.37,840.983 \n",
" 1199.62,840.961 1200.87,840.94 1202.12,840.92 1203.37,840.899 1204.62,840.879 1205.87,840.86 1207.11,840.841 1208.36,840.822 1209.61,840.803 1210.86,840.785 \n",
" 1212.11,840.767 1213.36,840.75 1214.61,840.732 1215.86,840.716 1217.11,840.699 1218.36,840.683 1219.61,840.668 1220.85,840.653 1222.1,840.638 1223.35,840.624 \n",
" 1224.6,840.61 1225.85,840.596 1227.1,840.583 1228.35,840.57 1229.6,840.558 1230.85,840.546 1232.1,840.535 1233.34,840.524 1234.59,840.514 1235.84,840.504 \n",
" 1237.09,840.494 1238.34,840.485 1239.59,840.476 1240.84,840.468 1242.09,840.46 1243.34,840.453 1244.59,840.446 1245.84,840.439 1247.08,840.434 1248.33,840.428 \n",
" 1249.58,840.423 1250.83,840.419 1252.08,840.414 1253.33,840.411 1254.58,840.408 1255.83,840.405 1257.08,840.403 1258.33,840.401 1259.57,840.4 1260.82,840.399 \n",
" 1262.07,840.399 1263.32,840.399 1264.57,840.4 1265.82,840.401 1267.07,840.403 1268.32,840.405 1269.57,840.408 1270.82,840.411 1272.06,840.414 1273.31,840.419 \n",
" 1274.56,840.423 1275.81,840.428 1277.06,840.434 1278.31,840.439 1279.56,840.446 1280.81,840.453 1282.06,840.46 1283.31,840.468 1284.56,840.476 1285.8,840.485 \n",
" 1287.05,840.494 1288.3,840.504 1289.55,840.514 1290.8,840.524 1292.05,840.535 1293.3,840.546 1294.55,840.558 1295.8,840.57 1297.05,840.583 1298.29,840.596 \n",
" 1299.54,840.61 1300.79,840.624 1302.04,840.638 1303.29,840.653 1304.54,840.668 1305.79,840.683 1307.04,840.699 1308.29,840.716 1309.54,840.732 1310.79,840.75 \n",
" 1312.03,840.767 1313.28,840.785 1314.53,840.803 1315.78,840.822 1317.03,840.841 1318.28,840.86 1319.53,840.879 1320.78,840.899 1322.03,840.92 1323.28,840.94 \n",
" 1324.52,840.961 1325.77,840.983 1327.02,841.004 1328.27,841.026 1329.52,841.048 1330.77,841.071 1332.02,841.093 1333.27,841.116 1334.52,841.14 1335.77,841.163 \n",
" 1337.02,841.187 1338.26,841.211 1339.51,841.236 1340.76,841.26 1342.01,841.285 1343.26,841.31 1344.51,841.335 1345.76,841.361 1347.01,841.387 1348.26,841.413 \n",
" 1349.51,841.439 1350.75,841.465 1352,841.491 1353.25,841.518 1354.5,841.545 1355.75,841.572 1357,841.599 1358.25,841.626 1359.5,841.654 1360.75,841.681 \n",
" 1362,841.709 1363.24,841.737 1364.49,841.765 1365.74,841.793 1366.99,841.821 1368.24,841.85 1369.49,841.878 1370.74,841.906 1371.99,841.935 1373.24,841.964 \n",
" 1374.49,841.992 1375.74,842.021 1376.98,842.05 1378.23,842.079 1379.48,842.108 1380.73,842.136 1381.98,842.165 1383.23,842.194 1384.48,842.223 1385.73,842.252 \n",
" 1386.98,842.281 1388.23,842.31 1389.47,842.339 1390.72,842.368 1391.97,842.397 1393.22,842.426 1394.47,842.455 1395.72,842.484 1396.97,842.513 1398.22,842.542 \n",
" 1399.47,842.571 1400.72,842.599 1401.97,842.628 1403.21,842.657 1404.46,842.685 1405.71,842.713 1406.96,842.742 1408.21,842.77 1409.46,842.798 1410.71,842.826 \n",
" 1411.96,842.854 1413.21,842.882 1414.46,842.91 1415.7,842.938 1416.95,842.965 1418.2,842.993 1419.45,843.02 1420.7,843.047 1421.95,843.074 1423.2,843.101 \n",
" 1424.45,843.128 1425.7,843.155 1426.95,843.181 1428.2,843.207 1429.44,843.234 1430.69,843.26 1431.94,843.286 1433.19,843.311 1434.44,843.337 1435.69,843.362 \n",
" 1436.94,843.387 1438.19,843.413 1439.44,843.437 1440.69,843.462 1441.93,843.487 1443.18,843.511 1444.43,843.535 1445.68,843.559 1446.93,843.583 1448.18,843.606 \n",
" 1449.43,843.63 1450.68,843.653 1451.93,843.676 1453.18,843.699 1454.42,843.721 1455.67,843.744 1456.92,843.766 1458.17,843.788 1459.42,843.81 1460.67,843.831 \n",
" 1461.92,843.853 1463.17,843.874 1464.42,843.895 1465.67,843.916 1466.92,843.936 1468.16,843.957 1469.41,843.977 1470.66,843.997 1471.91,844.016 1473.16,844.036 \n",
" 1474.41,844.055 1475.66,844.074 1476.91,844.093 1478.16,844.112 1479.41,844.13 1480.65,844.148 1481.9,844.166 1483.15,844.184 1484.4,844.202 1485.65,844.219 \n",
" 1486.9,844.236 1488.15,844.253 1489.4,844.27 1490.65,844.286 1491.9,844.303 1493.15,844.319 1494.39,844.335 1495.64,844.35 1496.89,844.366 1498.14,844.381 \n",
" 1499.39,844.396 1500.64,844.411 1501.89,844.426 1503.14,844.44 1504.39,844.454 1505.64,844.468 1506.88,844.482 1508.13,844.496 1509.38,844.509 1510.63,844.522 \n",
" 1511.88,844.535 1513.13,844.548 1514.38,844.561 1515.63,844.573 1516.88,844.586 1518.13,844.598 1519.38,844.61 1520.62,844.621 1521.87,844.633 1523.12,844.644 \n",
" 1524.37,844.655 1525.62,844.666 1526.87,844.677 1528.12,844.688 1529.37,844.698 1530.62,844.709 1531.87,844.719 1533.11,844.729 1534.36,844.738 1535.61,844.748 \n",
" 1536.86,844.757 1538.11,844.767 1539.36,844.776 1540.61,844.785 1541.86,844.794 1543.11,844.802 1544.36,844.811 1545.61,844.819 1546.85,844.827 1548.1,844.835 \n",
" 1549.35,844.843 1550.6,844.851 1551.85,844.858 1553.1,844.866 1554.35,844.873 1555.6,844.88 1556.85,844.887 1558.1,844.894 1559.34,844.901 1560.59,844.908 \n",
" 1561.84,844.914 1563.09,844.921 1564.34,844.927 1565.59,844.933 1566.84,844.939 1568.09,844.945 1569.34,844.951 1570.59,844.956 1571.83,844.962 1573.08,844.967 \n",
" 1574.33,844.973 1575.58,844.978 1576.83,844.983 1578.08,844.988 1579.33,844.993 1580.58,844.998 1581.83,845.002 1583.08,845.007 1584.33,845.011 1585.57,845.016 \n",
" 1586.82,845.02 1588.07,845.024 1589.32,845.028 1590.57,845.032 1591.82,845.036 1593.07,845.04 1594.32,845.044 1595.57,845.047 1596.82,845.051 1598.06,845.054 \n",
" 1599.31,845.058 1600.56,845.061 1601.81,845.064 1603.06,845.068 1604.31,845.071 1605.56,845.074 1606.81,845.077 1608.06,845.08 1609.31,845.082 1610.56,845.085 \n",
" 1611.8,845.088 1613.05,845.091 1614.3,845.093 1615.55,845.096 1616.8,845.098 1618.05,845.1 1619.3,845.103 1620.55,845.105 1621.8,845.107 1623.05,845.109 \n",
" 1624.29,845.111 1625.54,845.113 1626.79,845.115 1628.04,845.117 1629.29,845.119 1630.54,845.121 1631.79,845.123 1633.04,845.125 1634.29,845.126 1635.54,845.128 \n",
" 1636.79,845.13 1638.03,845.131 1639.28,845.133 1640.53,845.134 1641.78,845.136 1643.03,845.137 1644.28,845.138 1645.53,845.14 1646.78,845.141 1648.03,845.142 \n",
" 1649.28,845.144 1650.52,845.145 1651.77,845.146 1653.02,845.147 1654.27,845.148 1655.52,845.149 1656.77,845.15 1658.02,845.151 1659.27,845.152 1660.52,845.153 \n",
" 1661.77,845.154 1663.01,845.155 1664.26,845.156 1665.51,845.157 1666.76,845.158 1668.01,845.158 1669.26,845.159 1670.51,845.16 1671.76,845.161 1673.01,845.161 \n",
" 1674.26,845.162 1675.51,845.163 1676.75,845.163 1678,845.164 1679.25,845.165 1680.5,845.165 1681.75,845.166 1683,845.166 1684.25,845.167 1685.5,845.168 \n",
" 1686.75,845.168 1688,845.169 1689.24,845.169 1690.49,845.169 1691.74,845.17 1692.99,845.17 1694.24,845.171 1695.49,845.171 1696.74,845.172 1697.99,845.172 \n",
" 1699.24,845.172 1700.49,845.173 1701.74,845.173 1702.98,845.173 1704.23,845.174 1705.48,845.174 1706.73,845.174 1707.98,845.175 1709.23,845.175 1710.48,845.175 \n",
" 1711.73,845.175 1712.98,845.176 1714.23,845.176 1715.47,845.176 1716.72,845.176 1717.97,845.177 1719.22,845.177 1720.47,845.177 1721.72,845.177 1722.97,845.178 \n",
" 1724.22,845.178 1725.47,845.178 1726.72,845.178 1727.97,845.178 1729.21,845.178 1730.46,845.179 1731.71,845.179 1732.96,845.179 1734.21,845.179 1735.46,845.179 \n",
" 1736.71,845.179 1737.96,845.179 1739.21,845.18 1740.46,845.18 1741.7,845.18 1742.95,845.18 1744.2,845.18 1745.45,845.18 1746.7,845.18 1747.95,845.18 \n",
" 1749.2,845.18 1750.45,845.181 1751.7,845.181 1752.95,845.181 1754.19,845.181 1755.44,845.181 1756.69,845.181 1757.94,845.181 1759.19,845.181 1760.44,845.181 \n",
" 1761.69,845.181 1762.94,845.181 1764.19,845.181 1765.44,845.181 1766.69,845.181 1767.93,845.181 1769.18,845.182 1770.43,845.182 1771.68,845.182 1772.93,845.182 \n",
" 1774.18,845.182 1775.43,845.182 1776.68,845.182 1777.93,845.182 1779.18,845.182 1780.42,845.182 1781.67,845.182 1782.92,845.182 1784.17,845.182 1785.42,845.182 \n",
" 1786.67,845.182 1787.92,845.182 1789.17,845.182 1790.42,845.182 1791.67,845.182 1792.92,845.182 1794.16,845.182 1795.41,845.182 1796.66,845.182 1797.91,845.182 \n",
" 1799.16,845.182 1800.41,845.182 1801.66,845.182 1802.91,845.182 1804.16,845.182 1805.41,845.182 1806.65,845.182 1807.9,845.182 1809.15,845.182 1810.4,845.182 \n",
" 1811.65,845.182 1812.9,845.183 1814.15,845.183 1815.4,845.183 1816.65,845.183 1817.9,845.183 1819.15,845.183 1820.39,845.183 1821.64,845.183 1822.89,845.183 \n",
" 1824.14,845.183 1825.39,845.183 1826.64,845.183 1827.89,845.183 1829.14,845.183 1830.39,845.183 1831.64,845.183 1832.88,845.183 1834.13,845.183 1835.38,845.183 \n",
" 1836.63,845.183 1837.88,845.183 1839.13,845.183 1840.38,845.183 1841.63,845.183 1842.88,845.183 1844.13,845.183 1845.37,845.183 1846.62,845.183 1847.87,845.183 \n",
" 1849.12,845.183 1850.37,845.183 1851.62,845.183 1852.87,845.183 1854.12,845.183 1855.37,845.183 1856.62,845.183 1857.87,845.183 1859.11,845.183 1860.36,845.183 \n",
" 1861.61,845.183 1862.86,845.183 1864.11,845.183 1865.36,845.183 1866.61,845.183 1867.86,845.183 1869.11,845.183 1870.36,845.183 1871.6,845.183 1872.85,845.183 \n",
" 1874.1,845.183 1875.35,845.183 1876.6,845.183 1877.85,845.183 1879.1,845.183 1880.35,845.183 1881.6,845.183 1882.85,845.183 1884.1,845.183 1885.34,845.183 \n",
" 1886.59,845.183 1887.84,845.183 1889.09,845.183 1890.34,845.183 1891.59,845.183 1892.84,845.183 1894.09,845.183 1895.34,845.183 1896.59,845.183 1897.83,845.183 \n",
" 1899.08,845.183 1900.33,845.183 1901.58,845.183 1902.83,845.183 1904.08,845.183 1905.33,845.183 1906.58,845.183 1907.83,845.183 1909.08,845.183 1910.33,845.183 \n",
" 1911.57,845.183 1912.82,845.183 1914.07,845.183 1915.32,845.183 1916.57,845.183 1917.82,845.183 1919.07,845.183 1920.32,845.183 1921.57,845.183 1922.82,845.183 \n",
" 1924.06,845.183 1925.31,845.183 1926.56,845.183 1927.81,845.183 1929.06,845.183 1930.31,845.183 1931.56,845.183 1932.81,845.183 1934.06,845.183 1935.31,845.183 \n",
" 1936.56,845.183 1937.8,845.183 1939.05,845.183 1940.3,845.183 1941.55,845.183 1942.8,845.183 1944.05,845.183 1945.3,845.183 1946.55,845.183 1947.8,845.183 \n",
" 1949.05,845.183 1950.29,845.183 1951.54,845.183 1952.79,845.183 1954.04,845.183 1955.29,845.183 1956.54,845.183 1957.79,845.183 1959.04,845.183 1960.29,845.183 \n",
" 1961.54,845.183 1962.78,845.183 1964.03,845.183 1965.28,845.183 1966.53,845.183 1967.78,845.183 1969.03,845.183 1970.28,845.183 1971.53,845.183 1972.78,845.183 \n",
" 1974.03,845.183 1975.28,845.183 1976.52,845.183 1977.77,845.183 1979.02,845.183 1980.27,845.183 1981.52,845.183 1982.77,845.183 1984.02,845.183 1985.27,845.183 \n",
" 1986.52,845.183 1987.77,845.183 1989.01,845.183 1990.26,845.183 1991.51,845.183 1992.76,845.183 1994.01,845.183 1995.26,845.183 1996.51,845.183 1997.76,845.183 \n",
" 1999.01,845.183 2000.26,845.183 2001.51,845.183 2002.75,845.183 2004,845.183 2005.25,845.183 2006.5,845.183 2007.75,845.183 2009,845.183 2010.25,845.183 \n",
" 2011.5,845.183 2012.75,845.183 2014,845.183 2015.24,845.183 2016.49,845.183 2017.74,845.183 2018.99,845.183 2020.24,845.183 2021.49,845.183 2022.74,845.183 \n",
" 2023.99,845.183 2025.24,845.183 2026.49,845.183 2027.74,845.183 2028.98,845.183 2030.23,845.183 2031.48,845.183 2032.73,845.183 2033.98,845.183 2035.23,845.183 \n",
" 2036.48,845.183 2037.73,845.183 2038.98,845.183 2040.23,845.183 2041.47,845.183 2042.72,845.183 2043.97,845.183 2045.22,845.183 2046.47,845.183 2047.72,845.183 \n",
" 2048.97,845.183 2050.22,845.183 2051.47,845.183 2052.72,845.183 2053.96,845.183 2055.21,845.183 2056.46,845.183 2057.71,845.183 2058.96,845.183 2060.21,845.183 \n",
" 2061.46,845.183 2062.71,845.183 2063.96,845.183 2065.21,845.183 2066.46,845.183 2067.7,845.183 2068.95,845.183 2070.2,845.183 2071.45,845.183 2072.7,845.183 \n",
" 2073.95,845.183 2075.2,845.183 2076.45,845.183 2077.7,845.183 2078.95,845.183 2080.19,845.183 2081.44,845.183 2082.69,845.183 2083.94,845.183 2085.19,845.183 \n",
" 2086.44,845.183 2087.69,845.183 2088.94,845.183 2090.19,845.183 2091.44,845.183 2092.69,845.183 2093.93,845.183 2095.18,845.183 2096.43,845.183 2097.68,845.183 \n",
" 2098.93,845.183 2100.18,845.183 2101.43,845.183 2102.68,845.183 2103.93,845.183 2105.18,845.183 2106.42,845.183 2107.67,845.183 2108.92,845.183 2110.17,845.183 \n",
" 2111.42,845.183 2112.67,845.183 2113.92,845.183 2115.17,845.183 2116.42,845.183 2117.67,845.183 2118.92,845.183 2120.16,845.183 2121.41,845.183 2122.66,845.183 \n",
" 2123.91,845.183 2125.16,845.183 2126.41,845.183 2127.66,845.183 2128.91,845.183 2130.16,845.183 2131.41,845.183 2132.65,845.183 2133.9,845.183 2135.15,845.183 \n",
" 2136.4,845.183 2137.65,845.183 2138.9,845.183 2140.15,845.183 2141.4,845.183 2142.65,845.183 2143.9,845.183 2145.14,845.183 2146.39,845.183 2147.64,845.183 \n",
" 2148.89,845.183 2150.14,845.183 2151.39,845.183 2152.64,845.183 2153.89,845.183 2155.14,845.183 2156.39,845.183 2157.64,845.183 2158.88,845.183 2160.13,845.183 \n",
" 2161.38,845.183 2162.63,845.183 2163.88,845.183 2165.13,845.183 2166.38,845.183 2167.63,845.183 2168.88,845.183 2170.13,845.183 2171.37,845.183 2172.62,845.183 \n",
" 2173.87,845.183 2175.12,845.183 2176.37,845.183 2177.62,845.183 2178.87,845.183 2180.12,845.183 2181.37,845.183 2182.62,845.183 2183.87,845.183 2185.11,845.183 \n",
" 2186.36,845.183 2187.61,845.183 2188.86,845.183 2190.11,845.183 2191.36,845.183 2192.61,845.183 2193.86,845.183 2195.11,845.183 2196.36,845.183 2197.6,845.183 \n",
" 2198.85,845.183 2200.1,845.183 2201.35,845.183 2202.6,845.183 2203.85,845.183 2205.1,845.183 2206.35,845.183 2207.6,845.183 2208.85,845.183 2210.1,845.183 \n",
" 2211.34,845.183 2212.59,845.183 2213.84,845.183 2215.09,845.183 2216.34,845.183 2217.59,845.183 2218.84,845.183 2220.09,845.183 2221.34,845.183 2222.59,845.183 \n",
" 2223.83,845.183 2225.08,845.183 2226.33,845.183 2227.58,845.183 2228.83,845.183 2230.08,845.183 2231.33,845.183 2232.58,845.183 2233.83,845.183 2235.08,845.183 \n",
" 2236.33,845.183 2237.57,845.183 2238.82,845.183 2240.07,845.183 2241.32,845.183 2242.57,845.183 2243.82,845.183 2245.07,845.183 2246.32,845.183 2247.57,845.183 \n",
" 2248.82,845.183 2250.06,845.183 2251.31,845.183 2252.56,845.183 2253.81,845.183 2255.06,845.183 2256.31,845.183 2257.56,845.183 2258.81,845.183 2260.06,845.183 \n",
" 2261.31,845.183 \n",
" \"/>\n",
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" 487.667,845.183 488.916,845.183 490.165,845.183 491.414,845.183 492.663,845.183 493.912,845.183 495.161,845.183 496.41,845.183 497.659,845.183 498.908,845.183 \n",
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" 550.119,845.183 551.368,845.183 552.617,845.183 553.866,845.183 555.115,845.183 556.364,845.183 557.613,845.183 558.862,845.183 560.111,845.183 561.36,845.183 \n",
" 562.609,845.183 563.858,845.183 565.107,845.183 566.356,845.183 567.605,845.183 568.854,845.183 570.104,845.183 571.353,845.183 572.602,845.183 573.851,845.183 \n",
" 575.1,845.183 576.349,845.183 577.598,845.183 578.847,845.183 580.096,845.183 581.345,845.183 582.594,845.183 583.843,845.183 585.092,845.183 586.341,845.183 \n",
" 587.59,845.183 588.839,845.183 590.088,845.183 591.337,845.183 592.586,845.183 593.835,845.183 595.084,845.183 596.333,845.183 597.582,845.183 598.831,845.183 \n",
" 600.081,845.183 601.33,845.183 602.579,845.183 603.828,845.183 605.077,845.183 606.326,845.183 607.575,845.183 608.824,845.183 610.073,845.183 611.322,845.183 \n",
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" 625.061,845.183 626.31,845.183 627.559,845.183 628.808,845.183 630.058,845.183 631.307,845.183 632.556,845.183 633.805,845.183 635.054,845.183 636.303,845.183 \n",
" 637.552,845.183 638.801,845.183 640.05,845.183 641.299,845.183 642.548,845.183 643.797,845.183 645.046,845.183 646.295,845.183 647.544,845.183 648.793,845.183 \n",
" 650.042,845.183 651.291,845.183 652.54,845.183 653.789,845.183 655.038,845.183 656.287,845.183 657.536,845.183 658.785,845.183 660.035,845.183 661.284,845.183 \n",
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" 687.513,845.184 688.762,845.184 690.012,845.184 691.261,845.184 692.51,845.184 693.759,845.184 695.008,845.184 696.257,845.184 697.506,845.184 698.755,845.184 \n",
" 700.004,845.185 701.253,845.185 702.502,845.185 703.751,845.185 705,845.185 706.249,845.185 707.498,845.185 708.747,845.185 709.996,845.185 711.245,845.185 \n",
" 712.494,845.185 713.743,845.186 714.992,845.186 716.241,845.186 717.49,845.186 718.739,845.186 719.989,845.186 721.238,845.186 722.487,845.186 723.736,845.187 \n",
" 724.985,845.187 726.234,845.187 727.483,845.187 728.732,845.187 729.981,845.187 731.23,845.188 732.479,845.188 733.728,845.188 734.977,845.188 736.226,845.189 \n",
" 737.475,845.189 738.724,845.189 739.973,845.189 741.222,845.189 742.471,845.19 743.72,845.19 744.969,845.19 746.218,845.191 747.467,845.191 748.716,845.191 \n",
" 749.966,845.192 751.215,845.192 752.464,845.192 753.713,845.193 754.962,845.193 756.211,845.193 757.46,845.194 758.709,845.194 759.958,845.195 761.207,845.195 \n",
" 762.456,845.196 763.705,845.196 764.954,845.197 766.203,845.197 767.452,845.198 768.701,845.198 769.95,845.199 771.199,845.199 772.448,845.2 773.697,845.201 \n",
" 774.946,845.201 776.195,845.202 777.444,845.203 778.693,845.204 779.943,845.204 781.192,845.205 782.441,845.206 783.69,845.207 784.939,845.208 786.188,845.208 \n",
" 787.437,845.209 788.686,845.21 789.935,845.211 791.184,845.212 792.433,845.213 793.682,845.215 794.931,845.216 796.18,845.217 797.429,845.218 798.678,845.219 \n",
" 799.927,845.22 801.176,845.222 802.425,845.223 803.674,845.225 804.923,845.226 806.172,845.227 807.421,845.229 808.67,845.231 809.92,845.232 811.169,845.234 \n",
" 812.418,845.236 813.667,845.237 814.916,845.239 816.165,845.241 817.414,845.243 818.663,845.245 819.912,845.247 821.161,845.249 822.41,845.251 823.659,845.254 \n",
" 824.908,845.256 826.157,845.258 827.406,845.261 828.655,845.263 829.904,845.266 831.153,845.269 832.402,845.271 833.651,845.274 834.9,845.277 836.149,845.28 \n",
" 837.398,845.283 838.647,845.286 839.897,845.29 841.146,845.293 842.395,845.296 843.644,845.3 844.893,845.304 846.142,845.307 847.391,845.311 848.64,845.315 \n",
" 849.889,845.319 851.138,845.323 852.387,845.328 853.636,845.332 854.885,845.336 856.134,845.341 857.383,845.346 858.632,845.35 859.881,845.355 861.13,845.361 \n",
" 862.379,845.366 863.628,845.371 864.877,845.377 866.126,845.382 867.375,845.388 868.624,845.394 869.874,845.4 871.123,845.406 872.372,845.412 873.621,845.419 \n",
" 874.87,845.426 876.119,845.432 877.368,845.439 878.617,845.447 879.866,845.454 881.115,845.461 882.364,845.469 883.613,845.477 884.862,845.485 886.111,845.493 \n",
" 887.36,845.502 888.609,845.51 889.858,845.519 891.107,845.528 892.356,845.537 893.605,845.547 894.854,845.556 896.103,845.566 897.352,845.576 898.601,845.586 \n",
" 899.851,845.597 901.1,845.607 902.349,845.618 903.598,845.63 904.847,845.641 906.096,845.653 907.345,845.664 908.594,845.676 909.843,845.689 911.092,845.701 \n",
" 912.341,845.714 913.59,845.727 914.839,845.741 916.088,845.754 917.337,845.768 918.586,845.783 919.835,845.797 921.084,845.812 922.333,845.827 923.582,845.842 \n",
" 924.831,845.858 926.08,845.873 927.329,845.89 928.578,845.906 929.828,845.923 931.077,845.94 932.326,845.957 933.575,845.975 934.824,845.993 936.073,846.011 \n",
" 937.322,846.03 938.571,846.049 939.82,846.068 941.069,846.087 942.318,846.107 943.567,846.128 944.816,846.148 946.065,846.169 947.314,846.19 948.563,846.212 \n",
" 949.812,846.234 951.061,846.256 952.31,846.278 953.559,846.301 954.808,846.325 956.057,846.348 957.306,846.372 958.555,846.397 959.805,846.421 961.054,846.446 \n",
" 962.303,846.472 963.552,846.497 964.801,846.524 966.05,846.55 967.299,846.577 968.548,846.604 969.797,846.632 971.046,846.659 972.295,846.688 973.544,846.716 \n",
" 974.793,846.745 976.042,846.775 977.291,846.804 978.54,846.834 979.789,846.865 981.038,846.895 982.287,846.927 983.536,846.958 984.785,846.99 986.034,847.022 \n",
" 987.283,847.054 988.532,847.087 989.781,847.12 991.031,847.154 992.28,847.188 993.529,847.222 994.778,847.257 996.027,847.291 997.276,847.327 998.525,847.362 \n",
" 999.774,847.398 1001.02,847.434 1002.27,847.47 1003.52,847.507 1004.77,847.544 1006.02,847.581 1007.27,847.619 1008.52,847.657 1009.77,847.695 1011.02,847.734 \n",
" 1012.26,847.772 1013.51,847.811 1014.76,847.851 1016.01,847.89 1017.26,847.93 1018.51,847.97 1019.76,848.01 1021.01,848.05 1022.26,848.091 1023.51,848.132 \n",
" 1024.75,848.173 1026,848.214 1027.25,848.255 1028.5,848.297 1029.75,848.338 1031,848.38 1032.25,848.422 1033.5,848.464 1034.75,848.506 1036,848.548 \n",
" 1037.25,848.591 1038.49,848.633 1039.74,848.676 1040.99,848.718 1042.24,848.761 1043.49,848.804 1044.74,848.846 1045.99,848.889 1047.24,848.932 1048.49,848.974 \n",
" 1049.74,849.017 1050.98,849.06 1052.23,849.102 1053.48,849.145 1054.73,849.187 1055.98,849.229 1057.23,849.272 1058.48,849.314 1059.73,849.355 1060.98,849.397 \n",
" 1062.23,849.439 1063.47,849.48 1064.72,849.521 1065.97,849.562 1067.22,849.603 1068.47,849.644 1069.72,849.684 1070.97,849.724 1072.22,849.763 1073.47,849.803 \n",
" 1074.72,849.842 1075.97,849.88 1077.21,849.919 1078.46,849.957 1079.71,849.994 1080.96,850.031 1082.21,850.068 1083.46,850.104 1084.71,850.14 1085.96,850.175 \n",
" 1087.21,850.21 1088.46,850.244 1089.7,850.278 1090.95,850.311 1092.2,850.343 1093.45,850.375 1094.7,850.407 1095.95,850.437 1097.2,850.467 1098.45,850.497 \n",
" 1099.7,850.525 1100.95,850.553 1102.2,850.581 1103.44,850.607 1104.69,850.633 1105.94,850.658 1107.19,850.682 1108.44,850.706 1109.69,850.728 1110.94,850.75 \n",
" 1112.19,850.771 1113.44,850.791 1114.69,850.81 1115.93,850.828 1117.18,850.846 1118.43,850.862 1119.68,850.878 1120.93,850.892 1122.18,850.906 1123.43,850.918 \n",
" 1124.68,850.93 1125.93,850.94 1127.18,850.949 1128.43,850.958 1129.67,850.965 1130.92,850.971 1132.17,850.976 1133.42,850.98 1134.67,850.983 1135.92,850.985 \n",
" 1137.17,850.986 1138.42,850.985 1139.67,850.983 1140.92,850.98 1142.16,850.976 1143.41,850.971 1144.66,850.964 1145.91,850.957 1147.16,850.948 1148.41,850.937 \n",
" 1149.66,850.926 1150.91,850.913 1152.16,850.899 1153.41,850.884 1154.65,850.867 1155.9,850.849 1157.15,850.83 1158.4,850.81 1159.65,850.788 1160.9,850.765 \n",
" 1162.15,850.741 1163.4,850.715 1164.65,850.688 1165.9,850.66 1167.15,850.63 1168.39,850.599 1169.64,850.567 1170.89,850.533 1172.14,850.498 1173.39,850.462 \n",
" 1174.64,850.425 1175.89,850.386 1177.14,850.346 1178.39,850.304 1179.64,850.261 1180.88,850.217 1182.13,850.172 1183.38,850.125 1184.63,850.077 1185.88,850.028 \n",
" 1187.13,849.978 1188.38,849.926 1189.63,849.873 1190.88,849.818 1192.13,849.763 1193.38,849.706 1194.62,849.648 1195.87,849.589 1197.12,849.529 1198.37,849.467 \n",
" 1199.62,849.404 1200.87,849.34 1202.12,849.275 1203.37,849.209 1204.62,849.142 1205.87,849.073 1207.11,849.004 1208.36,848.933 1209.61,848.862 1210.86,848.789 \n",
" 1212.11,848.715 1213.36,848.641 1214.61,848.565 1215.86,848.488 1217.11,848.411 1218.36,848.332 1219.61,848.253 1220.85,848.173 1222.1,848.091 1223.35,848.009 \n",
" 1224.6,847.927 1225.85,847.843 1227.1,847.759 1228.35,847.673 1229.6,847.588 1230.85,847.501 1232.1,847.414 1233.34,847.326 1234.59,847.237 1235.84,847.148 \n",
" 1237.09,847.058 1238.34,846.968 1239.59,846.877 1240.84,846.786 1242.09,846.694 1243.34,846.602 1244.59,846.509 1245.84,846.416 1247.08,846.323 1248.33,846.229 \n",
" 1249.58,846.135 1250.83,846.04 1252.08,845.946 1253.33,845.851 1254.58,845.756 1255.83,845.661 1257.08,845.565 1258.33,845.47 1259.57,845.374 1260.82,845.278 \n",
" 1262.07,845.183 1263.32,845.087 1264.57,844.991 1265.82,844.896 1267.07,844.8 1268.32,844.705 1269.57,844.61 1270.82,844.515 1272.06,844.42 1273.31,844.325 \n",
" 1274.56,844.231 1275.81,844.137 1277.06,844.043 1278.31,843.95 1279.56,843.856 1280.81,843.764 1282.06,843.672 1283.31,843.58 1284.56,843.488 1285.8,843.398 \n",
" 1287.05,843.307 1288.3,843.218 1289.55,843.128 1290.8,843.04 1292.05,842.952 1293.3,842.865 1294.55,842.778 1295.8,842.692 1297.05,842.607 1298.29,842.523 \n",
" 1299.54,842.439 1300.79,842.356 1302.04,842.274 1303.29,842.193 1304.54,842.113 1305.79,842.033 1307.04,841.955 1308.29,841.877 1309.54,841.801 1310.79,841.725 \n",
" 1312.03,841.65 1313.28,841.576 1314.53,841.504 1315.78,841.432 1317.03,841.362 1318.28,841.292 1319.53,841.224 1320.78,841.156 1322.03,841.09 1323.28,841.025 \n",
" 1324.52,840.961 1325.77,840.899 1327.02,840.837 1328.27,840.777 1329.52,840.717 1330.77,840.659 1332.02,840.603 1333.27,840.547 1334.52,840.493 1335.77,840.44 \n",
" 1337.02,840.388 1338.26,840.338 1339.51,840.288 1340.76,840.24 1342.01,840.194 1343.26,840.148 1344.51,840.104 1345.76,840.061 1347.01,840.02 1348.26,839.98 \n",
" 1349.51,839.941 1350.75,839.903 1352,839.867 1353.25,839.832 1354.5,839.799 1355.75,839.767 1357,839.736 1358.25,839.706 1359.5,839.678 1360.75,839.651 \n",
" 1362,839.625 1363.24,839.601 1364.49,839.578 1365.74,839.556 1366.99,839.535 1368.24,839.516 1369.49,839.498 1370.74,839.482 1371.99,839.467 1373.24,839.453 \n",
" 1374.49,839.44 1375.74,839.428 1376.98,839.418 1378.23,839.409 1379.48,839.401 1380.73,839.395 1381.98,839.389 1383.23,839.385 1384.48,839.382 1385.73,839.381 \n",
" 1386.98,839.38 1388.23,839.381 1389.47,839.382 1390.72,839.385 1391.97,839.389 1393.22,839.394 1394.47,839.4 1395.72,839.408 1396.97,839.416 1398.22,839.426 \n",
" 1399.47,839.436 1400.72,839.447 1401.97,839.46 1403.21,839.473 1404.46,839.488 1405.71,839.503 1406.96,839.52 1408.21,839.537 1409.46,839.555 1410.71,839.575 \n",
" 1411.96,839.595 1413.21,839.616 1414.46,839.637 1415.7,839.66 1416.95,839.683 1418.2,839.708 1419.45,839.733 1420.7,839.758 1421.95,839.785 1423.2,839.812 \n",
" 1424.45,839.84 1425.7,839.869 1426.95,839.898 1428.2,839.928 1429.44,839.959 1430.69,839.99 1431.94,840.022 1433.19,840.055 1434.44,840.088 1435.69,840.122 \n",
" 1436.94,840.156 1438.19,840.191 1439.44,840.226 1440.69,840.262 1441.93,840.298 1443.18,840.334 1444.43,840.371 1445.68,840.409 1446.93,840.447 1448.18,840.485 \n",
" 1449.43,840.524 1450.68,840.563 1451.93,840.602 1453.18,840.642 1454.42,840.682 1455.67,840.722 1456.92,840.762 1458.17,840.803 1459.42,840.844 1460.67,840.885 \n",
" 1461.92,840.927 1463.17,840.968 1464.42,841.01 1465.67,841.052 1466.92,841.094 1468.16,841.136 1469.41,841.179 1470.66,841.221 1471.91,841.263 1473.16,841.306 \n",
" 1474.41,841.349 1475.66,841.391 1476.91,841.434 1478.16,841.477 1479.41,841.519 1480.65,841.562 1481.9,841.605 1483.15,841.647 1484.4,841.69 1485.65,841.732 \n",
" 1486.9,841.775 1488.15,841.817 1489.4,841.859 1490.65,841.902 1491.9,841.944 1493.15,841.986 1494.39,842.027 1495.64,842.069 1496.89,842.111 1498.14,842.152 \n",
" 1499.39,842.193 1500.64,842.234 1501.89,842.275 1503.14,842.315 1504.39,842.356 1505.64,842.396 1506.88,842.436 1508.13,842.476 1509.38,842.515 1510.63,842.554 \n",
" 1511.88,842.593 1513.13,842.632 1514.38,842.67 1515.63,842.709 1516.88,842.746 1518.13,842.784 1519.38,842.821 1520.62,842.858 1521.87,842.895 1523.12,842.932 \n",
" 1524.37,842.968 1525.62,843.004 1526.87,843.039 1528.12,843.074 1529.37,843.109 1530.62,843.144 1531.87,843.178 1533.11,843.212 1534.36,843.245 1535.61,843.278 \n",
" 1536.86,843.311 1538.11,843.344 1539.36,843.376 1540.61,843.408 1541.86,843.439 1543.11,843.47 1544.36,843.501 1545.61,843.531 1546.85,843.561 1548.1,843.591 \n",
" 1549.35,843.62 1550.6,843.649 1551.85,843.678 1553.1,843.706 1554.35,843.734 1555.6,843.762 1556.85,843.789 1558.1,843.816 1559.34,843.842 1560.59,843.868 \n",
" 1561.84,843.894 1563.09,843.919 1564.34,843.944 1565.59,843.969 1566.84,843.993 1568.09,844.017 1569.34,844.041 1570.59,844.064 1571.83,844.087 1573.08,844.11 \n",
" 1574.33,844.132 1575.58,844.154 1576.83,844.175 1578.08,844.197 1579.33,844.217 1580.58,844.238 1581.83,844.258 1583.08,844.278 1584.33,844.298 1585.57,844.317 \n",
" 1586.82,844.336 1588.07,844.354 1589.32,844.373 1590.57,844.391 1591.82,844.408 1593.07,844.426 1594.32,844.443 1595.57,844.46 1596.82,844.476 1598.06,844.492 \n",
" 1599.31,844.508 1600.56,844.524 1601.81,844.539 1603.06,844.554 1604.31,844.569 1605.56,844.583 1606.81,844.597 1608.06,844.611 1609.31,844.625 1610.56,844.638 \n",
" 1611.8,844.651 1613.05,844.664 1614.3,844.677 1615.55,844.689 1616.8,844.701 1618.05,844.713 1619.3,844.725 1620.55,844.736 1621.8,844.747 1623.05,844.758 \n",
" 1624.29,844.769 1625.54,844.779 1626.79,844.79 1628.04,844.8 1629.29,844.809 1630.54,844.819 1631.79,844.828 1633.04,844.838 1634.29,844.847 1635.54,844.855 \n",
" 1636.79,844.864 1638.03,844.872 1639.28,844.881 1640.53,844.889 1641.78,844.896 1643.03,844.904 1644.28,844.912 1645.53,844.919 1646.78,844.926 1648.03,844.933 \n",
" 1649.28,844.94 1650.52,844.947 1651.77,844.953 1653.02,844.959 1654.27,844.966 1655.52,844.972 1656.77,844.978 1658.02,844.983 1659.27,844.989 1660.52,844.994 \n",
" 1661.77,845 1663.01,845.005 1664.26,845.01 1665.51,845.015 1666.76,845.02 1668.01,845.025 1669.26,845.029 1670.51,845.034 1671.76,845.038 1673.01,845.042 \n",
" 1674.26,845.046 1675.51,845.051 1676.75,845.054 1678,845.058 1679.25,845.062 1680.5,845.066 1681.75,845.069 1683,845.073 1684.25,845.076 1685.5,845.079 \n",
" 1686.75,845.082 1688,845.085 1689.24,845.088 1690.49,845.091 1691.74,845.094 1692.99,845.097 1694.24,845.1 1695.49,845.102 1696.74,845.105 1697.99,845.107 \n",
" 1699.24,845.11 1700.49,845.112 1701.74,845.114 1702.98,845.116 1704.23,845.118 1705.48,845.121 1706.73,845.123 1707.98,845.124 1709.23,845.126 1710.48,845.128 \n",
" 1711.73,845.13 1712.98,845.132 1714.23,845.133 1715.47,845.135 1716.72,845.137 1717.97,845.138 1719.22,845.14 1720.47,845.141 1721.72,845.142 1722.97,845.144 \n",
" 1724.22,845.145 1725.47,845.146 1726.72,845.148 1727.97,845.149 1729.21,845.15 1730.46,845.151 1731.71,845.152 1732.96,845.153 1734.21,845.154 1735.46,845.155 \n",
" 1736.71,845.156 1737.96,845.157 1739.21,845.158 1740.46,845.159 1741.7,845.16 1742.95,845.161 1744.2,845.161 1745.45,845.162 1746.7,845.163 1747.95,845.164 \n",
" 1749.2,845.164 1750.45,845.165 1751.7,845.166 1752.95,845.166 1754.19,845.167 1755.44,845.167 1756.69,845.168 1757.94,845.168 1759.19,845.169 1760.44,845.169 \n",
" 1761.69,845.17 1762.94,845.17 1764.19,845.171 1765.44,845.171 1766.69,845.172 1767.93,845.172 1769.18,845.173 1770.43,845.173 1771.68,845.173 1772.93,845.174 \n",
" 1774.18,845.174 1775.43,845.174 1776.68,845.175 1777.93,845.175 1779.18,845.175 1780.42,845.176 1781.67,845.176 1782.92,845.176 1784.17,845.176 1785.42,845.177 \n",
" 1786.67,845.177 1787.92,845.177 1789.17,845.177 1790.42,845.178 1791.67,845.178 1792.92,845.178 1794.16,845.178 1795.41,845.178 1796.66,845.178 1797.91,845.179 \n",
" 1799.16,845.179 1800.41,845.179 1801.66,845.179 1802.91,845.179 1804.16,845.179 1805.41,845.18 1806.65,845.18 1807.9,845.18 1809.15,845.18 1810.4,845.18 \n",
" 1811.65,845.18 1812.9,845.18 1814.15,845.18 1815.4,845.18 1816.65,845.181 1817.9,845.181 1819.15,845.181 1820.39,845.181 1821.64,845.181 1822.89,845.181 \n",
" 1824.14,845.181 1825.39,845.181 1826.64,845.181 1827.89,845.181 1829.14,845.181 1830.39,845.181 1831.64,845.181 1832.88,845.182 1834.13,845.182 1835.38,845.182 \n",
" 1836.63,845.182 1837.88,845.182 1839.13,845.182 1840.38,845.182 1841.63,845.182 1842.88,845.182 1844.13,845.182 1845.37,845.182 1846.62,845.182 1847.87,845.182 \n",
" 1849.12,845.182 1850.37,845.182 1851.62,845.182 1852.87,845.182 1854.12,845.182 1855.37,845.182 1856.62,845.182 1857.87,845.182 1859.11,845.182 1860.36,845.182 \n",
" 1861.61,845.182 1862.86,845.182 1864.11,845.182 1865.36,845.182 1866.61,845.182 1867.86,845.182 1869.11,845.182 1870.36,845.182 1871.6,845.182 1872.85,845.182 \n",
" 1874.1,845.183 1875.35,845.183 1876.6,845.183 1877.85,845.183 1879.1,845.183 1880.35,845.183 1881.6,845.183 1882.85,845.183 1884.1,845.183 1885.34,845.183 \n",
" 1886.59,845.183 1887.84,845.183 1889.09,845.183 1890.34,845.183 1891.59,845.183 1892.84,845.183 1894.09,845.183 1895.34,845.183 1896.59,845.183 1897.83,845.183 \n",
" 1899.08,845.183 1900.33,845.183 1901.58,845.183 1902.83,845.183 1904.08,845.183 1905.33,845.183 1906.58,845.183 1907.83,845.183 1909.08,845.183 1910.33,845.183 \n",
" 1911.57,845.183 1912.82,845.183 1914.07,845.183 1915.32,845.183 1916.57,845.183 1917.82,845.183 1919.07,845.183 1920.32,845.183 1921.57,845.183 1922.82,845.183 \n",
" 1924.06,845.183 1925.31,845.183 1926.56,845.183 1927.81,845.183 1929.06,845.183 1930.31,845.183 1931.56,845.183 1932.81,845.183 1934.06,845.183 1935.31,845.183 \n",
" 1936.56,845.183 1937.8,845.183 1939.05,845.183 1940.3,845.183 1941.55,845.183 1942.8,845.183 1944.05,845.183 1945.3,845.183 1946.55,845.183 1947.8,845.183 \n",
" 1949.05,845.183 1950.29,845.183 1951.54,845.183 1952.79,845.183 1954.04,845.183 1955.29,845.183 1956.54,845.183 1957.79,845.183 1959.04,845.183 1960.29,845.183 \n",
" 1961.54,845.183 1962.78,845.183 1964.03,845.183 1965.28,845.183 1966.53,845.183 1967.78,845.183 1969.03,845.183 1970.28,845.183 1971.53,845.183 1972.78,845.183 \n",
" 1974.03,845.183 1975.28,845.183 1976.52,845.183 1977.77,845.183 1979.02,845.183 1980.27,845.183 1981.52,845.183 1982.77,845.183 1984.02,845.183 1985.27,845.183 \n",
" 1986.52,845.183 1987.77,845.183 1989.01,845.183 1990.26,845.183 1991.51,845.183 1992.76,845.183 1994.01,845.183 1995.26,845.183 1996.51,845.183 1997.76,845.183 \n",
" 1999.01,845.183 2000.26,845.183 2001.51,845.183 2002.75,845.183 2004,845.183 2005.25,845.183 2006.5,845.183 2007.75,845.183 2009,845.183 2010.25,845.183 \n",
" 2011.5,845.183 2012.75,845.183 2014,845.183 2015.24,845.183 2016.49,845.183 2017.74,845.183 2018.99,845.183 2020.24,845.183 2021.49,845.183 2022.74,845.183 \n",
" 2023.99,845.183 2025.24,845.183 2026.49,845.183 2027.74,845.183 2028.98,845.183 2030.23,845.183 2031.48,845.183 2032.73,845.183 2033.98,845.183 2035.23,845.183 \n",
" 2036.48,845.183 2037.73,845.183 2038.98,845.183 2040.23,845.183 2041.47,845.183 2042.72,845.183 2043.97,845.183 2045.22,845.183 2046.47,845.183 2047.72,845.183 \n",
" 2048.97,845.183 2050.22,845.183 2051.47,845.183 2052.72,845.183 2053.96,845.183 2055.21,845.183 2056.46,845.183 2057.71,845.183 2058.96,845.183 2060.21,845.183 \n",
" 2061.46,845.183 2062.71,845.183 2063.96,845.183 2065.21,845.183 2066.46,845.183 2067.7,845.183 2068.95,845.183 2070.2,845.183 2071.45,845.183 2072.7,845.183 \n",
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" 2173.87,845.183 2175.12,845.183 2176.37,845.183 2177.62,845.183 2178.87,845.183 2180.12,845.183 2181.37,845.183 2182.62,845.183 2183.87,845.183 2185.11,845.183 \n",
" 2186.36,845.183 2187.61,845.183 2188.86,845.183 2190.11,845.183 2191.36,845.183 2192.61,845.183 2193.86,845.183 2195.11,845.183 2196.36,845.183 2197.6,845.183 \n",
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" 974.793,838.675 976.042,838.588 977.291,838.5 978.54,838.413 979.789,838.325 981.038,838.237 982.287,838.149 983.536,838.062 984.785,837.974 986.034,837.886 \n",
" 987.283,837.798 988.532,837.711 989.781,837.624 991.031,837.536 992.28,837.449 993.529,837.363 994.778,837.276 996.027,837.19 997.276,837.105 998.525,837.019 \n",
" 999.774,836.934 1001.02,836.85 1002.27,836.766 1003.52,836.683 1004.77,836.6 1006.02,836.518 1007.27,836.437 1008.52,836.356 1009.77,836.276 1011.02,836.197 \n",
" 1012.26,836.119 1013.51,836.042 1014.76,835.966 1016.01,835.891 1017.26,835.816 1018.51,835.743 1019.76,835.671 1021.01,835.6 1022.26,835.531 1023.51,835.462 \n",
" 1024.75,835.395 1026,835.33 1027.25,835.265 1028.5,835.202 1029.75,835.141 1031,835.081 1032.25,835.023 1033.5,834.967 1034.75,834.912 1036,834.859 \n",
" 1037.25,834.807 1038.49,834.758 1039.74,834.71 1040.99,834.664 1042.24,834.621 1043.49,834.579 1044.74,834.539 1045.99,834.502 1047.24,834.466 1048.49,834.433 \n",
" 1049.74,834.402 1050.98,834.373 1052.23,834.347 1053.48,834.323 1054.73,834.301 1055.98,834.282 1057.23,834.265 1058.48,834.251 1059.73,834.239 1060.98,834.23 \n",
" 1062.23,834.223 1063.47,834.22 1064.72,834.219 1065.97,834.22 1067.22,834.225 1068.47,834.232 1069.72,834.242 1070.97,834.255 1072.22,834.271 1073.47,834.29 \n",
" 1074.72,834.312 1075.97,834.337 1077.21,834.364 1078.46,834.395 1079.71,834.429 1080.96,834.466 1082.21,834.506 1083.46,834.549 1084.71,834.596 1085.96,834.645 \n",
" 1087.21,834.698 1088.46,834.754 1089.7,834.813 1090.95,834.875 1092.2,834.941 1093.45,835.01 1094.7,835.082 1095.95,835.157 1097.2,835.235 1098.45,835.317 \n",
" 1099.7,835.402 1100.95,835.49 1102.2,835.581 1103.44,835.676 1104.69,835.774 1105.94,835.875 1107.19,835.979 1108.44,836.087 1109.69,836.197 1110.94,836.311 \n",
" 1112.19,836.428 1113.44,836.548 1114.69,836.671 1115.93,836.797 1117.18,836.926 1118.43,837.059 1119.68,837.194 1120.93,837.332 1122.18,837.473 1123.43,837.617 \n",
" 1124.68,837.764 1125.93,837.914 1127.18,838.066 1128.43,838.221 1129.67,838.379 1130.92,838.54 1132.17,838.703 1133.42,838.868 1134.67,839.037 1135.92,839.207 \n",
" 1137.17,839.38 1138.42,839.555 1139.67,839.733 1140.92,839.912 1142.16,840.094 1143.41,840.278 1144.66,840.464 1145.91,840.652 1147.16,840.842 1148.41,841.033 \n",
" 1149.66,841.227 1150.91,841.421 1152.16,841.618 1153.41,841.816 1154.65,842.015 1155.9,842.216 1157.15,842.418 1158.4,842.622 1159.65,842.826 1160.9,843.031 \n",
" 1162.15,843.238 1163.4,843.445 1164.65,843.653 1165.9,843.861 1167.15,844.07 1168.39,844.28 1169.64,844.49 1170.89,844.701 1172.14,844.911 1173.39,845.122 \n",
" 1174.64,845.333 1175.89,845.543 1177.14,845.754 1178.39,845.964 1179.64,846.174 1180.88,846.383 1182.13,846.592 1183.38,846.8 1184.63,847.008 1185.88,847.215 \n",
" 1187.13,847.42 1188.38,847.625 1189.63,847.829 1190.88,848.031 1192.13,848.232 1193.38,848.431 1194.62,848.629 1195.87,848.826 1197.12,849.02 1198.37,849.213 \n",
" 1199.62,849.404 1200.87,849.593 1202.12,849.78 1203.37,849.965 1204.62,850.147 1205.87,850.327 1207.11,850.505 1208.36,850.68 1209.61,850.852 1210.86,851.022 \n",
" 1212.11,851.188 1213.36,851.352 1214.61,851.513 1215.86,851.671 1217.11,851.825 1218.36,851.977 1219.61,852.125 1220.85,852.27 1222.1,852.411 1223.35,852.549 \n",
" 1224.6,852.683 1225.85,852.813 1227.1,852.94 1228.35,853.063 1229.6,853.182 1230.85,853.297 1232.1,853.408 1233.34,853.514 1234.59,853.617 1235.84,853.716 \n",
" 1237.09,853.81 1238.34,853.9 1239.59,853.986 1240.84,854.068 1242.09,854.145 1243.34,854.217 1244.59,854.285 1245.84,854.349 1247.08,854.408 1248.33,854.462 \n",
" 1249.58,854.512 1250.83,854.557 1252.08,854.597 1253.33,854.633 1254.58,854.664 1255.83,854.69 1257.08,854.712 1258.33,854.728 1259.57,854.74 1260.82,854.748 \n",
" 1262.07,854.75 1263.32,854.748 1264.57,854.74 1265.82,854.728 1267.07,854.712 1268.32,854.69 1269.57,854.664 1270.82,854.633 1272.06,854.597 1273.31,854.557 \n",
" 1274.56,854.512 1275.81,854.462 1277.06,854.408 1278.31,854.349 1279.56,854.285 1280.81,854.217 1282.06,854.145 1283.31,854.068 1284.56,853.986 1285.8,853.9 \n",
" 1287.05,853.81 1288.3,853.716 1289.55,853.617 1290.8,853.514 1292.05,853.408 1293.3,853.297 1294.55,853.182 1295.8,853.063 1297.05,852.94 1298.29,852.813 \n",
" 1299.54,852.683 1300.79,852.549 1302.04,852.411 1303.29,852.27 1304.54,852.125 1305.79,851.977 1307.04,851.825 1308.29,851.671 1309.54,851.513 1310.79,851.352 \n",
" 1312.03,851.188 1313.28,851.022 1314.53,850.852 1315.78,850.68 1317.03,850.505 1318.28,850.327 1319.53,850.147 1320.78,849.965 1322.03,849.78 1323.28,849.593 \n",
" 1324.52,849.404 1325.77,849.213 1327.02,849.02 1328.27,848.826 1329.52,848.629 1330.77,848.431 1332.02,848.232 1333.27,848.031 1334.52,847.829 1335.77,847.625 \n",
" 1337.02,847.42 1338.26,847.215 1339.51,847.008 1340.76,846.8 1342.01,846.592 1343.26,846.383 1344.51,846.174 1345.76,845.964 1347.01,845.754 1348.26,845.543 \n",
" 1349.51,845.333 1350.75,845.122 1352,844.911 1353.25,844.701 1354.5,844.49 1355.75,844.28 1357,844.07 1358.25,843.861 1359.5,843.653 1360.75,843.445 \n",
" 1362,843.238 1363.24,843.031 1364.49,842.826 1365.74,842.622 1366.99,842.418 1368.24,842.216 1369.49,842.015 1370.74,841.816 1371.99,841.618 1373.24,841.421 \n",
" 1374.49,841.227 1375.74,841.033 1376.98,840.842 1378.23,840.652 1379.48,840.464 1380.73,840.278 1381.98,840.094 1383.23,839.912 1384.48,839.733 1385.73,839.555 \n",
" 1386.98,839.38 1388.23,839.207 1389.47,839.037 1390.72,838.868 1391.97,838.703 1393.22,838.54 1394.47,838.379 1395.72,838.221 1396.97,838.066 1398.22,837.914 \n",
" 1399.47,837.764 1400.72,837.617 1401.97,837.473 1403.21,837.332 1404.46,837.194 1405.71,837.059 1406.96,836.926 1408.21,836.797 1409.46,836.671 1410.71,836.548 \n",
" 1411.96,836.428 1413.21,836.311 1414.46,836.197 1415.7,836.087 1416.95,835.979 1418.2,835.875 1419.45,835.774 1420.7,835.676 1421.95,835.581 1423.2,835.49 \n",
" 1424.45,835.402 1425.7,835.317 1426.95,835.235 1428.2,835.157 1429.44,835.082 1430.69,835.01 1431.94,834.941 1433.19,834.875 1434.44,834.813 1435.69,834.754 \n",
" 1436.94,834.698 1438.19,834.645 1439.44,834.596 1440.69,834.549 1441.93,834.506 1443.18,834.466 1444.43,834.429 1445.68,834.395 1446.93,834.364 1448.18,834.337 \n",
" 1449.43,834.312 1450.68,834.29 1451.93,834.271 1453.18,834.255 1454.42,834.242 1455.67,834.232 1456.92,834.225 1458.17,834.22 1459.42,834.219 1460.67,834.22 \n",
" 1461.92,834.223 1463.17,834.23 1464.42,834.239 1465.67,834.251 1466.92,834.265 1468.16,834.282 1469.41,834.301 1470.66,834.323 1471.91,834.347 1473.16,834.373 \n",
" 1474.41,834.402 1475.66,834.433 1476.91,834.466 1478.16,834.502 1479.41,834.539 1480.65,834.579 1481.9,834.621 1483.15,834.664 1484.4,834.71 1485.65,834.758 \n",
" 1486.9,834.807 1488.15,834.859 1489.4,834.912 1490.65,834.967 1491.9,835.023 1493.15,835.081 1494.39,835.141 1495.64,835.202 1496.89,835.265 1498.14,835.33 \n",
" 1499.39,835.395 1500.64,835.462 1501.89,835.531 1503.14,835.6 1504.39,835.671 1505.64,835.743 1506.88,835.816 1508.13,835.891 1509.38,835.966 1510.63,836.042 \n",
" 1511.88,836.119 1513.13,836.197 1514.38,836.276 1515.63,836.356 1516.88,836.437 1518.13,836.518 1519.38,836.6 1520.62,836.683 1521.87,836.766 1523.12,836.85 \n",
" 1524.37,836.934 1525.62,837.019 1526.87,837.105 1528.12,837.19 1529.37,837.276 1530.62,837.363 1531.87,837.449 1533.11,837.536 1534.36,837.624 1535.61,837.711 \n",
" 1536.86,837.798 1538.11,837.886 1539.36,837.974 1540.61,838.062 1541.86,838.149 1543.11,838.237 1544.36,838.325 1545.61,838.413 1546.85,838.5 1548.1,838.588 \n",
" 1549.35,838.675 1550.6,838.762 1551.85,838.849 1553.1,838.935 1554.35,839.022 1555.6,839.108 1556.85,839.194 1558.1,839.279 1559.34,839.364 1560.59,839.449 \n",
" 1561.84,839.533 1563.09,839.617 1564.34,839.7 1565.59,839.783 1566.84,839.866 1568.09,839.947 1569.34,840.029 1570.59,840.11 1571.83,840.19 1573.08,840.27 \n",
" 1574.33,840.349 1575.58,840.427 1576.83,840.505 1578.08,840.582 1579.33,840.659 1580.58,840.735 1581.83,840.81 1583.08,840.885 1584.33,840.959 1585.57,841.032 \n",
" 1586.82,841.105 1588.07,841.176 1589.32,841.247 1590.57,841.318 1591.82,841.387 1593.07,841.456 1594.32,841.524 1595.57,841.592 1596.82,841.658 1598.06,841.724 \n",
" 1599.31,841.789 1600.56,841.853 1601.81,841.917 1603.06,841.979 1604.31,842.041 1605.56,842.102 1606.81,842.163 1608.06,842.222 1609.31,842.281 1610.56,842.339 \n",
" 1611.8,842.396 1613.05,842.453 1614.3,842.508 1615.55,842.563 1616.8,842.617 1618.05,842.67 1619.3,842.723 1620.55,842.774 1621.8,842.825 1623.05,842.875 \n",
" 1624.29,842.924 1625.54,842.973 1626.79,843.021 1628.04,843.068 1629.29,843.114 1630.54,843.16 1631.79,843.204 1633.04,843.248 1634.29,843.292 1635.54,843.334 \n",
" 1636.79,843.376 1638.03,843.417 1639.28,843.457 1640.53,843.497 1641.78,843.536 1643.03,843.574 1644.28,843.612 1645.53,843.649 1646.78,843.685 1648.03,843.721 \n",
" 1649.28,843.755 1650.52,843.79 1651.77,843.823 1653.02,843.856 1654.27,843.888 1655.52,843.92 1656.77,843.951 1658.02,843.981 1659.27,844.011 1660.52,844.04 \n",
" 1661.77,844.069 1663.01,844.097 1664.26,844.125 1665.51,844.151 1666.76,844.178 1668.01,844.204 1669.26,844.229 1670.51,844.253 1671.76,844.278 1673.01,844.301 \n",
" 1674.26,844.324 1675.51,844.347 1676.75,844.369 1678,844.391 1679.25,844.412 1680.5,844.433 1681.75,844.453 1683,844.473 1684.25,844.492 1685.5,844.511 \n",
" 1686.75,844.529 1688,844.547 1689.24,844.565 1690.49,844.582 1691.74,844.599 1692.99,844.615 1694.24,844.631 1695.49,844.646 1696.74,844.662 1697.99,844.677 \n",
" 1699.24,844.691 1700.49,844.705 1701.74,844.719 1702.98,844.732 1704.23,844.745 1705.48,844.758 1706.73,844.771 1707.98,844.783 1709.23,844.794 1710.48,844.806 \n",
" 1711.73,844.817 1712.98,844.828 1714.23,844.839 1715.47,844.849 1716.72,844.859 1717.97,844.869 1719.22,844.878 1720.47,844.888 1721.72,844.897 1722.97,844.906 \n",
" 1724.22,844.914 1725.47,844.922 1726.72,844.93 1727.97,844.938 1729.21,844.946 1730.46,844.953 1731.71,844.961 1732.96,844.968 1734.21,844.975 1735.46,844.981 \n",
" 1736.71,844.988 1737.96,844.994 1739.21,845 1740.46,845.006 1741.7,845.012 1742.95,845.017 1744.2,845.023 1745.45,845.028 1746.7,845.033 1747.95,845.038 \n",
" 1749.2,845.043 1750.45,845.047 1751.7,845.052 1752.95,845.056 1754.19,845.06 1755.44,845.065 1756.69,845.069 1757.94,845.072 1759.19,845.076 1760.44,845.08 \n",
" 1761.69,845.083 1762.94,845.087 1764.19,845.09 1765.44,845.093 1766.69,845.096 1767.93,845.099 1769.18,845.102 1770.43,845.105 1771.68,845.108 1772.93,845.11 \n",
" 1774.18,845.113 1775.43,845.115 1776.68,845.118 1777.93,845.12 1779.18,845.122 1780.42,845.125 1781.67,845.127 1782.92,845.129 1784.17,845.131 1785.42,845.133 \n",
" 1786.67,845.134 1787.92,845.136 1789.17,845.138 1790.42,845.139 1791.67,845.141 1792.92,845.143 1794.16,845.144 1795.41,845.146 1796.66,845.147 1797.91,845.148 \n",
" 1799.16,845.15 1800.41,845.151 1801.66,845.152 1802.91,845.153 1804.16,845.154 1805.41,845.155 1806.65,845.156 1807.9,845.157 1809.15,845.158 1810.4,845.159 \n",
" 1811.65,845.16 1812.9,845.161 1814.15,845.162 1815.4,845.163 1816.65,845.164 1817.9,845.164 1819.15,845.165 1820.39,845.166 1821.64,845.166 1822.89,845.167 \n",
" 1824.14,845.168 1825.39,845.168 1826.64,845.169 1827.89,845.169 1829.14,845.17 1830.39,845.17 1831.64,845.171 1832.88,845.171 1834.13,845.172 1835.38,845.172 \n",
" 1836.63,845.173 1837.88,845.173 1839.13,845.174 1840.38,845.174 1841.63,845.174 1842.88,845.175 1844.13,845.175 1845.37,845.175 1846.62,845.176 1847.87,845.176 \n",
" 1849.12,845.176 1850.37,845.176 1851.62,845.177 1852.87,845.177 1854.12,845.177 1855.37,845.177 1856.62,845.178 1857.87,845.178 1859.11,845.178 1860.36,845.178 \n",
" 1861.61,845.179 1862.86,845.179 1864.11,845.179 1865.36,845.179 1866.61,845.179 1867.86,845.179 1869.11,845.18 1870.36,845.18 1871.6,845.18 1872.85,845.18 \n",
" 1874.1,845.18 1875.35,845.18 1876.6,845.18 1877.85,845.18 1879.1,845.18 1880.35,845.181 1881.6,845.181 1882.85,845.181 1884.1,845.181 1885.34,845.181 \n",
" 1886.59,845.181 1887.84,845.181 1889.09,845.181 1890.34,845.181 1891.59,845.181 1892.84,845.181 1894.09,845.181 1895.34,845.182 1896.59,845.182 1897.83,845.182 \n",
" 1899.08,845.182 1900.33,845.182 1901.58,845.182 1902.83,845.182 1904.08,845.182 1905.33,845.182 1906.58,845.182 1907.83,845.182 1909.08,845.182 1910.33,845.182 \n",
" 1911.57,845.182 1912.82,845.182 1914.07,845.182 1915.32,845.182 1916.57,845.182 1917.82,845.182 1919.07,845.182 1920.32,845.182 1921.57,845.182 1922.82,845.182 \n",
" 1924.06,845.182 1925.31,845.182 1926.56,845.182 1927.81,845.182 1929.06,845.182 1930.31,845.182 1931.56,845.182 1932.81,845.182 1934.06,845.183 1935.31,845.183 \n",
" 1936.56,845.183 1937.8,845.183 1939.05,845.183 1940.3,845.183 1941.55,845.183 1942.8,845.183 1944.05,845.183 1945.3,845.183 1946.55,845.183 1947.8,845.183 \n",
" 1949.05,845.183 1950.29,845.183 1951.54,845.183 1952.79,845.183 1954.04,845.183 1955.29,845.183 1956.54,845.183 1957.79,845.183 1959.04,845.183 1960.29,845.183 \n",
" 1961.54,845.183 1962.78,845.183 1964.03,845.183 1965.28,845.183 1966.53,845.183 1967.78,845.183 1969.03,845.183 1970.28,845.183 1971.53,845.183 1972.78,845.183 \n",
" 1974.03,845.183 1975.28,845.183 1976.52,845.183 1977.77,845.183 1979.02,845.183 1980.27,845.183 1981.52,845.183 1982.77,845.183 1984.02,845.183 1985.27,845.183 \n",
" 1986.52,845.183 1987.77,845.183 1989.01,845.183 1990.26,845.183 1991.51,845.183 1992.76,845.183 1994.01,845.183 1995.26,845.183 1996.51,845.183 1997.76,845.183 \n",
" 1999.01,845.183 2000.26,845.183 2001.51,845.183 2002.75,845.183 2004,845.183 2005.25,845.183 2006.5,845.183 2007.75,845.183 2009,845.183 2010.25,845.183 \n",
" 2011.5,845.183 2012.75,845.183 2014,845.183 2015.24,845.183 2016.49,845.183 2017.74,845.183 2018.99,845.183 2020.24,845.183 2021.49,845.183 2022.74,845.183 \n",
" 2023.99,845.183 2025.24,845.183 2026.49,845.183 2027.74,845.183 2028.98,845.183 2030.23,845.183 2031.48,845.183 2032.73,845.183 2033.98,845.183 2035.23,845.183 \n",
" 2036.48,845.183 2037.73,845.183 2038.98,845.183 2040.23,845.183 2041.47,845.183 2042.72,845.183 2043.97,845.183 2045.22,845.183 2046.47,845.183 2047.72,845.183 \n",
" 2048.97,845.183 2050.22,845.183 2051.47,845.183 2052.72,845.183 2053.96,845.183 2055.21,845.183 2056.46,845.183 2057.71,845.183 2058.96,845.183 2060.21,845.183 \n",
" 2061.46,845.183 2062.71,845.183 2063.96,845.183 2065.21,845.183 2066.46,845.183 2067.7,845.183 2068.95,845.183 2070.2,845.183 2071.45,845.183 2072.7,845.183 \n",
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" 1137.17,833.577 1138.42,833.117 1139.67,832.663 1140.92,832.217 1142.16,831.779 1143.41,831.349 1144.66,830.928 1145.91,830.515 1147.16,830.112 1148.41,829.717 \n",
" 1149.66,829.332 1150.91,828.957 1152.16,828.592 1153.41,828.237 1154.65,827.893 1155.9,827.56 1157.15,827.238 1158.4,826.927 1159.65,826.627 1160.9,826.34 \n",
" 1162.15,826.064 1163.4,825.801 1164.65,825.549 1165.9,825.311 1167.15,825.085 1168.39,824.872 1169.64,824.672 1170.89,824.485 1172.14,824.312 1173.39,824.152 \n",
" 1174.64,824.006 1175.89,823.874 1177.14,823.755 1178.39,823.651 1179.64,823.56 1180.88,823.484 1182.13,823.422 1183.38,823.375 1184.63,823.342 1185.88,823.323 \n",
" 1187.13,823.319 1188.38,823.329 1189.63,823.354 1190.88,823.394 1192.13,823.448 1193.38,823.516 1194.62,823.599 1195.87,823.696 1197.12,823.808 1198.37,823.935 \n",
" 1199.62,824.075 1200.87,824.23 1202.12,824.399 1203.37,824.582 1204.62,824.779 1205.87,824.99 1207.11,825.215 1208.36,825.453 1209.61,825.705 1210.86,825.97 \n",
" 1212.11,826.248 1213.36,826.539 1214.61,826.843 1215.86,827.159 1217.11,827.488 1218.36,827.829 1219.61,828.181 1220.85,828.546 1222.1,828.922 1223.35,829.309 \n",
" 1224.6,829.707 1225.85,830.116 1227.1,830.536 1228.35,830.965 1229.6,831.404 1230.85,831.853 1232.1,832.311 1233.34,832.778 1234.59,833.254 1235.84,833.738 \n",
" 1237.09,834.23 1238.34,834.729 1239.59,835.236 1240.84,835.75 1242.09,836.27 1243.34,836.796 1244.59,837.329 1245.84,837.867 1247.08,838.41 1248.33,838.957 \n",
" 1249.58,839.509 1250.83,840.065 1252.08,840.625 1253.33,841.188 1254.58,841.753 1255.83,842.321 1257.08,842.891 1258.33,843.463 1259.57,844.035 1260.82,844.609 \n",
" 1262.07,845.183 1263.32,845.757 1264.57,846.33 1265.82,846.903 1267.07,847.475 1268.32,848.045 1269.57,848.613 1270.82,849.178 1272.06,849.741 1273.31,850.3 \n",
" 1274.56,850.856 1275.81,851.408 1277.06,851.956 1278.31,852.499 1279.56,853.037 1280.81,853.569 1282.06,854.096 1283.31,854.616 1284.56,855.13 1285.8,855.636 \n",
" 1287.05,856.136 1288.3,856.628 1289.55,857.112 1290.8,857.587 1292.05,858.054 1293.3,858.512 1294.55,858.961 1295.8,859.401 1297.05,859.83 1298.29,860.249 \n",
" 1299.54,860.658 1300.79,861.056 1302.04,861.444 1303.29,861.82 1304.54,862.184 1305.79,862.537 1307.04,862.878 1308.29,863.207 1309.54,863.523 1310.79,863.827 \n",
" 1312.03,864.118 1313.28,864.396 1314.53,864.661 1315.78,864.912 1317.03,865.151 1318.28,865.375 1319.53,865.586 1320.78,865.783 1322.03,865.966 1323.28,866.135 \n",
" 1324.52,866.29 1325.77,866.431 1327.02,866.557 1328.27,866.669 1329.52,866.767 1330.77,866.85 1332.02,866.918 1333.27,866.972 1334.52,867.011 1335.77,867.036 \n",
" 1337.02,867.047 1338.26,867.042 1339.51,867.024 1340.76,866.991 1342.01,866.943 1343.26,866.881 1344.51,866.805 1345.76,866.715 1347.01,866.61 1348.26,866.492 \n",
" 1349.51,866.36 1350.75,866.214 1352,866.054 1353.25,865.88 1354.5,865.694 1355.75,865.494 1357,865.281 1358.25,865.055 1359.5,864.816 1360.75,864.565 \n",
" 1362,864.301 1363.24,864.026 1364.49,863.738 1365.74,863.439 1366.99,863.128 1368.24,862.806 1369.49,862.472 1370.74,862.128 1371.99,861.773 1373.24,861.408 \n",
" 1374.49,861.033 1375.74,860.649 1376.98,860.254 1378.23,859.85 1379.48,859.438 1380.73,859.016 1381.98,858.586 1383.23,858.148 1384.48,857.702 1385.73,857.249 \n",
" 1386.98,856.788 1388.23,856.321 1389.47,855.846 1390.72,855.366 1391.97,854.879 1393.22,854.387 1394.47,853.889 1395.72,853.386 1396.97,852.878 1398.22,852.366 \n",
" 1399.47,851.849 1400.72,851.329 1401.97,850.805 1403.21,850.278 1404.46,849.748 1405.71,849.215 1406.96,848.68 1408.21,848.143 1409.46,847.605 1410.71,847.065 \n",
" 1411.96,846.524 1413.21,845.982 1414.46,845.44 1415.7,844.898 1416.95,844.356 1418.2,843.814 1419.45,843.273 1420.7,842.733 1421.95,842.195 1423.2,841.658 \n",
" 1424.45,841.122 1425.7,840.59 1426.95,840.059 1428.2,839.531 1429.44,839.006 1430.69,838.485 1431.94,837.966 1433.19,837.452 1434.44,836.941 1435.69,836.435 \n",
" 1436.94,835.933 1438.19,835.436 1439.44,834.944 1440.69,834.456 1441.93,833.975 1443.18,833.498 1444.43,833.027 1445.68,832.563 1446.93,832.104 1448.18,831.652 \n",
" 1449.43,831.206 1450.68,830.767 1451.93,830.334 1453.18,829.909 1454.42,829.49 1455.67,829.079 1456.92,828.675 1458.17,828.279 1459.42,827.891 1460.67,827.51 \n",
" 1461.92,827.137 1463.17,826.772 1464.42,826.416 1465.67,826.067 1466.92,825.727 1468.16,825.395 1469.41,825.072 1470.66,824.757 1471.91,824.451 1473.16,824.153 \n",
" 1474.41,823.865 1475.66,823.584 1476.91,823.313 1478.16,823.051 1479.41,822.797 1480.65,822.553 1481.9,822.317 1483.15,822.09 1484.4,821.872 1485.65,821.663 \n",
" 1486.9,821.463 1488.15,821.272 1489.4,821.09 1490.65,820.916 1491.9,820.752 1493.15,820.596 1494.39,820.45 1495.64,820.311 1496.89,820.182 1498.14,820.061 \n",
" 1499.39,819.949 1500.64,819.846 1501.89,819.751 1503.14,819.664 1504.39,819.586 1505.64,819.516 1506.88,819.454 1508.13,819.4 1509.38,819.355 1510.63,819.317 \n",
" 1511.88,819.287 1513.13,819.265 1514.38,819.251 1515.63,819.244 1516.88,819.245 1518.13,819.253 1519.38,819.268 1520.62,819.291 1521.87,819.32 1523.12,819.356 \n",
" 1524.37,819.4 1525.62,819.449 1526.87,819.506 1528.12,819.569 1529.37,819.638 1530.62,819.713 1531.87,819.795 1533.11,819.882 1534.36,819.975 1535.61,820.074 \n",
" 1536.86,820.178 1538.11,820.288 1539.36,820.403 1540.61,820.523 1541.86,820.648 1543.11,820.778 1544.36,820.913 1545.61,821.052 1546.85,821.196 1548.1,821.344 \n",
" 1549.35,821.496 1550.6,821.653 1551.85,821.813 1553.1,821.977 1554.35,822.144 1555.6,822.316 1556.85,822.49 1558.1,822.668 1559.34,822.849 1560.59,823.033 \n",
" 1561.84,823.22 1563.09,823.409 1564.34,823.601 1565.59,823.796 1566.84,823.993 1568.09,824.192 1569.34,824.393 1570.59,824.596 1571.83,824.801 1573.08,825.008 \n",
" 1574.33,825.216 1575.58,825.426 1576.83,825.637 1578.08,825.85 1579.33,826.063 1580.58,826.278 1581.83,826.494 1583.08,826.71 1584.33,826.927 1585.57,827.145 \n",
" 1586.82,827.364 1588.07,827.582 1589.32,827.802 1590.57,828.021 1591.82,828.24 1593.07,828.46 1594.32,828.68 1595.57,828.899 1596.82,829.118 1598.06,829.337 \n",
" 1599.31,829.556 1600.56,829.774 1601.81,829.991 1603.06,830.208 1604.31,830.424 1605.56,830.64 1606.81,830.855 1608.06,831.068 1609.31,831.281 1610.56,831.493 \n",
" 1611.8,831.704 1613.05,831.913 1614.3,832.122 1615.55,832.329 1616.8,832.535 1618.05,832.74 1619.3,832.943 1620.55,833.144 1621.8,833.345 1623.05,833.543 \n",
" 1624.29,833.741 1625.54,833.936 1626.79,834.13 1628.04,834.322 1629.29,834.513 1630.54,834.701 1631.79,834.888 1633.04,835.073 1634.29,835.257 1635.54,835.438 \n",
" 1636.79,835.617 1638.03,835.795 1639.28,835.971 1640.53,836.144 1641.78,836.316 1643.03,836.486 1644.28,836.654 1645.53,836.819 1646.78,836.983 1648.03,837.145 \n",
" 1649.28,837.304 1650.52,837.462 1651.77,837.617 1653.02,837.771 1654.27,837.922 1655.52,838.071 1656.77,838.219 1658.02,838.364 1659.27,838.507 1660.52,838.648 \n",
" 1661.77,838.787 1663.01,838.923 1664.26,839.058 1665.51,839.191 1666.76,839.322 1668.01,839.45 1669.26,839.577 1670.51,839.701 1671.76,839.824 1673.01,839.944 \n",
" 1674.26,840.063 1675.51,840.179 1676.75,840.294 1678,840.406 1679.25,840.517 1680.5,840.625 1681.75,840.732 1683,840.837 1684.25,840.94 1685.5,841.041 \n",
" 1686.75,841.14 1688,841.237 1689.24,841.333 1690.49,841.426 1691.74,841.518 1692.99,841.608 1694.24,841.697 1695.49,841.783 1696.74,841.868 1697.99,841.952 \n",
" 1699.24,842.033 1700.49,842.113 1701.74,842.191 1702.98,842.268 1704.23,842.343 1705.48,842.417 1706.73,842.488 1707.98,842.559 1709.23,842.628 1710.48,842.695 \n",
" 1711.73,842.761 1712.98,842.826 1714.23,842.889 1715.47,842.951 1716.72,843.011 1717.97,843.07 1719.22,843.127 1720.47,843.184 1721.72,843.239 1722.97,843.292 \n",
" 1724.22,843.345 1725.47,843.396 1726.72,843.446 1727.97,843.495 1729.21,843.543 1730.46,843.589 1731.71,843.635 1732.96,843.679 1734.21,843.722 1735.46,843.765 \n",
" 1736.71,843.806 1737.96,843.846 1739.21,843.885 1740.46,843.923 1741.7,843.96 1742.95,843.996 1744.2,844.032 1745.45,844.066 1746.7,844.1 1747.95,844.132 \n",
" 1749.2,844.164 1750.45,844.195 1751.7,844.225 1752.95,844.254 1754.19,844.283 1755.44,844.31 1756.69,844.337 1757.94,844.364 1759.19,844.389 1760.44,844.414 \n",
" 1761.69,844.438 1762.94,844.462 1764.19,844.485 1765.44,844.507 1766.69,844.528 1767.93,844.549 1769.18,844.57 1770.43,844.589 1771.68,844.609 1772.93,844.627 \n",
" 1774.18,844.645 1775.43,844.663 1776.68,844.68 1777.93,844.697 1779.18,844.713 1780.42,844.728 1781.67,844.743 1782.92,844.758 1784.17,844.772 1785.42,844.786 \n",
" 1786.67,844.8 1787.92,844.813 1789.17,844.825 1790.42,844.837 1791.67,844.849 1792.92,844.861 1794.16,844.872 1795.41,844.882 1796.66,844.893 1797.91,844.903 \n",
" 1799.16,844.913 1800.41,844.922 1801.66,844.931 1802.91,844.94 1804.16,844.949 1805.41,844.957 1806.65,844.965 1807.9,844.973 1809.15,844.98 1810.4,844.988 \n",
" 1811.65,844.995 1812.9,845.002 1814.15,845.008 1815.4,845.015 1816.65,845.021 1817.9,845.027 1819.15,845.032 1820.39,845.038 1821.64,845.043 1822.89,845.048 \n",
" 1824.14,845.053 1825.39,845.058 1826.64,845.063 1827.89,845.067 1829.14,845.072 1830.39,845.076 1831.64,845.08 1832.88,845.084 1834.13,845.088 1835.38,845.091 \n",
" 1836.63,845.095 1837.88,845.098 1839.13,845.101 1840.38,845.105 1841.63,845.108 1842.88,845.111 1844.13,845.113 1845.37,845.116 1846.62,845.119 1847.87,845.121 \n",
" 1849.12,845.124 1850.37,845.126 1851.62,845.128 1852.87,845.13 1854.12,845.133 1855.37,845.135 1856.62,845.136 1857.87,845.138 1859.11,845.14 1860.36,845.142 \n",
" 1861.61,845.144 1862.86,845.145 1864.11,845.147 1865.36,845.148 1866.61,845.15 1867.86,845.151 1869.11,845.152 1870.36,845.153 1871.6,845.155 1872.85,845.156 \n",
" 1874.1,845.157 1875.35,845.158 1876.6,845.159 1877.85,845.16 1879.1,845.161 1880.35,845.162 1881.6,845.163 1882.85,845.164 1884.1,845.165 1885.34,845.165 \n",
" 1886.59,845.166 1887.84,845.167 1889.09,845.167 1890.34,845.168 1891.59,845.169 1892.84,845.169 1894.09,845.17 1895.34,845.17 1896.59,845.171 1897.83,845.172 \n",
" 1899.08,845.172 1900.33,845.173 1901.58,845.173 1902.83,845.173 1904.08,845.174 1905.33,845.174 1906.58,845.175 1907.83,845.175 1909.08,845.175 1910.33,845.176 \n",
" 1911.57,845.176 1912.82,845.176 1914.07,845.177 1915.32,845.177 1916.57,845.177 1917.82,845.177 1919.07,845.178 1920.32,845.178 1921.57,845.178 1922.82,845.178 \n",
" 1924.06,845.179 1925.31,845.179 1926.56,845.179 1927.81,845.179 1929.06,845.179 1930.31,845.179 1931.56,845.18 1932.81,845.18 1934.06,845.18 1935.31,845.18 \n",
" 1936.56,845.18 1937.8,845.18 1939.05,845.18 1940.3,845.18 1941.55,845.181 1942.8,845.181 1944.05,845.181 1945.3,845.181 1946.55,845.181 1947.8,845.181 \n",
" 1949.05,845.181 1950.29,845.181 1951.54,845.181 1952.79,845.181 1954.04,845.181 1955.29,845.182 1956.54,845.182 1957.79,845.182 1959.04,845.182 1960.29,845.182 \n",
" 1961.54,845.182 1962.78,845.182 1964.03,845.182 1965.28,845.182 1966.53,845.182 1967.78,845.182 1969.03,845.182 1970.28,845.182 1971.53,845.182 1972.78,845.182 \n",
" 1974.03,845.182 1975.28,845.182 1976.52,845.182 1977.77,845.182 1979.02,845.182 1980.27,845.182 1981.52,845.182 1982.77,845.182 1984.02,845.182 1985.27,845.182 \n",
" 1986.52,845.182 1987.77,845.182 1989.01,845.182 1990.26,845.182 1991.51,845.183 1992.76,845.183 1994.01,845.183 1995.26,845.183 1996.51,845.183 1997.76,845.183 \n",
" 1999.01,845.183 2000.26,845.183 2001.51,845.183 2002.75,845.183 2004,845.183 2005.25,845.183 2006.5,845.183 2007.75,845.183 2009,845.183 2010.25,845.183 \n",
" 2011.5,845.183 2012.75,845.183 2014,845.183 2015.24,845.183 2016.49,845.183 2017.74,845.183 2018.99,845.183 2020.24,845.183 2021.49,845.183 2022.74,845.183 \n",
" 2023.99,845.183 2025.24,845.183 2026.49,845.183 2027.74,845.183 2028.98,845.183 2030.23,845.183 2031.48,845.183 2032.73,845.183 2033.98,845.183 2035.23,845.183 \n",
" 2036.48,845.183 2037.73,845.183 2038.98,845.183 2040.23,845.183 2041.47,845.183 2042.72,845.183 2043.97,845.183 2045.22,845.183 2046.47,845.183 2047.72,845.183 \n",
" 2048.97,845.183 2050.22,845.183 2051.47,845.183 2052.72,845.183 2053.96,845.183 2055.21,845.183 2056.46,845.183 2057.71,845.183 2058.96,845.183 2060.21,845.183 \n",
" 2061.46,845.183 2062.71,845.183 2063.96,845.183 2065.21,845.183 2066.46,845.183 2067.7,845.183 2068.95,845.183 2070.2,845.183 2071.45,845.183 2072.7,845.183 \n",
" 2073.95,845.183 2075.2,845.183 2076.45,845.183 2077.7,845.183 2078.95,845.183 2080.19,845.183 2081.44,845.183 2082.69,845.183 2083.94,845.183 2085.19,845.183 \n",
" 2086.44,845.183 2087.69,845.183 2088.94,845.183 2090.19,845.183 2091.44,845.183 2092.69,845.183 2093.93,845.183 2095.18,845.183 2096.43,845.183 2097.68,845.183 \n",
" 2098.93,845.183 2100.18,845.183 2101.43,845.183 2102.68,845.183 2103.93,845.183 2105.18,845.183 2106.42,845.183 2107.67,845.183 2108.92,845.183 2110.17,845.183 \n",
" 2111.42,845.183 2112.67,845.183 2113.92,845.183 2115.17,845.183 2116.42,845.183 2117.67,845.183 2118.92,845.183 2120.16,845.183 2121.41,845.183 2122.66,845.183 \n",
" 2123.91,845.183 2125.16,845.183 2126.41,845.183 2127.66,845.183 2128.91,845.183 2130.16,845.183 2131.41,845.183 2132.65,845.183 2133.9,845.183 2135.15,845.183 \n",
" 2136.4,845.183 2137.65,845.183 2138.9,845.183 2140.15,845.183 2141.4,845.183 2142.65,845.183 2143.9,845.183 2145.14,845.183 2146.39,845.183 2147.64,845.183 \n",
" 2148.89,845.183 2150.14,845.183 2151.39,845.183 2152.64,845.183 2153.89,845.183 2155.14,845.183 2156.39,845.183 2157.64,845.183 2158.88,845.183 2160.13,845.183 \n",
" 2161.38,845.183 2162.63,845.183 2163.88,845.183 2165.13,845.183 2166.38,845.183 2167.63,845.183 2168.88,845.183 2170.13,845.183 2171.37,845.183 2172.62,845.183 \n",
" 2173.87,845.183 2175.12,845.183 2176.37,845.183 2177.62,845.183 2178.87,845.183 2180.12,845.183 2181.37,845.183 2182.62,845.183 2183.87,845.183 2185.11,845.183 \n",
" 2186.36,845.183 2187.61,845.183 2188.86,845.183 2190.11,845.183 2191.36,845.183 2192.61,845.183 2193.86,845.183 2195.11,845.183 2196.36,845.183 2197.6,845.183 \n",
" 2198.85,845.183 2200.1,845.183 2201.35,845.183 2202.6,845.183 2203.85,845.183 2205.1,845.183 2206.35,845.183 2207.6,845.183 2208.85,845.183 2210.1,845.183 \n",
" 2211.34,845.183 2212.59,845.183 2213.84,845.183 2215.09,845.183 2216.34,845.183 2217.59,845.183 2218.84,845.183 2220.09,845.183 2221.34,845.183 2222.59,845.183 \n",
" 2223.83,845.183 2225.08,845.183 2226.33,845.183 2227.58,845.183 2228.83,845.183 2230.08,845.183 2231.33,845.183 2232.58,845.183 2233.83,845.183 2235.08,845.183 \n",
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" 1299.54,809.469 1300.79,810.83 1302.04,812.221 1303.29,813.642 1304.54,815.091 1305.79,816.566 1307.04,818.067 1308.29,819.592 1309.54,821.14 1310.79,822.709 \n",
" 1312.03,824.298 1313.28,825.905 1314.53,827.529 1315.78,829.169 1317.03,830.823 1318.28,832.49 1319.53,834.168 1320.78,835.856 1322.03,837.551 1323.28,839.254 \n",
" 1324.52,840.961 1325.77,842.673 1327.02,844.386 1328.27,846.1 1329.52,847.814 1330.77,849.525 1332.02,851.232 1333.27,852.934 1334.52,854.63 1335.77,856.317 \n",
" 1337.02,857.994 1338.26,859.661 1339.51,861.315 1340.76,862.955 1342.01,864.58 1343.26,866.188 1344.51,867.778 1345.76,869.349 1347.01,870.899 1348.26,872.427 \n",
" 1349.51,873.932 1350.75,875.412 1352,876.867 1353.25,878.295 1354.5,879.695 1355.75,881.066 1357,882.406 1358.25,883.715 1359.5,884.992 1360.75,886.235 \n",
" 1362,887.444 1363.24,888.618 1364.49,889.755 1365.74,890.855 1366.99,891.917 1368.24,892.941 1369.49,893.925 1370.74,894.869 1371.99,895.771 1373.24,896.633 \n",
" 1374.49,897.452 1375.74,898.228 1376.98,898.96 1378.23,899.649 1379.48,900.294 1380.73,900.894 1381.98,901.449 1383.23,901.958 1384.48,902.422 1385.73,902.839 \n",
" 1386.98,903.211 1388.23,903.536 1389.47,903.814 1390.72,904.046 1391.97,904.231 1393.22,904.369 1394.47,904.46 1395.72,904.505 1396.97,904.503 1398.22,904.455 \n",
" 1399.47,904.361 1400.72,904.22 1401.97,904.033 1403.21,903.801 1404.46,903.524 1405.71,903.202 1406.96,902.835 1408.21,902.424 1409.46,901.969 1410.71,901.471 \n",
" 1411.96,900.931 1413.21,900.348 1414.46,899.724 1415.7,899.059 1416.95,898.353 1418.2,897.608 1419.45,896.824 1420.7,896.001 1421.95,895.141 1423.2,894.245 \n",
" 1424.45,893.312 1425.7,892.344 1426.95,891.341 1428.2,890.306 1429.44,889.237 1430.69,888.137 1431.94,887.006 1433.19,885.845 1434.44,884.655 1435.69,883.437 \n",
" 1436.94,882.193 1438.19,880.922 1439.44,879.626 1440.69,878.305 1441.93,876.962 1443.18,875.597 1444.43,874.211 1445.68,872.805 1446.93,871.38 1448.18,869.937 \n",
" 1449.43,868.478 1450.68,867.003 1451.93,865.513 1453.18,864.009 1454.42,862.493 1455.67,860.965 1456.92,859.428 1458.17,857.88 1459.42,856.325 1460.67,854.762 \n",
" 1461.92,853.193 1463.17,851.618 1464.42,850.04 1465.67,848.459 1466.92,846.875 1468.16,845.291 1469.41,843.706 1470.66,842.122 1471.91,840.54 1473.16,838.961 \n",
" 1474.41,837.386 1475.66,835.816 1476.91,834.251 1478.16,832.693 1479.41,831.142 1480.65,829.6 1481.9,828.067 1483.15,826.544 1484.4,825.033 1485.65,823.532 \n",
" 1486.9,822.045 1488.15,820.57 1489.4,819.11 1490.65,817.665 1491.9,816.235 1493.15,814.821 1494.39,813.425 1495.64,812.046 1496.89,810.685 1498.14,809.343 \n",
" 1499.39,808.02 1500.64,806.718 1501.89,805.436 1503.14,804.175 1504.39,802.936 1505.64,801.719 1506.88,800.525 1508.13,799.353 1509.38,798.205 1510.63,797.081 \n",
" 1511.88,795.981 1513.13,794.906 1514.38,793.856 1515.63,792.831 1516.88,791.831 1518.13,790.857 1519.38,789.91 1520.62,788.988 1521.87,788.094 1523.12,787.225 \n",
" 1524.37,786.384 1525.62,785.57 1526.87,784.782 1528.12,784.022 1529.37,783.29 1530.62,782.584 1531.87,781.906 1533.11,781.256 1534.36,780.632 1535.61,780.037 \n",
" 1536.86,779.468 1538.11,778.927 1539.36,778.414 1540.61,777.927 1541.86,777.468 1543.11,777.035 1544.36,776.63 1545.61,776.251 1546.85,775.898 1548.1,775.572 \n",
" 1549.35,775.272 1550.6,774.998 1551.85,774.75 1553.1,774.527 1554.35,774.329 1555.6,774.157 1556.85,774.009 1558.1,773.885 1559.34,773.786 1560.59,773.71 \n",
" 1561.84,773.658 1563.09,773.629 1564.34,773.623 1565.59,773.639 1566.84,773.678 1568.09,773.738 1569.34,773.82 1570.59,773.923 1571.83,774.046 1573.08,774.19 \n",
" 1574.33,774.353 1575.58,774.536 1576.83,774.739 1578.08,774.959 1579.33,775.198 1580.58,775.455 1581.83,775.73 1583.08,776.021 1584.33,776.329 1585.57,776.653 \n",
" 1586.82,776.993 1588.07,777.348 1589.32,777.717 1590.57,778.102 1591.82,778.5 1593.07,778.912 1594.32,779.336 1595.57,779.774 1596.82,780.224 1598.06,780.685 \n",
" 1599.31,781.158 1600.56,781.642 1601.81,782.136 1603.06,782.641 1604.31,783.155 1605.56,783.679 1606.81,784.211 1608.06,784.752 1609.31,785.3 1610.56,785.857 \n",
" 1611.8,786.42 1613.05,786.991 1614.3,787.567 1615.55,788.15 1616.8,788.739 1618.05,789.332 1619.3,789.931 1620.55,790.534 1621.8,791.142 1623.05,791.753 \n",
" 1624.29,792.368 1625.54,792.985 1626.79,793.606 1628.04,794.229 1629.29,794.854 1630.54,795.481 1631.79,796.109 1633.04,796.739 1634.29,797.369 1635.54,798 \n",
" 1636.79,798.631 1638.03,799.263 1639.28,799.894 1640.53,800.524 1641.78,801.154 1643.03,801.782 1644.28,802.41 1645.53,803.035 1646.78,803.659 1648.03,804.281 \n",
" 1649.28,804.901 1650.52,805.518 1651.77,806.133 1653.02,806.744 1654.27,807.353 1655.52,807.958 1656.77,808.56 1658.02,809.158 1659.27,809.753 1660.52,810.344 \n",
" 1661.77,810.93 1663.01,811.512 1664.26,812.09 1665.51,812.663 1666.76,813.232 1668.01,813.796 1669.26,814.355 1670.51,814.909 1671.76,815.458 1673.01,816.001 \n",
" 1674.26,816.54 1675.51,817.073 1676.75,817.6 1678,818.122 1679.25,818.638 1680.5,819.148 1681.75,819.653 1683,820.152 1684.25,820.645 1685.5,821.132 \n",
" 1686.75,821.613 1688,822.088 1689.24,822.556 1690.49,823.019 1691.74,823.476 1692.99,823.926 1694.24,824.371 1695.49,824.809 1696.74,825.241 1697.99,825.666 \n",
" 1699.24,826.086 1700.49,826.499 1701.74,826.906 1702.98,827.307 1704.23,827.702 1705.48,828.091 1706.73,828.473 1707.98,828.849 1709.23,829.219 1710.48,829.583 \n",
" 1711.73,829.941 1712.98,830.293 1714.23,830.639 1715.47,830.979 1716.72,831.313 1717.97,831.641 1719.22,831.964 1720.47,832.28 1721.72,832.591 1722.97,832.896 \n",
" 1724.22,833.195 1725.47,833.489 1726.72,833.777 1727.97,834.06 1729.21,834.337 1730.46,834.609 1731.71,834.875 1732.96,835.136 1734.21,835.392 1735.46,835.643 \n",
" 1736.71,835.888 1737.96,836.129 1739.21,836.364 1740.46,836.595 1741.7,836.821 1742.95,837.041 1744.2,837.258 1745.45,837.469 1746.7,837.676 1747.95,837.878 \n",
" 1749.2,838.076 1750.45,838.27 1751.7,838.459 1752.95,838.644 1754.19,838.824 1755.44,839.001 1756.69,839.173 1757.94,839.341 1759.19,839.506 1760.44,839.666 \n",
" 1761.69,839.823 1762.94,839.976 1764.19,840.125 1765.44,840.271 1766.69,840.413 1767.93,840.552 1769.18,840.687 1770.43,840.819 1771.68,840.947 1772.93,841.072 \n",
" 1774.18,841.194 1775.43,841.313 1776.68,841.429 1777.93,841.542 1779.18,841.652 1780.42,841.759 1781.67,841.864 1782.92,841.965 1784.17,842.064 1785.42,842.16 \n",
" 1786.67,842.254 1787.92,842.345 1789.17,842.434 1790.42,842.52 1791.67,842.604 1792.92,842.685 1794.16,842.764 1795.41,842.841 1796.66,842.916 1797.91,842.989 \n",
" 1799.16,843.06 1800.41,843.129 1801.66,843.195 1802.91,843.26 1804.16,843.323 1805.41,843.384 1806.65,843.443 1807.9,843.501 1809.15,843.557 1810.4,843.611 \n",
" 1811.65,843.664 1812.9,843.715 1814.15,843.764 1815.4,843.812 1816.65,843.859 1817.9,843.904 1819.15,843.947 1820.39,843.99 1821.64,844.031 1822.89,844.071 \n",
" 1824.14,844.109 1825.39,844.147 1826.64,844.183 1827.89,844.218 1829.14,844.252 1830.39,844.285 1831.64,844.316 1832.88,844.347 1834.13,844.377 1835.38,844.406 \n",
" 1836.63,844.434 1837.88,844.461 1839.13,844.487 1840.38,844.512 1841.63,844.536 1842.88,844.56 1844.13,844.583 1845.37,844.605 1846.62,844.626 1847.87,844.647 \n",
" 1849.12,844.667 1850.37,844.686 1851.62,844.704 1852.87,844.722 1854.12,844.739 1855.37,844.756 1856.62,844.772 1857.87,844.788 1859.11,844.803 1860.36,844.817 \n",
" 1861.61,844.831 1862.86,844.845 1864.11,844.858 1865.36,844.87 1866.61,844.882 1867.86,844.894 1869.11,844.905 1870.36,844.916 1871.6,844.927 1872.85,844.937 \n",
" 1874.1,844.946 1875.35,844.956 1876.6,844.965 1877.85,844.973 1879.1,844.982 1880.35,844.99 1881.6,844.998 1882.85,845.005 1884.1,845.012 1885.34,845.019 \n",
" 1886.59,845.026 1887.84,845.032 1889.09,845.038 1890.34,845.044 1891.59,845.05 1892.84,845.055 1894.09,845.061 1895.34,845.066 1896.59,845.07 1897.83,845.075 \n",
" 1899.08,845.08 1900.33,845.084 1901.58,845.088 1902.83,845.092 1904.08,845.096 1905.33,845.1 1906.58,845.103 1907.83,845.106 1909.08,845.11 1910.33,845.113 \n",
" 1911.57,845.116 1912.82,845.119 1914.07,845.121 1915.32,845.124 1916.57,845.127 1917.82,845.129 1919.07,845.131 1920.32,845.134 1921.57,845.136 1922.82,845.138 \n",
" 1924.06,845.14 1925.31,845.142 1926.56,845.144 1927.81,845.145 1929.06,845.147 1930.31,845.149 1931.56,845.15 1932.81,845.152 1934.06,845.153 1935.31,845.154 \n",
" 1936.56,845.156 1937.8,845.157 1939.05,845.158 1940.3,845.159 1941.55,845.16 1942.8,845.161 1944.05,845.162 1945.3,845.163 1946.55,845.164 1947.8,845.165 \n",
" 1949.05,845.166 1950.29,845.167 1951.54,845.167 1952.79,845.168 1954.04,845.169 1955.29,845.169 1956.54,845.17 1957.79,845.171 1959.04,845.171 1960.29,845.172 \n",
" 1961.54,845.172 1962.78,845.173 1964.03,845.173 1965.28,845.174 1966.53,845.174 1967.78,845.175 1969.03,845.175 1970.28,845.175 1971.53,845.176 1972.78,845.176 \n",
" 1974.03,845.176 1975.28,845.177 1976.52,845.177 1977.77,845.177 1979.02,845.177 1980.27,845.178 1981.52,845.178 1982.77,845.178 1984.02,845.178 1985.27,845.179 \n",
" 1986.52,845.179 1987.77,845.179 1989.01,845.179 1990.26,845.179 1991.51,845.18 1992.76,845.18 1994.01,845.18 1995.26,845.18 1996.51,845.18 1997.76,845.18 \n",
" 1999.01,845.18 2000.26,845.181 2001.51,845.181 2002.75,845.181 2004,845.181 2005.25,845.181 2006.5,845.181 2007.75,845.181 2009,845.181 2010.25,845.181 \n",
" 2011.5,845.181 2012.75,845.181 2014,845.182 2015.24,845.182 2016.49,845.182 2017.74,845.182 2018.99,845.182 2020.24,845.182 2021.49,845.182 2022.74,845.182 \n",
" 2023.99,845.182 2025.24,845.182 2026.49,845.182 2027.74,845.182 2028.98,845.182 2030.23,845.182 2031.48,845.182 2032.73,845.182 2033.98,845.182 2035.23,845.182 \n",
" 2036.48,845.182 2037.73,845.182 2038.98,845.182 2040.23,845.182 2041.47,845.182 2042.72,845.182 2043.97,845.182 2045.22,845.182 2046.47,845.182 2047.72,845.183 \n",
" 2048.97,845.183 2050.22,845.183 2051.47,845.183 2052.72,845.183 2053.96,845.183 2055.21,845.183 2056.46,845.183 2057.71,845.183 2058.96,845.183 2060.21,845.183 \n",
" 2061.46,845.183 2062.71,845.183 2063.96,845.183 2065.21,845.183 2066.46,845.183 2067.7,845.183 2068.95,845.183 2070.2,845.183 2071.45,845.183 2072.7,845.183 \n",
" 2073.95,845.183 2075.2,845.183 2076.45,845.183 2077.7,845.183 2078.95,845.183 2080.19,845.183 2081.44,845.183 2082.69,845.183 2083.94,845.183 2085.19,845.183 \n",
" 2086.44,845.183 2087.69,845.183 2088.94,845.183 2090.19,845.183 2091.44,845.183 2092.69,845.183 2093.93,845.183 2095.18,845.183 2096.43,845.183 2097.68,845.183 \n",
" 2098.93,845.183 2100.18,845.183 2101.43,845.183 2102.68,845.183 2103.93,845.183 2105.18,845.183 2106.42,845.183 2107.67,845.183 2108.92,845.183 2110.17,845.183 \n",
" 2111.42,845.183 2112.67,845.183 2113.92,845.183 2115.17,845.183 2116.42,845.183 2117.67,845.183 2118.92,845.183 2120.16,845.183 2121.41,845.183 2122.66,845.183 \n",
" 2123.91,845.183 2125.16,845.183 2126.41,845.183 2127.66,845.183 2128.91,845.183 2130.16,845.183 2131.41,845.183 2132.65,845.183 2133.9,845.183 2135.15,845.183 \n",
" 2136.4,845.183 2137.65,845.183 2138.9,845.183 2140.15,845.183 2141.4,845.183 2142.65,845.183 2143.9,845.183 2145.14,845.183 2146.39,845.183 2147.64,845.183 \n",
" 2148.89,845.183 2150.14,845.183 2151.39,845.183 2152.64,845.183 2153.89,845.183 2155.14,845.183 2156.39,845.183 2157.64,845.183 2158.88,845.183 2160.13,845.183 \n",
" 2161.38,845.183 2162.63,845.183 2163.88,845.183 2165.13,845.183 2166.38,845.183 2167.63,845.183 2168.88,845.183 2170.13,845.183 2171.37,845.183 2172.62,845.183 \n",
" 2173.87,845.183 2175.12,845.183 2176.37,845.183 2177.62,845.183 2178.87,845.183 2180.12,845.183 2181.37,845.183 2182.62,845.183 2183.87,845.183 2185.11,845.183 \n",
" 2186.36,845.183 2187.61,845.183 2188.86,845.183 2190.11,845.183 2191.36,845.183 2192.61,845.183 2193.86,845.183 2195.11,845.183 2196.36,845.183 2197.6,845.183 \n",
" 2198.85,845.183 2200.1,845.183 2201.35,845.183 2202.6,845.183 2203.85,845.183 2205.1,845.183 2206.35,845.183 2207.6,845.183 2208.85,845.183 2210.1,845.183 \n",
" 2211.34,845.183 2212.59,845.183 2213.84,845.183 2215.09,845.183 2216.34,845.183 2217.59,845.183 2218.84,845.183 2220.09,845.183 2221.34,845.183 2222.59,845.183 \n",
" 2223.83,845.183 2225.08,845.183 2226.33,845.183 2227.58,845.183 2228.83,845.183 2230.08,845.183 2231.33,845.183 2232.58,845.183 2233.83,845.183 2235.08,845.183 \n",
" 2236.33,845.183 2237.57,845.183 2238.82,845.183 2240.07,845.183 2241.32,845.183 2242.57,845.183 2243.82,845.183 2245.07,845.183 2246.32,845.183 2247.57,845.183 \n",
" 2248.82,845.183 2250.06,845.183 2251.31,845.183 2252.56,845.183 2253.81,845.183 2255.06,845.183 2256.31,845.183 2257.56,845.183 2258.81,845.183 2260.06,845.183 \n",
" 2261.31,845.183 \n",
" \"/>\n",
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" 275.33,845.183 276.579,845.183 277.828,845.183 279.077,845.183 280.326,845.183 281.575,845.183 282.824,845.183 284.073,845.183 285.322,845.183 286.571,845.183 \n",
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" 387.743,845.183 388.992,845.183 390.242,845.183 391.491,845.183 392.74,845.183 393.989,845.183 395.238,845.183 396.487,845.183 397.736,845.183 398.985,845.183 \n",
" 400.234,845.183 401.483,845.183 402.732,845.183 403.981,845.183 405.23,845.183 406.479,845.183 407.728,845.183 408.977,845.183 410.226,845.183 411.475,845.183 \n",
" 412.724,845.183 413.973,845.183 415.222,845.183 416.471,845.183 417.72,845.183 418.969,845.183 420.219,845.183 421.468,845.183 422.717,845.183 423.966,845.183 \n",
" 425.215,845.183 426.464,845.183 427.713,845.183 428.962,845.183 430.211,845.183 431.46,845.183 432.709,845.183 433.958,845.183 435.207,845.183 436.456,845.183 \n",
" 437.705,845.183 438.954,845.183 440.203,845.183 441.452,845.183 442.701,845.184 443.95,845.184 445.199,845.184 446.448,845.184 447.697,845.184 448.946,845.184 \n",
" 450.196,845.184 451.445,845.184 452.694,845.184 453.943,845.184 455.192,845.184 456.441,845.184 457.69,845.184 458.939,845.184 460.188,845.184 461.437,845.185 \n",
" 462.686,845.185 463.935,845.185 465.184,845.185 466.433,845.185 467.682,845.185 468.931,845.185 470.18,845.185 471.429,845.186 472.678,845.186 473.927,845.186 \n",
" 475.176,845.186 476.425,845.186 477.674,845.186 478.923,845.187 480.173,845.187 481.422,845.187 482.671,845.187 483.92,845.187 485.169,845.188 486.418,845.188 \n",
" 487.667,845.188 488.916,845.189 490.165,845.189 491.414,845.189 492.663,845.19 493.912,845.19 495.161,845.19 496.41,845.191 497.659,845.191 498.908,845.192 \n",
" 500.157,845.192 501.406,845.193 502.655,845.193 503.904,845.194 505.153,845.194 506.402,845.195 507.651,845.196 508.9,845.196 510.15,845.197 511.399,845.198 \n",
" 512.648,845.198 513.897,845.199 515.146,845.2 516.395,845.201 517.644,845.202 518.893,845.203 520.142,845.204 521.391,845.205 522.64,845.206 523.889,845.207 \n",
" 525.138,845.209 526.387,845.21 527.636,845.211 528.885,845.213 530.134,845.214 531.383,845.216 532.632,845.218 533.881,845.22 535.13,845.221 536.379,845.223 \n",
" 537.628,845.225 538.877,845.227 540.127,845.23 541.376,845.232 542.625,845.234 543.874,845.237 545.123,845.24 546.372,845.243 547.621,845.245 548.87,845.249 \n",
" 550.119,845.252 551.368,845.255 552.617,845.259 553.866,845.262 555.115,845.266 556.364,845.27 557.613,845.274 558.862,845.279 560.111,845.283 561.36,845.288 \n",
" 562.609,845.293 563.858,845.298 565.107,845.304 566.356,845.31 567.605,845.315 568.854,845.322 570.104,845.328 571.353,845.335 572.602,845.342 573.851,845.35 \n",
" 575.1,845.357 576.349,845.365 577.598,845.374 578.847,845.382 580.096,845.392 581.345,845.401 582.594,845.411 583.843,845.422 585.092,845.432 586.341,845.444 \n",
" 587.59,845.455 588.839,845.468 590.088,845.48 591.337,845.494 592.586,845.508 593.835,845.522 595.084,845.537 596.333,845.553 597.582,845.569 598.831,845.586 \n",
" 600.081,845.604 601.33,845.622 602.579,845.641 603.828,845.661 605.077,845.682 606.326,845.703 607.575,845.725 608.824,845.749 610.073,845.773 611.322,845.798 \n",
" 612.571,845.824 613.82,845.851 615.069,845.88 616.318,845.909 617.567,845.94 618.816,845.971 620.065,846.004 621.314,846.038 622.563,846.074 623.812,846.111 \n",
" 625.061,846.149 626.31,846.189 627.559,846.23 628.808,846.272 630.058,846.317 631.307,846.363 632.556,846.411 633.805,846.46 635.054,846.511 636.303,846.564 \n",
" 637.552,846.62 638.801,846.677 640.05,846.736 641.299,846.797 642.548,846.861 643.797,846.927 645.046,846.995 646.295,847.066 647.544,847.139 648.793,847.215 \n",
" 650.042,847.293 651.291,847.374 652.54,847.458 653.789,847.545 655.038,847.635 656.287,847.728 657.536,847.824 658.785,847.924 660.035,848.026 661.284,848.133 \n",
" 662.533,848.243 663.782,848.356 665.031,848.474 666.28,848.595 667.529,848.72 668.778,848.85 670.027,848.983 671.276,849.121 672.525,849.264 673.774,849.411 \n",
" 675.023,849.563 676.272,849.719 677.521,849.881 678.77,850.048 680.019,850.22 681.268,850.397 682.517,850.58 683.766,850.769 685.015,850.963 686.264,851.164 \n",
" 687.513,851.37 688.762,851.583 690.012,851.803 691.261,852.029 692.51,852.261 693.759,852.501 695.008,852.748 696.257,853.002 697.506,853.263 698.755,853.532 \n",
" 700.004,853.809 701.253,854.094 702.502,854.387 703.751,854.688 705,854.998 706.249,855.317 707.498,855.644 708.747,855.981 709.996,856.327 711.245,856.682 \n",
" 712.494,857.048 713.743,857.423 714.992,857.808 716.241,858.204 717.49,858.61 718.739,859.027 719.989,859.455 721.238,859.894 722.487,860.344 723.736,860.806 \n",
" 724.985,861.28 726.234,861.766 727.483,862.264 728.732,862.775 729.981,863.298 731.23,863.835 732.479,864.384 733.728,864.947 734.977,865.524 736.226,866.114 \n",
" 737.475,866.719 738.724,867.338 739.973,867.971 741.222,868.619 742.471,869.282 743.72,869.96 744.969,870.654 746.218,871.363 747.467,872.089 748.716,872.83 \n",
" 749.966,873.587 751.215,874.361 752.464,875.152 753.713,875.96 754.962,876.785 756.211,877.627 757.46,878.486 758.709,879.364 759.958,880.259 761.207,881.172 \n",
" 762.456,882.104 763.705,883.054 764.954,884.023 766.203,885.011 767.452,886.017 768.701,887.043 769.95,888.088 771.199,889.152 772.448,890.236 773.697,891.339 \n",
" 774.946,892.463 776.195,893.606 777.444,894.769 778.693,895.952 779.943,897.156 781.192,898.38 782.441,899.624 783.69,900.888 784.939,902.173 786.188,903.479 \n",
" 787.437,904.805 788.686,906.151 789.935,907.518 791.184,908.906 792.433,910.314 793.682,911.742 794.931,913.191 796.18,914.66 797.429,916.149 798.678,917.658 \n",
" 799.927,919.188 801.176,920.737 802.425,922.306 803.674,923.895 804.923,925.503 806.172,927.131 807.421,928.777 808.67,930.442 809.92,932.126 811.169,933.828 \n",
" 812.418,935.548 813.667,937.286 814.916,939.041 816.165,940.814 817.414,942.603 818.663,944.408 819.912,946.229 821.161,948.066 822.41,949.917 823.659,951.783 \n",
" 824.908,953.664 826.157,955.557 827.406,957.464 828.655,959.384 829.904,961.315 831.153,963.257 832.402,965.21 833.651,967.174 834.9,969.146 836.149,971.127 \n",
" 837.398,973.116 838.647,975.112 839.897,977.115 841.146,979.123 842.395,981.136 843.644,983.153 844.893,985.173 846.142,987.195 847.391,989.218 848.64,991.242 \n",
" 849.889,993.265 851.138,995.287 852.387,997.305 853.636,999.321 854.885,1001.33 856.134,1003.34 857.383,1005.33 858.632,1007.32 859.881,1009.3 861.13,1011.27 \n",
" 862.379,1013.23 863.628,1015.18 864.877,1017.11 866.126,1019.03 867.375,1020.93 868.624,1022.81 869.874,1024.67 871.123,1026.51 872.372,1028.33 873.621,1030.13 \n",
" 874.87,1031.9 876.119,1033.65 877.368,1035.37 878.617,1037.06 879.866,1038.72 881.115,1040.35 882.364,1041.95 883.613,1043.51 884.862,1045.03 886.111,1046.52 \n",
" 887.36,1047.97 888.609,1049.38 889.858,1050.74 891.107,1052.06 892.356,1053.34 893.605,1054.57 894.854,1055.75 896.103,1056.89 897.352,1057.97 898.601,1059 \n",
" 899.851,1059.97 901.1,1060.89 902.349,1061.75 903.598,1062.56 904.847,1063.3 906.096,1063.98 907.345,1064.6 908.594,1065.16 909.843,1065.65 911.092,1066.07 \n",
" 912.341,1066.42 913.59,1066.7 914.839,1066.92 916.088,1067.06 917.337,1067.12 918.586,1067.11 919.835,1067.03 921.084,1066.86 922.333,1066.62 923.582,1066.3 \n",
" 924.831,1065.9 926.08,1065.41 927.329,1064.85 928.578,1064.2 929.828,1063.46 931.077,1062.64 932.326,1061.73 933.575,1060.74 934.824,1059.65 936.073,1058.48 \n",
" 937.322,1057.22 938.571,1055.87 939.82,1054.43 941.069,1052.89 942.318,1051.27 943.567,1049.55 944.816,1047.75 946.065,1045.85 947.314,1043.86 948.563,1041.77 \n",
" 949.812,1039.6 951.061,1037.33 952.31,1034.97 953.559,1032.51 954.808,1029.97 956.057,1027.33 957.306,1024.6 958.555,1021.79 959.805,1018.88 961.054,1015.88 \n",
" 962.303,1012.8 963.552,1009.62 964.801,1006.36 966.05,1003.02 967.299,999.584 968.548,996.069 969.797,992.471 971.046,988.792 972.295,985.033 973.544,981.195 \n",
" 974.793,977.28 976.042,973.29 977.291,969.226 978.54,965.09 979.789,960.884 981.038,956.609 982.287,952.269 983.536,947.865 984.785,943.398 986.034,938.872 \n",
" 987.283,934.289 988.532,929.651 989.781,924.96 991.031,920.22 992.28,915.432 993.529,910.6 994.778,905.727 996.027,900.814 997.276,895.865 998.525,890.884 \n",
" 999.774,885.872 1001.02,880.834 1002.27,875.772 1003.52,870.69 1004.77,865.59 1006.02,860.477 1007.27,855.354 1008.52,850.223 1009.77,845.089 1011.02,839.955 \n",
" 1012.26,834.825 1013.51,829.702 1014.76,824.589 1016.01,819.492 1017.26,814.412 1018.51,809.355 1019.76,804.324 1021.01,799.322 1022.26,794.353 1023.51,789.422 \n",
" 1024.75,784.531 1026,779.686 1027.25,774.889 1028.5,770.144 1029.75,765.456 1031,760.828 1032.25,756.264 1033.5,751.768 1034.75,747.343 1036,742.993 \n",
" 1037.25,738.722 1038.49,734.534 1039.74,730.432 1040.99,726.42 1042.24,722.502 1043.49,718.68 1044.74,714.959 1045.99,711.341 1047.24,707.831 1048.49,704.431 \n",
" 1049.74,701.145 1050.98,697.976 1052.23,694.926 1053.48,691.999 1054.73,689.199 1055.98,686.526 1057.23,683.985 1058.48,681.578 1059.73,679.308 1060.98,677.176 \n",
" 1062.23,675.186 1063.47,673.339 1064.72,671.638 1065.97,670.084 1067.22,668.68 1068.47,667.427 1069.72,666.326 1070.97,665.38 1072.22,664.59 1073.47,663.957 \n",
" 1074.72,663.481 1075.97,663.165 1077.21,663.008 1078.46,663.012 1079.71,663.177 1080.96,663.504 1082.21,663.991 1083.46,664.641 1084.71,665.452 1085.96,666.425 \n",
" 1087.21,667.559 1088.46,668.854 1089.7,670.308 1090.95,671.921 1092.2,673.693 1093.45,675.621 1094.7,677.705 1095.95,679.943 1097.2,682.333 1098.45,684.875 \n",
" 1099.7,687.565 1100.95,690.402 1102.2,693.383 1103.44,696.507 1104.69,699.77 1105.94,703.169 1107.19,706.703 1108.44,710.368 1109.69,714.161 1110.94,718.078 \n",
" 1112.19,722.117 1113.44,726.273 1114.69,730.543 1115.93,734.924 1117.18,739.41 1118.43,743.999 1119.68,748.685 1120.93,753.465 1122.18,758.335 1123.43,763.289 \n",
" 1124.68,768.322 1125.93,773.432 1127.18,778.611 1128.43,783.856 1129.67,789.161 1130.92,794.522 1132.17,799.933 1133.42,805.389 1134.67,810.884 1135.92,816.414 \n",
" 1137.17,821.972 1138.42,827.553 1139.67,833.152 1140.92,838.763 1142.16,844.381 1143.41,849.999 1144.66,855.613 1145.91,861.215 1147.16,866.802 1148.41,872.367 \n",
" 1149.66,877.904 1150.91,883.408 1152.16,888.872 1153.41,894.292 1154.65,899.662 1155.9,904.976 1157.15,910.229 1158.4,915.414 1159.65,920.527 1160.9,925.562 \n",
" 1162.15,930.514 1163.4,935.378 1164.65,940.148 1165.9,944.82 1167.15,949.387 1168.39,953.847 1169.64,958.192 1170.89,962.42 1172.14,966.525 1173.39,970.503 \n",
" 1174.64,974.349 1175.89,978.059 1177.14,981.63 1178.39,985.057 1179.64,988.336 1180.88,991.464 1182.13,994.438 1183.38,997.253 1184.63,999.907 1185.88,1002.4 \n",
" 1187.13,1004.72 1188.38,1006.87 1189.63,1008.85 1190.88,1010.66 1192.13,1012.29 1193.38,1013.74 1194.62,1015.01 1195.87,1016.1 1197.12,1017.01 1198.37,1017.73 \n",
" 1199.62,1018.26 1200.87,1018.61 1202.12,1018.78 1203.37,1018.75 1204.62,1018.54 1205.87,1018.15 1207.11,1017.56 1208.36,1016.79 1209.61,1015.84 1210.86,1014.7 \n",
" 1212.11,1013.37 1213.36,1011.86 1214.61,1010.18 1215.86,1008.31 1217.11,1006.27 1218.36,1004.05 1219.61,1001.66 1220.85,999.094 1222.1,996.364 1223.35,993.47 \n",
" 1224.6,990.414 1225.85,987.2 1227.1,983.83 1228.35,980.31 1229.6,976.641 1230.85,972.829 1232.1,968.877 1233.34,964.79 1234.59,960.572 1235.84,956.228 \n",
" 1237.09,951.762 1238.34,947.179 1239.59,942.484 1240.84,937.683 1242.09,932.78 1243.34,927.781 1244.59,922.692 1245.84,917.517 1247.08,912.263 1248.33,906.935 \n",
" 1249.58,901.54 1250.83,896.082 1252.08,890.568 1253.33,885.005 1254.58,879.398 1255.83,873.753 1257.08,868.077 1258.33,862.375 1259.57,856.655 1260.82,850.922 \n",
" 1262.07,845.183 1263.32,839.444 1264.57,833.711 1265.82,827.99 1267.07,822.289 1268.32,816.613 1269.57,810.968 1270.82,805.361 1272.06,799.797 1273.31,794.284 \n",
" 1274.56,788.826 1275.81,783.43 1277.06,778.103 1278.31,772.848 1279.56,767.674 1280.81,762.584 1282.06,757.585 1283.31,752.682 1284.56,747.881 1285.8,743.187 \n",
" 1287.05,738.604 1288.3,734.138 1289.55,729.793 1290.8,725.575 1292.05,721.488 1293.3,717.537 1294.55,713.724 1295.8,710.056 1297.05,706.535 1298.29,703.166 \n",
" 1299.54,699.951 1300.79,696.896 1302.04,694.001 1303.29,691.272 1304.54,688.71 1305.79,686.318 1307.04,684.099 1308.29,682.056 1309.54,680.189 1310.79,678.502 \n",
" 1312.03,676.995 1313.28,675.671 1314.53,674.53 1315.78,673.574 1317.03,672.803 1318.28,672.219 1319.53,671.821 1320.78,671.611 1322.03,671.588 1323.28,671.751 \n",
" 1324.52,672.101 1325.77,672.637 1327.02,673.359 1328.27,674.265 1329.52,675.354 1330.77,676.625 1332.02,678.076 1333.27,679.705 1334.52,681.512 1335.77,683.493 \n",
" 1337.02,685.646 1338.26,687.968 1339.51,690.458 1340.76,693.112 1342.01,695.928 1343.26,698.901 1344.51,702.029 1345.76,705.309 1347.01,708.736 1348.26,712.306 \n",
" 1349.51,716.017 1350.75,719.863 1352,723.841 1353.25,727.946 1354.5,732.173 1355.75,736.519 1357,740.978 1358.25,745.546 1359.5,750.217 1360.75,754.988 \n",
" 1362,759.851 1363.24,764.803 1364.49,769.839 1365.74,774.952 1366.99,780.137 1368.24,785.389 1369.49,790.703 1370.74,796.073 1371.99,801.493 1373.24,806.958 \n",
" 1374.49,812.462 1375.74,817.999 1376.98,823.563 1378.23,829.15 1379.48,834.753 1380.73,840.367 1381.98,845.985 1383.23,851.602 1384.48,857.214 1385.73,862.813 \n",
" 1386.98,868.394 1388.23,873.952 1389.47,879.482 1390.72,884.977 1391.97,890.433 1393.22,895.843 1394.47,901.204 1395.72,906.51 1396.97,911.755 1398.22,916.934 \n",
" 1399.47,922.043 1400.72,927.077 1401.97,932.031 1403.21,936.9 1404.46,941.68 1405.71,946.367 1406.96,950.955 1408.21,955.442 1409.46,959.822 1410.71,964.092 \n",
" 1411.96,968.249 1413.21,972.287 1414.46,976.205 1415.7,979.997 1416.95,983.662 1418.2,987.196 1419.45,990.596 1420.7,993.859 1421.95,996.982 1423.2,999.964 \n",
" 1424.45,1002.8 1425.7,1005.49 1426.95,1008.03 1428.2,1010.42 1429.44,1012.66 1430.69,1014.74 1431.94,1016.67 1433.19,1018.44 1434.44,1020.06 1435.69,1021.51 \n",
" 1436.94,1022.81 1438.19,1023.94 1439.44,1024.91 1440.69,1025.72 1441.93,1026.37 1443.18,1026.86 1444.43,1027.19 1445.68,1027.35 1446.93,1027.36 1448.18,1027.2 \n",
" 1449.43,1026.88 1450.68,1026.41 1451.93,1025.78 1453.18,1024.99 1454.42,1024.04 1455.67,1022.94 1456.92,1021.69 1458.17,1020.28 1459.42,1018.73 1460.67,1017.03 \n",
" 1461.92,1015.18 1463.17,1013.19 1464.42,1011.06 1465.67,1008.79 1466.92,1006.38 1468.16,1003.84 1469.41,1001.17 1470.66,998.366 1471.91,995.44 1473.16,992.39 \n",
" 1474.41,989.221 1475.66,985.934 1476.91,982.535 1478.16,979.024 1479.41,975.407 1480.65,971.686 1481.9,967.864 1483.15,963.945 1484.4,959.933 1485.65,955.831 \n",
" 1486.9,951.643 1488.15,947.372 1489.4,943.023 1490.65,938.598 1491.9,934.101 1493.15,929.537 1494.39,924.909 1495.64,920.221 1496.89,915.477 1498.14,910.68 \n",
" 1499.39,905.834 1500.64,900.944 1501.89,896.012 1503.14,891.044 1504.39,886.042 1505.64,881.01 1506.88,875.953 1508.13,870.874 1509.38,865.776 1510.63,860.664 \n",
" 1511.88,855.541 1513.13,850.411 1514.38,845.277 1515.63,840.143 1516.88,835.012 1518.13,829.888 1519.38,824.775 1520.62,819.676 1521.87,814.593 1523.12,809.531 \n",
" 1524.37,804.493 1525.62,799.482 1526.87,794.5 1528.12,789.552 1529.37,784.639 1530.62,779.765 1531.87,774.933 1533.11,770.146 1534.36,765.405 1535.61,760.715 \n",
" 1536.86,756.077 1538.11,751.493 1539.36,746.967 1540.61,742.501 1541.86,738.097 1543.11,733.756 1544.36,729.482 1545.61,725.276 1546.85,721.14 1548.1,717.076 \n",
" 1549.35,713.086 1550.6,709.171 1551.85,705.333 1553.1,701.574 1554.35,697.894 1555.6,694.296 1556.85,690.781 1558.1,687.35 1559.34,684.003 1560.59,680.743 \n",
" 1561.84,677.569 1563.09,674.484 1564.34,671.486 1565.59,668.579 1566.84,665.761 1568.09,663.034 1569.34,660.397 1570.59,657.853 1571.83,655.4 1573.08,653.039 \n",
" 1574.33,650.77 1575.58,648.593 1576.83,646.509 1578.08,644.518 1579.33,642.618 1580.58,640.811 1581.83,639.096 1583.08,637.472 1584.33,635.94 1585.57,634.498 \n",
" 1586.82,633.147 1588.07,631.886 1589.32,630.714 1590.57,629.631 1591.82,628.635 1593.07,627.727 1594.32,626.906 1595.57,626.17 1596.82,625.519 1598.06,624.952 \n",
" 1599.31,624.468 1600.56,624.065 1601.81,623.744 1603.06,623.502 1604.31,623.339 1605.56,623.253 1606.81,623.244 1608.06,623.309 1609.31,623.449 1610.56,623.661 \n",
" 1611.8,623.944 1613.05,624.297 1614.3,624.719 1615.55,625.208 1616.8,625.763 1618.05,626.382 1619.3,627.064 1620.55,627.807 1621.8,628.611 1623.05,629.473 \n",
" 1624.29,630.392 1625.54,631.367 1626.79,632.396 1628.04,633.478 1629.29,634.611 1630.54,635.794 1631.79,637.024 1633.04,638.301 1634.29,639.624 1635.54,640.989 \n",
" 1636.79,642.397 1638.03,643.846 1639.28,645.333 1640.53,646.858 1641.78,648.419 1643.03,650.015 1644.28,651.644 1645.53,653.305 1646.78,654.995 1648.03,656.715 \n",
" 1649.28,658.462 1650.52,660.235 1651.77,662.032 1653.02,663.853 1654.27,665.695 1655.52,667.558 1656.77,669.44 1658.02,671.34 1659.27,673.257 1660.52,675.188 \n",
" 1661.77,677.134 1663.01,679.092 1664.26,681.063 1665.51,683.043 1666.76,685.033 1668.01,687.03 1669.26,689.035 1670.51,691.045 1671.76,693.06 1673.01,695.079 \n",
" 1674.26,697.1 1675.51,699.123 1676.75,701.147 1678,703.171 1679.25,705.193 1680.5,707.213 1681.75,709.229 1683,711.242 1684.25,713.251 1685.5,715.253 \n",
" 1686.75,717.249 1688,719.238 1689.24,721.219 1690.49,723.192 1691.74,725.155 1692.99,727.108 1694.24,729.051 1695.49,730.982 1696.74,732.901 1697.99,734.808 \n",
" 1699.24,736.702 1700.49,738.582 1701.74,740.448 1702.98,742.3 1704.23,744.137 1705.48,745.958 1706.73,747.763 1707.98,749.552 1709.23,751.324 1710.48,753.079 \n",
" 1711.73,754.817 1712.98,756.537 1714.23,758.239 1715.47,759.923 1716.72,761.589 1717.97,763.235 1719.22,764.862 1720.47,766.471 1721.72,768.059 1722.97,769.628 \n",
" 1724.22,771.178 1725.47,772.707 1726.72,774.217 1727.97,775.706 1729.21,777.175 1730.46,778.624 1731.71,780.052 1732.96,781.46 1734.21,782.847 1735.46,784.214 \n",
" 1736.71,785.561 1737.96,786.887 1739.21,788.192 1740.46,789.477 1741.7,790.742 1742.95,791.986 1744.2,793.21 1745.45,794.413 1746.7,795.596 1747.95,796.76 \n",
" 1749.2,797.903 1750.45,799.026 1751.7,800.13 1752.95,801.214 1754.19,802.278 1755.44,803.323 1756.69,804.349 1757.94,805.355 1759.19,806.343 1760.44,807.311 \n",
" 1761.69,808.262 1762.94,809.193 1764.19,810.107 1765.44,811.002 1766.69,811.879 1767.93,812.739 1769.18,813.581 1770.43,814.406 1771.68,815.214 1772.93,816.004 \n",
" 1774.18,816.778 1775.43,817.536 1776.68,818.277 1777.93,819.002 1779.18,819.712 1780.42,820.405 1781.67,821.084 1782.92,821.747 1784.17,822.395 1785.42,823.028 \n",
" 1786.67,823.647 1787.92,824.251 1789.17,824.842 1790.42,825.418 1791.67,825.981 1792.92,826.531 1794.16,827.067 1795.41,827.591 1796.66,828.101 1797.91,828.6 \n",
" 1799.16,829.086 1800.41,829.56 1801.66,830.022 1802.91,830.472 1804.16,830.911 1805.41,831.339 1806.65,831.756 1807.9,832.162 1809.15,832.558 1810.4,832.943 \n",
" 1811.65,833.318 1812.9,833.683 1814.15,834.039 1815.4,834.385 1816.65,834.721 1817.9,835.049 1819.15,835.367 1820.39,835.677 1821.64,835.979 1822.89,836.272 \n",
" 1824.14,836.557 1825.39,836.833 1826.64,837.103 1827.89,837.364 1829.14,837.618 1830.39,837.865 1831.64,838.104 1832.88,838.337 1834.13,838.563 1835.38,838.782 \n",
" 1836.63,838.995 1837.88,839.202 1839.13,839.402 1840.38,839.597 1841.63,839.785 1842.88,839.968 1844.13,840.146 1845.37,840.318 1846.62,840.485 1847.87,840.646 \n",
" 1849.12,840.803 1850.37,840.955 1851.62,841.102 1852.87,841.244 1854.12,841.382 1855.37,841.516 1856.62,841.645 1857.87,841.771 1859.11,841.892 1860.36,842.009 \n",
" 1861.61,842.123 1862.86,842.233 1864.11,842.339 1865.36,842.442 1866.61,842.542 1867.86,842.638 1869.11,842.731 1870.36,842.821 1871.6,842.907 1872.85,842.991 \n",
" 1874.1,843.073 1875.35,843.151 1876.6,843.227 1877.85,843.3 1879.1,843.371 1880.35,843.439 1881.6,843.505 1882.85,843.568 1884.1,843.63 1885.34,843.689 \n",
" 1886.59,843.746 1887.84,843.801 1889.09,843.854 1890.34,843.906 1891.59,843.955 1892.84,844.003 1894.09,844.049 1895.34,844.093 1896.59,844.136 1897.83,844.177 \n",
" 1899.08,844.217 1900.33,844.255 1901.58,844.292 1902.83,844.327 1904.08,844.361 1905.33,844.394 1906.58,844.426 1907.83,844.457 1909.08,844.486 1910.33,844.514 \n",
" 1911.57,844.541 1912.82,844.567 1914.07,844.593 1915.32,844.617 1916.57,844.64 1917.82,844.662 1919.07,844.684 1920.32,844.705 1921.57,844.725 1922.82,844.744 \n",
" 1924.06,844.762 1925.31,844.78 1926.56,844.797 1927.81,844.813 1929.06,844.829 1930.31,844.844 1931.56,844.858 1932.81,844.872 1934.06,844.885 1935.31,844.898 \n",
" 1936.56,844.91 1937.8,844.922 1939.05,844.933 1940.3,844.944 1941.55,844.954 1942.8,844.964 1944.05,844.974 1945.3,844.983 1946.55,844.992 1947.8,845 \n",
" 1949.05,845.008 1950.29,845.016 1951.54,845.023 1952.79,845.031 1954.04,845.037 1955.29,845.044 1956.54,845.05 1957.79,845.056 1959.04,845.062 1960.29,845.067 \n",
" 1961.54,845.072 1962.78,845.077 1964.03,845.082 1965.28,845.087 1966.53,845.091 1967.78,845.095 1969.03,845.099 1970.28,845.103 1971.53,845.107 1972.78,845.111 \n",
" 1974.03,845.114 1975.28,845.117 1976.52,845.12 1977.77,845.123 1979.02,845.126 1980.27,845.129 1981.52,845.131 1982.77,845.134 1984.02,845.136 1985.27,845.138 \n",
" 1986.52,845.14 1987.77,845.142 1989.01,845.144 1990.26,845.146 1991.51,845.148 1992.76,845.149 1994.01,845.151 1995.26,845.153 1996.51,845.154 1997.76,845.155 \n",
" 1999.01,845.157 2000.26,845.158 2001.51,845.159 2002.75,845.16 2004,845.162 2005.25,845.163 2006.5,845.164 2007.75,845.165 2009,845.165 2010.25,845.166 \n",
" 2011.5,845.167 2012.75,845.168 2014,845.169 2015.24,845.169 2016.49,845.17 2017.74,845.171 2018.99,845.171 2020.24,845.172 2021.49,845.172 2022.74,845.173 \n",
" 2023.99,845.173 2025.24,845.174 2026.49,845.174 2027.74,845.175 2028.98,845.175 2030.23,845.176 2031.48,845.176 2032.73,845.176 2033.98,845.177 2035.23,845.177 \n",
" 2036.48,845.177 2037.73,845.178 2038.98,845.178 2040.23,845.178 2041.47,845.178 2042.72,845.179 2043.97,845.179 2045.22,845.179 2046.47,845.179 2047.72,845.179 \n",
" 2048.97,845.18 2050.22,845.18 2051.47,845.18 2052.72,845.18 2053.96,845.18 2055.21,845.18 2056.46,845.18 2057.71,845.181 2058.96,845.181 2060.21,845.181 \n",
" 2061.46,845.181 2062.71,845.181 2063.96,845.181 2065.21,845.181 2066.46,845.181 2067.7,845.181 2068.95,845.181 2070.2,845.182 2071.45,845.182 2072.7,845.182 \n",
" 2073.95,845.182 2075.2,845.182 2076.45,845.182 2077.7,845.182 2078.95,845.182 2080.19,845.182 2081.44,845.182 2082.69,845.182 2083.94,845.182 2085.19,845.182 \n",
" 2086.44,845.182 2087.69,845.182 2088.94,845.182 2090.19,845.182 2091.44,845.182 2092.69,845.182 2093.93,845.182 2095.18,845.182 2096.43,845.182 2097.68,845.182 \n",
" 2098.93,845.182 2100.18,845.182 2101.43,845.183 2102.68,845.183 2103.93,845.183 2105.18,845.183 2106.42,845.183 2107.67,845.183 2108.92,845.183 2110.17,845.183 \n",
" 2111.42,845.183 2112.67,845.183 2113.92,845.183 2115.17,845.183 2116.42,845.183 2117.67,845.183 2118.92,845.183 2120.16,845.183 2121.41,845.183 2122.66,845.183 \n",
" 2123.91,845.183 2125.16,845.183 2126.41,845.183 2127.66,845.183 2128.91,845.183 2130.16,845.183 2131.41,845.183 2132.65,845.183 2133.9,845.183 2135.15,845.183 \n",
" 2136.4,845.183 2137.65,845.183 2138.9,845.183 2140.15,845.183 2141.4,845.183 2142.65,845.183 2143.9,845.183 2145.14,845.183 2146.39,845.183 2147.64,845.183 \n",
" 2148.89,845.183 2150.14,845.183 2151.39,845.183 2152.64,845.183 2153.89,845.183 2155.14,845.183 2156.39,845.183 2157.64,845.183 2158.88,845.183 2160.13,845.183 \n",
" 2161.38,845.183 2162.63,845.183 2163.88,845.183 2165.13,845.183 2166.38,845.183 2167.63,845.183 2168.88,845.183 2170.13,845.183 2171.37,845.183 2172.62,845.183 \n",
" 2173.87,845.183 2175.12,845.183 2176.37,845.183 2177.62,845.183 2178.87,845.183 2180.12,845.183 2181.37,845.183 2182.62,845.183 2183.87,845.183 2185.11,845.183 \n",
" 2186.36,845.183 2187.61,845.183 2188.86,845.183 2190.11,845.183 2191.36,845.183 2192.61,845.183 2193.86,845.183 2195.11,845.183 2196.36,845.183 2197.6,845.183 \n",
" 2198.85,845.183 2200.1,845.183 2201.35,845.183 2202.6,845.183 2203.85,845.183 2205.1,845.183 2206.35,845.183 2207.6,845.183 2208.85,845.183 2210.1,845.183 \n",
" 2211.34,845.183 2212.59,845.183 2213.84,845.183 2215.09,845.183 2216.34,845.183 2217.59,845.183 2218.84,845.183 2220.09,845.183 2221.34,845.183 2222.59,845.183 \n",
" 2223.83,845.183 2225.08,845.183 2226.33,845.183 2227.58,845.183 2228.83,845.183 2230.08,845.183 2231.33,845.183 2232.58,845.183 2233.83,845.183 2235.08,845.183 \n",
" 2236.33,845.183 2237.57,845.183 2238.82,845.183 2240.07,845.183 2241.32,845.183 2242.57,845.183 2243.82,845.183 2245.07,845.183 2246.32,845.183 2247.57,845.183 \n",
" 2248.82,845.183 2250.06,845.183 2251.31,845.183 2252.56,845.183 2253.81,845.183 2255.06,845.183 2256.31,845.183 2257.56,845.183 2258.81,845.183 2260.06,845.183 \n",
" 2261.31,845.183 \n",
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" 412.724,845.18 413.973,845.18 415.222,845.18 416.471,845.18 417.72,845.18 418.969,845.18 420.219,845.179 421.468,845.179 422.717,845.179 423.966,845.179 \n",
" 425.215,845.179 426.464,845.178 427.713,845.178 428.962,845.178 430.211,845.178 431.46,845.177 432.709,845.177 433.958,845.177 435.207,845.176 436.456,845.176 \n",
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" 450.196,845.17 451.445,845.169 452.694,845.168 453.943,845.168 455.192,845.167 456.441,845.166 457.69,845.165 458.939,845.164 460.188,845.163 461.437,845.162 \n",
" 462.686,845.161 463.935,845.159 465.184,845.158 466.433,845.157 467.682,845.155 468.931,845.154 470.18,845.152 471.429,845.151 472.678,845.149 473.927,845.147 \n",
" 475.176,845.145 476.425,845.143 477.674,845.141 478.923,845.139 480.173,845.136 481.422,845.134 482.671,845.131 483.92,845.128 485.169,845.126 486.418,845.122 \n",
" 487.667,845.119 488.916,845.116 490.165,845.112 491.414,845.109 492.663,845.105 493.912,845.101 495.161,845.096 496.41,845.092 497.659,845.087 498.908,845.082 \n",
" 500.157,845.077 501.406,845.072 502.655,845.066 503.904,845.06 505.153,845.053 506.402,845.047 507.651,845.04 508.9,845.033 510.15,845.025 511.399,845.017 \n",
" 512.648,845.009 513.897,845 515.146,844.991 516.395,844.981 517.644,844.971 518.893,844.96 520.142,844.949 521.391,844.938 522.64,844.926 523.889,844.913 \n",
" 525.138,844.9 526.387,844.886 527.636,844.871 528.885,844.856 530.134,844.84 531.383,844.824 532.632,844.806 533.881,844.788 535.13,844.769 536.379,844.749 \n",
" 537.628,844.728 538.877,844.706 540.127,844.684 541.376,844.66 542.625,844.635 543.874,844.609 545.123,844.582 546.372,844.554 547.621,844.525 548.87,844.494 \n",
" 550.119,844.462 551.368,844.428 552.617,844.393 553.866,844.357 555.115,844.318 556.364,844.279 557.613,844.237 558.862,844.194 560.111,844.149 561.36,844.102 \n",
" 562.609,844.053 563.858,844.002 565.107,843.948 566.356,843.893 567.605,843.835 568.854,843.775 570.104,843.712 571.353,843.647 572.602,843.579 573.851,843.508 \n",
" 575.1,843.434 576.349,843.358 577.598,843.278 578.847,843.195 580.096,843.108 581.345,843.018 582.594,842.924 583.843,842.827 585.092,842.726 586.341,842.621 \n",
" 587.59,842.511 588.839,842.397 590.088,842.279 591.337,842.156 592.586,842.029 593.835,841.896 595.084,841.758 596.333,841.615 597.582,841.467 598.831,841.313 \n",
" 600.081,841.152 601.33,840.986 602.579,840.814 603.828,840.635 605.077,840.449 606.326,840.256 607.575,840.057 608.824,839.849 610.073,839.634 611.322,839.412 \n",
" 612.571,839.181 613.82,838.941 615.069,838.693 616.318,838.436 617.567,838.17 618.816,837.894 620.065,837.608 621.314,837.312 622.563,837.006 623.812,836.689 \n",
" 625.061,836.36 626.31,836.021 627.559,835.669 628.808,835.305 630.058,834.929 631.307,834.539 632.556,834.137 633.805,833.72 635.054,833.29 636.303,832.845 \n",
" 637.552,832.385 638.801,831.91 640.05,831.419 641.299,830.912 642.548,830.388 643.797,829.847 645.046,829.288 646.295,828.711 647.544,828.116 648.793,827.501 \n",
" 650.042,826.867 651.291,826.212 652.54,825.537 653.789,824.841 655.038,824.123 656.287,823.382 657.536,822.619 658.785,821.832 660.035,821.021 661.284,820.185 \n",
" 662.533,819.323 663.782,818.436 665.031,817.523 666.28,816.582 667.529,815.613 668.778,814.615 670.027,813.589 671.276,812.532 672.525,811.445 673.774,810.326 \n",
" 675.023,809.176 676.272,807.992 677.521,806.776 678.77,805.525 680.019,804.239 681.268,802.917 682.517,801.56 683.766,800.164 685.015,798.731 686.264,797.259 \n",
" 687.513,795.748 688.762,794.196 690.012,792.603 691.261,790.968 692.51,789.291 693.759,787.569 695.008,785.804 696.257,783.993 697.506,782.136 698.755,780.233 \n",
" 700.004,778.281 701.253,776.281 702.502,774.232 703.751,772.133 705,769.983 706.249,767.781 707.498,765.526 708.747,763.218 709.996,760.855 711.245,758.437 \n",
" 712.494,755.964 713.743,753.433 714.992,750.845 716.241,748.199 717.49,745.494 718.739,742.729 719.989,739.903 721.238,737.015 722.487,734.066 723.736,731.053 \n",
" 724.985,727.977 726.234,724.837 727.483,721.631 728.732,718.36 729.981,715.022 731.23,711.618 732.479,708.145 733.728,704.605 734.977,700.996 736.226,697.317 \n",
" 737.475,693.569 738.724,689.75 739.973,685.861 741.222,681.9 742.471,677.867 743.72,673.763 744.969,669.586 746.218,665.337 747.467,661.014 748.716,656.618 \n",
" 749.966,652.149 751.215,647.607 752.464,642.99 753.713,638.3 754.962,633.537 756.211,628.699 757.46,623.788 758.709,618.803 759.958,613.745 761.207,608.614 \n",
" 762.456,603.41 763.705,598.133 764.954,592.785 766.203,587.364 767.452,581.873 768.701,576.311 769.95,570.679 771.199,564.977 772.448,559.207 773.697,553.37 \n",
" 774.946,547.465 776.195,541.495 777.444,535.46 778.693,529.362 779.943,523.201 781.192,516.979 782.441,510.697 783.69,504.357 784.939,497.96 786.188,491.507 \n",
" 787.437,485.001 788.686,478.443 789.935,471.835 791.184,465.179 792.433,458.477 793.682,451.731 794.931,444.943 796.18,438.116 797.429,431.251 798.678,424.352 \n",
" 799.927,417.421 801.176,410.46 802.425,403.472 803.674,396.461 804.923,389.428 806.172,382.377 807.421,375.312 808.67,368.234 809.92,361.149 811.169,354.058 \n",
" 812.418,346.965 813.667,339.875 814.916,332.79 816.165,325.715 817.414,318.653 818.663,311.608 819.912,304.585 821.161,297.586 822.41,290.617 823.659,283.683 \n",
" 824.908,276.786 826.157,269.932 827.406,263.125 828.655,256.37 829.904,249.671 831.153,243.033 832.402,236.462 833.651,229.962 834.9,223.537 836.149,217.194 \n",
" 837.398,210.937 838.647,204.771 839.897,198.702 841.146,192.735 842.395,186.874 843.644,181.127 844.893,175.497 846.142,169.991 847.391,164.614 848.64,159.372 \n",
" 849.889,154.27 851.138,149.313 852.387,144.508 853.636,139.86 854.885,135.375 856.134,131.058 857.383,126.916 858.632,122.953 859.881,119.175 861.13,115.588 \n",
" 862.379,112.199 863.628,109.011 864.877,106.031 866.126,103.265 867.375,100.718 868.624,98.3949 869.874,96.3018 871.123,94.4439 872.372,92.8265 873.621,91.4547 \n",
" 874.87,90.3338 876.119,89.4688 877.368,88.8646 878.617,88.5261 879.866,88.4582 881.115,88.6654 882.364,89.1523 883.613,89.9234 884.862,90.9829 886.111,92.335 \n",
" 887.36,93.9836 888.609,95.9328 889.858,98.1861 891.107,100.747 892.356,103.619 893.605,106.806 894.854,110.309 896.103,114.133 897.352,118.28 898.601,122.752 \n",
" 899.851,127.551 901.1,132.679 902.349,138.139 903.598,143.931 904.847,150.058 906.096,156.519 907.345,163.316 908.594,170.45 909.843,177.921 911.092,185.728 \n",
" 912.341,193.872 913.59,202.352 914.839,211.167 916.088,220.316 917.337,229.798 918.586,239.612 919.835,249.754 921.084,260.224 922.333,271.018 923.582,282.134 \n",
" 924.831,293.568 926.08,305.317 927.329,317.377 928.578,329.744 929.828,342.414 931.077,355.382 932.326,368.642 933.575,382.19 934.824,396.019 936.073,410.124 \n",
" 937.322,424.498 938.571,439.135 939.82,454.027 941.069,469.167 942.318,484.548 943.567,500.161 944.816,515.998 946.065,532.051 947.314,548.31 948.563,564.767 \n",
" 949.812,581.412 951.061,598.234 952.31,615.225 953.559,632.373 954.808,649.668 956.057,667.098 957.306,684.654 958.555,702.322 959.805,720.092 961.054,737.951 \n",
" 962.303,755.887 963.552,773.887 964.801,791.94 966.05,810.032 967.299,828.149 968.548,846.28 969.797,864.409 971.046,882.524 972.295,900.611 973.544,918.655 \n",
" 974.793,936.644 976.042,954.561 977.291,972.394 978.54,990.127 979.789,1007.75 981.038,1025.24 982.287,1042.59 983.536,1059.78 984.785,1076.8 986.034,1093.63 \n",
" 987.283,1110.26 988.532,1126.67 989.781,1142.86 991.031,1158.79 992.28,1174.47 993.529,1189.87 994.778,1204.99 996.027,1219.8 997.276,1234.29 998.525,1248.46 \n",
" 999.774,1262.27 1001.02,1275.74 1002.27,1288.82 1003.52,1301.53 1004.77,1313.83 1006.02,1325.73 1007.27,1337.2 1008.52,1348.24 1009.77,1358.83 1011.02,1368.97 \n",
" 1012.26,1378.63 1013.51,1387.81 1014.76,1396.51 1016.01,1404.7 1017.26,1412.38 1018.51,1419.55 1019.76,1426.18 1021.01,1432.28 1022.26,1437.84 1023.51,1442.84 \n",
" 1024.75,1447.28 1026,1451.16 1027.25,1454.47 1028.5,1457.2 1029.75,1459.34 1031,1460.91 1032.25,1461.88 1033.5,1462.26 1034.75,1462.05 1036,1461.23 \n",
" 1037.25,1459.82 1038.49,1457.81 1039.74,1455.2 1040.99,1451.99 1042.24,1448.17 1043.49,1443.77 1044.74,1438.77 1045.99,1433.17 1047.24,1426.99 1048.49,1420.22 \n",
" 1049.74,1412.88 1050.98,1404.96 1052.23,1396.47 1053.48,1387.42 1054.73,1377.82 1055.98,1367.67 1057.23,1356.99 1058.48,1345.77 1059.73,1334.04 1060.98,1321.81 \n",
" 1062.23,1309.07 1063.47,1295.86 1064.72,1282.17 1065.97,1268.02 1067.22,1253.42 1068.47,1238.4 1069.72,1222.96 1070.97,1207.12 1072.22,1190.89 1073.47,1174.29 \n",
" 1074.72,1157.34 1075.97,1140.05 1077.21,1122.45 1078.46,1104.54 1079.71,1086.36 1080.96,1067.91 1082.21,1049.22 1083.46,1030.31 1084.71,1011.19 1085.96,991.891 \n",
" 1087.21,972.432 1088.46,952.832 1089.7,933.113 1090.95,913.296 1092.2,893.403 1093.45,873.457 1094.7,853.479 1095.95,833.492 1097.2,813.518 1098.45,793.58 \n",
" 1099.7,773.7 1100.95,753.901 1102.2,734.205 1103.44,714.635 1104.69,695.214 1105.94,675.964 1107.19,656.908 1108.44,638.068 1109.69,619.465 1110.94,601.122 \n",
" 1112.19,583.061 1113.44,565.302 1114.69,547.868 1115.93,530.779 1117.18,514.056 1118.43,497.718 1119.68,481.787 1120.93,466.28 1122.18,451.217 1123.43,436.618 \n",
" 1124.68,422.499 1125.93,408.878 1127.18,395.772 1128.43,383.199 1129.67,371.173 1130.92,359.71 1132.17,348.824 1133.42,338.53 1134.67,328.841 1135.92,319.769 \n",
" 1137.17,311.327 1138.42,303.525 1139.67,296.374 1140.92,289.884 1142.16,284.063 1143.41,278.92 1144.66,274.462 1145.91,270.696 1147.16,267.627 1148.41,265.259 \n",
" 1149.66,263.597 1150.91,262.644 1152.16,262.403 1153.41,262.873 1154.65,264.057 1155.9,265.953 1157.15,268.56 1158.4,271.876 1159.65,275.897 1160.9,280.62 \n",
" 1162.15,286.041 1163.4,292.152 1164.65,298.947 1165.9,306.419 1167.15,314.56 1168.39,323.36 1169.64,332.809 1170.89,342.895 1172.14,353.608 1173.39,364.934 \n",
" 1174.64,376.861 1175.89,389.373 1177.14,402.456 1178.39,416.094 1179.64,430.27 1180.88,444.968 1182.13,460.169 1183.38,475.854 1184.63,492.005 1185.88,508.602 \n",
" 1187.13,525.624 1188.38,543.049 1189.63,560.857 1190.88,579.025 1192.13,597.53 1193.38,616.349 1194.62,635.458 1195.87,654.835 1197.12,674.453 1198.37,694.288 \n",
" 1199.62,714.316 1200.87,734.511 1202.12,754.847 1203.37,775.298 1204.62,795.838 1205.87,816.442 1207.11,837.082 1208.36,857.733 1209.61,878.367 1210.86,898.959 \n",
" 1212.11,919.483 1213.36,939.91 1214.61,960.216 1215.86,980.374 1217.11,1000.36 1218.36,1020.14 1219.61,1039.7 1220.85,1059.01 1222.1,1078.04 1223.35,1096.78 \n",
" 1224.6,1115.18 1225.85,1133.24 1227.1,1150.93 1228.35,1168.22 1229.6,1185.1 1230.85,1201.53 1232.1,1217.51 1233.34,1233 1234.59,1247.99 1235.84,1262.46 \n",
" 1237.09,1276.39 1238.34,1289.76 1239.59,1302.55 1240.84,1314.75 1242.09,1326.34 1243.34,1337.31 1244.59,1347.64 1245.84,1357.32 1247.08,1366.33 1248.33,1374.66 \n",
" 1249.58,1382.31 1250.83,1389.26 1252.08,1395.5 1253.33,1401.03 1254.58,1405.83 1255.83,1409.91 1257.08,1413.25 1258.33,1415.86 1259.57,1417.72 1260.82,1418.84 \n",
" 1262.07,1419.21 1263.32,1418.84 1264.57,1417.72 1265.82,1415.86 1267.07,1413.25 1268.32,1409.91 1269.57,1405.83 1270.82,1401.03 1272.06,1395.5 1273.31,1389.26 \n",
" 1274.56,1382.31 1275.81,1374.66 1277.06,1366.33 1278.31,1357.32 1279.56,1347.64 1280.81,1337.31 1282.06,1326.34 1283.31,1314.75 1284.56,1302.55 1285.8,1289.76 \n",
" 1287.05,1276.39 1288.3,1262.46 1289.55,1247.99 1290.8,1233 1292.05,1217.51 1293.3,1201.53 1294.55,1185.1 1295.8,1168.22 1297.05,1150.93 1298.29,1133.24 \n",
" 1299.54,1115.18 1300.79,1096.78 1302.04,1078.04 1303.29,1059.01 1304.54,1039.7 1305.79,1020.14 1307.04,1000.36 1308.29,980.374 1309.54,960.216 1310.79,939.91 \n",
" 1312.03,919.483 1313.28,898.959 1314.53,878.367 1315.78,857.733 1317.03,837.082 1318.28,816.442 1319.53,795.838 1320.78,775.298 1322.03,754.847 1323.28,734.511 \n",
" 1324.52,714.316 1325.77,694.288 1327.02,674.453 1328.27,654.835 1329.52,635.458 1330.77,616.349 1332.02,597.53 1333.27,579.025 1334.52,560.857 1335.77,543.049 \n",
" 1337.02,525.624 1338.26,508.602 1339.51,492.005 1340.76,475.854 1342.01,460.169 1343.26,444.968 1344.51,430.27 1345.76,416.094 1347.01,402.456 1348.26,389.373 \n",
" 1349.51,376.861 1350.75,364.934 1352,353.608 1353.25,342.895 1354.5,332.809 1355.75,323.36 1357,314.56 1358.25,306.419 1359.5,298.947 1360.75,292.152 \n",
" 1362,286.041 1363.24,280.62 1364.49,275.897 1365.74,271.876 1366.99,268.56 1368.24,265.953 1369.49,264.057 1370.74,262.873 1371.99,262.403 1373.24,262.644 \n",
" 1374.49,263.597 1375.74,265.259 1376.98,267.627 1378.23,270.696 1379.48,274.462 1380.73,278.92 1381.98,284.063 1383.23,289.884 1384.48,296.374 1385.73,303.525 \n",
" 1386.98,311.327 1388.23,319.769 1389.47,328.841 1390.72,338.53 1391.97,348.824 1393.22,359.71 1394.47,371.173 1395.72,383.199 1396.97,395.772 1398.22,408.878 \n",
" 1399.47,422.499 1400.72,436.618 1401.97,451.217 1403.21,466.28 1404.46,481.787 1405.71,497.718 1406.96,514.056 1408.21,530.779 1409.46,547.868 1410.71,565.302 \n",
" 1411.96,583.061 1413.21,601.122 1414.46,619.465 1415.7,638.068 1416.95,656.908 1418.2,675.964 1419.45,695.214 1420.7,714.635 1421.95,734.205 1423.2,753.901 \n",
" 1424.45,773.7 1425.7,793.58 1426.95,813.518 1428.2,833.492 1429.44,853.479 1430.69,873.457 1431.94,893.403 1433.19,913.296 1434.44,933.113 1435.69,952.832 \n",
" 1436.94,972.432 1438.19,991.891 1439.44,1011.19 1440.69,1030.31 1441.93,1049.22 1443.18,1067.91 1444.43,1086.36 1445.68,1104.54 1446.93,1122.45 1448.18,1140.05 \n",
" 1449.43,1157.34 1450.68,1174.29 1451.93,1190.89 1453.18,1207.12 1454.42,1222.96 1455.67,1238.4 1456.92,1253.42 1458.17,1268.02 1459.42,1282.17 1460.67,1295.86 \n",
" 1461.92,1309.07 1463.17,1321.81 1464.42,1334.04 1465.67,1345.77 1466.92,1356.99 1468.16,1367.67 1469.41,1377.82 1470.66,1387.42 1471.91,1396.47 1473.16,1404.96 \n",
" 1474.41,1412.88 1475.66,1420.22 1476.91,1426.99 1478.16,1433.17 1479.41,1438.77 1480.65,1443.77 1481.9,1448.17 1483.15,1451.99 1484.4,1455.2 1485.65,1457.81 \n",
" 1486.9,1459.82 1488.15,1461.23 1489.4,1462.05 1490.65,1462.26 1491.9,1461.88 1493.15,1460.91 1494.39,1459.34 1495.64,1457.2 1496.89,1454.47 1498.14,1451.16 \n",
" 1499.39,1447.28 1500.64,1442.84 1501.89,1437.84 1503.14,1432.28 1504.39,1426.18 1505.64,1419.55 1506.88,1412.38 1508.13,1404.7 1509.38,1396.51 1510.63,1387.81 \n",
" 1511.88,1378.63 1513.13,1368.97 1514.38,1358.83 1515.63,1348.24 1516.88,1337.2 1518.13,1325.73 1519.38,1313.83 1520.62,1301.53 1521.87,1288.82 1523.12,1275.74 \n",
" 1524.37,1262.27 1525.62,1248.46 1526.87,1234.29 1528.12,1219.8 1529.37,1204.99 1530.62,1189.87 1531.87,1174.47 1533.11,1158.79 1534.36,1142.86 1535.61,1126.67 \n",
" 1536.86,1110.26 1538.11,1093.63 1539.36,1076.8 1540.61,1059.78 1541.86,1042.59 1543.11,1025.24 1544.36,1007.75 1545.61,990.127 1546.85,972.394 1548.1,954.561 \n",
" 1549.35,936.644 1550.6,918.655 1551.85,900.611 1553.1,882.524 1554.35,864.409 1555.6,846.28 1556.85,828.149 1558.1,810.032 1559.34,791.94 1560.59,773.887 \n",
" 1561.84,755.887 1563.09,737.951 1564.34,720.092 1565.59,702.322 1566.84,684.654 1568.09,667.098 1569.34,649.668 1570.59,632.373 1571.83,615.225 1573.08,598.234 \n",
" 1574.33,581.412 1575.58,564.767 1576.83,548.31 1578.08,532.051 1579.33,515.998 1580.58,500.161 1581.83,484.548 1583.08,469.167 1584.33,454.027 1585.57,439.135 \n",
" 1586.82,424.498 1588.07,410.124 1589.32,396.019 1590.57,382.19 1591.82,368.642 1593.07,355.382 1594.32,342.414 1595.57,329.744 1596.82,317.377 1598.06,305.317 \n",
" 1599.31,293.568 1600.56,282.134 1601.81,271.018 1603.06,260.224 1604.31,249.754 1605.56,239.612 1606.81,229.798 1608.06,220.316 1609.31,211.167 1610.56,202.352 \n",
" 1611.8,193.872 1613.05,185.728 1614.3,177.921 1615.55,170.45 1616.8,163.316 1618.05,156.519 1619.3,150.058 1620.55,143.931 1621.8,138.139 1623.05,132.679 \n",
" 1624.29,127.551 1625.54,122.752 1626.79,118.28 1628.04,114.133 1629.29,110.309 1630.54,106.806 1631.79,103.619 1633.04,100.747 1634.29,98.1861 1635.54,95.9328 \n",
" 1636.79,93.9836 1638.03,92.335 1639.28,90.9829 1640.53,89.9234 1641.78,89.1523 1643.03,88.6654 1644.28,88.4582 1645.53,88.5261 1646.78,88.8646 1648.03,89.4688 \n",
" 1649.28,90.3338 1650.52,91.4547 1651.77,92.8265 1653.02,94.4439 1654.27,96.3018 1655.52,98.3949 1656.77,100.718 1658.02,103.265 1659.27,106.031 1660.52,109.011 \n",
" 1661.77,112.199 1663.01,115.588 1664.26,119.175 1665.51,122.953 1666.76,126.916 1668.01,131.058 1669.26,135.375 1670.51,139.86 1671.76,144.508 1673.01,149.313 \n",
" 1674.26,154.27 1675.51,159.372 1676.75,164.614 1678,169.991 1679.25,175.497 1680.5,181.127 1681.75,186.874 1683,192.735 1684.25,198.702 1685.5,204.771 \n",
" 1686.75,210.937 1688,217.194 1689.24,223.537 1690.49,229.962 1691.74,236.462 1692.99,243.033 1694.24,249.671 1695.49,256.37 1696.74,263.125 1697.99,269.932 \n",
" 1699.24,276.786 1700.49,283.683 1701.74,290.617 1702.98,297.586 1704.23,304.585 1705.48,311.608 1706.73,318.653 1707.98,325.715 1709.23,332.79 1710.48,339.875 \n",
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" 1824.14,778.281 1825.39,780.233 1826.64,782.136 1827.89,783.993 1829.14,785.804 1830.39,787.569 1831.64,789.291 1832.88,790.968 1834.13,792.603 1835.38,794.196 \n",
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" 1849.12,809.176 1850.37,810.326 1851.62,811.445 1852.87,812.532 1854.12,813.589 1855.37,814.615 1856.62,815.613 1857.87,816.582 1859.11,817.523 1860.36,818.436 \n",
" 1861.61,819.323 1862.86,820.185 1864.11,821.021 1865.36,821.832 1866.61,822.619 1867.86,823.382 1869.11,824.123 1870.36,824.841 1871.6,825.537 1872.85,826.212 \n",
" 1874.1,826.867 1875.35,827.501 1876.6,828.116 1877.85,828.711 1879.1,829.288 1880.35,829.847 1881.6,830.388 1882.85,830.912 1884.1,831.419 1885.34,831.91 \n",
" 1886.59,832.385 1887.84,832.845 1889.09,833.29 1890.34,833.72 1891.59,834.137 1892.84,834.539 1894.09,834.929 1895.34,835.305 1896.59,835.669 1897.83,836.021 \n",
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},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = plot()\n",
"for k=0:6\n",
" H_k = Fun(GaussWeight(Hermite(),1/2),[zeros(k);1])\n",
" plot!(xx, H_k.(xx); label=\"H_$k\")\n",
"end\n",
"p"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare this to weighting by $w(x) = \\E^{-x^2}$:"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
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" 1312.03,652.487 1313.28,652.533 1314.53,652.58 1315.78,652.628 1317.03,652.676 1318.28,652.725 1319.53,652.774 1320.78,652.825 1322.03,652.875 1323.28,652.927 \n",
" 1324.52,652.979 1325.77,653.031 1327.02,653.084 1328.27,653.137 1329.52,653.191 1330.77,653.246 1332.02,653.3 1333.27,653.355 1334.52,653.411 1335.77,653.466 \n",
" 1337.02,653.522 1338.26,653.578 1339.51,653.635 1340.76,653.692 1342.01,653.748 1343.26,653.805 1344.51,653.863 1345.76,653.92 1347.01,653.977 1348.26,654.035 \n",
" 1349.51,654.092 1350.75,654.15 1352,654.207 1353.25,654.265 1354.5,654.322 1355.75,654.379 1357,654.436 1358.25,654.494 1359.5,654.55 1360.75,654.607 \n",
" 1362,654.664 1363.24,654.72 1364.49,654.777 1365.74,654.833 1366.99,654.888 1368.24,654.944 1369.49,654.999 1370.74,655.054 1371.99,655.108 1373.24,655.162 \n",
" 1374.49,655.216 1375.74,655.27 1376.98,655.323 1378.23,655.375 1379.48,655.428 1380.73,655.48 1381.98,655.531 1383.23,655.582 1384.48,655.632 1385.73,655.683 \n",
" 1386.98,655.732 1388.23,655.781 1389.47,655.83 1390.72,655.878 1391.97,655.925 1393.22,655.972 1394.47,656.019 1395.72,656.065 1396.97,656.11 1398.22,656.155 \n",
" 1399.47,656.199 1400.72,656.243 1401.97,656.286 1403.21,656.328 1404.46,656.37 1405.71,656.412 1406.96,656.452 1408.21,656.493 1409.46,656.532 1410.71,656.571 \n",
" 1411.96,656.61 1413.21,656.647 1414.46,656.685 1415.7,656.721 1416.95,656.757 1418.2,656.793 1419.45,656.827 1420.7,656.862 1421.95,656.895 1423.2,656.928 \n",
" 1424.45,656.961 1425.7,656.993 1426.95,657.024 1428.2,657.054 1429.44,657.085 1430.69,657.114 1431.94,657.143 1433.19,657.171 1434.44,657.199 1435.69,657.227 \n",
" 1436.94,657.253 1438.19,657.279 1439.44,657.305 1440.69,657.33 1441.93,657.355 1443.18,657.379 1444.43,657.402 1445.68,657.425 1446.93,657.447 1448.18,657.469 \n",
" 1449.43,657.491 1450.68,657.512 1451.93,657.532 1453.18,657.552 1454.42,657.572 1455.67,657.591 1456.92,657.609 1458.17,657.627 1459.42,657.645 1460.67,657.662 \n",
" 1461.92,657.679 1463.17,657.695 1464.42,657.711 1465.67,657.727 1466.92,657.742 1468.16,657.757 1469.41,657.771 1470.66,657.785 1471.91,657.799 1473.16,657.812 \n",
" 1474.41,657.825 1475.66,657.837 1476.91,657.849 1478.16,657.861 1479.41,657.873 1480.65,657.884 1481.9,657.894 1483.15,657.905 1484.4,657.915 1485.65,657.925 \n",
" 1486.9,657.935 1488.15,657.944 1489.4,657.953 1490.65,657.962 1491.9,657.97 1493.15,657.978 1494.39,657.986 1495.64,657.994 1496.89,658.002 1498.14,658.009 \n",
" 1499.39,658.016 1500.64,658.023 1501.89,658.029 1503.14,658.035 1504.39,658.042 1505.64,658.048 1506.88,658.053 1508.13,658.059 1509.38,658.064 1510.63,658.069 \n",
" 1511.88,658.074 1513.13,658.079 1514.38,658.084 1515.63,658.088 1516.88,658.093 1518.13,658.097 1519.38,658.101 1520.62,658.105 1521.87,658.109 1523.12,658.112 \n",
" 1524.37,658.116 1525.62,658.119 1526.87,658.122 1528.12,658.125 1529.37,658.128 1530.62,658.131 1531.87,658.134 1533.11,658.137 1534.36,658.139 1535.61,658.142 \n",
" 1536.86,658.144 1538.11,658.146 1539.36,658.149 1540.61,658.151 1541.86,658.153 1543.11,658.155 1544.36,658.157 1545.61,658.158 1546.85,658.16 1548.1,658.162 \n",
" 1549.35,658.163 1550.6,658.165 1551.85,658.166 1553.1,658.168 1554.35,658.169 1555.6,658.17 1556.85,658.172 1558.1,658.173 1559.34,658.174 1560.59,658.175 \n",
" 1561.84,658.176 1563.09,658.177 1564.34,658.178 1565.59,658.179 1566.84,658.18 1568.09,658.18 1569.34,658.181 1570.59,658.182 1571.83,658.183 1573.08,658.183 \n",
" 1574.33,658.184 1575.58,658.185 1576.83,658.185 1578.08,658.186 1579.33,658.186 1580.58,658.187 1581.83,658.188 1583.08,658.188 1584.33,658.188 1585.57,658.189 \n",
" 1586.82,658.189 1588.07,658.19 1589.32,658.19 1590.57,658.19 1591.82,658.191 1593.07,658.191 1594.32,658.191 1595.57,658.192 1596.82,658.192 1598.06,658.192 \n",
" 1599.31,658.192 1600.56,658.193 1601.81,658.193 1603.06,658.193 1604.31,658.193 1605.56,658.194 1606.81,658.194 1608.06,658.194 1609.31,658.194 1610.56,658.194 \n",
" 1611.8,658.194 1613.05,658.195 1614.3,658.195 1615.55,658.195 1616.8,658.195 1618.05,658.195 1619.3,658.195 1620.55,658.195 1621.8,658.195 1623.05,658.195 \n",
" 1624.29,658.196 1625.54,658.196 1626.79,658.196 1628.04,658.196 1629.29,658.196 1630.54,658.196 1631.79,658.196 1633.04,658.196 1634.29,658.196 1635.54,658.196 \n",
" 1636.79,658.196 1638.03,658.196 1639.28,658.196 1640.53,658.196 1641.78,658.196 1643.03,658.196 1644.28,658.196 1645.53,658.197 1646.78,658.197 1648.03,658.197 \n",
" 1649.28,658.197 1650.52,658.197 1651.77,658.197 1653.02,658.197 1654.27,658.197 1655.52,658.197 1656.77,658.197 1658.02,658.197 1659.27,658.197 1660.52,658.197 \n",
" 1661.77,658.197 1663.01,658.197 1664.26,658.197 1665.51,658.197 1666.76,658.197 1668.01,658.197 1669.26,658.197 1670.51,658.197 1671.76,658.197 1673.01,658.197 \n",
" 1674.26,658.197 1675.51,658.197 1676.75,658.197 1678,658.197 1679.25,658.197 1680.5,658.197 1681.75,658.197 1683,658.197 1684.25,658.197 1685.5,658.197 \n",
" 1686.75,658.197 1688,658.197 1689.24,658.197 1690.49,658.197 1691.74,658.197 1692.99,658.197 1694.24,658.197 1695.49,658.197 1696.74,658.197 1697.99,658.197 \n",
" 1699.24,658.197 1700.49,658.197 1701.74,658.197 1702.98,658.197 1704.23,658.197 1705.48,658.197 1706.73,658.197 1707.98,658.197 1709.23,658.197 1710.48,658.197 \n",
" 1711.73,658.197 1712.98,658.197 1714.23,658.197 1715.47,658.197 1716.72,658.197 1717.97,658.197 1719.22,658.197 1720.47,658.197 1721.72,658.197 1722.97,658.197 \n",
" 1724.22,658.197 1725.47,658.197 1726.72,658.197 1727.97,658.197 1729.21,658.197 1730.46,658.197 1731.71,658.197 1732.96,658.197 1734.21,658.197 1735.46,658.197 \n",
" 1736.71,658.197 1737.96,658.197 1739.21,658.197 1740.46,658.197 1741.7,658.197 1742.95,658.197 1744.2,658.197 1745.45,658.197 1746.7,658.197 1747.95,658.197 \n",
" 1749.2,658.197 1750.45,658.197 1751.7,658.197 1752.95,658.197 1754.19,658.197 1755.44,658.197 1756.69,658.197 1757.94,658.197 1759.19,658.197 1760.44,658.197 \n",
" 1761.69,658.197 1762.94,658.197 1764.19,658.197 1765.44,658.197 1766.69,658.197 1767.93,658.197 1769.18,658.197 1770.43,658.197 1771.68,658.197 1772.93,658.197 \n",
" 1774.18,658.197 1775.43,658.197 1776.68,658.197 1777.93,658.197 1779.18,658.197 1780.42,658.197 1781.67,658.197 1782.92,658.197 1784.17,658.197 1785.42,658.197 \n",
" 1786.67,658.197 1787.92,658.197 1789.17,658.197 1790.42,658.197 1791.67,658.197 1792.92,658.197 1794.16,658.197 1795.41,658.197 1796.66,658.197 1797.91,658.197 \n",
" 1799.16,658.197 1800.41,658.197 1801.66,658.197 1802.91,658.197 1804.16,658.197 1805.41,658.197 1806.65,658.197 1807.9,658.197 1809.15,658.197 1810.4,658.197 \n",
" 1811.65,658.197 1812.9,658.197 1814.15,658.197 1815.4,658.197 1816.65,658.197 1817.9,658.197 1819.15,658.197 1820.39,658.197 1821.64,658.197 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
" 2073.95,658.197 2075.2,658.197 2076.45,658.197 2077.7,658.197 2078.95,658.197 2080.19,658.197 2081.44,658.197 2082.69,658.197 2083.94,658.197 2085.19,658.197 \n",
" 2086.44,658.197 2087.69,658.197 2088.94,658.197 2090.19,658.197 2091.44,658.197 2092.69,658.197 2093.93,658.197 2095.18,658.197 2096.43,658.197 2097.68,658.197 \n",
" 2098.93,658.197 2100.18,658.197 2101.43,658.197 2102.68,658.197 2103.93,658.197 2105.18,658.197 2106.42,658.197 2107.67,658.197 2108.92,658.197 2110.17,658.197 \n",
" 2111.42,658.197 2112.67,658.197 2113.92,658.197 2115.17,658.197 2116.42,658.197 2117.67,658.197 2118.92,658.197 2120.16,658.197 2121.41,658.197 2122.66,658.197 \n",
" 2123.91,658.197 2125.16,658.197 2126.41,658.197 2127.66,658.197 2128.91,658.197 2130.16,658.197 2131.41,658.197 2132.65,658.197 2133.9,658.197 2135.15,658.197 \n",
" 2136.4,658.197 2137.65,658.197 2138.9,658.197 2140.15,658.197 2141.4,658.197 2142.65,658.197 2143.9,658.197 2145.14,658.197 2146.39,658.197 2147.64,658.197 \n",
" 2148.89,658.197 2150.14,658.197 2151.39,658.197 2152.64,658.197 2153.89,658.197 2155.14,658.197 2156.39,658.197 2157.64,658.197 2158.88,658.197 2160.13,658.197 \n",
" 2161.38,658.197 2162.63,658.197 2163.88,658.197 2165.13,658.197 2166.38,658.197 2167.63,658.197 2168.88,658.197 2170.13,658.197 2171.37,658.197 2172.62,658.197 \n",
" 2173.87,658.197 2175.12,658.197 2176.37,658.197 2177.62,658.197 2178.87,658.197 2180.12,658.197 2181.37,658.197 2182.62,658.197 2183.87,658.197 2185.11,658.197 \n",
" 2186.36,658.197 2187.61,658.197 2188.86,658.197 2190.11,658.197 2191.36,658.197 2192.61,658.197 2193.86,658.197 2195.11,658.197 2196.36,658.197 2197.6,658.197 \n",
" 2198.85,658.197 2200.1,658.197 2201.35,658.197 2202.6,658.197 2203.85,658.197 2205.1,658.197 2206.35,658.197 2207.6,658.197 2208.85,658.197 2210.1,658.197 \n",
" 2211.34,658.197 2212.59,658.197 2213.84,658.197 2215.09,658.197 2216.34,658.197 2217.59,658.197 2218.84,658.197 2220.09,658.197 2221.34,658.197 2222.59,658.197 \n",
" 2223.83,658.197 2225.08,658.197 2226.33,658.197 2227.58,658.197 2228.83,658.197 2230.08,658.197 2231.33,658.197 2232.58,658.197 2233.83,658.197 2235.08,658.197 \n",
" 2236.33,658.197 2237.57,658.197 2238.82,658.197 2240.07,658.197 2241.32,658.197 2242.57,658.197 2243.82,658.197 2245.07,658.197 2246.32,658.197 2247.57,658.197 \n",
" 2248.82,658.197 2250.06,658.197 2251.31,658.197 2252.56,658.197 2253.81,658.197 2255.06,658.197 2256.31,658.197 2257.56,658.197 2258.81,658.197 2260.06,658.197 \n",
" 2261.31,658.197 \n",
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" 425.215,658.197 426.464,658.197 427.713,658.197 428.962,658.197 430.211,658.197 431.46,658.197 432.709,658.197 433.958,658.197 435.207,658.197 436.456,658.197 \n",
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" 500.157,658.197 501.406,658.197 502.655,658.197 503.904,658.197 505.153,658.197 506.402,658.197 507.651,658.197 508.9,658.197 510.15,658.197 511.399,658.197 \n",
" 512.648,658.197 513.897,658.197 515.146,658.197 516.395,658.197 517.644,658.197 518.893,658.197 520.142,658.197 521.391,658.197 522.64,658.197 523.889,658.197 \n",
" 525.138,658.197 526.387,658.197 527.636,658.197 528.885,658.197 530.134,658.197 531.383,658.197 532.632,658.197 533.881,658.197 535.13,658.197 536.379,658.197 \n",
" 537.628,658.197 538.877,658.197 540.127,658.197 541.376,658.197 542.625,658.197 543.874,658.197 545.123,658.197 546.372,658.197 547.621,658.197 548.87,658.197 \n",
" 550.119,658.197 551.368,658.197 552.617,658.197 553.866,658.197 555.115,658.197 556.364,658.197 557.613,658.197 558.862,658.197 560.111,658.197 561.36,658.197 \n",
" 562.609,658.197 563.858,658.197 565.107,658.197 566.356,658.197 567.605,658.197 568.854,658.197 570.104,658.197 571.353,658.197 572.602,658.197 573.851,658.197 \n",
" 575.1,658.197 576.349,658.197 577.598,658.197 578.847,658.197 580.096,658.197 581.345,658.197 582.594,658.197 583.843,658.197 585.092,658.197 586.341,658.197 \n",
" 587.59,658.197 588.839,658.197 590.088,658.197 591.337,658.197 592.586,658.197 593.835,658.197 595.084,658.197 596.333,658.197 597.582,658.197 598.831,658.197 \n",
" 600.081,658.197 601.33,658.197 602.579,658.197 603.828,658.197 605.077,658.197 606.326,658.197 607.575,658.197 608.824,658.197 610.073,658.197 611.322,658.197 \n",
" 612.571,658.197 613.82,658.197 615.069,658.197 616.318,658.197 617.567,658.197 618.816,658.197 620.065,658.197 621.314,658.197 622.563,658.197 623.812,658.197 \n",
" 625.061,658.197 626.31,658.197 627.559,658.197 628.808,658.197 630.058,658.197 631.307,658.197 632.556,658.197 633.805,658.197 635.054,658.197 636.303,658.197 \n",
" 637.552,658.197 638.801,658.197 640.05,658.197 641.299,658.197 642.548,658.197 643.797,658.197 645.046,658.197 646.295,658.197 647.544,658.197 648.793,658.197 \n",
" 650.042,658.197 651.291,658.197 652.54,658.197 653.789,658.197 655.038,658.197 656.287,658.197 657.536,658.197 658.785,658.197 660.035,658.197 661.284,658.197 \n",
" 662.533,658.197 663.782,658.197 665.031,658.197 666.28,658.197 667.529,658.197 668.778,658.197 670.027,658.197 671.276,658.197 672.525,658.197 673.774,658.197 \n",
" 675.023,658.197 676.272,658.197 677.521,658.197 678.77,658.197 680.019,658.197 681.268,658.197 682.517,658.197 683.766,658.197 685.015,658.197 686.264,658.197 \n",
" 687.513,658.197 688.762,658.197 690.012,658.197 691.261,658.197 692.51,658.197 693.759,658.197 695.008,658.197 696.257,658.197 697.506,658.197 698.755,658.197 \n",
" 700.004,658.197 701.253,658.197 702.502,658.197 703.751,658.197 705,658.197 706.249,658.197 707.498,658.197 708.747,658.197 709.996,658.197 711.245,658.197 \n",
" 712.494,658.197 713.743,658.197 714.992,658.197 716.241,658.197 717.49,658.197 718.739,658.197 719.989,658.197 721.238,658.197 722.487,658.197 723.736,658.197 \n",
" 724.985,658.197 726.234,658.197 727.483,658.197 728.732,658.197 729.981,658.197 731.23,658.197 732.479,658.197 733.728,658.197 734.977,658.197 736.226,658.197 \n",
" 737.475,658.197 738.724,658.197 739.973,658.197 741.222,658.197 742.471,658.197 743.72,658.197 744.969,658.197 746.218,658.197 747.467,658.197 748.716,658.197 \n",
" 749.966,658.197 751.215,658.197 752.464,658.197 753.713,658.197 754.962,658.197 756.211,658.197 757.46,658.197 758.709,658.197 759.958,658.197 761.207,658.197 \n",
" 762.456,658.197 763.705,658.197 764.954,658.197 766.203,658.197 767.452,658.197 768.701,658.197 769.95,658.197 771.199,658.197 772.448,658.197 773.697,658.197 \n",
" 774.946,658.197 776.195,658.197 777.444,658.197 778.693,658.197 779.943,658.197 781.192,658.197 782.441,658.197 783.69,658.197 784.939,658.197 786.188,658.197 \n",
" 787.437,658.197 788.686,658.197 789.935,658.197 791.184,658.197 792.433,658.197 793.682,658.197 794.931,658.197 796.18,658.197 797.429,658.197 798.678,658.197 \n",
" 799.927,658.197 801.176,658.197 802.425,658.197 803.674,658.197 804.923,658.197 806.172,658.197 807.421,658.197 808.67,658.197 809.92,658.197 811.169,658.197 \n",
" 812.418,658.197 813.667,658.197 814.916,658.197 816.165,658.197 817.414,658.197 818.663,658.197 819.912,658.197 821.161,658.197 822.41,658.197 823.659,658.197 \n",
" 824.908,658.197 826.157,658.197 827.406,658.197 828.655,658.197 829.904,658.197 831.153,658.197 832.402,658.197 833.651,658.197 834.9,658.197 836.149,658.197 \n",
" 837.398,658.197 838.647,658.198 839.897,658.198 841.146,658.198 842.395,658.198 843.644,658.198 844.893,658.198 846.142,658.198 847.391,658.198 848.64,658.198 \n",
" 849.889,658.198 851.138,658.198 852.387,658.198 853.636,658.198 854.885,658.198 856.134,658.198 857.383,658.198 858.632,658.198 859.881,658.198 861.13,658.198 \n",
" 862.379,658.199 863.628,658.199 864.877,658.199 866.126,658.199 867.375,658.199 868.624,658.199 869.874,658.199 871.123,658.199 872.372,658.2 873.621,658.2 \n",
" 874.87,658.2 876.119,658.2 877.368,658.2 878.617,658.2 879.866,658.201 881.115,658.201 882.364,658.201 883.613,658.201 884.862,658.201 886.111,658.202 \n",
" 887.36,658.202 888.609,658.202 889.858,658.203 891.107,658.203 892.356,658.203 893.605,658.204 894.854,658.204 896.103,658.204 897.352,658.205 898.601,658.205 \n",
" 899.851,658.206 901.1,658.206 902.349,658.207 903.598,658.207 904.847,658.208 906.096,658.208 907.345,658.209 908.594,658.21 909.843,658.21 911.092,658.211 \n",
" 912.341,658.212 913.59,658.213 914.839,658.213 916.088,658.214 917.337,658.215 918.586,658.216 919.835,658.217 921.084,658.218 922.333,658.219 923.582,658.221 \n",
" 924.831,658.222 926.08,658.223 927.329,658.224 928.578,658.226 929.828,658.227 931.077,658.229 932.326,658.23 933.575,658.232 934.824,658.234 936.073,658.236 \n",
" 937.322,658.237 938.571,658.239 939.82,658.242 941.069,658.244 942.318,658.246 943.567,658.248 944.816,658.251 946.065,658.253 947.314,658.256 948.563,658.259 \n",
" 949.812,658.262 951.061,658.265 952.31,658.268 953.559,658.271 954.808,658.275 956.057,658.278 957.306,658.282 958.555,658.286 959.805,658.29 961.054,658.294 \n",
" 962.303,658.298 963.552,658.303 964.801,658.308 966.05,658.313 967.299,658.318 968.548,658.323 969.797,658.328 971.046,658.334 972.295,658.34 973.544,658.346 \n",
" 974.793,658.352 976.042,658.359 977.291,658.366 978.54,658.373 979.789,658.38 981.038,658.388 982.287,658.396 983.536,658.404 984.785,658.412 986.034,658.421 \n",
" 987.283,658.43 988.532,658.44 989.781,658.449 991.031,658.459 992.28,658.47 993.529,658.48 994.778,658.491 996.027,658.503 997.276,658.514 998.525,658.527 \n",
" 999.774,658.539 1001.02,658.552 1002.27,658.565 1003.52,658.579 1004.77,658.593 1006.02,658.608 1007.27,658.623 1008.52,658.639 1009.77,658.655 1011.02,658.671 \n",
" 1012.26,658.688 1013.51,658.705 1014.76,658.723 1016.01,658.742 1017.26,658.761 1018.51,658.78 1019.76,658.8 1021.01,658.821 1022.26,658.842 1023.51,658.864 \n",
" 1024.75,658.886 1026,658.909 1027.25,658.932 1028.5,658.956 1029.75,658.981 1031,659.006 1032.25,659.032 1033.5,659.058 1034.75,659.086 1036,659.113 \n",
" 1037.25,659.142 1038.49,659.171 1039.74,659.201 1040.99,659.231 1042.24,659.262 1043.49,659.294 1044.74,659.326 1045.99,659.36 1047.24,659.393 1048.49,659.428 \n",
" 1049.74,659.463 1050.98,659.499 1052.23,659.536 1053.48,659.573 1054.73,659.611 1055.98,659.65 1057.23,659.69 1058.48,659.73 1059.73,659.771 1060.98,659.812 \n",
" 1062.23,659.855 1063.47,659.898 1064.72,659.941 1065.97,659.986 1067.22,660.031 1068.47,660.077 1069.72,660.123 1070.97,660.17 1072.22,660.218 1073.47,660.267 \n",
" 1074.72,660.316 1075.97,660.365 1077.21,660.416 1078.46,660.467 1079.71,660.518 1080.96,660.571 1082.21,660.623 1083.46,660.677 1084.71,660.731 1085.96,660.785 \n",
" 1087.21,660.84 1088.46,660.895 1089.7,660.951 1090.95,661.007 1092.2,661.064 1093.45,661.121 1094.7,661.178 1095.95,661.236 1097.2,661.294 1098.45,661.353 \n",
" 1099.7,661.412 1100.95,661.471 1102.2,661.53 1103.44,661.589 1104.69,661.649 1105.94,661.708 1107.19,661.768 1108.44,661.828 1109.69,661.888 1110.94,661.947 \n",
" 1112.19,662.007 1113.44,662.067 1114.69,662.126 1115.93,662.186 1117.18,662.245 1118.43,662.304 1119.68,662.362 1120.93,662.42 1122.18,662.478 1123.43,662.536 \n",
" 1124.68,662.593 1125.93,662.649 1127.18,662.705 1128.43,662.761 1129.67,662.815 1130.92,662.869 1132.17,662.922 1133.42,662.975 1134.67,663.027 1135.92,663.077 \n",
" 1137.17,663.127 1138.42,663.176 1139.67,663.224 1140.92,663.27 1142.16,663.316 1143.41,663.36 1144.66,663.403 1145.91,663.445 1147.16,663.486 1148.41,663.525 \n",
" 1149.66,663.562 1150.91,663.599 1152.16,663.633 1153.41,663.666 1154.65,663.698 1155.9,663.728 1157.15,663.756 1158.4,663.782 1159.65,663.807 1160.9,663.829 \n",
" 1162.15,663.85 1163.4,663.869 1164.65,663.886 1165.9,663.9 1167.15,663.913 1168.39,663.924 1169.64,663.932 1170.89,663.939 1172.14,663.943 1173.39,663.944 \n",
" 1174.64,663.944 1175.89,663.941 1177.14,663.936 1178.39,663.928 1179.64,663.918 1180.88,663.906 1182.13,663.891 1183.38,663.874 1184.63,663.854 1185.88,663.832 \n",
" 1187.13,663.807 1188.38,663.779 1189.63,663.749 1190.88,663.717 1192.13,663.681 1193.38,663.644 1194.62,663.603 1195.87,663.56 1197.12,663.515 1198.37,663.466 \n",
" 1199.62,663.415 1200.87,663.362 1202.12,663.306 1203.37,663.247 1204.62,663.186 1205.87,663.122 1207.11,663.056 1208.36,662.987 1209.61,662.915 1210.86,662.841 \n",
" 1212.11,662.765 1213.36,662.686 1214.61,662.605 1215.86,662.521 1217.11,662.435 1218.36,662.347 1219.61,662.256 1220.85,662.163 1222.1,662.068 1223.35,661.971 \n",
" 1224.6,661.871 1225.85,661.77 1227.1,661.666 1228.35,661.561 1229.6,661.454 1230.85,661.344 1232.1,661.233 1233.34,661.12 1234.59,661.006 1235.84,660.89 \n",
" 1237.09,660.772 1238.34,660.653 1239.59,660.532 1240.84,660.41 1242.09,660.287 1243.34,660.162 1244.59,660.037 1245.84,659.91 1247.08,659.782 1248.33,659.653 \n",
" 1249.58,659.524 1250.83,659.393 1252.08,659.262 1253.33,659.131 1254.58,658.998 1255.83,658.865 1257.08,658.732 1258.33,658.599 1259.57,658.465 1260.82,658.331 \n",
" 1262.07,658.197 1263.32,658.063 1264.57,657.929 1265.82,657.795 1267.07,657.662 1268.32,657.529 1269.57,657.396 1270.82,657.264 1272.06,657.132 1273.31,657.001 \n",
" 1274.56,656.87 1275.81,656.741 1277.06,656.612 1278.31,656.484 1279.56,656.357 1280.81,656.232 1282.06,656.107 1283.31,655.984 1284.56,655.862 1285.8,655.741 \n",
" 1287.05,655.622 1288.3,655.504 1289.55,655.388 1290.8,655.274 1292.05,655.161 1293.3,655.05 1294.55,654.941 1295.8,654.833 1297.05,654.728 1298.29,654.624 \n",
" 1299.54,654.523 1300.79,654.423 1302.04,654.326 1303.29,654.231 1304.54,654.138 1305.79,654.047 1307.04,653.959 1308.29,653.873 1309.54,653.789 1310.79,653.708 \n",
" 1312.03,653.629 1313.28,653.553 1314.53,653.479 1315.78,653.407 1317.03,653.338 1318.28,653.272 1319.53,653.208 1320.78,653.147 1322.03,653.088 1323.28,653.032 \n",
" 1324.52,652.979 1325.77,652.928 1327.02,652.88 1328.27,652.834 1329.52,652.791 1330.77,652.75 1332.02,652.713 1333.27,652.677 1334.52,652.645 1335.77,652.615 \n",
" 1337.02,652.587 1338.26,652.562 1339.51,652.54 1340.76,652.52 1342.01,652.503 1343.26,652.488 1344.51,652.476 1345.76,652.466 1347.01,652.458 1348.26,652.453 \n",
" 1349.51,652.45 1350.75,652.45 1352,652.451 1353.25,652.456 1354.5,652.462 1355.75,652.47 1357,652.481 1358.25,652.494 1359.5,652.508 1360.75,652.525 \n",
" 1362,652.544 1363.24,652.565 1364.49,652.587 1365.74,652.612 1366.99,652.638 1368.24,652.666 1369.49,652.696 1370.74,652.728 1371.99,652.761 1373.24,652.795 \n",
" 1374.49,652.832 1375.74,652.869 1376.98,652.908 1378.23,652.949 1379.48,652.991 1380.73,653.034 1381.98,653.078 1383.23,653.124 1384.48,653.171 1385.73,653.218 \n",
" 1386.98,653.267 1388.23,653.317 1389.47,653.368 1390.72,653.419 1391.97,653.472 1393.22,653.525 1394.47,653.579 1395.72,653.634 1396.97,653.689 1398.22,653.745 \n",
" 1399.47,653.801 1400.72,653.858 1401.97,653.916 1403.21,653.974 1404.46,654.032 1405.71,654.09 1406.96,654.149 1408.21,654.208 1409.46,654.268 1410.71,654.327 \n",
" 1411.96,654.387 1413.21,654.447 1414.46,654.506 1415.7,654.566 1416.95,654.626 1418.2,654.686 1419.45,654.745 1420.7,654.805 1421.95,654.864 1423.2,654.923 \n",
" 1424.45,654.982 1425.7,655.041 1426.95,655.1 1428.2,655.158 1429.44,655.216 1430.69,655.273 1431.94,655.33 1433.19,655.387 1434.44,655.443 1435.69,655.499 \n",
" 1436.94,655.554 1438.19,655.609 1439.44,655.664 1440.69,655.717 1441.93,655.771 1443.18,655.823 1444.43,655.876 1445.68,655.927 1446.93,655.978 1448.18,656.029 \n",
" 1449.43,656.078 1450.68,656.127 1451.93,656.176 1453.18,656.224 1454.42,656.271 1455.67,656.317 1456.92,656.363 1458.17,656.408 1459.42,656.453 1460.67,656.496 \n",
" 1461.92,656.54 1463.17,656.582 1464.42,656.623 1465.67,656.664 1466.92,656.705 1468.16,656.744 1469.41,656.783 1470.66,656.821 1471.91,656.858 1473.16,656.895 \n",
" 1474.41,656.931 1475.66,656.966 1476.91,657.001 1478.16,657.035 1479.41,657.068 1480.65,657.1 1481.9,657.132 1483.15,657.163 1484.4,657.193 1485.65,657.223 \n",
" 1486.9,657.252 1488.15,657.281 1489.4,657.309 1490.65,657.336 1491.9,657.362 1493.15,657.388 1494.39,657.413 1495.64,657.438 1496.89,657.462 1498.14,657.485 \n",
" 1499.39,657.508 1500.64,657.531 1501.89,657.552 1503.14,657.573 1504.39,657.594 1505.64,657.614 1506.88,657.633 1508.13,657.652 1509.38,657.671 1510.63,657.689 \n",
" 1511.88,657.706 1513.13,657.723 1514.38,657.74 1515.63,657.756 1516.88,657.771 1518.13,657.786 1519.38,657.801 1520.62,657.815 1521.87,657.829 1523.12,657.842 \n",
" 1524.37,657.855 1525.62,657.868 1526.87,657.88 1528.12,657.891 1529.37,657.903 1530.62,657.914 1531.87,657.925 1533.11,657.935 1534.36,657.945 1535.61,657.955 \n",
" 1536.86,657.964 1538.11,657.973 1539.36,657.982 1540.61,657.99 1541.86,657.998 1543.11,658.006 1544.36,658.014 1545.61,658.021 1546.85,658.028 1548.1,658.035 \n",
" 1549.35,658.042 1550.6,658.048 1551.85,658.054 1553.1,658.06 1554.35,658.066 1555.6,658.071 1556.85,658.076 1558.1,658.082 1559.34,658.086 1560.59,658.091 \n",
" 1561.84,658.096 1563.09,658.1 1564.34,658.104 1565.59,658.108 1566.84,658.112 1568.09,658.116 1569.34,658.119 1570.59,658.123 1571.83,658.126 1573.08,658.129 \n",
" 1574.33,658.132 1575.58,658.135 1576.83,658.138 1578.08,658.141 1579.33,658.143 1580.58,658.146 1581.83,658.148 1583.08,658.15 1584.33,658.153 1585.57,658.155 \n",
" 1586.82,658.157 1588.07,658.159 1589.32,658.16 1590.57,658.162 1591.82,658.164 1593.07,658.165 1594.32,658.167 1595.57,658.168 1596.82,658.17 1598.06,658.171 \n",
" 1599.31,658.172 1600.56,658.174 1601.81,658.175 1603.06,658.176 1604.31,658.177 1605.56,658.178 1606.81,658.179 1608.06,658.18 1609.31,658.181 1610.56,658.181 \n",
" 1611.8,658.182 1613.05,658.183 1614.3,658.184 1615.55,658.184 1616.8,658.185 1618.05,658.186 1619.3,658.186 1620.55,658.187 1621.8,658.187 1623.05,658.188 \n",
" 1624.29,658.188 1625.54,658.189 1626.79,658.189 1628.04,658.19 1629.29,658.19 1630.54,658.19 1631.79,658.191 1633.04,658.191 1634.29,658.191 1635.54,658.192 \n",
" 1636.79,658.192 1638.03,658.192 1639.28,658.193 1640.53,658.193 1641.78,658.193 1643.03,658.193 1644.28,658.194 1645.53,658.194 1646.78,658.194 1648.03,658.194 \n",
" 1649.28,658.194 1650.52,658.194 1651.77,658.195 1653.02,658.195 1654.27,658.195 1655.52,658.195 1656.77,658.195 1658.02,658.195 1659.27,658.195 1660.52,658.195 \n",
" 1661.77,658.196 1663.01,658.196 1664.26,658.196 1665.51,658.196 1666.76,658.196 1668.01,658.196 1669.26,658.196 1670.51,658.196 1671.76,658.196 1673.01,658.196 \n",
" 1674.26,658.196 1675.51,658.196 1676.75,658.196 1678,658.196 1679.25,658.196 1680.5,658.196 1681.75,658.196 1683,658.197 1684.25,658.197 1685.5,658.197 \n",
" 1686.75,658.197 1688,658.197 1689.24,658.197 1690.49,658.197 1691.74,658.197 1692.99,658.197 1694.24,658.197 1695.49,658.197 1696.74,658.197 1697.99,658.197 \n",
" 1699.24,658.197 1700.49,658.197 1701.74,658.197 1702.98,658.197 1704.23,658.197 1705.48,658.197 1706.73,658.197 1707.98,658.197 1709.23,658.197 1710.48,658.197 \n",
" 1711.73,658.197 1712.98,658.197 1714.23,658.197 1715.47,658.197 1716.72,658.197 1717.97,658.197 1719.22,658.197 1720.47,658.197 1721.72,658.197 1722.97,658.197 \n",
" 1724.22,658.197 1725.47,658.197 1726.72,658.197 1727.97,658.197 1729.21,658.197 1730.46,658.197 1731.71,658.197 1732.96,658.197 1734.21,658.197 1735.46,658.197 \n",
" 1736.71,658.197 1737.96,658.197 1739.21,658.197 1740.46,658.197 1741.7,658.197 1742.95,658.197 1744.2,658.197 1745.45,658.197 1746.7,658.197 1747.95,658.197 \n",
" 1749.2,658.197 1750.45,658.197 1751.7,658.197 1752.95,658.197 1754.19,658.197 1755.44,658.197 1756.69,658.197 1757.94,658.197 1759.19,658.197 1760.44,658.197 \n",
" 1761.69,658.197 1762.94,658.197 1764.19,658.197 1765.44,658.197 1766.69,658.197 1767.93,658.197 1769.18,658.197 1770.43,658.197 1771.68,658.197 1772.93,658.197 \n",
" 1774.18,658.197 1775.43,658.197 1776.68,658.197 1777.93,658.197 1779.18,658.197 1780.42,658.197 1781.67,658.197 1782.92,658.197 1784.17,658.197 1785.42,658.197 \n",
" 1786.67,658.197 1787.92,658.197 1789.17,658.197 1790.42,658.197 1791.67,658.197 1792.92,658.197 1794.16,658.197 1795.41,658.197 1796.66,658.197 1797.91,658.197 \n",
" 1799.16,658.197 1800.41,658.197 1801.66,658.197 1802.91,658.197 1804.16,658.197 1805.41,658.197 1806.65,658.197 1807.9,658.197 1809.15,658.197 1810.4,658.197 \n",
" 1811.65,658.197 1812.9,658.197 1814.15,658.197 1815.4,658.197 1816.65,658.197 1817.9,658.197 1819.15,658.197 1820.39,658.197 1821.64,658.197 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
" 2073.95,658.197 2075.2,658.197 2076.45,658.197 2077.7,658.197 2078.95,658.197 2080.19,658.197 2081.44,658.197 2082.69,658.197 2083.94,658.197 2085.19,658.197 \n",
" 2086.44,658.197 2087.69,658.197 2088.94,658.197 2090.19,658.197 2091.44,658.197 2092.69,658.197 2093.93,658.197 2095.18,658.197 2096.43,658.197 2097.68,658.197 \n",
" 2098.93,658.197 2100.18,658.197 2101.43,658.197 2102.68,658.197 2103.93,658.197 2105.18,658.197 2106.42,658.197 2107.67,658.197 2108.92,658.197 2110.17,658.197 \n",
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" 2136.4,658.197 2137.65,658.197 2138.9,658.197 2140.15,658.197 2141.4,658.197 2142.65,658.197 2143.9,658.197 2145.14,658.197 2146.39,658.197 2147.64,658.197 \n",
" 2148.89,658.197 2150.14,658.197 2151.39,658.197 2152.64,658.197 2153.89,658.197 2155.14,658.197 2156.39,658.197 2157.64,658.197 2158.88,658.197 2160.13,658.197 \n",
" 2161.38,658.197 2162.63,658.197 2163.88,658.197 2165.13,658.197 2166.38,658.197 2167.63,658.197 2168.88,658.197 2170.13,658.197 2171.37,658.197 2172.62,658.197 \n",
" 2173.87,658.197 2175.12,658.197 2176.37,658.197 2177.62,658.197 2178.87,658.197 2180.12,658.197 2181.37,658.197 2182.62,658.197 2183.87,658.197 2185.11,658.197 \n",
" 2186.36,658.197 2187.61,658.197 2188.86,658.197 2190.11,658.197 2191.36,658.197 2192.61,658.197 2193.86,658.197 2195.11,658.197 2196.36,658.197 2197.6,658.197 \n",
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" 2261.31,658.197 \n",
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" 874.87,658.181 876.119,658.18 877.368,658.179 878.617,658.178 879.866,658.177 881.115,658.176 882.364,658.174 883.613,658.173 884.862,658.172 886.111,658.17 \n",
" 887.36,658.169 888.609,658.167 889.858,658.166 891.107,658.164 892.356,658.162 893.605,658.161 894.854,658.159 896.103,658.157 897.352,658.154 898.601,658.152 \n",
" 899.851,658.15 901.1,658.147 902.349,658.145 903.598,658.142 904.847,658.139 906.096,658.136 907.345,658.133 908.594,658.13 909.843,658.127 911.092,658.123 \n",
" 912.341,658.12 913.59,658.116 914.839,658.112 916.088,658.108 917.337,658.103 918.586,658.099 919.835,658.094 921.084,658.089 922.333,658.084 923.582,658.078 \n",
" 924.831,658.073 926.08,658.067 927.329,658.061 928.578,658.055 929.828,658.048 931.077,658.041 932.326,658.034 933.575,658.027 934.824,658.019 936.073,658.011 \n",
" 937.322,658.003 938.571,657.994 939.82,657.985 941.069,657.976 942.318,657.966 943.567,657.956 944.816,657.945 946.065,657.934 947.314,657.923 948.563,657.912 \n",
" 949.812,657.9 951.061,657.887 952.31,657.874 953.559,657.861 954.808,657.847 956.057,657.832 957.306,657.818 958.555,657.802 959.805,657.786 961.054,657.77 \n",
" 962.303,657.753 963.552,657.735 964.801,657.717 966.05,657.698 967.299,657.679 968.548,657.659 969.797,657.639 971.046,657.617 972.295,657.596 973.544,657.573 \n",
" 974.793,657.55 976.042,657.526 977.291,657.501 978.54,657.476 979.789,657.45 981.038,657.423 982.287,657.395 983.536,657.367 984.785,657.338 986.034,657.308 \n",
" 987.283,657.277 988.532,657.246 989.781,657.213 991.031,657.18 992.28,657.146 993.529,657.111 994.778,657.075 996.027,657.039 997.276,657.001 998.525,656.963 \n",
" 999.774,656.923 1001.02,656.883 1002.27,656.842 1003.52,656.8 1004.77,656.757 1006.02,656.713 1007.27,656.668 1008.52,656.622 1009.77,656.575 1011.02,656.528 \n",
" 1012.26,656.479 1013.51,656.429 1014.76,656.379 1016.01,656.327 1017.26,656.275 1018.51,656.222 1019.76,656.168 1021.01,656.113 1022.26,656.057 1023.51,656 \n",
" 1024.75,655.942 1026,655.884 1027.25,655.824 1028.5,655.764 1029.75,655.703 1031,655.641 1032.25,655.579 1033.5,655.515 1034.75,655.451 1036,655.386 \n",
" 1037.25,655.321 1038.49,655.255 1039.74,655.188 1040.99,655.121 1042.24,655.053 1043.49,654.985 1044.74,654.916 1045.99,654.847 1047.24,654.777 1048.49,654.707 \n",
" 1049.74,654.637 1050.98,654.566 1052.23,654.496 1053.48,654.425 1054.73,654.354 1055.98,654.283 1057.23,654.212 1058.48,654.141 1059.73,654.07 1060.98,653.999 \n",
" 1062.23,653.929 1063.47,653.859 1064.72,653.789 1065.97,653.72 1067.22,653.651 1068.47,653.583 1069.72,653.515 1070.97,653.449 1072.22,653.383 1073.47,653.318 \n",
" 1074.72,653.253 1075.97,653.19 1077.21,653.129 1078.46,653.068 1079.71,653.009 1080.96,652.951 1082.21,652.894 1083.46,652.839 1084.71,652.786 1085.96,652.735 \n",
" 1087.21,652.685 1088.46,652.637 1089.7,652.592 1090.95,652.548 1092.2,652.507 1093.45,652.468 1094.7,652.432 1095.95,652.398 1097.2,652.366 1098.45,652.338 \n",
" 1099.7,652.312 1100.95,652.289 1102.2,652.269 1103.44,652.252 1104.69,652.238 1105.94,652.228 1107.19,652.221 1108.44,652.217 1109.69,652.217 1110.94,652.221 \n",
" 1112.19,652.228 1113.44,652.239 1114.69,652.254 1115.93,652.273 1117.18,652.296 1118.43,652.323 1119.68,652.354 1120.93,652.39 1122.18,652.429 1123.43,652.474 \n",
" 1124.68,652.523 1125.93,652.576 1127.18,652.634 1128.43,652.696 1129.67,652.763 1130.92,652.835 1132.17,652.912 1133.42,652.993 1134.67,653.08 1135.92,653.171 \n",
" 1137.17,653.267 1138.42,653.368 1139.67,653.474 1140.92,653.585 1142.16,653.701 1143.41,653.822 1144.66,653.948 1145.91,654.079 1147.16,654.215 1148.41,654.355 \n",
" 1149.66,654.501 1150.91,654.651 1152.16,654.807 1153.41,654.967 1154.65,655.132 1155.9,655.302 1157.15,655.476 1158.4,655.655 1159.65,655.838 1160.9,656.026 \n",
" 1162.15,656.218 1163.4,656.415 1164.65,656.616 1165.9,656.821 1167.15,657.03 1168.39,657.243 1169.64,657.459 1170.89,657.68 1172.14,657.903 1173.39,658.131 \n",
" 1174.64,658.361 1175.89,658.595 1177.14,658.832 1178.39,659.071 1179.64,659.314 1180.88,659.558 1182.13,659.806 1183.38,660.055 1184.63,660.307 1185.88,660.56 \n",
" 1187.13,660.815 1188.38,661.071 1189.63,661.329 1190.88,661.588 1192.13,661.848 1193.38,662.109 1194.62,662.37 1195.87,662.631 1197.12,662.893 1198.37,663.154 \n",
" 1199.62,663.415 1200.87,663.676 1202.12,663.936 1203.37,664.195 1204.62,664.453 1205.87,664.709 1207.11,664.964 1208.36,665.217 1209.61,665.468 1210.86,665.716 \n",
" 1212.11,665.962 1213.36,666.206 1214.61,666.446 1215.86,666.684 1217.11,666.918 1218.36,667.148 1219.61,667.375 1220.85,667.598 1222.1,667.816 1223.35,668.031 \n",
" 1224.6,668.24 1225.85,668.445 1227.1,668.645 1228.35,668.839 1229.6,669.029 1230.85,669.213 1232.1,669.391 1233.34,669.563 1234.59,669.729 1235.84,669.889 \n",
" 1237.09,670.043 1238.34,670.19 1239.59,670.33 1240.84,670.464 1242.09,670.591 1243.34,670.71 1244.59,670.823 1245.84,670.928 1247.08,671.026 1248.33,671.117 \n",
" 1249.58,671.199 1250.83,671.275 1252.08,671.342 1253.33,671.402 1254.58,671.454 1255.83,671.498 1257.08,671.534 1258.33,671.562 1259.57,671.582 1260.82,671.594 \n",
" 1262.07,671.598 1263.32,671.594 1264.57,671.582 1265.82,671.562 1267.07,671.534 1268.32,671.498 1269.57,671.454 1270.82,671.402 1272.06,671.342 1273.31,671.275 \n",
" 1274.56,671.199 1275.81,671.117 1277.06,671.026 1278.31,670.928 1279.56,670.823 1280.81,670.71 1282.06,670.591 1283.31,670.464 1284.56,670.33 1285.8,670.19 \n",
" 1287.05,670.043 1288.3,669.889 1289.55,669.729 1290.8,669.563 1292.05,669.391 1293.3,669.213 1294.55,669.029 1295.8,668.839 1297.05,668.645 1298.29,668.445 \n",
" 1299.54,668.24 1300.79,668.031 1302.04,667.816 1303.29,667.598 1304.54,667.375 1305.79,667.148 1307.04,666.918 1308.29,666.684 1309.54,666.446 1310.79,666.206 \n",
" 1312.03,665.962 1313.28,665.716 1314.53,665.468 1315.78,665.217 1317.03,664.964 1318.28,664.709 1319.53,664.453 1320.78,664.195 1322.03,663.936 1323.28,663.676 \n",
" 1324.52,663.415 1325.77,663.154 1327.02,662.893 1328.27,662.631 1329.52,662.37 1330.77,662.109 1332.02,661.848 1333.27,661.588 1334.52,661.329 1335.77,661.071 \n",
" 1337.02,660.815 1338.26,660.56 1339.51,660.307 1340.76,660.055 1342.01,659.806 1343.26,659.558 1344.51,659.314 1345.76,659.071 1347.01,658.832 1348.26,658.595 \n",
" 1349.51,658.361 1350.75,658.131 1352,657.903 1353.25,657.68 1354.5,657.459 1355.75,657.243 1357,657.03 1358.25,656.821 1359.5,656.616 1360.75,656.415 \n",
" 1362,656.218 1363.24,656.026 1364.49,655.838 1365.74,655.655 1366.99,655.476 1368.24,655.302 1369.49,655.132 1370.74,654.967 1371.99,654.807 1373.24,654.651 \n",
" 1374.49,654.501 1375.74,654.355 1376.98,654.215 1378.23,654.079 1379.48,653.948 1380.73,653.822 1381.98,653.701 1383.23,653.585 1384.48,653.474 1385.73,653.368 \n",
" 1386.98,653.267 1388.23,653.171 1389.47,653.08 1390.72,652.993 1391.97,652.912 1393.22,652.835 1394.47,652.763 1395.72,652.696 1396.97,652.634 1398.22,652.576 \n",
" 1399.47,652.523 1400.72,652.474 1401.97,652.429 1403.21,652.39 1404.46,652.354 1405.71,652.323 1406.96,652.296 1408.21,652.273 1409.46,652.254 1410.71,652.239 \n",
" 1411.96,652.228 1413.21,652.221 1414.46,652.217 1415.7,652.217 1416.95,652.221 1418.2,652.228 1419.45,652.238 1420.7,652.252 1421.95,652.269 1423.2,652.289 \n",
" 1424.45,652.312 1425.7,652.338 1426.95,652.366 1428.2,652.398 1429.44,652.432 1430.69,652.468 1431.94,652.507 1433.19,652.548 1434.44,652.592 1435.69,652.637 \n",
" 1436.94,652.685 1438.19,652.735 1439.44,652.786 1440.69,652.839 1441.93,652.894 1443.18,652.951 1444.43,653.009 1445.68,653.068 1446.93,653.129 1448.18,653.19 \n",
" 1449.43,653.253 1450.68,653.318 1451.93,653.383 1453.18,653.449 1454.42,653.515 1455.67,653.583 1456.92,653.651 1458.17,653.72 1459.42,653.789 1460.67,653.859 \n",
" 1461.92,653.929 1463.17,653.999 1464.42,654.07 1465.67,654.141 1466.92,654.212 1468.16,654.283 1469.41,654.354 1470.66,654.425 1471.91,654.496 1473.16,654.566 \n",
" 1474.41,654.637 1475.66,654.707 1476.91,654.777 1478.16,654.847 1479.41,654.916 1480.65,654.985 1481.9,655.053 1483.15,655.121 1484.4,655.188 1485.65,655.255 \n",
" 1486.9,655.321 1488.15,655.386 1489.4,655.451 1490.65,655.515 1491.9,655.579 1493.15,655.641 1494.39,655.703 1495.64,655.764 1496.89,655.824 1498.14,655.884 \n",
" 1499.39,655.942 1500.64,656 1501.89,656.057 1503.14,656.113 1504.39,656.168 1505.64,656.222 1506.88,656.275 1508.13,656.327 1509.38,656.379 1510.63,656.429 \n",
" 1511.88,656.479 1513.13,656.528 1514.38,656.575 1515.63,656.622 1516.88,656.668 1518.13,656.713 1519.38,656.757 1520.62,656.8 1521.87,656.842 1523.12,656.883 \n",
" 1524.37,656.923 1525.62,656.963 1526.87,657.001 1528.12,657.039 1529.37,657.075 1530.62,657.111 1531.87,657.146 1533.11,657.18 1534.36,657.213 1535.61,657.246 \n",
" 1536.86,657.277 1538.11,657.308 1539.36,657.338 1540.61,657.367 1541.86,657.395 1543.11,657.423 1544.36,657.45 1545.61,657.476 1546.85,657.501 1548.1,657.526 \n",
" 1549.35,657.55 1550.6,657.573 1551.85,657.596 1553.1,657.617 1554.35,657.639 1555.6,657.659 1556.85,657.679 1558.1,657.698 1559.34,657.717 1560.59,657.735 \n",
" 1561.84,657.753 1563.09,657.77 1564.34,657.786 1565.59,657.802 1566.84,657.818 1568.09,657.832 1569.34,657.847 1570.59,657.861 1571.83,657.874 1573.08,657.887 \n",
" 1574.33,657.9 1575.58,657.912 1576.83,657.923 1578.08,657.934 1579.33,657.945 1580.58,657.956 1581.83,657.966 1583.08,657.976 1584.33,657.985 1585.57,657.994 \n",
" 1586.82,658.003 1588.07,658.011 1589.32,658.019 1590.57,658.027 1591.82,658.034 1593.07,658.041 1594.32,658.048 1595.57,658.055 1596.82,658.061 1598.06,658.067 \n",
" 1599.31,658.073 1600.56,658.078 1601.81,658.084 1603.06,658.089 1604.31,658.094 1605.56,658.099 1606.81,658.103 1608.06,658.108 1609.31,658.112 1610.56,658.116 \n",
" 1611.8,658.12 1613.05,658.123 1614.3,658.127 1615.55,658.13 1616.8,658.133 1618.05,658.136 1619.3,658.139 1620.55,658.142 1621.8,658.145 1623.05,658.147 \n",
" 1624.29,658.15 1625.54,658.152 1626.79,658.154 1628.04,658.157 1629.29,658.159 1630.54,658.161 1631.79,658.162 1633.04,658.164 1634.29,658.166 1635.54,658.167 \n",
" 1636.79,658.169 1638.03,658.17 1639.28,658.172 1640.53,658.173 1641.78,658.174 1643.03,658.176 1644.28,658.177 1645.53,658.178 1646.78,658.179 1648.03,658.18 \n",
" 1649.28,658.181 1650.52,658.182 1651.77,658.182 1653.02,658.183 1654.27,658.184 1655.52,658.185 1656.77,658.185 1658.02,658.186 1659.27,658.187 1660.52,658.187 \n",
" 1661.77,658.188 1663.01,658.188 1664.26,658.189 1665.51,658.189 1666.76,658.19 1668.01,658.19 1669.26,658.19 1670.51,658.191 1671.76,658.191 1673.01,658.192 \n",
" 1674.26,658.192 1675.51,658.192 1676.75,658.192 1678,658.193 1679.25,658.193 1680.5,658.193 1681.75,658.193 1683,658.194 1684.25,658.194 1685.5,658.194 \n",
" 1686.75,658.194 1688,658.194 1689.24,658.195 1690.49,658.195 1691.74,658.195 1692.99,658.195 1694.24,658.195 1695.49,658.195 1696.74,658.195 1697.99,658.195 \n",
" 1699.24,658.196 1700.49,658.196 1701.74,658.196 1702.98,658.196 1704.23,658.196 1705.48,658.196 1706.73,658.196 1707.98,658.196 1709.23,658.196 1710.48,658.196 \n",
" 1711.73,658.196 1712.98,658.196 1714.23,658.196 1715.47,658.196 1716.72,658.196 1717.97,658.196 1719.22,658.197 1720.47,658.197 1721.72,658.197 1722.97,658.197 \n",
" 1724.22,658.197 1725.47,658.197 1726.72,658.197 1727.97,658.197 1729.21,658.197 1730.46,658.197 1731.71,658.197 1732.96,658.197 1734.21,658.197 1735.46,658.197 \n",
" 1736.71,658.197 1737.96,658.197 1739.21,658.197 1740.46,658.197 1741.7,658.197 1742.95,658.197 1744.2,658.197 1745.45,658.197 1746.7,658.197 1747.95,658.197 \n",
" 1749.2,658.197 1750.45,658.197 1751.7,658.197 1752.95,658.197 1754.19,658.197 1755.44,658.197 1756.69,658.197 1757.94,658.197 1759.19,658.197 1760.44,658.197 \n",
" 1761.69,658.197 1762.94,658.197 1764.19,658.197 1765.44,658.197 1766.69,658.197 1767.93,658.197 1769.18,658.197 1770.43,658.197 1771.68,658.197 1772.93,658.197 \n",
" 1774.18,658.197 1775.43,658.197 1776.68,658.197 1777.93,658.197 1779.18,658.197 1780.42,658.197 1781.67,658.197 1782.92,658.197 1784.17,658.197 1785.42,658.197 \n",
" 1786.67,658.197 1787.92,658.197 1789.17,658.197 1790.42,658.197 1791.67,658.197 1792.92,658.197 1794.16,658.197 1795.41,658.197 1796.66,658.197 1797.91,658.197 \n",
" 1799.16,658.197 1800.41,658.197 1801.66,658.197 1802.91,658.197 1804.16,658.197 1805.41,658.197 1806.65,658.197 1807.9,658.197 1809.15,658.197 1810.4,658.197 \n",
" 1811.65,658.197 1812.9,658.197 1814.15,658.197 1815.4,658.197 1816.65,658.197 1817.9,658.197 1819.15,658.197 1820.39,658.197 1821.64,658.197 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
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" 1224.6,637.474 1225.85,637.962 1227.1,638.469 1228.35,638.995 1229.6,639.538 1230.85,640.1 1232.1,640.679 1233.34,641.275 1234.59,641.887 1235.84,642.515 \n",
" 1237.09,643.158 1238.34,643.816 1239.59,644.488 1240.84,645.173 1242.09,645.871 1243.34,646.581 1244.59,647.303 1245.84,648.035 1247.08,648.778 1248.33,649.529 \n",
" 1249.58,650.289 1250.83,651.058 1252.08,651.833 1253.33,652.614 1254.58,653.402 1255.83,654.193 1257.08,654.989 1258.33,655.788 1259.57,656.59 1260.82,657.393 \n",
" 1262.07,658.197 1263.32,659.001 1264.57,659.804 1265.82,660.606 1267.07,661.405 1268.32,662.201 1269.57,662.993 1270.82,663.78 1272.06,664.561 1273.31,665.336 \n",
" 1274.56,666.105 1275.81,666.865 1277.06,667.617 1278.31,668.359 1279.56,669.091 1280.81,669.813 1282.06,670.523 1283.31,671.221 1284.56,671.906 1285.8,672.578 \n",
" 1287.05,673.236 1288.3,673.879 1289.55,674.507 1290.8,675.119 1292.05,675.715 1293.3,676.294 1294.55,676.856 1295.8,677.4 1297.05,677.925 1298.29,678.432 \n",
" 1299.54,678.92 1300.79,679.389 1302.04,679.837 1303.29,680.266 1304.54,680.674 1305.79,681.061 1307.04,681.428 1308.29,681.773 1309.54,682.097 1310.79,682.4 \n",
" 1312.03,682.681 1313.28,682.94 1314.53,683.177 1315.78,683.393 1317.03,683.586 1318.28,683.758 1319.53,683.908 1320.78,684.035 1322.03,684.142 1323.28,684.226 \n",
" 1324.52,684.289 1325.77,684.33 1327.02,684.351 1328.27,684.35 1329.52,684.328 1330.77,684.286 1332.02,684.224 1333.27,684.142 1334.52,684.04 1335.77,683.918 \n",
" 1337.02,683.778 1338.26,683.618 1339.51,683.441 1340.76,683.246 1342.01,683.033 1343.26,682.803 1344.51,682.557 1345.76,682.294 1347.01,682.016 1348.26,681.723 \n",
" 1349.51,681.414 1350.75,681.092 1352,680.756 1353.25,680.408 1354.5,680.046 1355.75,679.672 1357,679.287 1358.25,678.891 1359.5,678.485 1360.75,678.069 \n",
" 1362,677.643 1363.24,677.209 1364.49,676.767 1365.74,676.317 1366.99,675.861 1368.24,675.398 1369.49,674.929 1370.74,674.454 1371.99,673.975 1373.24,673.492 \n",
" 1374.49,673.006 1375.74,672.516 1376.98,672.024 1378.23,671.529 1379.48,671.034 1380.73,670.537 1381.98,670.04 1383.23,669.543 1384.48,669.046 1385.73,668.551 \n",
" 1386.98,668.057 1388.23,667.565 1389.47,667.076 1390.72,666.589 1391.97,666.105 1393.22,665.626 1394.47,665.15 1395.72,664.679 1396.97,664.213 1398.22,663.752 \n",
" 1399.47,663.296 1400.72,662.846 1401.97,662.403 1403.21,661.966 1404.46,661.536 1405.71,661.113 1406.96,660.697 1408.21,660.289 1409.46,659.888 1410.71,659.496 \n",
" 1411.96,659.111 1413.21,658.736 1414.46,658.368 1415.7,658.01 1416.95,657.66 1418.2,657.319 1419.45,656.988 1420.7,656.665 1421.95,656.352 1423.2,656.048 \n",
" 1424.45,655.754 1425.7,655.469 1426.95,655.194 1428.2,654.928 1429.44,654.672 1430.69,654.425 1431.94,654.188 1433.19,653.96 1434.44,653.742 1435.69,653.534 \n",
" 1436.94,653.334 1438.19,653.145 1439.44,652.964 1440.69,652.792 1441.93,652.63 1443.18,652.477 1444.43,652.332 1445.68,652.197 1446.93,652.07 1448.18,651.951 \n",
" 1449.43,651.841 1450.68,651.739 1451.93,651.645 1453.18,651.56 1454.42,651.482 1455.67,651.411 1456.92,651.349 1458.17,651.293 1459.42,651.245 1460.67,651.204 \n",
" 1461.92,651.169 1463.17,651.141 1464.42,651.12 1465.67,651.104 1466.92,651.095 1468.16,651.092 1469.41,651.094 1470.66,651.102 1471.91,651.116 1473.16,651.134 \n",
" 1474.41,651.157 1475.66,651.185 1476.91,651.218 1478.16,651.255 1479.41,651.296 1480.65,651.342 1481.9,651.391 1483.15,651.444 1484.4,651.5 1485.65,651.559 \n",
" 1486.9,651.622 1488.15,651.687 1489.4,651.756 1490.65,651.827 1491.9,651.9 1493.15,651.976 1494.39,652.054 1495.64,652.134 1496.89,652.215 1498.14,652.299 \n",
" 1499.39,652.384 1500.64,652.47 1501.89,652.557 1503.14,652.646 1504.39,652.736 1505.64,652.826 1506.88,652.918 1508.13,653.01 1509.38,653.102 1510.63,653.195 \n",
" 1511.88,653.288 1513.13,653.381 1514.38,653.475 1515.63,653.568 1516.88,653.662 1518.13,653.755 1519.38,653.848 1520.62,653.94 1521.87,654.033 1523.12,654.124 \n",
" 1524.37,654.215 1525.62,654.306 1526.87,654.396 1528.12,654.485 1529.37,654.573 1530.62,654.66 1531.87,654.747 1533.11,654.832 1534.36,654.917 1535.61,655 \n",
" 1536.86,655.083 1538.11,655.164 1539.36,655.244 1540.61,655.323 1541.86,655.401 1543.11,655.477 1544.36,655.553 1545.61,655.627 1546.85,655.7 1548.1,655.771 \n",
" 1549.35,655.841 1550.6,655.91 1551.85,655.978 1553.1,656.044 1554.35,656.109 1555.6,656.172 1556.85,656.235 1558.1,656.295 1559.34,656.355 1560.59,656.413 \n",
" 1561.84,656.47 1563.09,656.526 1564.34,656.58 1565.59,656.633 1566.84,656.685 1568.09,656.735 1569.34,656.784 1570.59,656.832 1571.83,656.879 1573.08,656.924 \n",
" 1574.33,656.968 1575.58,657.011 1576.83,657.053 1578.08,657.094 1579.33,657.133 1580.58,657.172 1581.83,657.209 1583.08,657.245 1584.33,657.28 1585.57,657.314 \n",
" 1586.82,657.347 1588.07,657.379 1589.32,657.41 1590.57,657.44 1591.82,657.469 1593.07,657.498 1594.32,657.525 1595.57,657.551 1596.82,657.577 1598.06,657.601 \n",
" 1599.31,657.625 1600.56,657.648 1601.81,657.671 1603.06,657.692 1604.31,657.713 1605.56,657.733 1606.81,657.752 1608.06,657.771 1609.31,657.789 1610.56,657.806 \n",
" 1611.8,657.822 1613.05,657.838 1614.3,657.854 1615.55,657.869 1616.8,657.883 1618.05,657.897 1619.3,657.91 1620.55,657.923 1621.8,657.935 1623.05,657.947 \n",
" 1624.29,657.958 1625.54,657.969 1626.79,657.979 1628.04,657.989 1629.29,657.999 1630.54,658.008 1631.79,658.017 1633.04,658.025 1634.29,658.033 1635.54,658.041 \n",
" 1636.79,658.048 1638.03,658.055 1639.28,658.062 1640.53,658.069 1641.78,658.075 1643.03,658.081 1644.28,658.086 1645.53,658.092 1646.78,658.097 1648.03,658.102 \n",
" 1649.28,658.107 1650.52,658.111 1651.77,658.116 1653.02,658.12 1654.27,658.124 1655.52,658.127 1656.77,658.131 1658.02,658.134 1659.27,658.137 1660.52,658.141 \n",
" 1661.77,658.144 1663.01,658.146 1664.26,658.149 1665.51,658.152 1666.76,658.154 1668.01,658.156 1669.26,658.158 1670.51,658.16 1671.76,658.162 1673.01,658.164 \n",
" 1674.26,658.166 1675.51,658.168 1676.75,658.169 1678,658.171 1679.25,658.172 1680.5,658.174 1681.75,658.175 1683,658.176 1684.25,658.177 1685.5,658.179 \n",
" 1686.75,658.18 1688,658.181 1689.24,658.181 1690.49,658.182 1691.74,658.183 1692.99,658.184 1694.24,658.185 1695.49,658.185 1696.74,658.186 1697.99,658.187 \n",
" 1699.24,658.187 1700.49,658.188 1701.74,658.189 1702.98,658.189 1704.23,658.189 1705.48,658.19 1706.73,658.19 1707.98,658.191 1709.23,658.191 1710.48,658.192 \n",
" 1711.73,658.192 1712.98,658.192 1714.23,658.192 1715.47,658.193 1716.72,658.193 1717.97,658.193 1719.22,658.193 1720.47,658.194 1721.72,658.194 1722.97,658.194 \n",
" 1724.22,658.194 1725.47,658.194 1726.72,658.195 1727.97,658.195 1729.21,658.195 1730.46,658.195 1731.71,658.195 1732.96,658.195 1734.21,658.195 1735.46,658.196 \n",
" 1736.71,658.196 1737.96,658.196 1739.21,658.196 1740.46,658.196 1741.7,658.196 1742.95,658.196 1744.2,658.196 1745.45,658.196 1746.7,658.196 1747.95,658.196 \n",
" 1749.2,658.196 1750.45,658.196 1751.7,658.196 1752.95,658.196 1754.19,658.197 1755.44,658.197 1756.69,658.197 1757.94,658.197 1759.19,658.197 1760.44,658.197 \n",
" 1761.69,658.197 1762.94,658.197 1764.19,658.197 1765.44,658.197 1766.69,658.197 1767.93,658.197 1769.18,658.197 1770.43,658.197 1771.68,658.197 1772.93,658.197 \n",
" 1774.18,658.197 1775.43,658.197 1776.68,658.197 1777.93,658.197 1779.18,658.197 1780.42,658.197 1781.67,658.197 1782.92,658.197 1784.17,658.197 1785.42,658.197 \n",
" 1786.67,658.197 1787.92,658.197 1789.17,658.197 1790.42,658.197 1791.67,658.197 1792.92,658.197 1794.16,658.197 1795.41,658.197 1796.66,658.197 1797.91,658.197 \n",
" 1799.16,658.197 1800.41,658.197 1801.66,658.197 1802.91,658.197 1804.16,658.197 1805.41,658.197 1806.65,658.197 1807.9,658.197 1809.15,658.197 1810.4,658.197 \n",
" 1811.65,658.197 1812.9,658.197 1814.15,658.197 1815.4,658.197 1816.65,658.197 1817.9,658.197 1819.15,658.197 1820.39,658.197 1821.64,658.197 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
" 2073.95,658.197 2075.2,658.197 2076.45,658.197 2077.7,658.197 2078.95,658.197 2080.19,658.197 2081.44,658.197 2082.69,658.197 2083.94,658.197 2085.19,658.197 \n",
" 2086.44,658.197 2087.69,658.197 2088.94,658.197 2090.19,658.197 2091.44,658.197 2092.69,658.197 2093.93,658.197 2095.18,658.197 2096.43,658.197 2097.68,658.197 \n",
" 2098.93,658.197 2100.18,658.197 2101.43,658.197 2102.68,658.197 2103.93,658.197 2105.18,658.197 2106.42,658.197 2107.67,658.197 2108.92,658.197 2110.17,658.197 \n",
" 2111.42,658.197 2112.67,658.197 2113.92,658.197 2115.17,658.197 2116.42,658.197 2117.67,658.197 2118.92,658.197 2120.16,658.197 2121.41,658.197 2122.66,658.197 \n",
" 2123.91,658.197 2125.16,658.197 2126.41,658.197 2127.66,658.197 2128.91,658.197 2130.16,658.197 2131.41,658.197 2132.65,658.197 2133.9,658.197 2135.15,658.197 \n",
" 2136.4,658.197 2137.65,658.197 2138.9,658.197 2140.15,658.197 2141.4,658.197 2142.65,658.197 2143.9,658.197 2145.14,658.197 2146.39,658.197 2147.64,658.197 \n",
" 2148.89,658.197 2150.14,658.197 2151.39,658.197 2152.64,658.197 2153.89,658.197 2155.14,658.197 2156.39,658.197 2157.64,658.197 2158.88,658.197 2160.13,658.197 \n",
" 2161.38,658.197 2162.63,658.197 2163.88,658.197 2165.13,658.197 2166.38,658.197 2167.63,658.197 2168.88,658.197 2170.13,658.197 2171.37,658.197 2172.62,658.197 \n",
" 2173.87,658.197 2175.12,658.197 2176.37,658.197 2177.62,658.197 2178.87,658.197 2180.12,658.197 2181.37,658.197 2182.62,658.197 2183.87,658.197 2185.11,658.197 \n",
" 2186.36,658.197 2187.61,658.197 2188.86,658.197 2190.11,658.197 2191.36,658.197 2192.61,658.197 2193.86,658.197 2195.11,658.197 2196.36,658.197 2197.6,658.197 \n",
" 2198.85,658.197 2200.1,658.197 2201.35,658.197 2202.6,658.197 2203.85,658.197 2205.1,658.197 2206.35,658.197 2207.6,658.197 2208.85,658.197 2210.1,658.197 \n",
" 2211.34,658.197 2212.59,658.197 2213.84,658.197 2215.09,658.197 2216.34,658.197 2217.59,658.197 2218.84,658.197 2220.09,658.197 2221.34,658.197 2222.59,658.197 \n",
" 2223.83,658.197 2225.08,658.197 2226.33,658.197 2227.58,658.197 2228.83,658.197 2230.08,658.197 2231.33,658.197 2232.58,658.197 2233.83,658.197 2235.08,658.197 \n",
" 2236.33,658.197 2237.57,658.197 2238.82,658.197 2240.07,658.197 2241.32,658.197 2242.57,658.197 2243.82,658.197 2245.07,658.197 2246.32,658.197 2247.57,658.197 \n",
" 2248.82,658.197 2250.06,658.197 2251.31,658.197 2252.56,658.197 2253.81,658.197 2255.06,658.197 2256.31,658.197 2257.56,658.197 2258.81,658.197 2260.06,658.197 \n",
" 2261.31,658.197 \n",
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" 337.782,658.197 339.031,658.197 340.28,658.197 341.529,658.197 342.778,658.197 344.027,658.197 345.276,658.197 346.525,658.197 347.774,658.197 349.023,658.197 \n",
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" 375.253,658.197 376.502,658.197 377.751,658.197 379,658.197 380.249,658.197 381.498,658.197 382.747,658.197 383.996,658.197 385.245,658.197 386.494,658.197 \n",
" 387.743,658.197 388.992,658.197 390.242,658.197 391.491,658.197 392.74,658.197 393.989,658.197 395.238,658.197 396.487,658.197 397.736,658.197 398.985,658.197 \n",
" 400.234,658.197 401.483,658.197 402.732,658.197 403.981,658.197 405.23,658.197 406.479,658.197 407.728,658.197 408.977,658.197 410.226,658.197 411.475,658.197 \n",
" 412.724,658.197 413.973,658.197 415.222,658.197 416.471,658.197 417.72,658.197 418.969,658.197 420.219,658.197 421.468,658.197 422.717,658.197 423.966,658.197 \n",
" 425.215,658.197 426.464,658.197 427.713,658.197 428.962,658.197 430.211,658.197 431.46,658.197 432.709,658.197 433.958,658.197 435.207,658.197 436.456,658.197 \n",
" 437.705,658.197 438.954,658.197 440.203,658.197 441.452,658.197 442.701,658.197 443.95,658.197 445.199,658.197 446.448,658.197 447.697,658.197 448.946,658.197 \n",
" 450.196,658.197 451.445,658.197 452.694,658.197 453.943,658.197 455.192,658.197 456.441,658.197 457.69,658.197 458.939,658.197 460.188,658.197 461.437,658.197 \n",
" 462.686,658.197 463.935,658.197 465.184,658.197 466.433,658.197 467.682,658.197 468.931,658.197 470.18,658.197 471.429,658.197 472.678,658.197 473.927,658.197 \n",
" 475.176,658.197 476.425,658.197 477.674,658.197 478.923,658.197 480.173,658.197 481.422,658.197 482.671,658.197 483.92,658.197 485.169,658.197 486.418,658.197 \n",
" 487.667,658.197 488.916,658.197 490.165,658.197 491.414,658.197 492.663,658.197 493.912,658.197 495.161,658.197 496.41,658.197 497.659,658.197 498.908,658.197 \n",
" 500.157,658.197 501.406,658.197 502.655,658.197 503.904,658.197 505.153,658.197 506.402,658.197 507.651,658.197 508.9,658.197 510.15,658.197 511.399,658.197 \n",
" 512.648,658.197 513.897,658.197 515.146,658.197 516.395,658.197 517.644,658.197 518.893,658.197 520.142,658.197 521.391,658.197 522.64,658.197 523.889,658.197 \n",
" 525.138,658.197 526.387,658.197 527.636,658.197 528.885,658.197 530.134,658.197 531.383,658.197 532.632,658.197 533.881,658.197 535.13,658.197 536.379,658.197 \n",
" 537.628,658.197 538.877,658.197 540.127,658.197 541.376,658.197 542.625,658.197 543.874,658.197 545.123,658.197 546.372,658.197 547.621,658.197 548.87,658.197 \n",
" 550.119,658.197 551.368,658.197 552.617,658.197 553.866,658.197 555.115,658.197 556.364,658.197 557.613,658.197 558.862,658.197 560.111,658.197 561.36,658.197 \n",
" 562.609,658.197 563.858,658.197 565.107,658.197 566.356,658.197 567.605,658.197 568.854,658.197 570.104,658.197 571.353,658.197 572.602,658.197 573.851,658.197 \n",
" 575.1,658.197 576.349,658.197 577.598,658.197 578.847,658.197 580.096,658.197 581.345,658.197 582.594,658.197 583.843,658.197 585.092,658.197 586.341,658.197 \n",
" 587.59,658.197 588.839,658.197 590.088,658.197 591.337,658.197 592.586,658.197 593.835,658.197 595.084,658.197 596.333,658.197 597.582,658.197 598.831,658.197 \n",
" 600.081,658.197 601.33,658.197 602.579,658.197 603.828,658.197 605.077,658.197 606.326,658.197 607.575,658.197 608.824,658.197 610.073,658.197 611.322,658.197 \n",
" 612.571,658.197 613.82,658.197 615.069,658.197 616.318,658.197 617.567,658.197 618.816,658.197 620.065,658.197 621.314,658.197 622.563,658.197 623.812,658.197 \n",
" 625.061,658.197 626.31,658.197 627.559,658.197 628.808,658.197 630.058,658.197 631.307,658.197 632.556,658.197 633.805,658.197 635.054,658.197 636.303,658.197 \n",
" 637.552,658.197 638.801,658.197 640.05,658.197 641.299,658.197 642.548,658.197 643.797,658.197 645.046,658.197 646.295,658.197 647.544,658.197 648.793,658.197 \n",
" 650.042,658.197 651.291,658.197 652.54,658.197 653.789,658.197 655.038,658.197 656.287,658.197 657.536,658.197 658.785,658.197 660.035,658.197 661.284,658.197 \n",
" 662.533,658.197 663.782,658.197 665.031,658.197 666.28,658.197 667.529,658.197 668.778,658.197 670.027,658.197 671.276,658.197 672.525,658.197 673.774,658.197 \n",
" 675.023,658.197 676.272,658.197 677.521,658.197 678.77,658.197 680.019,658.197 681.268,658.197 682.517,658.197 683.766,658.197 685.015,658.197 686.264,658.197 \n",
" 687.513,658.197 688.762,658.197 690.012,658.197 691.261,658.197 692.51,658.197 693.759,658.197 695.008,658.197 696.257,658.197 697.506,658.197 698.755,658.197 \n",
" 700.004,658.197 701.253,658.197 702.502,658.197 703.751,658.197 705,658.197 706.249,658.197 707.498,658.197 708.747,658.197 709.996,658.197 711.245,658.197 \n",
" 712.494,658.197 713.743,658.197 714.992,658.197 716.241,658.197 717.49,658.197 718.739,658.197 719.989,658.197 721.238,658.197 722.487,658.197 723.736,658.197 \n",
" 724.985,658.197 726.234,658.197 727.483,658.197 728.732,658.197 729.981,658.197 731.23,658.197 732.479,658.197 733.728,658.197 734.977,658.197 736.226,658.196 \n",
" 737.475,658.196 738.724,658.196 739.973,658.196 741.222,658.196 742.471,658.196 743.72,658.196 744.969,658.196 746.218,658.196 747.467,658.196 748.716,658.196 \n",
" 749.966,658.196 751.215,658.196 752.464,658.196 753.713,658.196 754.962,658.195 756.211,658.195 757.46,658.195 758.709,658.195 759.958,658.195 761.207,658.195 \n",
" 762.456,658.195 763.705,658.194 764.954,658.194 766.203,658.194 767.452,658.194 768.701,658.194 769.95,658.193 771.199,658.193 772.448,658.193 773.697,658.192 \n",
" 774.946,658.192 776.195,658.192 777.444,658.191 778.693,658.191 779.943,658.191 781.192,658.19 782.441,658.19 783.69,658.189 784.939,658.189 786.188,658.188 \n",
" 787.437,658.188 788.686,658.187 789.935,658.186 791.184,658.186 792.433,658.185 793.682,658.184 794.931,658.183 796.18,658.182 797.429,658.181 798.678,658.18 \n",
" 799.927,658.179 801.176,658.178 802.425,658.177 803.674,658.176 804.923,658.174 806.172,658.173 807.421,658.171 808.67,658.17 809.92,658.168 811.169,658.166 \n",
" 812.418,658.164 813.667,658.162 814.916,658.16 816.165,658.158 817.414,658.156 818.663,658.153 819.912,658.151 821.161,658.148 822.41,658.145 823.659,658.142 \n",
" 824.908,658.139 826.157,658.135 827.406,658.132 828.655,658.128 829.904,658.124 831.153,658.12 832.402,658.115 833.651,658.11 834.9,658.106 836.149,658.1 \n",
" 837.398,658.095 838.647,658.089 839.897,658.083 841.146,658.077 842.395,658.071 843.644,658.064 844.893,658.056 846.142,658.049 847.391,658.041 848.64,658.033 \n",
" 849.889,658.024 851.138,658.015 852.387,658.005 853.636,657.995 854.885,657.984 856.134,657.973 857.383,657.962 858.632,657.95 859.881,657.937 861.13,657.924 \n",
" 862.379,657.91 863.628,657.896 864.877,657.881 866.126,657.865 867.375,657.849 868.624,657.832 869.874,657.814 871.123,657.795 872.372,657.776 873.621,657.756 \n",
" 874.87,657.735 876.119,657.713 877.368,657.69 878.617,657.667 879.866,657.642 881.115,657.617 882.364,657.59 883.613,657.562 884.862,657.533 886.111,657.504 \n",
" 887.36,657.473 888.609,657.441 889.858,657.407 891.107,657.373 892.356,657.337 893.605,657.3 894.854,657.261 896.103,657.221 897.352,657.18 898.601,657.137 \n",
" 899.851,657.093 901.1,657.048 902.349,657 903.598,656.952 904.847,656.901 906.096,656.849 907.345,656.796 908.594,656.74 909.843,656.683 911.092,656.625 \n",
" 912.341,656.564 913.59,656.502 914.839,656.437 916.088,656.371 917.337,656.303 918.586,656.233 919.835,656.161 921.084,656.088 922.333,656.012 923.582,655.934 \n",
" 924.831,655.854 926.08,655.773 927.329,655.689 928.578,655.603 929.828,655.515 931.077,655.425 932.326,655.333 933.575,655.239 934.824,655.143 936.073,655.045 \n",
" 937.322,654.945 938.571,654.843 939.82,654.739 941.069,654.633 942.318,654.525 943.567,654.415 944.816,654.303 946.065,654.189 947.314,654.074 948.563,653.957 \n",
" 949.812,653.838 951.061,653.717 952.31,653.595 953.559,653.472 954.808,653.347 956.057,653.221 957.306,653.093 958.555,652.965 959.805,652.835 961.054,652.704 \n",
" 962.303,652.573 963.552,652.441 964.801,652.308 966.05,652.175 967.299,652.042 968.548,651.908 969.797,651.775 971.046,651.641 972.295,651.508 973.544,651.376 \n",
" 974.793,651.244 976.042,651.113 977.291,650.983 978.54,650.855 979.789,650.728 981.038,650.603 982.287,650.479 983.536,650.359 984.785,650.24 986.034,650.125 \n",
" 987.283,650.012 988.532,649.903 989.781,649.797 991.031,649.695 992.28,649.597 993.529,649.504 994.778,649.416 996.027,649.333 997.276,649.255 998.525,649.183 \n",
" 999.774,649.117 1001.02,649.057 1002.27,649.004 1003.52,648.959 1004.77,648.921 1006.02,648.89 1007.27,648.868 1008.52,648.855 1009.77,648.85 1011.02,648.855 \n",
" 1012.26,648.87 1013.51,648.895 1014.76,648.93 1016.01,648.976 1017.26,649.034 1018.51,649.103 1019.76,649.184 1021.01,649.277 1022.26,649.383 1023.51,649.503 \n",
" 1024.75,649.635 1026,649.782 1027.25,649.943 1028.5,650.119 1029.75,650.309 1031,650.515 1032.25,650.736 1033.5,650.973 1034.75,651.227 1036,651.496 \n",
" 1037.25,651.783 1038.49,652.087 1039.74,652.408 1040.99,652.746 1042.24,653.102 1043.49,653.477 1044.74,653.869 1045.99,654.28 1047.24,654.709 1048.49,655.156 \n",
" 1049.74,655.622 1050.98,656.108 1052.23,656.611 1053.48,657.134 1054.73,657.675 1055.98,658.236 1057.23,658.815 1058.48,659.413 1059.73,660.029 1060.98,660.664 \n",
" 1062.23,661.317 1063.47,661.988 1064.72,662.676 1065.97,663.383 1067.22,664.107 1068.47,664.847 1069.72,665.605 1070.97,666.378 1072.22,667.167 1073.47,667.971 \n",
" 1074.72,668.791 1075.97,669.624 1077.21,670.471 1078.46,671.331 1079.71,672.203 1080.96,673.087 1082.21,673.981 1083.46,674.886 1084.71,675.8 1085.96,676.723 \n",
" 1087.21,677.653 1088.46,678.59 1089.7,679.533 1090.95,680.481 1092.2,681.432 1093.45,682.386 1094.7,683.341 1095.95,684.297 1097.2,685.252 1098.45,686.206 \n",
" 1099.7,687.156 1100.95,688.102 1102.2,689.042 1103.44,689.976 1104.69,690.902 1105.94,691.817 1107.19,692.723 1108.44,693.615 1109.69,694.495 1110.94,695.359 \n",
" 1112.19,696.207 1113.44,697.037 1114.69,697.847 1115.93,698.637 1117.18,699.405 1118.43,700.148 1119.68,700.867 1120.93,701.56 1122.18,702.224 1123.43,702.859 \n",
" 1124.68,703.462 1125.93,704.034 1127.18,704.572 1128.43,705.074 1129.67,705.54 1130.92,705.969 1132.17,706.358 1133.42,706.706 1134.67,707.013 1135.92,707.277 \n",
" 1137.17,707.497 1138.42,707.671 1139.67,707.799 1140.92,707.879 1142.16,707.911 1143.41,707.893 1144.66,707.825 1145.91,707.705 1147.16,707.533 1148.41,707.308 \n",
" 1149.66,707.029 1150.91,706.696 1152.16,706.309 1153.41,705.865 1154.65,705.366 1155.9,704.811 1157.15,704.199 1158.4,703.53 1159.65,702.805 1160.9,702.022 \n",
" 1162.15,701.183 1163.4,700.286 1164.65,699.333 1165.9,698.324 1167.15,697.258 1168.39,696.137 1169.64,694.96 1170.89,693.729 1172.14,692.445 1173.39,691.107 \n",
" 1174.64,689.716 1175.89,688.275 1177.14,686.783 1178.39,685.242 1179.64,683.652 1180.88,682.016 1182.13,680.335 1183.38,678.61 1184.63,676.842 1185.88,675.034 \n",
" 1187.13,673.186 1188.38,671.301 1189.63,669.381 1190.88,667.427 1192.13,665.441 1193.38,663.425 1194.62,661.382 1195.87,659.314 1197.12,657.222 1198.37,655.11 \n",
" 1199.62,652.979 1200.87,650.831 1202.12,648.67 1203.37,646.498 1204.62,644.317 1205.87,642.13 1207.11,639.939 1208.36,637.747 1209.61,635.557 1210.86,633.371 \n",
" 1212.11,631.192 1213.36,629.022 1214.61,626.865 1215.86,624.723 1217.11,622.599 1218.36,620.494 1219.61,618.413 1220.85,616.358 1222.1,614.331 1223.35,612.335 \n",
" 1224.6,610.372 1225.85,608.446 1227.1,606.559 1228.35,604.712 1229.6,602.909 1230.85,601.153 1232.1,599.444 1233.34,597.786 1234.59,596.182 1235.84,594.632 \n",
" 1237.09,593.139 1238.34,591.706 1239.59,590.334 1240.84,589.024 1242.09,587.78 1243.34,586.602 1244.59,585.492 1245.84,584.452 1247.08,583.484 1248.33,582.587 \n",
" 1249.58,581.764 1250.83,581.017 1252.08,580.345 1253.33,579.749 1254.58,579.232 1255.83,578.793 1257.08,578.433 1258.33,578.152 1259.57,577.951 1260.82,577.831 \n",
" 1262.07,577.791 1263.32,577.831 1264.57,577.951 1265.82,578.152 1267.07,578.433 1268.32,578.793 1269.57,579.232 1270.82,579.749 1272.06,580.345 1273.31,581.017 \n",
" 1274.56,581.764 1275.81,582.587 1277.06,583.484 1278.31,584.452 1279.56,585.492 1280.81,586.602 1282.06,587.78 1283.31,589.024 1284.56,590.334 1285.8,591.706 \n",
" 1287.05,593.139 1288.3,594.632 1289.55,596.182 1290.8,597.786 1292.05,599.444 1293.3,601.153 1294.55,602.909 1295.8,604.712 1297.05,606.559 1298.29,608.446 \n",
" 1299.54,610.372 1300.79,612.335 1302.04,614.331 1303.29,616.358 1304.54,618.413 1305.79,620.494 1307.04,622.599 1308.29,624.723 1309.54,626.865 1310.79,629.022 \n",
" 1312.03,631.192 1313.28,633.371 1314.53,635.557 1315.78,637.747 1317.03,639.939 1318.28,642.13 1319.53,644.317 1320.78,646.498 1322.03,648.67 1323.28,650.831 \n",
" 1324.52,652.979 1325.77,655.11 1327.02,657.222 1328.27,659.314 1329.52,661.382 1330.77,663.425 1332.02,665.441 1333.27,667.427 1334.52,669.381 1335.77,671.301 \n",
" 1337.02,673.186 1338.26,675.034 1339.51,676.842 1340.76,678.61 1342.01,680.335 1343.26,682.016 1344.51,683.652 1345.76,685.242 1347.01,686.783 1348.26,688.275 \n",
" 1349.51,689.716 1350.75,691.107 1352,692.445 1353.25,693.729 1354.5,694.96 1355.75,696.137 1357,697.258 1358.25,698.324 1359.5,699.333 1360.75,700.286 \n",
" 1362,701.183 1363.24,702.022 1364.49,702.805 1365.74,703.53 1366.99,704.199 1368.24,704.811 1369.49,705.366 1370.74,705.865 1371.99,706.309 1373.24,706.696 \n",
" 1374.49,707.029 1375.74,707.308 1376.98,707.533 1378.23,707.705 1379.48,707.825 1380.73,707.893 1381.98,707.911 1383.23,707.879 1384.48,707.799 1385.73,707.671 \n",
" 1386.98,707.497 1388.23,707.277 1389.47,707.013 1390.72,706.706 1391.97,706.358 1393.22,705.969 1394.47,705.54 1395.72,705.074 1396.97,704.572 1398.22,704.034 \n",
" 1399.47,703.462 1400.72,702.859 1401.97,702.224 1403.21,701.56 1404.46,700.867 1405.71,700.148 1406.96,699.405 1408.21,698.637 1409.46,697.847 1410.71,697.037 \n",
" 1411.96,696.207 1413.21,695.359 1414.46,694.495 1415.7,693.615 1416.95,692.723 1418.2,691.817 1419.45,690.902 1420.7,689.976 1421.95,689.042 1423.2,688.102 \n",
" 1424.45,687.156 1425.7,686.206 1426.95,685.252 1428.2,684.297 1429.44,683.341 1430.69,682.386 1431.94,681.432 1433.19,680.481 1434.44,679.533 1435.69,678.59 \n",
" 1436.94,677.653 1438.19,676.723 1439.44,675.8 1440.69,674.886 1441.93,673.981 1443.18,673.087 1444.43,672.203 1445.68,671.331 1446.93,670.471 1448.18,669.624 \n",
" 1449.43,668.791 1450.68,667.971 1451.93,667.167 1453.18,666.378 1454.42,665.605 1455.67,664.847 1456.92,664.107 1458.17,663.383 1459.42,662.676 1460.67,661.988 \n",
" 1461.92,661.317 1463.17,660.664 1464.42,660.029 1465.67,659.413 1466.92,658.815 1468.16,658.236 1469.41,657.675 1470.66,657.134 1471.91,656.611 1473.16,656.108 \n",
" 1474.41,655.622 1475.66,655.156 1476.91,654.709 1478.16,654.28 1479.41,653.869 1480.65,653.477 1481.9,653.102 1483.15,652.746 1484.4,652.408 1485.65,652.087 \n",
" 1486.9,651.783 1488.15,651.496 1489.4,651.227 1490.65,650.973 1491.9,650.736 1493.15,650.515 1494.39,650.309 1495.64,650.119 1496.89,649.943 1498.14,649.782 \n",
" 1499.39,649.635 1500.64,649.503 1501.89,649.383 1503.14,649.277 1504.39,649.184 1505.64,649.103 1506.88,649.034 1508.13,648.976 1509.38,648.93 1510.63,648.895 \n",
" 1511.88,648.87 1513.13,648.855 1514.38,648.85 1515.63,648.855 1516.88,648.868 1518.13,648.89 1519.38,648.921 1520.62,648.959 1521.87,649.004 1523.12,649.057 \n",
" 1524.37,649.117 1525.62,649.183 1526.87,649.255 1528.12,649.333 1529.37,649.416 1530.62,649.504 1531.87,649.597 1533.11,649.695 1534.36,649.797 1535.61,649.903 \n",
" 1536.86,650.012 1538.11,650.125 1539.36,650.24 1540.61,650.359 1541.86,650.479 1543.11,650.603 1544.36,650.728 1545.61,650.855 1546.85,650.983 1548.1,651.113 \n",
" 1549.35,651.244 1550.6,651.376 1551.85,651.508 1553.1,651.641 1554.35,651.775 1555.6,651.908 1556.85,652.042 1558.1,652.175 1559.34,652.308 1560.59,652.441 \n",
" 1561.84,652.573 1563.09,652.704 1564.34,652.835 1565.59,652.965 1566.84,653.093 1568.09,653.221 1569.34,653.347 1570.59,653.472 1571.83,653.595 1573.08,653.717 \n",
" 1574.33,653.838 1575.58,653.957 1576.83,654.074 1578.08,654.189 1579.33,654.303 1580.58,654.415 1581.83,654.525 1583.08,654.633 1584.33,654.739 1585.57,654.843 \n",
" 1586.82,654.945 1588.07,655.045 1589.32,655.143 1590.57,655.239 1591.82,655.333 1593.07,655.425 1594.32,655.515 1595.57,655.603 1596.82,655.689 1598.06,655.773 \n",
" 1599.31,655.854 1600.56,655.934 1601.81,656.012 1603.06,656.088 1604.31,656.161 1605.56,656.233 1606.81,656.303 1608.06,656.371 1609.31,656.437 1610.56,656.502 \n",
" 1611.8,656.564 1613.05,656.625 1614.3,656.683 1615.55,656.74 1616.8,656.796 1618.05,656.849 1619.3,656.901 1620.55,656.952 1621.8,657 1623.05,657.048 \n",
" 1624.29,657.093 1625.54,657.137 1626.79,657.18 1628.04,657.221 1629.29,657.261 1630.54,657.3 1631.79,657.337 1633.04,657.373 1634.29,657.407 1635.54,657.441 \n",
" 1636.79,657.473 1638.03,657.504 1639.28,657.533 1640.53,657.562 1641.78,657.59 1643.03,657.617 1644.28,657.642 1645.53,657.667 1646.78,657.69 1648.03,657.713 \n",
" 1649.28,657.735 1650.52,657.756 1651.77,657.776 1653.02,657.795 1654.27,657.814 1655.52,657.832 1656.77,657.849 1658.02,657.865 1659.27,657.881 1660.52,657.896 \n",
" 1661.77,657.91 1663.01,657.924 1664.26,657.937 1665.51,657.95 1666.76,657.962 1668.01,657.973 1669.26,657.984 1670.51,657.995 1671.76,658.005 1673.01,658.015 \n",
" 1674.26,658.024 1675.51,658.033 1676.75,658.041 1678,658.049 1679.25,658.056 1680.5,658.064 1681.75,658.071 1683,658.077 1684.25,658.083 1685.5,658.089 \n",
" 1686.75,658.095 1688,658.1 1689.24,658.106 1690.49,658.11 1691.74,658.115 1692.99,658.12 1694.24,658.124 1695.49,658.128 1696.74,658.132 1697.99,658.135 \n",
" 1699.24,658.139 1700.49,658.142 1701.74,658.145 1702.98,658.148 1704.23,658.151 1705.48,658.153 1706.73,658.156 1707.98,658.158 1709.23,658.16 1710.48,658.162 \n",
" 1711.73,658.164 1712.98,658.166 1714.23,658.168 1715.47,658.17 1716.72,658.171 1717.97,658.173 1719.22,658.174 1720.47,658.176 1721.72,658.177 1722.97,658.178 \n",
" 1724.22,658.179 1725.47,658.18 1726.72,658.181 1727.97,658.182 1729.21,658.183 1730.46,658.184 1731.71,658.185 1732.96,658.186 1734.21,658.186 1735.46,658.187 \n",
" 1736.71,658.188 1737.96,658.188 1739.21,658.189 1740.46,658.189 1741.7,658.19 1742.95,658.19 1744.2,658.191 1745.45,658.191 1746.7,658.191 1747.95,658.192 \n",
" 1749.2,658.192 1750.45,658.192 1751.7,658.193 1752.95,658.193 1754.19,658.193 1755.44,658.194 1756.69,658.194 1757.94,658.194 1759.19,658.194 1760.44,658.194 \n",
" 1761.69,658.195 1762.94,658.195 1764.19,658.195 1765.44,658.195 1766.69,658.195 1767.93,658.195 1769.18,658.195 1770.43,658.196 1771.68,658.196 1772.93,658.196 \n",
" 1774.18,658.196 1775.43,658.196 1776.68,658.196 1777.93,658.196 1779.18,658.196 1780.42,658.196 1781.67,658.196 1782.92,658.196 1784.17,658.196 1785.42,658.196 \n",
" 1786.67,658.196 1787.92,658.196 1789.17,658.197 1790.42,658.197 1791.67,658.197 1792.92,658.197 1794.16,658.197 1795.41,658.197 1796.66,658.197 1797.91,658.197 \n",
" 1799.16,658.197 1800.41,658.197 1801.66,658.197 1802.91,658.197 1804.16,658.197 1805.41,658.197 1806.65,658.197 1807.9,658.197 1809.15,658.197 1810.4,658.197 \n",
" 1811.65,658.197 1812.9,658.197 1814.15,658.197 1815.4,658.197 1816.65,658.197 1817.9,658.197 1819.15,658.197 1820.39,658.197 1821.64,658.197 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
" 2073.95,658.197 2075.2,658.197 2076.45,658.197 2077.7,658.197 2078.95,658.197 2080.19,658.197 2081.44,658.197 2082.69,658.197 2083.94,658.197 2085.19,658.197 \n",
" 2086.44,658.197 2087.69,658.197 2088.94,658.197 2090.19,658.197 2091.44,658.197 2092.69,658.197 2093.93,658.197 2095.18,658.197 2096.43,658.197 2097.68,658.197 \n",
" 2098.93,658.197 2100.18,658.197 2101.43,658.197 2102.68,658.197 2103.93,658.197 2105.18,658.197 2106.42,658.197 2107.67,658.197 2108.92,658.197 2110.17,658.197 \n",
" 2111.42,658.197 2112.67,658.197 2113.92,658.197 2115.17,658.197 2116.42,658.197 2117.67,658.197 2118.92,658.197 2120.16,658.197 2121.41,658.197 2122.66,658.197 \n",
" 2123.91,658.197 2125.16,658.197 2126.41,658.197 2127.66,658.197 2128.91,658.197 2130.16,658.197 2131.41,658.197 2132.65,658.197 2133.9,658.197 2135.15,658.197 \n",
" 2136.4,658.197 2137.65,658.197 2138.9,658.197 2140.15,658.197 2141.4,658.197 2142.65,658.197 2143.9,658.197 2145.14,658.197 2146.39,658.197 2147.64,658.197 \n",
" 2148.89,658.197 2150.14,658.197 2151.39,658.197 2152.64,658.197 2153.89,658.197 2155.14,658.197 2156.39,658.197 2157.64,658.197 2158.88,658.197 2160.13,658.197 \n",
" 2161.38,658.197 2162.63,658.197 2163.88,658.197 2165.13,658.197 2166.38,658.197 2167.63,658.197 2168.88,658.197 2170.13,658.197 2171.37,658.197 2172.62,658.197 \n",
" 2173.87,658.197 2175.12,658.197 2176.37,658.197 2177.62,658.197 2178.87,658.197 2180.12,658.197 2181.37,658.197 2182.62,658.197 2183.87,658.197 2185.11,658.197 \n",
" 2186.36,658.197 2187.61,658.197 2188.86,658.197 2190.11,658.197 2191.36,658.197 2192.61,658.197 2193.86,658.197 2195.11,658.197 2196.36,658.197 2197.6,658.197 \n",
" 2198.85,658.197 2200.1,658.197 2201.35,658.197 2202.6,658.197 2203.85,658.197 2205.1,658.197 2206.35,658.197 2207.6,658.197 2208.85,658.197 2210.1,658.197 \n",
" 2211.34,658.197 2212.59,658.197 2213.84,658.197 2215.09,658.197 2216.34,658.197 2217.59,658.197 2218.84,658.197 2220.09,658.197 2221.34,658.197 2222.59,658.197 \n",
" 2223.83,658.197 2225.08,658.197 2226.33,658.197 2227.58,658.197 2228.83,658.197 2230.08,658.197 2231.33,658.197 2232.58,658.197 2233.83,658.197 2235.08,658.197 \n",
" 2236.33,658.197 2237.57,658.197 2238.82,658.197 2240.07,658.197 2241.32,658.197 2242.57,658.197 2243.82,658.197 2245.07,658.197 2246.32,658.197 2247.57,658.197 \n",
" 2248.82,658.197 2250.06,658.197 2251.31,658.197 2252.56,658.197 2253.81,658.197 2255.06,658.197 2256.31,658.197 2257.56,658.197 2258.81,658.197 2260.06,658.197 \n",
" 2261.31,658.197 \n",
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" 774.946,658.23 776.195,658.232 777.444,658.234 778.693,658.237 779.943,658.239 781.192,658.242 782.441,658.245 783.69,658.248 784.939,658.251 786.188,658.255 \n",
" 787.437,658.258 788.686,658.262 789.935,658.266 791.184,658.27 792.433,658.275 793.682,658.279 794.931,658.284 796.18,658.29 797.429,658.295 798.678,658.301 \n",
" 799.927,658.307 801.176,658.314 802.425,658.321 803.674,658.328 804.923,658.336 806.172,658.344 807.421,658.352 808.67,658.361 809.92,658.371 811.169,658.381 \n",
" 812.418,658.391 813.667,658.402 814.916,658.414 816.165,658.426 817.414,658.439 818.663,658.452 819.912,658.466 821.161,658.481 822.41,658.496 823.659,658.512 \n",
" 824.908,658.529 826.157,658.547 827.406,658.566 828.655,658.586 829.904,658.606 831.153,658.627 832.402,658.65 833.651,658.673 834.9,658.698 836.149,658.724 \n",
" 837.398,658.751 838.647,658.779 839.897,658.808 841.146,658.838 842.395,658.87 843.644,658.904 844.893,658.938 846.142,658.975 847.391,659.012 848.64,659.052 \n",
" 849.889,659.093 851.138,659.135 852.387,659.18 853.636,659.226 854.885,659.274 856.134,659.324 857.383,659.376 858.632,659.43 859.881,659.485 861.13,659.544 \n",
" 862.379,659.604 863.628,659.666 864.877,659.731 866.126,659.798 867.375,659.868 868.624,659.94 869.874,660.014 871.123,660.091 872.372,660.171 873.621,660.254 \n",
" 874.87,660.339 876.119,660.427 877.368,660.518 878.617,660.611 879.866,660.708 881.115,660.808 882.364,660.91 883.613,661.016 884.862,661.125 886.111,661.237 \n",
" 887.36,661.353 888.609,661.471 889.858,661.593 891.107,661.718 892.356,661.846 893.605,661.978 894.854,662.113 896.103,662.251 897.352,662.393 898.601,662.538 \n",
" 899.851,662.686 901.1,662.838 902.349,662.993 903.598,663.151 904.847,663.312 906.096,663.477 907.345,663.645 908.594,663.816 909.843,663.989 911.092,664.166 \n",
" 912.341,664.346 913.59,664.528 914.839,664.713 916.088,664.901 917.337,665.091 918.586,665.283 919.835,665.477 921.084,665.674 922.333,665.872 923.582,666.072 \n",
" 924.831,666.273 926.08,666.475 927.329,666.679 928.578,666.883 929.828,667.087 931.077,667.292 932.326,667.497 933.575,667.701 934.824,667.905 936.073,668.108 \n",
" 937.322,668.309 938.571,668.509 939.82,668.707 941.069,668.902 942.318,669.094 943.567,669.283 944.816,669.468 946.065,669.649 947.314,669.826 948.563,669.997 \n",
" 949.812,670.162 951.061,670.321 952.31,670.473 953.559,670.618 954.808,670.755 956.057,670.884 957.306,671.003 958.555,671.113 959.805,671.212 961.054,671.3 \n",
" 962.303,671.376 963.552,671.44 964.801,671.491 966.05,671.528 967.299,671.55 968.548,671.557 969.797,671.548 971.046,671.522 972.295,671.478 973.544,671.417 \n",
" 974.793,671.335 976.042,671.234 977.291,671.112 978.54,670.969 979.789,670.803 981.038,670.615 982.287,670.402 983.536,670.164 984.785,669.901 986.034,669.612 \n",
" 987.283,669.296 988.532,668.952 989.781,668.579 991.031,668.177 992.28,667.744 993.529,667.281 994.778,666.787 996.027,666.26 997.276,665.701 998.525,665.108 \n",
" 999.774,664.481 1001.02,663.819 1002.27,663.123 1003.52,662.39 1004.77,661.622 1006.02,660.817 1007.27,659.975 1008.52,659.096 1009.77,658.18 1011.02,657.226 \n",
" 1012.26,656.233 1013.51,655.203 1014.76,654.135 1016.01,653.028 1017.26,651.883 1018.51,650.7 1019.76,649.48 1021.01,648.221 1022.26,646.926 1023.51,645.593 \n",
" 1024.75,644.224 1026,642.819 1027.25,641.379 1028.5,639.904 1029.75,638.395 1031,636.853 1032.25,635.279 1033.5,633.674 1034.75,632.04 1036,630.376 \n",
" 1037.25,628.686 1038.49,626.969 1039.74,625.228 1040.99,623.465 1042.24,621.68 1043.49,619.876 1044.74,618.054 1045.99,616.217 1047.24,614.366 1048.49,612.504 \n",
" 1049.74,610.633 1050.98,608.756 1052.23,606.874 1053.48,604.99 1054.73,603.108 1055.98,601.229 1057.23,599.357 1058.48,597.494 1059.73,595.643 1060.98,593.808 \n",
" 1062.23,591.991 1063.47,590.195 1064.72,588.425 1065.97,586.683 1067.22,584.972 1068.47,583.297 1069.72,581.66 1070.97,580.065 1072.22,578.515 1073.47,577.015 \n",
" 1074.72,575.568 1075.97,574.177 1077.21,572.847 1078.46,571.581 1079.71,570.382 1080.96,569.255 1082.21,568.202 1083.46,567.229 1084.71,566.338 1085.96,565.533 \n",
" 1087.21,564.818 1088.46,564.197 1089.7,563.672 1090.95,563.247 1092.2,562.926 1093.45,562.713 1094.7,562.609 1095.95,562.619 1097.2,562.745 1098.45,562.991 \n",
" 1099.7,563.359 1100.95,563.852 1102.2,564.473 1103.44,565.223 1104.69,566.106 1105.94,567.124 1107.19,568.277 1108.44,569.569 1109.69,571.001 1110.94,572.574 \n",
" 1112.19,574.29 1113.44,576.149 1114.69,578.152 1115.93,580.301 1117.18,582.595 1118.43,585.034 1119.68,587.619 1120.93,590.35 1122.18,593.225 1123.43,596.244 \n",
" 1124.68,599.406 1125.93,602.71 1127.18,606.154 1128.43,609.736 1129.67,613.454 1130.92,617.307 1132.17,621.29 1133.42,625.402 1134.67,629.64 1135.92,633.999 \n",
" 1137.17,638.477 1138.42,643.069 1139.67,647.771 1140.92,652.579 1142.16,657.488 1143.41,662.493 1144.66,667.589 1145.91,672.77 1147.16,678.031 1148.41,683.365 \n",
" 1149.66,688.767 1150.91,694.23 1152.16,699.747 1153.41,705.313 1154.65,710.918 1155.9,716.558 1157.15,722.223 1158.4,727.907 1159.65,733.601 1160.9,739.299 \n",
" 1162.15,744.991 1163.4,750.671 1164.65,756.329 1165.9,761.957 1167.15,767.547 1168.39,773.09 1169.64,778.579 1170.89,784.004 1172.14,789.356 1173.39,794.628 \n",
" 1174.64,799.81 1175.89,804.894 1177.14,809.871 1178.39,814.734 1179.64,819.472 1180.88,824.079 1182.13,828.547 1183.38,832.865 1184.63,837.028 1185.88,841.027 \n",
" 1187.13,844.854 1188.38,848.502 1189.63,851.964 1190.88,855.232 1192.13,858.3 1193.38,861.161 1194.62,863.809 1195.87,866.237 1197.12,868.44 1198.37,870.413 \n",
" 1199.62,872.151 1200.87,873.647 1202.12,874.899 1203.37,875.901 1204.62,876.651 1205.87,877.144 1207.11,877.377 1208.36,877.349 1209.61,877.056 1210.86,876.497 \n",
" 1212.11,875.671 1213.36,874.575 1214.61,873.211 1215.86,871.577 1217.11,869.674 1218.36,867.503 1219.61,865.065 1220.85,862.36 1222.1,859.393 1223.35,856.163 \n",
" 1224.6,852.676 1225.85,848.933 1227.1,844.94 1228.35,840.699 1229.6,836.215 1230.85,831.494 1232.1,826.541 1233.34,821.362 1234.59,815.962 1235.84,810.349 \n",
" 1237.09,804.53 1238.34,798.511 1239.59,792.301 1240.84,785.907 1242.09,779.337 1243.34,772.601 1244.59,765.708 1245.84,758.666 1247.08,751.484 1248.33,744.174 \n",
" 1249.58,736.744 1250.83,729.205 1252.08,721.567 1253.33,713.841 1254.58,706.037 1255.83,698.166 1257.08,690.24 1258.33,682.268 1259.57,674.263 1260.82,666.236 \n",
" 1262.07,658.197 1263.32,650.158 1264.57,642.131 1265.82,634.126 1267.07,626.154 1268.32,618.228 1269.57,610.357 1270.82,602.553 1272.06,594.827 1273.31,587.189 \n",
" 1274.56,579.65 1275.81,572.22 1277.06,564.91 1278.31,557.729 1279.56,550.686 1280.81,543.793 1282.06,537.057 1283.31,530.488 1284.56,524.094 1285.8,517.883 \n",
" 1287.05,511.864 1288.3,506.045 1289.55,500.432 1290.8,495.032 1292.05,489.853 1293.3,484.9 1294.55,480.179 1295.8,475.695 1297.05,471.454 1298.29,467.461 \n",
" 1299.54,463.718 1300.79,460.231 1302.04,457.002 1303.29,454.034 1304.54,451.329 1305.79,448.891 1307.04,446.72 1308.29,444.817 1309.54,443.183 1310.79,441.819 \n",
" 1312.03,440.723 1313.28,439.897 1314.53,439.338 1315.78,439.045 1317.03,439.017 1318.28,439.25 1319.53,439.743 1320.78,440.493 1322.03,441.495 1323.28,442.747 \n",
" 1324.52,444.244 1325.77,445.981 1327.02,447.954 1328.27,450.157 1329.52,452.586 1330.77,455.233 1332.02,458.094 1333.27,461.162 1334.52,464.43 1335.77,467.892 \n",
" 1337.02,471.54 1338.26,475.367 1339.51,479.366 1340.76,483.529 1342.01,487.848 1343.26,492.315 1344.51,496.922 1345.76,501.661 1347.01,506.523 1348.26,511.5 \n",
" 1349.51,516.584 1350.75,521.767 1352,527.038 1353.25,532.391 1354.5,537.815 1355.75,543.304 1357,548.847 1358.25,554.437 1359.5,560.066 1360.75,565.723 \n",
" 1362,571.403 1363.24,577.095 1364.49,582.793 1365.74,588.487 1366.99,594.171 1368.24,599.837 1369.49,605.476 1370.74,611.082 1371.99,616.647 1373.24,622.164 \n",
" 1374.49,627.627 1375.74,633.029 1376.98,638.363 1378.23,643.624 1379.48,648.805 1380.73,653.901 1381.98,658.906 1383.23,663.815 1384.48,668.623 1385.73,673.325 \n",
" 1386.98,677.917 1388.23,682.395 1389.47,686.754 1390.72,690.992 1391.97,695.104 1393.22,699.087 1394.47,702.94 1395.72,706.658 1396.97,710.24 1398.22,713.684 \n",
" 1399.47,716.988 1400.72,720.15 1401.97,723.169 1403.21,726.044 1404.46,728.775 1405.71,731.36 1406.96,733.799 1408.21,736.093 1409.46,738.242 1410.71,740.245 \n",
" 1411.96,742.105 1413.21,743.82 1414.46,745.393 1415.7,746.825 1416.95,748.117 1418.2,749.271 1419.45,750.288 1420.7,751.171 1421.95,751.921 1423.2,752.542 \n",
" 1424.45,753.035 1425.7,753.403 1426.95,753.649 1428.2,753.775 1429.44,753.785 1430.69,753.682 1431.94,753.468 1433.19,753.147 1434.44,752.722 1435.69,752.197 \n",
" 1436.94,751.576 1438.19,750.861 1439.44,750.056 1440.69,749.165 1441.93,748.192 1443.18,747.139 1444.43,746.012 1445.68,744.813 1446.93,743.547 1448.18,742.217 \n",
" 1449.43,740.826 1450.68,739.379 1451.93,737.879 1453.18,736.329 1454.42,734.734 1455.67,733.097 1456.92,731.422 1458.17,729.711 1459.42,727.969 1460.67,726.199 \n",
" 1461.92,724.403 1463.17,722.586 1464.42,720.751 1465.67,718.9 1466.92,717.037 1468.16,715.165 1469.41,713.286 1470.66,711.404 1471.91,709.52 1473.16,707.638 \n",
" 1474.41,705.761 1475.66,703.89 1476.91,702.028 1478.16,700.177 1479.41,698.34 1480.65,696.519 1481.9,694.714 1483.15,692.929 1484.4,691.166 1485.65,689.425 \n",
" 1486.9,687.708 1488.15,686.018 1489.4,684.354 1490.65,682.72 1491.9,681.115 1493.15,679.541 1494.39,677.999 1495.64,676.491 1496.89,675.016 1498.14,673.575 \n",
" 1499.39,672.17 1500.64,670.801 1501.89,669.469 1503.14,668.173 1504.39,666.914 1505.64,665.694 1506.88,664.511 1508.13,663.366 1509.38,662.259 1510.63,661.191 \n",
" 1511.88,660.161 1513.13,659.168 1514.38,658.214 1515.63,657.298 1516.88,656.419 1518.13,655.577 1519.38,654.772 1520.62,654.004 1521.87,653.271 1523.12,652.575 \n",
" 1524.37,651.913 1525.62,651.286 1526.87,650.693 1528.12,650.134 1529.37,649.607 1530.62,649.113 1531.87,648.65 1533.11,648.218 1534.36,647.815 1535.61,647.443 \n",
" 1536.86,647.098 1538.11,646.782 1539.36,646.493 1540.61,646.23 1541.86,645.992 1543.11,645.779 1544.36,645.591 1545.61,645.425 1546.85,645.282 1548.1,645.16 \n",
" 1549.35,645.059 1550.6,644.978 1551.85,644.916 1553.1,644.872 1554.35,644.846 1555.6,644.837 1556.85,644.844 1558.1,644.866 1559.34,644.903 1560.59,644.954 \n",
" 1561.84,645.018 1563.09,645.094 1564.34,645.182 1565.59,645.281 1566.84,645.391 1568.09,645.51 1569.34,645.639 1570.59,645.776 1571.83,645.921 1573.08,646.073 \n",
" 1574.33,646.232 1575.58,646.397 1576.83,646.569 1578.08,646.745 1579.33,646.926 1580.58,647.111 1581.83,647.3 1583.08,647.492 1584.33,647.687 1585.57,647.885 \n",
" 1586.82,648.085 1588.07,648.286 1589.32,648.489 1590.57,648.693 1591.82,648.897 1593.07,649.102 1594.32,649.307 1595.57,649.511 1596.82,649.715 1598.06,649.919 \n",
" 1599.31,650.121 1600.56,650.322 1601.81,650.522 1603.06,650.72 1604.31,650.917 1605.56,651.111 1606.81,651.303 1608.06,651.493 1609.31,651.681 1610.56,651.866 \n",
" 1611.8,652.048 1613.05,652.228 1614.3,652.405 1615.55,652.579 1616.8,652.749 1618.05,652.917 1619.3,653.082 1620.55,653.243 1621.8,653.401 1623.05,653.556 \n",
" 1624.29,653.708 1625.54,653.856 1626.79,654.001 1628.04,654.143 1629.29,654.281 1630.54,654.416 1631.79,654.548 1633.04,654.676 1634.29,654.801 1635.54,654.923 \n",
" 1636.79,655.042 1638.03,655.157 1639.28,655.269 1640.53,655.378 1641.78,655.484 1643.03,655.586 1644.28,655.686 1645.53,655.783 1646.78,655.876 1648.03,655.967 \n",
" 1649.28,656.055 1650.52,656.141 1651.77,656.223 1653.02,656.303 1654.27,656.38 1655.52,656.454 1656.77,656.526 1658.02,656.596 1659.27,656.663 1660.52,656.728 \n",
" 1661.77,656.79 1663.01,656.851 1664.26,656.909 1665.51,656.965 1666.76,657.018 1668.01,657.07 1669.26,657.12 1670.51,657.168 1671.76,657.214 1673.01,657.259 \n",
" 1674.26,657.301 1675.51,657.342 1676.75,657.382 1678,657.419 1679.25,657.456 1680.5,657.49 1681.75,657.524 1683,657.556 1684.25,657.586 1685.5,657.616 \n",
" 1686.75,657.644 1688,657.67 1689.24,657.696 1690.49,657.721 1691.74,657.744 1692.99,657.767 1694.24,657.788 1695.49,657.809 1696.74,657.828 1697.99,657.847 \n",
" 1699.24,657.865 1700.49,657.882 1701.74,657.898 1702.98,657.913 1704.23,657.928 1705.48,657.942 1706.73,657.956 1707.98,657.968 1709.23,657.98 1710.48,657.992 \n",
" 1711.73,658.003 1712.98,658.013 1714.23,658.023 1715.47,658.033 1716.72,658.042 1717.97,658.05 1719.22,658.058 1720.47,658.066 1721.72,658.073 1722.97,658.08 \n",
" 1724.22,658.087 1725.47,658.093 1726.72,658.099 1727.97,658.104 1729.21,658.11 1730.46,658.115 1731.71,658.119 1732.96,658.124 1734.21,658.128 1735.46,658.132 \n",
" 1736.71,658.136 1737.96,658.14 1739.21,658.143 1740.46,658.146 1741.7,658.149 1742.95,658.152 1744.2,658.155 1745.45,658.157 1746.7,658.16 1747.95,658.162 \n",
" 1749.2,658.164 1750.45,658.166 1751.7,658.168 1752.95,658.17 1754.19,658.171 1755.44,658.173 1756.69,658.175 1757.94,658.176 1759.19,658.177 1760.44,658.179 \n",
" 1761.69,658.18 1762.94,658.181 1764.19,658.182 1765.44,658.183 1766.69,658.184 1767.93,658.185 1769.18,658.185 1770.43,658.186 1771.68,658.187 1772.93,658.188 \n",
" 1774.18,658.188 1775.43,658.189 1776.68,658.189 1777.93,658.19 1779.18,658.19 1780.42,658.191 1781.67,658.191 1782.92,658.192 1784.17,658.192 1785.42,658.192 \n",
" 1786.67,658.193 1787.92,658.193 1789.17,658.193 1790.42,658.193 1791.67,658.194 1792.92,658.194 1794.16,658.194 1795.41,658.194 1796.66,658.195 1797.91,658.195 \n",
" 1799.16,658.195 1800.41,658.195 1801.66,658.195 1802.91,658.195 1804.16,658.195 1805.41,658.196 1806.65,658.196 1807.9,658.196 1809.15,658.196 1810.4,658.196 \n",
" 1811.65,658.196 1812.9,658.196 1814.15,658.196 1815.4,658.196 1816.65,658.196 1817.9,658.196 1819.15,658.196 1820.39,658.196 1821.64,658.196 1822.89,658.197 \n",
" 1824.14,658.197 1825.39,658.197 1826.64,658.197 1827.89,658.197 1829.14,658.197 1830.39,658.197 1831.64,658.197 1832.88,658.197 1834.13,658.197 1835.38,658.197 \n",
" 1836.63,658.197 1837.88,658.197 1839.13,658.197 1840.38,658.197 1841.63,658.197 1842.88,658.197 1844.13,658.197 1845.37,658.197 1846.62,658.197 1847.87,658.197 \n",
" 1849.12,658.197 1850.37,658.197 1851.62,658.197 1852.87,658.197 1854.12,658.197 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
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" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
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" 1112.19,479.48 1113.44,465.078 1114.69,450.603 1115.93,436.076 1117.18,421.52 1118.43,406.957 1119.68,392.412 1120.93,377.907 1122.18,363.467 1123.43,349.118 \n",
" 1124.68,334.884 1125.93,320.791 1127.18,306.865 1128.43,293.132 1129.67,279.618 1130.92,266.351 1132.17,253.356 1133.42,240.661 1134.67,228.292 1135.92,216.276 \n",
" 1137.17,204.639 1138.42,193.409 1139.67,182.612 1140.92,172.273 1142.16,162.418 1143.41,153.073 1144.66,144.263 1145.91,136.012 1147.16,128.343 1148.41,121.281 \n",
" 1149.66,114.847 1150.91,109.064 1152.16,103.953 1153.41,99.5333 1154.65,95.8252 1155.9,92.8468 1157.15,90.6154 1158.4,89.1475 1159.65,88.4582 1160.9,88.5615 \n",
" 1162.15,89.4705 1163.4,91.1966 1164.65,93.7501 1165.9,97.1402 1167.15,101.374 1168.39,106.459 1169.64,112.398 1170.89,119.195 1172.14,126.853 1173.39,135.371 \n",
" 1174.64,144.747 1175.89,154.98 1177.14,166.064 1178.39,177.993 1179.64,190.76 1180.88,204.356 1182.13,218.768 1183.38,233.986 1184.63,249.993 1185.88,266.776 \n",
" 1187.13,284.316 1188.38,302.594 1189.63,321.59 1190.88,341.281 1192.13,361.644 1193.38,382.654 1194.62,404.285 1195.87,426.507 1197.12,449.292 1198.37,472.61 \n",
" 1199.62,496.427 1200.87,520.712 1202.12,545.429 1203.37,570.543 1204.62,596.018 1205.87,621.815 1207.11,647.897 1208.36,674.224 1209.61,700.756 1210.86,727.451 \n",
" 1212.11,754.27 1213.36,781.168 1214.61,808.104 1215.86,835.036 1217.11,861.919 1218.36,888.709 1219.61,915.365 1220.85,941.84 1222.1,968.093 1223.35,994.08 \n",
" 1224.6,1019.76 1225.85,1045.08 1227.1,1070.01 1228.35,1094.5 1229.6,1118.5 1230.85,1141.99 1232.1,1164.92 1233.34,1187.25 1234.59,1208.93 1235.84,1229.95 \n",
" 1237.09,1250.24 1238.34,1269.79 1239.59,1288.55 1240.84,1306.5 1242.09,1323.6 1243.34,1339.82 1244.59,1355.14 1245.84,1369.52 1247.08,1382.94 1248.33,1395.38 \n",
" 1249.58,1406.81 1250.83,1417.22 1252.08,1426.58 1253.33,1434.88 1254.58,1442.11 1255.83,1448.24 1257.08,1453.28 1258.33,1457.2 1259.57,1460.01 1260.82,1461.7 \n",
" 1262.07,1462.26 1263.32,1461.7 1264.57,1460.01 1265.82,1457.2 1267.07,1453.28 1268.32,1448.24 1269.57,1442.11 1270.82,1434.88 1272.06,1426.58 1273.31,1417.22 \n",
" 1274.56,1406.81 1275.81,1395.38 1277.06,1382.94 1278.31,1369.52 1279.56,1355.14 1280.81,1339.82 1282.06,1323.6 1283.31,1306.5 1284.56,1288.55 1285.8,1269.79 \n",
" 1287.05,1250.24 1288.3,1229.95 1289.55,1208.93 1290.8,1187.25 1292.05,1164.92 1293.3,1141.99 1294.55,1118.5 1295.8,1094.5 1297.05,1070.01 1298.29,1045.08 \n",
" 1299.54,1019.76 1300.79,994.08 1302.04,968.093 1303.29,941.84 1304.54,915.365 1305.79,888.709 1307.04,861.919 1308.29,835.036 1309.54,808.104 1310.79,781.168 \n",
" 1312.03,754.27 1313.28,727.451 1314.53,700.756 1315.78,674.224 1317.03,647.897 1318.28,621.815 1319.53,596.018 1320.78,570.543 1322.03,545.429 1323.28,520.712 \n",
" 1324.52,496.427 1325.77,472.61 1327.02,449.292 1328.27,426.507 1329.52,404.285 1330.77,382.654 1332.02,361.644 1333.27,341.281 1334.52,321.59 1335.77,302.594 \n",
" 1337.02,284.316 1338.26,266.776 1339.51,249.993 1340.76,233.986 1342.01,218.768 1343.26,204.356 1344.51,190.76 1345.76,177.993 1347.01,166.064 1348.26,154.98 \n",
" 1349.51,144.747 1350.75,135.371 1352,126.853 1353.25,119.195 1354.5,112.398 1355.75,106.459 1357,101.374 1358.25,97.1402 1359.5,93.7501 1360.75,91.1966 \n",
" 1362,89.4705 1363.24,88.5615 1364.49,88.4582 1365.74,89.1475 1366.99,90.6154 1368.24,92.8468 1369.49,95.8252 1370.74,99.5333 1371.99,103.953 1373.24,109.064 \n",
" 1374.49,114.847 1375.74,121.281 1376.98,128.343 1378.23,136.012 1379.48,144.263 1380.73,153.073 1381.98,162.418 1383.23,172.273 1384.48,182.612 1385.73,193.409 \n",
" 1386.98,204.639 1388.23,216.276 1389.47,228.292 1390.72,240.661 1391.97,253.356 1393.22,266.351 1394.47,279.618 1395.72,293.132 1396.97,306.865 1398.22,320.791 \n",
" 1399.47,334.884 1400.72,349.118 1401.97,363.467 1403.21,377.907 1404.46,392.412 1405.71,406.957 1406.96,421.52 1408.21,436.076 1409.46,450.603 1410.71,465.078 \n",
" 1411.96,479.48 1413.21,493.787 1414.46,507.98 1415.7,522.038 1416.95,535.943 1418.2,549.677 1419.45,563.221 1420.7,576.56 1421.95,589.677 1423.2,602.557 \n",
" 1424.45,615.186 1425.7,627.55 1426.95,639.637 1428.2,651.435 1429.44,662.932 1430.69,674.119 1431.94,684.986 1433.19,695.524 1434.44,705.726 1435.69,715.584 \n",
" 1436.94,725.093 1438.19,734.247 1439.44,743.042 1440.69,751.473 1441.93,759.538 1443.18,767.234 1444.43,774.56 1445.68,781.514 1446.93,788.096 1448.18,794.308 \n",
" 1449.43,800.149 1450.68,805.622 1451.93,810.729 1453.18,815.473 1454.42,819.857 1455.67,823.885 1456.92,827.562 1458.17,830.893 1459.42,833.882 1460.67,836.537 \n",
" 1461.92,838.862 1463.17,840.866 1464.42,842.554 1465.67,843.935 1466.92,845.016 1468.16,845.804 1469.41,846.309 1470.66,846.538 1471.91,846.5 1473.16,846.204 \n",
" 1474.41,845.66 1475.66,844.875 1476.91,843.86 1478.16,842.624 1479.41,841.176 1480.65,839.526 1481.9,837.684 1483.15,835.658 1484.4,833.458 1485.65,831.095 \n",
" 1486.9,828.577 1488.15,825.913 1489.4,823.114 1490.65,820.188 1491.9,817.145 1493.15,813.993 1494.39,810.741 1495.64,807.399 1496.89,803.974 1498.14,800.476 \n",
" 1499.39,796.911 1500.64,793.29 1501.89,789.618 1503.14,785.904 1504.39,782.156 1505.64,778.38 1506.88,774.583 1508.13,770.772 1509.38,766.955 1510.63,763.136 \n",
" 1511.88,759.322 1513.13,755.519 1514.38,751.732 1515.63,747.967 1516.88,744.229 1518.13,740.522 1519.38,736.851 1520.62,733.22 1521.87,729.634 1523.12,726.096 \n",
" 1524.37,722.609 1525.62,719.178 1526.87,715.805 1528.12,712.493 1529.37,709.245 1530.62,706.062 1531.87,702.949 1533.11,699.905 1534.36,696.934 1535.61,694.036 \n",
" 1536.86,691.214 1538.11,688.467 1539.36,685.799 1540.61,683.208 1541.86,680.696 1543.11,678.263 1544.36,675.91 1545.61,673.636 1546.85,671.442 1548.1,669.328 \n",
" 1549.35,667.294 1550.6,665.338 1551.85,663.461 1553.1,661.662 1554.35,659.94 1555.6,658.294 1556.85,656.724 1558.1,655.228 1559.34,653.806 1560.59,652.455 \n",
" 1561.84,651.176 1563.09,649.966 1564.34,648.824 1565.59,647.749 1566.84,646.739 1568.09,645.793 1569.34,644.909 1570.59,644.086 1571.83,643.322 1573.08,642.615 \n",
" 1574.33,641.964 1575.58,641.366 1576.83,640.821 1578.08,640.326 1579.33,639.88 1580.58,639.482 1581.83,639.128 1583.08,638.818 1584.33,638.551 1585.57,638.323 \n",
" 1586.82,638.134 1588.07,637.982 1589.32,637.865 1590.57,637.782 1591.82,637.731 1593.07,637.711 1594.32,637.72 1595.57,637.756 1596.82,637.818 1598.06,637.904 \n",
" 1599.31,638.014 1600.56,638.145 1601.81,638.297 1603.06,638.468 1604.31,638.657 1605.56,638.862 1606.81,639.083 1608.06,639.317 1609.31,639.565 1610.56,639.825 \n",
" 1611.8,640.096 1613.05,640.376 1614.3,640.666 1615.55,640.963 1616.8,641.268 1618.05,641.579 1619.3,641.895 1620.55,642.216 1621.8,642.541 1623.05,642.868 \n",
" 1624.29,643.199 1625.54,643.531 1626.79,643.864 1628.04,644.197 1629.29,644.531 1630.54,644.865 1631.79,645.197 1633.04,645.528 1634.29,645.857 1635.54,646.184 \n",
" 1636.79,646.508 1638.03,646.829 1639.28,647.147 1640.53,647.461 1641.78,647.771 1643.03,648.077 1644.28,648.379 1645.53,648.676 1646.78,648.969 1648.03,649.256 \n",
" 1649.28,649.539 1650.52,649.816 1651.77,650.088 1653.02,650.354 1654.27,650.615 1655.52,650.87 1656.77,651.12 1658.02,651.364 1659.27,651.602 1660.52,651.835 \n",
" 1661.77,652.061 1663.01,652.282 1664.26,652.498 1665.51,652.707 1666.76,652.911 1668.01,653.109 1669.26,653.302 1670.51,653.489 1671.76,653.671 1673.01,653.847 \n",
" 1674.26,654.018 1675.51,654.184 1676.75,654.345 1678,654.5 1679.25,654.65 1680.5,654.796 1681.75,654.937 1683,655.073 1684.25,655.204 1685.5,655.331 \n",
" 1686.75,655.453 1688,655.571 1689.24,655.685 1690.49,655.795 1691.74,655.9 1692.99,656.002 1694.24,656.1 1695.49,656.194 1696.74,656.285 1697.99,656.372 \n",
" 1699.24,656.455 1700.49,656.536 1701.74,656.613 1702.98,656.687 1704.23,656.758 1705.48,656.826 1706.73,656.892 1707.98,656.954 1709.23,657.014 1710.48,657.072 \n",
" 1711.73,657.127 1712.98,657.179 1714.23,657.23 1715.47,657.278 1716.72,657.324 1717.97,657.368 1719.22,657.41 1720.47,657.45 1721.72,657.488 1722.97,657.524 \n",
" 1724.22,657.559 1725.47,657.592 1726.72,657.624 1727.97,657.654 1729.21,657.683 1730.46,657.71 1731.71,657.736 1732.96,657.761 1734.21,657.784 1735.46,657.807 \n",
" 1736.71,657.828 1737.96,657.848 1739.21,657.867 1740.46,657.885 1741.7,657.903 1742.95,657.919 1744.2,657.935 1745.45,657.95 1746.7,657.964 1747.95,657.977 \n",
" 1749.2,657.989 1750.45,658.001 1751.7,658.013 1752.95,658.023 1754.19,658.033 1755.44,658.043 1756.69,658.052 1757.94,658.061 1759.19,658.069 1760.44,658.076 \n",
" 1761.69,658.083 1762.94,658.09 1764.19,658.097 1765.44,658.103 1766.69,658.108 1767.93,658.114 1769.18,658.119 1770.43,658.124 1771.68,658.128 1772.93,658.133 \n",
" 1774.18,658.137 1775.43,658.14 1776.68,658.144 1777.93,658.147 1779.18,658.15 1780.42,658.153 1781.67,658.156 1782.92,658.159 1784.17,658.161 1785.42,658.164 \n",
" 1786.67,658.166 1787.92,658.168 1789.17,658.17 1790.42,658.171 1791.67,658.173 1792.92,658.175 1794.16,658.176 1795.41,658.178 1796.66,658.179 1797.91,658.18 \n",
" 1799.16,658.181 1800.41,658.182 1801.66,658.183 1802.91,658.184 1804.16,658.185 1805.41,658.186 1806.65,658.187 1807.9,658.187 1809.15,658.188 1810.4,658.189 \n",
" 1811.65,658.189 1812.9,658.19 1814.15,658.19 1815.4,658.191 1816.65,658.191 1817.9,658.192 1819.15,658.192 1820.39,658.192 1821.64,658.193 1822.89,658.193 \n",
" 1824.14,658.193 1825.39,658.194 1826.64,658.194 1827.89,658.194 1829.14,658.194 1830.39,658.194 1831.64,658.195 1832.88,658.195 1834.13,658.195 1835.38,658.195 \n",
" 1836.63,658.195 1837.88,658.195 1839.13,658.196 1840.38,658.196 1841.63,658.196 1842.88,658.196 1844.13,658.196 1845.37,658.196 1846.62,658.196 1847.87,658.196 \n",
" 1849.12,658.196 1850.37,658.196 1851.62,658.196 1852.87,658.196 1854.12,658.196 1855.37,658.197 1856.62,658.197 1857.87,658.197 1859.11,658.197 1860.36,658.197 \n",
" 1861.61,658.197 1862.86,658.197 1864.11,658.197 1865.36,658.197 1866.61,658.197 1867.86,658.197 1869.11,658.197 1870.36,658.197 1871.6,658.197 1872.85,658.197 \n",
" 1874.1,658.197 1875.35,658.197 1876.6,658.197 1877.85,658.197 1879.1,658.197 1880.35,658.197 1881.6,658.197 1882.85,658.197 1884.1,658.197 1885.34,658.197 \n",
" 1886.59,658.197 1887.84,658.197 1889.09,658.197 1890.34,658.197 1891.59,658.197 1892.84,658.197 1894.09,658.197 1895.34,658.197 1896.59,658.197 1897.83,658.197 \n",
" 1899.08,658.197 1900.33,658.197 1901.58,658.197 1902.83,658.197 1904.08,658.197 1905.33,658.197 1906.58,658.197 1907.83,658.197 1909.08,658.197 1910.33,658.197 \n",
" 1911.57,658.197 1912.82,658.197 1914.07,658.197 1915.32,658.197 1916.57,658.197 1917.82,658.197 1919.07,658.197 1920.32,658.197 1921.57,658.197 1922.82,658.197 \n",
" 1924.06,658.197 1925.31,658.197 1926.56,658.197 1927.81,658.197 1929.06,658.197 1930.31,658.197 1931.56,658.197 1932.81,658.197 1934.06,658.197 1935.31,658.197 \n",
" 1936.56,658.197 1937.8,658.197 1939.05,658.197 1940.3,658.197 1941.55,658.197 1942.8,658.197 1944.05,658.197 1945.3,658.197 1946.55,658.197 1947.8,658.197 \n",
" 1949.05,658.197 1950.29,658.197 1951.54,658.197 1952.79,658.197 1954.04,658.197 1955.29,658.197 1956.54,658.197 1957.79,658.197 1959.04,658.197 1960.29,658.197 \n",
" 1961.54,658.197 1962.78,658.197 1964.03,658.197 1965.28,658.197 1966.53,658.197 1967.78,658.197 1969.03,658.197 1970.28,658.197 1971.53,658.197 1972.78,658.197 \n",
" 1974.03,658.197 1975.28,658.197 1976.52,658.197 1977.77,658.197 1979.02,658.197 1980.27,658.197 1981.52,658.197 1982.77,658.197 1984.02,658.197 1985.27,658.197 \n",
" 1986.52,658.197 1987.77,658.197 1989.01,658.197 1990.26,658.197 1991.51,658.197 1992.76,658.197 1994.01,658.197 1995.26,658.197 1996.51,658.197 1997.76,658.197 \n",
" 1999.01,658.197 2000.26,658.197 2001.51,658.197 2002.75,658.197 2004,658.197 2005.25,658.197 2006.5,658.197 2007.75,658.197 2009,658.197 2010.25,658.197 \n",
" 2011.5,658.197 2012.75,658.197 2014,658.197 2015.24,658.197 2016.49,658.197 2017.74,658.197 2018.99,658.197 2020.24,658.197 2021.49,658.197 2022.74,658.197 \n",
" 2023.99,658.197 2025.24,658.197 2026.49,658.197 2027.74,658.197 2028.98,658.197 2030.23,658.197 2031.48,658.197 2032.73,658.197 2033.98,658.197 2035.23,658.197 \n",
" 2036.48,658.197 2037.73,658.197 2038.98,658.197 2040.23,658.197 2041.47,658.197 2042.72,658.197 2043.97,658.197 2045.22,658.197 2046.47,658.197 2047.72,658.197 \n",
" 2048.97,658.197 2050.22,658.197 2051.47,658.197 2052.72,658.197 2053.96,658.197 2055.21,658.197 2056.46,658.197 2057.71,658.197 2058.96,658.197 2060.21,658.197 \n",
" 2061.46,658.197 2062.71,658.197 2063.96,658.197 2065.21,658.197 2066.46,658.197 2067.7,658.197 2068.95,658.197 2070.2,658.197 2071.45,658.197 2072.7,658.197 \n",
" 2073.95,658.197 2075.2,658.197 2076.45,658.197 2077.7,658.197 2078.95,658.197 2080.19,658.197 2081.44,658.197 2082.69,658.197 2083.94,658.197 2085.19,658.197 \n",
" 2086.44,658.197 2087.69,658.197 2088.94,658.197 2090.19,658.197 2091.44,658.197 2092.69,658.197 2093.93,658.197 2095.18,658.197 2096.43,658.197 2097.68,658.197 \n",
" 2098.93,658.197 2100.18,658.197 2101.43,658.197 2102.68,658.197 2103.93,658.197 2105.18,658.197 2106.42,658.197 2107.67,658.197 2108.92,658.197 2110.17,658.197 \n",
" 2111.42,658.197 2112.67,658.197 2113.92,658.197 2115.17,658.197 2116.42,658.197 2117.67,658.197 2118.92,658.197 2120.16,658.197 2121.41,658.197 2122.66,658.197 \n",
" 2123.91,658.197 2125.16,658.197 2126.41,658.197 2127.66,658.197 2128.91,658.197 2130.16,658.197 2131.41,658.197 2132.65,658.197 2133.9,658.197 2135.15,658.197 \n",
" 2136.4,658.197 2137.65,658.197 2138.9,658.197 2140.15,658.197 2141.4,658.197 2142.65,658.197 2143.9,658.197 2145.14,658.197 2146.39,658.197 2147.64,658.197 \n",
" 2148.89,658.197 2150.14,658.197 2151.39,658.197 2152.64,658.197 2153.89,658.197 2155.14,658.197 2156.39,658.197 2157.64,658.197 2158.88,658.197 2160.13,658.197 \n",
" 2161.38,658.197 2162.63,658.197 2163.88,658.197 2165.13,658.197 2166.38,658.197 2167.63,658.197 2168.88,658.197 2170.13,658.197 2171.37,658.197 2172.62,658.197 \n",
" 2173.87,658.197 2175.12,658.197 2176.37,658.197 2177.62,658.197 2178.87,658.197 2180.12,658.197 2181.37,658.197 2182.62,658.197 2183.87,658.197 2185.11,658.197 \n",
" 2186.36,658.197 2187.61,658.197 2188.86,658.197 2190.11,658.197 2191.36,658.197 2192.61,658.197 2193.86,658.197 2195.11,658.197 2196.36,658.197 2197.6,658.197 \n",
" 2198.85,658.197 2200.1,658.197 2201.35,658.197 2202.6,658.197 2203.85,658.197 2205.1,658.197 2206.35,658.197 2207.6,658.197 2208.85,658.197 2210.1,658.197 \n",
" 2211.34,658.197 2212.59,658.197 2213.84,658.197 2215.09,658.197 2216.34,658.197 2217.59,658.197 2218.84,658.197 2220.09,658.197 2221.34,658.197 2222.59,658.197 \n",
" 2223.83,658.197 2225.08,658.197 2226.33,658.197 2227.58,658.197 2228.83,658.197 2230.08,658.197 2231.33,658.197 2232.58,658.197 2233.83,658.197 2235.08,658.197 \n",
" 2236.33,658.197 2237.57,658.197 2238.82,658.197 2240.07,658.197 2241.32,658.197 2242.57,658.197 2243.82,658.197 2245.07,658.197 2246.32,658.197 2247.57,658.197 \n",
" 2248.82,658.197 2250.06,658.197 2251.31,658.197 2252.56,658.197 2253.81,658.197 2255.06,658.197 2256.31,658.197 2257.56,658.197 2258.81,658.197 2260.06,658.197 \n",
" 2261.31,658.197 \n",
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" 1944.98,191.244 2088.98,191.244 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 208.744)\" x=\"2112.98\" y=\"208.744\">H_0</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,251.724 2088.98,251.724 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 269.224)\" x=\"2112.98\" y=\"269.224\">H_1</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,312.204 2088.98,312.204 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 329.704)\" x=\"2112.98\" y=\"329.704\">H_2</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#c271d2; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,372.684 2088.98,372.684 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 390.184)\" x=\"2112.98\" y=\"390.184\">H_3</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#ac8d18; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,433.164 2088.98,433.164 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 450.664)\" x=\"2112.98\" y=\"450.664\">H_4</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#00a9ad; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,493.644 2088.98,493.644 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 511.144)\" x=\"2112.98\" y=\"511.144\">H_5</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip3601)\" style=\"stroke:#ed5d92; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1944.98,554.124 2088.98,554.124 \n",
" \"/>\n",
"<g clip-path=\"url(#clip3601)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2112.98, 571.624)\" x=\"2112.98\" y=\"571.624\">H_6</text>\n",
"</g>\n",
"</svg>\n"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = plot()\n",
"for k=0:6\n",
" H_k = Fun(GaussWeight(Hermite()),[zeros(k);1])\n",
" plot!(xx, H_k.(xx); label=\"H_$k\")\n",
"end\n",
"p"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.0.2",
"language": "julia",
"name": "julia-1.0"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.0.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}