sine_to_bram.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32768,)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 2**12 # 4096 pt FFT \n",
    "fs = 2**15 # 32768Hz sampling\n",
    "\n",
    "# Create 1s worth of x samples\n",
    "x = np.linspace(0.0, 1.0, fs)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32768,)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yt = np.sin(2 * np.pi * 180 * x)# + np.sin(2 * np.pi * 110 * x)\n",
    "yt.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f992ac63978>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eLGNKiIMdY4V1NU56sCbzxu2XztEX1lJBY3k1AlSuhHZqJaSAMwZ9jAe9+m+OrNGwM+xjXPRFysTltTPMu6/xoKe0kAvV85ovDZYrU47TKLxqD53Z1Vvx9nlJ96EV1jkew86w9FwlRk05pnzO1+8M0COIkwUOZnb/lntKKnM2QdekYph4FpcEX5zMVzAG2LWbQoqbThcgaja7fFOUWUnjoo/pYiXKH7fC6NSowLCQH/7pYoXxoJcnQKuNKxVqdu1HFS+JALXXWIUiPZCNZS0X1vbe7X2pPCGlwnM9IZVlXfEaF/3W7yTHOBCZ1jsZa5WQy0ujhOZlFtneSL6Gqyorq94bSijpjNKIstmC46KP5cqImiy2z4p8jgfTMttqVFTetVDmbIKuScXQCEL5gltrfFf5cPcra2ZU9EAk24CzxQrzpWlBExKFYjHq3WGBcdFTwQVjR4CKhFplmWkhFx8GkVhBrrU7UkETy1roAjp4Z1zx0t1Xr1F4GZ6Q9OBPPIWn8brKvaGDXHYdhSdSQjWvvirGMHEC1u6cpbwslCSCQmdlFtnesI9+j0R7ykJkLchQMEfrnTSyQ2kcKnhtiq5JxTCZLzEqdAtuBfN4UGK0i5URBU7tISYijAoZLGQFmFpYz5cY9An9HunwcasoC/2BVCuG2cqzrHUxhvGgJ3apO1CSxjsZKL2TmS+sJZZ12zs5yhhDY7X2MFZlCi3qtSjnLIfIdod9jIdyRX5Q1SPUnpAAFvLjNKUVL4uR2XMpVV7TRYkauPCOZB2tYhgXfYyFMqCe47DYKobjoulihVHRw6DfQ79HIktyXgmIYeF4GgKh4XZSlFoLbV5ya3e+XGFY8ZLCBYtlGdRqK0pFjGHYU0FrvrWrsqwz4IKdgW4NXV7jQU+kTCwvF4vXekLaoPqO0pJ04Z1xoVnDEqYZD+XPy08WkEKhBxVE1uuVRpQGInMFqGScxe/tPKVjAJTwjmrtS+XaswabUG40qMEWSjoWKqGkalMUMqFmA7KDfk91IOdLg2GFEUoPZJuXfFPMl6sWL5HQdTyhOlNIeCB7BAz7PfF92YKu7IyaQV98iIHGKszxTmpPSBEQdmErUezEjzFohPWawWe5EirhjGG/h54QCj10oJNGUQqMjQq2AqwRpVeugHxP2et3hjIDoPGEGiUkMQAOnPsaCj0GF36qldALLfhMRK8joi8Q0UNE9ObA928nok9X/32RiC463y2d7+7ZxHw4KqEk14qX4f6AL6xlQn7Qp4qXLJPBvrZx0NfBO23vRKbwJq5w0gQzXVdc6J3YbBWbhVPyl0Mu41qoyeGdsWNxqQLdSiveVnSrFJ4TVFd7XcMSlgDyvK6FInDaglwUCs9VXlKLfHdQ1GNlsJWjhIa6jDArrKVQUuMlN2svVcq1ISrcUy3PtbBJMsfnMaz9oh4i6gN4B4DvAvAogHuJ6B5jzOfsNcaYn3Cu/58AfLvzE4fGmFetOw8N2eAzoIB3lgF4R+JpLHwoSe4xtHnJMFDLSxo4ddNOVe7xvHHFR0Vf9NayFsSghCaGRU8VO6mzVXKDz9ocfM87OVRY8bt1PGMpehOejWcU/R6KHqksUN9b414Y40Iu0gKyg5bC0xkbtl5CyquVAbXQ8GpQA6limFUG29BBDSQew3xpMBo0BptEwFtDdOgaoi8wj+HVAB4yxjxsjJkBeDeAOxLXvwnA72+AbzZNF2XwGUBZJyB8uED5oEZKK97CO1JhXSuhPtUbSqa8GthKau1aF3+kzNKazFwrqCdM+W2Ek2YNXbdfqhjsfbUFocyDshDZSOjhuRBZk1qoCQiXStkYGeTiWqBSodaCkhQQ1HS+qp+VFO5qeaEKaG0yX9aWuJ5XT6WEJrP2npLMz57LUdFTpZDOFss69ieFJ0PGobRtxyZoE4rhNgCPOH8/Wn3WISJ6KYCXA/hz5+MxEZ0noo8R0Rs2MB+WpnPHYyhk/VVCUJLMWmgCwtIU0jYvRfB54fBSQkmjQp+DrxXWTaBQt9kP3UNcyDw8v84CkOPjLnQyW/AVpzZbxQ2ciryTmV17dz2E8I711oQeb21Zt2AQnWEjF6CNEaXJZnJ57QjjIK4ArfevgNfM5SWGQvPjjDVqIIzHNcahDqHYFB138PmNAN5njHFX5qXGmHMA/hmAf01E/0loIBHdVSmQ8xcuXFhrEhPHY5AK0GZT0HpQklCZlLx6Dr4ojGcUNp4h42XvoV3gpoOScqxWDfbs8pIGTl3YatiX15BMFu1sFYA3AOpUZseylginyaKEyKwScucdo1XV82hUCzWZt1Z7hkp4crZcYVjFyEZFT+TRuLCrnedsKeVVedfCth2uFW8F/VQQO3HP5bAvu6/GYNPJgLkfZxRlJjpxRoVhsynahGJ4DMBLnL9vrz4L0RvhwUjGmMeq/z8M4MNoxx/c6+42xpwzxpw7e/bsWhMu3ePjwf1nS4NB4VrxWl66rCStZTJt1Uzo0h/HSuVqhd5okB+8kwZO3SCyKnA6a2esSeZYK/JC563NFwYjx8MreaXnOF81e6OcoxQfbyxQTbHa3I1bFT1Rh1rXsKmFtXA9amFd9EQC3uU1UgRpS++Eal6SNjAz5zmrElAWba9LJgOWDS8F7Lop2oRiuBfAK4jo5UQ0RCn8O9lFRPQtAM4A+Kjz2RkiGlX/vhnAdwD4nD9209RKV5VifqFgkLAmYdh3rPhcKEm4Ae3B2hEWFk1rj8GtLZAdktGg7QlxFaczx7K2gVNpYZGryAF+PazCax1IiQdVWfEAxF6NGxOyvERCd7lylImUVwPT2HHyjDUqCy0z41ZDoWJwLeuRwoqfOx7vsJB5Qq5lPay9E50RJfdOusFnKQKgTkCp78vxToTFlpugtRWDMWYB4McBfADA5wG81xjzABG9lYhe71z6RgDvNm3p8a0AzhPRZwD8BYC3udlMR0Vl8LmxgnRQkj6FVFvHENyAQl7ufYlyx+sYgwNbKWMno6Inar7XQAwNNCGyQBduAN/Gdzhe1RpaodaXxXfcOE0taDhejnACdJa1hRgsT84TmjtGg52jVhBaXtwcjTFVurXl1ZfBNAGPQaRQlisM+zbTTXZf05bHYL0T2RkbZqyhvV6Tbt2CyKQp606MQZPQsClaO10VAIwx7wfwfu+zn/f+/t8D4z4C4Ns2MQcpGVO+ulELJbmbolelE0qzC9q1BTpemirr2XKFG7zNzqU/Nq0+ysBp0SOhsG67/QAq7Lsfn19IqAkPiVWQUqHmHizLS5K37ypXK6Q4XrXbX/Ea9OXQhGuNS3i5Bko5R+kami4vBvdfrNrKdZRhxdfCWqooXXhHaDQA5TpYm1O69gPtfblKSAEluWdlXJQJDauVQa8XP5ctedMjDPvyOpdN0DVX+Ww3zWigw8dny1AwSLZx28FnZaBb450sTMsCNaY53DFy0/0AnbAeONZ4+VmaV0eoZVjWA6FiCCohkWIIK7w0r7bHIL8vPa/potkbGl5ty1+rhHRY/Hy5Qr9X9uyyhoJYeTlelybQPShI5Z34Hq/IO/EgMiKpd+IoIbHH296/mvb7m6BrTjG42Rnl//uYKWMMms0+cyw1CzFwWPzUEWoqK365wrBoSu8lc3QL3CxPscVVCwypZR0QoCJeAQHKjJv5Qk1oWQcFKGNZ+xCZ2IoPwFYcVONakvb/IgG6aAtCgBdOvnIdib0TPRy3XJVV8S7unx3oFq6Hr1y5c+l6oXVTTDFE1ngMgCRG1l778aAvbtm/CbrmFEONqQ8aAarBF9exTOxD5qz40OGXC7Vms0vmaDf2KMNj0GPxHryjEDSDIo9XK8sl0xPSWneajBot7j/PVK7teIZUked5eK19WN+XTLnqeRkQAUUFt5S8lAZAv4eVwLv299RAoyiL9rlkY0lekoH0rGyKrjnFYAOQo0IpnByhZt1kUW72Qi+sOwJUalmHAqfMuDorqWgw/GwYRGhZNziyzAoKKSF18Fml8HTPa7ZsPy9p8NkVoCPp3vAhhrWel044aeAdP57BeichD0+hXIkIRXU2JUF1dz2sUSRVyi0EQFszId6//lmRxcg2RdeeYvCgpGFRWQsCaIII6Pcs1k2ivu8tq1ApaAZa5ZVhgU4XSxQ9qgNhWZtdaVmrs0Ec5ToS3ldHgIp5mdYYGa/Kim8pIV16sVoJZXmTmR6eVrnmrGGA11LwzhMXIgNssZow5bfQnZWOB5WjlKXZZ/5Z2XoMR0tuQRfQPGROyM8cywSQPajVymCxCmWDSOGCJuAqDZxqLTXXurPjxIKm0Fm7M0+AltausEjQE2rcwcqNMQQVuTCFtHWIhdauem+Egs9SRb5uBpQ4JtSsYdEv23XneCf2t3heTXaPZP92DRRZa/CZt/YDoRUfjlsJeRW6td8UXXOKYeJDSWKLpqlSLcfxMIhvYagzanpKaCJgxUus3Y5iYDZg6YpnxBi8AzkoZEH12WKpt3Y3YVlneifDolenbKbHdS1JMZyREacZdnB/nXIdVe85lnjXvrDOidNI5ugq8nKO/P4NZVvJeZHKOKzPip/Bx+wPH54sEYqtYjgysh7DyMvemQrw8YErQAUPyheEUivIbkAL70iEmi1G8vFxbo5uq247V0kGiTGBQyy2drWWdYbXtU6cpmgsQvtZcswaaZ05wqnkpY+dDBwh4847PqYLkYnGLZrsOECWYdSBT8WZU6a9fwu+kNHnJe3n5CshCe5vz8qw7+0pjlcgBXqblXSE5LaZBuSYtRtEBqQuayaW6QtrgaCxGRX6AKOH0R7hfc2XK/ScOE1OHUN29s46cRqp21+Pk6ValgVuXnqxGCJrnvNiZdhXZ7pp00QkWvuZr1wVz3mo9BgaXo13IuVlBXvNS/u8qvF8T6y2Ehr0BfcViEsAMoi314ppbmMMR0p2ce1msji5pDirI6yPyT0e9HnLpAOdKA5xR+FlCCcJr9nSt+767LrbOE12AF9tWet5rZMB5Ss8sQD10h8lVnwLchEItfz96z1nUUA4zEsyxzaUxCvlDhynUMraeFzX8pfLG5fXaJuVdLTUjfbLc7q1WHwnWCXMSJj5uL/AWohZQSLrTsnLbxpXx0603omE1yoiMDJwZG2MQVoIFgvSsgVTi6bSl4hUa59jgXY8Q6EB4KZnSnjNOsJ6nfuSQLzrxTPEyROBDChxEkShlzdaQ3STdM0qhiwBqrTiQ6mFObxEbn82Rru+J6SppB14ylVcj2B5CQ9WJ1AogBiaoLoWtmorIV0saTNrn+UZClNI/ThIznPmhW63RsD+VnKc551IMt18g01jAGi9a/u8RhuQN9uspCOk2rWzUJIwENcRoApXXNv2IBTPkArQkS8wBN5JJ3indo/zhFNpSXJBuFzlGhIYaSveD6rX7Ui0BsBasSRGqHmxE7m31n3O2upbjRIaes/56Kz49nurRwOFx6u04juKXOPh2YSGPrU+j1FI3swZXpuka04x1JZ1z8NoRYJGZ3F1g5J5MQaJy1pbd3W/HuFmX3SxTHGMwU/BE4zTBtVzPTz/YEnqVfwsHMuPO5C1ouzp4yAtGEQiaDIVpdtNVMwrtvZH6AnlVLh3C9yUCk9Y+exnQJV1DLJ3kGTFaQqdd7JJuuYUQ9QyUQaeVLipd4glgWR1PCM7IBxwWZUxBs1m18YY/FRQaTuSkBJyfy/FS4vFz5erVvX40WaEhQWoGh/XGDY1vCN7zaxfGzMq+nIDwA+qHwVEFjFsJPEMdewvFlSXyBtlBtQm6dpVDNpgUMAC5d3BdgWzvE2F3mWNWyaS3Gyl1ZobpwlAJ1w7Ej/jRzzHRTdlkpujvzfEvAIeHsdruTJYObCVnaO6OOtYss90Ci8EkUnfm90YbH0xr/ykkA0oVyUc1xS46c7KCzIriYheR0RfIKKHiOjNge9/mIguENGnq/9+1PnuTiJ6sPrvzk3MJ0WddhOFDPPLyeqoA0/HEHwOVfoCeYdYgn8CzcEqegQStT3oZpBwc/SVkB0nEoSewHDnnuLlKxSZIs9UQmoPyrR6djVrqCzOyomRrQGF5qaQirKSPAEqLnDLSRZoQX985f46cJw2NXaTtPYb3IioD+AdAL4LwKMA7iWiewKv6HyPMebHvbE3AvgFAOcAGACe9J4eAAAgAElEQVSfrMY+t+68YlQLtZ5+s28shVRgZdgXttvxUizTLaF3P4+OC2xAWzAVe8OU7x5LUy078I6z9rvD9H3pLetuLn35eUJYe0F1y0uSGuuvIZDGx/2Adc1L6Lm62VYcL9tN1Od1ebJI8vKNDc1LZrTKdZ2aiVyDraOE2AK3FU6NG5GpyeyyPOpYl/KsDPqNd104nx8VbYLDqwE8ZIx52BgzA/BuAHcIx34PgA8aY56tlMEHAbxuA3OKUhQPVma55Gx2aa+kPNy0W+kr5eUfLICz4i28o88fD/ISWdZtuEubS68R1jmZJ9p4RtOyQy9A3TWUZO/4e8OOO6o9FYaSlB5vn39edlz7eUkK3PIMNj+DTwInT739K/auF91kl3LufA+uTdAmFMNtAB5x/n60+synf0pE9xHR+4joJcqxG6MoHqyEXCR5xbECoRx4hyuY8g9WbcVzFZZ+rxnBgfR7HgHS5mVdq5Xj5XtCdlxOyqT7e7ExQJ4A9VNjeV4RYS3K+HGVJB8j8y1kQIfFF05bBvf34vxMN7NLnL3Tjp1IxrnwzqAQ9DDzaiYsepCTFMK1I/HPSq53LTUqN0VH75OU9P8CeJkx5h+i9Arepf0BIrqLiM4T0fkLFy5kTySUdgpIIRc/B1+Hm0ofbje1kK+18HFTQJh5Esi24uboK6FyjnrLWqIogymkR2XF1/elX8PjijGsc185SQbDAGyVEta2mWNLqPUkDSe9+ozqGcg6ubbXUFyNXI3rVZlukthavnftPWeBEvJ7QAF8s89N0SYUw2MAXuL8fXv1WU3GmGeMMdPqz18H8J9Jxzq/cbcx5pwx5tzZs2ezJxvC1O3nKYoFn1NWvI+P94UbcL5ceS2++QMZtazZLo75aZ1aaM0v3JMoyljwWWIVtg8jb1lnxzMW7W6iEsVQZ+E4c5SkCoe6iXK8/LoTOy73eaXW3jZzHHn3JdnzLg+5d9JN61yZMusrRqGzInnxViiDDzjC5ImAF/pCgpLuBfAKIno5EQ0BvBHAPe4FRHSr8+frAXy++vcHAHw3EZ0hojMAvrv67MioIwgzcdNBvwfDbMBsSy0C7xxNlkskU0gAg+TAO9r7inpCWktSI0AzrPhgaqzEO8losRAybFICND+A3/ZcC0HVbmjPD4oeFgJIyBpOQANfsVCoB0+q5li0lZ5ECeXuKW2GUUfeFLJkkk3R2llJxpgFEf04SoHeB/BOY8wDRPRWAOeNMfcA+BdE9HoACwDPAvjhauyzRPQvUSoXAHirMebZdeeUIv/h9qtgkGhTRDyNWJZAEHKRQhMtYa3AkZW8Op6QArPOyRTSu+IBT2gtyCXuQYVwf2ngfyOKPOt5ZSpyQZB2FihILD9PxZ+6a2jjccaYGpbqzrFtjVssPnUulyuD5Sqy9stV/ZbGEC9/jiIIKmJUypSyVgn59yWrt9oUra0YAMAY834A7/c++3nn328B8JbI2HcCeOcm5iEhP8YgCQbV6X6RAxlLtfSLdgA5NNE+WLwV5PfQkfBaLFdYma7lD+gzhWQwSFhYp1L3YgL04IBPtRwWAbdfEFRvrwdftRu7r6NSDCEPL5kssCE4w/47Zf1bDLwt1Kp4wap99lzyPTygtP61e0OSDmrPStHzhDXzVrX50nQgMuCIAv/+/hV4hpukTUBJLygKbUAunS4YQNIEaTvWLv9av41k7zDCOtYbqJxD3LKuraCcgHBIqEksUGW+fyi9GBAK0BbEwBcxhfoQ2c+jY0I1E6LAaaw+QxLr8oqzmBiZD1v1e4Qe412HvBNJvMAPttpxatjKKi8G4nWD6oAsmykHnoxDvIL3MQSMw+Nqi3HNKQZ/swN8mmAQ5xYGntyaCYC3FppXdDqBJ80GLNrYbgqjDWHqjXfCN5vzrSD77oQUv6BQ08YY+r3kwQdCMSGb5aJbD1EDQy/G0FjWEuivvTf49Mxl5HnpYEb7G1yMzLfwuTRtv5mjyytlkftxtYaXIIhcdNeD8wx9GcDdVwi2GohkQABay0ANpNmTm6JrUjGENmDSZY1AQgCP7Xa8k3661bTf+rnFS3Ag2x4DJYVT+GDJrDv3WvvvnAwSgLfugOY9DEAFMSitO9l9ha1dTgl1IBdBFlnjTTr3JUzrdOdnY2SiflPKOfrK1f5GUsAH7kvS2j50Lrn9G4sJufOI8/IUXk/onXgp64A0080Zx8iAkl+7FmQkuK9N0rWnGBZdnJOz4mOBXYCDC7obkMN2Q7CVBMucLVetHjoAUAg3e8ja5QJqPY/XoE9s5kn3nblrZJAoM4Xq+xJlkXkKTwlbNRk1+vtarAwL7/gxMs6ybnjp5ujDVvY30rGuOLyTGjcNCWuGVzLGwHiG3ftKp6vGYgUAfy7DsJWyFkQgAzZJ15xiCMYYGHw8GEQWCuuuy5reFDE4A+CCz+0eOgAPJYUPlgRKCntd2a64skJ40O8lBTwQcMUFsFUYsxa8qCeQygwwQdqEF6q14rkCsljdScmLgVz8gDDDKxS3kqyH/7zsOMlZ0Xq8fi1IwyvPYEuelZBxKIz9aVOgN0nXnGLw4QxAHuTSuuKhg8V5J00QuS3gAT5NcOTzEkJJOUoodw1D2HMKqvHbMpRzlEEu2hz8GLQmgZL8IC1XyBiCd+w9sjCIb2xwlnUkZRJghHXQsBF614Gzwo3L5+V4yULYKsQrpxak5JVKge4+Lx41yFN4m6RrUjGE3OO0ZR2yFvggl5+tUo7Tu8dSa1fLK2RxFYINGOZFQuxZByWFXPGCgXdSrrjI2vXGWW8nPq4NW5XjOMWQgkHScwwrZYFlnaOEAlCoLAOqHevieXXvizMAgt1wpWclYMVLoKQwapBa+xzvJM5rm5V0RORbkkAZDFLn0ksFqBK2SsUzeIihvdkLdrOHgq3VIWYzSLrZKotEVlJQuUoC+IH74gShtfCHHiTkziM8x4CwFryvI5RkMOjJrF2/Qlgyx64AzRA0khhZUKgxXmhmjCFcx8AZNt2aCWlCQ+i+tLETm1HGeicB1EDb5Vf6DuxN0TWnGEICdFCkceRpwBWXtSKIWXc6l7VJi2Nc1sBmz8mxBpBMPY26/dpipJ5MEHZc8T5hvorn4Id4lUFa3op32zK055h+ZiF4J5kaG6wFkUJJvgEgtKy1uH+Ox5vYv5v2QkO1IJIMqJnXRsP+hr4mSdZ/K5QeL4I0g3GrrWI4EtpYjEEUOA3ji+rgc10hnB7nb8AhY8Un01U5iCxocekghqa2QGu1pvtUhSAGgM/S8ruktucY5hWCrew4fYxBqIQC6yGrz9Bnn4XOigR2HbXgSQu7auG4dG1M412HaiZS97XsriEbpwl5vPz+DabGCgPdfk2S+91R0zWpGDYB7zRWPHewAgVConTVLgyidVml2LO7cQsh5BLilYaSurwkfapCvJo4SHiOoW6ilrc644fxDEOwVclLCiV1obWcwL+El18LYn8vNS6IxR8B7BqtmRAZbN3OthyE2lnDHpctGIettPUZ3LkM3ZckvXiTdA0qhozc7IC1OxLiwZ3NzsBWwc0u8E5CB4vtNZOErZSYerXZY/BOKABKRBUWr62+TR+SRhCGvDW9cpXwyjn8Pmw1FCnlMO6vzQiTBml9L5SDrUJKWRpUD66hIKEhWGW9YSs+DFsJzmXkvrRFcduspCMmv3MpUHkMWutOuAFD8I5MCWk3e6Bwj7mvVB44iz1HhHVMqMXgHYlQ6yrXNN4aEhiWNwcXhOZX/qb+vrggbUg4ufP3KVQLYsflZFsBfKpwfkZNaP/qvbW0Eurel6hwL4NXCLYSGYeBGAPXp6rZv804a0RwRaSbomtKMZRdUkNWIRPkyk5XjVlBOotLFOiOBIQl7Sb8FgtcDn5MYKTmGIV3ih5TaxFew5KXPPgMWGuXC7aGhXVsjnHYijcAQlk47vxD8yt5hVJjdbUgMngynDwh6l/UipHJguqhYlB1GxhpS4ygwaaviud4haC/2rCJnM3QGpb8+PqdTdE1pRhCfYgAAcQQyhIQZSUtuw+Xa78R4CV5aUlMWKdy8EPZKpaf/hCnPY2QJWnHsVBSYH7ub/oUcvvt39qUSSmU5MNWheC+Qge//C69hjnJE522DEIoKQSFSpoDZnnXyv5F4SaQkvsKKTwZHKfvNqv3DEMeHgA2BXqTdE0phuiCCyGXEEbLY/HhHPy4G9n1TiTvjAgHadMCdBoR1rz1FI7TALwADQf9dAKDy8EPxTPs3/oYg0xYd+FJRoAGPCEuSJvav7x3EhNO4ftarUz1/oQ82ErfmDG0p2T9i/wWJoCs7XaLF3NfoRYm9m9t7K9RXkojikmB3iRtRDEQ0euI6AtE9BARvTnw/U8S0eeI6D4i+hARvdT5bklEn67+u8cfu0kKZeEA8qwkbeApZFlzuGQo+8HOOSeeAcQPibWq3GwVQBaM73anTCuhaJBWEhDO9k60AeE4bBWFkhICg4cztJZkjBdfdR7K0AIQzSQLGUOWtxa2ajKg0hlyQThOEqTNyBaM3RdrsAWUOZuVFIBPgealRp35BbyTco4vICiJiPoA3gHgewG8EsCbiOiV3mWfAnDOGPMPAbwPwC873x0aY15V/ff6deeTopA7aP+WBIS1/XDC1gKTUVPDIKFWBEqLq65i1mHWEihJHWNIwDvpHPxUjCG2hmEDgC0ES7j9nHcS9kIZQRjx8GL5/qF9aHml8v1TaxgzbFKwlSRt2oWtuAwoY0w8XVVSTR+EknRrz6W5xpSy5FyGWn1IeHUbGL6woKRXA3jIGPOwMWYG4N0A7nAvMMb8hTHmoPrzYwBu3wBfNaUsyVWqYCphLajb+zKHJG4t6F1WLpiZsnY5aC0UOyl5MZs9YKlxMZeoAD2GgDAf6A7vjQGXKhwKStYeHqeEQtCfFiIT3pfSas3B1FO1INqAsKyBYbhrbGqOqRhZujo7sfYxGRA5l5IXOW2KNqEYbgPwiPP3o9VnMfoRAH/q/D0movNE9DEiekNsEBHdVV13/sKFC1kTjacWpq2nuADlW074ryvksibiGQkCYR1Iw7XfxeYHtN1+O0c+XTVmBWXAIEolVAtQpbCWZJ6EBCEg8LpCnhBj7ao9oZglKYCSYvcVm2MSjuMMlBj0FzW84rySyRPLbi1IOY6vOtd7vBFjg3klaAgy5GRAKF21nGM6brVJKo6FS0VE9IMAzgH4r5yPX2qMeYyIvgnAnxPRZ40xX/LHGmPuBnA3AJw7dy5LbcYsLhfe2UG/M26+7L6YBoDgBT8JF14pQEeMtRC0CuuS/Vg8o+wZ47r9JW/+YHUKn5h2Dmncf7MWaIxX0SfMJzq3vxFqOthKYu12hDXT+iRl2KjXkGnKlo6daKG/dGp3qN1EOcfG2Oj3uucyVAsCIJm9E60FYWN/cYMt9c7ynEy3pj7Dh3j5tyRuijbhMTwG4CXO37dXn7WIiF4L4OcAvN4YM7WfG2Meq/7/MIAPA/j2DcwpSDGLi3ttXugQA2nrKbYBuSrmWByEs9RiLzpxfzPEy18LQPDmt4zWEaFakHKOTOZJBpSUdPuVnlBziLXtN/iXP8UC+JuHyMLdXwEJpt7NtuIaGPp7imtgGIvTcFlaIegPSCc0ROOMnMcbUcqSFiExjzdeNFn+XigpJBW32iRtQjHcC+AVRPRyIhoCeCOAVnYREX07gF9DqRSecj4/Q0Sj6t83A/gOAJ/bwJyClLJa3e99mkY2YCrwFAvsctiuffA+vMN1gA1ldVgrPipoAsKp5CUInAaKrAB+s6tTLZfdNulcMDOK0bK8woVPKV7JGENmAJ+t6A54vHqFx9SCJCzkZAPDlBGlhch6zJ6KGDap18zGUQPeiArDVjlJITLjUJsCvUlaG0oyxiyI6McBfABAH8A7jTEPENFbAZw3xtwD4P8AcArAH1SwxVerDKRvBfBrRLRCqaTeZow5esUQwUBTDyq8AeMWaDSXXhBj8LM6Gl7hMWVFd8A7KQQHK3CI+Zewp6wg3eGXwCBxeGezgdPwOy1kWHxO1Xl2AH8Da2gbGEaVUAy2cuZYdNGdIGzVzDGdbdUxNjhPPuAJWV7xrL/480ryitxXKiBsUYNo3GrDsOsmaSMxBmPM+wG83/vs551/vzYy7iMAvm0Tc5DQLJIKym7AhBUUe+FGPLWQh0GCGzABTYRaHdv5Ael2Dtar8MfF1mK5MlgFqsflGVBdaze/L5M2xqB3+1koKeUJJaG/BBafITAWqzIH3zco7BxHgxC8E/cMU9lx9vtQPC4EW9l7y7kv9/vQuLBhExfWqSJBO/8QhWIF5Tj9fbEFmoFaEKDcv/uz+DtZNkmbgJJeMBSzuLhX9IWs8XJc3AKNbgqJdxLa7AnYinOP4xu3a80A6XYOqewiILWGK1AggM+mq6ZwfzZTKOB1Ja34RDUyk16sffnTPABbWdw/CoPEcG6BpxEUaom0Tu45py1rXTyOjzGkhHXEO1FnkXFtVroZhvZ3ogF8DraKjjNB1OA4oaRrUjHEIBctFp+MMSwi2LPAO8l1j+ObPY77h72TeA5+KpceSOXgl0J3ExAZH6eJBxj1QXWZd9Jt9ZGGkkJCrcfk4MdgK7Z3VMSwkQVpdVh8KG/fjtNDf5lnJZFCuk6MIWwcpmRAZB8KFLk2TrNp2ioGCDZ7SlhzAjQWzIzwigW6U20PUjg3ELdMFqv4fXHpmd0+/QK3X31f8ViBnX94jpVl3euuB/tmuk4VOBPPSEBJXA5+dD0YiCFerKaHQrWVvs2eSngnRciK5yGXWJ+qFIQa9HgT6aqpOA2Q9q6jnlBijPvbXV5hWCgGJ3PvcN8kXVOKoUmZDFu7Kfcz5kbyhzgC7yg3+7DoC6ygWJBWaUmmAoWcK54SGBG3ny+yUubgL5coeoReAKNNQ0nxJnpcfCdU+OTeQ2ic2jOsjY1YjEynhFLWbqqoE0C0VUUOlBRVroJEDb0VHzY2hmzNjz74nGqf7c6lM8dUPCNh2GySrinFwG3ANJQUxv21WHwDW8Ut0JglyQa6lYHTGJRUJDZgKp8byBMYfKwgjMWnAoypmFAoBz8WVJfn4EeMjQTMELPitc0B+Rz8+HNOwU9hXpx33S0SBDJjZMxzjsYYEl1Z400q+ee1MdSAkTfR9PiEEbVpurYUwxoBYbVlEsW5y0yOFIYfcsXTvGIuK9/OQbsBswNqiWyVbO9EGRMa9OM5+LG9YT9jg7QebGVx/5iQnyasQq2w5qrO054hAxlmQUlKL5SNkemNjXg33DS8k1JeIdRgmIhnNLCV0miIoAapNdw0bRUD3E2Rbh3hU8q1i252QTAz5p1olRAHJc0Dldl2nLrzo6BjpL7wKez2szn4MV4JyCWm8ADbbTZ+XyHYKgWDNG8SDCsvNT6+RkID3/RQ513HYKuil4oxxFpi8LyimUIZzRxLXlp4RwD9ZXgnwTVkGjNukq4pxVDHGDrwTr4bmYv7p2Cr3GK6eLpqCkrSbUBOCWnrM2y2SgjeiUFkXA5+7BDX2TsBRRkLqtvPcqw7ILwesTcJAkwOfqQWRNLGOVbIyKer6mpIsjL4GE8+Cq1FvFCJJx+FyBIQqjp2wsmAlCcfQw22UNLmKRq8YwKMoc6lAC8wgHjRmbaOIYllskEunbBOvXyE2+wpfDzmCZXfK+GdZFpnRGAU8cMfg+PsZzkBUPd3g7yCNSTxXPX5Ml4LYr+PzzGW5cLAVptKIU3ETrhiOj0vfX0G97bDULsUO+eYQp5GjI2mkFFbTLeFko6EYsFnSXvq2IOKBYRjG5B/g1tM0JSueMiyZtNVI/cVenWjHRd/UXlYgHJ98GM4dyoHP1YtDSCZg58qfCp56WMM6WyVsIAHwnBXzJu0n3Fr6NeCpFKFY6/oLHmlITJAnxobbWx3FN5JSoAmisfsNf6YFC8O+gufyzAv+6pe7RoWfUqmQG+Sri3FUD2I0PsH3O874yLwTjLTItGO2f2+y6v7nmh3jiGBzVrxUSEfP1ixDRjDaIH0m99SWTju74Z4aYOZKegvxisZY0jl4C/iAsP93daYSFDSjktBZLGMtfL7wPNaZSqh3KLJpUng/nmB7pSnHNyHiTW0v9V5TwoXZ4zsX/sMg+cycl9ApSgzerPZ74+arinFECs1l2QkBN1IEe7ftax7xFgmge5kSaHGHOJ0tlVYEMZ4pSzrFAQVeuEOkA4IxzqX2s/Sa5gSoPH7CmaeMLxie8O9hxCvaEZYKv6U5BWHyLR1OPNl5B0kmfBOXlZdWljHeWW0+shMCkkprxh0XX6WXo8YxAvEDb1N0jWlGFIBUICxTDIt63CKW3xThPr0c3OMFe4RUdqKTxxi9x78Me58WnMs0jn4sfYbObxSOfip4jH7vU8x5Wo/09ZMNDGXUKA7Hs9I31c8VmC/7/JK3Ve86nyWiHXFeKVhq/grMHPTkkMvVrK/o29dzik8bk/pIcNkZlck/gTEY4abpGtPMSQsybgLH8k8SVgZ6QPJbIqEZR2EJmqXNexpRGMM0c0ez8GPYbR2nBo3TeTgp+AdHvdPxRg2p4S4GEPoecUKnyx/fVAy3sCQi51ECxJjWTh1AD8BWwXhHb7Vh7brccyTHwiqkbvvLskLCKeK1WJJIfYzfSfXLZR0JBSzkLlgUCp7B9Af/nQL7bC1MJJAE5EeNclAd8TNdX+3xSux2bkeNbFDXH4fx2hzlGtKWIfhuLyspFRQsvxenoZb80q1S0l4eKF6lZRyZeG4lBJSCkL+eVGgm2h8DW0tSGpvpALCoRRofj3iMiAJhUaMUe3aN90FXiBQEhG9joi+QEQPEdGbA9+PiOg91fcfJ6KXOd+9pfr8C0T0PZuYT4xmi/DBAsoHFRLWKfdYlv4YFhpql9W20ghCSQnMmskf9yt2AdSfpRWerm9MXKiloKQjOlgJ5RpMS05CSQwcl8CewynQlGxgqLUkU2tYMI0Zg7wSHl4q5Zfbh9pgq60FCQvrRECY8wyTge4EapCKMSjXI/7K0hcQlEREfQDvAPC9AF4J4E1E9Ervsh8B8Jwx5psBvB3AL1VjX4nyVaD/AMDrAPzf1e8dCcUsfyAeDOJwQvea1riUG8m4umosM2FZx97fHOsNBLgQmRaaSOfgbxLe4TJqsjOglPfFCYyQkE8Kpx6jhCIwDRCBd9ZYQ7U3yaxhMk4TWEObqKE1hriAcCiobsflpKy78/HHlNdkGIeBtb9+Z4BvOruHwLuYNk6b8BheDeAhY8zDxpgZgHcDuMO75g4A76r+/T4A30ml33gHgHcbY6bGmC8DeKj6vSOh2MMF4m51KohcC5rAgbQ4d+iNWrEWxMaYKnsnAVslvJPgHCMNxdLwUzxwygdptfBOboyBETQJGEQfY0jh/rH6jF79fXcMA5Gl+mglvJOUgaJWDEw8IwmRRc7KcmWwCljxMV71HIOV6mnoD4jEyCKKvOYVha3Swecc5ZVupNm1j1/zLbfgz/+Xf4yX3rQXHLdJ2oRiuA3AI87fj1afBa8xxiwAPA/gJuHYjVFKMQwiwaDUwUoFnmJuf8OrO8a6vuk+P5s5/LUgjLzaE4hZQfEUUi5/XCtoasglx9pNel26oDr3MhY9lJSCXPRZZElFnooxJKG/CLyThJLSFjKAaDuSGMQ77IezmZIB/FRAOGkchtc+BcelaqD44HP4fQyx2N9x0kbe+XwcRER3AbgLAL7xG78x6zduuW6M0SCMVJUttJWHmLFAY5ZJDF9MYpKZ7nHcE0rFQATCOlLsE4eSIu+ZSME7a3gnIfw+CSVxxUhaXoKMtZw3ne0E9q8kgB9rbJdMBQ08r14vngLN1Z3Ya0ae1IllkQFxiLf25HPOZcxgY8+lNvgcbrBY8iJM5rqYy3HSJhTDYwBe4vx9e/VZ6JpHiagAcD2AZ4RjAQDGmLsB3A0A586dywrL/+J/923R72KViClBmHYjw64nEBfWnOVfzie8AWNKqIhALlaAx1Im3Wt8XimMVpvZJYGSosHnjBedxHhx0Jq2B1RjIetgvKKXaOewWOH6nUFgTDxTKB3AbxoY+pAn513nxJ+ASlGNuuPivGJKiIdCw0o5fi5j+5fLtoryYmTA5cmi8/liuYrG/o6TNsH9XgCvIKKXE9EQZTD5Hu+aewDcWf37+wD8uSlzye4B8MYqa+nlAF4B4BMbmJOaYlY8l0sPxN3IeAZUGEpKprimXFb2EG8wqJ7gFYOSuH49QCwHn0khjb4USF/gxscYlLws5KLFnov0KzBT+zCkvLjMGHsPnTlGCi3L3wpn8Nm+Yem05NBZCXsndt7pwK5WWMdhmhicPE+cy1R3gfQahmVAas8fJ63tMRhjFkT04wA+AKAP4J3GmAeI6K0Azhtj7gHwGwB+h4geAvAsSuWB6rr3AvgcgAWAHzPGhIG3I6bYBuSyi4B4RkLKPT447N5mHUROCNBQ0z5OCW0USkqk/A5jXleiX08yBz/RRC/ZhIyz4oMKLw0ZqnkloCQOe472torwSjUwTCkht4GhL5jnyxX2fMzHzjEKu/JGVPyspLzrkOLig8/BmGFGjCHXiEp58lwWZGzccdFGYgzGmPcDeL/32c87/54A+P7I2F8E8IubmMc6FNfgm4d3yoBaQhBGcund+fi8Uq54CMtcSO4rsh4hy8mOC6dnxrFn1rqLZHbFcvDTL8HhoSR90Vm6wC2cS5+Gd2ybFR+uS2HPcdzfChqlx7tc4UzK2EiclVi/qfKayFlR8polnteQUcq5RlRo3CjpCaUVnrbB4nHS1VVLJ4hGTOApFTiNu5Gx4DODmybd/vDGTafg5VlBsRz8lHuc7kOkz8HXQmSpl+DU2Sohoca1+I4FhKOtPuIQQxq2SgWt05i1GnJJBq31WPyRwDsZZ4XjpT0rR8MrbNikeB0nbRVDRXGhlnBZU5YJI9RyWgqkeemENVeZXf6uzhUvIthzo1y7GTWpHPxU8I6FyBKKPDXarZkAACAASURBVFYRG3oJDoD6pUDBt8xFPKjyLXOcUMvwDKMCNBwgT+X752bVxWpI0vAOh8UrYwwpRZ67p4pwjCxZn5HqHZUKPsegpEQCynHSVjFUFAuoNZif/hAnLZNkm94Ubqp3WfVWUKrMPxVj4Da7spguhQdHcvBFmHoocFrxChck9mAMOl10beGTFpoQeWtKpRxTQtPkenDGxgYDwsnkiYxMoYQnn4J4U0ZULEbGFVoCzTp3eWWu4VWOMWwVQ0VRC5TpXAqEA8JJAcpZJokgbWgcn666Ofd4tlgmN3uqP026cC+cgx/DWllMPTCu3yMQxWGaUNDfnaN/b6lYAZDw1gSB06ixEY0xpC3r9LswYoZNRIAy1m5On6q0saHLWOP6VKm9UMl9RXjF9m/ciIrHM46TtoqhIjbTItI0zr3GpVSqWqzqkWtCFuOVE7zjUkEBRHLww31ccnmlc/C5QLfpwDsphVfCO+F4AccrNMcUJGTHxZ6XzSTyKdmuOxm3YmoLgh5vqpBxjRiDtraAha10sb9kcSF3VpTwZNqI0nc/SCULHCdtFUNFsVbYyc6l2ZZJun9R8u1jGRhtUBAyqaAxXtx9bTbnPI3R2mtc4jDaWEZYOqgeXnsuUJgSaimjobymfV+26WFKgMYKEt3fbY/JFWr6wGmqXfc8K9+f31NhXpzCC8FPyygv1mBLGBurADy5DT6fMIpimSJXPIxlaltipLBMC4OEi87C3SnLeeuhpPR7C9YppgvfV79HWZh6aI4cRhuD1jg8uPxtTwmxiiEeB+F4+UKeV0KxtTfRoDpXda5OnmDScIGIYcMEhIOxE4lhE1v76LkMGzZNUD1UqW4VXrj/Fm/YtPltg88njOKueGqzp2GQlMu6CHSaTCkhC4PELK4o9hyzkFf5OHcoT92OC1pBifsqx8WVVzzGEDtYaYy2XMPwc06NCfFK5beX4yJKKJlLH95TKeUKxKvOrYcX6/JbzicUVNfj4ynvJFVlnfJC4zGGfE9IDyWVn4X2vX3BTywFmjNs4s95qxhOBGVlWtjWyhnwDhDHrGOexqgf7jSZChTGA6B8poUae45guymMFijXUVsRG/PWOIx22A+/D1hyiDv3lShILMfFBU0KYiiviSjXhGcYu69UYBfo1qvUL8HR5vuLen1FhLU2xpDkxaXhamNk+ZBhKoAPhODJbfD5RNGwSlf1g5mpVMteL5WrHg/SxtJc2Q1Y9Gq8szXHpMVFmK+698UHafX4eKwls+S+Yr3zU/eVwyuVpZUS8OU1m4GSuMAuEIKS0j10Ukoohd/ba1S8EoHueINFJslAHcBPePKpQkYGItP20bL8cuFJrXF4XLRVDBXVB9KHdwSHP+ZGhlJcgfzAaTTox3gnoRz8FJQExN/8JsH9fSHPwSBRyCURO4lCSUeI+2vx4Ph98YFuf09JYgzaLr9FhBe/hpEmegwkBHTXMNVg0c4hOylEqZSHVfJE3DhMwV06b62JucQMtm1W0omgWDAohWUCcYtmKrJA/QOZdiPjQet4S4wickhkuL+yr03mGqZy8PW81rGslVASY92ljAYWIosaKPp2JDFeIwaOiyc0xAShIE7jK7wVA5FxabjarseSwH9n7QVxq2DDvrhhE40xbIPPJ4tq1863nhbxl20A4WK1JnjHbIqIVZjTgpjj5beotryKiKCJvkwole5Xv85St9lThz8eKwjHQTiFl3pLFx98jhS4KRV5KsYQ67/FKddYRo0snhF+XrHgc1bsJKqE8gL4Fn4KBdXtu6L9ccaYKvgcbytif9vnBXDKS3cuY833Tkp31a1iqCj2OsCUJQmErac6eJcQGEFeiXiG5aXt+x4PcjFYfARKSmLxRURYMxZoKgdfC+80vOLZO/HMGC0WL4EY8mIMetgqP8aQA1tps4tiFnIqiGw/j2Xwpc5lyIhaMPBpFN5hzmUMWsvaU1uP4WTRqB+3aFLaO7QpuCycGN46W8YbuZW89DBIEbHiU030yrlHGqXlYPEcrxjkIhCgm8LHuYIu97e7vHTPK9mvh7Fak/BOrC2D0mNgPddYvn/KaMhNTLBz7Hi88b0B2PWIZazFvUl7H/64nHMpykyMZSVtPYaTQbW1GxA0nGWSY9251/m8Qu4xEIZcbPAu5eYC3YDwfFlCZDFeebBVZLNXf48iwfhBP1ydnVN0xsM7/eCb31KFT1F8nHvORcrD08GMbH1GrP+WoMjKH5fqkmrnMA8EaVPCOvau6FShmuVlf7s1x4TCA8KZQqkeVe7nnTkKzqV/VrhzGctK4oyN46K1FAMR3UhEHySiB6v/nwlc8yoi+igRPUBE9xHRf+9891tE9GUi+nT136vWmc86FH1QCUwSCOOLzUtElFhmopFbOceupSaxkN3ral4SiCyjk6v9bZ8XEId34r2jEkVWRfy+gJRQSxXTaYO0XBO9BO7PrGE8jVFZdLbG80oZAKFMt9limcy/D0FQfFwt0o4kkZhgx0Uz1rQeVCKobsd1xiTeWgg0zzEKu/Ze2B7DmwF8yBjzCgAfqv726QDADxlj/gGA1wH410R0g/P9TxtjXlX99+k155NNKbw11QJ30O91uqvyLqvl5VtBS5aXOiiZcFlTVklI4dl+PZwFGt3s2uCzwBWPx06UsNUivh6N0dBWXqkeOkC6QpiFdzL6MsVwbjYxISPGUF4n9xhic2SDzwloLbV/Qx5vc1b0weeUdxKKJbGea+U9dxAKJtnluGhdxXAHgHdV/34XgDf4FxhjvmiMebD699cAPAXg7Jp8N04pbDdlLYQOP5+FE6ukZYR1yDIRtH4O8uJc8cTB4tJwuxBZOcciitGmigQ5JRRZe20r7JSwrgP4flAyHTtJtVlh01WVyjUn+Bzrv5Uq6nQ/D3uhOmNDqoRCMTI+KURpoERahPBKKKDwuDWMdglIe/LHRevO4BZjzOPVv58AcEvqYiJ6NYAhgC85H/9iBTG9nYhGa84nm6JYJpP9EDr84s0esNSSlknGwUopvCLhroaK6VLv2bVjYryGCYw2ZMUbY7IqR7k5DmO4f5JXOviczm/Pg+O6vBjcv4hk7yQEaKz/Fge5RFMtE60t7Ny18E4qxsDG/gLWuP0uNqbktYE4oxC2Cim8qx14BgSKgYj+jIjuD/x3h3udKSNRXfOo+Z1bAfwOgH9ujLGr8RYA3wLgHwG4EcDPJsbfRUTniej8hQsX+DtTUsraTcM7cSxTnT8u2IChOgs7jxSvrhUUb9lRzr0fTS3kAt2hcUmLKxC8s6mFqUZuQCjQzQcYtbi/DZqrs3dSvKJeV6TGhS1IrPbUyt8faXgy1H+Lry1IwTvKGINw/4aUUPJcBt4VnX0umXhGKPgsqZZ2r3PneBI8hoK7wBjz2th3RPQkEd1qjHm8EvxPRa67DsCfAPg5Y8zHnN+23saUiH4TwE8l5nE3gLsB4Ny5c1EFlEupRmnpgHAI9+cLn4BYoFt3sLjNngrSpl3xRBpuRjCTFU6ZEEPIW4v16ynnmICtovBOXpsKy8sY0/KWUmsf61MlCeDbOY6cd2unCvfK34uvPR8HCaR2czEGtdcVX/tUUkgYCpUpvE3UMtm/U52I3TnV45hkl+OidVXTPQDurP59J4A/9i8goiGAPwLw28aY93nf3Vr9n1DGJ+5fcz7ZFLV2l/HcbCBs7eZaC+wGDPDig8/hINd8uUpmPgQzLTIhshScUfPyYStBtbQ7J3eOLJzhzW+5Mlgy/XrCvHh4J9inSrIeMWiChfE2gI9zvDKLQUNrL+WV9ZzVsGtsDblaprjXpd2/qbTp46R1Z/A2AN9FRA8CeG31N4joHBH9enXNDwD4LwH8cCAt9XeJ6LMAPgvgZgD/as35ZFOua5e2dnXdOrkNGLJ2Wegk0Qo7DSWlhFNGVkfSak2k4XJpjEo4LhkTilVLR17GIoXxtPh4aI68oozDXWrcn60tiKw9A+8E95SgZqLkJY+d2HHZsFXQYEsZh939K8kic69r87r6ioGFklJkjHkGwHcGPj8P4Eerf/87AP8uMv416/DfJCWxTK21y8I7qRgD4x53FFeVMqkOcmXgwax3YnlprdaQJZmOMdi5h1KFOTjOdtC08A53X0QUDfzH+vW4c5wtVtgZloKb69djx3Xvq1yPODQRK4zL8ULzYgyS/auvY4gYG+y5JFya5AWE82RAewxXuBdNnmBqJo6Lrv4MTghlQxMha5fNfkhYXEo8OPXaQSAftgoKJ6l1twnhxAW6owKDsSQD6aCc22/5qdcwALlw/Xosr81ln6UFTTjdOl2fkQo+szEGZR1OKjWWNQAiiRraGANXZZ0D8aYyE78eoKSvG2o2RaD0PhM35aygkLUbswiBxj12WxFwQa540RlXMxHK6mC8k+xAd1wQxlJqYy0W5stVtGOs5eX+PtAcztS4YPZZVYwU59U1ABrYKi1AQ/fF9esBNuUZpnt9pTLdjqo2JtyqJh37U8eEEgkNufs3th72Xedh5frCDz5/3VAq/ZEr2tEHhOMWl8TanQWEWo51x+PcYe9E23M/9b4IO25l2m8tmzIegx3nP68pi6l3IRfuedl5dBWlqbH92Bj394HG69K2WJBkrLm/DzT9ejiFF2tEmGrxDejhnaB3Ig7SduMF6hgDZ7AlCk+5tfffdc55eKk5noQYw9WfwQmhVCUiVw7vv/Wphlwi42LWLo9ldrMmpEGucEsMpSteH6x4kJYoBJGle+iE4R1eWIdeJsT20AkIa0kP/BC0VqaG8sLaXccp43XZeXTbpfC59PY6d4z7XWyO8cCpsrZA5J1oYdcYr/z6opz26lyrGqD9nLmgup2HNiZ0XHT1Z3BCKIqPCza7n5I4ZTagHafvNdOdozTQnYPR+pW0XDdRW0k77fDiPQZ/jjOBxxAqwmO7bqZ4ZVl36Wfs86qDyIIAuUt8VXHXsOEsfyBeTS8JqmthkNC7oo8yxhCFd5S4Px9U786RM6LK78Ie1FYxnCBK9Y1RW7sCQRNz4bkgV8mrK2iimz3RBz+JxVteK7kSsvMI1SRw8Qx7XTM/SZCWIqmF8TGhTqkcxGDnEQqqc2vh82p6OTE9sbQ1LgGhxgXwa17B2IlEuTb3tViukg0Wy3H6nkJp2FWXwWd5FZE5ptriyGRAd+21XjkXZzwuuvozOCEU6xsjCd4BvlUosXbDvLg0RqAdtOZccQtb+RtwIcgDL+ekxE0jFqjEig8Fabme+znV4/Y6d4z7XYjilnXmfUXeTQEg2M5B6nVpPYawcOLqabqeq+QFM+EYQ1mpHhPW0bgVp5RDtSBcjCGztiCkvCRnJQatpQy246KtYnDI7xtj20xzRWdAOJjJBp60aZ3JDcjBVlqIrHtfEsgllr0jSyHtBp/198Vhz7kxhnARnsTDCysh5X1xXlci0M2nQLcF6JSDrQLxOIlyzdqHAQ+vfglOSrlG9iEQ37/9aIxMaNg4skO6p0LQ2raO4YSRn+Im1frutYCT/phIZQxZu1yQKxmkVVpPrCu+RpA2CJFlWtZc+m4nSMt6DAE8ONPtlyYLaAPCw1Cge7lKZkCF4B2bXswmT4SsceXzmgp4heJq0thJaA2TrWoCMTLuFbNx1IDx1uo4XvO+juwYGbMex0VXfwYniHwMVGK1hiy1WVVUFAvelb/ZVkLGGPBNyOLCmhVq/mYXeidBzJoZpw+c6iEyoKvIAQtb8c8rFM9IKqEIL0lW0lzrdQVThZk3CWZmxgyDsJU0gN8tElS3PuEyuwIxMilEBngxskW6/bv9Tdfy59q/l2O673EQBf4jmVNbxXDCyBfW9pBpUxI5tx/oWrtS1xPQC9Bgp9RE0zh3HkEllCFAOeFUXqf0hCKVtJzicn8fkK5h+L0FsjUMxGkEhYwuscI6BO8IvK6cmonUGkpiDH6BZmoNQ6nd0qB6+fttXpzQ9SEo6Rra36/HiWBXvbd2XHT1Z3CCyA8Ia6Akfxy7AYuwEso5kEVVRRkdV4S8E1mgO5RquflgZrcBnNQT0teCrBGnCbzBTfK8ghDDpuM0awRAw20Z+PTMoCfECFA/tVsCnfgQlMxjCM+RM9j8PTVn4CcgYkQt+Fd0hlCDrcdwAsnHWyWbPZT+KNnsvrW7zgaUHaxmzHJlYEw8E6ScXzegJgsIdwNq4sK9DWUKiWCQRft52d+LjgvmnHMvi+muoTSzK+gJSXDuDGEdyt5JCd1QkFYXj2tDUFzevg/xSp+XOy87TnJWtDUuMeOQva+i14Lj7Lnc1jGcMOpAScJgK9C1drXCutnsggDjQrkBPYVnD2ayVUKgMI4rfCrn3z5YEivI8poG1p5z4f3eVlNhBlQwIMwoL31qbDdwKm714fFi7ysgdLlKXzsPv3Kfy0pqgrRdo0EbSJ4KoBPfAFjHk+fOip+okXsuZcZhT1Wsepx09Wdwgii6KSSH398Uys0ute6ADCXkWSZHeV8xV1wSOG3lxUsCp/0ebCfQhh/fiNDnJfUMwwWJuoZ9Ejgu1pRN5gnp409A0/XV8mIFaMSw0Sdq6I0oiRIKKUquj1bJi7z6DMF9BZUy/+5mP/AvOZfHRVd/BieIfKtQEmwNWdZcamHJq52SKEotrHl51h2zkUaeZWJTC0UC1Le4BFZQsEGdMg13tlzWHShjlAVbBYK0ucVIXKA7JayPAt7pReCdnOQJrvrWj4NoePmBZJmxoTVsIlCS0rAReUKRug4tL4m8OS5aawZEdCMRfZCIHqz+fyZy3dJ5e9s9zucvJ6KPE9FDRPSe6jWgV418yKXOShJh8f6m4LOSghswgxd7iGOWiUhYtw+/erMLawSAdpCWawtu5+jHTriCxBjEYH8vNU6rhGJrWP5eOihpXzdajxO8wCXmhebU4UjgybC1y0MufiGYxIoPJkFIYCvPSNHGGKT1NO61gNwT0sqb46J1Z/BmAB8yxrwCwIeqv0N0aIx5VfXf653PfwnA240x3wzgOQA/suZ81qKYeyyz4pX4ogdbNZs9/QrBHF7RgJrSuuNwbvub2jYaTfDZC+ArYyfSgLV7rfvvZEFiJHsntYahV4LqPKi2oEllCtVzVCq80P4VC9BQUF2QzeTvRVGm0KaCz9kQmc7rmgvvKwjxvtA9BgB3AHhX9e93AXiDdCCVEczXAHhfzvijoFiQ62iCzzF8UWBxaQNqvgBdynlNWxaXEUAMbV4iPDgKxykV3pp4sCSoboO0q5VhM2qIKOoZaiumS8glDU/GsurUQeucGJkggB+DJ2VGVBd21d6XLI2cEEyNVUOhPK9RR97wcbXjonVncIsx5vHq308AuCVy3ZiIzhPRx4jICv+bAFw0xiyqvx8FcFuMERHdVf3G+QsXLqw57TCtY4H6KYm51q66944w+NzGdWUNzwBfYCwFHoPv9mcKDEnsJAKd5BQj8ZZkO0hrK2pzg5mibp2tuJDMY2gLUAHkUnQhF67fVMmLMhReZO0F8bj2PpTV04R4aSEyaZfU8vfb9Sq8DNBDvMdFBXcBEf0ZgBcHvvo59w9jjCEiE7gOAF5qjHmMiL4JwJ8T0WcBPK+ZqDHmbgB3A8C5c+difNaiaCGNMgVPugFnAStIL6xl7rGaVxAf5zMt1kn59RUeL5z0sJUNaOdgz/ZaV6lLLGt/b0gKn0pe5b01BYk6GC8/SJt+sZIdpw4+B/bUVAS5hJNCslJjtR6vgpcvO9RxGgGv4yJWMRhjXhv7joieJKJbjTGPE9GtAJ6K/MZj1f8fJqIPA/h2AH8I4AYiKiqv4XYAj2Xcw8bIP8SagLA2h7lr7fIFbrEMkt3d9GMsrdZAzrkEzlj4Ck8QVFemncYgMolwskFaV9jnwHgSPNheuzuUFSTacVroxH/Oi6rwSWKB5gTVXV6ABsZTFgkGegpx6cWW15Xpov5bpfB8AyAzxiDx8HwD4PSYO5elIl+tDHrO/uX21HHQuqrpHgB3Vv++E8Af+xcQ0RkiGlX/vhnAdwD4nCnB2r8A8H2p8cdJflOr3BQ8qWUS8k5SvEIpiZI3PmXVTMQCoJxw8i1klXXXFjQ8r3aaoMRjsN9rg63+4ZcUPtW8Frr78nk1gV2dtTtflu864NqluDzKfwsyoCIBYRnur9tTvrDOT4GWxv6UL3EKNPqTKLx6jhUsKZEBx0XrzuBtAL6LiB4E8NrqbxDROSL69eqabwVwnog+g1IRvM0Y87nqu58F8JNE9BDKmMNvrDmftWitGINyU/gpiZLgs+Xnu/2igLASi2/6/Og8IavwbJBWYgWFgrQSnNufo9QV94O0U6FwAhpBI0k7tXPx74ufX1vhaWCrLn6vuy+7JyVKeSOJGtJ8/0ALE4l37cfWctOtU+NCjf5EBoC/pwTy5riIhZJSZIx5BsB3Bj4/D+BHq39/BMC3RcY/DODV68xhkxRtbCdJSfTxcYW12+/1FTCIXxgnO/zBrCTJIVYG1d3eUW5lp6Rgqq2Ul2w+tx+kzRWgoiIrL0grybYCQvclE4SAoxgUHoPaw/OgJM0+vDLpwjtcyi+gz0qKvSdFHfuTBPAzeJX8umdMsjeAav+OTlaM4erP4ASRbXdsrV3JprDWrg+DSFxxwIUmbAqerjAuq8JSIEDrIG2r6Eyx2T1rVwt3zZdGlIUDuJALn4Vjx2khBr8DrCS7yM5l3RiDtPDJf5eANDPGzguQC6dOjEGU8tuGDCUpv3aO2n5TsU7ER5Hya+fov/ddAru6c9y2xDihFMKRidJWENANZqow64VOqGXBBUUPK6fdsS5Iq8T9+/59yQVNjsIDGq9Gc4jVnTC9YLzKkswNdHsKT2Ltbix2kmGgcIrLDwhLU36jRWc9icer9Bi8PS/1DP23sUkD+C4PSav546KrP4MTRH7amcWeU1YQ0BbW1grSpD8COktN37bYs0Azsfh17ksyx3YxXX6QNqcVAQ8lha07dV68Qljb5yyOPwVgKznOrV1D/4U2SxHU5fKQWsihtORBn0n59dbQGCNWXqGiM0mdS6vuRIEa+Ovx9RB8/roivxeRZCMBbUGjEbolr0oJiQ9JALMWwjvdjBpeQPkuvFZY63B/LbwTxv05i7yTKqwJdK+pXKVZOIBjWQsD3SGhlgtbiRSel5asjp0o4hndF+7o9rwGZnTfFS2e4xqQYccA2CqGk0W+VSh5uEAbLpC0BnB5uQJ0KPBOXF7SNz6NvPuSK6FeJw+cTcFbQ4B2GxHqBI080K2HrWJWvBZ7zknDlcMZ3fYbapxb6jEUfoyBh2mauJqN4QmFddEtcGPH9MJ7Q2rYNCmkfJdf+7udDD7xntLN8Tjo6s/gBFEH8xNY44C1QNspZ1pr17rHMl7tQywRhJaHyzMn/VGKj2tT8ELpj3LIRW/tdiufpffVtkAluep+ppD0eXUgsgzIRe5N+rCVHveXZnapExNCcBwzxk8h1cTV3OslXX7LcU29iqTLb4uXco7HQVd/BieIQpif1GOY+xZyhlst9k46br+8atfOkcNo7bgutivb7L4AzQvS5glQWRGetrdVeV/Tztrr7ksUO1kjgN9KZV7w7d9HNtvKD4Bq03CXfM+jrjfJt2ax41am7UFJrOph0cN0rltDv7ZAovDKcV0llPucuWSX46CtYnCoAxcIDjHQdnU1+H3JK0MJ+UI3I3Aq2eyuoFmtDBYryVupPIhMgY/nBro3AVsdVZA2lP54VLBVqHJfAtPYa11eXGxtVPQxXSxbhYycEir6PfR7hGmVmt00w2OU16DryUsCtKOi2b+SJn8AMB70q+urOQrhZNcz1MQlAEfhVbw4OPk4aKsYHOoG4viAmh2XA2e0eEnjGY6122xAqaXmHGLJZnetIClG692XNJ4R6pSqrRyV10xsErbSB4S12TtiJRSArXLTi7k5jgelFb9Y6fbUyLHipYp8VO3v6XxZz1FisFnl5fLiFIpVQpN585zVMqBGDXTwpDTZ5TjoZMzihFAH85NaCxlZST4MIhGEllen0pcVGF0sU2sFWQHPvy3OV64yKygUVJf2mvGVkLZFyHSuF6CSrpv2e33ls4WtltX/5caGDyVxY4oegUifRWaF9UQprMeDPia1x2B5pQ2bccBjkOzf8aBZDynMWCshZ45qiFcJW1mDbb7kOwofF52MWZwQ6sYYlmIBqoWS3NYRQKWERLipA1uJMdp+a25SiGzYcsVLXtbVjtHIE9aTOd/LyY6zlmQt4AdS2KotQFmr0OFlx0nvq16PuXw9XGE9mS9rQRejGs6w61H9XzJuuTJYOMqcmx8RYVz0OwKU3b++sBYaUe7aS9Nwu0qIhxntODtGqvBqJeTMUQQn90OevMxg00K8x0EnYxYnhLrpY/lQkrgK1HUjlTEGKUY7rt1jnRXkHix7UHihay2uRjiNGKjL/m4jdC0vmSU5mTfKayTwTlyrdbkqvROpsK7XQ6iExoNyDS0WL1mPouqi6ytlblxIeYmU8qDXuS8Wi/eEtVSojQd9+AF8qRHljhNl8Dkeg5xX4L5ExiF1oD+pF6qNMx4HnYxZnBAKFftIoaS6LYMiqyOfVyZG6whr2SHuegwjxgL1ldB0wVvI5bhGCU1q70QnnKZzmXJ1eTXVpnqhSySLnbhYvGQ9iKi9HgqPobzeriOv8IByHbUKLxQQlsAgo6KrhLj921HKggwooLwvP57BQ0ldT0gM8SrhuG58R5Yaexy0VQwO+Rp8KniTFdCuelRvCmU8Ixh8FmK0tTAU4PdAW2DUwkl6iBf5wlrqMfjCabpYsoqr/N1S4RljHIiMweL7PRQ9agldqXcClGu/rNqlSDwo16tZz2MQrIdrAMyX9WdpXm24azJf1oqam2MuPOnOkduHQOUJLdp7Su0ZzmXK1U1Zn8xlRpQvbybC53UctFUMDjWYdSl4J+JNQfWmbaw72WZ3N4XkYJWBbiushZb1wHePZbGT0aDfgmnsZ8kx9hC34J1cgaHzGKTPazzojNA4wgAAGVhJREFUw5hSQU6ESsiOq9dDIXSBUqg1a6iPufSIx+I36TGw+9caGwsdr1HLE7IKj/NO2h5vGacR7ql5W1hrldBkIePlNjCs11Cc2m0cXidDJJ+MWZwQ8lMtpRvQdSOlwtrv/ijl5bZY0G72iRK2KoW1LsbQ8RgUAsNa8VJh3euVLc8nGUoIKBVJY40r10MhdEteS7HXBViPoW1J8t5Jc1+L5QrLlcw7cT2Gek9JvRNHUYqFdaYR5RoAsthJk646EXsnASUkNth0SshPdikNm68Dj4GIbiSiDxLRg9X/zwSu+a+J6NPOfxMiekP13W8R0Zed7161znzWJb/YR6wYHChJugH9XkmT+UpkSbZ5ydzj2uJyrEKphVxbXEq3fzJvCzWeV8CyzlBeUoFR8lqKhZO9Rntfbl681OsCrLXrPC+Rl+Hcl3BvAF3IUOWdKD0GN/gshZL8dFWpFV/GM3wlJMtK0nqhbYNNtqdaL+qBjT99HSgGAG8G8CFjzCsAfKj6u0XGmL8wxrzKGPMqAK8BcADgPziX/LT93hjz6TXnsxZ1MD/hgRy0rAVrFQo3xdINSko8hqb7Y+OKKw/WfIkdkSAs3ePlyog9BiKqWhFkCrX5SgxnAG24Syowxo61q1VCrickG9MIaynODVT3pbRaW0pIuDfsOFfhjQe8d+J6DPNqj4hjDMq4lZ8pJMX9R04arvSsBD0GrXEoRA36Xg2JVAkdB607izsAvKv697sAvIG5/vsA/Kkx5mBNvkdCbsHUalX2b5dsdrenUBN4YvDFDmwl5wWUm0maS192bfVccaUFKs1WAcqD7qaeSu5r7GDWUuzZjpvO8z0GrRKaznUCw4V3Jgu5sB572Tu5z0stQAXvEC9/1/W6ZPuww2u+RNEjFFymkGPYGGPkBsAgoIRY79ryauIg0jTy2mATekJE1Cq2lBoAx0HrKoZbjDGPV/9+AsAtzPVvBPD73me/SET3EdHbiWgUG0hEdxHReSI6f+HChTWmHCf3dZsagWEL3IwxdRqjxLJ23yQmKXxy5zh3AqeS9Ec/uKsRatP5SnX4/dRTiVBzsXhpgRvQ7Yej8Rgmzn2J5jhoxxhUAnS+FHtd5XzaAlSlXN37Eo6btqxxeZym3Bvy5zV2aiakmLrbEqM8Z3olVMNWwthJ44XK5lijDSvnXEo8KCfVvTTYXiCKgYj+jIjuD/x3h3udKSt4TORnQES3Avg2AB9wPn4LgG8B8I8A3AjgZ2PjjTF3G2POGWPOnT17lpt2FjUBYSN2B4GmwGyxMuI0RstvvigDhYuVESshoISgsoW12IpvcGSNx9AqmBJb8d0Yg3SObpaLRlhPtMLayxRSCdCFUrlmwHHjgCckhbsaj0EprBdL1fPK807cNVR4rhUUWsKuZe0O11G4hkIXyxo1kAhrFwHQGBtuqvtUaBweBxXcBcaY18a+I6IniehWY8zjleB/KvFTPwDgj4wxc+e3rbcxJaLfBPBTwnkfCdkXcsyXK7E7CLQLVaQQA9DgkppAYYvXonyJiKhHjRNgPBRuwGD2jkiotQ+/TBB2s3ekwlCP+7tKSBd8fnZ/Vs/zhp2BaIy93r7sReoxtDB1RbaV3sPrZShX1zvReQwuTCPN+iOyXpcOtgIapSyZH2CV8qr25qXBZ6A02Jr4jjRorTsrx0Hrqqd7ANxZ/ftOAH+cuPZN8GCkSpmASvP6DQDuX3M+a5N9UFKYphzjwjtynND2V9EcYvd9B6XlL3uENsBoA4Wy4HMgeyejWE1nxSsDp16uulTA2+tV8Qwv318Kddnr1R6Da1krPAa1h+fh/lqPQRtjmC9NmdAgXEMXCtV4DM3aL1UZPzbNVZq6CzQdjkuDTYcazBYrp/jxZHgM687ibQC+i4geBPDa6m8Q0Tki+nV7ERG9DMBLAPylN/53ieizAD4L4GYA/2rN+axNtkOlblM0sQlNZoHNfc7nJd/s46KvPsSuVTitvBMuUGjHTeZNZbGuEEyZapnhMbSUkLAlhp2jHvcPxE6OSLmGPAaRh5cB/Q36ZT8n15uUBfAdYa0womzfLo0n3xg2K3HtQ8mr14qd6M7KUlzTAQA7gz4O57pzeRzEQkkpMsY8A+A7A5+fB/Cjzt9fAXBb4LrXrMP/KMgWq2kelI8vSh+u752I6hi84LNYMVTCWuMJtQLCqoPVx8FsgfmyfMWhjteq9gCk/ZxaBW4q3N89kEfjMbiKwSpVbSX4RHhf6yihRdWVdbpY4obdITumtOL7LW9SmrFWzlFnRNn1mCqEtVsYpzKiqsC/Zm/sDsvfPpgtVfe1O+xXY6xx+PXhMXzdUY37K4R1UxhXBZ+1MQYVlNSOMUhxU4tZayxJNyCswT+tsJb2+LFjACvUZGmM9rftm8Sk0Fqux9BSQtICtyCUJPcYykw3mVK2XVldKEkfIFcI64HnXQtTfkteemHd9hh0CQ3SrD/AFsbpvJOdYWljH8wWqrOyM+zjcOZ6ySfDY9gqBo/sOwg0m6KFt85kDb7sOCsIxby8Iia5K97DxDnEkhjDKNdjqOAdXdpp2+3XKqH6DV1KS1JV4DZwWyzoYgxq2Kqw7zk2YnzcdmVtQUnKLC2VAVDvX03NhAN3CbOS7Dh9nKbtQWnOijae0fYY5Odyd1jgYL44cVDSVjF4tDsscDBzsh8ED7i1KRQHq3Ej5YHdXdcyUVh3pcDQt4AAyoN1MF9iZ6g4WPMVDmdyJeR6DNKsqZJXZUnOdNAJUCqhw/lSlMYI2KKzMlAoLX6su7K6hXvK1FMNPm5jLtIuqUDXqxELUN9jUKZAawyAhpeiRqDjMSi9E4WwtntcCyXtDPs4mOqq4o+DTsYsThDtDfu10AVkD2pvVAnrqXWPZcu6Nyra+KJgA+6Nmg14mIObalxxx7o7nC1rBSjjtcRBpRjs+iR5uUpothCNKceVAmN/tgAAnJLwcjyGg+myXlPpHC8elCmr0nHWij+YLdDvkTod9GC2EN0X0Cjl/WrtJePaWVoyTwhoPAaNseGnQGu9E41ydT1ebTxjoow/2bNxWFn/Ujh5d9CvDUpA5vEeB20Vg0e7owL7U52wtptiv7bi5R7DfksJCRRD5THsTxcqK8jiptaKV3kMiyX2p4vaW2HHFSVuaoW1xNNwPYb96VLMa2fQx2yxwuVJyWtXIAh7vbKIaTIv5yi+r2o9nqlqGTTjDuv74vsQAW0ltDJyXjuDPg7mSxxMFyDSWfE1DCIV1n7gVCBAd2rveoHDmdKybgVp9Z68WFjXBpsc+ms8+WWdririVRui8vs6DtoqBo+sx3CggEH2HHjncC5rUGfHHUxLy1/Ky93sGl6nRgX2pwsVL2tt7k9L639P6DGcGpXCaX9aCus9gVAbVpDL/myJw/lC7J3Y375weVr9LV+PK9OFymM4VV1X81KM258uSk9IKOBPV2v/lJbXuHzO+7Mldgd9EUR2elzyunQ4x3SxEs/R3lf9nAVK2d1T+1P5etjn1fCS798rk0XFS7iGw6J+XiUvfo5W4R3OSqUsva+dYYHDynMFIN73R01bxeDR7rCoNy0g2xS71Sa146Ru/+6o9BiuTOYVLwmUVB2sWbXZxcLJP1gSiKGHHgFXpvPSshbe196ogDHA01dKoSbZ7ETUCLWpHLY6NbYCdAJA5p0AjaLUeAynRmWl85OXSl7ScXt27WfLeq9IxmTxcoSa5nkBwJPVGto15ehU5V1fmS0wLHqiCnx7Ni5P5jicL8WQ4d6oUXjunLkxgD0rOl5WmZR/6wy2/elCvIa7w7Lg7+JhKQOk446atorBo71R6TFcmZabXfJCG2sdXJ6UnoZ4A1aBbs1mHxWlsD6YltCEFVYsr1GBlSOsJcqLiOrDfzAtLVAJ2c395CVr7SqswonOsra/XVvWSmFdPi+psO5n8Wq8E4WFPPbvS65QLk8qQajw8IDmeZ1SKC9rbEiNoVPe89KMuzItz2UhjNM0Sqg0AOS8+tifLXG5UgynBWds0O9h0CcczJa4ojEOh20vVDruqGmrGDyyHoPm4VpYxj7c01JrYdTHcmXwzJUZBn3ZZici7A2bQyI9xFbQPP58ZRUK7+30eFApPHlA2P62tXa18M7+VG5Z15DLJR3kctoRalJr/PS4fV/SOVqFt68I4J/y7ktq/Z8eF9ifVR5DpiekUuRTa43rPKEnntfzsrDV3qgQxWnGgx76PcLTV6YwRr7n7ZwuXJ6iR/JMoZ1BH4eVUSldjx1PMUjX46hpqxg82hv2MVuucPFgLt5IvR5hd9ivXXGNxwCULrx0swOlQLpgLX+hEjrtCOt+jxSZU31cmc5xkCPUqs2ugXeuKLH42ju5rIV3+rXHII5nZHonpxxhrVaul3XKdW/Ur2AQvSeUoxj2KwNFuhZl8L2B/jQKxXq80nNZGlF9x2hQQmuXdOdyb1Tgmf0yWUDKq/YYrkxBBLFXftS0VQwe7daHf6LS3rvDAheUG7DeFJfkmx0oBZKWl2up7QkzY4Dy8D+3P8diZdRCzc5RbLmOM7D4YZuXXFgP6qC63LK2VrxVQnKhtl8FutVK6JI2dmLvS+4x1AbKJR2csTcqsFgZPLs/UwnrU8NCzcuFuzRn5dSoqBWe3Etu1kPDa2fYb1ADMdpgvZMJ9oaFKFngOGirGDyyltlTl6dimAYoLR9r3Uk3hRv002zA3VG/tri02O4Tz09weiyLSwClAH1CKQitFf/EpUntzktob1Tg4sEcs8UKuwPlIVYHn/sVFq/IVvE8Bul6nK5w/ytTTbZVG/fXZArNlitcPJyLefV6pWXdQH96yFBjRO05wlpsbIxdXppzWdT7V+3Ja+9rWDhZZNo1nKru66hpqxg8sg/08ed1wnpvWKhxU5eXZgOeGhX4mjpW0AhrzQY8PSrw2MVDAMANuzKFYuf02MVD3LDDN2RzeX1Nycuu22PPHWJ32BclC9g5Pncww+F8iesF71XweQHAdYpx08UKz+7PxLyKfg87gz4ef17PCwC+dvFQzMuOe0ptxTdxENVZGfXVVrwV1k9dmq6hhLTemu6+btgd1HtDOke7zx997uDExBeArWLo0E17pSCbLVaqB3XTqWHdM0a6AXN53bg3rN8VrbVMNPhn+ftlgByAWMhbXsuVEQv4klcJTQAaxVCu9WJlcEbQFbSZ46C5rz3ZuEG/h1FRvtv39KgQpWeWvIpmjkJeQLke86UBEcRC3vKaL42oS6o7zvabksat7D6aLVfihAvLy74jXTruVCav02OHlzCDL5fXjXvDeg2lqIHdD/OlEY85DtoqBo9uPNUcphsVh9i9VjquNUYhQG/aa16NLeXlbvAbFQLDhZ3EHoPDS6MYrnN4SYX8qOjXgXQVr51mjmdU48prNQLetfY1yuv6ao7X7wzEcNz1LV7y+7q+urZHEL2ZDmivt+asuApLOi5nTGfcKdm4M3t593Umg9eNmfd11LSWYiCi7yeiB4hoRUTnEte9joi+QEQPEdGbnc9fTkQfrz5/DxFd9ZVxha77b824HMVw8yk5L3fcTUJeZ3aHtXC5SbhpAeBFp5t5aYS1FRoaQfii6/S8AOBFp8fqMWcz7qvkNarGyIVum5d+XPZ9KQTN2VMNL2kA1OWlEWp23KBPYqimzUt+Vs6ecs+zbI7uWcxWDMJxO8PGsNHc11HTuh7D/QD+CYC/il1ARH0A7wDwvQBeCeBNRPTK6utfAvB2Y8w3A3gOwI+sOZ+1yT24GgFqrx32e6LeKkDZo8aewZsUisGdlxQu6PWoPiQaJXTLdeP63xoBdUslrDVwxi2OYtBY/1ZY68Y095XHK/e+9ApPNb/M52WVskaZ5BgNQFvhSbPjcr1ry4tI3tJ6POjXNUVSZVLOMc8ztNferJA3R01rKQZjzOeNMV9gLns1gIeMMQ8bY2YA3g3gjuo9z68B8L7qunehfO/zVSX35TAvdg4ZR/ahCvd5TRXM3RIePK/mWinE4F57i+K+3Gtd+IUjC13d/v+3d/6xdVZlHP88rPvR/eqvrVvbrbQXOkI3uk7XTRLS6FSGgK7qiGUBqyRCgpgsBkSs0an8oUiiif8YEgTkH5hLiCYQJ1s0EqNImTIpZFtpp9tQxoYoYwnb8PGP99ztvXd37Xvue+9779s9n+Sm5573nPd8n/ec8z7nvOe9PQ21kfOEb9Y+GrPXo82jrPD1XlY/N3K+rMbW+uLsavPKN9u7rPAIubU++jXMavS5OYVH+37XI9Dos/dAuJ23+FwPV9YMz4552q0VLK3zsCvUZqOuPwHUuH3cl9ZFr69yk8QaQxtwKPT9sItrAt5W1TN58RUn23lXLFkQOc/K1joAOhfN8yprVdvCIsoK8vg4LoDljYFdXUvmR86TWXzOnqiju6Cs4Gab8bgelzadu0FHfbsIzt2UOpqil9US6vB1HiPQdqfRx+GFZ6EtHp0/sziop/DIfCrC183nelzenC0ruj4RYaa7qV3WHL2sruagrYfrOwrZAUBWa7SygrTdrs9Ez7fAu6zulqAMH+cP0LlovndZ5WbKIaCI7AKWFjg0rKq/LL2kC+q4HbgdoL29vaxlPXjTap6fOH72JhCF7paF3NGf4YaeFq+yvrdpFb955Y2zjSoK7Y1z+cqGy+lfsdirrPsHrmL7yCHWdTRGzrNk4Ry+dWO3d8fa+rEu2upr2XBlc+Q8C+bM5P6BVd43jC/1dzJn5iUM9EYfV8yquYQfbu7x3jFrsG85b588xWDf8sh5RISf3LwmZ9/nKNy4uoWJYye47ZpOL40P3fpBjr7j91rnR65o5o7+DFvW+/Wth4f62P/GO14OZX2mkTs/fBkDa/zGgT/7wlqeO3DMa7BxVVsd92y8gv4uv77y48Fedo7+i562ush5ljXUMnz9lfS213uV9e1PdvPUniN8KNPkla+ciKrGP4nI74C7VXWkwLGrgW2qutF9v88d+j7wJrBUVc/kp5uMtWvX6sjIeUUZhmEYkyAiL6rqBV8UypLEo6QXgC73BtIsYBD4lQYe6bfAZpduCEhsBmIYhmEUJu7rqp8WkcPA1cDTIrLTxbeKyDMAbg3hLmAn8CqwXVVH3SnuBb4qImMEaw4Px9FjGIZhxKckj5KSxh4lGYZh+FNNj5IMwzCMFGGOwTAMw8jBHINhGIaRgzkGwzAMIwdzDIZhGEYOqXwrSUTeBP5eZPZFwLESyqkEabch7frBbKgW0m5D0vovVdUpfwaeSscQBxEZifK6VjWTdhvSrh/Mhmoh7TZUq357lGQYhmHkYI7BMAzDyOFidAwPVVpACUi7DWnXD2ZDtZB2G6pS/0W3xmAYhmFMzsU4YzAMwzAmYVo5BhG5TkT2iciYiHy9wPHZIvKkO/68iHSEjt3n4veJyJR7QpSDYvWLyMdF5EUR+Zv7uyFp7SGNRdeBO94uIidE5O6kNOcTsx31iMgfRWTU1UdF9muM0ZZmishjTvurof1TEiWC/n4R2SMiZ0Rkc96xIRE54D5Dyak+T2NRNohIb6gN7RWRzyWrHFDVafEBZgCvARlgFvAS0J2X5k7gpy48CDzpwt0u/Wyg051nRor0rwFaXXgVcCRtdRA6vgP4BcHGT6mygWBHxL3Aave9Kel2VAIbtgBPuPBc4CDQUYX6O4Ae4OfA5lB8IzDu/ja4cEOV1sGFbFgBdLlwK/BPoD5J/dNpxrAOGFPVcVU9BTwBbMpLswl4zIV3AB+VYCPjTQSd4T1VnQDG3PmSpGj9qvoXVX3dxY8CtSISfaPg0hGnDhCRAWCCwIZKEceGa4G9qvoSgKoeV9X3E9IdJo4NCswTkRqgFjgF/DcZ2WeZUr+qHlTVvcD/8vJuBJ5V1bdU9d/As8B1SYjOo2gbVHW/qh5w4deBo4Df3qQxmU6OoQ04FPp+2MUVTKPBBkL/IRjVRclbbuLoD/NZYI+qvlcmnZNRtA0iMp9g46bvJKBzMuLUwwpARWSne0TwtQT0FiKODTuAdwlGqf8AHlTVt8ot+ELaHD79sRr6csl0iMg6ghnHayXSFYnou4UbVY+IrAR+QDByTRvbgB+p6gk3gUgjNcA1QB9wEtjtNkbZXVlZXqwD3id4hNEAPCciu1R1vLKyLj5EpAV4HBhS1fyZUVmZTjOGI8Dy0PdlLq5gGjdVrgOOR8xbbuLoR0SWAU8Bn1fVREcXhfQ5fGxYDzwgIgeBrcA3ROSucgsuQBwbDgO/V9VjqnoSeAb4QNkVn08cG7YAv1bV06p6FPgDkPS/bIjTH6uhL8fWISILgaeBYVX9U4m1TU3SizLl+hCM1sYJFo+ziz0r89J8mdwFt+0uvJLcxedxkl98jqO/3qX/TFrrIC/NNiq3+BynHhqAPQSLtjXALuCGlNlwL/CIC88DXgF6qk1/KO2jnL/4POHqosGFG6uxDiaxYRawG9iatO6zGipVcJkq43pgP8HzuGEX913gUy48h+CNlzHgz0AmlHfY5dsHfCJN+oFvEjwX/mvo05wmG/LOsY0KOYYStKNbCBbPXwYeSJsNwHwXP0rgFO6pUv19BDO0dwlmOqOhvLc5u8aAL1ZxHRS0wbWh03n9uTdJ7fbLZ8MwDCOH6bTGYBiGYZQAcwyGYRhGDuYYDMMwjBzMMRiGYRg5mGMwDMMwcjDHYBiGYeRgjsEwDMPIwRyDYRiGkcP/AYJFAnfILVBzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], yt[:N])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([57.94091288+0.j        , 58.05559069+0.00556691j,\n",
       "       58.4023639 +0.01120032j, ..., 58.98961709-0.01696939j,\n",
       "       58.4023639 -0.01120032j, 58.05559069-0.00556691j])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp = np.fft.fft(yt[:N])\n",
    "sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins_to_shift = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.79409129e+01+0.00000000e+00j, -1.51023155e-02-4.96518758e-06j,\n",
       "       -1.51022647e-02-3.31012184e-06j, ...,\n",
       "       -1.51022647e-02+3.31012184e-06j, -1.51023155e-02+4.96518758e-06j,\n",
       "       -1.51023866e-02+6.62025922e-06j])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mag = np.absolute(sp)\n",
    "phase = np.angle(sp)\n",
    "mag_new = np.zeros(N)\n",
    "mag_new[0] = mag[0]\n",
    "mag_new[1:(N//2) + 1] = np.roll(mag[1:(N//2) + 1], bins_to_shift)\n",
    "mag_new[(N//2)+1:] = np.roll(mag[(N//2)-1:0:-1], -bins_to_shift)\n",
    "\n",
    "phase_new = np.zeros(N)\n",
    "phase_new[0] = phase[0]\n",
    "phase_new[1:N//2 + 1] = np.roll(phase[1:(N//2) + 1], bins_to_shift)\n",
    "phase_new[(N//2) + 1:] = np.roll(-phase[(N//2)-1:0:-1], -bins_to_shift)\n",
    "\n",
    "sp_new = mag_new * np.exp(1j*phase_new)\n",
    "sp_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00000000e+00,  9.58893858e-05,  1.91778586e-04, ...,\n",
       "       -2.87667417e-04, -1.91778586e-04, -9.58893858e-05])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], phase)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], phase_new)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vgeYiAeh9ACIiY2U6AST1W3MiIs2Q9Dkr0wlARCRNkv7KqgQgItIidBdQE1VjqZ4gEUmTckInrVwkABGRNGgLt/8k9aU12wlAGUBEUsTC/f+6AmgCJQARSZPq818lJYDofNSniEgrqz4BXC4rATRNUpdTIiJRVJ8ATuj8n48EoAfCRCQNqlcAJV0BNE+pPNktEBE5vbZwRm75QWAzW2Rmm83sSTPbYWafC+VzzWyTme0Kn3NCuZnZt8ysx8y2m9mKZh3E6SSVTUVEoknPXUAjwN+7+3LgEuB6M1sOrAXuc/dlwH1hHuAKYFn4WwN8N0Lddan2p6kLSETSoPocQFK9Fg0nAHff7+4Ph+mjwE5gAbAKWB9WWw9cFaZXAbd6xYPAbDOb33DLX4OkbqkSEYmiLY3PAZjZYuAdwBag0933h0XPAZ1hegGwr2az3lAWO3UBiUganHwOIKFzVkfUHZjZmcBPgM+7+8tW8yYbd3cze01HYmZrqHQR0dnZSbFYbLht7mXA2PHkTmYd3tXwfrKuv78/UpzzQnGqn2JVn9Fx+kPfIAC7n3mGYrEv9vojJQAzm0Ll5H+bu/80FD9vZvPdfX/o4jkQyvuARTWbLwxlp3D3bqAboKurywuFQuPt++U9gPOmN11A4aKFDe8n64rFIlHinBeKU/0Uq/qMjlPx5R2w91n++I9fT6Hwptjrj3IXkAHrgJ3u/vWaRRuA1WF6NXBXTfm14W6gS4AjNV1Fsahei2gMQETSoHrDSlLnrChXAJcCfwk8bmaPhrJ/BL4C3GFm1wF7gI+FZfcAVwI9wHHgkxHqfk2SeqxaRCSK6pkqqVNWwwnA3f+Pid9dvHKc9R24vtH6otD5X0TSoDr4q98CagJ1AYlImlRv/9RPQTRB9VkKdQGJSBqMlMIVgH4MLrrqF3/9GqiIpMHJLqA0PQjWqqpZVA+CiUgajJTVBdQ0ZV0BiEiKlBK+DTQnCWBy2yEiUo9SGAMYGC4lUl+mE0BJXUAikiLVLiAlgCaodv3oLiARSYNSuXLv4vEhJYDIqjHU+V9E0qB6BXBCCSCactkZCg8CDJWSCaaISBTD4U0wJ9QFFM3xmgCeGNJLgUWk9Q0MhwSgK4Bojg2OnJxOKpuKiERRHfzVGEBEL/YPnpw+MTTyKmuKiLSGwZHKFcBLxwYTeZd5ZhPAgaM1CUBXACKSAtWun4HhMkdODMdeX2YTwNMH+gFYMHsGJ4Y1BiAirW9gpMTrzpoGwJ6XjsdeXyYTwImhEvfueI65041Fc2eoC0hEWp67c3ywxKVL5wFw387nY68zkwng4PEhnnruKFcumcKZ0zo4OqAEICKt7dhQiaFSmQvOO4srLjyPLc8cjP0h1kgvhW9VC2bPoPgPf8L2h37Nzw9N5+G9hye7SSIir+rQsSEA5sycyteufiszprTT1jbRSxebI5NXAABzZ04FYP7Z0zl4bCix39YQEWnEcy8PAHDuWdM4a/oUOtrjPz1nNgFUnTdrOgD7jwxMcktERCb27IvHAFhyzszE6sx8Anjz/LMB2N6rbiARaV07/vAy06e0sWDOjMTqTDwBmNnlZvaUmfWY2dq467vgvLM4a3oHm393IO6qREQaUio79//uAO9cPJcpCXT9VCWaAMysHfgOcAWwHPi4mS2Ps86O9jauvmghd2/fz2+efinOqkREGvL9X+5m78Hj/Pk7FyVab9J3AV0M9Lj7bgAz+yGwCngyzko//4Hz+cVTL/AX67bwgTe/jve8cR6L583kvLOnc/aMDmZMaWfG1HamtrdhFu+ou4jkS7nslNwplZ2B4RKHjw9z+MQwLx4dZOPTQ3x756/ZtucQl72lkysvnJ9o25JOAAuAfTXzvcC74q501owp/Oz6S/nO5h7++5E+7t0x/gMWbQbtbUabGe1tRrsZbW1WUwZtZtSmiPESRm3RKdM1W55aPv7+TtlzjHnp+PHjnLG1GNv+47yTOc7fSxm95xMnTjDjoc3N2XdMzfYYo/1a2jwwMMD0LffHsu9WUg4n9lL1JF+qfI6UnXLZT/6+/6tZ9rphbvqz5Vz77sWx3/Y5Wss9B2Bma4A1AJ2dnRSLxYb31d/ff8r27zkD3v2edg4OzODggHNwwBkYcQZLMFhyhkqVl8eUqfyHLXvl06vTnPoPtTo50T9eP2V6nA2Z+OQ4Xj1xGZlRpqNjIM4cQ1ovrGqbPdJWpqNjcMJ1I+28iSzG/5L17nl4SpkpHfH/lk294vr3Z1S+ONb+tZvRZm1jytsMprQZZ06BmVOMM6caszjBubMdhvfwywf2xNPIV5F0AugDaju5Foayk9y9G+gG6Orq8kKh0HBlxWKRKNvnheJUH8WpfopVfSY7TknfBfQQsMzMlpjZVOAaYEPCbRARERK+AnD3ETP7DHAv0A7c4u47kmyDiIhUJD4G4O73APckXa+IiJwq808Ci4jI+JQARERySglARCSnlABERHJKCUBEJKcszkfpozKzF4Aoj8fNA15sUnOyTHGqj+JUP8WqPnHF6fXufu7pVmrpBBCVmW11967JbkerU5zqozjVT7Gqz2THSV1AIiI5pQQgIpJTWU8A3ZPdgJRQnOqjONVPsarPpMYp02MAIiIysaxfAYiIyAQymQCSfvF8KzKzW8zsgJk9UVM218w2mdmu8DknlJuZfSvEa7uZrajZZnVYf5eZrZ6MY4mTmS0ys81m9qSZ7TCzz4VyxaqGmU03s9+a2WMhTv8cypeY2ZYQjx+Fn3nHzKaF+Z6wfHHNvm4M5U+Z2WWTc0TxMrN2M3vEzO4O860ZJw9vvMrKH5WfmX4aeAMwFXgMWD7Z7ZqEOLwPWAE8UVP2NWBtmF4LfDVMXwlspPKCo0uALaF8LrA7fM4J03Mm+9iaHKf5wIowfRbwe2C5YjUmTgacGaanAFvC8d8BXBPKvwd8Okz/DfC9MH0N8KMwvTz8PzkNWBL+X22f7OOLIV43AP8F3B3mWzJOWbwCOPnieXcfAqovns8Vd38AODiqeBWwPkyvB66qKb/VKx4EZpvZfOAyYJO7H3T3Q8Am4PL4W58cd9/v7g+H6aPATirvrlasaoTj7Q+zU8KfA+8H7gzlo+NUjd+dwEqrvPB6FfBDdx9092eAHir/z2aGmS0EPgR8P8wbLRqnLCaA8V48v2CS2tJqOt19f5h+DugM0xPFLFexDJff76Dy7VaxGiV0azwKHKCS4J4GDrv7SFil9phPxiMsPwKcQw7iBHwT+AKV14hD5bhbMk5ZTABSB69cZ+oWsMDMzgR+Anze3V+uXaZYVbh7yd3fTuVd3hcDF0xyk1qOmX0YOODu2ya7LfXIYgI47Yvnc+z50F1B+DwQyieKWS5iaWZTqJz8b3P3n4ZixWoC7n4Y2Ay8m0oXWPXNgrXHfDIeYfks4CWyH6dLgY+Y2bNUup/fD9xMi8YpiwlAL56f2AagenfKauCumvJrwx0ulwBHQvfHvcAHzWxOuAvmg6EsM0J/6zpgp7t/vWaRYlXDzM41s9lhegbwp1TGSzYDV4fVRsepGr+rgfvDldQG4Jpw98sSYBnw22SOIn7ufqO7L3T3xVTOPfe7+ydo1ThN9mh5HH9U7tT4PZU+yi9NdnsmKQa3A/uBYSr9h9dR6Vu8D9gF/C8wN6xrwHdCvB4Humr28ykqA1A9wCcn+7hiiNN7qXTvbAceDX9XKlZj4vRW4JEQpyeAfwrlb6ByYuoBfgxMC+XTw3xPWP6Gmn19KcTvKeCKyT62GGNW4JW7gFoyTnoSWEQkp7LYBSQiInVQAhARySklABGRnFICEBHJKSUAEZGcUgIQEckpJQARkZxSAhARyan/BwHWGc57OdzqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(0, 4096), mag)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], mag_new)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], mag_new - mag, '.')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/holtrob/.local/lib/python3.6/site-packages/numpy/core/_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f992aa00710>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], np.fft.ifft(sp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f992a96c8d0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:N], np.fft.ifft(sp_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import struct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "with open(\"bram_sine_init.coe\", \"w\") as f:\n",
    "    f.write(f\"memory_initialization_radix=16;\\n\")\n",
    "    f.write(f\"memory_initialization_vector=\\n\")\n",
    "    for val in yt[:N]:\n",
    "        val = int(val * (10**4))\n",
    "        res = struct.pack(\"<h\", val)\n",
    "        print(val)\n",
    "        print(f\"{hex(res[1])[2:].zfill(2)}{hex(res[0])[2:].zfill(2)}\")\n",
    "        f.write(f\"{hex(res[1])[2:].zfill(2)}{hex(res[0])[2:].zfill(2)}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 10.,  9.,\n",
       "        8.,  7.,  6.,  5.,  4.,  3.,  2.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zerostest = np.zeros(N)\n",
    "source = np.linspace(1, N, N)\n",
    "zerostest[0] = source[0]\n",
    "zerostest[1:(N//2) + 1] = source[1:(N//2) + 1]\n",
    "zerostest[(N//2) + 1:] = source[(N//2)-1:0:-1]\n",
    "zerostest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12., 13.,\n",
       "       14., 15., 16., 17., 18., 19., 20.])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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