{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "##内容索引\n", "1. 利萨如曲线 --- 使用标准三角函数绘制\n", "2. 绘制方波 --- 利用无穷傅里叶级数表示\n", "3. 绘制锯齿波和三角波" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from matplotlib.pyplot import plot\n", "from matplotlib.pyplot import show\n", "import matplotlib.pyplot as plt\n", "import matplotlib.gridspec as gridspec" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##1. 利萨如曲线\n", "在NumPy中,所有标准三角函数如sin、cos、tan等均有对应的通用函数。利萨如曲线(Lissajous curve)是一种很有趣的使用三角函数的方式。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "利萨如曲线由如下参数方程定义:\n", "- x = A sin(at + π/2)\n", "- y = B sin(bt)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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h9V+kmhDIT/1XzoQ9TBPZczPAc14UDzOKGgZ1ZBN53ed0lZRh6oGSKj5DmfSP\n1HKPE0ESRTaswzs84SeC1RvpEZ8BO9s/B8SBv02GHgyootUEZK1frOy39ZBv9RVpcA0p4bMY0n8X\nSidWrFDlm/5oJEa/hHSRLe07HhH/TZwLK7gbtlPHOUe4qx9279Fi7rJN4L4mSuM9GxkUKzpEoMRp\npyM14V10kOA5pxGHIk5+n7Lf+qJ06DNRtbSsbBLdnYF8AXdtRZlKq+r1K/TxKtjQzkD4I3m3IJ37\nl86xXIH055kH71RYNN2RC+kMsF3yHtMGcVoQibmzkGF2Ff9+UYrF2f9EjGIUHelCgWX3UxJgRDFA\n7kPkqbJjZzjsKuA+EGWB/Qp5BA327xdGtpHZSD3YshJsHfxWQ04fNzsDsyWS2P5EzADChODpDnYj\ncjxYGamRN474bCGT8cKdgfBHNsQgX3tzzrPpgtFNTuCqvoAMVX8amPd4JoDTPMgl1kquK0mhVm0r\nXqg+6p9KcH+fDpgSo0Hc568w91d1knU9J1JPFfDaIWd4ujnxN7DzYjy3iDNhoRHC32pJ2laOcpMn\nP9rTP84G/p4aRNHaAsCcKGOmAQeGQJ98QWq8eZrZ1VA64G+Br4D/A5YBFssRtExaCMwJbA1sAHwM\njEOJw7ZBSdI6e5sPWBr4Dvga+CuwLrBeCC2Z0TdS83W9C8JlFvBPoL9/n0szZfCc7R+3CoF5Iz66\nMvChWWPZajsc4Q+B7sBNwHLAPIgonZ4yXFVhCYHhwJ3A/mbMA6yC8Hg3BIbmAVejzfHZFXgDjfHj\nwMJmLIDG+gHg1hB4MQS2znPDpNFCYJ4QOBn4FGVu3dGMFcxYCVgd1Qf4IASuCoGBOYKaSguBVULg\ndpT9cSqwpBnzAfMDZwFHAB+HwJF+OHaYFgLLAc8AxwI/NGMhYA3gUOCeGAQ3abi2A36Kss++ATwT\nAvNHeHRlYGzDL85b9CqKLhjYqDriTQ/XOz9XYhAp6Pu3zlhE64+8i56jQqCY64G/QD7d7TIPttLl\ntorDXF31BjWyINI2IVyn0HdXs2tUuXeRzqDvLsNprXK7Ro1710dJ1gouj5nlymkQt56O0ywUx9Cj\n7Pc+yE74KRnbrZC//vd6fdfbX4ycB2rSDFe7HqX/sdjvzntiiohgYN/VITh3ogjecheozZEPeSYG\nGuTKNw25llb16kA5Wi5Dbm97tZp+2AneGRRzBW0cFUbaJoTrkB4uKFDnYup4MlV5tuDhMhP5Za+e\nNz4N4N/FG5BmAAAgAElEQVRw4jSw5Sm6AV/XigegH1LvOo5L17l3F+SUcVwWjAxFf/2Tyr4PzliM\noXZq7hcKzG5nIPwTK20+H6Q/If/Wiu6RvglfLD/RE56sXsjl8QuwTWI8t65P5FPUSA2d3Vjbss4x\nfIUSXDWcK4i2Pu3j6QA+7ch75WrH/1Iixi5U6WsuOohPe8l8bY1ccZtOnIZy5Qx3ovkgdaJNM8Jx\nbhS0NcUZkqjMzEAk8T5Wi+gmBOP5fiBVysMTkDT1PlUkKmfW+ut/LPb7856kIiKYD0Q7K7sT20dr\nLVCK/v3XpsF5ooIhI1EiqNhBYn54nYBEzhPIIVumc6nXOZd6LgnmkKEYxfos8rTaP81DuEEYByFX\nvqailav0XRrF+iySQltNwtvCCVvD0co1+p7D8f8EqT+XzwnHnZEEcz0NxPX4Pj0fBbVtlhKMB3j/\nNQ8XP1Bfr/D9Ash7sFAz3WLDkMfkVEYSQ2J3eQrS7kitUlcM95P+eRQxm1jgFFJpzEApf5vazKiA\nyFNIAshEp+hE+cfOAV1Fyu6vSIXwMrID7Jo3AUT5ie7xOTyNFFNKIKlwfyT9vI6CcvLGfx1niiag\naOvUVBlIJXuMMzgnk5H0B7YEkjjGgW2aQH/bICnujKQYSd+HJ6PgzrppuZ32TS0/RH1/vVH8jMWG\nJYtJiTYoGNiBYDeXITkU7J0Yg9sb6VxfbJbAORd3tXMxsZOz1VkAe/mkXkaK+V2QAekRlLguMzHc\ncRyGbABvgW2V/Zqy9R33KUh3m1pG0grv7o6KoxQyVe6WJsGtAsNKyBD7JYpczUzKRGqTJ5D9JzX1\nl4/zkUiKHU6CaUNQNPtzSJ/elP0Q2cQud4Yvcl9IZXVy2XcHg91Y/IzFhierhVAfQQxsA7A3y5C8\nshzxiIN8BcqT01BqZlRt510Ump4Kh4xEtpuQzeBHCfdd2BCzkP0jlzw6Phd7OAf8XJpEwN9XqEHw\nHFK7HE6OaTMo5qYfiSSgfdMmwGBLIY+jmUitmFeZwgD2U2dwLk+awUGRuCORdJlKqm3fR6c5DsMa\n7KNhZtQZ31Fl310KdlzxMxYbpjwWRGUEMZRQ6Ru+111VFnUiDlhBrPqUGNWO/Lmf+ab5ORmI6U6o\nxjt31nTFKBRJPMI3RCpFXhqAqaeP5yQkkieaCMvnbXukXhlPzlXHqsC3lXOPn6EUH4kexii1wmXI\nhnEOLVKDGEUCFxicpiNlkT3hfKS6O4hsvHA2cfgvJF4xlbmdCWlI/UxR1b1cyXdPlx5CHZ7wO1Jf\n4nncUeGS0U1O2IF+eNTVpyMPjduQWmRwtvhbH1RLYKZzqbEXM1JNnVdyaLWcf73DeJxv2ltoMg2A\nb4wfI5XSGCRdtLRbKcrV/zgyQh5D8zV35/G1Mxtx1i3pW4+Myx9TIbFhjD5+gFSvd5JxgRvk/vwI\nkjJquof6/Yv6uryqmTXpz59U8nky2FLFz1jsPpsfDLZFIe0fA+1ySANDUcj3KL9OrdKPOVLP4IXO\nkbrmlAQmbAcnNFWLtoOtgar33NDsRmwS1pVR1r3X4xw+SGooJJxquvJYBnjOjaqQzfZ5jkWskASx\nL1KfjPQ5bikvmgg4rOmc4HQkncZVA/RFrqQzkLfSwLxxigjzeQ5zZOYEuY3ehqSlhlQuCcEf/LCe\nAbZbjfuW8wPqtGbXpe/tP/v/84B9WzpumRN+oDswARiIwtlHAyuV3TMUeDhCX+aIXQ52LNKNTiGh\nwBCwDX2D7V1hIn/hXPKeeS2oMpi6IVVAwe2yap1c2orRidoJMsJ1YaSznO241lRPIMnoUCcALyD1\nSYci+BVwWtmJ2iykoqnpLuyH3sHO+d0PtnLeODSAc0E//xI11JG+P/enWDYzN6asDK61nbBfRZkK\nB0VCTwH7eULv6uH4L4McFt5u+zsWu8/mAGID4MmSzycBZZFoDAUeidCXOZKHIh/cjcHeTXiyVnYC\neZx/ns83zp/Jye+4DryLIbH4Y7Aty34LKDhlqnPMkYpotOqFDJI3+mF3Iu2js+d0huBLFGCzYd4w\npzAGy6A4lK+Qa/PiZb938zn/GMUKdOjU2EhN90s/8E6jTHeOSmU+j2ptpFYruAn450HOH2MKhxcK\njptBlfrhTbzrGmSo3x/s1ra/YbH7aw4YdgOuL/m8N3BF2T2boexzY1DSr4rcSQnh3xRFgV4GdloK\nkzUA6fBfQ14fl9HilaNQsZOJSCe+oBPJx5Gr3Pp5w5cwrisiddWXKH/QgmCnOMdzbysSgBTGoD8q\nLvQVcideGkVHj0L5kbbMG8aE8V2SosvxhigW4lQ/EI6mxQIBy2APSGU1E7mvTidGVH+M92yJ3KIv\npF2aByx2f80Bw64RCP9cwBz+/zBgfJW+DBgO818Ap/wTnppJCi5azjX9FsxQ9FvLeH7UgbufH1Lm\n1ynlHFJnulAx8AKu/yblcniteCE12Msl43ASHVytVQPXALZ7Ca4v404eHeFCtkFDMRuJx4sgdc9M\nHY6/Plm08vvLYvfXHDCsX6bq+TUVDLxlz3wGtAulLgXeB3B2CoO3MCqv9yoK33/YP2cW2NME7Gv4\nif83ZNx5lhIXr85yocRplzi3ew0Kbx+BYio6nAG3yfl+DKW/OApFkM5Aqr818oYvBXzndenmO7C/\nIPtFouqSlOAuJFUb69LqDchJJPE5QulWrHzf50H4ewCfIONuLyobdxcBCjkl1gU+r9KXFf83A/sy\n4UGbyyfkNwXR0U/RG1x8TjUpUxNwz+ESygwngsHhPs5F4TPoIHV96+DZF0VezkZqjv4lvwWU/vl9\npKLbLG94UxyH5ZCr4lQUgNe75Ld+yM4xBexWOoD3VgR8C1HsU/ygn9e/38z36/3kUBYxIuw9kfr1\nDUrSKKOgtZkkH6tyrNPG7m2/x2L31TwwDAM+Qt49v/bvDgEO8f9/Abzvh8LrQEWddImOv1uJuJeI\nn64vrjvArq/y2zko6Keub27GC2sr5DlwFxXcHZFu9D6UgyU3F7cE5mYX52zvoYZ4j4yB+6CgvCfp\nRPp+pNe/1g/zU6ghhfoBcL7fezwdVOWHylu+iNQj7egC8uA624noobRQXApyNngcJY9s52mEgkA/\nqPRbg+/rjpxQjBIffv2Gxe4v7wEsBx65K32IfH3vTmjQfo4MoVVD18GOQOJl7nnVkUHzFmTQ3T7C\n/ds68b+/FuFstQvlknnGOfktYjzXC7ngTkGh8JEjs1vtQmk7LkSqrQuIUbQH5cR/DCUmqxqj0mqX\nH1wXOkH/RTkHW+H+wSiu5VVawHXV9+cIlBajqo3Q9/AfEnrnUX5I3gh2bNvfsNj95T2I5cAjN7Yz\nkeg/niZ905G/cCRDMYoAnQE2NKcFFVC63GlI3RHZ9uDc0enOBZ7UylwgcoO72OflqFqbp04/c6Lq\nSjORC/CAvHGLAXs/ip4r19BEqg7k9TUBpcLIvd5DDTgLWWInOVGMHLSHNAGHk0Iytpg4LOUH7XnU\nsTf5HI8F27fJdw70dbICyhr6Rtvfsdh95r0YSoH3hTERbFVHeDNfJA0lSfOBHxdn4FGUXM2ovJQW\n1NJIfTEabJ0m+lkGiZ/jaDG3P9+8P3NO/QYSyoeP4jF+g+wDF9NAvYQMx6A38l2fitSPiRjo/eA/\n2QnEWeSUmK0GfINQjpn3aMLdkWL65bHN9NPgu1d1enRUzGca9lB0mvgkmKvRraev8wHFe7DY/ea9\nIEqBR5WqxpWepMiSfVWDA3YrDYhaYEOQH/nhGSymHijsfhYKXGravZSiMfRzZB9oOvFbAjCtjYxg\nI5s52Oq8YzGUzbVg9E4t3XUDsHX3Q2+iH8ypqBRRnMpd/p7d6nGlGeA9B4rInoWMk4m4TyO70GRk\nF0k9GR2KL5oB9pMGnj2IOqrmGs/ujQLEepZ8dxPY0cXPWOx+81wUbRHEkN7v7DLE53UivHHMAduf\nJowrzjl/7NxTKpsH5Wp5B7lmRq73GqP/OZDhOtFNFxOGhZAaZqrPSRaZFJdBKRCmo7wqeaZlLhiv\nP0S+6bHWcRPvHYpcYJ8jhxiIMubjTlLwzEEqw6udPqRW8AdV9ZpBgzUlfCz+SAXnkjrPLeRreJ2y\n74eBvVb8jMWGKesFUR1JzBdJO07IN87YqBsYeQs07U6F/P7fQlJHkmXq5kR5R6ajRGOpcmVIN9i0\nmB3znT2QSmMmsldkniIYidkPoTQdByY5hxHfvxVyFR7lmzVT7tvnoFCk5NKs5oCiunEsGagbUXqX\nD32uG66fXKXvQ5BqsikPMoru5JHzgYHdDnZxhe97IWeATlNzd3y1zYE8Vs6KMFhzOqe/f0ITP5cT\nzYeokSwtRn/boARjt5Nh7ABNGNYaeNdQP2Ry4TYrwLMBSug2zscgVakDbD3HfTxKE52rG6Jzjtch\nqeuAtOAhRwcDZDs5ww+5I2gyNbfvlzOQ0TwRaRyVAJ1JtLKLw5DbckWNBcrG+kv9j8WGJauJqY8o\nBnZujYFYHIlbq9YZsJuQbj8x7spP2D+CvUKD9Vp9893uk5mb650fZAVXuqY3SFnfA5B7ZUvol8tg\nCyiX+9vIH3qbpOFDkuYDfrj+nBZLB0JbO0uiCd6cUOXuUoxchF9xPBuqqYHsMdcgNWyiDBKKRxhN\nDe0Fckr5HGzrGvdsD/aK/sdiw5HXBLVHBKNOmLNvphHViBUK7hlLOrkyuqFUAu8TQ5x0grMfrZdW\ntmbwTMy++qCgo1nIFbelPEoqzMduzv2/0Czu3udAJEVNRxHVTUuGKeLfzdfjFOQT3pRnFQoivJ8W\nCiKkbVrzc2oR2QrP9kFBkc+SQsZbX393g11d455LKas9XuGe3kjds3hnIPz1/GK7ObH6ZYXfVvSJ\nrikRJDBxv3KONkpcwLK+gN6hBaNMaRsufz0x3SD9+R180z9Ai0U+14G9B1J7fIHUeLHXDdgiKCX2\nbD/wOkxqbGQYvYgGYymQFHwSxZrOLZc2RETR7kW69c0i3D8vqg9wFynGCaAiRBPAdq/w23pIJVc3\nkA9pNo7o8IQ/4qCt4IttqZLv+iIPhkQKH0SAYV/n7ip6aDhBPN7hPI4WTivr8M6DMn9OJ2JVJJ+H\nJ5xz/kHeODSBex+U+ncaUsUNjPDM3M5JznbuLJF4hJzwXwnZsCJHT6MSimORAbdlA8ZK4N0Rqd9u\noIo2AMUHvOv7IAvPszWR6rq0lm4vZBuL5DLqTNdL/xOE3xH+NQpqKBRlvw4Fw2SmU0ZpEqaj4ggl\nZdCsBzK8jOhIHLDDvgYKjR8JtlaVe+ZCSeNmIemnZSOEY+I+FzLmzUL5YSrlX+mGXFKn+BwvlTfc\nCeEekMviZ6gWQkUdvXPQdyL9845Z7rcEcJwbqePepEyydQI6zddzljTkCGRv6u2fT/PDNBIMSMvx\n6f8S4e+Jghr2QpnwxpNDsA7Sb74K9hQS+/uiVM9PVCIcHeEqIW7TUDDUfP59QS00mU6SGbIK/ks4\n5z/J8S0wFxsiw/DrpBSAlvfl67dw+J2Gq298vx3r359LC9tw6uAXUIT3WN+7vZGr8USwjXKC5z6k\nLlzJxzeyYRxVY7u/EcJfSJecewshmJmF6PezDvCmfxxixuh0IKsLRw9UDOFoYE7gTuBnZvwrD3iS\naiEwP3AusBNwF7AO0Bc40ozX84QtixYCGwKXobTi/0S4nwjcaUZrbJqUWggMBC4GhgD3AdsCU4Ej\nzBifI2iJtBA4FuH3HfA0cKAZX+UEy7woc/FSaHyvjPHsb4FvIZwVh3YCdIsHZrothFjwvFf4Jy+i\n7+/+N/B7RPQBJgL/zQuepJpvhFOBSehQ2whtkE5P9L2NAh4FBgDLA28AL3R2og9gxufA4UBv4FfA\nYHTgd3ii722a/50D+E1eRB/AjK+B5/3jUzEfH4LWaezWUoQfWDbGvb8DHgM+D4FtU4KnbguBZYBX\ngTOARdFkvBQCS+YFU7MtBLqHwKHAh0iqWgg4DHg6BH4XAnPnCmCKLQRCCPwYGAusAiwNzAN8CrwX\nAieFQJ88YUyz+dwXamjcAcwPHAu8GgIXduS5D4E5Q+AmtFeHAD8CHg2BrXOEaQlgB+B64M4Q6B3x\nuUAThD93vVtRX4VRwb2pim5rd+QONQ8KyvmcHMonopTPX4IdVvJdN+TRM50OUDquAk4boxQDL1GW\nPgMFod3oOP+0Ixn3IuI+BOXTGU0F9z9UHetBVBxnp06I//rI9fhFyiKuwRZF+ee/RPEyHQp336tj\nkVG+X8n3m/he/XEOMAW3CZ7h/z8IdmnEZ/sjr6BARzfugv0mAsLLId/jtUq+uyXqgCU4aRv7gql4\nWPkm+swNNy3n41wB3sVLjJo/qbWx3dA5GqUlaCjdbCtdKCfTdcigfTD1C4NsjdKCPEuD0aGtdKHC\nItcjb6W96sz9+ih/1Wu0YGxKBXgDipadCbZPlXtW9wPt0Ixh293XUcGrZ35nYusyjKgGw1P6H4v9\n7rwnpogIBvZk7XusN3J/OrLs+wVQ0MN6GU3YD30h1fRfRwEhf3IOelDeY1wFxl7IJXUWKi4RSXKi\nbRK230Z9rpUux/1Yx+ESYiQxc/yPcK7r98SonNUqF5JOf+4MzGVErHvhzx3kB+W1tGj9A99/9/r+\nq5kfBwVbfoK8mVKXZpzITwXboOz79Xw+BtZ5/jSw8/U/Fvv9eU9OEREMbFodZK9A7k/tJsa51PdI\n2a8cBW9Ni3rIOMdRCB9vqhJPCrhsi6IaH6XBgiAoB/7tKAI2tdS4KeC+neP+ONiKTfSzgBP+GX4Q\ntHSwXgnca6F4jdepkyqlRh/zgV3uuP+ilXCnKHFfTvSsvoshN/HUg7hQTrErqvx2HIoDqkrLUJqM\nPfQ/Fvv9eU9QERHMuc6K/uFOVD6txpU5gX0U7NQUJ+sYJ3Cx1RsoRfCHyAc+V+7YuZuHUL2BujV9\nI/Y5FImtT4Itn/d6qgHnik7sPwLbLsF+V0Wqr/dpMG97RvjPh+IzppFQpk7H/QWk/ts0Z/y6oYJG\n08F2bOD5eZGd53ZSSrKH0nVPpErskdOyR8AuqtHHZ7gU0xkI/zOVNiPK7z2DOhkFUVDGzGY4uBoT\ncR5KT9Bw5kGUMvoGJzpDsh9jm5NiYZaTSDgfCQr0KVQTO4sWSlbmG/p3vj6OqcVNNblOdkIqgwdJ\nqKxigrDth9QLV4PNn0L/uztjdAc5VH1DQZRPoaDKZvZpIRDzcRIOxETFkT6px3AhSXIi2A8r/DYf\n2N8Kh3ZnIPwXgJ1ShmQvFGZ9dLR+7AiUljURUQ2laL0OGbQSyZ+PPGJmoiIZWegTyzdlosUqKrxv\nCbB7kITWbuFmu66sO1K1FfTRqefVQfl/CgnMzq/G2WU4Bqv6nniLlKOO02Yuarx3K2SgPZsEVE7O\nxNyCVGGJHZJO4+6IeO+GSHIZUPb95mCvFj9jseHIYlKiIYk5Qby3DMnfOfcUNX9Fd5+spi30tE3R\nmujmRd5JbztuiXJfZe8ZDPY80l1mKoYjV9vxzj1lnrcIqZ9GI9fUPCSsxZH74BRUbzfTgiwoP83v\nkLR8KAnWXojw7mV93seToEqtwnt6oDQSX5JwtS+kNroIqe+almBQYrbpcZgPpLZ6jbY1d48F+33x\nMxYblqwWQn0EMaR//aQEwRWdU4tFGCmWXmyY0KGkXc8hr5xUuBYkzVyCRLpEa7FS1HXmanhDnlgn\no0yWp5OB+gflx/8Tco37cVSmIUV41kWFQd4C2zCD9xXyKn2JjIiZVXqrAMswJ/63psA8LelE8ck4\nxLSBsTwR6dQbtl2hIkUfg+0d87luzrgdUPLdbWAHFj9jseHJa0G0RxBzbv0b3K0M7DDqFCSoMWBb\nOvGPlGq27NmFnRu/JgsuCbmHTkPFTJp+HwnpOhPGcSnkWvcp2I/SIMZIzXC2HzKnZXHIxICtG8Uk\nd38kJXUb8kl/Bbk9b5DGOxqclxv8AEhE8kLZRKejYMks0igfRIO1d33tfwJ2XIPvPhjstpLP75fC\n0eEJvyP1Oh41ifTRBzTepw0lgr99hUn6yAlIlilal0AqiWdpIvMlCes6U8Bza2Qkf6wZDqqszwKH\nO8mJ6oAk+k0J/35pHE7I4HeFE8NDsmBYGoCxadsWUr/+3jnwpqunxXz3LkiCHhrjmWUc1qOaeO+K\nYJ/7/33BvqNEC9FZCP9VqDBGcO6oKeKAImxnEkHPiFREk5qZpCZh7Q42HHlebBvz2Z7I8yhxXWcK\nePaiWKjmXJrwnABbx5mFt8khtW4TcC9NAuoolyQORBLj1bR4IBlN2LbABiGbzZ+IEWyXMPybO/GP\nEl27PHKoOLzJdwZ/55K+3ke3/R2L3WfeC6EceBRJeItvjGlJcN1gG/jA7VDjnvWdW4qlg0tnLGyo\nH0C/JYIvsUspqeo6U8Kzv3PoX8QlfijY5g9I/N6fjA2nCc/1GCTtxQqkciIwEtkPWj59QgncsW1b\nKHBypkszedts1nLm7MAa9wxyxjWRqoAoYGsvpPb5Q9vfsNj95b0IyoEHWxuVQNsX7J4EJ2sdJ+w7\nV/htG19UiQQzJQTvQkgdUrOSF0XxMxNdZ0q4buZz/izYynXuLXeV7DB1bmvgVHA5nY5cTmsaY1Fu\nneuc+GTuLZQg3gXb1qlUUU0h1ditKPgx1XraMWFfAalwTqjw28pI8v5Zgu87Gtkcr6as5nhnIfx9\nwP7hk31ksu+wNX2h7V7y3U98w7WcmgCJ8cc6Yf9x2W99UATmp2SUoyhlXHsg3e9M5EI3d9nvLRsc\nleAYzEeNIDM/IA739XApOak7Esa5P8oG+hxlti2ULfUjZBhuuYp2DvsHYBcWpBAUMzGFhDUHLmV8\n4IzgJm1/w2L3l/fgVQLeuT+jwRwidQZwdSf+eyI3x8mtxElUgXkdJ3jXIOPOikg9cE9n2PxluC6M\nXBC/BNvbCf5glwY+ANs6bxgzGIOVkNpuHNgw/24jlGzsxVZfrw3g2x2lJp6K8keFEibgp3nDVwf2\n+ZGq7WakrZhGxGLpMd/TA+xbp4tlTBEWu7+8B64S8KhmrZGSZ4ITEvOrQxRER8E4d5bAfTAdJCFa\ng/gWkmwV8O0wCdASwj+AbY9C8wtjUDNddke/kMrv747rmI4i1SF31RkOd2o2QmQLs/bf0+67eler\nVeAqtDkBzPhP0h17ecfDUB3VfwNbJP2OlJoheAvt39Vu7OjN6xivDcwF/D/gP8CK/vl/pfUAVqA4\n7/8E1kXVwDprK93v/6XjlDAdDPQE/g4cHEJqc/RNUh21KuFPZYOHQC9UTm4wKpO4CjDcywy2bAuB\nNYE/o80/J4L7GOCPHbkUXqUWAluh4tM7A5ub0QsVPO8GjA2Bg2LWZu5wLQQ2R2MwDFjPjJ6oGHc/\nYFwIHBwC3fOEMcnm5R5PAe4F9kBzfQswwstgtmwLgY2AR4B9gLmBMaj06qIpvO7bxHrKW0yqJK64\nPjtRVQ/yDngKpSPuW/L9ssit7Ii8x6ACzAEVO5lRrjd0Xf+1qATl2nnDmgCudcsaIuP86yhpX6rJ\nxnIagwFgdyPf/p2rjEHN8pAd7UJuuc8id9Ylyn5b29f3tWBz5A1rBdg3dTvEtiXfBZSaZALYMgm/\n7zWni/3afo/F7ivvwSsH3nXZ3yI/9kTSK6MUpyOQ0bCdnhjFDHwGdkze41AG88Mov8uyNe7b3Q+G\nYzqi/hflRDqfYjbHmkUzkKfTfsgQeD055qFJcAx6g/3ax+DMekSOYrbVicjAPzBvHBrEe1ufx+HV\nmDynB3egNAWrZAlfHdi3cKJfsfYCSjfzJdhqCb0voGjv8ZQ5OHQWwr8t8ly4lwQs+sjl6kOUDrVW\nLdEl/ZRu55ebw6LaBBlyLiJC3ng/uEaiQjQdghD6Qv4Zcn27GWzxmM/PQzHzZEtVf4qJx7a+mR+K\nyyGi3O6nO0E4uxW54ipw90LBiZOIkP7A18oBTmgPypvBQVlnZ9aD3Q/nRFzFnT5NQdH5Z7X9DYvd\nX96LoBx4FMJ/NvJaeYkmglOcO3wJ7MyI9/f3TZhaFa867++O8rdMI2Yq25LNNB13g8x7TmvAujyq\n2PQmdYrrROhrsDMKo0k4w2nKY7A0Um1NiDvXFfoqqIg+ofXTdWzg3PtDcZkU5Ob6LthdRKwPnAL8\n2znRjxpxXJBqmkqlAfYblNFgGNiLbX/DYveX90IoBx5lFtzaieAIsEOaGKxDvI/ItgKkcxyLxM8s\nk7QtjtKvvkATub+Rz/8Y5BK7VN7zWgZbT4pRt0fHmZc6/QawPZyDvI0mktxlMAZ9fW3NRumqI9WD\njdj3D5GkeBMp1nhoELa5UP3bqc4JN5qbqC+KXv2EjO08YDsgCTNW1lMUbHdLE+8d4gzdIkjS/ZbO\nlKQNRaN+ixsvnJub2QghRNkuZ4ENbuDZRZwrOTcL4u+n+DQktieRlrmnE5VZYEclRWCbhGktFID0\nFCnppJEBv2AvOJaUaqY2CFsh8vgzpJdPJV22E9grkFog91oEDtMwZI/4Q1IHkuM2AxUmzyItcyEN\ndGwJ1dflZ8RMvOjP9kAptn9W8t07lNR16AyEfxOwt8oQPxOJhXESeAVkGI2k4qnSx0LOOde0DTS5\nmHohPf4kUvDQQImiXkJST+wDMCEY5kAh7dPB9snoIB3kB8yHtIDqA+V1eSJLeFDZvg9976RaarMG\nDAuhouWfkEIBeqQuG4FyWqVm23IJZRpNJMJDdoHPKfPIifDcCWBPl+4bsMvATip+xmLDk8eCqIwg\nhgqRXFyGeG9fwLtH78v2QOH9TVXOQp417yBRLVGChfJ0vwn2CNiC6Y2rdUP2kpmoAHomNVD93Vv5\npr+DjLOGVuCwM8/R75zeb1wCOS5rCcT3znCf+0Oz4IxLxn5vJ5YXkWKeHSTdno9Sr2yeQv97Oh6r\nJ9DXzWCXxbh/eV87S5d9vyvYY8XPWGxYslgI0ZDEUH6SdnmukUEokoHEifVUEqo+hBJnvYmKPyRV\nwBTg9JAAACAASURBVH0P34xHZcEB+zv7I2PiWFJOSIfyl9yExPtcM57SXqee+sFHi9kckMp0BPL/\nH5Tyu5ZC0s0YMowvQRl2pyINQSIeXihD8BQSkpZ9X0yJQpucYXsR7OgKvy0C9jWuwu0MhP+v1bhf\nJN7UNZAgy3fkUzXihM2DAoeubYb4I7XHdaj25lrZj7EFsN188V1JwimNvf8fe/9XkHCN1SZhWwap\nPT7GE5+l9J7ByEA/hrIsijnj3x0lPpuFJOu6bsIN9H+U9/9rcrCvUAwGe5km1VuouM1ksJUShnF3\nImgjkJRe1TEFZS1dQ/9jseHIenKqI4qBfVBjIPohHdk2Ne7Zhgb0aBEnbC7kcXRTtcmo8/wqyGD8\nx6QJbgOwzIdS3X4B9sOE+lzCCeuHZFBQvAk4t3PiH9tvvk6/86DiIi0dV+Ac+ePILbIpV9qSPgsS\nxUtgK+SMX3ck2U2nRuGlOn0ciqS1xHFx5ughsOE17umPNAJVJQ3fv0fqfyw2HHlOUltEMLBr6gza\nNkhn246wRzkYEpi0fs7N3RqV+PtE/9wncn9awMuiBLYtkB/5nTSog0ci6WGO3xn1OJlWuIgZKRsB\n/4JKoENEEvuaLOiuL6FBHbyP41k+9wfTQgVhUBrriSjIL/KaRFlgJ1IjWj4B2KoSdp+bB6njmEJJ\noarOQPj3ijBot4JdWuH7SKqgBCZtDrBnnFjW5OqcC7zLuatERcaE8SkEfu0X52BCdQFeQfnIWyac\nPgb8dXPj1Hl+CMqf8lZS3HPG+C+IbBCfxWWYnLCOBXuAmFHXGeI3v8P3ZyLU7kZpTz4jg1TtVFHl\nIFXph/UOK+TRNFUHBRb7/c0jwLbAOOBj4MQq91zuv48BhlS5x4jg20wF4y0xjL8JTVpfZMD6E1V0\nmWDrIo+WqyhJCteqF0qA9g5yHau58JEb6qnOMR9Zvng72oUknw+QC2hd46cTlKv8sDyolTjdBvHf\n1g+/W+vtIZQ750qUh2aXvGGPgFtAqreZYHvWuO8EJP2mEl9R4X3tjLeVaFsdvCaDLZ854Qe6AxOA\ngSgf9WhgpbJ7tgMe9//XA0ZU6Ssy8JS4a/r1AdgeGS+oPig3zgOUGMp8Qo9Dut5ds4QpAZx6+AYo\nBEBVSmi3rkswj2e1STLCvafjXKjlW0md2N05tenIy6ulomObxL8fUotMBfsplTODFiKDrwebL2+Y\nY+K3BjKI3kSZasuZmPE0ETHfIExt3DWJ7+55B9gBeRD+DYAnSz6fBJxUds81wB4ln8cBi1ToKzLw\nFAO0hvv1cKWFmsHE9UL6uEf8AFrICeIbdNCMiY7Xcih9xFt4dsESwjCtGmHoDBfyDLkVGfe+r3gF\ntp6Px6ukUBK0VS7H8z1napb07xZBKssJYFvkDWMTuPVz4joWbDWnI8P9cy4ut2AnIik7doAXsq39\nIQ/CvxtwfcnnvYEryu55BCgNL34WaOfKGBd45EVifuUSmehw9EQqn+/AvkIBOy2TKqAJvAoZEWeA\nve2c4K2kGGzWShfYxijx2wco8+n3NYDzhi0D3EtVeW8jNcn5dACVZUT89nHcZiNPu3aMaIaw9HBJ\nxIhvZxkM9kkjhL/ZSkYW8b4Q5bkQwvCSa2idPqdW+T/TZsb/A+4E+gLzAX/07zp0M8OAh5FdZi1U\nsewGM2blClh2bQRwM7AyKnn4FPCoj0unbmb8C1Wq+wea+37ArWb8I1fAkmtPALOA+YGXgRl5AWLG\nvynSr9FRngkhDA0hDIeF9oNTl2jkvc0S/i+BASWfBwCT69yzhH/XrpnZ8JLrxTrvPhJ4xa8j4wCd\nZAuBXYGrgXWA/YEXQuDnIbQ77DpMC4EQAj8F3vdrLmAX4I4QuCbFmqIt0UJgU+AdYAdUpnNhVA92\nbAjs15lLP4ZAjxA4DngTOWX0Bo5F5QTPCIHeuQLYZPO5HYU0EUsAGwPn5bVfQ2B9YBBwPXBFlGfM\n7EUzGw4zX4dzXmjoxc2JKfQAPkHG3V7UN+6uTzLG3aVdVFvBr3b5LDIS0/ZwnfeQku9WRFGbd5NT\nzvAmcVoSJb16D2y9st/mBbsGeRO0S63R0S+UGvt2ZMBsl9kSGbbfRFHcDSfsatULbHW3YzwHtlzZ\nbwOQLesDEkqHkjFu3VH226mURG4jl9ZRKKdQpmo8V6m973SkLzIw7xjj+UvATo5DO79/tnngGQZ8\nhLx7fu3fHQIcUnLP7/33MUDFDQMYEQJJXPf8NG2y09lJlGWwy2DS9kJBO+1Kq/kkXgn2KR3Ev9s3\nxhF+iJ5KjZB+sM18kf4JbNG8YU8A915gv3Lcz621DpHX1oF+4F9NRi7EKePfx/Gegew6FfcRxZKP\nU1Fu/ZZJyVEHv/7IdfJ5KsQcIPfct0khGWMduM6gxDEF1fCdHJVh9EN6k1wIf3KDgBHBYwAFGb1D\niQEVGVhHge2X0YTth4x9K9e5bxffTL+ihX29UTqJ11EwVqQ6x1GJRatfqOjPWOSNVTfIp+S5+VA+\noumo4E+HjGXwQ/wjP8QjebY4ofwDinBNLe9RQvht74f0qbXmCEmzI1B8Rhb5/VdBRvPyAvNXg10b\n4fm5UO2SPp2B8A+vg+wivtHaBYGhAKQZpGyhRwE7k2MQyIFOVJ8g49TEEWArpO2dhVzDYi94aqgH\nWvlCKq17kVT2o0YPLsf/FRQd2mFUICiq/FqaUNuhtNufovxTLZWqAklxFyO1XaRkeSg47TUUp5Aa\n8UfS9Rtgh1aBoW4tYuT++Yr+x+LC0GpGqk3q/H4F8AczRpX/YMY7wE1ENJA00kLgMOB0YHMzxkV5\nxozPgc2QQemdENgiLfjitBDYABkw1wTWMONqM/4btx8zxqB4jseAESFwfAj0SBba5FoI9AmBUxDu\n7wKrmPGwWWPeOo7/psDvgHtD4KYQWDg5iJNvIbAT8AFgCP8HG+nHjGeBVYEpwHshsHcrODWEwLLA\na8BywBAzXonynBl/Q5kIBgE3hkD3lEA8AvgXcF0VGA4Hrg+BvjX62AR5JDXW8j6ZiycYBvYNVXTL\nYDsivXJVX2IaMJDEOKWPRAEWDWd0dLXCFFRMPpfsjRRL8zVV+7RK38sgW8s7laSyvC8X+yeA3U8K\nAXbOrV3kIvwv85rjGvAt6lLOR2CbJtz32iju4ck0xjYGHD/x8T+yCSluTmQPuC3pOXQNwCzqZP5E\nAXO/rfH7i3gpRzqBqmcM2PoVkJzHRdLNIgzsZsQwkEScrGNR3p2lEuhrUSeOr5BxVSiUkngiKRbj\nRgbA/ZBK7re1DuoM8V4WeaR8RIrZW0vetzLKC/9ulDWbATwBGaRngJ1DggXey97TEzlazAI7mgzt\nHk6sb3DGr2mPK5S88GmUjDGRgEyfh6cocUypce/Cvofa4YJUtN/i6d07A+G/Auz4CoheS52UzRXu\nr2sgidjXSSh/e2JEGnmGnOQTm7h0UuF9C6G8HqnUPq3yzkKY/8ekUBIvIgxzIOlqFgqNT7T4SJ13\nF4refOFjn2kemBI4StNvNF0+MOI7V3COdCTYqhm8b1WU0fI2EvQ0Qg4MjyMpqem1g1Ipj4p6kKAI\n43b3o8yofy5+xmLDksVCiIYkhlQPD5chORQZOyJz8CUSwtAmJ+o0sHFpbVqUVfRz5BqXeB57Jz77\n+AFzIU3knW8Chh3IOLGX470rkm7uJN+UHnMi76dZYMdndfjQPuFepl5HztwU6lCkUuvZ5/kQf8d+\nKeHRG7lcPtgMDhQdUyJLI47fk+USgjONlxY/Y7HhyXIx1EYSQwmyvsIt6khn/zHYjxoY6B/5s7FV\nDT7gZ6JglVT91JFb4H1IL55YxR+kS3wK6V0zL/NYBsvcKJvll6ScsRQF0D2NAmOG5ol3GVzLO/c4\nDmzrlN9VmmI7sSpjDcKyOMpgOxZs4wT7nRfsHl/fadcR7oXsQo/SoJoMBXSe38BzS/nhPajku8dL\n91GHJ/yO1Me4eIh0xHc3MWF3U8NAUuWZAHYe0s9m4n7p7yxUsdqnyb66I/3qLOcMWiZhHMXiHfeT\ncPEOZLS+gGIR+5bBu2yed0AukPeRgM2orP+Gi+pkgPsufvA3XesZZRD9zJmJVOwVFd7Z0w+aJ+My\nk86E1nRMqfP8L1Ed4W6+v78upU2dhfDfBHa4cy3TacIvn6J4tXbE+wPyyhhFDlkoUarYsSh1bOy6\nwShb30ikX8219mkNGHsjaWomEtOb8pemWEZwMgoqyi3TYgyY+yA14mz/2zTxom0ZzZYcAyTdXo9U\nt7FrPTvhOwEZqXfOAf4eKGbhWSKqTZFkMokmjPxO7F9HtYDXABvX9ncsdp95L4Zy4FFd2jtRTph2\nht4GBm035EJZU7fmBORSFLqdW4ENpBP+A/JAiZT33WE/lBasfVoD5sEoWOZtsI0a7GM154TeoYUL\nvNeAfyCSfj6h8cLgSyPj4+eN9pED3ps7x35F1EMPebk86QRwqRxh7w52izNXNZkz5FTxNtiFCbx3\nQ5Q/60iw69v+hsXuL+9FUA48cr37EiXDSkQniOqpzqCKd4lzEleikO158x4Lh2lvJ+S/oIbI7hzF\nvWSg60wBx4CKukxCni+RPKcc58t9Tg+lg6ZLKMFnGz/oHyVi9DMqKnIOUumdQgu4zcbEubBuR9Vb\nt2BbOk04jxZQ4Tm9uAG5ZFf0IkK6+Y+QYbtplRuSlL9Dbsn7tP0Ni91f3oNYDrwTg+lgVm1QGxy4\nzakgIvokXufcZ1O6x+THxJZHqQAeqCSFgK0fl3NqxculnDOdiJ1OFTHa52p/FHx2DZ2oKAwyIBa8\ncM6hSqI4H4O9kWrrNnJyE00I51KvnH0r/N7Dx2IKKRvEG4C9G8qr8wZlHocoD88XYL9M+J2jnS4O\nbPs9FruvvAewEvDIIyM2MhEGbk0nGgf65+5IrfJykodMwjD3RiqoibhKxBfdiX5Adpr0yM4l3e24\ntokqRpGhI/zK1Usp5THo79LPRKSmLB2DdZ3QvEkHygsUAeeCH/6tuPoE5VJ6FXmmtarNIjjT9Rbu\nquzM2DSwvVJ436tO+MvShWOx+8p78CoB75s7NjIRB28F55JPdo7p+WrcVStdyDNgOthlYM/4Iug0\nxc7LcN0UqQBeRonArvUD+2d0APtFQmOwGdLpPotUHbcgdcd+nXEMKEbefoQSB0535qalcXXifwmy\nM+3p0st2Kb1rdCW62Ajh9zzQ+bcQgplZ0P88A2xllk7CpxBYCvjcP/Yz4+9pvCfpFgL7oXKAAAPM\n2lU76zQtBHqh8odD/KtBZozPEaTMWwj0Az5GZS8B+psxJUeQUm0h0AdV8FsAlX7c26z1S116YrrP\ngKWAncx4KKX3TACWLaeLpbQzamu17JyF1hMghO8XfGLNCcrFiKiMAq5s5WyS8H05vHOB81D2wLOA\nt0Jgm3whS6eFwIbASOAblPnyEuC1EDjO569TNy99uTPKHjoC2Agd+G+FwF6tkAEz6RYCg4A3gBdR\nGdMVgftDYP484YrYDkfVCB8Czg2BRVJ6z9wAiWQNzVtUKhdXXHT6yvWYuyUsKvVGodcP+/9zojz5\nD9OiXhGu63ytXNeJjNWTUcBO7p4OCeG6KIphmIy8fUr124OQ18t4lGWzZYKTEh6DVVFtg/cpy6uE\nUnz82VVgmeTdyQjnfV1FcmhhXn1/XkKJbavVLqdVw1HQ6dL+3ekoFidSUZsY7+qP4j4+ASsvb2ux\n+8t78MqBR77NXyIPh8sTHLg+TjjupyRfCvKmuMM3U0u4cpbAtrPrOk+opOtEfsKPI4PfwLzhbQLP\nnijaeKYfZFUN7WDDUNqDJ8o3QEe+wBZALsXTUQBjxXTAyCHhEL/vCjLKf5QSzv3cdjGWCiVM/Z4f\nImPpKbSQ2y5ysPi96/YXKfvtZGdQEssRhdJNP4gqpe3Z9jcsbn+tqOoZglQwr1C/MEuk5gUNHgS+\nA/Yw41+F3/z/vVGh+BfTUC/FbV4s5PdIxbGjGRdYhSIpZswEfgj8CXgzBHbNGNSmWwhsjuZ7e2AT\nM04045tq95vxBCr+8RTwcgj8LgTmywba5FsI9AyBI4GxwH+Alcy4yox/V7rfjP+YcS2wMlKJjg2B\nA0Noyb1ctYXAGsCfgX8Da5vxbqX7zHgUWBv4AfBUCCyWHZSVm6sb7wAGo6JM00t/N+M8VGTlRbcn\nJtE2QTRxFEW7V+Mt75Oz/NRCAQ/nOCf+LU3m1Uf5S55FodZViyq42HYaCnvPLbGVqzRGo+CWyBII\n2DouBl5Ni6qtyuBdAqVtnojyuMRW3bjEc41zhB2u7i0qzPMB8tJapcE+1nKJbyQRU5PkjHMAO8Kl\nuz1jPNfD1SpTyaCmQg04+iG16wPUiZ1xKfYzXA3U5HvfRe68w8CebfsbFru/vBdCOfAoMm1X//95\nmnCN8kl60cXJSEQBJUv7spromfKiaqfrjPn8PE5M321VNQjS3Z6IApXOIoFU0Sh/yYuokM/QvHGM\nAO9yYA85k9Fwvd+S/rohV9epKBixJQPbUJH2B5CdoqH6zChNey62LaSOGwF2Yy0msuyZXzhz03A9\nah+3vyGV6KJI119i/8Ji95n3YigH3id1Gf//TLDfNDhYc6GQ6huI6QuMgodmELFIcwILqh8KXqmq\n64zRV0AF4WeCHdAsUUkYz0JqgofBlk2470Lhk8+RtNQ0l5UC/nM7wZqF7DaJ5qhHaRAu9bV7eFRm\nJyPcN3ICeEmzeCNJ7zEnwpnMM5JQP/T5i7WnUP6sSTSYOBFldH2m5PNUSmJ4Ojzh9wn9mqJlfysk\nwsYd6L4omdPVcYl+SR8/cOIZO4tgzPcMcWJ4IwkGkqGw8fdRwrtM0kvXgGWgc3oTwLZP+V19wU51\nrugcGshymgJM3fwQnoKyz6Zd42FVJAGNIufkdcip4gykjktsL/mYHuuHXKLefxXeNcgZioaTRqJU\nI5MbYXjAfgd2esnnxymp3NcZCP8PwF4sQbA3il78ecyBOg/lO29WhF7PF2y7PCIJLKaAMu3F0nXG\nfMccYBeTU456n79TnMM9lQzzCTmHdrtvtr0bZQASgGMjlKHxdbB1MnxvIQHel37YLJQx3oXaAxP8\n0E+lChop27ZQqpCpYPsn0Nev/ECOvBZRmpmZlNgdUUW34cXPWGxYslwMtRHEkO73d2WIr+SIR1KB\n8P/bO+9wOcrqj3/eJARIqKEESYAQCBCI0qSD9C5NapAmRYoICEoXoqBUpYNIFwkgSg0gvQhKD6GG\nFAgl7d4ExJ8gKnh+f3zPsnP3bpnZndnZG/Y8zzx3787sO+e85bznPVX63o60pCp//3tgx6Y4mQYg\n16y6dZ110PCQnwCaUv8WGS7fQrrsIfnNK1sf5VL5G9jaTXzvUshN+H0Uyp+Lyg2pl35NEzOZorQo\nhWpjWzXhfQXb1qtgK6fY7ubeb6nUxUauuM/FFWR97CaB7Vny/W5gdxX/xxLjkvWgxO8UDKklymXp\n288nUa38131cujow5Ym1tL//lymcIjYkJV1nwvcG5D0zBVUSyiTPj0vaf0BVpjJVkyXAqRfKcTMN\nBYilGlxT8q5+KIhnFrJRtUQeKFS74C++CWZy8kC2qrOd9h/T/OL2qdm2nLl20EABlSrj0EmNCnRO\nz61gvylzb3mw94r/Y4nxaNbA1O4QzJnr1yt0xHXIAFotN/1xKOoxdekK2R+eR14TiaUm3+1PQYE3\nuTFEZ0yjSFn9gjwOfkLRW6flXEqRwf8simUpU1M9+ULd0zf1W8mxWEgNHPenmNY6lYJDdK2C9rss\nN9YYuBRsWzdRZ5p1ZIydBrZ6RjieAfanGs8chrzUuq0jF2Q+BltE/2OJcchrgLoTg4F9QgU9NEqv\n8DoVdG1gQ31Bp+otUvKO+VFMwJ+SMA1URP5hFB2cia6zDlqGOB1vg+3UyGaJMkm+jiokDcubthj4\nLof0zpPBdk5BOlzDpemxYN/Km74Y+C6MooRnuHRct/0DbFWKVdBaIrWCCzdXIjVJ7NgG38BO9jWR\nmQoWGbzHg32nwv3V0KmgYoEa7/Mt9BlLjEPeg1QkBAN7vkaHreIdskrJ9wHpsBsu1Rhj0OZGYdOP\nxpEowLZxCWsUMX1/m9vvtiVyI/1ztYlW4bdLIAPqe2C7NspAc6B9C5cOHwYbUcfvF0c1ZGeAHUIL\nuU/GxH9N5DX3NDHLfEZ+OwDscnSCbcngOeSW3YkCqarOTZeiL0B2gqpqmJRw2wgZ3hcq+X5+lO6h\naj5/lJ79J/qMJX5/3oNTJAQD+22MDvueS5f9I9/t7xJHUxgrUtv8BtkTyrpKItXHOej4u0ne/VuD\nnrmQa9wssHOpUZQG2VKO8kV1Ni3gMtkA7X1QkE0Hyr2ySIzf9EVqxU7kNdVSOZ4S0t/LN61CrYeq\nkfI+9w/z5y8jx/rUMekbigyq91AhsM3n/42oxkXTch8hT6QrI/8HpKK6KsZvDwAbrc9Y4nfnPTBF\nQjCww2MQHJAe8Vr/f6BPwqrF1DMYtIB0dW9Ros9FBbCfQUEmTXWja5CmQnbMqcgFspuUhDJEjkUn\nnpaMDq6T9kVQ0rMO5GbbTeXoY769S2Rj6GE1jmvQvyg6vUwD+26Fsd/ABawelR3UN+rzkIfVt0ru\n9fOxvJcUosgT4rWgC4Yb+/8HoxNHTTyQiu1NfcYSvzvvQSkSgoGtG7PD5kPqiX2RJ9A5OU6qo31C\nreL/F7wBjqXFqwdVoWk9dJp5CjdwIeP2Nb4pdEmZPCddYCOQ6ud1InVekUvs/Ug3u23eeGZI/7rO\n3B/DXSORjepGyqTL7kkXynMzHXld9Ua2jqectlxSmyP72gQUj9AZV5jyU8qnYP3nBMYfe8dF0Ynm\nV1N36jK47IOs7GORwbBpgToZ0tQbqQA6wL4A+xzpQFuqIH1GtAdfkJNdur2Hoq54jqh9EGPsj0RR\n9P8D+wx5Q/VYlV6EtiXRafUtFN19Qd4CmgsURsJAURQHtF49jL+lKk+Z8WmCx6dkhUcd8BKqjrMa\nSvv8fM74NAxmfBECY4GPgcX864nQM8pUNgJmWAiMQaX0LvKvrwOuNeO/+WHWHPCxnwgYEIC50Rzv\n8WNvxrQQOBwY7189bGVSnjcZCim1xyX83VjEc+p+YU+EXwLXAjdTXJxNBS+RdyDwBHAIsCFwSQiM\nzAOftCAEBoTAFcAY4BdAb+AbwB7AiyGkUyehVSEENkGM7jso9/mSfuutEDiwp+W+TwIhMDQE7gQu\nA/Y11XfdGDgN5cNfIVcEG4QQWB14DDgMlfW8IgR+lVdJzxA4ABgMHAVcnbAM7MvUm5s/76NX8dgS\n/7iCwvCnuo6u4P6USb6bKjjMj0LyXyPiXuoqqA/8qNyjdKHIw+N7yD3xMko8HCgGKb2PvA8G5Y1z\nyvQvi1x1p7itJpTcXwvl3HmBFvFZT5H2fshZYTbyZZ+n5H7U8+vMvNWrddK4MSVJ3ZBR/y4UnJlZ\nDFAFfFZ2FeIqvrYeIUFqGGRsfz4J7/zyt3kPRpGIeMgjP/o3SgavEPBQV9rTOgbsa6hYyjXlFoAz\nkNd9Qi2Vd9/GpGlV5M/9LNiaNZ7tjxJFzUL5lZqWeiIj2geCXexM76dUiTqmGKX6no9v2UjznnI5\nPbujiONbas1XVPv1FlRgZMe88Y9JY3/kdjuTkjrGkT442gWedZqEUz8XGg+MfLe8r6lYhaB8zU76\nqjD+USjBWak0drgz40wzQIINQ5F9p1aT6H2DOt0H8khaMMDF8VwQ5XCfiULVk2QOXB4ZPifQQMGc\nHGlfyKXX2d4HsdNXo+jLH3m//T7uYm2lyyXNR1Dhno0T/nZz5OF0TyvTjmpAvONjVNW1GtX37aQJ\nXlsuNN5Yho8dD/ZgNd4SeXYU2K97POOnRvAMxcjdbioGikmNrshwsNZC7mAHJ/jNcBTO/7dWkg69\nv76L/LavpoGqTWDbgU10JtDU43Kd+PbzBdaBUhYv00BbC0Q2+MvIMU9NApyjBVuOpM7AR+Qff6LT\nflrWQldC3BZH6sh3SFCqEbkyzySDVOyRd+xDhaSTKKDwpTjv9xNDXV49uQ9QkQgM7KAqRPZ25nlY\nlWcKaUz3yGCwtvZNJ3GKVqQ7P9R/f2beCwTpFh/zCRYrdiJGm3NHmMAvaJGslCU4zoWiTqeiKl2p\nBaChAKhf+enhLJoYAZoAx0JBmEKJxlSCC1H22tt9898mZxoLiehmgp1fzzz09fEuSjqYqp0ObCXn\nAxWFQJT7aSZVTqAuUH6gMcUS45HnIHUlBAP7cxVCj3TJuaoqwjutgxSTLLlkPBNswwbbWdIZzgRy\nSOOAAt/O9YmXifoJ6YBvQjrwPdNeOHXi1Avp5SehY3RmRclRHv6rvI9PapUNEBXqftaFp0zoRwFS\nk1Dyv6bbtpDq8WEXaBqK5EfpxV9D6dNT8fNH1eFeIUY+fl+nN1e5fxrYhfqMJcal2YNTmRAMBUF1\ny/3hEsUssJVidvCRKLihYaMj8mR4j5LEcA22uRPyjLm6HL3p9+2X9WjfQ+kuBjbhnRshm8tj1aSb\nJtD9bZTe9hmaVITG370iUj1OQ7mAmpabvgSPgUifPA3Vtcg0WIliqcWC4T9zutFJrnDaPI6UcnZR\njOy9KQ06UMbQ0XGEIaSOnEyFFO4otcMG+owlxiXrQYnfKZhLCt/r+r0FlEfj1AQdHLytSxoYpF4o\nv8cbZFC0BKmlLvUFmZlkjKohPeDSS1NTBiN95RHoBHYxzU2A9S1ftK/RYNrpBvFYA0Vmvo1SjDTF\nyO/M8Bh08jifJkdco9TX96LUKptl+J61XMB4gAwKr7uUfpe3XzV5YY12RqKTfuw2kAH9vdLfIHXR\n1MImPicw/r3A7ishci/f3RLtuMiA9TbYrnUMUiFb39+Ika2xwYm1njOnMWluMC4xnBmRgnJLNYD0\n37+hCemLUfH6pjPaGHh9C7nLvpr1RgS2mc+pB8kxkZ4LYDujuIibSTHdMVJbXuhzqmxSuRTfFSjb\nugAAIABJREFU1Qep7ypm463x+xV8A06U+tp/e22pAIs8Ci8u/o8lbjevSdGdQAwFRX1ckAxRcMV0\n6qyV6tJABwnczXxC3Y88VJoSpIK8I051Jn10o8wKbEfkzXALLRRk5dLv076AUjEqR9pegRZQrdTA\nsaB6esWFik1Sbn9pFID2DtguWTLDhHhF4z5+RIOqGORF9i7YDTTgjVbH2J2BDNhJ+Mk86ERSM/Nw\nhd8P8Dm9fuS7cWAbFf/HEreb96QoRR5VRtrfP19PSfH1OjruGBSVV1Pf75Lps77LNr1oCtILP47y\nhydOe4sCx+5BrmLdAlVa4fIFtC86ql4PtkSD7Q2mBY2pNXDu5VLqZKRCqBowF6O9eVDg2SykX2+5\nspeO54qoYNIr1OEogewVt3i/5TK/kepyalzpHRWr+UMjmzAKsHsDec6t4MJw7+J9LHGbeU+GUuSR\n98UYVBlqCg1mBHRGcyduAa/y3BCUsa/hguoN4tsL5eXuQG6BNRdxycI/Kc4ml/eFbBznOc7HklAV\n5Zv0+ch98mxavCBIBRqi7qW3EdN5IfL7QhbRt5FNa0jeNMXEeQ/king9MVQn/puDfE2cTf7ZeAup\n16vaLpzOSdQobhOT/rt8Uz8Z7NKu97HEbdaPDAOAh4AJwINA2SpEKIvmKyiT3HNV2jMncgGUAng2\nKfkEo+PSFLCdK9z/hk/Eo/KcUCU4LYFUF5PANq/y3Nbo+HkHLVjgOwadK6Gyj2/EkeKQOvA03zAu\npwcETMWgqR/ygOlEHjg1bT0uPcfut1a7fBzPdwZ6BBXUmy7hPoZO7Yl15Bniv6njXjZmCBm3O2jw\nNBdpb7DPj39TEmXdbMZ/LnC8fz4BOLvCc+8ANaWxKPLgmKU7UOv6QIwo+X5j/37PvCdTBby/jfSZ\n1xMxNCN/+T+iY2+PS5dQQmNUcr2dMq6zfqo5Bhnzfk8PiBCuox8WQrrwQp74bgFWKCL1fGcCP6KH\n1wdAhW+eQO7Xa0W+7wt2im/wx1TaGHLGfTV0Wjuy5PsBTs8PU37fr5w39u76PZa4rfqRYDww0D8v\nAYyv8Nw7QIw6pkXknbjJGQzU3r5gDnJm8x1n+hUl6la4XDq6COn29kVxCp1gP6dF9bl10jmvS74z\nfQNYE3lUHOib3920UNqLDPthCVQGcjbYz9ApeLDPgQ9RaoiGbCOtdFG0+8xAnjpbIO+n+2jxUyyy\nq01AHnQBbEOfq+eRftTvyc4bF+36PZa4rfqR4KPI5xD9v+S5t13N8wJQMWItouqZ24n7lAZ1YxU6\nbxXk6mZg/0eTa/U2iPvBhdMQc3b5v/4uzRZo/ZyIV8NX5XKm8lSkHy5lDlBtVaF3SITWm9JmnBni\nvZhL+OYnlLJBVym8p/COjbp+jyVtq2rS/xDCQy7Nl8Ip0X/MzEIIVqGZDcxseghhMeChEMJ4M/tL\nhfeNghUWhx1nwboTYNcdgN9Xw7EOeAO4H1gF6I82rZaGEJgXFcI4GPgBsBBwYwicBVxkxud54pcm\nhEAANgC+C7yOTpZrAGeFwC+Ah8yoNNfmGAiBVYCTgZWA21EVtJ2AcSFw3Zw05gAhsCNwKSqudB9w\nNnBbCBxlxrRckasNvYH/+Of3gEfTfkEIDEUFW66H83cO4SebN9Rg/bsP44El/PPXqKDqKfnN6cBx\nFe6Z72p7It31fmB3prxj9kFh0y8i17A9XWVydKtKF37snYTc2JaIfD8MpdR9AS+I3tMvZId5DHlX\n7c6XkYnWB2U0fAO5uu5EDy1kH6MP1nQ11wyUhmCByL11fMwnII+RHt8HqLbFbchBYdPI9/O6+qQT\npVxvSVqR9+E0XO2K7E9Pk7KXGcom+xvkAXdR13tY4vbqR4RzgRP884mUMe4C/YD5/XN/4Glgqwrt\nmRP4M+/EhVAwVyqh5j4odyA/4vkj3y/nzPOutAerQXwXQ3l1plDBeIt0igcgnfh59MCqSE7HCO//\n95D9pWwMBXJ13RUl4XoVhcG3nNGvzj7YCHnpvO+CSMWxdGHgee+HbVtVaKlBby9U/6ETGbTL2qqQ\navZpv1LLl5UC/n2Q6/dUIm6dTtf5qBBTaonqfLw3B9sG7KGu97DE7dWPCAOAhylx50T1Se/1z0NR\nXciXgdeAk6q0Z07gbWAj/fMYUiipiJItPYnCxrtFdCIPgl8jo0xDGThTwDVxWlnk6TEaecWU3Vhb\n8QIbilJjzEQ6/Vjpqr2PtkX674m+WbRcpG5MOrZCXi2TUTqLWDEYFJ0T3vC53WNKQSIX3idRsOQ3\nYjzfC8U7tEpa86V9I/ozFeIQwH7s/GTlFN63LHJC6QO2DNjUrvexxG3mPQlKkfedclX/fADY7Q12\n2iCXDi+kdkrnHZwJnVzr2YwmVEF98yJ1GJ2dGU5xZppKrvWM6Pwa8kwpRJrWdapz5rcxOsW9i7yd\nWt7LyRnZzi7FvY6ieOsthtLH18kUFLVdk5HmSHdfijEYPyThaQ2lNS+ohTJL/FYDh52cRxwfg5/s\n68825Jjgm8hvI3Pnn2ALFe9jidvMezJEkUeRjJ8VFi+S1D+mzuhdlyymIBfBWMdhlE/9L85MmuIy\nR1ef5YZymaBcQ4X6ovvFpbtJdC6MjsezHcfU8qygfPN3IZfX42kgk2KG9PdG6qlXfXP/TloCBvKG\nOwrZBm6ixeIcUGHw131zakgF4gJaIbalWbl65kYZZqeArZfgd9ugk8oODbz7WbAtI/8/H8VhTmD8\nK4FNLCH6PrC96uisdX0R7F/Hb/ughEzToh2e0YRan2J2zmVSbPebYGNRhsZca6KiyNQTfQFc3ejC\nr/GubyCVXic6TeRut/GN/SCXVP/izCCrNNzzU0zfcQUpZsSsE58FUYT1NGSwT4VuF3Au8DW+b5YC\nDjqJv4jSYiROLe5CyXQihdUT/HYZn8tzRb67gS5F2rHE7eY5KboSiLkEdFcJ4QeC/TFhZ23vnbV9\ngwO+OTLe/LIRKbxC29EFsUcWExedoH7iTOD4tGmI8f6+KBx/GkpUtWIT370CSrY3G+wcmlB8pgwO\n8yKVxnu+ATetHgLKbHtehP6mb4AoQ+gHqMxjJrUYIgLOQ2RwyqEY9HlEI2vU5+M76GQfux3kxXN1\nyXcngJ1f/B9LjE+zJ0NlAjGUmvisEiIHIHVPrKyLSN85g/RqyQ5EGRSfJoV8+UgvvatvKFdmtSBK\n3rmcL4yxZFh2MPK+3sj98m1kAEslX0mduCyDAp8+REf1zEsCutR9vEt5dxJJRZAD/YN8nnU602ko\n6WGCd96O3HI3bsL7+iA9+Cx0smw4jQUKIrzGaUglRxCyUYxDUdmx7BsofffWJd/tQKRuyZzA+EeD\n7VuG+D+DHRGjkw5HOrhEWQ5jtNuLYiqBxMXWI+0shdIOvEGTvYcohsXPRP7AWUhHvdHp5VWwvzZj\n0SfAbQlUx/RDpG5KrSZz5B0DwEY5kx1NC6WXQOqKm30zOjauIJXwHQsjx4hCOpGmet8g75f7Udrn\nugU/5F78BnKnTnWjRCf9x5EDRlXJHxUVmlW6kbkgN6X4P5YYj2YOTHUiMVSwoJtE6gMxnSqunSi4\npYMMyq9F3rGebywXkyD1sTPEo30Qf5rktxnQsCjym+5EHhJ1FbkpaXMu5II63iWU7WtN6hzpXwTF\ninQiI+iIFNosbCqzXUocljedVXBdFandZqITQNmsugnbHEIxj9D1aQteCXEJqGrfNHTSi+0x5r8t\nxBbsnyGO86AYjCOrPLM60lzsXuZeb5TSZj79jyXGIa8B6k4MFiWmDLGrIPXIfmXuVU27nPKgLYyO\nsS/GWeAog99zvss3TccdA6/5fDOagvzIv01CDxOfwIcj3eUjqORfSzL8MrgvgE5xM1BgX2IVGPLn\nvsQZ3iVkUJs5Q/qHIyPhLBcEErv/OnMa7RveubRWtbcBqEDP+3H4ApLEb0WqmMw3LrDlfYMpJ+iu\n6RtzxbKxRITkOYHxT6nRWSshY1HEov1lkYKGKnUlHLSAyvt1UuEUgjxZzvUBPLBVGSLSj450CeQN\nx7XqiQTpP4/1jXgMCdzbWu3ycTrKGcQDxDDAIrXJNRGG12MzZSL1yBW+ef2aGl5APve3BnvY++zH\nNLmQe0L6voVOoneADa7wzFoogO5ymhgHgtSik4kko0QeQDVVyr7h7qfPWOJ35z0wRUIwSgqtVyB4\nBZ9w3/f/f+QSddMjN13imeBMoH/k+62RYfMm6ijOnE//W0BeTH9Gx+QTKVEDoDQapyKV2h9oocIY\nKdDfF2U/nYSiSrcu3ayRynG0b/ijaAFX0RTpH+SM/0NkA1q25P5cyEY0DunQ98tjzdVJ29wUbS9H\n4oZVn/PH+nzeLSfcLkMq14BUyR3EyO7p6/BsfcYSvzfvQSkSghFxUapB9HIUAzhmlk7SJg/c/MhQ\n8wZSddzkTH/rvHBKgaZvIMNWQQpcg2KBkBvIUYfbBNr7IBe+11EOp11cCruTFg4OS5H+xVBahFk+\n1muDHefC1iNkGIPQBNqG+6b+jK/VMSg4Kk/+UdD33+xMP1bVQeT6frc+Y4nfm/dgFAnBSBDg4MzI\nwB7NH3cLPqEM7CN6aLK0MnSt4zQVrsxtKK1yIU+uCyK0/21OZvhl6F+5ZOwTBx+14uXjekOErtRr\nftSB00GOywkJfvNlsGs9jL8XrQVvxHnIc7afBtwJLBMCx2aKVXVcVgQeA+YBRgLvA9eFwIJ54dQo\nhMCyIfAbVLfgAmBlVF7zshB4MAS29DGY4yAEQghsAzwBfBvVQNgR+C8wNgQODoG+eeKYJYTAiBC4\nHngKuAjVrTgWOCMExoTAenni1wiEQG9US2Rr4HvALcBLIbBljjhtjmoPXAl8PwHfmAwM9lodySHv\n3a64gxF790U1OJ9DetmlUCh87N0ypV16bpRwqhMZBwt6w3mRsWwyOQbu1EnTcFfxzPLj/mIl9/ui\nALnXUDDYd+nhNV8jtPXy4/MLTt9ISiKdkaHwAVd7HDUHnewCKh5+n6uzTqHEfuEqicOQB9ejyB7U\nY1Q+KDHgI6jew6DI99s6TU1PbIgys3bgDgXIuHxb3H71eboqPV3VE5PYtSnx10eGqbfATm3SgG2I\ndPp3USESFOUl6UDG55ZeIMhI/Udi+nY7o9jOF9G7TmOPVIMgnf53kU7/eZQ1s1bWxbWQl8h05BLa\nsl4tMWjf0+kej9JCVw26Qkbe/fz5Z5AbcKvP7619rE6nTMQs8lI73+f/Ac2gx9dPB5F02r65jiVG\nsKo/f5sEFCzx+/MelCIRtZFHPvTvgO1S5t7XnBmPymrg/P1XIpfS79R6D3KVexZlJGxKFsGE9KwP\ndi9yy/wRdURzolwpt6JTwln0kJqw6MR2CDqZlfXiidHGCGTM70RBYYvkTVdMvPujHEJvo5oGiSua\noSCi3ZE/+cvINbGliuL4JnUOOqFtHOP5NdCJ71GwFTLEawdn+t2ii5GrcCcx0rL7nDtjjmb8LmXe\nAXZhlWcGouPPmWkzfxSNOhW5X8U2CCH1yHkR6bDhSMkG6Si4bT7mm+ihpBBJjIqqFIKZriGFAhQZ\n0b+cz4+pyHV1oxTaXB6lgfgQBQ2t24pSMCrYc4Yzlj+RQvyFz6ftkfF7PIrgzlX95wx/H+R2ei8J\nVDjoFHSMCzI/TnszQ15iM6miBkansEm1+Ixv3r/r8YwfbEgVIo9GR9KqvsPIHW0c2NlpLD7krnmV\nM8mNG2hnVYoukhdWozWb/rXgksYzYG+i43rqCxSlRPgpiogdgwql5MoEkd1lH9/sOpG3TsOpGsq8\n52so/mECUh0dSwvEcaDYlyt97l1BBiklfH5thvTo76CI7mbn6lkQZaMtuJ7WXZYSndafRFHtqbh7\ngu3m6yKONH8FipUpi79vbhPBtpgTGP/vKhBZ0OvHyivvzGcsKvbRSCrVjdBx+GrSq/07mGJel1vI\nOFsmOpLv6Zvhy+h4nvmR3Jntoc4En2vWeyPvD0gNdbn39f2+8DLPk+Tv/hZyG/w7kq63ayb9jsf6\n6JTcgdQCTdmE0InnHnSqyiQhXMn7lva1PhsVO189pXZ7oxiGThqMvvc1OIOYQY9I3/8y2OEV7h+G\n196dExj/DEpKx1HU638nYUcPQPq6i5IOGNL/nosiWOuunFPjHQv4ongX5fHZgRTLPbpEcAAyev+V\nnBKn+eLZxXGYjFJdZOYN45v+Ub7RvYNOH5mnYq4xzt9Htp4PkJops+pYFMs6Ph3p70wZbxVcVkNS\naweKNE1VzYl08oVcQeeTUa4kZMsZizLrJq7rgJwHppMwWytFff/qJd/3d960pv7HEuOUx4QoTyTm\nC/beCIEFvf5FdQ7YQr7gLovLVH2yvupSWubuXc6gR6Kkb7E8K2q0Nw8qGjEFHXc3zYPhV8BtAxQB\nW5BAU+lfZ3ZbISPz35HBdbM0N9KU8ByBIqE7kNppH1LKDePj/n3f6J+nySesGrithE4/s1FRo7rH\n3cd6O2SAfR9J5JkHYSFb3ZlIOI0thCKbx1TqtHmhTKOTiGgckOfdLcX/scTt5j0posgjSftLXbpv\nBM/TwPEc6f3+inScFRkBMuqc5Isy01JuFd5f8KW+1yfXT0ngCYSybR7nksA9pFSIJiNaV0RVmT5C\nusy6cuOjIiuj0KnpJSTdZl7YJgX6+yK10/3ODC9HaqnEcw6dbE+lhWwqVXCNJoS7gATZPH1jOwh5\n7uUWQ4Ly6UxE9rpabs8HoVNeQylOvM9udR6xKDI8L1+8jyVuM+/JUIq8D+gzJNTr1+i4+ZGh5ppy\nUhDyyvgrkpBzT62LwuWvdsZ4OVWMcehU81Pvq1vBVs0b/wR0DnQpquBlUnOzcgawJyplOAt5EqWi\n082pD5by8XsHqaeOIoZbqDPRi52JXgu2St60JKB5SaSTL5sQruTZRZCEOx0FmOUeOIZULZe5wLF5\nhWcORSU3GzakU9T3H4ZOjJd1vY8lbjPvSVCKPDrKTQEzEur1YwzWY+jIGc3OdxjF6NtWUw0sEWGM\nt4OtH7m3GDo2zybn4hcp0Dmf9/87qBj5jqVjgbyiLnZm/zBSjzXVayTjPuhFMcnf35Hhf8sy/bCm\n35uFPNdyLabeIM2LUkwI9zuw4ZF7y1EsmXktGXhhpYD/1kiiv4iIyg6dPN8lRVsO0vebX0t0vYcl\nbS/4D3OHEIKZWfAcMJ+i3DdzmfF5eu+gH3A3MBM4CfgtsAiwrxnj03pP2hAC/YEDUM6UuYAALACM\nBs414538sEsPQqAPsBvwE6AfcA3wBfBdYHHgOuD6OYXeShACCwN7Aweh+Xk9MB3YA1geuBC42ox/\n5IVjmhACCwE/AI5COZH+jeb3b4FLzZieI3pVIQQGAJcCqwP7AesDxwCbpT1PQ+AzYG5gwejYF3hn\nosby3jVLdy0UlPACUr0cnMEuPW9k5zyXHpJrhmKQUAH3T8nRYyNDOnshW8fUCK2Pk6NnTo59sYBL\nkxa59pmTTjpOZ8Hz6+UInU+g1Cgtaa8oQ8PICO5Z1LP+Ogr8Gk3EsKt7WNL2Wi07J0iqPQj4EXB6\n3dnnyoDvztcBU1Am0AOAU0JgkbTekSZ4psitQmAM8Dck9S1mRgC2ADYHpoTAmSGwRJ64NgohMCgE\nTgEmAhcD5wGLAd9AmQhfDoFnQuD4EBiWI6qZQggs7hlA7wU+AIaibJL90CngAOCDELg4BFbND9PG\nIQT6hcARwHjgROAX6EQ7DzrNXge8EAL7h8A8+WFaGUJg7hA4GPgZ8A7wGnBrCAxP+VW/BM4CDgS2\nDIElG2ot750yumu5EeMzPCsiMvgdn9KOuY3r4y4o6ONQRGMh1P7XVCjNloP0MB9yyXwTGfwOooLb\nn+v+LkeG4Ktp0VQJFXDvC7YrMtoVDH1rlZPykNvrlk7rdJSa4+cowVyPkAqr9MMyKDL9Cdfv34rc\n+MoGDSLD7s+Q8fAFFCWbayqQhPQO9LHrQO69ZSV7iq6bf3Zp9wxapK6vr9Fjnafcj3tT+XUosssd\nTQp2QxRIOgX3bkR2sE2K97HEbebdgVHkUUH1NyMEr+gdWLeLHjLqXoGMLZtVeGYwxbJzV5NhgqYa\nuC7neMz2TS+2ax4ylBVSJdxLC/nvl8F1ZeTVMdOZ3X4kCOpyhrAeyoE0CRmFf+0MpCV812vgH7wP\nTkHxG53I4+zbJFDjIBXJ1ihI6u8oanXTNJhNRnSvRNGN9zdgKyb8bcHYe7OPfx4BiYv4ptvpG3RZ\njzKkmn0axRvU7Snoc+WvYPtGvrsGLz2r/7HE7eY9GaLIIz3fXSWE/xbsnDo7bX3kc3s9MYI8fFBP\nd0nkNmLk1EhhIgWwLVBUYCfKJrhMA+3Ni4LAxjtTGUkL2DGQvvoQ5Ko7FXkkpeHqFlCpyNORjngG\nitnYhhaqCet4ro0ymI5HwUcXg21CSd7/OttfFCUXexVF7J5CC0jHTvfGKLZkpo9TIwFcCzqdk1GM\nz740Jw3HYKQtKCTiqzl3fWM+0df1/vVsVChz6itRgQYlezy/+D+WuN28J0YU+VKCnMhBSAKOrYZB\nKoRfIpVAtxTOMX4/H0pT/AEqvLFJ2tIFOokchgJSXkWFvlNLZYCk4m8jw+i76Fja1Lzxvug3BLsO\nSXm3O04NM7oq7xyKAtme9nfehIKl5msm7Y5LHySBX+KMfrzPy7LqrBT7fC0kUX+I1Gi7NnsTpGuu\n/wlI/ZFKlLK339vn0oO+2f+MDFKCI63DNd6Xv6pnM0WuyK/4/E+aKfR1sO1Lvv+y3q7+xxLj1MzJ\nUJ1IjJIjTITQs8CujtlZX0eSX115NUramhvp1yegtLPd/MvraHMoxYRSt2exqZR551rI93s28mTK\n1JaB4g9OQOkD3kTpbRsaizrx+Jpvrg+A/QMVzjmADPPmIzvVDsj3vBPp4E8m4qPeRPr7ITXaE0ja\n/hUZ24BQsOQxSCf9ZBprJsY7h6OAqsJGv04Kba6JTv0d6JTS0JxxXnIOEkZ3jPmbA33sQsn3I8DG\nF//HEuOT9eSL3zEYJUaLCKEL+QBUXDwuARzvi+17aTJTikUnXkJGxX1IILVSzIF/FwpWOZcmp2V2\nPIZQPK7eSMxMgTHb7uOL/C5fgNcgVVtL2BlQsr99kO3kYxSl/QNSUIcgNdZIirr2x5Fhb5m86Y7g\nOAydNqa5EHMIKVZNQyfzs31+/yEN5lsHDguhk/rbKCPsPiRQA1FMm/IgOqEdQ8ru0ugEPNnXR8UT\nOFLZvkf5Yi3z0sUJBkuMRx6TsDyhmEslZSMRUZ7t2yvcG+qbxuNZMlSfGFtRLGJyBFWOr0idc6hv\nFq+hJFq5+907EzwB6dofQgbCuqQydBQ+2yWZp11KaekyjEgS3hlFi85GifxOIIFRHxU1ORipUv6B\n8uQcRJPrttZBex+kIrnDN6nraMBfHtlXbnBh4iJSyl3fII290anrIZ+XoyiJdi15vhfSpT+DTqkH\nkqFqDJ2KfkuVGh/olHxHlTam4PECcwLj/2elCei73ASXJoZFvt8SnQaOrZd51Tl46yLpdjpK7rZg\n5N4Q5HEyC7mrbVbvwsqYhr7I6PSy9+EtzsyGVPnN3MgY/Stkn5jhtDZdlZFSH5RzEz2DMm6iyO3y\nGKTCKLhd7knPrbk70BnMG+gkcC062VZ0DUUOELsjG8IkFx5OoqQ4e6tcyFPwCnQK/T3Y2iVjv6+P\n+YvIFtTMmhHbe78fV5hrKOneuc47qmk4HgTbVp+xpO9uqZQNYGPNWKPyM/QDjgaOA25FAU0/BHY3\n48nmYNoNpxHA8cD2KPjof8CKKPjkcjPezgOvpBACy6CAsM1RcNg/gYf9ehtYG9gW2BgFv93v14tm\n/C8PnNOGEOgFrAN8B9gF6ANfpvJYAhiEUn7cATxsxmd54JkFhMDyaHy3BTYEXkbj+zhKn1CYG8OA\nv1CcG6+Z0RpMpAp4GowDgSOBfwCfAEPQ+J6FxrPpdITA0sC9wIvABBS4+ifg52ZMq/K7S4GJZlzU\n41M2UBKKXGW3WwzM/LqZHFULSG1wCDruF3C6vprU3OoXMlAeA/ZFhCZDes+9ybCQSt6XH/vXRuor\nK7muQeX8MncfzJH+gifSU2Xov4gWV2XVoK2QyTZK02nk4HgQwam3r7UCPhVr8Zb87ig8Syd1SPyt\nlrJhQq0HPIXDFcBTwDdRUqeJIfDDEOibMX5RPJYJgXOAd4EdkJTYC0mG01Co+Y1+Imh5CIEhIXB4\nCF8msdsThaGvjULoNwSuBg4DOkLg8RA4NQTW9eRqPRZCoE8IbBYClwDvAb9DJ7e1gF6mFBnLoZPO\nqcCMEBgdAruFwHy5IZ4CeFqQ4b5+7gRmARcBz6FT7AJIyj/K/04OgSdD4KQQWM2TKrY0hMASIXA2\nSv2xPDDCx/Tr6BQ3PgR+FwLfbCJOIQR2AF5BvGMj4ErgmhBYKkYTE4AV6kYg7124uINhYPvU2OUG\nIgPMTVGpC/nJ3oes5XuRka6fYjDKn5BR8NdUSMiEAk1OcL3x3WDr5d3HJfiV6uo7kLFzJDVc11Cc\nw3b+23FI332XSyEr04L2jDI0zIu8kK5zfWpst0u6u4neTcZuoinTPgi5ef4O6ejf9dPMyFrSr/fb\ntij4bCIxbQM50bksst18iGIplqnw3ADkPDIFRcnuRYZBj8jb7S8ofufLkqjOX36M4ofWrNHGULB3\n9RlLjEPeg1MkBCNieClD6MrITetnlRiLH1GfQ4aaLVIcqHmRx8Y4FIRzBDEDgvy3hzvujyMPmlwY\nIzI6H+6M6mPk1nca8vOve7NEHi57oXQXU5wZ3IgMxy2R/8jxXBCpqm5z+h/3zaqRkPpybqJHthjd\nCyEvpktQXMVs74PDUGqBRoqIL48y6ha8m55Ext7VcpznI5AhdxbYL4hZZB6puXZBXntTUWWz1ArU\no3iDO5Cb5v5UMCSjAK1Oqvj7IxXRZ+IvWGJc8p6URUIwKuTkQZJpB9h+MTo3IOv8BGTC/CI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 为简单起见,令A和B为1\n", "t = np.linspace(-np.pi, np.pi, 201)\n", "a = 9\n", "b = 8\n", "\n", "x = np.sin(a*t + np.pi/2)\n", "y = np.sin(b*t)\n", "\n", "plot(x, y)\n", "show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lissajous(a, b):\n", " t = np.linspace(-np.pi, np.pi, 201)\n", " x = np.sin(a*t + np.pi/2)\n", " y = np.sin(b*t)\n", " return x, y" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vymZywMNlm6U1pZ6BVAKPKuhBOcufEJQ9NU0p5sS5YprsBN/elb1cZrT6mV7k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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# matplotlib.gridspec.GridSpecBase\n", "# 指定figure中subplot的位置\n", "gs = gridspec.GridSpec(3,3)\n", "fig = plt.figure()\n", "ax = []\n", "\n", "for a in xrange(3):\n", " for b in xrange(3):\n", " ax.append(fig.add_subplot(gs[a,b]))\n", " a1 = a + 6\n", " b1 = b + 6\n", " x, y = lissajous(a1, b1)\n", " ax[-1].set_title('a=%d,b=%d' % (a1,b1))\n", " ax[-1].plot(x, y)\n", "\n", "# 使得子图适应figure的间距\n", "fig.tight_layout()\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##2. 绘制方波\n", "方波可以近似表示为多个正弦波的叠加。事实上,任意一个方波信号都可以用无穷傅里叶级数表示。" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$\\sum_{k=1}^\\infty\\frac{4\\sin((2k-1)t)}{(2k-1)\\pi}$" ], "text/plain": [ "" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Latex(r\"$\\sum_{k=1}^\\infty\\frac{4\\sin((2k-1)t)}{(2k-1)\\pi}$\")" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-np.pi, np.pi, 201)\n", "k = np.arange(1,99)\n", "k = 2*k - 1\n", "f = np.zeros_like(t)\n", "\n", "for i in range(len(t)):\n", " f[i] = np.sum(np.sin(k * t[i])/k)\n", "f = (4/np.pi) * f\n", "\n", "plot(t, f)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##锯齿波和三角波\n", "锯齿波和三角波也是常见的波形。和方波类似,我们也可以将它们表示成无穷傅里叶级数。对锯齿波取绝对值即可得到三角波。" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$\\sum_{k=1}^\\infty\\frac{-2\\sin(2\\pi kt)}{k\\pi}$" ], "text/plain": [ "" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 锯齿波的无穷级数表达式\n", "Latex(r\"$\\sum_{k=1}^\\infty\\frac{-2\\sin(2\\pi kt)}{k\\pi}$\")" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-np.pi, np.pi, 201)\n", "k = np.arange(1,99)\n", "f = np.zeros_like(t)\n", "\n", "for i in range(len(t)):\n", " f[i] = np.sum(np.sin(2*np.pi*k * t[i])/k)\n", "f = (-2/np.pi) * f\n", "\n", "plot(t, f)\n", "show()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(t, np.abs(f),c='g',lw=2.0)\n", "show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.5" } }, "nbformat": 4, "nbformat_minor": 0 }