{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Shadow and critical curve of a Kerr black hole\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.3.beta7, Release Date: 2021-02-07'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions $\\ell_{\\rm c}(r_0)$ and $q_{\\rm c}(r_0)$ for critical null geodesics\n", "\n", "We use $m=1$ and denote $r_0$ simply by $r$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a, r = var('a r') " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, r \\right) \\ {\\mapsto} \\ -\\frac{a^{2} {\\left(r + 1\\right)} + {\\left(r - 3\\right)} r^{2}}{a {\\left(r - 1\\right)}}\n", "\\end{math}" ], "text/plain": [ "(a, r) |--> -(a^2*(r + 1) + (r - 3)*r^2)/(a*(r - 1))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lsph(a, r) = (r^2*(3 - r) - a^2*(r + 1))/(a*(r -1))\n", "lsph" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, r \\right) \\ {\\mapsto} \\ -\\frac{{\\left({\\left(r - 3\\right)}^{2} r - 4 \\, a^{2}\\right)} r^{3}}{a^{2} {\\left(r - 1\\right)}^{2}}\n", "\\end{math}" ], "text/plain": [ "(a, r) |--> -((r - 3)^2*r - 4*a^2)*r^3/(a^2*(r - 1)^2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qsph(a, r) = r^3 / (a^2*(r - 1)^2) * (4*a^2 - r*(r - 3)^2)\n", "qsph" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The radii $r_+$ and $r_-$ of the two horizons:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "rp(a) = 1 + sqrt(1 - a^2)\n", "rm(a) = 1 - sqrt(1 - a^2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Critical radii $r_{\\rm ph}^{**}$, $r_{\\rm ph}^*$, $r_{\\rm ph}^+$, $r_{\\rm ph}^-$, $r_{\\rm ph}^{\\rm ms}$ and $r_{\\rm ph}^{\\rm pol}$ " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ \\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{2}{3} \\, \\arcsin\\left(a\\right)\\right) + \\frac{1}{2}\n", "\\end{math}" ], "text/plain": [ "a |--> cos(2/3*pi + 2/3*arcsin(a)) + 1/2" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_ss(a) = 1/2 + cos(2/3*asin(a) + 2*pi/3)\n", "rph_ss" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{4}{3} \\, \\pi + \\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(4/3*pi + 1/3*arccos(-a))^2" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_s(a) = 4*cos(acos(-a)/3 + 4*pi/3)^2\n", "rph_s" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(-a))^2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_p(a) = 4*cos(acos(-a)/3)^2\n", "rph_p" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(a))^2" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_m(a) = 4*cos(acos(a)/3)^2\n", "rph_m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We add the radius of the marginally stable orbit:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ -{\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} + 1\n", "\\end{math}" ], "text/plain": [ "a |--> -(-a^2 + 1)^(1/3) + 1" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_ms(a) = 1 - (1 - a^2)^(1/3)\n", "rph_ms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "as well as the radius of outer and inner polar orbits:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 2 \\, \\sqrt{-\\frac{1}{3} \\, a^{2} + 1} \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(-\\frac{a^{2} - 1}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}}\\right)\\right) + 1\n", "\\end{math}" ], "text/plain": [ "a |--> 2*sqrt(-1/3*a^2 + 1)*cos(1/3*arccos(-(a^2 - 1)/(-1/3*a^2 + 1)^(3/2))) + 1" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_pol(a) = 1 + 2*sqrt(1 - a^2/3)*cos(1/3*arccos((1 - a^2)/(1 - a^2/3)^(3/2)))\n", "rph_pol" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 2 \\, \\sqrt{-\\frac{1}{3} \\, a^{2} + 1} \\cos\\left(\\frac{2}{3} \\, \\pi + \\frac{1}{3} \\, \\arccos\\left(-\\frac{a^{2}}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}} + \\frac{1}{{\\left(-\\frac{1}{3} \\, a^{2} + 1\\right)}^{\\frac{3}{2}}}\\right)\\right) + 1\n", "\\end{math}" ], "text/plain": [ "a |--> 2*sqrt(-1/3*a^2 + 1)*cos(2/3*pi + 1/3*arccos(-a^2/(-1/3*a^2 + 1)^(3/2) + 1/(-1/3*a^2 + 1)^(3/2))) + 1" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rph_pol_in(a) = 1 + 2*sqrt(1 - a^2/3)*cos(1/3*arccos((1 - a^2)/(1 - a^2/3)^(3/2)) + 2*pi/3)\n", "rph_pol_in" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{**} = -0.477673658836338\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{**} = -0.477673658836338" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{\\rm ms} = 0.539741795874205\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{\\rm ms} = 0.539741795874205" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{*} = 0.658372153864346\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{*} = 0.658372153864346" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_- = 0.687750100080080\n", "\\end{math}" ], "text/plain": [ "r_- = 0.687750100080080" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_+ = 1.31224989991992\n", "\\end{math}" ], "text/plain": [ "r_+ = 1.31224989991992" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^+ = 1.38628052846298\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^+ = 1.38628052846298" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^- = 3.95534731767268\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^- = 3.95534731767268" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{\\rm pol} = 2.49269429554008\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{\\rm pol} = 2.49269429554008" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}r_{\\rm ph}^{\\rm pol,in} = -0.399338575773941\n", "\\end{math}" ], "text/plain": [ "r_{\\rm ph}^{\\rm pol,in} = -0.399338575773941" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a0 = 0.95\n", "# a0 = 1\n", "show(LatexExpr(r'r_{\\rm ph}^{**} = '), n(rph_ss(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{\\rm ms} = '), n(rph_ms(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{*} = '), n(rph_s(a0)))\n", "show(LatexExpr(r'r_- = '), n(rm(a0)))\n", "show(LatexExpr(r'r_+ = '), n(rp(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^+ = '), n(rph_p(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^- = '), n(rph_m(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{\\rm pol} = '), n(rph_pol(a0)))\n", "show(LatexExpr(r'r_{\\rm ph}^{\\rm pol,in} = '), n(rph_pol_in(a0)))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(1.38628052846298, 3.95534731767268\\right)\n", "\\end{math}" ], "text/plain": [ "(1.38628052846298, 3.95534731767268)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r1 = rph_p(a0)\n", "r2 = rph_m(a0)\n", "\n", "#r1 = n(rph_ss(a0))\n", "#r2 = 0\n", "\n", "r1, r2" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r = var('r')\n", "plot(qsph(a0, r), (r, r1, r2)) + plot(r^3*(4 - r), (r, r1, r2), color='red')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def alpha(a, th_obs, r0):\n", " if a == 1:\n", " ell = - r0^2 + 2*r0 + 1\n", " else:\n", " ell = lsph(a, r0)\n", " return - ell / sin(th_obs)\n", "\n", "def Theta(a, th_obs, r0):\n", " if a == 1:\n", " ell = - r0^2 + 2*r0 + 1\n", " q = r0^3 * (4 - r0)\n", " else:\n", " ell = lsph(a, r0)\n", " q = qsph(a, r0)\n", " return q + cos(th_obs)^2 * (a^2 - ell^2/sin(th_obs)^2)\n", "\n", "def beta(a, th_obs, r0, eps_theta=1):\n", " return eps_theta * sqrt(Theta(a, th_obs, r0,))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def r0_bounds(a, th_obs, outer=True):\n", " r\"\"\"\n", " Return (r0_min, r0_max)\n", " \"\"\"\n", " if outer:\n", " r1 = n(rph_p(a))\n", " r2 = n(rph_m(a))\n", " r3 = rph_pol(a)\n", " else:\n", " r1 = n(rph_ss(a))\n", " r2 = 0\n", " r3 = rph_pol_in(a)\n", " #\n", " # Computation of rmin:\n", " try:\n", " if a == 1:\n", " th_crit = n(asin(sqrt(3) - 1))\n", " if n(th_obs) < th_crit or n(th_obs) > n(pi) - th_crit:\n", " rmin = find_root(lambda r: Theta(a, th_obs, r), r1, r3)\n", " else:\n", " rmin = 1\n", " else:\n", " rmin = find_root(lambda r: Theta(a, th_obs, r), r1, r3)\n", " except TypeError: # special case th_obs = pi/2\n", " rmin = r1 \n", " #\n", " # Computation of rmax:\n", " try:\n", " rmax = find_root(lambda r: Theta(a, th_obs, r), r3, r2)\n", " except TypeError: # special case th_obs = pi/2\n", " rmax = r2 \n", " #\n", " return (rmin, rmax)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\theta_{\\mathscr{O}} = 1.57079632679490\n", "\\end{math}" ], "text/plain": [ "\\theta_{\\mathscr{O}} = 1.57079632679490" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "th_obs = pi/2 \n", "#th_obs = n(160/180*pi) # M87 value\n", "# th_obs = 1.e-3\n", "show(LatexExpr(r'\\theta_{\\mathscr{O}} = '), n(th_obs))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "fa = lambda r: alpha(a0, th_obs, r)\n", "fb = lambda r: beta(a0, th_obs, r)\n", "fbm = lambda r: beta(a0, th_obs, r, eps_theta=-1)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(Theta(a0, th_obs, r), (r, r1, r2))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0.000000000000000, 0.000000000000000\\right)\n", "\\end{math}" ], "text/plain": [ "(0.000000000000000, 0.000000000000000)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rmin, rmax = r0_bounds(a0, th_obs)\n", "rmin - r1, rmax - r2" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(-2.58221244493685, 6.91641650063537\\right)\n", "\\end{math}" ], "text/plain": [ "(-2.58221244493685, 6.91641650063537)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fa(rmin), fa(rmax)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(5.73939650993649 \\times 10^{-24} + 9.37314581466670 \\times 10^{-8}i, 5.90445633372987 \\times 10^{-8}\\right)\n", "\\end{math}" ], "text/plain": [ "(5.73939650993649e-24 + 9.37314581466670e-8*I, 5.90445633372987e-8)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fb(rmin), fb(rmax)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def shadow_plot(a, th_obs, outer=True, color=None, number_colors=5, \n", " range_col=None, thickness=2, linestyle='-', plot_points=200,\n", " legend='automatic', legend_loc=(1.02, 0.36), fill=True, \n", " fillcolor='grey', draw_NHEKline=True, frame=True, axes=True, \n", " axes_labels='automatic', gridlines=True):\n", " if a==0:\n", " # Case a = 0:\n", " rs = 3*sqrt(3)\n", " if color is None:\n", " color = 'black'\n", " if legend == 'automatic':\n", " legend = None\n", " g = parametric_plot((rs*cos(x), rs*sin(x)), (x, 0, 2*pi), \n", " color=color, thickness=thickness,\n", " linestyle=linestyle, legend_label=legend, \n", " fill=fill, fillcolor=fillcolor, frame=frame, \n", " axes=axes, gridlines=gridlines)\n", " else:\n", " # Case a != 0\n", " rmin, rmax = r0_bounds(a, th_obs, outer=outer)\n", " if rmin > 0:\n", " rmin = 1.00000001*rmin\n", " rmax = 0.99999999*rmax\n", " else:\n", " rmin = 0.9999999*rmin\n", " rmax = 1.0000001*rmax\n", " print(\"rmin : \", rmin, \" rmax : \", rmax)\n", " fa = lambda r: alpha(a, th_obs, r)\n", " fb = lambda r: beta(a, th_obs, r)\n", " fbm = lambda r: beta(a, th_obs, r, eps_theta=-1)\n", " if range_col is None:\n", " range_col = r0_bounds(a, pi/2, outer=outer)\n", " rmin_col, rmax_col = range_col \n", " print(\"rmin_col : \", rmin_col, \" rmax_col : \", rmax_col)\n", " dr = (rmax_col - rmin_col) / number_colors\n", " rm = rmin_col + int((rmin - rmin_col)/dr)*dr\n", " r1s = rmin\n", " r_ranges = []\n", " while rm + dr < rmax:\n", " col = hue((rm - rmin_col)/(rmax_col - rmin_col + 0.1))\n", " r2s = rm + dr\n", " r_ranges.append((r1s, r2s, col))\n", " rm += dr\n", " r1s = r2s\n", " if color is None:\n", " col = hue((rm - rmin_col)/(rmax_col - rmin_col + 0.1))\n", " else:\n", " col = color\n", " r_ranges.append((r1s, rmax, col))\n", " g = Graphics()\n", " legend_label = None # a priori\n", " if a == 1 and draw_NHEKline:\n", " th_crit = asin(sqrt(3) - 1)\n", " if th_obs > th_crit and th_obs < pi - th_crit:\n", " # NHEK line\n", " alpha0 = -2/sin(th_obs)\n", " beta0 = sqrt(3 - cos(th_obs)**2 *(6 + cos(th_obs)**2))/sin(th_obs)\n", " if legend == 'automatic':\n", " legend_label = r\"$r_0 = m$\"\n", " if color is None:\n", " colNHEK = 'maroon'\n", " else:\n", " colNHEK = color\n", " g += line([(alpha0, beta0), (alpha0, -beta0)], color=colNHEK, \n", " thickness=thickness, linestyle=linestyle,\n", " legend_label=legend_label)\n", " if fill:\n", " g += polygon2d([(fa(rmax), 0), (alpha0, beta0), (alpha0, -beta0)], \n", " color=fillcolor, alpha=0.5)\n", " for rg in r_ranges:\n", " r1s, r2s = rg[0], rg[1]\n", " col = rg[2]\n", " if legend:\n", " if legend == 'automatic':\n", " if draw_NHEKline and abs(r1s - 1) < 1e-5:\n", " legend_label = r\"${:.2f}\\, m < r_0 \\leq {:.2f}\\, m$\".format(\n", " float(r1s), float(r2s))\n", " else:\n", " legend_label = r\"${:.2f}\\, m \\leq r_0 \\leq {:.2f}\\, m$\".format(\n", " float(r1s), float(r2s))\n", " else:\n", " legend_label = legend\n", " g += parametric_plot((fa, fb), (r1s, r2s), plot_points=plot_points, color=col, \n", " thickness=thickness, linestyle=linestyle,\n", " legend_label=legend_label, \n", " frame=frame, axes=axes, gridlines=gridlines)\n", " g += parametric_plot((fa, fbm), (r1s, r2s), plot_points=plot_points, color=col, \n", " thickness=thickness, linestyle=linestyle)\n", " if fill:\n", " g += parametric_plot((fa, fb), (rmin, rmax), fill=True, fillcolor=fillcolor, \n", " thickness=0)\n", " g += parametric_plot((fa, fbm), (rmin, rmax), fill=True, fillcolor=fillcolor, \n", " thickness=0)\n", " # end of case a != 0\n", " if axes_labels:\n", " if axes_labels == 'automatic':\n", " g.axes_labels([r\"$(r_{\\mathscr{O}}/m)\\; \\alpha$\", \n", " r\"$(r_{\\mathscr{O}}/m)\\; \\beta$\"])\n", " else:\n", " g.axes_labels(axes_labels)\n", " g.set_aspect_ratio(1)\n", " if legend:\n", " g.set_legend_options(handlelength=2, loc=legend_loc)\n", " return g" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shadow_plot(0, pi/2)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.38628054232578 rmax : 3.95534727811920\n", "rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(a0, pi/2)\n", "g1.set_axes_range(-4, 8, -6, 6)\n", "g1.save('gik_shadow_a95_th90.pdf')\n", "g1" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.54632082701639 rmax : 3.53769021424612\n", "rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(a0, pi/4, legend=None)\n", "g1.set_axes_range(-4.5, 7.5, -6, 6)\n", "g1.save('gik_shadow_a95_th45.pdf')\n", "g1" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.76846188276999 rmax : 3.23697774665377\n", "rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 12 graphics primitives" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(a0, pi/6, legend=None)\n", "g1.set_axes_range(-4.5, 7.5, -6, 6)\n", "g1.save('gik_shadow_a95_th30.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Case $\\theta_{\\mathscr{O}} = 0$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 2.49118715973461 rmax : 2.49420141399888\n", "rmin_col : 1.3862805284629751 rmax_col : 3.95534731767268\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(a0, 1e-3, legend=None)\n", "g1.set_axes_range(-6, 6, -6, 6)\n", "g1.save('gik_shadow_a95_th00.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Shadow radius for the on-axis observer:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def R_shad(a):\n", " r0 = rph_pol(a)\n", " return 2*sqrt(r0*(r0^2 - a^2))/(r0 - 1)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}4.87509181305858\n", "\\end{math}" ], "text/plain": [ "4.87509181305858" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R_shad(a0)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = plot(R_shad, (0, 1), thickness=2, \n", " axes_labels=[r'$a/m$', r'$(r_{\\mathscr{O}}/m) \\; R_{\\rm shad}$'],\n", " frame=True, axes=False, gridlines=True)\n", "g1.save('gik_shadow_radius_axis.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extremal values:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(5.19615242270663, 4.82842712474619\\right)\n", "\\end{math}" ], "text/plain": [ "(5.19615242270663, 4.82842712474619)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R_a_0 = n(3*sqrt(3))\n", "R_a_1 = n(2*(sqrt(2)+1))\n", "R_a_0, R_a_1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Relative amplitude:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.0707687665884322\n", "\\end{math}" ], "text/plain": [ "0.0707687665884322" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 - R_a_1 / R_a_0 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shadow for $a=1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The partial shadow boundary:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.99999996000000\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(1, pi/2, fill=False, draw_NHEKline=False)\n", "g1.set_axes_range(-4, 8, -6, 6)\n", "g1.save('gik_shadow_a1_th90_part.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the NHEK line:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.99999996000000\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(1, pi/2)\n", "g1.set_axes_range(-4, 8, -6, 6)\n", "g1.save('gik_shadow_a1_th90.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As soon as $a\\neq m$, the shadow boundary is a smooth closed curve:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.01637428079421 rmax : 3.99991107028894\n", "rmin_col : 1.01637427063047 rmax_col : 3.9999111102880467\n" ] }, { "data": { "image/png": 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GZ8+eLbbfjIwMgoODiY6OZvHixWzatIlt27Yxb948Tp48ydixY8nLy2PMmDHk5eUxduxYTp48ybx589i2bRubNm1i8eLFREdHExwcTEZGRrH9nz17lhkzZrB7927WrFnD8uXL2b9/P59//jlJSUnFtk1OTmbKlCkcOHCA77//nrVr1xIeHs7MmTNJSEgotm1mZiYTJkwgOjqab775htDQULZu3cr8+fM5ceIE48aNIzc3t9h7Tp06xZw5c9i+fTsbN25kyZIlHD58mODgYNLT04ttm5iYSEhICHv27GH16tWsWLGCffv2MXXqVC5evFhs25SUFCZPnkxkZCTLli1j3bp1hIeHM2vWLOLj44ttm5WVxYQJEzh27BiLFi0iNDSULVu2sGDBAmJjYwkKCiInJ6fYe0JDQ/nqq6/YsWMHGzZs4NtvvyUqKoqJEyeSlpZWbNvz588zffp0IiIiWLVqFStXriQiIoJp06Zx4cKFYtumpqYyadIkIiMjWbp0KevXr2fnzp3Mnj2bsxfj+bHTGG75L2hldFUcnwdrBmSwcMa3hIWFERYWxsKFC4mJiWH8+PFkZ2cX2398fDyzZ89m586drF+/nqVLlxIZGcmkSZNITU0ttu327duZNm0aERERrFy5klWrVhEREcH06dM5f/58sW3T0tKYOHEiUVFRfPvtt2zYsIEdO3bw1VdfERcXV2zbnJwcgoKCiI2NZcGCBWzZsoXQ0FAWLVrEsWPHSv2OKPj5EcJOfPp2U6VUB2AX8KDWem/+ulAgQms9qpz3BAABDqsaAXFl3W4ZHx9P27ZtXRB5kSRmc4bhhc9b8D4teB+VP7GYq9npdlN3tKcnsDrPk0th+x8gN9N43vhauH8dNOho3jGszrGA3G4q7MjXeyxuBa4CdiulcpRSOcA9wF/yn5c6j6C1ztJapxQ8gHKnVpo9e7bLAgdIYRlnGFH4vAX/piUfuK2osBtXt6ensDrPjk8YA2oFtDSep0TB+rsg2cTrLa3OUQg78/Uei0bA1SVWfwVEAeO11geqsA9LhvS+zI/5t5QaJ6Gb8iatmOj2osJOPRbCvdKOw6ZBkBptPA9oYcw/0vxWa+Myk/RYCDvy6R4LrXWq1vqA4wO4DFyoSlFRGVcNG5zJPuJ4vLCoCOR5WvGp9FS4mF2GgfaUPBteAw9uhaY3G8+zzhuTmJ0Nq/BtVeIpOQphRz7dY1GWyq6xKGP7cnsssrKyCAgIKPuNNZRDAse5jRxOAdCQR2nPUhRuHA/ZgZ16LFzRnp7I0/K8kgyhQ4z5RQBq1YUB30Pbh2q+T0/JUXoshB35dI9FWbTW91a1qKjMZ599ZsZuCuWRzikeLSwq6tKXdiyyrKiwG7Pb01N5Wp51Ao2LN9sONp7nZsLmxyB+Xc336Wk5CmEntisszPTEE0+Yti9NHvG8QCbhAPjTgfb8Dz/qm3YMUTEz29OTeWKe/vXhnv9Bx6eM53lZsPn/4Mz6mu3PE3MUwi6ksHDCL7/8Ytq+LvAJqXwHgB8N6cAqatPGtP2LypnZnp7MU/P0qw13LYSOTxrPC4uLSoe1K81TcxTCDqSwcEKbNub84b/MTyTy9/xnirYsoi43mbJvUXVmtaen8+Q8/WrDXV8XzY6amwmbH4WEn6q3H0/OUQhfJ4WFE2rVcn447WziOc0zQB4ALfgXjRji9H5F9ZnRnt7A0/P0qw13LYL2jxnPczOM4uLCrqrvw9NzFMKXSWHhhBMnTjj1fk0OpxlGLucAaMCDtODfZoQmasDZ9vQW3pBnrTpw92Jo94jxPCcNfhoMKUeq9n5vyFEIXyWFhRPuvvtup95/nrFkYNxj508H2rJQJhWzkLPt6S28Jc9adaD/ErhqgPE86zxsehDST1f+Xm/JUQhfJIWFE7755psavzeDnZzno/xntWjPEvxpYU5gokacaU9v4k151qoL96yApr2M55dPGKN1Zl2s+H3elKMQvsZ2A2RVV0UDZOXk5ODvX/0xJvJII4beZHMUgBb8h5YeegrETgNk1bQ9vY035plxxphPJO248bzlXfDAj0bhURZPyVEGyBJ2JD0W5VBKvaaUigTKvW8tKCioRvs+y98Ki4p69KNF4R0hwko1bU9v44151msD96+HulcZzxO3wY4RUN7/Rd6YoxC+QnosKmH2JGSXCeUk9xn7pgGdiaAOXZ3er6vYqcdCeL4Lu2FDf+NOEYBeY+EGD67LpcdC2JH0WDihuhMd5ZFJAn8ufH4V4z26qLAbu0xc5c15Nr8V7lxQ9HzvP+Dkd6W38+YchfB2Ulg44Y9//GO1tr/Ax1zBuF+uHnfQlFddEJWoqeq2p7fy9jw7DoVeHxc93/586TEuvD1HIbyZFBZO2LBhQ5W3zSKS8xSc961Na2ag5OP3KNVpT2/mC3le/x5c87yxnJthTFqWea7odV/IUQhvJX/ZnNCzZ88qbafRnGUUkA1Ac96lLje4LjBRI1VtT2/nC3kqBbfPgJb5w1VknIatv4O8HOO5L+QohLeSwsIJqampVdoujTVcxvgPqjadaME/XBmWqKGqtqe385U8awUYA2jVbW08P7sJ9v7LWPaVHIXwRlJYOCEpKanSbXRGCuey3yx8fhUT8KOcm++FparSnr7Al/Ks18YoLlT+gLWRQXDqf76VoxDeRgoLJ9x4442VbnNpxwtcqX0MgHrZ/WjEk64OS9RQVdrTF/hanlf1h96fFD3/+Xno1vgW6wISwuaksHDCDz/8UOHrOamxJN78v8LnrU68iUK5OixRQ5W1p6/wxTyvHQUd82v27BSIGNGAvGxLQxLCtmSArEpUNEBWWloaDRs2LPe9ueP+zgU1jov/Dxr/cg1t+8e4OFrz2WmArMra01f4ap7ZqfDDrZAabTy/fjTc/HHF73E1GSBL2JH0WDhh0qRJ5b+YkkKt8V9w1WjofEMtrmq/0G1xiZqpsD19iK/mWbsR3PU1qPwpQg4GwdlQS0MSwpakx6ISNR7SOygIRo82ll98EWbPdkl8rmanHgvhGw6Oh4j3jOX67eHhvRDQzJpYpMdC2JH0WDih3GGD09Ph00+NZT8/eO899wUlaswuw0D7ep7XvQ0ZnY1pUNPj4BcZ4FYIt5LCohxVmd30lVdeKfuFL7+ExERj+amnoHt3F0QozFZue/oYX89T+cFDywOpk99LcXIJnPjW2piEsBMpLMqhtZ6qtb4OuK28bb77rozZj3JzYeLEoud/9+CpF0UxZbanD7JDnqu2LaHvF0XPw1+DzETr4hHCTqSwcEK/fv1Kr1y9GmJjjeVBg+Cmm9wak6i5MtvTB9khz379+nH109BhqPE8KxF2vWFtTELYhRQWToiLiyu98vPPi5bfkN9k3qTM9vRBdsgzLi4OpaDvFxSeEjmxGE4uszYuIexACgsnlLqjJioKCmZV7NwZHnrI/UGJGrPLHVJ2yLMgx3qtoM+UovW73jDGuxBCuI4UFk7o0KFD8RUhIUXLr70GtWq5NyDhlFLt6aPskKdjjp1+B21/ayxnxMO+DywJSQjbkMLCCT///HPRk5wc+PprY7lOHfjjHy2JSdRcsfb0YXbI0zFHpaDPZKiVP/ff4c/g0j6LAhPCBqSwcMLTTz9d9GT9ejh3zlh+9FFoZtGIPKLGirWnD7NDniVzbNQZrv+HsaxzjbEtdJ4FgQlhA1JYOGHatGlFT+bNK1p+/nn3ByOcVqw9fZgd8iwrx+vehkbdjOXz2yFmjntjEsIuZEjvSlRpSO/UVGjZErKyoEULiI+H2rXdGqeryJDewpec2QCbHjSWA1rAo0ehTqDrjidDegs7kh4LJxQOjfzDD0ZRATBsmM8UFXbj60NdF7BDnuXl2GYgdMw/S5J13pioTAhhLumxqERFPRapqak0atQInn0WFi0yVv74IzzwgPsDdRE79VgUtqePs0OeFeWYdhxWXgt5V8AvAB45DA2vdk0c0mMh7Eh6LJwwa9YsuHLFGG0ToEkTGDDA0phEzc2aNcvqENzCDnlWlGPDa6DHm8ZyXhbs/YebghLCJqSwcMKDDz4IoaGQkv+PyJAhchrEiz344INWh+AWdsizshxv+DsENDeWYxfChXA3BCWETUhh4YRDhw7BunVFKx591LpghNMOHTpkdQhuYYc8K8uxThO48f2i57++49p4hLATKSzKUZVp0xs1agSbNhW8waeurbAjX7/uoIAd8qxKjt1eKbr99GwoJPzk2piEsAspLMpRlWnTmwNERBhPeveWQbG8XP5Fdj7PDnlWJUe/2sV7Lfa9D3ItuxDOk8LCCUnLlxc9uf9+y+IQ5jh48KDVIbiFHfKsao5XPwONrzWWE7fA2U0uDEoIm5DCwgm3F4xdAXDffdYFIkzxkE1mo7VDnlXN0a9W8V6Lvf+WXgshnCWFhROSCqZIB7jjDusCEaaYPXu21SG4hR3yrE6OHZ+CwOuM5fPbIWFDxdsLISomA2RVotwBsrKzoXFjyMyErl0hOtqyGF3JTgNkCfs6sQS2DjOWW/aHB8PM2a8MkCXsSHosaurgQaOoAOjTx9pYhCnsMNQ12CPP6ubY8Ulo3NNYTtwC53e6ICghbEIKi5ratatoWQoLn/Duu+9aHYJb2CHP6uao/KDn34qeH/qvyQEJYSNSWNSU41XnN99sWRjCPJ9++qnVIbiFHfKsSY7X/AHqtjKWTy2D1GMmByWETUhhUVOHDxctX3utdXEI0zz11FNWh+AWdsizJjnWCoAefzGWdR5ETTQ5KCFswqcLC6XUaKVUuFIqVSl1Tim1XCnVw5SdHzlifG3YENq2NWWXwlo///yz1SG4hR3yrGmO3V4F/wbG8rHZkHXBxKCEsAmfLiyAe4CpQD9gIOAPrFdKNXBqr1lZcPy4sdy9uzGct/B6HTp0sDoEt7BDnjXNMaApdBluLOdmQMwc82ISwi58urDQWj+ktZ6jtT6otd4LvAh0BG51asenTkFenrHcrZuzYQohPEj3kUXL0dON0yJCiKrz6cKiDAUTCFwsbwOlVIBSqnHBAyg9m1F8fNFyu3YmhyiscurUKatDcAs75OlMjo17QOv8+QRTj0LCRpOCEsImbFNYKKUU8CmwVWt9oIJNRwPJDo84gJiYGCZMmEBWVhbLPv+8cOPkBg2YNWsW4eHhrFu3jmXLlhEZGcnkyZNJSUkpvJ9+zJgxXLx4kalTp7Jv3z5WrFjB6tWr2bNnDyEhISQmJhbbNj09neDgYA4fPsySJUvYuHEj27dvZ86cOZw6darYtrm5uYwbN44TJ04wf/58tm7dSmhoKN988w3R0dF88sknZGZmFntPQkICM2fOJDw8nLVr1/L9999z4MABpkyZQnJycuG2EyZMACAkJIT9+/ezfPly1qxZw+7du5kxYwZnz54ttt+MjAyCg4OJjo5m8eLFbNq0iW3btjFv3jxOnjzJ2LFjycvLY8yYMeTl5TF27FhOnjzJvHnz2LZtG5s2bWLx4sVER0cTHBxMRkZGsf2fPXuWGTNmsHv3btasWcPy5cvZv38/n3/+OUlJScW2TU5OZsqUKRw4cIDvv/+etWvXEh4ezsyZM0lISCi2bWZmJvv37yc6OppvvvmG0NBQtm7dyvz58zlx4gTjxo0jNze32HtOnTrFnDlz2L59Oxs3bmTJkiUcPnyY4OBg0tPTi22bmJhISEgIe/bsYfXq1axYsYJ9+/YxdepULl68WGzblJQUJk+eTGRkJMuWLWPdunWEh4cza9Ys4uPji22blZXFhAkTOHbsGIsWLSI0NJQtW7awYMECYmNjCQoKIicnp9h7OnXqxFdffcWOHTvYsGED3377LVFRUUycOJG0tLRi254/f57p06cTERHBqlWrWLlyJREREUybNo0LFy4U2zY1NZVJkyYRGRnJ0qVLWb9+PTt37mT27Nml4s7Ozmb8+PHExMSwcOFCwsLCCAsLY+HChcTExDB+/Hiys7OLvSc+Pp7Zs2ezc+dO1q9fz9KlS4mMjGTSpEmkpqYW2/baa69l2rRpREREsHLlSlatWkVERATTp0/n/PnzxbZNS0tj4sSJREVF8e2337Jhwwb0A0cKf8ZXvhlVuG1OTg5BQUHExsayYMECtmzZQmhoKIsWLeLYsWOFvyNK/vwIYSe2GXlTKTUV+C1wt9Y6roLtAoAAh1WNgLhiI09OnAh//aux/PXX8LvfuShq69lp5M3x48fbYowHO+TpbI552bD8asg4Y4xx8dgJqN+++vuRkTeFHdmix0IpNQV4FLivoqICQGudpbVOKXgAqaU2cjwV0qaNucEKy/y1oFj0cXbI09kc/WpD1xHGss6DmPkmBCWETfh0YaEMnwNDgfu11sdN2fGlS0XLLVqYskthvfHjx1sdglvYIU8zcuz8x6Ll4/Nk1lMhqsqnT4Uopb4AngX+D3AY0YpkrXVGFfdRehKyYcNgyRJjOTYWrr7avKA9jJ1OhQhR0oZ74Fz+hGSDdkKL26r3fjkVIuzIp3ssgFcx7gQJBc44PIY5tdcUh98PjUrfNCK8kx0m5wJ75GlWjp1fKFo+Ps+UXQrh83y6x8IMZfZY3H03bNtmLF+5ArVrWxafq9mpxyI+Pp62NhhF1Q55mpVjdgosbW0MllWnGQyNN4b+rqryeix2797dEZDzqMLbnL/11ltPVraRvzsi8TmpxvWcOf7++PtwUWE3a9eu5aWXXrI6DJezQ55m5Vi7MbR/DE4sgisXIeFHaPdb5/aZX1QcBuo6HaAQ7pW5e/fuHpUVF1JY1ER+YaEbNrQ4EGGm66+/3uoQ3MIOeZqZY6dnjMIC4OR3zhcWGD0VdTt16kS9evWc3pkQ7pCRkUFsbGxdjO9fKSxMd/kyADkBAUh/he9ITk62OgS3sEOeZubY5kHwbwg5aRC3HHJDoFYd5/dbr1496tev7/yOhHCj6OjoFv/5z3/aAOkrVqwo8wfN1y/edI3sbABy/OTj8yWpqaWHLPFFdsjTzBxr1YV2jxjLV5Lg7CbTdi2E19m5c+frwDjgn48++mhgWdvIX8aauHIFgNry34ZP6dmzp9UhuIUd8jQ7x6ufKlo++Z2puxbCq/j7+ycBGUBLoMw/glJY1ER+j0VKZqbFgQgzrV+/3uoQ3MIOeZqdY5uHwL+BsRz3P8jLNXX3QngNPz+/DOByhdu4KRbfkl9YNG/VyuJAhJmGDx9udQhuYYc8zc7Rv55xrQVA1nm4uMvU3QvhU6SwqK7c3MKxfePPn7c4GGGmzz77zOoQ3MIOeboix7YPFy3HrzF990L4jBoXFkqpBkqppmYG40mUUq8ppSKBX4q9kH99BUCHa65xc1TClf75z39aHYJb2CFPV+TYdnDRcvwPpu9eCJ9R7cJCKeWvlJoDJAHnlVLhSqk+JbbppJS6QSnltQM9aK2naq2vA4rPDpB/GgQgJq7CiVKFl7HDUNdgjzxdkWP9dtC0l7F8IRwyzpp+CCF8Qk16LP4GNADeAIKAAGC7UuohpdT/KaVigGPAXuCCUmqNUuou0yK2mkNh0V56LHzKq6++anUIbmGHPF2VYxuHXosz61xyCI+WlpbGE088wcmT5Y+PFB4ezqhRo5g7dy4vv/wyx48XTSq9c+dOgoOD+eCDDxg0aBCbN292R9gkJCTw/vvvs3z5co84XlU+xwJffvklY8aMYe7cucyePbtG+3C3mgyQ1VNr7XDzFf9QSj0MzMAYket/wCKgOXAzMBAYpJT6r9b6XSfjtZ5DYXH63DmktPAdS5YsscUfXTvk6aoc2w6GyCBj+cwG6Py86YfwWLNnz+bEiRMsW7aM4ODgMrfJysriqaeeYufOnbRq1Yru3bvz4osvEhoaSnp6OsuXL2fcuHEAfPfddwwePJjo6GjatWvnkphjYmIICQkhICCAkSNH0rp1a5ccpzrHq8rnWCAkJISYmBjGjx9PdHQ0ffr04cUXX+Srr76q8j6sUJPCIrvkCq31GqXUT0C21vpPjq8ppZoDI4B3lVJ5WuvRNQvVQzhcY9FE7grxKXfccYfVIbiFHfJ0VY4t+hkDZuVmQuIWlxzCYxXMvfLhhx+Wu01YWBiNGzemVf7vxttuu40dO3Zw9uxZzp49S1BQEMOHD6dr164MGjSIjIwMtm3bxtNPP21qrPv27WP27Nm0bt2a0aNH06RJE1P378zxqvI5glGkjR49ml9//RWArl27snfvXpRSVd6HVWpSWEQqpa7XWh8ssT4LKDVVqtb6AhCklFoA/KCUWqK1/rUGx/UMDj0Wl69cwWevXrWhU6dOcfPNN1sdhsvZIU9X5VirDrS4A87+BJdPQNoJaHi16YfxWrGxsTRr1qzwea1atWjUqBEHDx7kvvvuY9u2bXTp0gWgsAu/W7duhdsnJSUxa9YswsLCGD16NBEREaSlpREXF8czzzzD4cOHOXz4MM2bN+dvf/tbqePv2LGD+fPn07NnT8aNG1fpXCyHDh1i/fr1LFiwgM6dO9OiRQtCQ0M5eLDkn7eyVfd41bF9+3YuXbpEdHQ0O3bsICoqikGDBtGpU6dK3+vs5+ismhQWM4EpSqnhWus8h/V55b0BQGsdp5QaBryW//BODoWFrlXLwkCE2ZRSVofgFnbI05U5XjXAKCzA6LVwS2HRpw8kJJi7z9atYZe5A3KcP3+eunWLT9pat25dkpKSUEpx5513Fq4PCgpi1KhR9O7du3Dd0qVLee2115g5cyZHjhzhlVdeIT09naZNmzJs2DBeeOEFIiMjGTZsWJl/EPfv309mZia9e/eu0h/5Y8eO8eabbxIUFMT48ePp378/CdX4nKt7vOo4c+YMAHXq1GHYsGGcP3+eXr16cejQIRo3blzhe539HJ1V7Ys3tdZpwOfA50opx6l4xgKTKnlvJOC1d4oAxQqL+oFlDpMuvFT79u2tDsEt7JCnK3O8akDR8rkwlx2muIQEOH3a3IfZhQoQGBiI1sU7rtPS0mjRokWxdQWnDT799NNi65988kmSkpJISUnh+eeNC1j27t1Lnz59Ck9v7dq1i+uuu67M448YMYJp06YRFRXFiBEjWLt2bYXxDhkyhKioKJo0acL9999P7dq16dChA+np6fzrX/9i48aNFZ5uqO7xqiMw/+9L3759AWjRogV5eXls3bq10vc6+zk6q0bjWGitdwNfAPOVUnfnrzultY6qwtu9e0bVnJzCxQQZIMun7Nixw+oQ3MIOeboyxxb9QOX/FnNbYdG6NbRrZ+7DBRcyXnvttZw7d67weVZWFqmpqVx9dVG3zpo1a8jNzeWTTz4hKyuL2NjYwtcCAwP58ccfeeCBBwrXlXz+9ddf88QTT3Dp0qUyY6hTpw7Dhw8nJCSE1NRURowYwZIlS8jLK7tTveT+AebNm0fPnj154IEHyM7OJiys/Iau7vGqqnfv3iilyM0tGj++5PPymPE5OqPGA2RprQ8AzwF9lFILlFJ/VUrdrCrog1RKvQCsrukxPYLDN0vnrl0tDESY7cknn7Q6BLewQ56uzNG/PjQ3/okk5bCbxrPYtQvi4sx9mHQa5Mcff2Tv3r0ADBgwgHPnzhGXP8bP5s2b6du3b2FhERYWRnx8PI888ggJCQmsXbu2sMvfcX/l/UG8dOkSP//8M48++iizZs2qMC4/Pz+eeuopZs6cSdOmTRk5cmSZPQobN27k/vvvL7YuMjKSjh07AtCxY8fC/Mw4XkUcP8u2bdtyzz33sG3bNgASExNRSpWKtaJ9mfE51oRTvQda6yvkn/5QSt0E3Av8Jb+4iAK2Yoxp0RQYCjTTWpt/QsedHLr5DkRG0tfCUIS5pk+fbotRKe2Qp6tzvGoAnP/ZWD7/M3R4zGWH8hiLFi0q/M/9vffeY8CAAYwcOZKpU6fSt29fevXqhb+/P3PnzmXs2LH069ePzZs3s3DhQsC4FXPIkCGlprRPTk4u9vzo0aOFt6RqrUlMTCzsvq9bty633347CxYsYMiQIVWOfeDAgQwcOJCMjIxSr504cYL77ruv2Lq8vDz8/Y0/j7m5uYXLZhyvvM8RKPZZAsydO5f333+fyMhIjh07xsqVK2nQoEGF+yjgis+xqlTJ82Gm7VipnsCA/Ed/4BAwAdiutS79aXsopVRjIDk5Odm4YOaXX+D2240X33gDJk+2ND5XS0lJITAwkML8hRCcXApb8jtFbvgX9CrnNHzBzw8QqLVOAdi9e/ctwO6ePXtSv36Zs04Li4WEhNCyZUuGDh3K22+/zeDBg6vcU+Cr0tPTOXToEEuWLJlx6NChVIxxq0avWLHiTMltXXa9g9b6EEYxEQKglLoGo8iYqJSqB5wGNgPb8i8I9Q4Ohdgv4eElxvsW3mzMmDE+/5882CNPV+fY7Jai5Yt7XHYYUU1vvfUWUVHlX+o3dOjQwjEgKvL73/+e8ePH07RpU7TW3HvvvS49nq9x24WUWuvjwHFgLoBSqg1wD/BHjLtMvINDYXHzrbdaGIgw26hRo6wOwS3skKerc2zQCeo0gStJcEkKC4/x3//+15T9NGzYkI8++gig1GkSVxzP11g2bbrW+ozW+huttUcWFeXObupw8eb+AwfcHJVwpZkzZ1odglvYIU9X56gUNM3vtcg4Axnm37kphNeyrLDwdOXOburQY9Gpc2c3RyVcafDgwZVv5APskKc7cix2OsR7xxIWwnRSWFSXQ4/FeRnHwqfs37/f6hDcwg55uiNHx8JCTocIUUQKi+py6LGoY/IQrsJarp6oyFPYIU935Bh4Q9FyclWGBhTCJqSwqC6HHos6AQEWBiLM1qhRI6tDcAs75OmOHBt1BfKHA0w97PLDeYS0tDSeeOKJwgnEyvPll18yZswY5s6dy+zZs2u0DzMlJCTw/vvvs3z5csuPt3PnToKDg/nggw8YNGgQmzdvLnc/FW1rxedYVd49vLYVHHosLly4QDsLQxHmOnToEP369bM6DJezQ57uyNG/HjS4Gi7HGiNwam1c1OmrZs+ezYkTJ1i2bBnBwcHlbhcSEkJMTAzjx48nOjqaPn368OKLL6KUqvI+zBITE0NISAgBAQGMHDmS1i4Yxrw6x0tPT2f58uWFA1d99913DB48mOjoaNq1a1flbdetW+fWz7G6pLCoLrl402cNHDjQ6hDcwg55uivHxj2MwiI7BTLPQj3X/t2yVMF4DBVNypWVlcXo0aP59VfjatauXbuyd+/ewtlmq7IPM+zbt69worPRo0e7/NRYVY939OhRgoKCGD58OF27dmXQoEFkZGSwbds2nn766Spv667PsaZMKyyUUi2BXkAnIBAIANIwBsI6nD+3iPdzOBWyb/9+7rYwFGGuOXPm+PzAUWCPPN2VY+MecGadsZxy2LcLi6rYvn07ly5dIjo6mh07dhAVFcWgQYPo1KlTld6flJTErFmzCAsLY/To0URERJCWlkZcXBzPPPMMhw8f5vDhwzRv3rzM6b537NjB/Pnz6dmzJ+PGjat0KvNDhw6xfv16FixYQOfOnWnRogWhoaEcPHiwSvFW93g33ngj27Zto0uXLgCFpzG6devm1LYlOfs5OsupwkIp1RkYDjwO9MA445gLJANZQDOMAgOlVDKwBpintV7nzHEt5dBjcfeAARVsKLyNr/+xLWCHPN2VY+MeRcsph6HVPa45znH6kIO5g2X405prMGcisgIFE4rVqVOHYcOGcf78eXr16sWhQ4eqNCXA0qVLee2115g5cyZHjhzhlVdeIT09naZNmzJs2DBeeOEFIiMjGTZsWJl/EPfv309mZia9e/eu9I88wLFjx3jzzTcJCgpi/Pjx9O/fn4RqTCdf3eMppbjzzjsLnwcFBTFq1Ch69+7t1LYlOfs5OqtGF28qpVoqpeYCuzAKiunArRiTjNXWWrfQWrfTWtcDGgJdgNeAVOALpdRepZSLfgRdzKHHImzLFgsDEWYbM2aM1SG4hR3ydFeOjRz+eUyLcd1xckggh9MmP8wf1St/XhT69jWmZ2zRogV5eXls3bq1Su9/8sknSUpKIiUlheeffx6AvXv30qdPn8IJtHbt2sV1111X5vtHjBjBtGnTiIqKYsSIEZXOLjpkyBCioqJo0qQJ999/P7Vr16ZDhw6kp6fzr3/9i40bN1Z4uqG6x3NUcOrk008/NXVbcP5zdFa1Cwul1CDgJ+AI0Flr/aTWerLWOkJrnVRye611utb6uNb6a631K0BXYCzwqVJqQkXTrHskhx6Lu6THwqe89957VofgFnbI01051u9QtJwe57rj+NMaf9qZ/DD/vE3v3r1RSpGbm1u4ruTzigQGBlY43TfA119/zRNPPMGlS5fK3EedOnUYPnw4ISEhpKamMmLECJYsWUKewz+FjkruH2DevHn07NmTBx54gOzs7MKZRM04HsCaNWvIzc3lk08+ISsri9jYWFO2LWDG5+iMahUWSqnfAm8A/bXWY8sqJCqjDUu01rcCFwHzJ4N3JYdvlu3bt1sYiDCbXcb9t0Oe7sqxfvui5fRTrjvONeyiG3GmPsw6DfLjjz+yd+9eANq2bcs999zDtm3bAEhMTEQpVa2ZQSv6g3jp0iV+/vlnHn30UWbNqvhPh5+fH0899RQzZ86kadOmjBw5sswehY0bN5aKLzIyko4dOwLQsWPHwvzMOF5YWBjx8fE88sgjJCQksHbt2sJTSI6fZWXbVsasz7EmqnuNRU/gUa11+aVYNWitg5RSDyqlbvCaizsdeixuuPFGCwMRZnvmmWesDsEt7JCnu3Ks3bBoMjJX9lh4gkWLFhX+5/7ee+8xYMAARo4cydSpU+nbty+9evUCYO7cubz//vtERkZy7NgxVq5cSYMGDSrch6OjR48W3mKptSYxMbGw+75u3brcfvvtLFiwgCFDhlQ59oEDBzJw4EAyMjJKvXbixIlSE43l5eXh72/8eczNzS1cdvZ4MTExDBkyhNTU1GLrk5OTAYp9lhVta9XnWFVKO/yhFKUppRoDycnJycbFR6tWwSOPABDx5JPc/O231gboYikpKQQGBlKYvw9bsGABf/jDH6wOw+XskKc7c1x9EyTtB7868EwGKId+4IKfHyBQa50CsHv37luA3T179qR+/fpuiVFUT0hICC1btmTo0KG8/fbbDB48uFq9Lr4oPT2dQ4cOsWTJkhmHDh1KBVoAo1esWFGqC0XGsaguh1MhTZo2tTAQYbarr77a6hDcwg55ujPH+u2NwiLvCmSdh7pXue3QooS33nqLqKjyx1cfOnRo4RgQFfn973/P+PHjadq0KVpr7r33Xpcez9e4vLBQSr0EtAM+11qbf5WIiyilXsO4k6X4dSgOPTymnA8SHqOqF5h5Ozvk6c4cA1oWLV+5JIWFlcy6tqZhw4Z89NFHAKVOk7jieL7G9LlC8m9FLdyv1no28D0wWSlVfgt5mHKnTXfosUgpce5LeLeqXhTl7eyQpztz9G9YtJyd5rbDCuGxTCsslFL3KaXOAwlAilLqB6XUS0qpwPwLM58HXjHreJZx6LHoYIMuZTu57bbbKt/IB9ghT3fmWNuhsMiRwkIIU3ssPgSmYtyOOgfoDHwJnFFKLcIoKlqYeDxrlBjSW/iOpUuXWh2CW9ghT3fm6C+FhRDFmHmNxX6t9fuOK5RSNwLPYgz5PRCj6PBuDj0W/WWALJ/y5ptvWh2CW9ghT3fmKKdChCjO9GssHGmt92utR2utr80f5nuRK4/nFg6FxabNmy0MRJjtk08+sToEt7BDnu7M0b9B0bIv91js3LmT4OBgPvjgAwYNGsTmcn7/VbZdWloaTzzxROGkWu6QkJDA+++/z/Llyy0/XlU/R4Djx4/zxRdfMHv2bD7++OPCWWPBms+xqszssdiilHpMa73cxH16HodTIQ8++KCFgQiz2WFyLrBHnu7MsdipkMtuO6xbpaens3z58sIBl7777jsGDx5MdHQ07dq1q/J2s2fP5sSJEyxbtozg4GCXxx0TE0NISAgBAQGMHDmS1q1dO/1sZcer6udYYPr06YwfP77w+R/+8AcWLFjg9s+xukzrscjvjbhBKfUns/bpkRx6LNZt2GBhIMJsdpicC+yRpztztMPFm0ePHiUoKIijR48CMGjQIDIyMgqH7q7qdi+99BL/+c9/XB7vvn37GDVqFEuWLGH06NF8+OGHLi0qqnq8qn6OBZYtW1ZsiO+AgADAfZ9jTZnWY6GUug14EeiklHoPCC14aK19Z7Bbhx6LfvnDowrfYJeBbOyQpztzdMfFm314hwTMHQaoNU3ZxYQqbXvjjTeybds2unTpAlDY/d6tW7cabVeepKQkZs2aRVhYGKNHjyYiIoK0tDTi4uJ45plnOHz4MIcPH6Z58+ZlTve9Y8cO5s+fT8+ePRk3blylU5kfOnSI9evXs2DBAjp37kyLFi0IDQ3l4MGDVYq3user7ufz+uuv06dPH9544w0CAwP5y1/+UqW4nP0cnWXmqZBgYAOQAtwEPA28BGilVAzGjKgLtNblTxPnDRx6LA4eOsSdFoYizPXDDz8wfPhwq8NwOTvk6c4c3VFYJHCJ01x0zc6rQCnFnXcW/bYLCgpi1KhR9O7du0bblWfp0qW89tprzJw5kyNHjvDKK6+Qnp5O06ZNGTZsGC+88AKRkZEMGzaszD+I+/fvJzMzk969e1f6Rx7g2LFjvPnmmwQFBTF+/Hj69+9PQkLVp5Ov7vGq+/k888wzhIeHs3LlStLS0ujfv3+V4nL2c3SWmRdvHtBav6K1fkdr/RDQFLgT+CcQA/wOWGzi8apMKTVSKXVcKZWplNqtlKpa65TFoceibfv2FWwovM1NN91kdQhuYYc83ZljbTfcFdKaprSjmamP1tRsSoLZs2fTunVrPv30U1O2c/Tkk0+SlJRESkoKzz//PAB79+6lT58+hRNo7dq1i+uuu67M948YMYJp06YRFRXFiBEjypxd1NGQIUOIioqiSZMm3H///dSuXZsOHTqQnp7Ov/71LzZu3MiHH35Y7vurezxHlX0+qampvPLKK8yYMYP9+/fz5z//mccff5zjx49Xum9nP0dnmdljccXxidY6F9iR/xinlPIHmph4vCpRSg0DJgEjgW3An4EflFLXaa2rfzmtQ49Fenq6OUEKj3DxonX/EbqTHfJ0Z47u6LGo6ikLV1uzZg25ubl88sknZGZmkpCQQKdOnWq8XUmBgYGsXLmy3Om+Ab7++mteeuklLl26RNMy5muqU6cOw4cP58UXX2Tp0qWMGDGCgQMH8uSTT+LnV/p/6ZL7B5g3bx49e/bkgQceIDQ0lLCwMAaUM7xAdY9X1c9nw4YN3HPPPYUT1X3wwQdkZ2cTHh7ONddcU/YHmM+Mz9EZZvZYHFZK3VPei1rrHK31eROPV1V/BWZprb/UWh/SWo8CTgGv1mhvDsVEdpqPXqllU5cv++gl/SXYIU935uhYWGRdcNth3S4sLIz4+HgeeeQREhISWLt2LWfOnOHHH38sdoFhedtVVck/gI7PL126xM8//8yjjz7KrFmzKtyPn58fTz31FDNnzqRp06aMHDmyzB6FjRs3lpq5NDIyko4dOwLQsWPHYvk5e7yKPh/Hz7Jr165EREQUe29ubi633357pbEU7MuMz7EmzOyxmAZMUkrV0Vp7xO0SSqk6wK1AUImX1kPZl0copQKAAIdVjcCY/hiALVsKX2iakFC03kcV5OfreQK0b99e8vQR7swxNxcK/t04+TM4HtZXPueYmBiGDBlCaon5kZKTk3nhhRfo27cvvXr1qnA7gEWLFhEWZlxm99577zFgwABGjhxZbNujR48W3o6ptSYxMbGw+75u3brcfvvtLFiwgCFDhlQ5/oEDBzJw4EAyMjJKvXbixIlSE43l5eXh72/8eczNzS1cdvZ4lX0+U6dOLfwsb7rppsJrINq3b09WVha/+c1vuPrqqy37HKtKaYeufad2pNRgjKG8WwDrMC7kDNVa/1rR+1xJKdUWOA3cpbXe7rD+78ALWuseZbznA+D9kuuFEMIJgVrrFIDdu3ffAuzu2bNnYTe38CwhISG0bNmSoUOH8vbbbzN48OBSvRp2k56ezqFDh1iyZMmMQ4cOpWL8rR+9YsWKUt1RZvZY/AuYhzFF+t3AQxh3hCQBYRh3hXyvtT5l4jGrqmT1pMpYV2Ac4Hg1TSMg7tSpUzRu3BjGjoUJxvnOzNdeo+7HH5serCdJSUmhQ4cOFObvw1JSUnw+R7BHnu7MMTsVluVfx924GwzeVTyODh06uCUOAW+99RZRUVHlvj506NAq3Yr8+9//nvHjx9O0aVO01tx7770uPZ6vMbOwiNZav13wRCnVBXgAuDf/8X/A24A7f8rOA7lAyZFKrgLOlvUGrXUWkFXwXCkFQOPGjY1fVD17Fm679eRJHvbxX9AFCvP3YZMnT7bFqJR2yNOdOWakQ0G/Q+vrwcd/TDzaf//7X1P207BhQz766COAUqdJXHE8X2NmYTFDKTUX2IPRM3EMOAbMAFBKXQs0N/F4ldJaX1FK7caYAO17h5cGAv+r0U7zCw2AhwcPdiY84WF8/Y9tATvk6c4cHe8EcZw3RAi7MnNI723AH4GfgY5lvB6Vv427fQr8SSn1klKqp1JqIkZ802u0N4fC4oc1a0wJUHgGOwx1DfbI0505Os4P4niHiBB2ZWaPBdq4EvQXM/fpLK31YqVUc+DfQBvgAPCw1vpEjXbocF/ygLvvNiNE4SFKXlXtq+yQpztzzJYeCyGKqVaPhVLqSaXUCqXUMKVUXVcFZTat9Rda605a6wCt9a1ODSvu0GOxe9euCjYU3mbRokVWh+AWdsjTnTnmOvRY1PbhHouqTvdd0VTfINOmh4aGsnjxYmbPns3TTz/Nnj17qrTPd999ly35wx2Eh4czatQo5s6dy8svv1yl0TjdqVo9Flrr75RSp4HfY4ymuQVYCPyotc6r+N0+wqGw6NK5s4WBCLNVdRx+b2eHPN2Zo2OPRS0f7bGoznTf5U31Ddh+2nSAJ554gk8//bRw1Munn366cLbT8mzZsoU5c+YwePBgsrKyeOqpp9i5cyetWrWie/fuvPjii4SGhrooq+qr9qkQrfXPwM9KqVoYt5T+EZimlFoJLNRah5sboodxOBVy8eJF2lWwqfAusbGxtphHww55ujNHx4s3fbXHomC67+HDh9O1a9di030//fTTxbZdtmwZzz77LL169QKKpvqGollnK5p/wwz79u0rnItj9OjRNGnSxGOOFxoaSmeHf0rTKhnBOSUlhb1799Iz/47EsLAwGjduTKtWrQC47bbb2LFjB2fPni1cZ7UaX2ORPxfIamC1UqoBMBT4SCnVEWOysa+11tHmhOlBHHosalkYhjBfrVr2aFE75OnOHItdvOmjPRbVme67plN9g+9Pmw7GZ1lg5cqVxXp3yjJjxgzeeOMNvvvuO8Aomps1a1b4eq1atWjUqBEHDx4sLCx8Ytp0rfVlYD4wXyl1FfAMsCB/DIiFwDda63NmHMtyDoVF40aNLAxEmK1NmzZWh+AWdsjTnTkWu93URT0WfWZBgsnTn7RuALuqOLN8dab7rulU3+D706YX+OWXX1i1ahV9+/Zl2LBh5W63atUqHnrooWK9PufPn6du3eKXONatW5ekpKTC5740bToAWutzWuvJWuvbgT8AzYDNSqm1Sqnn8ns3vJfDqZBTbrz4SLheeLhvn8UrYIc83ZmjO3osEi7D6VRzHzUtVCqa7tuZqb7BPtOm33bbbXz44Yd06dKF/v37l3k6JD4+nosXL3LDDTcUWx8YGEjJqTjS0tJo0aJF4XOrp003vbBwpLWO1lp/oLXuiTH/Rl/ggFJqkVJqSP51Gt7FocfixuuvtzAQYbahQ4daHYJb2CFPd+bojh6L1g2gXSNzH61rUAQ5TvedlZVFbGxssdcdp/quW7cuH3zwAa+//nqVC73AwMAKZ+UEY7rvJ554gkuXLpW5j4JpzENCQkhNTWXEiBEsWbKEvLyy7y+obNr07Ozswgm/nD3ejh07aNWqVWGhde+997Jr164yC5J169Zx+vRpgoKCCAoK4siRI3z99ddcffXVnDtXdAIgKyuL1NRUrr766sJ1ZnyOznBpYeFIa71Ta/0XoCvGnCLPAEeVUlOVUlWbB9YTOBQWO3fssDAQYbaQkBCrQ3ALO+Tpzhzd0WOxazjE/cXcR1VPgxSoyrTpzk71Db49bbq/vz/dunUrvJMmJiaG2rVrF17o6vhZvvjii4wePZr33nuP9957jzp16vDss88yaNAgzp07R1xcHACbN2+mb9++xQqLkp9byefeNG16leRf9PkD8INSqj7wOPASsNPdsdSIw6mQB2w+252vscNQ12CPPN2ZY2Zi0XKdpm47rFtVddr0iqb6Bpk2vU+fPvz1r39l8uTJ1KpVi61bt7Jq1arCi2Adp00vEBcXx+TJk0lISCA4OJj09HTmzp3L2LFj6devH5s3b2bhwoWlYvCJadN9jVLqNeA1jF6dHsnJycYkXP/7Hzz2GACbfvMb7t+wwcIoXS8lJYXAwEAK8/dhY8aMscUfXTvk6c4c1/aDCzsBBc9kQq06Ra8V/Pwg06Z7FZk2vTSrpk33KVrrqcBUpVRjILnwBYdTIXfLkN4+5a9//avVIbiFHfJ0Z47pRo80da8qXlQI95Np0z2DSwqL/JlMj+dPQe5bHAqLX3bsQEoL3zFt2jSX3HrlaeyQp7tyzMuBzPy7E+u3d/nhRCVk2nTPYHphoZT6C3AKSMyfRr0zcAXYBEzTWpfqNvEqDtdY9OjRw8JAhNlcca7RE9khT3flmHkWdK6xXF+G4RUCcM1dIZ201t8DfweCtda3AfcA24EvlVLe/a+SQ4/F2fh4CwMRZqvKld++wA55uivHyw5D2dSTwkIIwDWFRcFZRr+CeUO01rla67Va698CqUqpcS44rns4FBb1qzHSmvB8zZs3tzoEt7BDnu7KMdVh7qhGXdxySCE8nisKi45KqdbADqXUUwUrlVJ+AFrrGcAppdQD5e3AozmcCqldzVuQhGerzpC83swOeborx1SH2ZAalZ42QwhbckVh8Q2wFGOCsmyl1PtKqf8H/MmhuPgCGOiCY7ueQ4/FhfPnLQxEmO3IkSNWh+AWdsjTXTmmOhymUXe3HNIyoaGhLF68mNmzZ/P000+zZ8+eSt/z7rvvsmXLlsLn4eHhjBo1irlz5/Lyyy9XeahvZyUkJPD++++zfPlyjzpeyc+npPI+L6s+x6oy/V9urfXXSqnfAVuAR7TWy8vZ1PxxRN3BobC4plMn6+IQpis5rK+vskOe7sqxoMdC+UHDzhVv6+2eeOIJPv30U1566SUuXbrE008/zdGjR8vdfsuWLcyZM4fBgwcDxtDTTz31FDt37qRVq1Z0796dF198kdDQUJfFHBMTQ0hICAEBAYwcOZLWrVu77FjVPV7Jz6ek8j6vdevWuf1zrC5XDen9NJCCMS/I/1NKlVXAqDLWeT6HUyH7bXARnJ3MnTvX6hDcwg55uiNHrSElv7Bo0Mn3x7AIDQ3lySefLHxe1sRZBVJSUti7dy89e/YsXBcWFkbjxo0Lp/a+7bbb2LFjB2fPnjU91n379jFq1CiWLFnC6NGj+fDDD11aVFT3eGV9PiWV93ktX77cbZ9jTbnkIgGtdYZS6j7gbeAD4D2l1EJgK3AWuAPIdMWxXc5xgCyHaYSF9/P10SgL2CFPd+SYcRpy8ke4dvVpkB/6QEbVZ/OuknqtYfCuqm9/4403Fi6vXLmS8ePHl7vtjBkzeOONN/juu+8K18XGxtKsWbPC57Vq1aJRo0YcPHiw8I9kUlISs2bNIiwsjNGjRxMREUFaWhpxcXE888wzHD58mMOHD9O8efMyxynZsWMH8+fPp2fPnowbN67Sa20OHTrE+vXrWbBgAZ07d6ZFixaEhoZy8ODBKn0m1T1egbI+n5LK+7ySkpJc/jk6y2WTkGmt87TW44HWwF/zj/Us8CJwSGs9yVXHdimHwmLb1q0WBiLMNmbMGKtDcAs75OmOHC9GFC037VXuZqbISDAKGVMfNShUfvnlF/7973/Tt29fhg0bVuY2q1at4qGHHiIgIKDY+vPnz1O3bt1i6+rWrUtSUlLh86VLl/Laa69x+PBhjhw5wiuvvMLIkSOZNm0aWmteeOEF/vCHPzBnzpwyj71//34yMzPp3bt3lf7IHzt2jDfffJO4uDj+/Oc/M2nSpCpPfV6T40H5n09J5X1e7vgcneXy2U211hla64Va61Fa6ye11n/SWq929XFdxqGwuKNfPwsDEWYbPXq01SG4hR3ydEeOSQ5nQl1dWNRrbYyTYeqjBmcGbrvtNj788EO6dOlC//79S50OiY+P5+LFi9xwww2l3hsYGEjJuanS0tJo0aJF4fMnn3ySpKQkUlJSeP755wFjTJI+ffoUTqC1a9currvuujLjGzFiBNOmTSMqKooRI0ZUWiQMGTKEqKgomjRpwv3330/t2rXp0KED6enp/Otf/2Ljxo18+OGH5b6/user6PMpqbzPKzc31+Wfo7NMKyyUUjcppT7z2ttIq8rhGoudO71jQlZRNRMmTLA6BLewQ57uyPFSRNGyqwuLwbtgaJy5j+qcBtmxYwetWrUqvPvg3nvvZdeuXaX+kK5bt47Tp08TFBREUFAQR44c4euvv+aHH37g2muv5dy5c4XbZmVlkZqaWmy678DAwAqn+wb4+uuveeKJJ7h0qezr/+vUqcPw4cMJCQkhNTWVESNGsGTJEvLy8srcvuT+AebNm0fPnj154IEHyM7OLpyR1dnjVfT5lFTR5+WOz9EpWmtTHsAyIAs4b9Y+rXxgzGwaCUQBOjk5WWuttQ4L09q4bksnvfyy9nXJycm6WP4+LDY21uoQ3MIOebojx/9103oBWi+qq3VudtnbFPz8AI11/u+WXbt23bJr1y59+fJll8dolvDwcH3XXXfprKwsrbXWq1ev1rVr19ZHjhzRGzZs0BEREWW+7+qrr9Y//fST1lrr7Oxs3bZtW33q1Cmttdbr1q3T/fr1K/WeF154QX/11VeFzwcMGKBDQ0O11lpfvHhRN27cWGdkZOhPPvmkyvGvX79e//nPf9Y//PBDqdcee+wxvXTp0mLr3njjDb1lyxattdYzZszQkydPrvKxKjueI8fPR2td7LMs7/Oy6nO8fPmy3rVrl37nnXdCHnnkkf8+8sgjcx555JE2uoy/n2ZevJkADAJ8Ylg/XYXZTeNOnSLQ/aEJFwkLC+O5556zOgyXs0Oers4xO61o1M3AG8DPx8fK69OnD3/961+ZPHkytWrVYuvWraxatYpu3brxzjvv0LdvX3r1Kuq2iYuLY/LkySQkJBAcHEx6ejoPP/wwc+fOZezYsfTr14/NmzezcOHCUsc6evQo48YZgzNrrUlMTCzsvq9bty633347CxYsqNZ8MAMHDmTgwIFkZGSUeu3EiROlJhrLy8vDP38AxNzc3MJlM44H5X8+U6dOLfws/f39y/y8yltfkis+x6pSusS5mhrvSKmJwATt7ZOMlVBQWCQnJ9O4cWPYvh3uuguA08OG0e6bb6wN0MVSUlIIDAykMH8ftnXrVu6+2/fnq7VDnq7O8dwW2DDAWO7yJ+g3s+ztCn5+gECtdQrA7t27bwF29+zZk/r167ssRlFzISEhtGzZkqFDh/L2228zePBg7r//fqvDslR6ejqHDh1iyZIlMw4dOpQKtABGr1ixotTffDPr7P8AM5RSY7XWvjvAg0OPRV5uroWBCLPl5ORYHYJb2CFPV+eYuK1ouYVcw+0x3nrrLaKiosp9fejQobz00kuV7uf3v/8948ePp2nTpmituffee116PF9jZmFxF8Yspo8ppbYCofmPHVrrKyYex1oOXWIZKSkWBiLMlpBg8kABHsoOebo6x8TtRcst73LpoUQ1/Pe//zVlPw0bNuSjjz4CKHWaxBXH8zVm3m76HjAZ+BLjOov3gZ+AJKXUJqXUv5RS15p4PGvUrl242MphkBLh/W699VarQ3ALO+Tpyhy1hvP5hUWdZtDYx+cIEaK6zCwsjgPjtNYjtda9gKuAZ4A5GINk/QfYZOLxrOFQWJw4dszCQITZ3DVBkdXskKcrc0w9AlkXjOWWdxrzhAghiph5KuS/wEyl1Glgaf51Ft/mP1BKtQJamXg8azicCrm+u/yr4kveeOMNq0NwCzvk6coci11fIaP6C1GKabW21nqf1no4Rg9FqUudtdZntdb7zDqeZRx6LA7t8/50RBG7nC+1Q56uzPGcw0j+cn2FEKVVq7BQSrVSSjWoaButdYzW+udq7rdHdba3lENhccO13n/JiChih8m5wB55uipHrSHhR2PZLwCa93XJYYTwatXtscgDZiul2pgVgFLqOeAvZu3P5RxOhUQdOGBhIMJsdpicC+yRp6tyTI2G9FPG8lX9wb9q804JYSvVKiy01onAu8ASpdRLStX8siWl1NVKqVnA/XhTYeHQY9GpXTsLAxFm+9Of/mR1CG5hhzxdleOZDUXLrX/jkkMI4fWqXRhorWOBwUA/IEopNVop1Usph5GjyqGUaqyUelgpNR8IB3ZqrV/UWnvPSFMOhUXiGZ8aZNT2Vq5caXUIbmGHPF2VY8FpEIA2A11yCCG8Xo3uCtFapwEvK6V6A28D/wJylFLhwGkgCWN+jTpAs/zHNcCNQCIwC7hOa33e2QTczqGwCKwn/aC+5Oabb7Y6BLewQ56uyDH3CiRsNJYDmkNT8w8hhE9w6nZTrfWvwLNKqUbAQOAOoCdGAdEQyMUoMmKB7zBOeWzTZk1QYgWHayxyMjMtDESY7cKFC1aH4BZ2yNMVOSZugZxUY7nNQ86PX1HeBFVCeKLqfL+aMo6F1joVY9r0ZWbszxMopV7DmDq9+K8Phx4LnZ3t3qCES9nlF70d8nRFjqdXFy23c25CyPNAZmxsbF3nIhLCvfLy8nKSk5PTK9vOxyf7rbkKp02vVQtyc6lXzal0hWfr1q2b1SG4hR3yNDtHrSFuubGsakGbQTXf16233npy9+7dPYAW0dHRLXbu3Pm6v79/kp+fn+9XfMKrJScnp8fHxydjnJEol/xlrAl/f8jN5XJSUumRwITX+umnn7jhhhusDsPl7JCn2Tle3ANpx43lVvdBQFPn9nfrrbeeBE7+5z//aQNcBDKAy87tVQi3aAhUOJ6VFBY1Ubs2ZGXRrHFjqyMRJnr++eetDsEt7JCn2Tme/LZoueNTpu46HeOC9paAXA0uvEkixvdvKVJY1ETdupCWRkpCAk7+4yI8yJQpU2wxKqUd8jQzR63h5HfGsvKDDo+ZslsAVqxYkfzoo4+OoYxpEITwcOkrVqxILusF5c03aLhDwTUWycnJNC7oobjmGoiNhVatICHByvBcLiUlhcDAQIrlL4SNXPwVfrjFWG51P/xmY9XfW/DzAwRqrVNcEZ8QnkYm/K2JhsZ1K1cuXbI4EGEmOwx1DfbI08wcC3orwPTTIEL4JOmxqESZPRZ33AE7dhjLubng57v1mZ16LJKSkmjSpInVYbicHfI0K0etYUVXSIsxToM8Hg/1WlX9/dJjIezId/8iulJDhztt0iu9pVd4iQULFlgdglvYIU+zckzcahQVYNwNUp2iQgi7ksKiJhwLi7Q06+IQprrnnnusDsEt7JCnWTnGzCla7vyiKbsUwuf5bGGhlOqklJqllDqulMpQSh1TSv1HKVXH6Z07FhapqU7vTniGY8eOWR2CW9ghTzNyzLkMJ/JvM/VvBB0ed3qXQtiCzxYWwLUY+f0ZuB74f8ArwMdO77mpw02mNph3wS7q1HG+5vQGdsjTjBxPfV80N8jVw8BfbggVokp8dhwLrfVaYK3DqhilVA/gVeAtp3beunXRso/fbmonrVrZ4wS6HfI0I8djs4qWO//R6d0JYRu+3GNRlkCM4XPLpZQKUEo1LngAjUptJIWFT9q9e7fVIbiFHfJ0Nsekg3A21Fhu1B1a3ul8TELYhW0KC6VUF+ANYHolm47GmHSs4BEHEBMTw4QJE8jKymJRaGjhxqnR0cyaNYvw8HDWrVvHsmXLiIyMZPLkyaSkpBTeTz9mzBguXrzI1KlT2bdvHytWrGD16tXs2bOHkJAQEhMTi22bnp5OcHAwhw8fZsmSJWzcuJHt27czZ84cTp06VWzb3Nxcxo0bx4kTJ5g/fz5bt24lNDSUb775hujoaD755BMyMzOLvSchIYGZM2cSHh7O2rVr+f777zlw4ABTpkwhOTm5cNsJEyYAEBISwv79+1m+fDlr1qxh9+7dzJgxg7Nnzxbbb0ZGBsHBwURHR7N48WI2bdrEtm3bmDdvHidPnmTs2LHk5eUxZswY8vLyGDt2LCdPnmTevHls27aNTZs2sXjxYqKjowkODiYjI6PY/s+ePcuMGTPYvXs3a9asYfny5ezfv5/PP/+cpKSkYtsmJyczZcoUDhw4wPfff8/atWsJDw9n5syZJCQkFNs2MzOTuLg4oqOj+eabbwgNDWXr1q3Mnz+fEydOMG7cOHJzc4u959SpU8yZM4ft27ezceNGlixZwuHDhwkODiY9Pb3YtomJiYSEhLBnzx5Wr17NihUr2LdvH1OnTuXixYvFtk1JSWHy5MlERkaybNky1q1bR3h4OLNmzSI+Pr7YtllZWUyYMIFjx46xaNEiQkND2bJlCwsWLCA2NpagoCBycnKKvadv37589dVX7Nixgw0bNvDtt98SFRXFxIkTSUtLK7bt+fPnmT59OhEREaxatYqVK1cSERHBtGnTuHDhQrFtU1NTmTRpEpGRkSxdupT169ezc+dOZs+eXSru7Oxsxo8fT0xMDAsXLiQsLIywsDAWLlxITEwM48ePJzs7u9h74uPjmT17Njt37mT9+vUsXbqUyMhIJk2aRGpqarFt+/fvz7Rp04iIiGDlypWsWrWKiIgIpk+fzvnz54ttm5aWxsSJE4mKiuLbb79lw4YNbPl30T8MsV3XoZSxbU5ODkFBQcTGxrJgwQK2bNlCaGgoixYt4tixY4W/I0r+/AhhK1prr3oAHwC6kkefEu9pC0QDX1Zh/wFAY4dHO0AnJyfrQnv2aG3c4q718OHalyUnJ+tS+fuojz76yOoQ3MIOeTqT45Vkrb9pqPUCtF5UX+usSzWPo+DnB2isPeD3pzzk4Y6H1w2QpZRqAbSoZLNYrXVm/vZtgZ+AncAftdZ51Txe6QGykpOhYPCde+4Bhx4MX2OnAbKEADj8Oex6w1ju+jLcHlLzfckAWcKOvO5UiNb6vNY6qpJHQVHRDggF9gAvVreoKFdgILRsaSxHR5uyS2E9Owx1DfbIs6Y5ag1Hvih63v01kwISwka8rseiqvJ7KjYDJ4HngdyC17TWVb7issweC4C774Zt24zl1NTiY1v4EDv1WGRkZFCvnu/PXG2HPGuaY/xa+GmwsdyyPzwY5lwc0mMh7Mjreiyq4UGgK3A/xgWYZxwezuvWrWhZei18whdffFH5Rj7ADnnWNMfI8UXL175pUjBC2IzPFhZa6zlaa1XWw5QDXH990fLevabsUljr0UcftToEt7BDnjXJ8fwvDreYdoP2j5kakhC24bOFhcvdckvRsg3GBbCDPXv2WB2CW9ghz5rk6Nhbcd3b4FfLxICEsBEpLGqqd++iZRv8oraDlgUX5Po4O+RZ3RxTjhhDeAPUbQ3XPOeCoISwCSksaqppUzLbtDGWIyIgJ8fScITzAgICrA7BLeyQZ3VzPDAWY7QJ4NpRUKuu6SEJYRtSWDghoUMHYyE93SguhFezw6yfYI88q5NjchTELjCW6zSFbq+4KCghbEIKCyc0fuSRoic+PEiWXdx7771Wh+AWdsizOjnu/wAKRrjp+TbUCXRJSELYhhQWTvg2MbHoyebN1gUiTDF//nyrQ3ALO+RZ1Rwv7YMTi43lgJbQ4w0XBiWETfjsAFlmKXeALCAvNxe/Nm0gMREaN4aLF6GWb11KbqcBsvLy8vDz8/1a2w55VjXHzY9D3HJj+ZZg6PlXc+OQAbKEHfn2bxcX+3jcOCjock1JgV9+sTQe4ZyPP/7Y6hDcwg55ViXHC7uKiop6baDbq66NSQi7kB6LciilXgNewyi+epTZY5GXh9+cOTB8uLFi9GjwsV/a0mPhe+yQZ2U5ag0b7oHELcbzPlOgx+vmxyE9FsKOfPu3ixO01lO11tcBt5W3zbhx4+C3vwWVP5jnihVuik64wrhx46wOwS3skGdlOZ5aVlRUNOpmzGIqhDCHFBZOeO6556BVK+jXz1hx8CAcP25tUKLGnnvOHqMi2SHPinLMzYJf3yl63vsTqFXHDUEJYRNSWDghtOAWU8fbTpctsyQW4bxQm9wybIc8K8rx8BRIizGWW90H7X1/6hQh3EoKCyd06dLFWHjyyaKVCxdaE4xwWmF7+jg75FlejpmJcOCj/CcKbvm06EymEMIcUlg4ISsry1jo1g1uy78U49dfjVMiwusUtqePs0Oe5eX46zuQnX8JZZeXoNnN7otJCLuQwsIJiY4DZP3+90XL0mvhlYq1pw+zQ55l5Xh2M8TMMZZrB0Kvse6NSQi7kMLCCbc4Tp0+bFjR4FgLF0JurjVBiRor1p4+zA55lswx9wr84jAHyM1BUK+Vm4MSwiaksHDCCsfbS1u1gkGDjOWTJ2HtWmuCEjW2wia3C9shz5I5HvovpEQZy81vh25ye6kQLiMDZFWioiG9MzIyqFevXtGKlSvh0fxLzB9+GFavdl+gLmKnAbJKtaePskOejjmmHoPVN0BuJig/eGi3+66tkAGyhB1Jj4UTgoODi694+GHo2NFY/uEHiIlxf1Cixkq1p4+yQ54FOeo82DHcKCoAerwpF2wK4WrSY1GJinosyjRuHPz978byW2/BJ5+4ND5Xs1OPhfA9UZ/B7lHGcoOr4bf7oXYj9x1feiyEHUmPhRPGjBlTeuXw4VAnfxi/GTMgOdm9QYkaK7M9fZAd8hwzZgwpRyBidNG6fl+5t6gQwq6ksHDCiBEjSq+86ip44QVjOSUFvvjCvUGJGiuzPX2QHfL800sj+PmPkJthPO/+OrS+z9KQhLANKSzKoZR6TSkVCZQ7F/r//ve/sl945x0omFlx4kRIT3dBhMJs5banj7FDnj+8cZzzPxvLjbpC7yBr4xHCTqSwKEdVZje99dZby36ha9eiYb4TE2H2bBdEKMxWbnv6GF/P8+IeCFiZ/2OroN8c8G9gaUhC2IoUFk44e/Zs+S++917RclAQOjPD9QEJp1TYnj7El/PMToWtz4DONn619XwLrrrL4qCEsBkpLJxw5cqV8l/s3RseeYSsnnBy5mmStj3vvsBEjVTYnj7El/MMfw1So43l5n2hl+9fpyqEx5HCwgmVzRKZHfQqMXvh8mBI7LWU3NQ4N0UmasIOs36C7+YZMw+OzzeW/RrkctciqFXH2piEsCMpLJywefPmCl+vfd1gGocbA2blttCcv/x3d4Qlaqiy9vQVvphn0kEIH1n0POXJH2nkm/WTEB5PBsiqREUDZCUlJdGkSZMK358d8xPHOj6I9s8BatOFSOrQ1WXxms1OA2RVpT19ga/leSUJ1t5WdAqk84vQ81PPyFEGyBJ2JD0WTvj8888r3aZ25/to5v9u/rNszvGOa4MSNVaV9vQFvpSnzoPtzxUVFU1vhr6f+1aOQngb6bGoRLWH9C5DHmkcpRu5JADQgfU0ZKCJUbqOnXoshPfZ9x/Y/4GxXKcZDN4FDa+xNKRipMdC2JH0WDihqkMj+9GQqxhX+DyBV8hDBs3yNHYY6hp8J8+4VUVFhfKDuxcVFRW+kqMQ3kh6LCpRUY9FcnJywX8jldLkcZL7SCcMgOa8w1WMNztc09mpx6I67enNfCHPS/tg/V2Qk2Y8v3kcXO8wdIyn5Cg9FsKOpMfCCfPmzavytgo/WjMDhXH/2wWCyeRXV4UmaqA67enNvD3PjDMQOqSoqOj4JFz3bvFtvD1HIbyZFBZOuO++6s1qFEAPmvPP/Ge5xDMcje8OVuRtqtue3sqb88y5DKGPQPop43nzvnDHXFCq+HbenKMQ3k4KCydER0dX+z0teJcArgcgi19J5D9mhyVqqCbt6Y28Nc+8XNj2B7i423hevyPcswL865fe1ltzFMIXSGHhhHr16lX7PYo6tGEe4A/ABYJIZ6vJkYmaqEl7eiNvzFNr2PU6xC03ntduDPethnqty97eG3MUwldIYVGOqkyb3rx58xrtux630JIP85/lEc9z5CLXdVmtpu3pbbwxz33/hujpxrLyh/7fQpMbyt/eG3MUwldIYVGOqkybHhERUeP9N+cd6nE3ANnEksDLaOQOHSs5057exNvyjJoEBxzuHr1jDrR5sOL3eFuOQvgSKSyc8Mgjj9T4vYpatGUefhi3cKawmEtMMSs0UQPOtKc38aY8Y+bB7v9X9PzWz+Ca31f+Pm/KUQhfI4WFE7788kun3l+Ha2jDnMLnZ/kb6fzsZFSippxtT2/hLXmeXAo7Xip6fuO/4dq/VO293pKjEL5IBsiqhBlDelfmLG9zkf8C4E87rmE3/rRyybGqy04DZAnPcXIpbH0GdI7xvPtr0GdK6dtKPZ0MkCXsSHosnGDWsMFXMY569Acgh9PE8Th5ZJqyb1F1dhkG2tPzLFlUdP4j9JlcvaLC03MUwpdJj0UlKuqxyMzMpG7duqYcJ5szxNKXHE4D0Jjf0ZaFKKz9F81OPRZmtqcn8+Q8yyoqbv8S/GpVbz+ekqP0WAg7kh4LJ0yZYt7FlrVpQ3tWoDBG+0lhEef5yLT9i8qZ2Z6ezFPzjF1sTlEBnpujEHYghYUTHnvsMVP3V49baMdCyO+lOM/7JLPA1GOI8pndnp7KE/M8Mg22/c6cogI8M0ch7EIKCyfs3r3b9H024rFis57G80dSWWX6cURprmhPT+RJeWoNB8ZC+EgoGMaly5+cKyrAs3IUwm5sUVgopQKUUhFKKa2Uutms/bZuXc54wk5qxls04dX8Z7mc5qnC6daF67iqPT2Np+Sp82DP32DvP4vWXfcu3D7DuaICPCdHIezIFoUFMAGIN3un/v7+Zu8SAIWiNVNozDMAaDI5xSMyzbqLuao9PY0n5JmbBdufh6iJRet6T4DeQebcUuoJOQphVz5fWCilBgMPAm+Zve/jx4+bvctCxsicc2nAYADySOEkA8kkwmXHtDtXtqcnsTrPzPOw8TcQu9B4rvyg3yy47m3zjmF1jkLYmU8XFkqpVsBM4DkgvYrvCVBKNS54AI3K23bAgAHmBFpeLNShPd9Rj7sAyOUCJ7ifDPa49Lh25er29BRW5plyBNb1g8T8CX1r1YP+S6HLSxW/r7rs0pZCeCKfLSyUUgqYA0zXWu+qxltHA8kOjziAmJgYJkyYQFZWVuHgO3/605+Ij49n1qxZhIeHs27dOpYtW0ZkZCSTJ08mJSWlcNsxY8Zw8eJFpk6dyr59+1ixYgWrV69mz549hISEkJiYWGzb9PR0goODiT58il3L/sSVpOsByOMSsXn3MXXWK4Xb5ubmMm7cOE6cOMH8+fPZunUroaGhfPPNN0RHR/PJJ5+QmZlZbP8JCQnMnDmT8PBw1q5dy/fff8+BAweYMmUKycnJhdtOmDABgJCQEPbv38/y5ctZs2YNu3fvZsaMGZw9e7bYfjMyMoy4o6NZvHgxmzZtYtu2bcybN4+TJ08yduxY8vLyGDNmDHl5eYwdO5aTJ08yb948tm3bxqZNm1i8eDHR0dEEBweTkZFRbP9nz55lxowZ7N69mzVr1rB8+XL279/P559/TlJSUrFtk5OTmTJlCgcOHOD7779n7dq1hIeHM3PmTBISEoptm5mZySuvvEJ0dDTffPMNoaGhbN26lfnz53PixAnGjRtHbm5usfecOnWKOXPmsH37djZu3MiSJUs4fPgwwcHBpKenF9s2MTGRkJAQ9uzZw+rVq1mxYgX79u1j6tSpXLx4sdi2KSkpTJ48mcjISJYtW8a6desIDw9n1qxZxMfHF9s2KyuLCRMmcOzYMRYtWkRoaChbtmxhwYIFxMbGEhQURE5OTrH3TJs2ja+++oodO3awYcMGvv32W6Kiopg4cSJpaWnFtj1//jzTp08nIiKCVatWsXLlSiIiIpg2bRoXLlwotm1qaiqTJk0iMjKSpUuXsn79enbu3Mns2bOJj4/nv8Pnsa4fpB0zftByG6Vx3ddxhF1eSFhYGGFhYSxcuJCYmBjGjx9PdnZ2sf3Hx8cze/Zsdu7cyfr161m6dCmRkZFMmjSJ1NTUYtt++eWXTJs2jYiICFauXMmqVauIiIhg+vTpnD9/vti2aWlpTJw4kaioKL799ls2bNjAjh07+Oqrr4iLiyu2bU5ODkFBQcTGxrJgwQK2bNlCaGgoixYt4tixY6V+RxT8/AhhJ143QJZS6gPg/Uo26wvcCQwDBmitc5VSnYDjQG+tdUQF+w8AAhxWNQLiyhogKjc3l1q1nLzKrIpySeUUvyWDLQD40ZgOrKJ+/oidrmKnAbLc2Z5WcneeWsORL2D3qKLbSZvcCPeuggYdXXNMT2lLGSBL2JE39lh8DvSs5HEAuB/oB2QppXKAo/nv36WUmlvezrXWWVrrlIIHkFretuPGjTMhnaqpRSM68gP1uRcouuYihe/dFoOvc2d7WsmdeeZkwM9/hF2vFxUVbR6CB7e6rqgA+7SlEJ7I63osqkop1RFw/Be7LbAOeBLYqbWOq+J+XD4JWXXkkU4cQ7nMuvw1frRmKk15xSXHs1OPhTBXWiyEDYVLDjcz9XwLbh4Hfja5aUN6LIQdeWOPRZVorU9qrQ8UPIAj+S8dq2pRURkrJjryoz4dWEFj/pC/Jo8EXuUc/0KT5/Z4fIldJq5yR56nf4C1fYqKCv8GcPdiuOUT9xQVdmlLITyRzxYW7vDCCy9YclxFHdoyl2YU3Z93gTGcZhh5XLYkJl9gVXu6myvzzM2C3X+F0Ich64KxrlFXGLQDrn7aZYctxS5tKYQnsk1hobWO1Vqrii7crK6NGzeatatqU/jRigm0YiIFc4uk8h2x3E02Jy2Ly5tZ2Z7u5Ko8U6Jh/Z3FB71q/yg8FA5NbnDJIctll7YUwhPZprBwhe7du1sdAs0YRXtW4Jc/3EYWERynL+lstTgy7+MJ7ekOZuepNcTMhR9ugYv5Q6z41YFbP4MBy6FOE1MPVyV2aUshPJEUFk7IyMiwOgQAGjGETuygNl0AyOUcJ7iPCwSj8c2Lc13BU9rT1czMMyMBwh437vzISTPWNepunPq49i/mDM9do7hs0pZCeCIpLJxw4cIFq0MoFMB1dGIn9bk/f00O53iLn3iMJM5YGpu38KT2dCWz8oxdDKuuh7j/Fa3r/EcYvBua9TblEDVml7YUwhNJYeGEXr16WR1CMf40pyPraM57AFzGnz+SyY2MYCPLLI7O83lae7qKs3lmJsKWp2HbM3DlorEuoCUMWAZ3fAW1G5oQpJPs0pZCeCIpLJywatUqq0MoReHPVYyjA6uZxK2coiFxBDCQBbzLfLLItjpEj+WJ7ekKNc1T58HRL2FlDzj5bdH6jk/DkIPQ4XGTAjSBXdpSCE/kswNkmaWiAbLS09OpX7++NYFVQRS/8hz/Zhd1CtfdxNUs4E1u5Ooq7cNOA2R5enuapSZ5XtoPv7wC57cXrQtoDn2/cO9tpFXlKW0pA2QJO5IeCyd8+umnVodQoWvpzc98x4fcT22MUYn2cYI+vMPHLOWK9F4U4+ntaZbq5JmdBnvegR96Fy8qrnkOhkR6ZlEB9mlLITyR9FhUwtOG9K6pCI7zHJM54DDGxfV0YAavcCfXlvs+O/VYiCJ5uXB8LkT8AzITitY36g63TYPW95f/XlFEeiyEHUmPRTmUUq8ppSKBX8rbxpuGDb6Za9jFBN7hMfzym/0gp7iLf/AqISTJiJ1e1Z7OqCzPs6HGcNw7hhcVFX4BcNOH8Nt93lFU2KUthfBE0mNRiYp6LBITE2nZsqU1gTlhDzG8zHR2c6xwXUsaM4bfMZwHqEXRdNN26rHw1vasrvLyTDoIe/8JccuLr+8wFHpPgEZd3BOfGTylLaXHQtiR9Fg4Ydky77yF8xY6s4NxTORFGlAXgERS+DMh3MLbbGK/xRFaw1vbs7pK5pkSDdv+AKtvLF5UNO0NvwmFAUu9q6gA+7SlEJ5ICgsn9O3b1+oQasyfWoxiCJFM4mnuLFy/jxM8wAf8H0Hs54SFEbqfN7dndRTkmXYCdvwJVvWE2IVQMEhrvTbQ7ysYvAta3WNdnM6wS1sK4YncMIGx7zpzxvtHtOxISxbzN97gYUbxVeHpkRWEs5JdPMGtFkfoPr7QnlUR90sKWZ9D7ALIc7gxKKA5XPcedB8J/tbfqekUu7SlEJ5IeiyckJuba3UIprmbnvxCEHN4nbY0A0Cj+Y6fAXiVEGJIqGgXXs+X2rMs53+BsKGQOvIeYr4qKipqB8JNH8H/HYfr3vL+ogJ8vy2F8GRSWDihU6dOVodgKj/8eIH7OMrnBPMCLSi6WPNrttCNN3iGT9lDjIVRuo6vtSdAXg6cWg4/3gfrbodT3wPamBmsdiBc/w/4vxi48Z9Qu5GloZrKF9tSCG8hhYUTtmzZYnUILlGPAP7KoxznC/7FU4Xr88hjMdu4lbcZyH/YwF6fmj3Vl9oz9SwcDIL/dTFmHz0bWvRaXuPL9P4EHj8JN4+BgGaWhekyvtSWQngbud20EhXdbnrx4kWaNfPB38oOCm6X+2fyXEIa/0Qixe+Yu5Z2vMKDvMB9NKGBRVGaw9vbU2vY9APsCYaWYVA7p/jrjbrDde9A4MMXadnGe/OsCk9pS7ndVNiR9Fg44YsvvrA6BLd5m8c4wXSm8TJdaF24PorTjOIr2vInhjOVXRz12l4Mb23PE8kwbhtcFwLzP4S2mxyKCgVtfwv3rYVHDkHX4RAyyzvzrA5vbUshfIH0WFTCV4b0rqmyBsjKJZfv+YUprCGMyFLvuYGOPMc9PEt/2tPc3SHbQlImfHcIFhyAzUWjtNP2HEyYDOn1IO8xePYj7xuDwpdIj4WwI+mxcIJdhw2uRS2e5A428xEHmMjrDKYxRbcSHOAk7zKfjvyZB/iA2WzkPJ7/O9XT2/NsGsz8FQYvgqsmwog1xYsKgK59QH8Gz5yBP39ddlHh6XmawQ45CuGppMeiEhX1WKSkpPh8L0ZVh/ROI4NFbGUOP7Gdw6Ve98OP/vTkcW7jMW7jaq5yZdg14mntqTVEX4TVR2HZYdh2ijJPMvVoDs/dAM/eANc0qXy/npanK3hKjtJjIexIeiycMGfOHKtD8BgNqccIBrKNjznKVD5gWLFrMfLIYzMHGcVXdOJVbuEt3mM+G9lHJlcsjLyIJ7TnxQzjFMfLq+GaqdBjOvz1R9haoqho3wje7AvhL8KhP8M/7q5aUQGekaer2SFHITyV9FiUQyn1GvAaRvHVo6z/2CMjI7nuuuusCM9tnJmETKPZSTTL2MH37ORoOQNs1aMO/enJb7iJu+nJLXQmgNpmhF8tVrRnQhpsizN6I7aegt0JkFfOj+S1zWFoD3i8B9zaBpSq2THt8H3rKTlKj4WwIxnSuxxa66nA1IJTIWVtExUV5RG/vDyVQtGP7vSjO+N5jkhO8T2/sJxfis2smsEV1rOX9ewFoA7+3EoX7qQHd9Cd3lxDJ64qnO7dVVzdnkmZsPcs/HoWdp+B7XEQk1T+9gG1oH9HGHgNPNoNrm1hThx2+L61Q45CeCopLJzQoIF3j9vgTgrF9XTkejryT57kHMn8yD42sJcN7OU0Fwu3vUIOP3OYnx2u1WhEPW7UV5Px01Nc16Q2A5o1ZXCztrRrBH41/M+9JLPaMykTjlyAIxeNx4FEiDgLx5Mqf+8NLeHBzvDgNUZRUd8FHTd2+L61Q45CeCopLJzgCQPweKurCORZ+vMs/dFoojjNFiLZzmG2c5hoik8ilUoG21PPwc838yuwMH99PX/o0hS6NoWOgdCmIbRtmP+1EbSsD4EBEFCF7/TK2jM7Fy5lGo/EdDidajziUiAu/+vRS8ZrVRFQC/q2hbvaG48720NzN8zTYYfvWzvkKISnksLCCfv27ZPpmU2gUPSkPT1pz8s8CEAiyfzMEcI5yl5i2UssJy+VvpMkI8foETiQWPExAmpBYF2jyAgMMJ77+xU9avvByVOtaBUNV3IhK7foa3J+MXE5u+JjVKR+beh1FfRuDb1bwc2t4KZWUKdWzfdZU3b4vrVDjkJ4Krl4sxIV3W4aHx9P27ZtrQnMTZy5eNNssZmpLD1znh0X06h1sR3pl5oRfdG4TuGKh0xm2bYhdG8O3ZsVPXo0N3pVannIPVh2+L71lBzl4k1hR9Jj4YTZs2fzz3/+0+owbKNT3Ub87ZpGcE3x9bl5xqmI06lwJg3iC76mwYV0SM4q/kjJKv/OC0f+fkaPQuM60LQeNK1b9GheD9o1Mh7tGxu3f7ZtBHW94CfKDt+3dshRCE8lPRaVkCG9PafHwixaG4VFTh5k5xlfc/KM9QH+RjFRp5Z5F4UK+5IeC2FHHtI5651k2GDvpJRxWiLAHxrWgSZ1oUV9CJk4hsYBRq+DLxcVdvi+tUOOQngq6bGoREU9FllZWQQEBFgTmJv4Yo9FeezQnmCPPD0lR+mxEHYkPRZO+Oyzz6wOQZjILu1phzztkKMQnsoLLjXzDCkppf/ZePDBB8tc70sK8vP1PMEe7Qn2yNNTcvSEGIRwNzkVUgmlVDsgzuo4hBBerb3W+rTVQQjhDlJYVEIppYC2QGqJlxphFBzty3itMr8At9UwpJq+t6bvkzxdd0xn3utNebr783Emx5oes6L3NQLitfyyFTYhp0Iqkf/LoNR/GqpoasnU6l6UpZTKq+mFXDV9rxPvK1iUPE0+pjPv9aY83f35OJNjTY9ZyfvkfIiwFbl40xpTLXivM8esKcnTde/1pjyt+Hyc4U1tIoTHkVMhNeQwnbpP30YmefoWO+RphxyF8GTSY1FzWcB/8r/6MsnTt9ghTzvkKITHkh4LIYQQQphGeiyEEEIIYRopLIQQQghhGikshBBCCGEaKSyEEEIIYRopLJyklOqklJqllDqulMpQSh1TSv1HKVXH6ticpZQamZ9XplJqt1Kqv9UxmUkpNVopFa6USlVKnVNKLVdK9bA6LlfLz1srpSZZHYvZlFLtlFILlFIXlFLpSqkIpdStVsclhJ1IYeG8azE+xz8D1wP/D3gF+NjKoJyllBoGTALGAr2BLcAPSqmOVsZlsnswBjXqBwzEGIl2vVKqgaVRuZBSqi/wMrDP6ljMppRqCmwDsoHBwHXA34AkC8MSwnbkdlMXUEq9Dbyqte5sdSw1pZTaCezRWr/qsO4QsFxrPdq6yFxHKdUSOAfco7UOszoesymlGgJ7gJHAP4EIrfUoS4MykVIqCLhLa+1TPWtCeBvpsXCNQOCi1UHUVP5pnFuB9SVeWg/c6f6I3CYw/6vXtl0lpgKrtdY/Wh2IizwK7FJKfZt/autXpdQIq4MSwm6ksDCZUqoL8AYw3epYnNACqAWcLbH+LNDa/eG4Xv4stp8CW7XWB6yOx2xKqWeAWwCf7G3K1xl4FYgGBmH8DE5WSj1vaVRC2IwUFuVQSn2Qf4FbRY8+Jd7TFlgLfKu1/tKayE1V8jyZKmOdr/gcuAn4ndWBmE0p1QH4DPiD1jrT6nhcyA/j9N3ftda/aq1DgJkYxYYQwk1k2vTyfQ58U8k2sQUL+UXFT8DPGBfHebPzQC6leyeuonQvhtdTSk3B6EYfoLWOszoeF7gVo+12O0wpXgsYoJR6HQjQWudaFZyJzgCRJdYdAp6wIBYhbEsKi3Jorc9j/IGtlFKqHUZRsRt4UWud58rYXE1rfUUptRvjTonvHV4aCPzPmqjMl3/6YwrwOHCv1vq4xSG5ykbgxhLrvgKigPE+UlSAcUdIyduFuwMnLIhFCNuSwsJJ+T0VocBJ4C2gZcF/hVrrBOsic9qnwHyl1C6KemE64t3XjpQ0FXgW+D8gVSlV0EOTrLXOsC4sc2mtU4Fi140opS4DF3zsepKJwHal1N+BJcBtGN+33t6DKIRXkcLCeQ8CXfMfJbvRVenNvYPWerFSqjnwb6ANxh+mh7XWvvTfX8G599AS618E5rg1EuE0rXW4UupxYBzG9+1xYJTWeqG1kQlhLzKOhRBCCCFMI3eFCCGEEMI0UlgIIYQQwjRSWAghhBDCNFJYCCGEEMI0UlgIIYQQwjRSWAghhBDCNFJYCCGEEMI0UlgIIYQQwjRSWAghhBDCNFJYCK+glLpKKdXG4hiecuG+31ZKDXHV/oUQwl2ksBAeTynVCWPCsDQLY7gTeMGFh/gUeFUp9ZALjyGEEC4nk5AJj6aUagQsAJ7Jn6XTKr8HXDaZldY6Vyn1HLBFKfWr1vqsq44lhBCuJD0WwtN9CszVWpecOdZtlFL+wMPA/1x5HK31ReAb4BNXHkcIIVxJCgvhsZRSvYH7gK8sDuUhYKvWOt0Nx/oceEQp1dUNxxJCCNNJYSE82TvAV1rrHIvjcOlpEEda60vAJmC4O44nhBBmU1prq2MQohSlVGPgLHCn1vpXC+NoCOwHurmrwFFKvQm8qrW+tprv6wC8AtQBmgA/aq0Xmx+hEEKUTy7eFJ7qN0AusK/kC0qpXsBbwDVAELANeB8IAFoD/9FaR5gUx1BgZcmiQil1N/Ay0A0YA/wAvApcC9QGbgDe0lrvUEo9C/TPf+uNwL+11psqOGYYMEkp1aqqF3EqpV4FRgFPaq33K6XqARuVUjdprf+Rv00/IFtrvbsq+xRCiJqQUyHCU90JhGutc8t47U3gRWAtMBuYiXHB4xLgt5h7GqHUaRCllB9GUfECRlHzFfAZEKm1fkNr/QpwEPhaKfVvIFNr/arW+lWM0xzf5u+jPLH5X3tVJUCl1OvAZOBZrfV+AK11BjABeE8p1SN/0xeBU1XZpxBC1JQUFsJT9QROl1yplOoCxOf3ILQFmgEfa61PA80xxrpYWcb7lFLqWaXUSqXUF0qpSUqpURUFoJRqBVyttd5Z4qW+wK/aOI/YFmgJrNZa/+SwTQpGj8pZrfUyh/Vn82NuWcGhkzB6azpVFF9+jNdiFFWzyuiJ+AXjZ3yoUqoW0Fxrfa6yfQohhDPkVIjwVO2A42WsbwUszV++G+NujT0AWuvvgO9KvkEpVR9YDLQAntBax+evf0IpdZ3WOrKcGJ7Jf19JAcD3+cv9gXVa67UltrkpP/4ZJdb3BDKAC+UcE621VkolA4HlbePgb0BdYHoZryXmf+0EvATMr8L+hBDCKVJYCE/VEEguuVJrvR1AKdUC4zqGDyvaSf5/6j8ATTEKkYfzrzXQwMdUPJrn74HnyoghLH/fXYH2wKQSx/THOJXzrS59dfSDwJYqXAiahVHAVOZJIKGsa0q01tlKKTB6coZijMUhhBAuJadChKfKxbi7oTz3AQoIrWQ/bwG9gSHAAxgdAqOARcDn+dcilKKU6o5x19ThCvZ9f/7XkjH0xSiMiq1XSt2IcbFnqV6VMjSjkiHMlVLNMe7+2FPJvh4G/l5GkSOEEKaTwkJ4qiSMP67luQ/jv/od5W2QfwrkH8CHWuuTQK+C2y+11r8AnSvYf1XGrrgvP86St8Pem/81tMT6Z/Nj/i4/vjIvMlVKNcDorSh1jUkJ2flfK7puQmPc1WLZLbtCCHuRUyHCU8VSeWGxQ2udWcE2j2P8IZ+c/7xwrpH80xXZZb0p3zCKCoTy3AuEaa3zyogtJr+YcTQUWKG1vpTfe9G+nP22yv9aUW8JWusUpVQExrUjpSilXgaukP8PhFKqtta6opyFEMJp0mMhPNU+jLsqSlFKtcYYLyK0kn3cBizUWl/Jf345v6AAGIhx62dZ++8HnNRaJ5S3Y6VUT4wxM0JLrK+NcX1FWbG1ADbn32r6Lsbw3WW5A+OukgPlHd/B/wPuUUrd7BBDH6XULIxCaibQXRkXW3ydP76FEEK4jPRYCE8VBnyolGqitU4q8VorjNs2l1Syj/YY11IU+NLhosk3gBHlvK8qp0GaA/HAshLrmwCXMWZkLekvwJ8wejqma63LuzNkALCmjJ6QUrTWoUqp+4G/KKVyMa5NiQBGaa1TlVKrgGBgHvBZedeUCCGEWWRIb+GR8v+rjwf+pLVeVcN9zMaYa2RLifV/BhprrUvNIprfo3EUuNGKadrz8z4KvK61XuPu4wshhLPkVIjwSPn/rX+JMZZETX2PcVoBKBwk6zWgc1lFRb4HgZ1WFBX5nsTo8fjBouMLIYRTpMdCeCylVEvgENBXa13WYFlV2cdfMQaQysO4GHSD1npDBdsvBBZrrVfU5HjOUkrtwZhjpKK5RIQQwmNJYSE8mlLqFeA2rfVLbjhWAyAS6GrF3RNKqdEYw26/5e5jCyGEWeRUiPBoWuvpQC2l1AtuONzjGBdNWlFUDAJ6YNwtIoQQXksKC+ENhgP98m/xdKV7MO6esMIZ4MVyZnMVQgivIadChBBCCGEa6bEQQgghhGmksBBCCCGEaaSwEEIIIYRppLAQQgghhGmksBBCCCGEaaSwEEIIIYRppLAQQgghhGmksBBCCCGEaaSwEEIIIYRppLAQQgghhGmksBBCCCGEaf4/qtmbKg7Vje0AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shadow_plot(0.9999, pi/2, fill=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Screen coordinates for $a=m$" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "th = var('th', latex_name=r'\\theta_{\\mathscr{O}}')\n", "r0 = var('r0', latex_name=r'r_0')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{r_0}^{2} - 2 \\, {r_0} - 1}{\\sin\\left({\\theta_{\\mathscr{O}}}\\right)}\n", "\\end{math}" ], "text/plain": [ "(r0^2 - 2*r0 - 1)/sin(th)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha(1, th, r0)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{\\frac{{r_0}^{4} + \\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{4} - 4 \\, {r_0}^{3} + 2 \\, {\\left({r_0}^{2} + 2 \\, {r_0}\\right)} \\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{2}}{\\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{2} - 1}}\n", "\\end{math}" ], "text/plain": [ "sqrt((r0^4 + cos(th)^4 - 4*r0^3 + 2*(r0^2 + 2*r0)*cos(th)^2)/(cos(th)^2 - 1))" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta(1, th, r0).simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Special values for $\\theta_{\\mathscr{O}} = \\pi/2$:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{r_0}^{2} - 2 \\, {r_0} - 1\n", "\\end{math}" ], "text/plain": [ "r0^2 - 2*r0 - 1" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha(1, pi/2, r0)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{-{r_0}^{4} + 4 \\, {r_0}^{3}}\n", "\\end{math}" ], "text/plain": [ "sqrt(-r0^4 + 4*r0^3)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta(1, pi/2, r0).simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Special values for $r_0 = m$:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2}{\\sin\\left({\\theta_{\\mathscr{O}}}\\right)}\n", "\\end{math}" ], "text/plain": [ "-2/sin(th)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha(1, th, 1)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{\\frac{\\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{4} + 6 \\, \\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{2} - 3}{\\cos\\left({\\theta_{\\mathscr{O}}}\\right)^{2} - 1}}\n", "\\end{math}" ], "text/plain": [ "sqrt((cos(th)^4 + 6*cos(th)^2 - 3)/(cos(th)^2 - 1))" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta(1, th, 1).simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Critical inclination for the existence of the NHEK line:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\arcsin\\left(\\sqrt{3} - 1\\right), 0.821327461377416, 47.0585971351201\\right)\n", "\\end{math}" ], "text/plain": [ "(arcsin(sqrt(3) - 1), 0.821327461377416, 47.0585971351201)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "th_crit = asin(sqrt(3) - 1)\n", "th_crit, n(th_crit), n(th_crit/pi*180)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cos(th_crit)^4 + 6*cos(th_crit)^2 - 3).simplify_full()" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\n", "\\end{math}" ], "text/plain": [ "0" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta(1, th_crit, 1).simplify_full()" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.59326048984047\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(1, th_crit, legend=False)\n", "g1.set_axes_range(-4, 8, -6, 6)\n", "g1.save('gik_shadow_a1_th_crit.pdf')\n", "g1" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.67516782408563\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shadow_plot(1, 1.1*th_crit)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.13415225868399 rmax : 3.50327928110302\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "shadow_plot(1, 0.9*th_crit)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.79787701838380\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(1, pi/3, legend=False)\n", "g1.set_axes_range(-4, 8, -6, 6)\n", "g1.save('gik_shadow_a1_th60.pdf')\n", "g1" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.73205080756888\n", "\\end{math}" ], "text/plain": [ "1.73205080756888" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(sqrt(3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cardiod shape for $\\theta_{\\mathscr{O}} = \\pi/2$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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8847RLSo+3QLsjh3u44gI4NZb9XoyEVmZyyX5sbmmTpVKXFagW4D9+mvgjz+kqPbjjwOBgXo9mYisrFYtYOZMOXY4gNGjZSNFK2AWgcaYRUBUeooiHbORI6WGrEmw4LbRGGCJbMtcaVpERP6EAZaILC0nx+gWFE7TAJucDHTrBrz7LnD8uJZPIiJ/c+ECMGWK5MaalaYBdtkyYPNmGZyuVw/47Tctn0ZE/mLjRqBFC2DGDGD5cuDHH41ukXeaBtjFi93HVauaavaPiCysenUgIcF9/n//Z86hAs0CrKJIr7VWLTm//XZTlx0jIgu5/npgzBg5rlsXeOopY9tTGM3TtBQF2LMHCA4GGjXy9VHWxTQtIm2cOiUFpCZNkvhiAObBGo0Blsi2mAdrFKfTicjISERFRRndFCIyCHuwGmMPlsi22IMlIv8RGwvcdZfUnzYDTfbkio6WFIpOnaS4drt2WjyFiEikpEhWwfLlct6woeTIGk2TIYK6dYETJ+T4zjs982H9DYcIiLSXnQ20bAns3y/nwcGycWLNmpo+Vv8hguPH3cEV8NzjnIhIC4GBwLRp7vO+fYErVwxrzlWqDxFcuQIMGwb8+itw7JgMExARaW3oUFmaP3q0eYYlNc0iOHECqFHDv1dwcYiAyLaKHCLQZJIrV506Wt6diMjcmKZFRKQRBlgisq3MTOCrryTLwAgMsERkO5cuSaH/Ro1k0n3pUmPaoeok16JF8he54QZ5DR4MBPh5COckF5H+kpOlXOrly3LeoQOwZYvqj9E3D3brVuCbb4CpU4H77pM9zK0sJiYGUVFRCA0NRXh4OG677TYcOHDA6GYRURGqV3fXiwWAnTslbVRvqgbY+Hj3cUSE9QPsxo0bER0djS1btmDdunXIyspC3759cfHiRaObRkRFiI6WIYI33wROnpQerd5UTdOqXh2oX19Wc0VEqHlnY3z//fce5/PmzUN4eDhiY2PRrVs3g1pFRMXRvDlw8KCxHT1VA+ycOfJnZqbs+Gg3aWlpAICqVasa3BIiKg6jP0WzHmwxKYqCIUOG4OzZs9i8eXOh17lcLrhcrqvn6enpqFu3Lie5iOyH9WDVMmHCBOzatQtffvnlNa+LiYlBWFjY1VfdunV1aiERmQ17sMUwceJELFu2DJs2bUKDBg2ueS17sETmtHs38NFHUpDq009VuSU3PSwNRVEwceJEfPvtt9iwYQOaNGlS4nswD5bIeC++CLz6qhyXKyc70lapUurb6lfsZc8e4McfgWrV5PXPfxq2la5qoqOjsXDhQixfvhyhoaE4deoUACAsLAzBVv/LEfmRDh3cxxkZwNdfAw8/rP1zVevBfvIJMHas+zwxUfNq4ppzFDIFOW/ePIwaNapY92APlsh4mZlS3S8pCejYEZgyBRgypNS31a8Hm796uB06eKX45UNEJlK2LDB/PtC4MeDDSJ/PVAuwGRme50FBat2ZiKj0BgzQ/5mqDRFcuQKkp0ugzcgAGjQwPsnXDDhEQGRb+g0RlC8vLyIiElxoQER+SVGkrKGWNN2Ti4jIbPbvBxYsABYvBlwu4PBh7YYzGWCJyK+sXOledAAAf/wBtG2rzbNUGyI4fx6Ii5PlaLGxBbMKiIjM4M47Pc8XL9buWar1YFesAEaOdJ8fPWqPmrBEZC8NG0qPNSsLuOsu4J57tHuWagE2f4nUlBQGWCIypw0bgNBQ7Z+j2hBBeLjneVKSWncmIlKXHsEVULEH26gR8PHHwHXXSbCNjFTrzkRE1sRyhRpxOp1wOp3Izs5GXFwcV3IR2Q/rwRqNS2WJzO/YMZn0atiwRN/GLWOIiAozfTrQqpXshj1jhvr3Z4AlIr+1aZPk7gPA+vXq31+TAJueDmzfDuTkaHF3IiJ19OrlPj50SIYK1KRqgF25UnYxCAsDoqKAEyfUvDsRkbr69AE6dwamTgU2bgT+8Q91769qLYJKlYDTp93nBw4A9eqp+QQiIvVERQE//6zd/VXtwebPfd2xQ827ExFZi6o92OuuA8aMkd0M2reX3w5ERP6KebAaYx4skW0xD5aIqLiSktxpW2pggCUivxcTI9t516gBjB6t3n0ZYInI7507J3mwALBzJ3Dhgjr31TTAHj8OLFyo5ROIiEqvUyf3cXa2ehlQmuzJtX49MHEisG+fnHfoIOUMiYjMKCoKGDoUaNNGdjto3Vqd+2oSYKtWdQdXAFizBpgwQYsnERGVXq1awNdfq39fTYYIbrxRlszm+u03LZ5CRGRumvRgAwKkx5qeDgwbpl5320ryFtwmIv/EhQYa40IDItviQgMiopJKT5edsUuLAZaI6H8GDQJq15aSq//6V+nvxwBLRPQ/x44BCQlyvH9/6e+nS4A9c0Z+G7RrB1y6pMcTiYhKrkUL93HeVFNfaZJFkNemTVI1PCNDzhcuBMaO1fqpREQl17cvEBICNG9esL61LzTPIrh8WcY0zp6V86ZNgb17gcBAXx9rLcwiILIt47MIgoOBRx+V44gI4PHHuRkiEfkHzYcIAGDyZOlyDxsGlNHliURExuNCA41xiIDItowfIiAisqrSDmcywBIR5TFrFtCtG1CvnpQuLA3DAuwvvwD9+wOnThnVAiKiguLjgc2bZcOAw4cB30dRDQiwKSnAHXcAXboAa9cCkybp3QIiosLVr+8+vnBBtpPxle5z+mFh8hsi1zffAKtWyRpgIiKjRUbKp+uaNT3rWvvCkCyCHTuA9u1l75tHHgHeeEMCrx0xi4DItorMIjAkK7VtW2DmTPmza1cjWqA9FtwmIubBaow9WCLbYh4sEZFRTBdgV60CTpwwuhVERKVnmgCbmQk89RRw661SMkyN7RqIiHzx+uvAyJGS3TR9uu/3MU3plQkTgDlz5HjfPvmLbdoElC1rbLuIyP+sXg38+qscl2a5rGl6sC+95E7wdTiAESMYXInIGJUru49Ls9DANAG2Vi3ghx+kOPfChdKjJSIyQoMGUmL15puBG27w/T6mS9O6fFmKdNsF07SIbMt6aVqFBVeXC9i1S9+2EBGVhukCrDeKIktq27cH5s0rXXUbIiK9WCLAvvMOMH++9GIffBB45hmjW0REVDTTB1hFAbZscZ+XLQsMH25ce4iIiss0ebCFcTiARYukMMyLLwKvvAK0bm10q4jIznbsANavlwVQGRnA88/7ljZquiyCa9m7F2jWDAgMLPjehAlA1arA0KHA9dcDASbpmzOLgMh6Zs3y3Azg/HmgYsUCl1kvi+BaIiO9B9fTp4HZs6V326oV8Pbb+reNiOyjXDnP84wM3+7j0xCBw+FwpKWl+fZElZ09C4wbB2Rlub/Wpg2Qnm5Me1wuF1wu19Xz8+fPA5CeLBFZQ2am+7hsWSA1FSiTL1qGhYVVAnBeucYwgE9DBA6HoxIAc0RYIiLjhCmKUmjvydcA60hLSytQAiE9PR1169bF8ePHSzXeGBUVhW3btl3zmpkzgZdfdp+/9ppU4Tp8GBgwoHj3UKsteeXvwSYmJqJ9+/bYu3cvateurVs7zHoPPf+N6HEPNe5jt5+Jv/w8wsLCwlBED9anIYJr3RAAKlWqVKofTGBgYJHfP2UK8Omn7tqxa9YAzz0H3HRT8e+hVluKIzQ0VPOfiVXuAejzb0SPe6h5H7v8TPzl53GtnmsuU05yRUdHF3lNSIhslti8OfDll8B//1vye6jVFj2o0Q6z3EMNZvq78Gei/j3UYIa/i6ppWlqkJF24AGzbBvToUfC9nBzZmdbMZQ1PnDhx9eNOnTp1jG6O4Zi2VhB/Jp4s9PPQN00rKCgIL730EoKCglS536FDQIcOMqa6Y0fB9wMCzB1cAVz9Waj1M7E6tf+N2AF/Jp7s9PMw7UKDgweBzp2BM2fkvH59IDYWqFZNy6eqz0K/jYnof955R3Lry5cHKlWS3VW8sO5Cg/r1gRtvdJ9nZwMJCca1h4j8x6lTwIEDwJ9/lq5MqmlrEZQrByxdKmOvgYHAypVAeLjRrSIif3Dxovu4NBsAmDbAAkBoqKRfhYQAFSoY3Roi8hedOgFXrshK0dBQ3+9j2jFYu+AYLJFtGTcGGx8fjzFjxqBBgwYIDg5Go0aN8NJLLyHDS9WEixeB++8H4uO1ag0ZLSYmBlFRUQgNDUV4eDhuu+02HDhwwOhmmUZMTAwcDgcee+wxo5tiqJMnT2LkyJGoVq0aQkJC0Lp1a8TGxhrdLJ9pFmD379+PnJwczJ49G3v27ME777yDf//733juuec8rlMUYMwY4D//AaKigA0btGoRGWnjxo2Ijo7Gli1bsG7dOmRlZaFv3764mHewy09t27YNc+bMQatWrYxuiqHOnj2Lzp07o2zZslizZg327t2LmTNnonLePbStRlEUX18lNmPGDKVBgwYeX3vvPUWRMCuvunUV5coVX+5uTmlpaQoAJS0tzeimmEpSUpICQNm4caPRTTHU+fPnlSZNmijr1q1TunfvrkyePNnoJhlmypQpSpcuXYxuRkkUGSd1TdNKS0tD1apVPb7Wt6/sVgBI5sBXXwE2yC+mIuSWu8z/78HfREdHY+DAgejdu7fRTTHcihUrcNNNN2Ho0KEIDw9HmzZtMHfuXKObVSq6ZREcPnwYs2bNwsyZMz2+3rw58NtvwNSpQEQE0LGjXi0ioyiKgieeeAJdunRBy5YtjW6OYRYtWoQdO3aoUtHLDo4cOYKPPvoITzzxBJ577jls3boVkyZNQlBQEO6//37d2nHpEnDHHUCVKvIaMUIWPfmkON3cvC8A0yAZBIW+tm3b5tGPPnnypNK4cWNlzJgx2nfaTYZDBAU9+uijSv369ZXjx48b3RTDHDt2TAkPD1d27tx59Wv+PkRQtmxZpWPHjh5fmzhxonLzzTfr2o6DBz2HLRcsKPTSIuOlLz3YDwAs2rdv377CLoiIiLh6nJCQgB49eqBjx46YM2eOD4+zJqfTCafTiezsbKObYioTJ07EihUrsGnTJr8ufhMbG4ukpCS0a9fu6teys7OxadMmfPDBB3C5XAj0tj+Sjf3jH/9AZGSkx9datGiBJUuW6NqOkyc9z0tRxrnkAVZRlGQAycW59uTJk+jRowfatWuHefPmISAgAFlZUgUr/543dhMdHY3o6OirebD+TlEUTJw4Ed9++y02bNiABg0aGN0kQ/Xq1Qu7d+/2+Nro0aPRvHlzTJkyxe+CKwB07ty5QOpeXFwc6tevr2s7goKAPn2k1vTJk6ULsJplEeQOC/Ts2VM5ceKEkpiYqCQmJioxMeeUpk0VZdUqRcnJ8akHbykcIhDjx49XwsLClA0bNlz9t5CYmKhcunTJ6KaZhr8PEWzdulUpU6aM8tprrykHDx5UFixYoISEhChffPGFoe26Rpwqeki1OBcV8rqmefPmeRmfraIAyVfHNu65x8e/sYUwwIqC/xbkNW/ePKObZhr+HmAVRVFWrlyptGzZUgkKClKaN2+uzJkzx+gmXUuRcVLXpbJTpgAzZrjPZ84EnnjC18dbA5fKEtlWkUtldS32MmmS7FAwd66kZE2YoOfTiYj0ZUixl/h44PRp2a3A7tiDJbItc/Vgc0VEyIuIyEzOnQPGjQOaNJFXnz5AabIJTV0PlohIT3FxwOLF7vMVK0oXYE27ZQwRkd4OHvQ8b9KkdPfTPMB++y3wxhtAaqrWTyIiKr1mzWS36oAAoGHD0t1L80mudu1ky+2QEMkiiInx9XHWxEkuIuvJypJVXEUsIjN2V9nduyW4AlKhxstmBkREplOmTJHBtVg0DbBHjwLXXec+HzNGy6cREZmLplkEgwdLN/uHH4CffwbyFcohIrI17iqrMY7BEtmWORcaEBGZzfz5wJ49QKtWQJs2gBqbbTDAaoQFt4ms5ZtvgO++k+OWLWWSvrQ4RKAxDhEQmZ+iSGHtxEQ5v/deYMGCIr/NmDStWbOAYcOAL74AUlK0eAIRkXouXpRFBeXLy/lNN6lzX016sN27A5s2yXHz5kDhu3fZH3uwRNaRkQHs2gXUqiWvIug/yeVyAVu3us979VL7CURE2ihXTr3eK6DBEEFKCtC1K1Cxopx37ar2E4iIrEH1HmytWrKwICtLZuH8fPNQIvJjmqVplSkjuWRERP6K9WCJyK99+ikwejTw+efA8ePq3pt5sBpjFgGRuQ0c6F5gUK8e8Pffxf5WY8sVEhGZWWamO6UUAHr0UPf+qgbYVatkK+5//1uqZ+XkqHl3IiJ1paZ6Zj317Knu/VWd5PrhB8DplOOKFYH0dDXvTkSkrho1ZHggMxOIjS39Hlz5qRpgjxxxHzdrBjiKHKEgIjJe2bLAzTerf19VhwgCAtxreevVU/PORETWo2oPdsUKqUqTkiJLZomI/JnqCw0cDqB6dbXvSkRkPUzT0ojT6URkZCSioqKMbgoR5aMoUtRl+HDgP/8BzpzR5jlcaKAxLjQgMp/du2VrmFxvvgk89VSJb8OFBkRE+S1Z4nl+663aPEe1MdiDB4Ht24EqVeTVtq2kPhARmU3nzsDddwOrVwMREZJWqgXVAuz69cD48e7zM2c42UVE5tSnj7wuXwaOHdPuOaoNEWRmep4HBal1ZyIibQQHa9d7BVQMsFlZnudluCE4Efk51cLg/fdLlzsrS17swRKRv1MtwFarJi8iIrPat0+W8VeooM/zmKZFRH5BUYB77pEKWqNGAb/+qv0zGWCJyC/8+acsMLh4EfjsM2DNGu2fyQBLRH5h4ULP8/vu0/6Zqo3BZmUBFy5IXtmVK0CdOlxoQETmMX060K6dbG6Yng40bar9M1XrwS5dKiu4atUCGjYE4uPVurMx4uPjMWbMGDRo0ADBwcFo1KgRXnrpJWRkZBjdNCLyQXCwjMGuXg389JM+z1StB1uliud5Sor62y/oaf/+/cjJycHs2bPRuHFj/PXXXxg3bhwuXryIt956y+jmEVEp6JWnr9pjatTwPD99Wq07G6N///7o37//1fOGDRviwIED+OijjxhgiahYVAuw9esDr70mgbZGDaB9e7XubB5paWmoWrXqNa9xuVxw5dnOIZ07PxL5LdaDLabDhw+jbdu2mDlzJsaOHVvoddOmTcP06dMLfJ31YIn0l5kJPPCAVM4aNEj1oQHWg81v2rRpcDgc13xt377d43sSEhLQv39/DB069JrBFQCeffZZpKWlXX0dP35cy78OEV3DypXAl18Ct98ONGgA/P67vs/3ux5scnIykpOTr3lNREQEyv9ve9yEhAT06NEDHTp0wPz58xEQULLfSdzRgMg4ffoAP/4ox8HBwMmTBSfkS6HIHqzf1byqXr06qhezUO3JkyfRo0cPtGvXDvPmzStxcCUi42RlAXXrAuXLS27+sGGqBtdi0aQHm5MDJCRITqxVY1JCQgK6d++OevXq4fPPP0dgYODV92rWrFns+7AHS2Ss1FRg/nygZ0+gdWtVb11kD1bVALt2rWwcdviwrOg6cQKoXdvX2xtr/vz5GD16tNf3SvIzY4Alsi19J7nKlAH++kuCKwDExal5d32NGjUKiqJ4fRERFYeqAbZ5c8/zXbvUvDsRkbWoOslVqxYweDDQqJHsKtutm5p3JyIq2m+/SQwKDze6JX6YpqU3jsES6SczE2jcGEhKAh58EHjySSk+pREuNCAi//HVV7IN95UrwIcfAl9/bWx7GGCJyDa+/959HBoKPPKIcW0BGGCJyEb+8x/g22+BG24AHn4YqFzZ2PZoOgZ74YLkxN54o6+PsD6OwRLpLydHhglCQjR9jDFjsAsXAjffLMvS+vSR3RyJiPQSEKB5cC1eO7S46dmzUrUmKws4c0b2Iici8jeaBNh//tPzPLeaDRGR2o4ckSEBM9KkmlZkJNClC9CmDTBwINC9uxZPISJ/d+kS0LUrULMm8OabUtDFTDQJsA4HsHmzFne2DqfTCafTiezsbKObQmRbb78tlfsSEoBevYAFC4B77zW6VW5cyaUxZhEQaSMjQ/YCPHVKzmvVAg4e1HVyiyu5iMieypUDYmOBsWMla+DVV82ROZAXe7AaYw+WSHv79gFNmwJ56uLrwRw92NRU4OOPgW3b9HgaEfmbFi10D67FommAzckB7rhDZvjGjZPiC0RE/kLTABsQIMvVMjPlfOlSwOXS8olEZGfnzwOHDhndiuLTfIhg+HD3cZkyXNVFRL57+WXg+uuBF1+UHFiz03yS6/x5YNIk4O67gd69gbJlfX2cNXGSi0gde/dK4aisLDnv3h3YsMHQJhU5yaXJQoO8QkOBefO0fgoR2d2SJe7gCgCPPWZYU4qNebBEZAkvvgh8843stTVgADBkiNEtKhrzYDXGIQIidaWkyPhr3bpGt8QkebDenD9v1JOJyMqqVTNFcC0WXQNsdrZs59ClC3DLLXo+mYhIf7oG2BdflIUHv/wC/PwzsHWrnk8nIitJSgJmzZKOmVXpGmDvv9/zfOZMPZ9ORFahKLJp4aRJ8ol3716jW+QbXQNs8+bAoEFA+fKyne4rr+j5dCKyio8/BpYtk+MtW4AHHrDm3n6a58Hm9+67QKVKwHXX6f1kfbHgNpHvqlaVLbfPnZOyhHPnSiF/q2GalsaYpkXkm2PHZFhx8GDgiSeMbo1XRYZ8BliNMcAS+S47W3quAeZcEmX8UlkiIl+ZscZrSRj+eyE1FXj+eWD8eKNbQkRGOXvWnqVMDQ2w8+cDERHA668D//4382KJ/FF2tlTb69YN+Ptvo1ujLkMDbNOmnktmH3/cmqkYROS7l18GfvxROlht2wI//WR0i9RjaIDt1Am45x45btoUeOYZI1tDRHo7d04+veZyuYB//MOw5qjO8DHYf/1LcmN37wZuvdWauW5E5JvKlYHt24Gbb5bzTz6RBUl2wTQtjTFNi6hoGRnAqlVSq8RCzFuukIgoV7lylguuxWLaAHvlCie8iOwod5dpf2DKAPvf/wI33AB89pnRLSEiNS1aBLRpAxw5YnRL9GG6ADt+PNCrl+x9/uSTUhOSiKxv2zZg9Ghgzx4gKspe6ViFMV2ArVfPfZyaypKGRHagKFKw5coVOU9NlU+qdme6APvUU0CrVnIcHS1pXERkbQ6HbBfVsaOc33YbMH26oU3ShSnTtHbtAhISgP79tXqCfpimReR2+TLw6qtSfyQkxOjWlBrLFRolb8HtuLg4Blgi+2GANRp7sOSPcnKAM2eAGjWMbomm7LXQYPVqYN06o1tBRNeSO6HVrp11NytUiyUCbHa2jNkMGgQMGyZbSRCROb38MvDee8DJk1KCcPt2o1tkHEsE2A8/lJqxgKR3DB1qz+K8RFaXkQGsWeM+T00Fjh41rj1Gs0SAfeghoH1793mnTqbdo4fIr5UrB6xd666ONXu2dIj8lWUmuY4dA7p3B2bMsNZ/ME5ykT9KT5fqWPfea3RLNGWvLILMTKBsWb2fWjoMsES2Za8sAqsFVyK7e+89YOdOo1thXpYKsIVZtAhISTG6FUT+Q1GAqVOBxx4D+vYF9u83ukXmZOkAm5MDTJkCDB8ua5svXza6RUT+Yc4cdyGmM2eA3r2BtDRj22RGlg6wTz4pk14A8PPPsoFiTo6xbSLyByNGuDMFACnSFBZmXHvMytIB9pFHgKpV3ee9e2uTvuVyudC6dWs4HA7s5IATESpWBL77TrbZnjtXhgqoIEsH2GbN5D9y5crAF18AkyZp85ynn34atWrV0ubmRBZVpQrw++/A2LFGt8S8LB1gAaBDB1kpMmKENvdfs2YNfvjhB7z11lvaPIDI5OLigF9/9f5emTL6tsVqbPHjqVzZ+9dzU3wdRWareXf69GmMGzcOy5YtQ4gNilcSldSvvwKDB0s9kF9+ASIjjW6RtVi+B1sYRZECMc8849vutIqiYNSoUXjkkUdw0003Ffv7XC4X0tPTPV5EVrRjh+yPl5ICnDsHDBgghfCp+GwZYBVFAmtMjGQZTJniDrLTpk2Dw+G45mv79u2YNWsW0tPT8eyzz5bo2TExMQgLC7v6qlu3rgZ/QyLttWoFdOniPq9bFyhf3rj2WJGllsoW19atMjabKyBABuNvuglITk5GcnLyNb8/IiICw4YNw8qVK+HIM76QnZ2NwMBAjBgxAp8Vsqe4y+WCK0+pr/T0dNStW5dLZcmSUlOl0NKNN8pEcnCw0S0yFXvVIiiJjz+WKlyKAnzyCfDggyX7/mPHjnl8vE9ISEC/fv2wePFidOjQAXXq1CnWfViLgKwuIUF2JggMNLolplNkgLXFJJc3Y8fKb9vk5JIHVwCol3f/cAAVK1YEADRq1KjYwZXIKlatkomsIUMKvscMRd/ZNsAC2qVuEdlFRgbw3HPAzJlAhQrAb78BN9xgdKvsw5aTXEXJyQEmT5ZZ0uKKiIiAoiho3bq1Zu0i0tuiRRJcAeDiRUnJYuEk9fhlgH3hBeD992W/oFWrjG4NkXFGjgQGDnSf33knEBpqXHvsxraTXIX55hvg7rvd56GhQHy8Z00DNXGSi8wuOVnyXV99Fbj1VqNbYyn2KrithgEDgFtucZ9/+ql2wZXITOLjvVebq14d+OMPBlct+F2ArVgRWL5cxmCffhq46y6jW0SkrZwcYNYsWeb64Yfer+EmotrwuyGCvBTFe52Cy5fVS6jmEAEZSVGkGP2KFXIeHCxbvDRtamSrbINDBNfiLbhmZgI9egAPPyyzqkRW5nDIli65Ll+W3QhIH34dYL2ZPl2W1c6ZA7RrB+zZY3SLiEpn/HgpRh8cDDidwJtvGt0i/+HXQwT5/f030LgxkJUl51WqAH/+KUUufMUhAtJLZqbsi1W9esH3TpyQ3muTJvq3y8Y4RFAS9esD69YBtWvL+dy5pQuuRHrJLWZ0773ey3PWqcPgagQG2Hz++U/ptc6eLUnXRGb34YeyAeGuXdJB+OILo1tEuRhgvahWTSpxebN/v0waxMXp2yaiwgwY4Fmn9ZVXpHALGY8BtgSys6Uy17p1Uox46tTCtwl3Op2IjIxEVFSUvo0kv9OggeR0AzJE8PPPLC1oFpzkKoH33vPcnviuu2Tp7bVwkovUsn07sHcvcP/9Bd+7dEmKF+XdgYA0x0kuNQ0ZIukuABASArz9trHtIf8QFwcMHQpERUnK1alTBa8JCWFwNSMG2BKIiAB++AFYuFBKvHnLMLhwQTaII1LL9u3A4sVyfOmSjLGSNTDAlpDDAQwfDjzyiPf333wTaNhQNlu8fFnftpE9DRsmY/65UlN92ymZ9McxWBUlJUlwzV1i26kTsGYNx2CpeBITpXSgtx0FvvtOPjW98YYMFZApcAxWT06nZ/2CwlK9iPKKjweioyUbYOxY773TAQOA9esZXK2GAVZFL7wgSd81agAtW0q1+PwURZY0EuV6/335d+NyyZbzP/5Y8BpvhYnI/BhgVVS2rMzyHj4skxLechHXr5dhhPfflwkLosmTPf+tfPmlcW0hdXEMVmP582B79gR++kneq1cPOHRIAjPZW1IS8PHHshAgIqLg+8OHAwcPyqegwYNZANsiivxcYettu81myxZ3cAWAPn0YXO3uyhVZ/bdkiWyRnZ4uE1X5zZ0r22ZzKMBe+HtSR5GR8j9XeLicT5jg/br164Hz5/VrF2mnfHlZKJCRIecffyxBN7+KFRlc7YgBVkeVKgFTpsis8eLFQOvWBa9JSZFNGWvWlJ7P3r16t5J8kZICbNvm/b2xY93HYWHAkSP6tImMxwBrgODgwkshLlggvZ1Ll4B58yQ3ksxr7VrZjbVmTeCee7ynWA0fDtxxB7BqlYyzRkbq304yBgOsySxd6j6uWVPq0+Z34QLLJZrFzp0SOLOygKNHpfB1fmFhMgY7cCAnr/wN/3ObzNq1wFdfSc3Ze+/1nuq1ZAnQrBnQooUMOVy4oH87/YWiyL5s777rvXc6bJjned5fkERM09JYacoVFrateL9+UnQGkAmzxET2jLQQGwvcfbd7zHT7dtkIM79bbgGuu05+IfbqBZRhbo6/YJqWUZxOJ5xOJ7JLUVreW3BNTpYsg1yFfeycP1/qg/bsCXTvLhs4UkE5OcC+fUCjRp67AgCyj1XeCakVK7wH2NWrmQFA3rEHqzG1C24riuy9tHw5sHIl8PzzwG23Fbwuby+3cWOZXCG3w4eBJ58ENm+W6lQ//ii9z/yaNnX/7IYMAZYt07WZZG7swdqNwwHceKO8pk71fk1GhgSOXN4mygBJbj9wQKo3tW3rvYqTVWVnS+9zzx7ZELBmTc/3w8Lkl1SuzZu9B9jx4+XnOXgw0Ly5tm0m+2GAtaHTp2UL5y1bpLBMz57er/v8c9m/CZBhhA0bCl5z9KgMQdSpY759nrKzpUeff8wzLk7qp7pccv7llwUno6pXl0nCffvkPO8vpLwef1zdNpN/4dSIDdWtC2zaBJw9K1kJ/foVvCYzUyZxchXWe33uOVk7HxIi+Z7eHDggAWrPntLl7SqK9BYTEyX9yVvVsQMHJHjWqAGUK+c5Hp2rfn1Jm8q1Z4/35915p+SofvQR8MEHvrebqDDswdpYhQqS7uXN6dOS6rV3rwS1wgLs4cPyZ0ZG4VX0nU5g1iw5Dg+Xe+f35ZcyXuxwyOuvvwpOKq1dK3VPcx05IjVS8ypfHti92/PvkV9QkIw7Hzgg54UFWG69QlpjgPVTdeoAf/whPb2DByXNyJtDh9zHtWt7vyY11X1cWLZCUpIMN1xLUJDn+enTBQNsjRoFr/Hm2WflF0JkpAwFEBmBAdbPlSlTeABSFODbbyXIHjlSeDX9vAG2alXv1+Tfn8xbWpO3AJtf+fJSyDwsTIJt167en/fAA96/TqQnpmlpTO00LTM6fBg4eVICbUiI92GJlStl1j73n9vs2QUnpxITpRZD5coSPNu3L9hjJTKRItO0GGA15g8BlshPcdNDIiKjMMASEWmEAZaISCMMsEREGinNJBcVg8PhqAQgDUCYoijpRreHiPTDAKsxh8PhABAK4LzCHzaRX2GAJSLSCMdgiYg0wgBLRKQRBlgiIo0wwBIRaYQBlohIIwywREQaYYAlItLI/wObc5nyNftykgAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cardioid = parametric_plot([4*(1 + cos(x))*cos(x) - 1, \n", " 4*(1 + cos(x))*sin(x)], (x, 0, 2*pi),\n", " linestyle=\":\", thickness=2.5)\n", "cardioid" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.99999996000000\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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Mbr0VoqMZRjRjCMRDlPHc/eWLHwwbZqyNdsLtfHMuLryQ6ed15GtvSbdWeQB8wWeI4iKYNk0rzuPtDQUFBhtqG6bxSzl69KhM3gaMzuRzc3Pd4hfE1s2lyNWruWXpi/DPP1UvXHEFR96dQdGIUfToYVCpYQfhLr6xhQotBQWwcn4uzx75EjHTX6uYWUHPnoy//Gce/vgSRl7nce6TGYyZ/AI19ahM3mQsWrTIaBNqJScHXhx9klvu8OSlOSMo/Kd8TG+XLtowyeho+jw9ChOt4VCJq/umPlRoadkSnnujLcLnGzh8GMaOrSyhvOn4ZUzddDnXXO/B8/dncNJFu+zN5BfQp0cFeTfgtttuM9qEc1NczKe37mBBkNZfe5h+TOJDLTAcPAjPP+/ywyD14NK+qSdn1dK9O8ycCbGxlN7/EO/yTeVLi4M7kDJuIpw65UQrbcNMfgF9esz76bMDQohxQog4OGOZIAM4cOCAkZc/N9HRMHw4n0fdR0+OAVr1x1NjXtECQ/V58ybEZX3TAGrVMnAg/yxZw+W3VlVCHMsshv74EQwYAN9/r42VdRHM5BfQp0cF+VqQUvpLKQcDVxlpR6tWrYy8fE3KyuCrr+DqqyE2lg5kM9/jVS7smMWvWy1MD+xW9zlMgsv5Rgd1aWnXDn74pRvbtpRy68VH+KrVZO2F9HSt9MSNN2o1oV0AM/kF9OlRQd4NcJVJHVLCwW1pcPvt8OmnlTVRGDKEu6MnEHeiI6NualzlkFzFN/bAVi2jbvbkl0N96HDgN20UVQURERRdNoInhx3kzz8s5z6BEzCTX0CfHhXk3YC9e/cabQK5ufD4jWkMu7E1f20tr4jXpAl88gns3g2XX37m6niNBlfwjb2ot5bzzoOVKyEkBPr1A+DTog8JjB7AiGFlTBqfiVF1wszkF9Cpp65axGozftGQY8eOGXLdCpIOW+TFnbMqa5UPYr/M63GxlL/+Wu9z2WP5P1fCaN/YE11a8vPltoenSUFZ5fukG6kyY/oybZlDJ2Mmv0hZU0996smrTN4NWLBggXEXLyqix8cv0iOjKpNIEBfz2/RIuOEG4+xyEQz1jZ3RpaVVKwbMepPR12VWPjWPl+j0xlPw9NOQl2cHC23HTH4BfXrUZCgbMHoylGEcPw4PPQR79pBBJ65mN5Z2HVkV2o7hVzUsP2joGq8K90BKWDy3iD9mbMd3/+1VL1x0EQQGmmams9GoyVAmw5Ap2nv3wogRWgEroHPLQkKmHyQqsUODA7wZMdP0eXtoEQKefaU5vrG3aUG94ov877/hmms49tlcEhMcn1iayS+gyho4HKMz+eLiYry8vJxyraIiSFqxm4Fv3KHdbQXo3Rt++klbYEInZsvknekbR+MQLYmJ8OSTsGcPJXhyE+HsbzqExUs9GP14c/te6wzM5BeoqUdl8rUghPhQCCGFEL5G22Ir3333nVOuk5cH945IY9Rz/TiQ20N78uqrITLSLgHejDjLN87AIVr69YOICHjvPd5nMju5jpySVjwwpjm+n2TY/3rlmMkvoFNPXXdmzbQBI4DDwJ+Abz2OM3R0zd9//+3wa6SnSzn8gozKkRHncVQeufV5KfPz7Xods42ucYZvnIUjtRQXSzlqcNX7qx2nZFzbq6UMDXXI9czkFylr6lGja86CEKI1sAz4D+B6xTZqYc8ex1dVaLJ8GZbDSZX7ec06cfzzuWCymYP2xhm+cRaO1NKsGYTFdOK9FzLxpISVPM6g3N1w991aCQw7Yya/gD49jSbIA/7ABinlL3U1FEJ4CSHaVmxAG8ebd2569Ojh2AvMm0fHN57mF25jOJF0a5HLtj0tGHl945q92hAc7hsn4mgtTZvClIBOHIwp4o7RLbQny8pg3Dh4801tEWA7YSa/gD49jSLICyGeAIYCH9p4yIdAzhlbCkBiYiJTpkyhuLi48m63t7c3x48fJyAggMjISEJCQlizZg1xcXFMnz6d3Nxcq7ZZWVn4+/uzd+9e1q9fz4YNG4iOjmbOnDmkp6dbtS0oKMDHx4djx46xcuVKwsLC2LlzJ4sWLSI5OdmqbVlZGRMnTuTIkSMsWbKE7du3Ex4eTmBgIPHx8UydOpWioiKrY1JTU9n2zDPaQs5AB7IJfHw+r7y7hj59re3Ozs7Gz8+Pffv2sW7dOjZu3EhUVBRz584lLS3Nqm1hYSE+Pj7Ex8ezYsUKtmzZwo4dO1i8eDHJyckAWCwWvL29sVgsTJgwgaNHj7J48WJ27NjBli1bWLFiBfHx8fj4+FBYWGh1/rS0NObOnUtUVBQbN25k3bp17Nu3Dz8/P7Kzs63a5uTkMGPGDGJjY1m7di2bNm0iMjKSefPmkZqaatW2qKiIqVOnEh8fT2BgIOHh4Wzfvp0lS5Zw5MgRJk6cSFlZmdUxGRkZLFq0iJ07dxIWFsbKlSs5ePAgPj4+FBQUWLVNT09nzpw5REdHs2HDBtavX8/evXvx9/cnKyvLqm1ubi7Tp08nLi6ONWvWEBISQmRkJAEBARw/ftyqbXFxMVOmTCEhIYHly5cTHh5OREQES5cuJSkpiUmTJlFaWmp1TEpKCgsXLmTXrl1s3ryZVatWkZKSwrRp08jPz6+hcfbs2cTExBAcHExQUBAxMTHMmjWLzMxMq7Z5eXn4+voSFxfH6tWrCQ0NZffu3SxYsKDS7n5XtMF72DDK3nmn6hP33Xck3PwAftN+Z9myZSQmJjJ58mRKSkpqfNYWLFjA7t27CQ0NZfXq1cTFxeHr60teXl5l26VLl5KZmcmsWbOIiYkhKCiI4OBgYmJimD17NhkZGVbnzc/PZ9q0aRw4cIBVq1axefNmdu3axcKFC0lJSbFqW1payqRJk0hKSmLp0qVEREQQHh7O8uXLSUhIcEiM+Pvvv2vECJupqz/H3TfgfCANuOKM58KppU8e8ELrh6/YemFgP/KSJUscc+JVq6Rs0kRWdpS+957DZyearU/eYb4xAEO0zJ8vpYeHLMRL3kyYbCpOy+UB/+g+rZn8ImVNPfXpkzc8CDt6Ax4s/2eUnrFJwFL+2MOGcxh64/Xw4cN2PV9JiZRvPpQkj3j2qwrw77zjlOnnZgvy9vaNkRilpXRdkHy4ydrKt6KgTM7/NlvXOc3kFylr6lE3Xq0JAy4Dhpyx/Y52E3aIlNKgEkq2ExgYaLdzSQljH03Hd20fri39lVgugRdegKlTtZksinphT98YjVFa5L330eauayv325HDVd8+oa1K1UDM5BfQp6dRToYSQoQDMVLKN21sb+hkqNLSUjw97XMTdMpHp3h/YtViHr2aZ/B3enuat3bOTVazTYayp2+MxkgtUsL4FzPxW9SKzfI2rmeHNglvyxZtEfF6Yia/QE09ajKUyZg0aZJ9TpSXxyNrnuYSYgHwFKXMC2zrtABvRuzmGxfASC1CwNQFnYjddorrB2VpTx49CjfdBPHx9T6fmfwC+vQ0yky+vhidydsFiwUefBCCgsijNc+0Ws0DE6/huf9z7uhQs2XyCgeQlga33gr792v7PXpwOmQrTS8doHoUy1GZvMmwS7GlCRMgKAiANu09WRPZ2+kB3oyYqRCWy2jp1g22boXLLgOg6EQWo0cc55PXbZ/D6DJa7IQuPXXdmVWb8aNrkpOT9Z1g82YphdCGLjRp4rCp5LZgttE1un3jQriclowMWXT5CHkPwZUjb6b875RNh7qcFp1U16NG15iMzZs3N/jYtfMyyBzzmvYZAfjyS22NVoVd0OMbV8PltHTqxNaPNrOReyuf+uxrL479WXdhM5fTohM9elSQdwMGDRrUoON2bS/l8VfaMyQrjG2MgnvugQ9tnfSrsIWG+sYVcUUtd41ph++XOQC0JYcQeQe9nru9zpWmXFGLHvToUcMq3IC8BiydlpMDT96fT6lsTwrnczNbiX4/nyuaqO91e9IQ37gqrqrlv5+0o7Q4i5vnPcXQk9shBnj0UQgO1grinAVX1dJQ9OhRn3g3IDs7u97HHN0UB9lVN6qeuOMUl49qZ0erFNAw37gqrqzlHe+ODP11GnQon+MRGqrVXDrH6EBX1tIQ9OhRQb4WhBDjhBBxgKF1Sy8rH2VgM0VFXPblY+zjMl7Dn4s6ZDJrVWc1/MwB1Ns3LozLaxk4ENavh4oVkhYtwvLZF2ftuXF5LfVEjx4V5GtBSukvpRwMXGWkHT///HP9Dvj0U4iLozX/4H9lADEJbVBD0h1DvX3jwriFluuvh2XLQAiK8OJfXw3krmEnKSqybuYWWuqBHj1qMpQNGD0ZKj8/n9atW9vWeO9eGDpUq9Pt5QVRUXDJJY41sB6YbTJUvXzj4riTlgzv2Tz4yaXs4HoAnrwjk2WbOlX+WnUnLbZQXY+aDGUyfH19bWtoscCrr2oBHuDjj10qwJsRm33jBriTluwxr3DAa0jl/srQdvwRml65705abEGPHpXJ24DRmbwtWCzwxq37eSn8KYbwJwwYAH/+WdV/6SKYLZNXGMf2rSXcciu0l6dYyePcdHURhIdD8+ZGm+ZwVCZvMmyZ0rxkVj7+4ZcwjCjG4cepyXNdLsCbETNNn3c3Ldff3JTAgAKieo7mJn6F3bu1ZQRxPy11oUePyuRtwOhMPiMjg86dO5/z9dxcuLhHHicLtFo0LT2K+CuxOb17O8tC2zFbJl+Xb9wJt9USEwPXXguFhdr+8uVk3Habe2o5B9V9ozJ5k/Hjjz/W+vqpvclcUbi7cv9/7xS5ZIA3I3X5xp1wWy1DhoC/f9X+f/7D5pkzDTPHEejxjQrybsDIkSNrfb2P/3hC5e2EcyOPDdzH21+0d45hijp94064tZbnnoN//xuAovwSwr+9kA1rTxtrkx3R4xsV5N2AlJSUc7+4bx+ULw12Y+c4Vu7q3RjuO7kMtfrGzXBrLULAzJkcvOAuRrKLuTlP8ey/TnPsmNGG2Qc9vlFB3g2o9b7JhAlVjz/6CNqp0gXOxEz3tNxeS+vWBNy4mD8ZAkBmUWueu/fkuSofuBV6fKOCvBtw/vnnn/2Fgwdh5UrtcZcu8MorzjNKAdTiGzfEDFq+mt2FYX208fJdOMlrSe8jsjINtko/enyjgrwb8Ntvv9V4Li8Pfnr1ZywVX/DvvAMtWzrXMMVZfeOumEGLlxf8ENKZB9oFs59LeChnEbzxhtFm6UaPb9QQyloQQowDxqF9GQ4wathfZmYmnTp1snrO9/Ns3vqiPf05yFst5/L8kc/x6uz6y/mZbQjl2XzjrphJS1ZsLB1HjYKK6o1r1sBDDxlqkx6q+0YNobQTrlKgbNasWVb7paXg66t9OR9iAF95fIZo6/oB3oxU9407YyYtM9etgxkzqp549VXIqHtFKVdFj29UJm8DRk+Gqs62sBJuus2DitUbJ36QwwcT3eOGq9kyeYULI6WWvf/0k7b7+Bjy5gWaoiKryuRNRvUpzTec/JEj9MGb/3F5uyReGe8eAd6MmGn6vOm0CAGzZ0PHjuxnMDetHMu/bjnhlqNtVFkDB2N0Jp+Xl0ebNmd0x1x/PezYoT3euhVuusnpNjUUs2XyNXzjxphVS8DLu3l13lBK0ZYKXPtDIQ8+2cJI8+pNdd+oTN5kBAQEVO3Ex1cF+MGD4cYbjTFKAVTzjZtjVi0j37iKM5dFe39cPhaLEVY1HD2+UUHeDbjjjjuqdn74oerxc8+h1vQzFivfuDlm1XLJpYK3/6OtEXgPG/g59zqa/LXfKNMahB7fqCDvBvz111/aAym1pc9AC+5PPmmcUQrgDN+YADNr+fTbDqwbs5xg7qNfWTy8/vo5FwF3RfT4RgV5N6CiL27aOyl8Hv8v9jMYeeNNcN55xhqmME0fNphbS6tW8MDCBxH9+mlPhIfDxo3ON6yB6PGNCvJuQLt27ZASpgW04Qs+51L283TBXKPNUkDFzS9TYHotLVrA5MlV+++/X7VUpoujxzcqyLsB+/fvJzoaknPbVz43/J6uxhmkqGT/fvfq262NRqHlkUfg6qsrGpE7+we3iPN6fKOCvBtw1113kR6XTj8SKp978Bn3H35oBu666y6jTbAbjUKLEDBlCiV4MpOxXPTG3SwNKHaucQ1Aj29UkHcDFixYwF0Fa0jgIuK5iIUPrOOCC4y2SgGab8xCY9Fiuf4Grm0fxzhmkm7pzMfjiykqcqJxDUCPb9RkqFpwlQJlgPYzc80a7XFkJAwfbowdOjHbZCiFe/Ll/6XzmV+Xyv2Zk/MYO959bjyryVB2wlUKlHl/9RVERGg77dvDlVcaaY7iDExXCsAk1KXlra+70Ll5Hh3JZBLv88yxiU6yrGGosgYOxuiyBiX79tH08su1nXvvheBgp9tgL8yWyZeUlNC0aVOjzbALjU3Lb0EZXPLYYNoWp0Pr1pCcrCVRLkh1PSqTNxlhn31WtXPDDcYZoqjBt99+a7QJdqOxabnm/s60ff4RbSc/H+bMcbBVDUePb1SQd3EsFlgY9RZTeZcIrqdg2CijTVKcwWOPPWa0CXajUWp5++2q0iC+vlDsmiNt9PhGBXkX59AhWHl0FOOZyg1EsHS/6o93JcywZF4FjVLLxRfDww9rj1NTq8qGuBh6fKOCvIvzZ1Sp1f6IUc0NskRxNsyw+HUFjVbLe+8BEM9FvPpOS35a63olKtVC3iYmP/EkHdFWmxdYGDjQYIMUCpMhr7qaZ7v+zAAOMif7CSa8n+NOtcvqxPRBXgjxoRAiUgiRJ4Q4KYRYJ4QYYLRdtvLiFb+TSWcy6MTu/wTQwr3WOjA9ycnJRptgNxqrFiGgzYiBlctpRsZ3YPt2R1nWMPT4xvRBHrgR8AdGArcDnkCoEKKVoVbZSmIiAJ3IUl01Lsg111xjtAl2ozFredu3N03QitgM43dK/3StOj56fGP6IC+lvEtKuUhKuV9K+SfwPNAbGGawabZRHuQBqCiTqnAZVq1aZbQJdqMxa+l3URO+ffJ39jCC3xnBzVs+cZBlDUOPbxrdZCghxEVAPHCZlDL2HG28AK8znmoDpBgygee++2DDBu3xiRPQvbtzr29n1GQo16XRayku1hKp48e1Ppz4eLjwQscYWE/UZCgbEUII4Ftg+7kCfDkfAjlnbCkAiYmJTJkyheLi4sppxt7e3hw/fpyAgAAiIyMJCQlhzZo1xMXFMX36dHJzc63aZmVl4e/vz969e1m/fj0bNmwgOjqaOXPmkJ6ebtW2oKCAk3/8AYDFw4Ow2Fh27tzJokWLSE5OtmpbVlbGxIkTOXLkCEuWLGH79u2Eh4cTGBhIfHw8U6dOpaioyOqY1NRU5s2bR2RkJJs2bWLt2rXExsYyY8YMcnJyrNpmZ2fj5+fHvn37WLduHRs3biQqKoq5c+eSlpZm1bawsBAfHx/i4+NZsWIFW7ZsYceOHSxevLiyb9FiseDt7Y3FYmHChAkcPXqUxYsXs2PHDrZs2cKKFSuIj4/Hx8eHwsJCq/OnpaUxd+5coqKi2LhxI+vWrWPfvn34+fmRnZ1t1TYnJ4cZM2YQGxvL2rVr2bRpE5GRkcybN4/U1FSrtkVFRUydOpX4+HgCAwMJDw9n+/btLFmyhCNHjjBx4kTKysqsjvnoo49YtGgRO3fuJCwsjJUrV3Lw4EF8fHwoKCiwapuens6cOXOIjo5mw4YNrF+/nr179+Lv709WVpZV29zcXKZPn05cXBxr1qwhJCSEyMhIAgICOH78uFXb4uJipkyZQkJCAsuXLyc8PJyIiAiWLl1KUlISkyZNorS01OqYlJQUFi5cyK5du9i8eTOrVq3i3XffZdq0aeTn51u1zcjIYPbs2cTExBAcHExQUBAxMTHMmjWLzMxMq7Z5eXn4+voSFxfH6tWrCQ0NZffu3SxYsKCG3SUlJUyePJnExESWLVvGtm3b2LZtG8uWLSMxMZHJkydTUlJS47O2YMECdu/eTWhoKKtXryYuLg5fX1/y8vIq2959991kZmYya9YsYmJiCAoKIjg4mJiYGGbPnk1GRobVefPz85k2cyYnn3hCiwBSkuLtzcKFC0lJSbFqW1payqRJk0hKSmLp0qVEREQQHh7O8uXLSUhIcEiM+O9//1sjRthKo8rkhRD+wL3A9VLKlFrauUQmn5QEYUPfpcepOLp3KuWSY6F4edV5mEtjtkxeYTJSU7UV18rKoFcvOHIEPDyMtqoGKpM/C0KIGcBo4ObaAjyAlLJYSplbsQF5TjGyGn9ES1469Q33spFhmaEkJNR9jMK5NKaiXu5Eg7V0767VhwI4dowjS7bZzygd6PGN6YO80PADHgZukVIeNtomWynIPm2138o9xgM1Kl544QWjTbAbSovGyYdfxYe3uYIYLn5hFJmZdjSsgejRY/ogjzZ88mngX0CeEKJ7+ebyI84Lckqs9lWQdz02bdpktAl2Q2nRiOp4O+/iw16uoER6smK+IT/krdCjpzEE+bFAOyAcOHHGNsZAm2ziiXvzOMTFxHAFO2/4wFWroDZqLrnkEqNNsBtKi8btd3vSrWVVYP9+1j/2MEkXevR42tEOl0RKKYy2oaG0aVZMG/7WdvYlg+ckYw1S1CAnJ8doE+yG0qLh6QlPPVLEj0uy+DdL+He3Q8Bi+xnXAHTpsaMdCntzZtlTV1+EspGSl2f8T3l7obRU8YV/Z6b+NpAmfx+C35vAyW+ga1c7WVd/9OhpDN017kuLFtC8vJRBs2bG2qI4K4MGDTLaBLuhtFTRuo2gyaPlJYgtFli3Tr9ROtCjRwV5V6Z3b+jUSXvcurWxtijOSmhoqNEm2A2lpRqPPFL1ePVq/efTgR49jWoyVEMxao3X06chr8+lFKdmcbpbb84/tssV52XUC7NNhsrLy6NNmzZGm2EXlJZqSAkXXKBNiPL0hLQ06NjRPgbWk+p61GQok7BqFXROjaUXx7kgbRdHjxptkaI63333ndEm2A2lpRpCVGbzKaXd+PGTP/Wfs4Ho0aMyeRswKpMPDYU776za37ULrr7aaZd3CGbL5BXmZvN3cXzyZi67GUkTykg96UGXLkZbpTJ5uyGEGCeEiAP2GHH96jfzT540wgpFbahSAK6JvbQ0GTyQ3YwEwIIHmzeW1HGEY9CjR2XyNmBUJp+dDXP7TKBrbjxdO1kYHrfYyFFcdsFsmXxmZiadKm6OuzlKS01On4YOrYopKNUqA7507wnmBffQfd76Ul2PyuRNQvv2ML7NLJ7je+5pvsXtA7wZWblypdEm2A2lpSbNmsHY2/7mf3gTzo34XznfLuetL3r0qMlQCoUOGvOSea6MPbV8M6cN9ClfKSpCAM5fNUot/6dQGERjXfza1bGrlt69q5be/O03KCy037ltRC3krVAYhLbYmDlQWmrh5pu1v6dPw86d9j23DejRo4K8m1AiPYmJgfR0oy1RnMl5551ntAl2Q2mphVtuqXq8dat9z20DevSoIO/ipJd15Dq20+7EX1x5Jaxfb7RFijPZtWuX0SbYDaWlFsoz+VS6se7HUlJT7Xv6utCjRwV5F6djk2z2cRmFUlvjZI8hI/YV5+LRRx812gS7obScm6MlPbigaTI9SOWhg5MIXe/cqrB69Kgg7+J4CAvD+b1yPyLCQGMUNZg9e7bRJtgNpeXc9OwJJ2XVVNddG5y7JqAePWoylA0YNRkKgPPOw//YA0S1HMUdAU9w6624xLTqhmK2yVCKxsNNFx/j1797ATCsbwa/H+5smC1qMpTJGMdMFnR4lyeecO8Ab0ZUKQDXxBFaXrr3BJMZz6/cwK/PLLD7+WtDlTVwMEZn8hw7Br16QUqKc6/tAMyWyefn59PaJLX+lZY6iIyEq67SHr/6KsyaZd/z10J1PSqTtxNGFyhTuD7z5s0z2gS7obTUwZnDGI8ds//5a0GPHhXka0FK6S+lHAxcZbQtCtfk7rvvNtoEu6G01EHXrlSu2uPkX9V69Kgg72YUF2tj5SdMMNoSBcC+ffuMNsFuKC114OGhDbMBp2fyevSoIO9GfP89dOsGDzwAH38Mf/1ltEWK9u3bG22C3VBabKBXLyRw7KQnocGncdYtTT16VJB3Iy69FHJyqvb9/IyzRaFhljVRQWmxhTXiYTqRyXkc4877mzktodejRwV5N2LYMLj2Wu1x69Zgos+k2/KXiX5OKS1106FnS05RtZh3fLxDLlMDPXpUPXk34+OPtTfWs8+CNoJKYSS333670SbYDaWlbi4aaB0yExKqClQ6Ej16VCbvZtx9N7zxhgrwrsKiRYuMNsFuKC1102twO97hG2YylpD//MgDDzjkMjXQo0dNhrIBNRnKfphtMpSikRERATfcoD1+802YNs0QM9RkKIXCSahSAK6Jw7QYNCFKlTVwMK6eyUdHw9q18NVXzjWtIZgtky8tLcXT0xy3tpQWGyguhubNtcfXXOO0VaKq61GZfCOhoADGj9fKaXh7qwVFjOCbb74x2gS7obTYgJdXVZVAJ3af6tGjgrwbc+gQfPstlJVp+2PHQkaGsTY1Np544gmjTbAbSouNVHTZnDhBfk4ZpaWOu1QFevSoIF8Lrl6gbMgQePvtqv3779fGzyucx/bt2402wW4oLbaxs8WtDOQv2pZm0qa9B7GxDrtUJXr0qCBfC+5QoOzzz7XumqVLYfbsqu5ChXPo06eP0SbYDaXFNpp178hBBpKHdk/p+HGHXaoSPXrMcZelEdOyJfz2GzRRX9eGUFbRV2YClBbb6NzX+udyVpbDLlWJHj0qyJsAFeCN48SJE0abYDeUFtvofHEH/sNc2pNN+/tv4IorRjrsWhXo0aOCvImZPx+GD9f67hWO4aqrXLYnr94oLbbR+qLuzKW8zMAlH8Bljg/yevSoHNCESKmNmf/Pf+DGGyE83GiLzMvq1auNNsFuKC020qtX1WMnDaPUo0dNhrIBV58MVR1/f3j99ar9Fi0gMRG6d3eQjfXAbJOhiouL8fLyMtoMu6C02EheHlS8d2++GbZsccx1zqC6HqdNhhJCtBJCdNBzDoX9eeYZuO22qv1p01wjwJuRqVOnGm2C3VBabKRNm6o6307K5PXoaVAmL4TwBOYDT6F9UUQDY6WUv5/Rpi/QGkiSUuY32EIXwN0yeYDTp+G556B/f22Ypatgtkxe0UgZPFhbmq1lS8jPByGcenm7Z/JCiDeqPfUO0Ar4P2AS4AXsFELcJYR4QAiRCCQAfwKZQoiNQojr6qnDrgghXhNCHBZCFAkhooQQo4y0x9E0a6aNnf/ss7O/HhMDhw871SRToop6uSaO1vJG/gRuIYxRBZv44K1ih14LdOqRUta5ATur7S86S5t7gKNAAbAcmADMBnYBJUAZMNmW69l7A8YAp4GXgEGAL5AP9Lbx+LaAzMnJkU6nVy8pQftrJ06flnLQICmbNJHywQeljIy026nrJCcnRxr2v3QAx44dM9oEu6G02M41XeKlNsRByvtucPx7ubqeis8R0FbWEb9s7ZOv/luk5CxfFhuBrcAPUsonpZT/k1K+KqUcCXQH/ge8LISYaOM17cnbQICUcr6U8i8p5ZtAMjDWAFsMZ/Zs7ZemxQLr1kFamtEWuS8///yz0SbYDaXFdpp6VE1OOn3C8QWj9OixdZx89Y77OCHEJVLK/dWeLz5LW6SUmcAkIcRS4GchxEop5R/1N7f+CCGaAcPQupXOJBS49hzHeKF1QVXQBrR+MKdjsVT9tcP1y8q0laUqaNoUhg61y6ltouJ/aMj/0gH069dPaXFBHK2lqLQAyKUJpcjcFHJzOzvsWlBTT7201ZXqy7N317QGFgJNqj0/G5hdx7kGA/62XNceG9AT7Yvn2mrPfwQcPMcxn5cfoza1qU1trrzV2V3ToBmvUsp8IYQf4CeEeFNKebr8pQloN2RrOzZOCGFErURZbV+c5bkKJgLfnrHfBkhJTk52/oiQgQPhxAno0QMOHNB1qjlztPrzFbzxBnz5pXMHBuTm5nL++edjyP/SAaxfv57Ro0cbbYZdUFpsJ+EFb3JXh1KGJ63m+jJozOUOuxbU1FPxObKFBpc1kFJGCSGKgSVCiBlSyu1SymQbD3dmOYUMtJu+1UeKdwXO2hstpSxG63oCQJRHwbZt2zo/MFUUpmnSpGoCRgN56y344QdtZE3Lltpi4EYtCG7I/9IBDB061BQ6QGmpD1da/kYbPAjc2Vv3Z7Mu9Ohp6I1XAKSUscC/geFCiKVCiLeFEEOEOHduKIR4FthQf1MbRvmvjCioKDZRye2Ac9buchE8PWHWLHj6aUhI0LJ4hT5++eUXo02wG0pLPaiYsyKE9ivbwejRY9NkKCHE01LKpTa0uxy4CRiC9sVwANiONma+A/Aw0FFK+U6DLW4AQogxwBLgVeA34GXgP8AlUsojNhzvdpOhjhwBVywPbrbJULm5uabQAUpLvejVSysk37271p3qYKrrsftkKFsCfHm7vVLK6VLKF6SUzwPrgUsBHyAEuAHYKIRoYcv57IWUcgXwJvApEFNuxz22BHh3ZOVKGDAATJSYuSzTp0832gS7obTYSGkppKZqjyuWAnQwevQ4tUCZEOICtAB7DdACOAb8CuyQLlz6wJ0y+Q0b4MEHtfdh27awYwdceqnjzbQVs2XyikZISgqJ599AK/6h7f030fynFc6uauC8AmX1RUp5WEr5ffkkqWeBGWjdOM850w6zIqU20aliYeHcXPjxR2NtMjuqFIBr4kgtMjmFARykO2m0DFrhlHtbevQYWk9eSnlCShkopfQz0g6zIASsWqUt6A3wwgvw6afG2mR2XnvtNaNNsBtKi20UJ52glKaV+xUFKR2JHj1q0RCT0bw5rF4NM2bA3LlqaUBHs3z5cqNNsBtKi23kJqRb7TsjyOvRo5b/MyFNm1ovGqJwHKNGmaeYqdJiG20ykwjmXlLpTuoL/2PEiH4Ou1YFevSoPE+h0EFSUpLRJtgNpcU2WqQlcS8beZEF/O/9UqesoaxHjwrybkxhITz6qDaDVWEMHh4eRptgN5QWGzl2rOrxmeu9OhA9elSQrwUhxDghRBywx2hbzsYXX2j97yNGgLd31agahfPo4YTZjs5CabGRiqHM7dtDq1pLddkNPXpUkK8FKaW/lHIwcJXRtlTn6FHw9dUel5bCzJna+sIK5xIZGWm0CXZDabEBKasyeSdNhAJ9elSQd1OKiuDaM6rhf/cddFBLqjudhx9+2GgT7IbSYgOZmWQXN8eCcFpXDejTo4K8m9K/P4SFwcaN2oLdjz5qtEWNkzlz5hhtgt1QWmwgJYXb2UxLChi0a+E511C2N3r0OLWsgbviTmUNXB1V1kDh1mzYQKf7RpJFJwDGjQM/A6ZyumxZA4XCbKhSAK6Jo7RkHzpZGeAB+jl+iDygT4+aDKVQ6ODtt9822gS7obTUjWfaMebwMon04/CoZxg6tKdDrlMdPXpUJu9GZGVBSIh2g1/hGsyaNctoE+yG0lI3rU8m8jLzmMSHrPDL4KabHHKZGujRo4K8G7FsGdx1l1Y6eP58KCkx2iLFfffdZ7QJdkNpsQEDJkKBPj0qyLsRixdrf+Pi4LPPVPExV+DPP/802gS7obTYQMXgh+bNoWNHx1zjLOjRo8KEm3C49Hx+/71q/6mnwESz0N2WTp061d3ITVBabKAik+/VC2euFKJHjwrybsIFnskcOqTVh7/gAvj3v422SAHQooVTV7J0KEpL7ZRm51OcU6jtOHG2K+jTo4J8Lbha7ZqLL9bq1SQkwGWXGW2NAuDQoUNGm2A3lJba2fNzJq34h8HsZ8zhScTH2/0S50SPHhXka8FVa9c4ez1Jxbm59dZbjTbBbigttfPHb0WU4clfDGbl0ZF4OnEAuh49KsgrFDr4/vvvjTbBbigttbMrqiqqd25VSN++dr/EOdGjR5U1sAFV1sB+qLIGCndl+4sLCVuQxC5G0mnUJSzd1tswW1RZA5OxnvtJKTNPrW8zoUoBuCaO0HJ9SiCf8SU/cw9LA4rtfv7a0KNHZfI2YGQmn9rjSnqk/gFAnz5aSeEHHnCqCXbFbJl8WVmZaVZUUlpqobRUWyTkn3+gRw/t17UTb45V16MyeRMRXVI1jObIEdD8qnAVpkyZYrQJdkNpqYXoaC3AA9x4o9NHP+jRo4K8ixNbMsBq/4orDDJEcVb+9a9/GW2C3VBaamHbtqrHN9xg33PbgB49Ksi7OC+1Wk4Yt/Bdu095+221+pOrse3MD7+bo7ScncJCOLopruqJG2+027ltRY8eFeRdnI5NsrmFrbzRegE+PkZbo6jOBRdcYLQJdkNpOTthoWX0CVvAhfzNS15LONF+kN3ObSt69Kggr1DooLS01GgT7IbScnbCAk8CkMiFLDr9JK3bOH82oh49KsgrFDpITU012gS7obScnQ0hTSsfX90vgzZt7HZqm9GjR60MpVDoYNiwYUabYDeUlppICWs7vMCGUwPZwL3c++RQu5y3vujRozL5WjC6QFlZGVikKlTjyqxbt85oE+yG0lITkfA3lyQGMZ6p/HrtR4z/yoA0Hn161GQoGzBqMtT69drEpzbk0s4jn7C4nvTv77TLOwSzTYYqKiqiefPmRpthF5SWs+DjA+++qz2ePBnGj9d/zgZQXY+aDGUScstdl0dbUsp6YpLPn6n45ptvjDbBbigtZ+Gnn6oejx5tn3M2AD16VCZvA0Zl8jNnwrhxVfunTmkzq90Zs2XyChOTkQHduoHFAv37w8GDRltUicrkTcLVlxfi3fJrxjOZV5p/b8hdfUXtqKJerok9tASMP8heyyVIMLxglCpQ5mAMK1AWG1u1BFTLllW1M9wYs2XyqampdO/e3Wgz7ILSUsXJk9CjWxkWPBjIX0ydLLlv/GA7Wlg/qutRmbxZOHNdR/Vl7JIEBQUZbYLdUFqqWL20EAta1ccDDKLFkAF1HOFY9OhRQd6VOfNOq5eXcXYozsmQIUOMNsFuKC1V/LE2qfJxt5a53HSrsSWY9ehRk6FcmTMz+WuuMc4OxTnJzMw02gS7obRUMbfked4lixWMweulV/HwMLZrUY8eU2fyQoi+QogAIcRhIUShECJBCPGFEKKZ0bbZxJmZfFGRcXYozklhYaHRJtgNpaWcv/6C3bvpTzyfXL6e8b497WdYA9Gjx+yZ/EC0L7JXgL+BS4F5QCvgXQPtsonIfc2ZwFoy6UTWrl6sT4ALLzTaKsWZXHzxxUabYDeUlnIWLqx6/MILTl8g5Gzo0WPqTF5KuUlK+byUMlRKmSilXA98AzxstG22kJvfhJ94kO2MIq6wHydPGm2Rojpbt2412gS7obQAJSWweLH2uGlTeOop+xmlAz2+MXsmfzbaAVm1NRBCeAFn3uk0ZIR6p07W+5kZEjA+q1BU8cwzzxhtgt1QWqBswyY80tK0nfvvh86d7WhVw9HjG1Nn8tURQlwI/B8wu46mHwI5Z2wpAImJiUyZMoXi4uLKyQne3t4cP36cgIAAIiMjCQkJYc2aNcTFxTF9+nRyc3Ot2mZlZeHv78/evXtZv349GzZsIDo6mjlz5pCenm7Vtk2bQs73TOY2NvMKs0lLDGfnzp0sWrSI5ORkq7ZlZWVMnDiRI0eOsGTJErZv3054eDiBgYHEx8czdepUioqKrI5JTU1l3rx5REZGsmnTJtauXUtsbCwzZswgJyfHqm12djZ+fn7s27ePdevWsXHjRqKiopg7dy5paWlWbQsLC/Hx8SE+Pp4VK1awZcsWduzYweLFi0lOTgbAYrHg7e2NxWJhwoQJHD16lMWLF7Njxw62bNnCihUriI+Px8fHh8LCQqvzp6WlMXfuXKKioti4cSPr1q1j3759+Pn5kZ2dbdU2JyeHGTNmEBsby9q1a9m0aRORkZHMmzeP1NRUq7ZFRUVMnTqV+Ph4AgMDCQ8PZ/v27SxZsoQjR44wceJEysrKrI7x9vZm0aJF7Ny5k7CwMFauXMnBgwfx8fGhoKDAqm16ejpz5swhOjqaDRs2sH79evbu3Yu/vz9ZWVlWbXNzc5k+fTpxcXGsWbOGkJAQIiMjCQgI4Pjx41Zti4uLmTJlCgkJCSxfvpzw8HAiIiJYunQpSUlJTJo0idLSUqtjUlJSWLhwIbt27WLz5s2sWrWKTz/9lGnTppGfn2/VNiMjg9mzZxMTE0NwcDBBQUHExMQwa9YsMjMzrdrm5eXh6+tLXFwcq1evJjQ0lN27d7NgwYIadpeUlDB58mQSExNZtmwZ27ZtY9u2bSxbtozExEQmT55MSUlJjc/aggUL2L17N6GhoaxevZq4uDh8fX3Jy8urbPvII4+QmZnJrFmziImJISgoiODgYGJiYpg9ezYZGRlW583Pz+ezz+Zx3phr+IQvOU4PDlx7LQsXLiQlJcWqbWlpKZMmTSIpKYmlS5cSERFBeHg4y5cvJyEhwSEx4sMPP6wRI2zFLSdDCSE+Bz6ro9kIKeXvZxzTE/gV+FVK+VId5z9bJp9iyASep5+GZcu0x3/9BQMHOvf6dsZsk6EU5uGjV7OYOKcjAJ6U8McfgkuHuGZnR2OYDOUHDKpji61oXB7gtwK/AS/XdXIpZbGUMrdiA/LsrsBWeveuepyYaJgZirOjSgG4JvXVUlAAc76vyusGdMvmkitcJ8Dr8Y1bBnkpZYaU8kAdWxGAEKIXEA5EA89LKS1G2l5vBpwx086FCiQpNF5//XWjTbAbjVlLk7wcvpYfMpC/APjvBy1dYVBNJXp845ZB3lbKM/hwIBltyGQXIUR3IYT7FOhQQd6lWbp0qdEm2I3GrKX5Dwt4pXgG+7mETfdO56mXWznIsoahxzeu83vEMdwBXFS+pVR7zYW+p2vhzCB/4IBxdijOyo033mi0CXaj0WopKYHvvgOgCZI7p94OLR1kWAPR4xtTZ/JSykVSSnG2zWjbbCXPswM+LT/gORZyeYQf69e5V2+T2UlISDDaBLvRaLUsXQpHjmiP774bBg1yjFE60OMbs2fybk+TJjC+wFuriGeByJAMRj/oGmN3FdCsmXtUyLCFRqmltBS+/rpq/+OPHWOQTvT4xtSZvBlo1Qou6lg11TVqp6ph40p069bNaBPsRmPU8uHDB/n17/LaNLfcAtde60CrGo4e36gg7wac1y2FNuRyH0E82OFXo81RnEFUVJTRJtiNxqZl53YLk4Iu4SZ+5QZ+JebJyU6wrGHo8Y1bToZyNoatDFXOgchELrp6IJ6yBAYPhv37nW6DvTDbZKi0tDTTZMCNSYuUcOulaWyN09oILMTGCgZf4pq366rraQyToRoVP4b8gOdVQ7WduDg4dsxYgxSVzJs3z2gT7EZj0nI6/zT9U8LwoBSAR0eddNkAD/p8ozJ5GzA6kwfgk0+gYtbbokXw7LPG2KETs2XyCjfFzw/+7/84wAA+7jKHryNuoP8A1w3y1VGZvJ0QQowTQsQBe4y0w9vbG26/veqJzZuNM0ZhRWMuBeDK1KolNxe+/BKAgRzkx42tXD7A6/GNyuRtwOhMvrCwkBYeHlrt4fx8Sjp0JTs2hS49mzrdFr2YLZMvLCykxZnLNLoxjUbLZ59VBnnGjIHAQOcZ1kCq61GZvMmYOXMmNGvGxis/4lkW0fXUAd56JsNosxSU+8YkNAotx46Bj4/2uGlTmDDBeUbpQI9vVJB3A0aPHg3A3MJnWMyzZNOBoIj2nD5tsGGKSt+YAbNrOX4c3rxlL6f+Kf8F/OqrbrOeph7fqCDvBkRHRwPwyMtVS0Xlnm7B5k1lRpmkKKfCN2bA7Fre/Xcq3x26m/4cIqD1f7F8+rnzDWsgenyjgrwb0KVLFwDue7Q5zZsUcyebWMlj3FYWYrBligrfmAEza9kaWsLyLVrx2Qy6MKvTx8gOHY0wrUHo8Y0K8m6Al5e2mEGHDnB8WTibuJvH+BGvJfMNtkxR4RszYGYtnutW0R+tVLfAwszAjnh4GGFZw9DjGxXk3YAzK9B1ePRW6F5eDj8oCNLTDbJKAY24cqOLY6UlJYVRi19mL5czUXzIG09mcNVI9wp9enzjXkobKTfddFPVjqcnVKzcXloK339viE0KDSvfuDmm1CIlvPIK/PMPXpzmg9fy8P2hq6G2NQQ9vlFB3g1YsmSJ9RMvvFD12M9PC/YKQ6jhGzfGlFoWLICNG7XH3bvDV18ZZ5QO9PhGTYayAaMnQ1ksFpo0qfZ9fM89lP4cyhoe5vcHvmLKugFnP9jFMNtkqLP6xk0xmxZx5Cji8ssgP197MigI7rvPWMMaSHXfqMlQJuPrMxc1KGfTdV9xMfGMYSVTfxrAX38ZYJjirL5xV8yk5e03Z3LZZZLN+SO1J154wW0DPOjzjcrkbcAVM/nfIyUjrqqqt/HivanMD3b99clVJu+6mEXL6dNw7UVpRCVrpXlfaLUCv4S7adHNfd9vKpN3EK5SoGzixIk1nhs+QnDjgFQA2pDLBQd+drZZCs7uG3fFLFr8PjtZGeABjg64Da8u7hvgQZ9vVCZvA0Zn8kePHqV37941nv8lpIzQJwJ4P/tDOpEFERFw/fVOt68+mC2TP5dv3BFTaCktpei6W/lozwNM4206ev3DvsRW9OxptGH6qO4blcmbjPDw8LM+f9udHkyZ1kwL8ACff+40mxQa5/KNO2IKLZ99RvM92/iWdwjp+TyLl3m4fYAHfb5RQd4NuLC2IkpPP11VZCksTNWadzK1+sbNcHstoaFQ3q1h8fDgjtWvcO8jzQ02yj7o8Y0K8m5AcXHxuV/09IQvvqjaf/ttNW7eidTqGzfDrbUcPQpPPaVNfgISX3wRRo402Cj7occ3Ksi7Ael1lS548kkYMQKAv2MLefuuOMpUgUqnUKdv3Ah31fLzumJW3+wHGeVrLNxzD1Emmr0L+nyjgrwbMHTo0NobNGlC/oTv+IgJXMJ+poVdToBfgXOMa+TU6Rs3wh21JCZI/jWmlEcTpzCeyZRecDEsXcrQ4cONNs2u6PGNCvJuwPr16+tsk3vJNczwfIvTaNXqPvrAQlaWoy1T2OIbd8HdtBQXwyM3ZZB9uhUAUxnP7DFboUMHt9NSF3r0qCGUNmD0EEpb196c8uEp3p/UAYB7CSbgpy50G321o82rF2YbQtlo1kV1QeSv25h4Syj/s2iLXF83IJ0te7vQrJn7aakLtcaryfGpWJOyDt78ogPX9j3OUp4iiPvp9v5zUFTkWOMaObb6xh1wKy0HDyIefoiPLBP4gSfp0zaLlVu0AA9upsUG9OhRmbwNGJ3J1wdZWoa47lrYUz5J9+OPXaryntkyeYUBpKdrI2cSE7X9O++k6Mdgmrf2NNYuJ6IyeZPh7e1tc1vh6QHz52tDK0EbN7x7t4MsU9THN66OW2gpLIQHHqgK8JddBitX1gjwbqGlHujRozL5WhBCjAPGoX0ZDjAq+0xLS6Nbt251NzyTzz6DL7/UHvfrR8GOP2jZ3fjM2WyZfIN846K4upaoPWVEvhrAq3+8oj3Rsyfs2gXnn1+jratrqS/V9ahM3k5IKf2llIOBq4y046effqr/QR9/DCNHYkEwLXE0/S6wcPSo/W1r7DTINy6KK2uJ2y+584YCxv7xMu/wDZaWrSE4+KwBHlxbS0PQo0cFeTdg2LBh9T+oaVOyZwdyr0cIbzONtKL2/Ov2k5w+bX/7GjMN8o2L4qpacnMkt4/MJbO4DQDf8g5THv8drrzynMe4qpaGokePCvJuQFpaWoOOazW4D9kXVH0Qdhzqyk9+yfYyS0HDfeOKuKqWtn5f82n+eAQWQBsq+X9+ta+E5qpaGooePSrIuwGnG5h+N20KP4R2pn2zf/CiiIU8x2OzboFTp+xsYeOlob5xRVxSy7ffwscf8wpzWcwzXNX3JBt2d6FVq9oPc0ktOtCjRwV5N0BPBboLLoBVqz3Y3v9FnuN7+PtvrZCTKm5jF9y+cuMZuJyWSZPgnXcqd5+eOoSdf3dFu99YOy6nRSeqCqXJ+fXXX3Udf9t9zRke+jV07qw98fPP8MEHdrBModc3roSraMnIAPnFl/Dhh1VPfvklvPsuHh62ncNVtNgLPXrUEEobMHoyVHZ2Nu3bt9d/oq1b4fbbq7L4776jZOwbNG2q/9S2YrYhlHbzjQvgClr+jpfcOjyHx3PnMYXxCNDmetQzKXEFLfakuh41hNJk+Pn52edEN98M/v4AWBCM/28x9wxLUyNudGA337gARms58JfkxqG5HM1tzze8x2d8AT4+DfrVabQWe6NHT6PJ5IUQXsBu4ArgSillTD2OdZuyBrZQ9OEXPDtpICsZA8DjN5/kh81dbf4prAezZfIKO1FSwoa7ZjB6y3+xoL0RL+mRye74TnXeZG2MqEz+7EwBjhttREOw9xTtpGc+ZVPT+yv3V2/tyK7Fh+x6jcaCmabPG6YlLw/uu497t7zDTF4D4Mrz0wnf2/AAbya/gE49UkrTb8DdwF/AYEACQ+p5fFtA5uTkSCPIzs62+zm3hJbI5k2KZFOK5WoekrJjRyljYux+nerk5ORII/+X9sYRvjEKQ7ScOCHllVdKqS3cJ6WXl5w/9nd56pS+05rJL1LW1FPxOQLayjril+kzeSFEN2Ae8G/ApuWShBBeQoi2FRvQxpE21sXixYvtfs6bb/dk9UoL6wZ9xMOshawsuPVW2LvX7tcyM47wjVE4U0tZGRT9eRCuuQb++EN7skMH+OUXXpw5DL33TM3kF9Cnx9RBXgghgEXAbCnl7/U49EMg54wtBSAxMZEpU6ZQXFxc+fPJ29ub48ePExAQQGRkJCEhIaxZs4a4uDimT59Obm6uVdusrCz8/f3Zu3cv69evZ8OGDURHRzNnzhzS09Ot2hYUFODj40Pfvn1ZuXIlYWFh7Ny5k0WLFpGcnGzVtqysjIkTJ3LkyBGWLFnC9u3bCQ8PJzAwkPj4eKZOnUpRUZHVMUOvy+Hkq73Jv+wyTXVmJqU33cTyDz4gJyfHqm12djZ+fn7s27ePdevWsXHjRqKiopg7dy5paWlWbQsLC/Hx8SE+Pp4VK1awZcsWduzYweLFi0lO1mbcWiwWvL29sVgsTJgwgaNHj7J48WJ27NjBli1bWLFiBfHx8fj4+FBYWGh1/rS0NObOnUtUVBQbN25k3bp17Nu3Dz8/P7Kzs63a5uTkMGPGDGJjY1m7di2bNm0iMjKSefPmkZqaatW2qKiIqVOnEh8fT2BgIOHh4Wzfvp0lS5Zw5MgRJk6cSFlZmdUxgwYNYtGiRezcuZOwsDBWrlzJwYMH8fHxoaCgwKpteno6c+bMITo6mg0bNrB+/Xr27t2Lv78/WVlZVm1zc3OZPn06cXFxrFmzhpCQECIjIwkICOD48eNWbYuLi5kyZQoJCQksX76c8PBwIiIiWLp0KUlJSUyaNInS0lKrY1JSUli4cCG7du1i8+bNrFq1ij59+jBt2jTy8/Ot2mZkZDB79mxiYmIIDg4mKCiImJgYZs2aRWZmplXbvLw8fH19iYuLY/Xq1YSGhrJ7924WLFhQaXd2Ngzr/SfPD9+HTEoC4J9OnYj09WWbxcKyZctITExk8uTJlJSU1PisLViwgN27dxMaGsrq1auJi4vD19eXvLy8yraHDh0iMzOTWbNmERMTQ1BQEMHBwcTExDB79mwyMjKszpufn8+0adM4cOAAq1atYvPmzezatYuFCxeSkpJi1ba0tJRJkyaRlJTE0qVLiYiIIDw8nOXLl5OQkOCQGNGtW7caMcJm6kr1XXEDPkf7qVLbNhx4A9gBeJQf1xcbumsAL7QumoqtFwZ2MaxZs8axF8jOlvLqqyt/Mpe2aS/93zwkT5+2/6XM1l3jcN84EWdo+SvOIvt3zqjsnZnI+1JecYWUx47Z9Tpm8ouUNfU0hu4aP2BQHVsscAswEigWQpQCf5cf/7sQ4vtznVxKWSylzK3YgDyHKbEBhy9j1q4dhIRUVq18Oe8bxvlezOiRaeQZqtz1MdMScw7XUlBA1hufk5TRuvKprz0/JX3tdq1ssB0xk19Anx63XEpFSpkBZNTVTgjxBvDxGU/1BEKAMWjDKd2CTp06Of4i7drBL78w/rJNLDj8CACbortx//ATbD3QAyEcb4I74hTfOAmHaomLgzFjuDY2llkk8yIL6Nv+FD9tbUeXC+yfa5rJL6BPj7tm8jYhpTwqpYyt2ICKcYIJUsoUI22rDzExMc65UKtW3On/AK09CwHwpIRPDj2N+PQTsFicY4Ob4TTfOAGHaJESFi6EESMgNhaAF1qvYuYrMUTGd+DyIY4JQWbyC+jUU1d/jpk2bOyTP8txhg6hPHHihFOvF/17mezZKlsu4pnKfnr50ENS5uXpPrfZ+uSd7RtHYm8tPwX+IzMefaXqPQRSXnqplPv32/U6Z8NMfpGypp7G0CffIKSUSVJKIesx29UVmD9/vlOvd+WwJhw43pZnvx0CTcrfImvXwnXXQfloCIWGs33jSOylJT8fxj6WwQNPtOT5H++hck79yy9rC8wPHmyX69SGmfwC+vQ0mrIGejBbWYN6sWkTPPEE5OQAkN/hfD64bhtfLOpLQ7oJVVkDk1NayhNDD7FiX1Ug9/H6kLe/HwJjxhhnl8lQZQ1MhqFTtO+6C3bvhosvRgIvnZqCf3BfruyXTUR4qXF2uQhmmj6vW0tcHFxzDV/se4jmFFY+nf2f95we4M3kF9CnR2XyNmB0Jl9UVETz5s2dfl0rTp3C94Y1vBX7YuVTA1sksS/Ggmf/fjafxmyZvEv4xk40WEtpqVYt8tNPqShp+q14m+/afEzA8lbcdk8zO1taN2byC9TUozJ5kzFjxgyjTYAOHbh9+Qv075IFQFNOs7TwETyHXg7z52u31RohLuEbO1FfLRkZsNU/DoYP18oBV9SsHjiQ/25/nNiUDoYEeDCXX0CnnrruzKrN+NE1hw4dMuS6ZyMvT8rn702VUzpOtB41cf/9Uqam1nm82UbXuJJv9GKrlrIyKed/lyc7euXJdpySqXTV3gNCSPnee1IWFDjY0roxk1+krKlHja4xGVFRUUabUEnr1rAguBvvHh4HL71U9UJQEAweTMSHG9kf23iyelfyjV5s0lJWRtAbm3npv63JKm5NDu15l2/giivgt99gyhRwgdmmZvIL6NOjgnwtCCHGCSHigD1G2tG9e3cjL39WRNs2MG8e/PQTdO0KQHZWGU9MuoIhl5fxzvNZ5NbaU2gOXNE3DaVOLaGhcOWV3O9/J0OpCjp/dL+b/PDf4eqrHWyh7ZjJL6BPjwrytSCl9JdSDgauMtIOT08Xrj4xejTs2wdPPsm7fMNxelEqPfl2UUfmPrgRs0d6l/ZNPTmbFinR/HvXXXDnnbBvH02Q+PAOLT2KmPxRDtFHOtO6vWv9H8zkF9CnRwV5N+Dw4cNGm1A7XbtS8v0PpF01uvKpi4jn/7Y+BP37Q0BA1eLhJsPlfVMPztSSmQkfv57NzT0PIK8YohWwq2D4cG769UuOpDZn/IR2NDPm3mqtmMkvoFNPXZ32ajP+xmtSUpIh160vFouUP60skn3bZcqfPe+zvjE7ZIiUISEyKzPbVDde3cU3tlChJWjOMdmmaUGl637ifu1B795SLlum3Xl1cczkFylr6lE3Xk3GDz/8YLQJNiEEjH7Mi4MnO3LXwe/gkUeqXoyJgTvv5F8XacU/ExONsdHeuItvbGHTd9/BM88w5NWRFJdUhYbPm3yFnDQZDh6Ef/2rqtSFC2Mmv4BOPXV9C6jN+Ey+tLTUkOvahfDwyjU8f2WUBC0DEWTJue8e0NJ/N8atfSOlLDltkXLnTikff1xamjSp/OU1jhkSpLyoY4b8fma+OyTvVri7X6pTXY/K5E3GxIkTjTah4dx4I/z+O3J5IB+28LV66aZv7oORI2HVKm3WpBvijr4pK4N1q0q4eXAa/3feGrj2Wli5ElFRTrpjRz54z8L3swr4K60Tz4xt5Q7JuxXu6Jfa0KNHlTWwAaPLGpiF8LAyxr98hMjEC3mYAFZTVSKBCy6At94i54FnaNq5HS1bGmenqUlK4on78lmx/1IAWvIPKZxHB7KhSxd45x147TVoY+ja9Yo6UGUNTIZZii3ddKsHm6M7A/DhFy21CTQVHD4Mb7zB5Avncl6Hf/jvmFT+iHb9BMQtfFNUBIGBcPvt0K8fj+7/vPKlAloxv+ensHAhE8eOhfffN0WAdwu/1ANdeurqz1Gb8X3yR48eNeS6jsCqrIHFImVoqJR33CElyEK8ZGdOVo7quK5ltJQzZkiZnm602efEFX1TUiLlhvWl8tk7T8jCl9+QskMHeeZIpxI8ZG+SZPMmRfKle4/L2H3afRFX1NJQzKRFypp6VJ+8yQgLCzPaBMcghJZdhoTAn3+y8pY5ZNCl8uVnC2bC//0f9OgB994Ly5ZBXh6FhbWc08m4lG/Kyvjr+z30apvLvaM9+D6kO0Fzj8OpU1Vt+vXD0/sLVvzUguQ0L+YF9+CSS7UFfF1Ki07MpAX06THXtDCT0r9/f6NNcDyXX86jQZdT+n0xAd9m80diOx63rNReKy2FjRth40bKmjbnwiYp9D+/iPvHtOSRlzrQt69xZhvpG4sFmuScgl9+0b4og4Ppl3aKgjPWuF/Cv3mseTA8+ii8+CLccAM0acLIs5zPTO8zM2kBfXpUkHcDCl0pdXUgLVvCC2O9eGFsN06ehHZp22HJEq0/OTkZgB0lIzhBJ078Db9OgK5LPqbvs03gttu02ileXk612Zm+KS2FRQssRKzLZNtvnrzTfgGvHx1vtci6F3AXm/iRx2gqSmh59eVYfk6jSfu6BwyY6X1mJi2gT48K8rUghBgHjMPgG9SZmZlGXt4QunYFul6mVTWcNAl27IAVK1j9/VDIr2p3x9F58NVJ+OorrfrhddeRN/J2/m/301x/f3tG3tySQYPAw8MxdjrcN3l52spcO3bgsX0H/wtbykmpFYSLyD6P16kK8DRvDnfdxSuDOnJL50LGPNeCjh372nwpM73PzKQFdOqpq9NebcbfeD1w4IAh13UEeuvJ79xhkePGpMve7U7JoS3jrG4oVmyh3Gb11ObbJ2s3cLdskTItTUqp3fO1xzwsu/nGYpFfjc+VD193Qg7ski4/HvSjlP37azXazxDzCKsqd3twTFoGDpLyzTel/PlnKf/5xzW0uABm0iJlTT31ufGqMnk3IDg4mAEDBhhthktwzbWCa67tzAwJp061h6JjWp/0li3alpxMBKOsjhm++WvYnFP1ROfO7O0zmuv+9Kdfp1wuOr+ISW+dpP+obtCzZ2Xab7FASUntPUC2+mbJEjh+uJi0wwWMuvAYD/X5A+Ljq7a//2ZFTgSxXAbAn+lNgUM1zjOq7V5+Kbyb6wZmcsO9bSn5Is5uBcLM9D4zkxbQp0dNhrIBoydDFRQU0NIks4McusarlJCYyEdvFTAz5EJyTrfkYuI5RM2bVmt4iEdYU7m/n8EM5i8twHfuDJ07c7TVIPrsWUVLz2JaeJbww70/cMfAo1q3UPPmICU5uSXcPP95ikubUFTiycfXhPF8ny1aieWcHG1LS6P73xGkyW4AvIY//rxew6YxBLISbcHrfiSQ4HUJXH45DBsG118P111HUbc+NG0mHNL9ZKb3mZm0QE099ZkMpTJ5N+Dbb7/l448/NtoM10cIuPBCvl4PX5XBX39B5one0OY32LsX9u+v3BJSL7Q6tCfHtQdlZZCWBmlpZJV/PApKvSgo9UKuXg2EWh3XCg/+4MPK/Yyf9wCza5jWjVTS0IJ8xV8ru/v04QrPf4jJPMngfkVcNrwNckY+oqn1R9SRS1Ob6X1mJi2gT4/K5G3A6EzeTDg0k68Hv67PYf2KQhLiy0g54UHkQxMRR49oo3gyMiAjg60FV3ELWyuPCeMWq/0KPCjFgpZaf8knfEK12Ylt23Jn6QZCC66nfdN/uPvCg/zwn3C46CK4+GLo18/po4IU7k19MnkV5G3A6CDv7e1tmqzEVYK8LSQdKOLHpUVknSyluKCM1+5P5sJO2VBYqJUKEIKVa9bw0/GpiCbg1QweGJXF6LtLoG1baNdO++vlxalT2hBRV47lZnqfmUkL1NSjgrydMTrIp6en06VLl7obugHuFORtwUy+UVpcl+p6VIEyk7FmzZq6GykMwUy+UVpcFz16VJB3A0aMGGG0CYpzYCbfKC2uix49Ksi7ASdOnDDaBMU5MJNvlBbXRY8eFeTdgLKyMqNNUJwDM/lGaXFd9OhRQd4N6GtkmUVFrZjJN0qL66JHjwrytSCEGCeEiAP2GGlHRESEkZdX1IKZfKO0uC569KghlDZg9BDKrKwsOnbs6PTrOgKzDaE0k2+UFteluh41hNJkzJw502gTFOfATL5RWlwXPXpUJm8DRmfyZsJsmbxCYQQqkzcZZlt53kyYyTdKi+uiR4/K5G3A6Ew+NzfXNFmv2TJ5s/lGaXFNqutRmbzJWLRokdEmKM6BmXyjtLguevSoIO8G3HbbbUaboDgHZvKN0uK66NHTKIK8EOJeIcRuIUShECJDCOFW1YsOHDhgtAmKc2Am3ygtrosePaZfGUoI8QgwD/gI2AIIKF9I001o1aqV0SYozoGZfKO0uC569Jg6yAshPIHvgPeklAFnvHTQIJMahJkmdZgNM/lGaXFd9Ogxe3fNUKAXYBFC/CGEOCGE+FkIcYnRhtWHvXv3Gm2C4hyYyTdKi+uiR4/Zg3y/8r+fA97AfcAp4FchxDm/GoUQXkKIthUb0MbhltbC3XffbeTlFbVgJt8oLa6LHj1uGeSFEJ8LIWQd23Cq9E2QUq6WUkYBzwMSeKyWS3wI5JyxpQAkJiYyZcoUiouLKycneHt7c/z4cQICAoiMjCQkJIQ1a9YQFxfH9OnTyc3NtWqblZWFv78/e/fuZf369WzYsIHo6GjmzJlDenq6VduCggJ8fHyYPHkyK1euJCwsjJ07d7Jo0SKSk5Ot2paVlTFx4kSOHDnCkiVL2L59O+Hh4QQGBhIfH8/UqVMpKiqyOiY1NZV58+YRGRnJpk2bWLt2LbGxscyYMYOcnByrttnZ2fj5+bFv3z7WrVvHxo0biYqKYu7cuaSlpVm1LSwsxMfHh/j4eFasWMGWLVvYsWMHixcvJjk5GQCLxYK3tzcWi4UJEyZw9OhRFi9ezI4dO9iyZQsrVqwgPj4eHx8fCgsLrc6flpbG3LlziYqKYuPGjaxbt459+/bh5+dHdna2VducnBxmzJhBbGwsa9euZdOmTURGRjJv3jxSU1Ot2hYVFTF16lTi4+MJDAwkPDyc7du3s2TJEo4cOcLEiRMpKyuzOmbatGksWrSInTt3EhYWxsqVKzl48CA+Pj4UFBRYtU1PT2fOnDlER0ezYcMG1q9fz969e/H39ycrK8uqbW5uLtOnTycuLo41a9YQEhJCZGQkAQEBHD9+3KptcXExU6ZMISEhgeXLlxMeHk5ERARLly4lKSmJSZMmUVpaanVMSkoKCxcuZNeuXWzevJlVq1YxefJkpk2bRn5+vlXbjIwMZs+eTUxMDMHBwQQFBRETE8OsWbPIzMy0apuXl4evry9xcXGsXr2a0NBQdu/ezYIFC2rYXVJSwuTJk0lMTGTZsmVs27aNbdu2sWzZMhITE5k8eTIlJSU1PmsLFixg9+7dhIaGsnr1auLi4vD19SUvL6+y7TPPPENmZiazZs0iJiaGoKAggoODiYmJYfbs2WRkZFidNz8/n2nTpnHgwAFWrVrF5s2b2bVrFwsXLiQlJcWqbWlpKZMmTSIpKYmlS5cSERFBeHg4y5cvJyEhwSExwtvbu0aMsBW3nAwlhOgMdK6jWRJwDdrN1lFSyu1nHL8b+EVK+b9znN8LOHPJ5TZAilkm8BiJ2SZDKRRGYPrJUFLKDCnlgTq2IiAKKAYGVBwrhGgK9AWO1HL+YillbsUG5DlYUq2YbYq2mTCTb5QW10WVNagFIYQv8CjwAlpgfw+4HxgopTxl4zkMLWtQXFyMl5dX3Q3dALNl8mbyjdLiulTXY/pMvp68BwQCS4BIoA9wi60B3hX47rvvjDZBcQ7M5BulxXXRo8f0mbw9qMjkk5OTDck+ExMT6devX90N3YDc3FzOP/98jPpf2hsz+UZpcV2q66n4HGFDJq+CvA0IIXpRPsJGoVAoXIjzpJTHamuggrwNCCEE0JOz34DdA1xVj9PVt30btC+Y885xfXtdx1nHNESPmbQ05Dpm0uKMY8ykBc6tpw1wXNYRxE1d1sBelP8Tz/ptKYSw1PVzSWf7iod5jryOs45piB4zaWngdUyjxRnHmElLefuKh9X12HSOxnDj1dH4O7h9Q2nIdZx1jDOu4apaGnIdM2lx5jHOuIaraqlEdde4OBU3fbHhBos7YCY9SotrYiYtoF+PyuRdn2Lgi/K/ZsBMepQW18RMWkCnHpXJKxQKhYlRmbxCoVCYGBXkFQqFwsSoIK9QKBQmRgV5hUKhMDEqyLsJQoi+QogAIcRhIUShECJBCPGFEKKZ0bbZihDitXL7i4QQUUKIUUbbVF+EEB8KISKFEHlCiJNCiHVCiAF1H+n6lGuT5ZVb3RIhRC8hxFIhRKYQokAIESOEGGa0XfVFCOEphPA+4/OeKIT4VAhR75itZry6DwPRvpRfAf4GLgXmAa2Adw20yyaEEGMAX+A1YAeajp+FEIOllEeNtK2e3Ig2mSUS7fMzAQgt1/GPoZbpQAgxAngZcNvFUYUQHdDeW1uBu4GTwIVAtoFmNZT3gVeBZ4H9wHBgIdp4+XqVpFRDKN0YIcR7wFgppcuX2ytfjStaSjn2jOf+AtZJKT80zjJ9CCG6oAWTG6WU24y2pyEIIVoD0WhfwB8DMVLKNw01qgEIISYB10kp3e4XYnWEEMFAmpTyxTOeWw0USCn/XZ9zqe4a96YdkGW0EXVR3qU0DAit9lIocK3zLbIr7cr/urwfasEf2CCl/MVoQ3QyGvhdCLGqvCvtDyHEf4w2qoFsB24VQvQHEEJcAVwPbKzviVR3jZsihLgQ+D/gHaNtsYHOgAeQVu35NKC7882xD+XVSb8FtkspY422pyEIIZ4AhgIjjLbFDvQDxqL55Gu0So/ThRDFUsrFhlpWfyajJRAHhBBlaJ+f/0kpl9f3RCqTNxghxOflN7tq24ZXO6YnsAlYJaWcb4zlDaJ636A4y3PuhB9wOfCk0YY0BCHE+Wj9u0+Xr4ns7jRB6xL8SEr5h5RyDtp9q7F1HOeKjAGeBv6F9iX8LPCuEOLZ+p5IZfLG44e2PGFtJFU8KA/wW4Hf0G6UuQMZQBk1s/au1Mzu3QIhxAy07oEbpJTuuqDMMDQfRJ1RztYDuEEI8TrgJaUsM8q4BnACiKv23F/AIwbYopepwCQpZUVs2CeE6AN8CHxfnxOpIG8wUsoMtCBYJ+UrVG0FooDnpZQWR9pmL6SUp4UQUcDtwNozXrod+MkYqxpGeRfNDOAh4CYp5WGDTdJDGHBZtecWAgeAyW4W4EEbWVN9OGt/4IgBtuilJVD9811GA3pfVJB3E8oz+HDgKNqQyS4V2ZeUMtU4y2zmW2CJEOJ3qn6F9AZmG2pV/fFH+wn9AJAnhKj4dZIjpSw0zqz6I6XMA6zuJQgh/gEy3fQewzRgpxDiI2AlWp/8y7jPL94zCQL+J4Q4ijaE8krgbWBBfU+khlC6CUKI59CyrBpIKcXZnnc1hBCvAeOBHmjB5S13G3YohDjXB+Z5KeUiZ9riCIQQ4bjpEEoAIcR9wETgYuAw8K2Ucp6xVtUfIUQb4Cu0X4xdgePAcuBLKeXpep1LBXmFQqEwL2p0jUKhUJgYFeQVCoXCxKggr1AoFCZGBXmFQqEwMSrIKxQKhYlRQV6hUChMjAryCoVCYWJUkFcoFAoTo4K8QqFQmBhVu0ahcAJCiH8D42ppEiil9HWSOYpGhCproFAoFCZGddcoFAqFiVFBXqFQKEyM6pNXKJxA+VJ7rwLNgPbAL1LKFYYapWgUqCCvUDgYIcRY4E3gUSnlPiFECyBMCHG5lPJ/5W1GAiVSyigDTVWYENVdo1A4kPK1UqcD/5JS7gMoX0FqCvCBEKJiubrngWRjrFSYGRXkFQoHIYQYiLYgc8BZMvQ9aJ+/h4UQHkAnKeVJZ9uoMD8qyCsUjuMdoDlnX8c2vfxvX+AFYImTbFI0MtQ4eYXCQQghTgFFUsoe53hdAquBVsA9Un0YFQ5A3XhVKByAEKIT2iiajXU0vQe4TgV4haNQ3TUKhWMoKf9bWz+7BIKklH84wR5FI0UFeYXCAUgpc4EYoPPZXhdCvAycpvwzKIRo6jTjFI0KFeQVCsfxFnCjEGJIxRNCiOFCiAAgD5gH9BdCCOCH8vHzCoVdUTdeFQoHIoQYDrwGlJVvMcAyKWWeEKIN4AO0AOZIKbcbZqjCtKggr1AoFCZGddcoFAqFiVFBXqFQKEyMCvIKhUJhYlSQVygUChOjgrxCoVCYGBXkFQqFwsSoIK9QKBQmRgV5hUKhMDEqyCsUCoWJUUFeoVAoTIwK8gqFQmFiVJBXKBQKE6OCvEKhUJgYFeQVCoXCxKggr1AoFCbm/wHAKhXVeImuowAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = shadow_plot(1, pi/2, fill=False, number_colors=1, color='red',\n", " legend=False) + cardioid\n", "g1.axes_labels([r\"$\\bar{\\alpha}$\", r\"$\\bar{\\beta}$\"])\n", "g1.set_axes_range(-3, 8, -6, 6)\n", "g1.save('gik_shadow_cardioid.pdf')\n", "g1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Radial polynomial $\\mathcal{R}(r)$ for $a=m$ and $\\ell = 2m$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generic form of $\\mathcal{R}(r)$:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, {\\ell}, q, r \\right) \\ {\\mapsto} \\ r^{4} - a^{2} q + {\\left(a^{2} - {\\ell}^{2} - q\\right)} r^{2} + 2 \\, {\\left({\\left(a - {\\ell}\\right)}^{2} + q\\right)} r\n", "\\end{math}" ], "text/plain": [ "(a, l, q, r) |--> r^4 - a^2*q + (a^2 - l^2 - q)*r^2 + 2*((a - l)^2 + q)*r" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l = var('l', latex_name=r'\\ell')\n", "q = var('q')\n", "R(a, l, q, r) = r^4 + (a^2 - l^2 - q)*r^2 + 2*(q + (l - a)^2)*r - a^2*q\n", "R" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Specialization to $a=m$ and $\\ell = 2m$:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( q, r \\right) \\ {\\mapsto} \\ r^{4} - {\\left(q + 3\\right)} r^{2} + 2 \\, {\\left(q + 1\\right)} r - q\n", "\\end{math}" ], "text/plain": [ "(q, r) |--> r^4 - (q + 3)*r^2 + 2*(q + 1)*r - q" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1(q, r) = R(1, 2, q, r)\n", "R1" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(r^{2} - q + 2 \\, r\\right)} {\\left(r - 1\\right)}^{2}\n", "\\end{math}" ], "text/plain": [ "(r^2 - q + 2*r)*(r - 1)^2" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1(q, r).factor()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(r + 3\\right)} {\\left(r - 1\\right)}^{3}\n", "\\end{math}" ], "text/plain": [ "(r + 3)*(r - 1)^3" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1(3, r).factor()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g0 = plot(R1(1, r), (r, 0, 2), color='blue', thickness=2, \n", " legend_label=r'$q = m^2$',\n", " axes_labels=[r'$r/m$', r'$\\mathcal{R}(r)/m^4$'],\n", " frame=True, gridlines=True)\n", "g0 += plot(R1(3, r), (r, 0, 2), color='red', thickness=2,\n", " legend_label=r'$q = 3 m^2$') \n", "g0 += plot(R1(5, r), (r, 0, 2), color='violet', thickness=2,\n", " legend_label=r'$q = 5 m^2$')\n", "g0 += line([(1, -2), (1, 2)], thickness=2, color='black')\n", "g0 += point((1, 0), size=60, color='red', zorder=100)\n", "g0 += point((sqrt(2) - 1, 0), size=60, color='blue', zorder=100)\n", "g0 += point((sqrt(6) - 1, 0), size=60, color='violet', zorder=100)\n", "g0 += line([(1, -0.9), (3, -0.9)], color='red', thickness=2, \n", " linestyle=':')\n", "g0 += line([(1, -1), (3, -1)], color='blue', thickness=2, \n", " linestyle=':')\n", "g0 += line([(sqrt(6) - 1, -0.8), (3, -0.8)], color='violet', \n", " thickness=2, linestyle=':')\n", "g0.set_legend_options(handlelength=2)\n", "g0.set_axes_range(ymin=-1, ymax=1.5, xmax=2)\n", "g0.save('gik_R_a_1_l_2m.pdf')\n", "g0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing the critical curves at the same inclination angle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\theta_{\\mathcal{O}} = \\frac{\\pi}{2}$" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 2.34729637880682 rmax : 3.53208885091707\n", "rmin_col : 2.3472963553338606 rmax_col : 3.5320888862379562\n", "rmin : 1.00000001000000 rmax : 3.99999996000000\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "th_obs = pi/2\n", "title = r'$\\theta_{\\mathscr{O}}={\\pi}/{2}$'\n", "g1 = shadow_plot(0, th_obs, number_colors=1, color='purple', \n", " legend=r'$a=0$', fill=False) \n", "g2 = shadow_plot(0.5, th_obs, number_colors=1, color='peru', \n", " legend=r'$a=0.5\\, m$', fill=False, plot_points=500) \n", "g3 = shadow_plot(1, th_obs, number_colors=1, color='red', \n", " legend=r'$a=m$', fill=False, plot_points=500)\n", "g = g1 + g2 + g3\n", "g.axes_labels(g1.axes_labels())\n", "g.set_axes_range(-7, 7, -6, 6)\n", "g.save('gik_shadow_comp_th90.pdf', title=title)\n", "show(g, title=title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\theta_{\\mathcal{O}} = \\frac{\\pi}{4}$" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 2.48552158277147 rmax : 3.33625142631788\n", "rmin_col : 2.3472963553338606 rmax_col : 3.5320888862379562\n", "rmin : 1.05826009412625 rmax : 3.55486581066046\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "th_obs = pi/4\n", "title = r'$\\theta_{\\mathscr{O}}={\\pi}/{4}$'\n", "g1 = shadow_plot(0, th_obs, number_colors=1, color='purple', \n", " legend=None, fill=False) \n", "g2 = shadow_plot(0.5, th_obs, number_colors=1, color='peru', \n", " legend=None, fill=False, plot_points=500) \n", "g3 = shadow_plot(1, th_obs, number_colors=1, color='red', \n", " legend=None, fill=False, plot_points=500)\n", "g = g1 + g2 + g3\n", "g.axes_labels(g1.axes_labels())\n", "g.set_axes_range(-7, 7, -6, 6)\n", "#g.save('gik_shadow_comp_th45.pdf', title=title)\n", "show(g, title=title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\theta_{\\mathcal{O}} = \\frac{\\pi}{6}$" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 2.59373553480987 rmax : 3.20003297615050\n", "rmin_col : 2.3472963553338606 rmax_col : 3.5320888862379562\n", "rmin : 1.50000001500015 rmax : 3.23205077524837\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "th_obs = pi/6\n", "title = r'$\\theta_{\\mathscr{O}}={\\pi}/{6}$'\n", "g1 = shadow_plot(0, th_obs, number_colors=1, color='purple', \n", " legend=None, fill=False) \n", "g2 = shadow_plot(0.5, th_obs, number_colors=1, color='peru', \n", " legend=None, fill=False, plot_points=500) \n", "g3 = shadow_plot(1, th_obs, number_colors=1, color='red', \n", " legend=None, fill=False, plot_points=500)\n", "g = g1 + g2 + g3\n", "g.axes_labels(g1.axes_labels())\n", "g.set_axes_range(-7, 7, -6, 6)\n", "g.save('gik_shadow_comp_th30.pdf', title=title)\n", "show(g, title=title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\theta_{\\mathcal{O}} = 0$" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 2.88260669342186 rmax : 2.88382889826327\n", "rmin_col : 2.3472963553338606 rmax_col : 3.5320888862379562\n", "rmin : 2.41250630313641 rmax : 2.41592046802216\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "th_obs = 0.001\n", "title = r'$\\theta_{\\mathscr{O}}=0$'\n", "g1 = shadow_plot(0, th_obs, number_colors=1, color='purple', \n", " legend=None, fill=False) \n", "g2 = shadow_plot(0.5, th_obs, number_colors=1, color='peru', \n", " legend=None, fill=False, plot_points=500) \n", "g3 = shadow_plot(1, th_obs, number_colors=1, color='red', \n", " legend=None, fill=False, plot_points=500)\n", "g = g1 + g2 + g3\n", "g.axes_labels(g1.axes_labels())\n", "g.set_axes_range(-7, 7, -6, 6)\n", "g.save('gik_shadow_comp_th00.pdf', title=title)\n", "show(g, title=title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparing the critical curves at the same value of $a$" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rmin : 1.00000001000000 rmax : 3.99999996000000\n", "rmin_col : 1 rmax_col : 4.0\n", "rmin : 1.50000001500015 rmax : 3.23205077524837\n", "rmin_col : 1 rmax_col : 4.0\n", "rmin : 2.41404287406783 rmax : 2.41438424713942\n", "rmin_col : 1 rmax_col : 4.0\n" ] }, { "data": { "image/png": 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