mfft_orthogonality_tests.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2f45104c",
   "metadata": {},
   "source": [
    "We will test the Sidlivovitch formulae for the cross-product of trigonometric series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "cf4e6e41",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q <- function(wT) {sin(wT)/(wT)*(pi^2)/(pi^2-(wT)^2)}\n",
    "Qprime <- function(y) {pi^2/(pi^2-y^2)/y*(cos(y)+(sin(y)/y)*(3*y^2-pi^2)/(pi^2-y^2))}\n",
    "Qsecond0 <- 2/pi^2 - 1./3. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9198f3d8",
   "metadata": {},
   "source": [
    "T is half the total time.  The product function between two series is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "20d32dda",
   "metadata": {},
   "outputs": [],
   "source": [
    "haan <- function(t, T) {1 - cos(pi*t/T)}\n",
    "hprod <- function (s1, s2, times){\n",
    "    T <- (diff(times)[1] * length(times))/2 \n",
    "    mean(s1 * Conj(s2) * haan(times, T))\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "285d9179",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "5.17312215217515e-04+1.00811440406426e-04i"
      ],
      "text/latex": [
       "5.17312215217515e-04+1.00811440406426e-04i"
      ],
      "text/markdown": [
       "5.17312215217515e-04+1.00811440406426e-04i"
      ],
      "text/plain": [
       "[1] 5.173122e-04+1.008114e-04i"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "times <- seq(0,100, 0.1)\n",
    "w1 <- 0.23\n",
    "w2 <- 0.54\n",
    "eiw1 <- exp(1i*w1*times)\n",
    "eiw2 <- exp(1i*w2*times)\n",
    "hprod(eiw1, eiw2, times)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99723c0f",
   "metadata": {},
   "source": [
    "In principle, this should correspond to the analytical estimate as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "15010567",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "500.5"
      ],
      "text/latex": [
       "500.5"
      ],
      "text/markdown": [
       "500.5"
      ],
      "text/plain": [
       "[1] 500.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "5.17312217126683e-04+1.00811440778522e-04i"
      ],
      "text/latex": [
       "5.17312217126683e-04+1.00811440778522e-04i"
      ],
      "text/markdown": [
       "5.17312217126683e-04+1.00811440778522e-04i"
      ],
      "text/plain": [
       "[1] 5.173122e-04+1.008114e-04i"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T <- (diff(times)[1] * length(times))/2 \n",
    "N <- T*2\n",
    "length(times)/2. \n",
    "analytical_estimate <- exp(1i*(w1-w2)*T) * Q((w1-w2)*T)\n",
    "analytical_estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88a62594",
   "metadata": {},
   "source": [
    "As we see it, the match is not perfect, let us see if at least we get the general shape right\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0045eb04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "50.05"
      ],
      "text/latex": [
       "50.05"
      ],
      "text/markdown": [
       "50.05"
      ],
      "text/plain": [
       "[1] 50.05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2PlwKjaCJ6v/J0k4v0/q0dMrOJuOHVMxXgCnD0oNelhaDjFGydB3caf3ehooz/S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\nb/50lClGyvSldUXy/qY9hMnMU6t3ah9HAOdesSYVafKQ/6L9Zm5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sfvGjr83r8+3eLMznBjKvRgK2oEEPsK/fqTSEGZtUmG0kXAqxxzfP\nFdY0sFScRTQhklb9b31jqrmzWXHcL2g/WUyyDzN2MK+RGPdhTiV7IqDbwzXmlSoeW+bF6qEj\n17/hORLjW+2ILitD+00YXtGsfgmj8OtNYydsfcdndRLejXQBlWLXuRaCsTAz842UEITCU4oS\ndbaRphVZsA6v3eQNtBf4rCYwyax+J+DZjgn9F93mOxLDnej8029zi3kkmHeJH1cG49+//2b9\nE36NtNhzVoxSGTMro01js/p1rbLVRR0Xo/AgeNxA5t1I8+HD3y7O2HzXfCM5rz09q+/ME/g9\n4jOMZbXmeLCiTHVvibO5RnqJb639dvVf/Brpf4icpp1/P/clL5nVb7PiYiwVEmev8OY1yPY6\nUg7ftm24faLjIrP6nSSooW+1t/1AwpRC6FaCdyONyPZIZ2NxiOYbyWkdTt0768fzacRBS9VZ\nwNDKOH3buP6L7rLHkszgBbO1B+Vc2pWIKsGRMr20S16uckuqaOcM583q99ZbU+EmxhmtwMTK\nNdZhnNyRrdNzmHYzs5CUP+qx/dSKsvbxPN5AeTfS8uy0VbWNLaWab6Ryfdc6M2FeUJz8x1J1\nFjCkSuaJpau1f6F2zc3r2MzRld05XkqYt7CbR0pOxI+XDRy+7o2HmQXVO6LEdWe3dSDrO/FY\nGy3Le1pnFFY7RuLnaV64ygtiYlk5uLX4e5OcvzgXfo3kMWbdMWfdgPcYbSwvjPlGWiolv0nF\n+JxayWcWw+WawuDrCmWuFjE9BYKO/eCni8SoQB7lRpleoqek/m/ZHu0k0nuZeR3jOtdzAEX5\nPS8oHu/3T+Asvji754Q9p83MlcxGYmS+0D7hMxKDVyN5I2DZh/EgmeMtIw3NN1K6XPrt0fM/\nRnp7jbFUnQUcQMUfYvxnNQ3zl3kdv4nMjsQoa3pWj7zTrJQT8mKYHtcJMw6as7CRGE/Zqzuf\nkRgP4eLLIxvOpuGLYF6qxydw4tXE6sEVB/1I87cjy++GbOq59ePbltVe1UK8fzXWznwjnYJv\ngghw6vDPaPM27fNG+Tiq+a4bv3ZF8WZ27FZf+81kS1LwGonRE3q81E7qvL2KmjnkKTEeb2lT\nskLPEyan4LYCmU7VpaQjeKxc4mRmZFJUh8Le/eYNj2R4nIEKFCJ00fg/jflG2qLC+A07PVpp\namk3K/CE+P33ihKgY/q6mdlzaHl8fWiN8l12VTO5ukreeaYqpxh34uYv8TDdzJ79izWVNP52\nZCXSjORDeacwtSwVPxpDu5paOCOHn1Go9vuTOZHQ8JfCo4DE2uGDxNvUH9ondV41w5yEM3nk\nHGjnG+k33+PfzIsUwHi3ZIa0RL+RtWjTa1jknTX2afOCAKQ1k0zPW/qBu1IpOxg8okRGBxLW\nZQcTGLr6xo1VrqS5SUwOEkxI88aFFMv9pnGiTB8FxUhvFFOCnJsNaahSmXVkLW/8Bed+6Fx/\n6CG8RWZmz6xiiJ3LPSpO8bgzM4kd9b64noGHmVu8Nk2t8WjYpSzq1DyZC2H6aVfveVc1gKqz\nep2ZPScVvzm1XceZD3AH83Zy84JQRnoW+Xn9txvO9h+Rm1/DcjAZp+2T2ZfgMegmy1Xj1rB7\nBaJ568rmdq1tp6zTt546cqqav7K3c4IezOnSZc4D3MPUgqw5nIfr8zs3Gvk/vNaMvFh5pRIb\n2PfXX+yxJDN7jkrQ/ki9h3Ff/k4kCWWkx/D5p2Tu3/2RXmbfkfAyhqo6sFOIZgGPK7SPlDQ7\n+T5lR5h9Ps974dqeKd1Xpj03J1NjHjmLZP4NG/orlgSYc6yP5XdgF0a0F6qdDBfC9FOz19U5\nPcZszcDBppa7zWGZa8b8UALsmpTryYkyfQhlpLQ9xr575g/tcMcG+/tVazThPo4xL+Y+L4wM\n6UVWGzogjiLMrqBtt0n7I1N7UyPNyIeXR/Yi7wfaP3QqoTY3HvEeOn26liPYJ/cL4kSZXsba\nE8F14uVFd6JTZvZ8rIxXjD5yeV0xMHPjOQ8UlDkSbtQ5+0l1/s7IlhuGD/esVG3gebXZSwZF\nJ74cEsE4VprLYz3Jsi2iHdpP7hciLWZ217hyktrrTm2og3gMuhmA6mivNI8SJeXN7toVuj7E\nL5c7epuTJC1v8G+kF3fu5botYIGR+ibin6r7uFScF8xfEqaInD/K37yoSi0j/IICpuxZ140w\nJ/tQ3kglDrxf0KREyuiNRKq5ffehYrdw1slYRzVvEVjPZUM1UUNm9XChzT8EVbesO2hA+fVF\nuMKBMr3wbKTzLd0AgPRs8pvRZhYY6QDVUNJ52Zr+SmReZHNeSOo+vrJP6R5/vpVtN7frc6Xy\nfxg/6UeRvGVruQt/fHjyh+k10XJY6BAGTgqoccuHt7K3m5VptwdXDqszs6+5a4wYh3yfdmHT\n8TcY2/NWXJRfI3VH4B5TvXppL4D2xtpZYCRcCn2nnXKs1yjNSSKaN0aTXoOXjo9TdFObfWL8\nPlEKHP2R784W5iQRzRPvqLXDkyLqf/9uN2X2SmGfmlmX1v1y+5MRNOcsLJT9ZEaE2X1D52iv\nG7t+e4bteNum49VIsyEpe954oREYq6dmiZGiI0mHYmrJ0IUOfBUdyopVlNLOcDJSwMyQVS27\nmMxr65ccS8ML/TlQpp+STNGBM7o4R9Yyv2BYb63d0y8fe4WbdORAmF42K88PrpHY53c8wPw7\nUsOm52JBQpLJwFu5D16NVCb443c8K97YPNACI2XSu29vmL75Ib7F2/T9f8TvFcjAOAe562iz\n+/7CbuG+uvQWL/O2vjD9PFKRA99qr9Tu5oasapnv+bKPHAAlepsbXWQxz2ky9qvBSWQvP3MX\n6zHeTcrrnc94u1OpMP+CbCG8Gknd6t/nQzRGGlpgpHTdib5/0vA/2QeeuGdWKMYn54/d8Kh3\nitl9b8CFDUURkDH1EjlQppfxhbe6aBISNI7otNl9H9v5+a25//q3MP5ihPYScnb6uIl0sCC+\nz5v4auexhZHuniOtrMog/N6RPkk0VsHKdyRcaObfTR2BLj6Y4esqNLmEdlzH/o2Gmh3YgHF8\nGDXg+IPDDaCH1XUZoGZP/HrD6NEbXgeZu8GJ2Vxx9Xdd3d2OjDJ/LdpCKrfpR4TWKyd3dTf/\ndN4DNK60DHw7P5zMW+Qlz3Okatmn6P9oChONNLTESMM97OPXXNw3gAi2TJz5/KSeHC2TRU9P\nr2XBxGEnhG+/e2m2U7g9XxHKlXKWkc0OudFSqnUFKUgS9p9GfJXBk27BV2Z1H7X5igX1wo5C\nKs5k06rvkFhfmH74XbXrDOBdtmatBH+A1sauM5YY6aVMtfHR873xjuQBi/WZx2NaPnrnzlGO\nsZQF9bNHh9WRALiPf+uy1PrK9NK29tel7Qs3+V+anblBoFocNuCMO9oZbgbJ09ju4xfzMZif\nwuQsPMKPdsze/nCDeXnH8gDP+0inmzix+0juTYz/Oiwx0inUVPvNJOvcqtPKQnHmMsaOHPQX\nfjKZiLKgc7P2OP0KOBdaSwAAIABJREFUe/KzymBr6zLAcuT1zcZ59ajGaqPJOfXjthJnXvlp\n76NU3mokuU4fVL5Q4phnvxPmHTRnea9ZMlQqD1UwRc1foLQQ/iMbnt26z0VkA17uhdMunEzF\neBJP5yKzvGb+XAikoK7ubUGOjZatMU49efQFrjjc+tL0UsXRY9N7/LQejLSgc3Kb/cFgzxDl\nJS+srcsAtamIkYsGB/hUt2RWNlihWZeJM4cAbxWdCkysHf7RS/vj6YV3vBmJTc6RdWPH2fdn\nzUzOoWNqwD+tKCBQknK99aXp4w840VdCuYFrWFcLem8nqW63cNpGxomnYx8vXeTV/8L4li9h\nVjLobM4iWad5U+uSnQhzSpTlhYJjpNPor0WB2rFdQrnWHCjSwz9wEWewYd8XwIIAtAdK14jt\nz98c9CQvW12ZXla5Yfz8wOqT78dZVH/LiWi9cN1Ql5IuPB06net+NgY8/FEh5hcLeo8vtqJu\nUFSrwziWr4OTBcdIuERh2ZjTDw9WhKnWF6SPTKc+ZaRgX/+Pxc6WlA2qi6otO7AgQRXFU0D1\nUl/tD3YMOtWSKd15+LFOIafy094P5Smgum0zjM+tXHQsI/5rC3qzyWV0tDT3VL2lFCAjrYGw\nlWd392divN5aX5E+ElDHXRfWJyq8+lrS229QA29UqPWfe3hKKHKY/K6sRl5i0vuWDS3ovVWZ\n/WSFpzVFGaZJp+wn1Swp1DO4EsbHf5i+600NcxOnWEoBMlKP+JauIIlZ+0q2zfqK9HCe9A36\n8dq1ZRqJJXn709gk5exuLl+RGGkqesCmHaNdoyQ/W9B7H5WGn+1b+tur7wtbXZlehsTNTPQK\nb3oky2euBb1/kR6JIQIipY4ynmagBclIVYZg/JQN5oviZ2zXN/5lT3sA+07Mbgt6Z7Gn1G/u\nOvXuJk+BlfMVTPPjb/+eTIZY0vs589NgKe1NqkPNy3JuMb+BXf/ls+qSTWT3LOidWUxS6ZZ2\nIloYWXLVsIQCZCT2aGzmtWuZuOhM6yvSQ9VB2h937mBczKJAztJf7QsHCcirOvITrR417H+x\nAODQQJNmSfduSod1aTi1GfB0jqK1g2reE/ygKViWdqGLxLHV121cgtrzdTa+ABlpcMmnHeQA\n8uYUP6ENrJEesV9Ky4y0kqG6/pH5bDoRxEum90xqr/a+cvR61h2wqH7lASRrO31UeaYbc9Pa\n0vTxmNoxyR4U4F7CvFJOOYRO/KF1Qsu5qX8BT4uiBchI1xi3Iutv316jlpidisQi+pVq5ghM\n9KqnFg3tcLqKaPPD0p6qivK11lam948jsi8vD+GiJf0HlFvROKJcz4u4EC9nZPfQGfj92S2X\n0ucHWNRfs+nDI2/JZQqQkXBlVPfHfXOinfz5ScK0EULWXNg7SBIRaNFY6QC1pk6gT9XFWW3r\nWVuZXgr3b+JPFW7/1zbpG0u6N84Z0lUbYEVRBtmWU4FNt89uPr4L8Os9M5edfQI87cgWICNl\nOoys7UUFd723zNGSfR1zyYouQvXYdWF9NHxvUf8lftlPpn2eKpMbmqLKi/bOjVOHmlnKKZv2\nTTC+vX3jNVzG/FOMFnAF1rUo5l9jQcaAchb1b5m02okp4gNBdhZd5cynABlJN2Zh5xvmlgGx\njFPo761x7IZsYiuL+q920Xr/+sGH+JtY6wrTz0O1l9+yP2/+5EiZfyqBZZHzlaogt4MI2uxk\nmBbhierNWNjTrqydJavfGF+gibFvtRNR0pGntP8FyEhP4AzGGTfe4DPAxxGf5eyYgw0RsjC2\n7zocm8yGwhcpwstIdGqhl1/ZA8ibKTdY1D/VS1H2ZCY+6ULyUph1HyFpfDrt6VzK07I1zUwX\nSVC7nuWILv481csqQEbCvtPOJEmAKNrS19p69MEaKZMdN1gaJFvTWT37ZvqFePjOqroM0IqN\nQLz1ZyauYGG0eTPar8fkTq6hlZKsqssANZudKg0kSJNlZido0nESzk1qXnvw/zBf9bIKkpEm\n2Enq7rz5eyfgJQ3CaTSuhIwuMuZtbQuDZLcgxwFLJyUydV0smv2bSbMO2U+SLDz/5DFjYt0S\nDWenHiT5qCfp/iPGjw6eef8Gfreo/5acWt8r3a0nyhgFyUivZMzgjRsHa2IIc5NFW0KGPT1s\n575JnsHEIcs+oHP1qVV8S3S88FbJx+77qKhpldxDGv+W7rrEov5pKDun5yMzS6JbRk5mx0xy\nv0X9DxKpH0KaZvKUtaEgGWm7dEacnV3cvMyKfEQqzlHZlVl1bk93ZOnxp8o55WOjJ1tLkxFO\nIvWgld83JJPtLDg8pSVLsh3jhwcupt2AG1aWpo/oYVPrRdWd9OI8WLb/+0ax9ENIU6FOuTe2\nBgXJSB/PBwziYxhfbOStls7AlOqlNrNaXw7J/bQ/7t3DOIyPLc6WLvSQU4+OVgFLTiWwlOty\nKFI7a1ElufGxuTCQ9Og+taevT1IZCz9guNR+XRp+Xd3CECOzKUhGmqGrsvAO4/7VrKxHD5m6\njCdP0v9NqW0uIyNe9HYEcGxHWDYNMIvH1O61oQAoupwlhyhYtlBkh/PpD0chcys5W0J6uCbo\nl1fpxzyJYxZ+whFEVOnfIUgzhJ+QpgJlpH30o18q2hEBXaMtOcJiJh9Dbh6AhVn7b8ncA5f+\n8ccPcrkFyUjMhQ25wc/Pv8Y/WBZyw84JUfWxExsxdWWWrZ+bxc/y6+1pxEBJ5SoLP2FA+QP9\nk5tMfMBTSFOBMlJGaATVZePheT7ARxH74CHdS7jGDvxns8zsIinZ1ETlZ677prCXTz+rCtPL\nNnn2k+WWhdxgfIja3TmuROtfcOv6uTfOKwMTMX59bM8DNqulZfAc0lSgjISXQcjiI+tbk2F8\nHIfugIpPXD023DXE0hQRmU5j20Y4xw57usiZ+8HSH7BrQFLZDttwf0tTpS7xzX4yzZKj6mbS\nPcesLSw9Ks6GNL0/e/w1TyFNBctIbSu18QWHpF+v8rBC+8zR02v+hWvLNcwdCz/hn5wwbIuS\np5iLHxE7aGx9ppb9PAs/YJWr9sf721l4rEXJU8xjYpFL45p1mPkIlxpl4Scscr7bjgEgqvAU\n0lSgjFRyIsa6fA0e3NcOneX1YpgbgF1r6RYLP+FjClGL0nmZyXGSaXD8/aNJpJ+lxwivwen1\nxSlQ1CjR3arK9HKVQMU7NPXXjCUsDUhK9bYL2/zk5TY7mo/V+gJmpOicmkvey6woRj9tWmh/\nPLqNccJICz8hy+u7e91DKZ+6X3lxP7RrVPtMHCCQVVVZnBkm2Yvuf+Da1qKw3JrC9DOfki96\ni1PrQDOLP6ID6cuGNIWU4mFKhwuYkZo1wusbhke13GBBBSBz+Vhxq6rFS4SjnRyjZu1elgw8\nJOTyWoLx09/Op70AS9eT8V7kOHTFjGS6gr+FG2emk+k5YYKK9KQUQZadj2Xxn/ghpGkXP9VJ\nCpSRdlOVZa3nTK2PXLi/xA8vva9v1Ubj72V5/mDpR7xRMqN37/7GKUTCffqTnBqQeTgx2jt+\nfAW3iFann0s4L3t7GW7hV4eXH3qx3NXSj9BlaWLhKUtTgTISjkE9j/+9LUlGc1+D9wwiqw3q\nHKruprD48NMBalSURBI1Nb0E92VvI749MK792H34quU5i5IGZT+J5DzZ6hHIToy8i7b0I7Jo\nNgHAmyy+KjgWKCNluDQL1s4Dav7Ro6y1FX3BULls6q3Mawlg6bISxjOLZhcq+6q69XQZYJCM\nim0WR1dqZX5l4xw+jmEjZlhHk2H+gj+Oz5/w8zM838fiz4jpf6+9LyjL9uAnS1OBMtKf8Dd+\n+VcmxtslXI/t3sh/nOMKJPiFWV6deErx7CeDuS8+UoWJPIXxMSfC8vJG/cvgtTX8/WsspLnP\nJxLkSQTGqFVzSnWx+COWSx1KLDq6tRUkWFGXYQqUkc5Ddv6gQ4jrk/oHiFSc+ef+v/F3FuVb\n1LFV/vru17Vi265O5Lz85SHqt2TQeIAvbXnQxyUqTtZ50aLOpKVRuqbz2hP1f4fTJxJKy+sD\nZrkS7Rav6qMpQfBS0alAGek5dSBr17CmAzfOsXxEYCL/HhzzsPgz3no20BTpM7aplPsKxyPi\ntOOln1ecyqjc3/IPqQf1Nh//MUGp5DwB5wSfZQ7q0sUYV3vLL4hn0bwUP4/EBZkpvOTRL1BG\nwjUqJTIVOyQppJynAz0F9/ZOHb3uaZ6OMi+H8IP/nB0rtW9lNV0G6NYg+0nLNpZ/SGC7impw\nb35jfKBVNBmh7FD86udx0/c9pQ5a/Bk/5mT7n8jLYfOCZaQrtGprxvtDUbJiGbk3zhOZHs5M\nVLy9aq7fN5Z/yIDgsiRAoQW/EpaGGZnK17GZp1duvI5xRcsD45+BdpbF/l5OAtfh6gELsp+4\nrLH4M5Z5Zz+ZHJ1nPSZQsIz0PyIaJDSqe15lQb1hs7hvhwa/welDkUcetvviRuHU80+0w3l7\nruUeJXzB3Q6qHKAtqBudzYOc7L+X4IGVZBmixHj84NBfWfi9xPIp3Qni9oOvk4s3ml+3hRWV\nGaRgGWlcNL6769fHGNexfLXHNPpErnahwzzAPy/hPcVy1pH9F1tDkxGOkuo9GJ8rQVe2/DMy\nNGvwviENey1fruH6fv9VQCgAuM5aLbU8K11WsYoOYf2ndlQj7jcVcUEzUv/k7CedLQ8tMY3g\nGTh13+wVF25Zlkn7AzW64RfrRo3f+oThOkK5dJMGKKJmMUKZl2wWHSJqUBW71rGTWHrI1mRm\nQbGzaTemyWV52an+FXn9dPXISKkrL/nDCpaRJhfB+O9Ny46nVetlZUWfY5Uk7Yvs5tvbly+t\nsLPjuMLxHTiDT87sPf3YzLysEzxQSha/erW3pNyH4/xhz+27uHg37VEeIYsDA7VM8K2rAiJ8\n8SV0xmrKDFOwjHQRba2FND7Ig+Y6HMx/Pr598CYbyXXa8g9JD0ed3uGXIwipRZVWTOd3yI75\n3snk4VOuoQoEQkT9P91nW0WVQVY6pD2f3aHu0CMV8nJ2mD1ce5s9vRxkWXJ28yhYRsKtqeAT\nGB90QDusK+gL2oX5aUfx3ktmOOdlvhAZRCh9CdeVlSw/LWASF+ABfs/GBK5xzMOn/OCHXx87\n9hrjThyfTBgdn/2kd608fEqlYdlPSkzKox5TKGBGGqcg/CoXRvW6B3IcIzQMYi+l//kNTecl\ntcYDOH1n2+Kjb/EqB6sJ00u6Y8uiFDi2vNM0JQ+fMrFU9pPhFa0hyjDf5uz8dM7LbKxtA5y6\naezYTS/t+ShAVcCMFDPy2qJh885qJwVnravoM25L+zt5NmgbhYi8nID4eDT2MHAcdRODOh68\nsLq0mrQwK6yOZW5Z+O72pcfeteD4BrqHmVbJxSNpVUbQt3n4lG2SBW6quDiVWsZHjuUCZqSP\nZ8yVlh4AN40ZAVnP5nVtOeFSkQl5+JQ7bCavh4dv4w2q3BvnhV/oZLrON4PLojzFJNxnlrcg\nFN7IRbbSWsL081ZN9V6zorssQp2nDavyqO4L/GIsSZ+wljAjFDAjBc/R/nj+Hr8juQ1f65Fz\nqLV5+7x8TMiQTUHaqZZX8dpW0GSEei3wrk7xiV9ttTSZ5QeGUJ4HM/FRN8RxSowxjs5h4zfM\nKAnd8vQxiYUZ2hO5LG7Ix/p3ATNS2ypPunsDXbSjlNvzxR9PENXL0+96LUkOuPTuSmXgOEF1\naM66lX2eNicXSSnXhEAieagLp8v1me6zHw0s5RjRvnuRvHzMO2r3030rjr/Fu2iOdxdYCpiR\nLlAO4QtP/doDhXG72LDabkaiZ0DdnW9dFuXlY/6RkCFN63trhpAWZms1kdA52U9yTpxbRo2u\nd1Z/Pf8MfslweiLpTs598zeUFwd8zCX9B9zNs6ZcKWBGwjFEVP8xDSSV5dyOPp5Imb4r/0/e\nWYBFtXV9fJ+YHrobpBVFEEERu0BBxQ4EQQxsxRbFxg7swO7ua3d3ce1usAOkZn8zMINBz16H\n93vm/p73wn7ue85iX5h1zt5rr/VfS8JYDzOizopLzR/PjOyx8D2uPApqZvnSqt2KcL82Mz7f\nJiu7LqWUpsdI2Z3zMiL57abQJzH+eu1tdu0Y52iYIyUxG0Y09uuyC/etDTujvxhgqus5Zes0\nVxRHZGaov3LQpT35nAphEyUNHdfNxqKKujKrOVRTlNWnZWCZPqdJtj8lW7cPj5xyDS8haxJW\nrdtpHwohq+rcCw9onCOdpJWVYJuM4GaTl1Tp+pf9vAwr9epIdqIySvXB7qiu7nHxqGsiGHb4\nWoI+Yf/XwZV+xLqwAo/+FLdlH8Eiab0QTyrMgUwU/TDDRFz4/G8z1AJoXoWhcY6kVLrg1pGu\nqw6AtusQ2dkp+Xw5wrNM4HxrTvvIXqDvr6nMR+adTOYXfXEhPBebWs04fmgAbc1p+vd3K1Gl\nAx+Tp7AGZHVPKbqsfdu29uKhpdE3R8McKYk59XNFV//ua/qQLWKK4AJSrrr/ERLZSXPwYoOm\nJfQRss8BZlUg0xXSQRnyT2U44QqyCe0aHddRWkWH02S7WRaP2rAI8euzb4js7BY/iu/aNf41\n9i8FkWUNcyQc7FlWv+2wNlKaU12BZPrM3gkDljzDk4gCtIr+GTbTdsyuITbvUvS16jO6pnIQ\nTZIhJN+8aM2PDaraaX3WaPVFvYpB4z7yH3X9VnqWobrNkXLIVWkazr1Kk8Y50jO+dOGN0xO1\nDatw2qDRTyr2DbLlDbWYSGanXUD/SroVuj7Yx/sIM7F8SbDIvLp6vXx/FNSDyM5d9DpncJTl\n8rdbRZUt4kbWIyxe9ZSLblzodSBomiNtk4SZIsZ17nMBl/nfH435dc/8+DCEtiIMrDoszvme\nwapfAl40r/mWyMoMee3ik3Vgy60xP85wuUlq0hMnn3qQhTMJs01PMa+fDKpXofUyj5iiLyZF\n0xypn/zh815RfFNrRJHXqs9ox8QGSL6Kr66tdm+HHCzWKAeSvcSTKpjbAnZ6Gn7iS/sXfW1h\npIh3yvYPazNoS5wrzMTyZ76em/yXqxe3UZBMZCerorfEe8TsLiKa2wzmbDTNkcJDlYOWZHla\nhVNlNMZfzt9I+8E7Rmao+jD8efuE+BMPVMIinNAoaJoW30nCmpFmbYe71RLUj2ok4XEqVr6d\nMjuU/mKxFn8koaFDlMnMfUub8SzagsyrUDTNkWL8MH5zcMcDmQfh7qVQ7BOUA5MNZIbmGsbr\n6FQtz9NzJp5TwXxnj+CvRxfve7NRhzBxKkkimHn3+gJTXXcO9bTTLKKq8L0Cy9A06ep8gEc/\nd2GZNlfOUJwGRbPRNEe6SO9vRgl0kSPNZfdLn3E4NfGzfK1DKoOd5kJFfsz8tzVjoHZPi6J5\niJSfo6ukgnTn6fYGCFnEvtTisFbuoOCr7NjUgYsftQojtJTbPtaA+9I+TXMk3JZ1Pp8pWyRk\nr0JO6C9ibH0ZhFzXLZMSyoDIbD35lBB5nqnAYWfzd4oem4p30RGG8EUy0Qvjt4qzaC7lzuar\nNmDjSXtqu89SDmyXE1oqGo1zpKE6rF5FXV50y+pFX6s2a5DdgbdXRvIEJBWcChLR8+8XD77A\neJb6WvxF4xQeZM669nnXy5fQUKnInSXYKQcxpBXtTbvjjPNLVl/7QrqVLQYa50hOs15unbn9\nNb5CkR2LF8Y34672OvXalKUostw1RTqYcrCDLNeocDqiuuuOzK2gx5KWDU93wzj91umPOIBE\nH68IrlMbulTxCj+EfQgE/7NZrbW5DG1vhcyNuG5OooGOxFcKcaWg81CzycNmndS0LcOjZt+r\npr6Sdg5X0Xv5qisJ40V2RV+sLrfZIKb+8CHVKWvSIq1/6cP9RYhCnoQHUoVjTQXGTWnF8xOQ\nttrLrEQFvcXvelG6XGura6Aj6W3J+f4OcRdtGK/Ky+9LWiKeYTjnbH0tpB3gxWHvkb418IV+\n9RsO2k8R96iO5JtsTE5bLWU4lEHYyDcrM3bz3KqIPCO+mgOPZ4Sst1ZWvxtccdE4R2oU9nN6\nPfPyHUcStNYpirgqykFPYoG3WUImZM/t7S6ILC+7UGrFKge5TR7UZr6AtqplT7VuyWGHB6+B\nX0ZXM3IL60v8kn5Pnf94bPPNDLxC7Z7OxUbjHOkwY2c6ZE18bRQIOaE/+Ud4aliT5iPvydzG\nkZp6w6e8u7W11g/R5y7Zzk/VecZ5IampmoMeroxdehvfJ1NRKYx0Vdu128RNL26qql1Ocy13\npoGOhCtSdSdM7yj0ZriLf6cbUH4D+lTmNRcTH/TF216f0K7rvA/ppsRviwLp3OzBov6Tj8g+\nkAevclOaxJylNH1Gyj/cM/SI0NRTVWX9LhGhpaLROEd6RSd0r+bRYTsOIOhNVwRr+dKqi46t\n9kJDiU11a6ccNOlPbKsgjlG0Q5PKAu+OZYjzEeyX5HzP5LAhs97apIPLTn7D+wWkUgsym0lP\nu7ry7UOacV9HoXGOtEuqDE3NKg81mzy4xjzr4sBYNm9BflbVtRQcaYRAOOnG2y1G1CFiU61b\n4V2dfepFJ7DvASaWPxHGPKEdqzOzbvOiry2ChSJp1fn7l7ghLvPFctA4R9qsqjFf7AQ0mTwk\nIUWfkCyMD5FmCsiXdnZZXxL6dZn1wIyzpV0Sf8tCO4TYGgbkda2naF9B28nDfSjSo91CCGQq\nXpWlxjJi0ug3xqk6VJ0h/b35jXWTACZWKBrnSFepV/jxphm7knoFQM7odx4iZdN64tw1jN9q\ndTU0bdbOhRF9IDVVEBv15T7/ITEN92xCbqwOarhg3VBjW4akc1GhHObtr4ck2shRQH6ivlV6\nfGDDpjH3M+1mFX0xGRrnSDLX8FDayENbIFgJOaPf+cYeT799RO5Mm7XIZSinonK7Eve0ZdhV\nADPLlzmqQtHcqL36pEpHtnUxqzszLZizrn09AjF+vm/XY5kZkfZmNrltM8LCiG0VgcY5Ej5J\na61Mf79en+WuLLKBqxbiIdeDNQG6MoR415UgacOL42y40oZdb5iFv3+RD3qTnwhcUEk2rrAk\ntlUAQar03ZpjiG0NVal+d+G4f4YmOtJefnnEIPGgTbwXgDP6g4ZUrftZ9zpTUtL4rBzTVVj2\nVu5DTxBXXfvesiH2FLIZlmQxu+iLi+AIo3T37brEtgqgXWfloMIMYlvLTTNlJ+LHbv7gSe6U\nRaB5jtQtGCeduJmGZVZLAGf0O3v5Kx0YxzK0sSGAODtPmbX2E50lN5YvqVZ03wuXF1jr2JK3\nfn0od/eUy1uv/IxzB5hZvsw1n6zITLn0kCZPlvygM8SDV8FPX8hwdn6sQvMcKTB3aTAaZjJ5\n6NgWZ55ZtPTiFyFAp1rLBIyzHn/G94mPHwtivFkIVbF9HTEfQs21YpcpOsgQ6elz9cvFz3ii\ngWvim7B2EG0BFyLbfz7dGMEya4q+lgzNc6QOqs9LOa4iNb4TlANXgAS5yGoPmosRKlOfs2Jz\n25n4xrSuI3eu0AOoDz/J8Kd9kR2zoYeR28qf1o4mZXrGRUiowwDGYiwrIoSc1k8w41QbFmui\nIy02+bamnolBrTEUVzlCdVRhDBvyuBJ+osWvsefZxaaIq76sP9CFnMEj9IzcWiJtgUykVJPl\nPI5eoK/oUx+ntKwSsrQhRGaKRxz+cv0DxsmIOPG9CDTPkVLsrMR9N2yOYoy5SlQc4rWus2+L\nCUl3QCo1yomlVesZaY0R7AAwlg+/ORKABMhYr6wb6/fIDblOJzeWH7CZKWaqJp1a3LZC1URH\nwiNpgw5DgsWVjccWfa1a3KT5Hcb1ctYvXxfAWCL6d/fEEes/4HCu2l/azTg0ocf0q3iVPsDS\nLqKjctCCIz1t2MyU7OW9fFX3jToNYK0wNNCRyo5cHBnQa0vWfFOOdHVbW/DrTVszTMpA6A5u\n1VcOFnCl2jCUx/dt7UG1KgORzdc7WDloQFocXABXqVeJGxIuZGCQzJRePt9GufP1anbX5rr7\npeY5Uqrqv4irjocP0YXErpXM64x3gjicyBVrmFsOwFo+ZFTUMZpx7tIQ1pCouaCSNXpfr/eq\n6dVpvZSoiWbByBxMkWkZ2m6tFkSqx1OpgfXUw9taIA5zA3PQPEf6ipRl0E/QE5jZ/MVKC+Vg\nMERy/iN0PXPHsI7jTrZuV/TF6rBO59UER5qyC6MgzlJS7TzZeqOntKZJxZoLItmYDr6R/iCA\n8gFZT9RnTVt18abaCoi6UBcDzXMkbLYEf9w3Y/3dbRJuog25r46JVSHMNfBxl9QP96MpjlT/\nOykc9If89+lI1ttBSQIyHTJvkJ2pHkc70AFup7wUmSnlQYrZP/J2LI7qMOE67s51RZIGOtIg\nxzipxN0M6XLUl3WX9Oe3i+e+yD+iIImbj3iSKad29Ga5mm7gQOWgFsgZaqPWY/1dG038tESf\nG02MMvNwdmbKTQSh/HOaUj5M13Ot2qCBjvTZjOr58v3ecvxK3BzCfdPxpCmaCjonJeuDpWSV\nbpQjo1Nz5yUqEcJcHsLlb6TPinidA0ibPT1lH+a3HKk0qYS+UhFEv8rjtPIzsMUAwFphaKIj\nSaoLEeK1v6nLTSHFe2Mq6l3KCXfWF2QVHxqCcXZIyZmbPrIbtDqYI77X2lMUSFasSjcwlSPd\nQIONOd9fI4jnyhv6In64Zty6J0NI5Y+LQgMdaZt2esadW/KFRyQ33az7lJ1vwJSR0kYwJTm5\nSy+OcgPv8SQzrh0expfCdNd0nI3xk30Xv12lXoPY+5tmTYfWtK49InmuEch6wr92J9qimhnN\n51DuLBsNdKTcYABAIVt+GC3HP04v2/NqlwjkbKKzwh+/fMTYbgGEuTzUrFmd7928PEXD6P4M\nczzghkSUwJGbXy5ehszHrIx1NZBOAzH3UCiY9OLOQj0BRMZuYWigI602Uw6iCRvU5c8XdCVn\n8BQ9hrC3Rfok1gYhi9YMJ9lr99Ft2bFJvWdf79AKxN4nC6r5XVliXcqLkx3oDys/QeUBI/wp\nHZjw+lmmgQhks323AAAgAElEQVQhk7Gn6esg9gpEAx3pKXXqVkRFk1qjy3CiHfNTlW1yB4Es\nbrKqSEzmXrkWzRgRC0DkxzY95WA+TLtKmZ0tJTFAbjt1Eoq+uOSsNPjxcESTun3/0doMYm9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8uwHOxx5dc6lO6kgLLTPxtZVzj6Y4wPYe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\nNmJ6QtCYtS83pGk3fHbOSVD1syx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awI\noAguw/o7cCdLwMzyGfyIDZChmaP9XoW6dro5W4/l/xaLHBW39zAhcY3xDq7wxMHhqnBHeYBf\nZIvWZV6hBrrJDoEEGWMaxmkVzDyH+b/7Fm23eI9JkCtLXBGHYLYGgA3QlHW43ytNXXlqtyqR\naFTkcslMs8WKoLTYBR+fvjMXO4pUugYDFbzcaFwVfnPQzNOE1DMeBbD8JCmjgaO1wKpdmewX\n3/r1zwbwvpvsEEjo3GBGW6ZeNk3bTajGE6Wabj22AEFVMt3GFapK4rEzHHcxhnHgRSjw8bbG\nfr5DIRnDr3j+wPoLluNVjfaO/Vb3kW7l0XVDmtAT4G8Hb+ZpQhrYItmY3n7mxkyFo5XWqCY0\nRgxAillAPlt3khVfxuqaXQQO/GAX4EUck9731RkKJKcXjCcNWSuq341nHewz+gbTKwp5Kd0z\n+8m5jMQTpvm24OD65ZVjFDvtN/oKFSVqWMw6LADjaUJapfG1btG/SKU6aBWgfO/Op4teCK3L\n7nKTHQJZWeT/ul8vwMFu89/Ax9fEP2WVI2Vdl+EZTHX+edmAJlH+jR3seH+9THtEM9Et4vVy\nxn5bSKyMlMAiqBTiwG2XW4Ge/9H3N7kPkMM9k54mpFtMhfvctW+OtgmiLtttdBqHWQcfJ1il\nkMoKbuQrMIzJiVVr1BMcpPT+Exre4y5/+3V0ddmSWz1gRLUowAzoUZIDd/0SrbF7FR+KDh4m\nr/eb46r1VaV1nvzhz/Wwg8laszYBgIEKwmEO80t4mpA4Vh8dallW7+GgLvxrQaZak2Zsu7ub\ncfTYkoI91CAMoK6YpHUQ/z1V09A6Rvoc5NyVYGFuWV37dZtPcrvpavYbDYJvLYc/g6Plyy9R\nxBht0faUT8BBBvKauO/HYxtWNKSlOExw6HFC0o9nfPxrDF7k62BiPinBhGkjzaKKAspWuJU/\nkXnQ9bMcl5/sINtqVldVWEKDF75qigUUUnIrv6A4q6R/pTV37TYq690970wBxw2FvZIZZpuf\noU3+mY0zXw7JtP+8L/TWWyeep3XYYXimxwkp01xUkWcBrLTbJheNu7JmWMd0VTN5Sm6XIEbB\nC+jejbPeKvvJYVND9CbQ0hAbLU8d5hJ46XbuHFAz05Rpv7robXgOI1BX6a2AP6U0zQaHwOSF\nVSaEsuy76/dhY6e3Xv8m758Qg8OqJB4npJnwPndxx8otEQn2nzYVH2SxzVLIu9DB045pPDSO\nBjqorv0lokDT+cJD69/uoddultAymwTUQ8hsBJNKaTd69iZQndNVgFB/cLQmLgW/Q1tNtdr9\nt3zpR9lt844pARgT0vv5hDt8L48T0kalIolmjEDn2M2+dh1XDezQYtTOG6nIefZ6N9OrqS8/\no1PUidbZ3c9xDLR/FfJ3y4JA1nnVCjeTUtdr6qQVR7mpYDf++3+In5AUnL49xKSXcfOxlUL/\noiB/LgfZLYqxFtXfOzwzIozq6zhrl8cJaasuXeGlr/LSAsZuOdDjEMBSkWGYDQWZysc+YkaQ\n/vtvf87jrrN2fcVvBkeq1KqKsxZRDiPaJWEMtsSjFXLTlXbD18YFhn39/meXuQs4S0LDbNMS\n7726tG+7HKriEHtN+kDRGlNPfS+Hb+VxQvoT0UXjtgqUvVRQJ6HBP1uGNm1rrs84L5XnZk6g\n5lzBsc2fL2RZe7vPFur0scjgh+jGjvbLSMMuyPq8QwTljdvYTVDbsqkCNDRVK1YloOakmxkR\nRrH6uECEEu266yPSQga1H/1hwQvgYNGW80AhcZGGq+fm9+rRCXuvtNNihiLXetyD5F7o4GGZ\nruGgx1AZ9ttp0Rsd4k68s2BdYKLDIGZJ2E1Fgq6sXhGj1NprkoEH9jYBYP/U6VJaZpNpSary\nmfWGHvrMfl4wJgYz5eNpLxq+cfhWniekLG8z4185HKjoyXZaNGiIA5mgZp/Phglus0IwmhzL\n/qnIcVF26wCXUU/9ZuOP97jpSL78v8X8CsYOr0zeeKmwGm3nN1jg5cv/PHPqLy/2A0lNs8VX\nKKWQ4/K5yyqVnWi7Ajr6j6VNo5O8U+Bnh2/leUJq3wBHmqPbfLUC9bDTIlkXRIdUCwM2WHZ3\nMselGYee/eqcpZbtAtsNbkN1QN7gOyQITktrmi0CNXncnx9t3B+pWm27wXeYbduz3dQjhYkq\n+0tNkqEJ/nVCEmv0CsJ21rS2UU25e7zYTlJGx8N8zxPSIkUn/ueNwt+QHbddoVfovT/m9ezT\nkdY6r5DpdkbD17dX9G0yKKqcnRxXN8FrsD/4UZAmuzuZpynuVx80XsBWsZMU4x2DEqKy4lGk\nQs4UfMX4RWF1Zg2tmbX3eByahv1pXdW39lJOUox5npCuQt3jXQJArSsDtqPt9iHDrlVvfFfA\nxTCyO+04boPC6G3MaqBD0VG2G3wOo7l7+9fvnq/Qye1O5umdSUOQGaq3oexkmVgEkz6tawAD\n1SBJWstsUiE5rH/TAWvufQh24n/aG32Zss2rUCjayc40TxSSEQe0bab3oeC4zQbLgtUQGIli\nJjB2vrqSsk1j1mAIGHTQ30603XNRPp0ymo4/fY12Xs/T/cwxlflsxcZfuQK1nQ+vBdp5+393\nb3CzFHJH2lkYgbZxv2+Y+c5wjZ0HTrz2+okJLeq1Z6NfdPxOniekQnVo+ewqHZfdm2anytWL\nVNPaKKIiC1UdRF5KxgVsvHnrwtFD9yrDAZsNGodjbU7PWGWYapTEptniNGqfv7J1Qo2aKmS7\noqRvooICqvLuCfChxKbZ4mOo2wn7VdZCkp/N85cpasXciRv+5loje07TB3iekLia6K/8bZMH\nvtLUy/bTuh66yB1eOeO9hr493WeEcKL0R3oqASgcYTsktYz24BAvAAVVdo7EltmEpkK0nYZV\nRkxRjPdTUDhY2/H5VP68Y3eyNHyGTRBW1agbYlTYPP8l0qOYWj7qoWZnVaM9UEiTcMdEVWa2\nD8TZrHlYqDOXiVIkDDz7Cmx3nxHCaRBImXqPTGejlDaj7S5h398+eHv3CS4VyR1MbcWUqECA\nKnwyGbbYOv0n6pS/sk1CjUxVaXCNcOcwXrlk6sZzXCfbyWE/gIatUGRNM8SZnbyTBwrptRCa\nSqmi85uptuk3ugY0Tp09LVajcpjsQjL6lPFrEZ85+H+32aq2Tn+kYEHH3xR2Rmpk3rhdRD20\n8+Ynq+dumcfYDA6ca4wZXDd70qkCXaDUltkkypi3NJnFoYrgabZO58KX9z5eMmHFcE2Gkzfy\nQCF9if3emzVpzt5bFfEFG6dPQa/9NWkAjbfDZBeS8QGafmdh83I1m1NqWyUpVlCJhoTRU+OR\n2XF0slS8BMs6I98KGhRt0yvXKwwChgxOVrdFjrItSkeO0ls9bOUonVpvcxyfHGqgAads/R6c\nxTN5oJDyteX+aI4wYKS3VQhvqrr11I79X/zjEiVfPfOSXIfgsr6DF7ehGPjdxunOcObciPrx\nLSoEOkrOJh3v6JCq58x2iuoqk63Taey6eDaxkgLihkptmU2GxNIKAL8plzQ2g7u9KHXc8vc6\nYy3tbIeKBwqJS2AV8Wu2D6EDFDNtnG0VBtG9WvkGzcUO0wRLxh3kDf6VvBTj+9ssHhitizKA\nscn+PWBzbCI53yO2a63UVq/eb4Zs7Nu7q/Lau7RP30kf1Feskt42G2zBg+4v7pTR7HmasREU\nfJVqdLajDsBE2d+o+ABPFFLTCJMe6PIbrlONbJyNUQ6mqw4bGgBBTlYOpCIatq3p2qrjrNGM\nrYJYNEZtv9rUigmz48yXmgJ99LW+agBWYbSR4XcfUDimst6wsj7lsJSKZOTj+PqqNi/2U1O2\ngoJXqSIbR5RttJELVjqLZ/JEIc1Hbx9vEQBeKZTP0ydv0uX2TqxTpf6IaIX8MaBWuuAt8dq6\nneIhwEZFyQuo46ZAFKoHFo5Ib5otKmPv6Hd/fztIqxzx9MktkMI2WbunI6LtRodLjEqPs4a2\n1KYNBhuDt1FmlPD6q12YVkwFZ+/jiUI6CuW1tdd+N0mBbFSY2sEAVa6i2uf9OnTpuGdyi/Qo\nfPk7IwwZGhuOrgWqSvWDwyu/dFKvkTk5ZDEdwxnwYuge55WVnz45EH5cV9kXQhN18tbNeEQy\nHjkwLS1zyjxkI9Iik13n75fdrSyEdHH2Pp4opLPAUFVblMO5Q+HYUyeX4nKKqUfO98bY7g5a\nifmI9artp49s9UEmerogVk8vaLBqSRtqoG3nuAy8jhfszvQCVTKy4WWsoFOgAEo94QSUisVu\nnoFoTwVN3W7pyPi0lzFfpxzbMCo286XOSieFzz1TSIVmZlPPCJMyNVM56amTLdH/cs0A4Ovl\nbOVAKm6z6dt89RmVVUjzdCahOO1Uuvb4GRngkyuDabb4G1INmet/WmtGNryMOoYaev3OW8YA\nbMthKgfrFFT09iNrEoNNT5fCOg7IPOylztrancF2vFMJPFFIXBY9lOq6etsArH46k1AwQ+kS\nNOzQfTDSnSa4QhlM5d65tSkwAo978tQNxtwtVm+O6F5b6ah4j5TcAUbZfmQLVeacpytDn0bd\nl5lwhD8ge/t/JOcbrAxHoIqfkwNHnzy3C3K0tVftXahFDqtrWPFIIU0xQsM3l/dQdPd7OjEg\nVjNvFBRu8gqG3e40wRWambSgQ3TNXcxTs46vAeLnrcg1VW+J7WdglphwNKeekQJzKvtUAvBF\nGg14KSFpdwzroP6DpOSrE9/TB2S3DkX6p8oMPo+GNDKpwK86cr6k6JFC2sRUyDKyWFkpCP54\n4tQPMLY7oymfSAH84k4TXGEefNAGhTZModBT9buWQH+q+/Zf1upQafGCcVx7PIAZuvPwIpZ+\nytXVg6J73C/8MdOfdZzbSkpSMR6fz32bFII6PXmqkpLp/fKIONOH2HkYhkcK6RZdIyns5T0f\nN4enFqzHa2mvyuFUwOpAvcPEmlJyBPx8vuS4j/TecOmJU80hOwghUKbgFFlMs8VSNbTcuL67\nPitB/eRHGGVaqjVm9swAY2nxNXBcT6MK+7IQOlUf9uQpXaC5/td3rzWjmCVO38YjhcQFY/27\nJze3o4eiJ8uN1ULUlELu72wvqoZbLXCFywBMcpwWpY2BJ6fowdj71U/fqKt4AxzUUZGYvSi2\nqgJ4m/2fDAe4ihGOiFBQWaPwG/LYZoN34NXKbPpzvfzgydKWB6BSGgMIUVrK+TDfM4XUgEph\n+F81BEPy4ycK9RGdaE1C8yqgtxVGIBMhxrlqY7XeDZGy2+Mn7lBpulrrblxtj7Hs2YofUqCO\nC6m669qVScA8sYNqH6gzbnAFK5SxchdyKsFl0Ied5LjdfmVh3+NnFirQwPdWd9Q0raJwnqfF\nM4U0A4Yzzx2+e6w8emI/1xFAZTrXCkLJ/dHHbrXAJdojxbB87vZsSvnE/u13qUhLsi5gtaVn\nRmdJvanfsGNUOt2NfWL/9iQYbWDLthjkg9hSseXDSgELONKXAq9WMP7xM43plIh5J7kf1CjB\n+dt4ppC+B9T1l7d6RivawInHTrwJvvV/LeB+MPtQpWaKxN8a1ahsgg5BZBnq8Tv5czSz6eaJ\nmVGJkTZDrWWiD+aHdkgfiNETVtWmFDkNIlhlX7r0+Bp43StH4PjeqxeZqCfygfowev4mRSOd\nwl7ithJ4ppCuUjojADL70syMx05kQwYGKqyeFpWGZFHF/ALtAnVVB28YivDjz8kYr7Jedaf8\n+K22FOTRfsQWqOvzdh5X2Ih9YgSn1+u3/s7d62pEz8tkmi3GYLys4MCbrelQ7WPPySuAOv59\nZkVDKhcEVBL2TCFxZYxe2V/fufObBtV87PUQSH5vSlYA6gJylxh7DJ0i6urJt0bGRKABJV++\nQWFDKObvmiGMw7KMEnMWIGd+lj9DN3r8G3gE4viZqaJyHaBlLhb/GJtpVqsBjMH0+CTpfWhM\nxXZaeLELBlsbQJ/AQ4XUj1av6BGKkDFYW3IIdwPHKlqOWntjEQ2vudcA10hHyBcpMIvhsVjP\nb4CZ+Ov5ffO8qpemKRJXYNCFAWiq5eqpx5Zm5lHsWytzolSmdHRRLttscIOqrkrKffv6tzSe\nVfL1HphKVAMFDK0VMMz3UCGtx8n8ndyn02D0oKZYEW9hRo/0SoU3ZSf3lUwMgTr6RhO2XOmD\n6cdfLssPUMtOzQaq9EzeeerQeO3vm6cPVekfC/ytzmrKZuVuuRLGlI69x8VEocQzI9P0Cj/l\nY+U8QtjwnZ/sXN3EqBSSls1DhXQb+1Q5unpUh1TdYxtLWyPzwbcmdExmygi5CUnHXoANryby\n46JY+LrEy0mQNieJvyF403aLpsnCy/yoTqPyw1hTsrplgRp7qzVBlAnjp2IIZKUrUiKFGlVI\nh5KRIxdQICAaqr6ioGbZv/YhHiokzh/KhCjL+dE0lLzd+BgsM45Kn8dATbtXysFV/iuJ/Bh9\nTx88+NGrdxk/dUp6j1Ubsa29NDJyBNKQPqTu9H0sWvHo1RNAjVjQv0MDcxK8KZ9tNlgPwRlz\nhvTtXVVTclvNaqTa3FXFP/Gj7dYBKYmnCqkx8tHqy9Wd1QWrH714FtCMquBnADWylc1BRqK1\nymk96lWsplSXyBX0EUJ+yoyKuDzGpSFraQl0dNf3y1nWt6j6j16cDkrw80Jt5sFTkU7ycgGg\nV5AhjZ8ylxyeNKBpPYrM3lFToxYybvZUIb0JzJ7KEOgL2hL3m5dBYcSm5CHNDXDSzf27SC72\nrqhq1EJtxCXm6R2QflhGGV9/KrKUJEB4SCZglFRNW6YblNjkUxGaDtWw4RQovErVjI7jvA0U\nABUzqSYqsb6lh1Q2KaccawJB5eY8VUingMU+jSKoHrFo0MMXa0A4XW14E5wGzhLUSs0uCOAH\nnbq4vjQ8yr7jQ2NT68q4QzaSv3js40wCtkllfwZpVY82992xLm+ixDl6qqGMptmiJQpb58fE\n+oCaulX82p9AJ0X4+vgG6Z4MeLCNpwqJ89NEtOLHcBge1enJV7JhPkoaFNh+JUSZKGTQzFhd\ni95eGOoWv3YBUK4fFZ1OYSgdOeIecRSoapoxC2uz3uhh0cPNYEjS5s4qr2Vx6cjE9Yj1GKH0\nAeVxey/YWPzadFBQHV9qQI/FwpYWpBfS9TN/OfWISSCkLiiQ6vV2f3UKDcWDpd1A485vDVbn\n+NmrliMfCYDNHeNor6bwcE43g39EtSjP+PRB/+J36F4KtZanD/AjZTqy+LUm2BIWiJU6L1Qq\nMtiW4BrWJkRgOkIB6OHDsixVNhTTYSZQqQVV5JZYSIe7+POfJhXU3vFOYwmEtA1YBT/SMPDm\nFDsWWiKjHujQioiBX93dvasMRcp6lKlOLy166ACPg3SFueVrKRqgS0kCoUfUR3WCI1/+pDGF\nUbFjQQNBfvM/H0E3glBZTbNFBMQa1q5uzlZ8eJu6ihDuNb+xMjEV2yy18BTSCmkQgoDKjRpV\nCQbo5aidBELiMMr0f3NDN23Yw2gBLaAWr3cNUGXR3m7v3VV+AgoPGpuiUERA66JXrmGkalVO\nARoVU3o29RXzFkKamtaQT3gQzHjI8oAC8OL/s5ldX1Z6W5+fTLQa4MeiV+aBRg+q5MFaqqQH\n3wGSCmkxZD2w80hbcJTgSAohxVLgy2IUqES4qMLlPrCMPdTt4mlwmsVMcgp1Sh0CddUuLNIU\nvTIHzLSi/MjXGF/kNFeU5NzCUAVX6DS5ggIerBV3Bm99u7G5AZHKUjcQ5bhvQWuuuaBfLBVY\nfJuKBdR4UCUdisH4iuNrHyCpkKrGPByDFFZ3lO1KCiGNh0i6SnaGPzbCS9YXsoGNa5vsi00I\ndri9d5fJhoC46VFgWWz/wvpCJKKahgKF+P+fldk2G0QBah6K1ZgGZM3KUqhBah9KjyvSWFHq\nBqJcgZLGJqymUvQP0mJctyzMU7hJOxbChL2FpELSd33057EGBw2lENLvgExe+lAUo4Ygy9/z\nFaDGQT6qvhRiSlV8UBGfWHzHDAqvgsCaufgKQoApqk4VHyhNOz6KGQYGivIJ8tOowJpD7GNQ\nIDBGRFGRSNicQ1rqQrSuVqBlCRm2Wv7+IjBB8fwdFRh4MhmBHaR9IpV75ACpJfcTifMHs8kf\nsXp+RGcpHrcKGMvdnR/c4dKStPQxaIyaKUOqMGqgLamsBgMK1iA/DT/nKE2be4r5HXBIlG8t\nb6UJvCx/TwUmFMeVp+MRvCu3bTbYBuCHE0xUWVyUfMAb9LhMHUV1P8ZOxe6nkHiO1PBQ0Z+O\ndQBHkYCSCGko/+H5VdKCEqAZ/9dwUCv0terTlZmnUoyUCtJ5jQdYMk0g61BUBXq6Rg1FuFZZ\n2qIwighAlgQo2ihkdc5f5x+fQQkspaGBtlUuTW7yGcBhlH9tM2tNgfIt/yHzzyMKELZRZ8Em\n0nrt+gGEVGvWPDMCoJujMBFJhPQnMIySiUxVKoG6w53gf+1l/K0ZEBjnqS5kYAMoy+HUVIvw\ndRy3nB+F+AH4sxj5ym2ZTUYDhIbVoC2fZzzH9bToH3yrKBhId36tDFRHFE5SIIZXfyeOSwR+\njuTf2BiLBK91S7yOdKC9t2UWF9D+M4fNJBESFwBKnZ+CVmkQdOOS+dsn0rJVaKaURX4Xk6ew\nWIgZI3+Pf4szWt0OkfoADDaqp5QC/kaWBViV2iKgY3mURVA6LagUpXJkx3FbQeGDglQWM3He\nb/yHS+mRRU1wRuAbSB/ZcPX0udIQ2cAzBbBaxeh9gAb8LS9vhTUYjIY9EvT9L2gKGIUpwmj+\n16tazFuqAqRkeYMF7IOWgwjQmFSBlvEdRORY12m86SAGnkoWWzoo5BVvYlXWFZAWZSzPT6Of\nUasHwVsQPTbWjucmZb3xWAfzmP8jhZVGbwaerkpQOjjK/3b5/1m/mhZ/EkIBWKeGWLntssMS\nwBRCOngAArWK5c3uLLdddujJz4dUJgXCD+zFSuu34hWh13uykLgawGpYWmO9DVk+NtaaNXKU\nFF3/GwKAUnuxuNjcB4raKrdZdsi3JCnlP1HqwYeL+L/xd65SuOZl5QL/qVJFbluruaDU8Jpi\nBMXZWZBLSFeTkx2clUhIvxTdK4tvQvznpsBASdL1v+ENi2747+PDmzzmLdfLbZVdegKlVCge\nfriUgqUpiJPbKrsk8U9Qhn1oLqJpBrsQ4iKXkC6Bo3eRSEgcPximWerhZ4csY6eWkvT8byjk\nn530I9XzOuJNn+/8Opm4iR+M6R58uNbD93JbZZf9FlPxw7tUkdHCMyvLJaS8XbscnJVKSN9Z\nJ0fowe/besSlbLNpSRbBg7HHo6eSoG3QMpFjibIp8bXk/xwtt00OiHko+qInKFW0vigQj54j\ncVxK8UzY+hla/it9ockl8Hpwb+cfRVbHA8BauU1ywG2LldgqIFT0p1KVfu9JTlhmSVB8V7VM\nRV0Z5ZceIZ308XqIGv5xSx9PcbXojkkV3TpR6b7DWzJCPrizF4+ZSvMd3hLJUmQmhR/I3nm9\nLjlpU/SZYlQ82J/nwsWlR0gFe3Y+ZD5IFUeyuPh5hIruRT9I1O+/pHOR7hFlnc6BwBB/2Yi3\n6t7qH7F8ujrBPjBZKDA8fBhZvwsuZcIoPUIqyVeSCclyG3p0k4c5UnX7b4l54O+4dGwAAAhg\nSURBVGco+mbukdscJ+Tpi55JqGibudPS4DJzgXrocuLRuvQd9HghcdklXEtTJev131IYW8Kn\nVMqy2dngtvGRufQx5+1l5jf60ahZ79rsQkohLTQ+hoOWUgqJW0kXe8C+dt5YfoYXu5Z8T8tt\nigAKGxfrKLa01DF3xN3EYnMbuDhZllJIxwcrQJfwEActJRUSxy0ro2I0KaX//l7E/UnBSlZf\ns5TP5h5yrb+fgjVln5LbDoH82crEKnz7XHf1OmmHdp9AE0HtJBYSgfBfkXiOVJYIifD/EomF\n1FFYAA4REuEZg3jtCAQRIEIiEESACIlAEAE5hLQtx1kLIiTCM4YcQprv9A2IkAjPGERIBIII\nECERCCJAhEQgiIAcQrp13lkLIiTCMwZxfxMIIkCERCCIABESgSACREgEgggQIREIIlA6hbQP\nCIRnjH0uf83dLyTupx/s0CBzjaxkkv49u/8G9r6ZP7n+LZdASHbp1k3Gzkn/pH8x+ydCIv2T\n/kWACIn0T/oXASIk0j/pXwSIkEj/pH8RIEIi/ZP+RYAIifRP+hcBIiTSP+lfBIiQSP+kfxEg\nQiL9k/5FQE4h9ekjY+ekf9K/mP3LKaQrMhd7JP2T/kVDTiERCP9vIEIiEESACIlAEAEiJAJB\nBIiQCAQRIEIiEESACIlAEAEiJAJBBIiQCAQRIEIiEESACIlAEAEiJAJBBIiQCAQRIEIiEESA\nCIlAEAEiJHm4+eafcpvgoRxf6Ja3lVFISzIMGUvk6Pju2Or6yPa/yWpEN9gmX/9f1NEHtJHv\n3395aJw6bugVmfofbHzwhxJdi2CFfELqBzFdysIg6Tu+Vh3ietVHqgMyGrERioQkS/8b2MAO\nzSnzHzL1fyUSavapAdHXZOl/h+KBkEp0LYYVsgnpADS4z92vjw5L3vMYGMj//BAnyWfEGZPW\nKiRZ+v+Drsx/h5dBV5n6HwuL+Z/zYaIM/XeMASgSUomuRbFCNiG1h4P8z/3QRfKey+nuWg51\n4YJcRhTWjhhrFZIs/Q+Fbyw2vLxUpv4bw9/8z7PQQob+WzZpoisSUomuRbFCNiF5B1sPAf6S\n9xzXxHpoBP+Ty4jZ+MsZViHJ0n9gyMM/ytL/ZFjH/1wN0+XpP6FISCW6FsUKuYR0FTKsx8pw\nQx4D/lb63ZfJiAPsGM4qJFn6vwnVf2rqG5JzXK5fwrWaTPuJ7em6N+Tpv0hIJboWxwq5hHQa\nmlmPjeCMLP0fi4aVMhlxOy75XpGQZOn/T4jSJvZogNX75PolvEEDALNGpn9/kZBKdC2OFXIJ\n6Rw0tx4bwV8y9P7PBJVykVxGDFQe4YqEJEv/JwFGF3LcTpQi07//JWh28NZPjWGuPP0XCalE\n1+JYIZeQCqhM67EKVSB95x+FQpP/yWXELniZeyAkWfo/D+Z8y7E+XJCl/8vK2Dz+cK+M+ros\n/RcJqUTX4lghm7MhINJ6CAmSvusJEP+5fEbMeViDfrks/RcoU63HfrBflv6/hv7WYy/YJ0v/\nD5wNJboWxQoZ3d/H+J9HoL3kPb8J7e7JaMTOfhYqQ8N+e+X5EBro71gONfA/svR/9sFIyuIF\nl6P/hGL398OuRbFCNiF9Bp04rrAtfCl1x4UxQXdkN6JoaCdP/9thID+GeRuayNR/ErWD//kx\nTpOn/wdCKtG1KFbIFyLUDWqPzYSekvf7O/g0KOKifEY8EJI8/XeDxD71IOBPmfo/pENZ/esi\nwy/y9P9ASCW7FsMK+YRUOLOqvups6fvd/XCOckY+I4qFJE//c6rp4gZdka3/v3rHqeP6npep\n/2IhlehaDCvINgoCQQSIkAgEESBCIhBEgAiJQBABIiQCQQSIkAgEESBCIhBEgAiJQBABIiQC\nQQSIkAgEESBCIhBEgAiJQBABIiQCQQSIkAgEESBCIhBEgAiJQBABIiQCQQSIkAgEESBCIhBE\ngAiJQBABIiQCQQSIkAgEESBCIhBEgAiJQBABIiQCQQSIkAgEESBCIhBEgAiJQBABIiQCQQSI\nkAgEESBCIhBEgAiJQBABIiQCQQSIkJ4dWpBfVumF/G6eCXaEv0+EVKohv5tngs2wluMunZHb\nDIJdiJCeCaxCKua2fHYQ7EGE9CxQ11KE/VIO/8vqZfymDPi0PP93z2hdrYOWc/nTqmjDB/1l\n+ePqKkZz5ifymuqpECE9C2wfDH3evGsVksJUZWxtSI4tP6YhRNznuHuZkNqnJoT+wXHTIKB9\nQzX+XG5rPRIipGcC69DOKiRoU8BxIVDjHsc1hKMcNx9e5M+vglYc5x1zl+M2QQ+5jfVIiJCe\nCUoI6Uf+r/3gA/7nDNjLcaHRBZYG6eytPDoij+MKj/wuq6WeChHSM0EJIV3k/zra8iziH0Z7\nuX8gfa2FWnCIawmxE3ffkttUD4UI6ZmghJAucRYh/Y8rEtLPUMzX3O3JkQDqDmflNtYjIUJ6\nJrArpEswsGS7Y2/UgMRCeWz0bIiQngnsCokzp1obzJ7AHX9hj+VP9eAP+ez0XIiQngk2wwo7\nQhoH0ziL164DdwIy8zguL1VxT2ZjPRIipGeCHZD64i2bQrqRABUHNKeCznBcM4ju084fxstt\nrEdChPRMcKez2XTFppC4O6MqqKP7WyIbbkyM1XhnvEWmSHJAhEQgiAAREoEgAkRIBIIIECER\nCCJAhEQgiAAREoEgAkRIBIIIECERCCJAhEQgiAAREoEgAkRIBIIIECERCCJAhEQgiAAREoEg\nAkRIBIIIECERCCJAhEQgiAAREoEgAkRIBIIIECERCCJAhEQgiAAREoEgAkRIBIIIECERCCJA\nhEQgiAAREoEgAkRIBIIIECERCCJAhEQgiAAREoEgAkRIBIII/B8xvGt/Uz1gTAAAAABJRU5E\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(times, Re(eiw1))\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3d958631",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>-1.4439838214031e-13-1.09623421451488e-12i</li><li>2.64954724826794e-13-6.84563516983872e-13i</li><li>2.26485497023532e-13-1.90958360235527e-13i</li><li>2.55351295663786e-14-5.1902926401226e-15i</li><li>5.56221735337203e-14+1.72084568816899e-14i</li><li>2.62345700718924e-13+2.70672373403613e-13i</li><li>2.18852713729234e-13+7.92366172674974e-13i</li><li>-2.6328939028986e-13+1.1189937865197e-12i</li><li>-7.50066675436756e-13+8.35553848332893e-13i</li><li>-5.75761660570606e-13+2.02837746599016e-13i</li><li>3.43447492667792e-13+5.6052384955763e-14i</li><li>1.20875531806064e-12+9.4235730330183e-13i</li><li>1.02742814256374e-12+2.37646013978576e-12i</li><li>-2.892460576609e-13+3.1220581675484e-12i</li><li>-1.61115565333603e-12+2.39130937274012e-12i</li><li>-1.55266424717304e-12+8.0318217354769e-13i</li><li>9.54859021712329e-14+2.2289502600407e-15i</li><li>1.9316562238636e-12+1.1153179074741e-12i</li><li>2.12667730647986e-12+3.49474268968031e-12i</li><li>2.3594342625499e-13+5.10605099868222e-12i</li><li>-2.14715571711377e-12+4.39627154125155e-12i</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -1.4439838214031e-13-1.09623421451488e-12i\n",
       "\\item 2.64954724826794e-13-6.84563516983872e-13i\n",
       "\\item 2.26485497023532e-13-1.90958360235527e-13i\n",
       "\\item 2.55351295663786e-14-5.1902926401226e-15i\n",
       "\\item 5.56221735337203e-14+1.72084568816899e-14i\n",
       "\\item 2.62345700718924e-13+2.70672373403613e-13i\n",
       "\\item 2.18852713729234e-13+7.92366172674974e-13i\n",
       "\\item -2.6328939028986e-13+1.1189937865197e-12i\n",
       "\\item -7.50066675436756e-13+8.35553848332893e-13i\n",
       "\\item -5.75761660570606e-13+2.02837746599016e-13i\n",
       "\\item 3.43447492667792e-13+5.6052384955763e-14i\n",
       "\\item 1.20875531806064e-12+9.4235730330183e-13i\n",
       "\\item 1.02742814256374e-12+2.37646013978576e-12i\n",
       "\\item -2.892460576609e-13+3.1220581675484e-12i\n",
       "\\item -1.61115565333603e-12+2.39130937274012e-12i\n",
       "\\item -1.55266424717304e-12+8.0318217354769e-13i\n",
       "\\item 9.54859021712329e-14+2.2289502600407e-15i\n",
       "\\item 1.9316562238636e-12+1.1153179074741e-12i\n",
       "\\item 2.12667730647986e-12+3.49474268968031e-12i\n",
       "\\item 2.3594342625499e-13+5.10605099868222e-12i\n",
       "\\item -2.14715571711377e-12+4.39627154125155e-12i\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -1.4439838214031e-13-1.09623421451488e-12i\n",
       "2. 2.64954724826794e-13-6.84563516983872e-13i\n",
       "3. 2.26485497023532e-13-1.90958360235527e-13i\n",
       "4. 2.55351295663786e-14-5.1902926401226e-15i\n",
       "5. 5.56221735337203e-14+1.72084568816899e-14i\n",
       "6. 2.62345700718924e-13+2.70672373403613e-13i\n",
       "7. 2.18852713729234e-13+7.92366172674974e-13i\n",
       "8. -2.6328939028986e-13+1.1189937865197e-12i\n",
       "9. -7.50066675436756e-13+8.35553848332893e-13i\n",
       "10. -5.75761660570606e-13+2.02837746599016e-13i\n",
       "11. 3.43447492667792e-13+5.6052384955763e-14i\n",
       "12. 1.20875531806064e-12+9.4235730330183e-13i\n",
       "13. 1.02742814256374e-12+2.37646013978576e-12i\n",
       "14. -2.892460576609e-13+3.1220581675484e-12i\n",
       "15. -1.61115565333603e-12+2.39130937274012e-12i\n",
       "16. -1.55266424717304e-12+8.0318217354769e-13i\n",
       "17. 9.54859021712329e-14+2.2289502600407e-15i\n",
       "18. 1.9316562238636e-12+1.1153179074741e-12i\n",
       "19. 2.12667730647986e-12+3.49474268968031e-12i\n",
       "20. 2.3594342625499e-13+5.10605099868222e-12i\n",
       "21. -2.14715571711377e-12+4.39627154125155e-12i\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -1.443984e-13-1.096234e-12i  2.649547e-13-6.845635e-13i\n",
       " [3]  2.264855e-13-1.909584e-13i  2.553513e-14-5.190293e-15i\n",
       " [5]  5.562217e-14+1.720846e-14i  2.623457e-13+2.706724e-13i\n",
       " [7]  2.188527e-13+7.923662e-13i -2.632894e-13+1.118994e-12i\n",
       " [9] -7.500667e-13+8.355538e-13i -5.757617e-13+2.028377e-13i\n",
       "[11]  3.434475e-13+5.605238e-14i  1.208755e-12+9.423573e-13i\n",
       "[13]  1.027428e-12+2.376460e-12i -2.892461e-13+3.122058e-12i\n",
       "[15] -1.611156e-12+2.391309e-12i -1.552664e-12+8.031822e-13i\n",
       "[17]  9.548590e-14+2.228950e-15i  1.931656e-12+1.115318e-12i\n",
       "[19]  2.126677e-12+3.494743e-12i  2.359434e-13+5.106051e-12i\n",
       "[21] -2.147156e-12+4.396272e-12i"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in xy.coords(x, y, xlabel, ylabel, log):\n",
      "“imaginary parts discarded in coercion”\n"
     ]
    },
    {
     "data": {
      "image/png": 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A7FDqgvQxPDoKvrD7+zscnG6Jartgkh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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in xy.coords(x, y):\n",
      "“imaginary parts discarded in coercion”\n"
     ]
    },
    {
     "data": {
      "image/png": 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/nMlZZvlFNdQZpFgf+oLkEWBCnDGeYzw4S2ozyFqkW7KKNcKYQgZSq2REGnItwM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\nQVpUTHUFrij7tuoKIJXWIDUoHp9QpQLnCZHV6IrSRZD2sDOqS3B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5pQTu213L8524xkEABMlTMZY/xDW+oBBmc/EuCJLHoh4T13abUeLa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\n4P9eu9/4YHV/swAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "omega2 <- 0.034\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- exp(1i*omega*times)\n",
    "eiw2 <- exp(1i*omega2*times)\n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ \n",
    "exp(1i*(omega-omega2)*T) * Q((omega-omega2)*T)})\n",
    "plot(omegas, Re(analytical_estimates), type='n')\n",
    "points(omegas, Re(numeric_estimates), col='blue')\n",
    "points(omegas, Re(analytical_estimates), col='red')\n",
    "numeric_estimates - analytical_estimates\n",
    "\n",
    "center_omegas <- omegas[-length(omegas)] + diff(omegas)[1]/2\n",
    "numeric_estimates_of_derivative <- diff(numeric_estimates) / diff(omegas)[1]\n",
    "analytical_estimates_of_derivative <- ( \n",
    "    1i*T*exp(1i*(center_omegas-omega2)*T)*Q((center_omegas-omega2)*T) + \n",
    "    exp(1i*(center_omegas-omega2)*T)*Qprime((center_omegas-omega2)*T)*T)             \n",
    "\n",
    "\n",
    "\n",
    "plot(center_omegas, numeric_estimates_of_derivative, 'p')\n",
    "lines(center_omegas, analytical_estimates_of_derivative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ed1c7bf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EExW6TheehC6VuktqO4E+guufyr3BGCgruaU9rl/ok7gvZGtedOEBQUidK0apS3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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(haan(times, T), type='l')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca812e25",
   "metadata": {},
   "source": [
    "Ok this is damned perfect. No lets' make sure we have the right formulas for the product of sines, cosines, etc. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7908feb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>-2.05502281858116e-13</li><li>-1.47659662275146e-13</li><li>6.38378239159465e-15</li><li>1.85365611748978e-13</li><li>2.66314748031959e-13</li><li>1.54931623086441e-13</li><li>-1.25843779841261e-13</li><li>-3.56381590904675e-13</li><li>-3.13471471002913e-13</li><li>2.92821322744885e-14</li><li>4.12527650928141e-13</li><li>4.77085385086617e-13</li><li>1.01075398051265e-13</li><li>-4.30549693120064e-13</li><li>-6.31903383785382e-13</li><li>-2.60280512420774e-13</li><li>4.07683869302344e-13</li><li>7.70239557898456e-13</li><li>4.42364027353204e-13</li><li>-3.42484070617322e-13</li><li>-8.8439932460771e-13</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -2.05502281858116e-13\n",
       "\\item -1.47659662275146e-13\n",
       "\\item 6.38378239159465e-15\n",
       "\\item 1.85365611748978e-13\n",
       "\\item 2.66314748031959e-13\n",
       "\\item 1.54931623086441e-13\n",
       "\\item -1.25843779841261e-13\n",
       "\\item -3.56381590904675e-13\n",
       "\\item -3.13471471002913e-13\n",
       "\\item 2.92821322744885e-14\n",
       "\\item 4.12527650928141e-13\n",
       "\\item 4.77085385086617e-13\n",
       "\\item 1.01075398051265e-13\n",
       "\\item -4.30549693120064e-13\n",
       "\\item -6.31903383785382e-13\n",
       "\\item -2.60280512420774e-13\n",
       "\\item 4.07683869302344e-13\n",
       "\\item 7.70239557898456e-13\n",
       "\\item 4.42364027353204e-13\n",
       "\\item -3.42484070617322e-13\n",
       "\\item -8.8439932460771e-13\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -2.05502281858116e-13\n",
       "2. -1.47659662275146e-13\n",
       "3. 6.38378239159465e-15\n",
       "4. 1.85365611748978e-13\n",
       "5. 2.66314748031959e-13\n",
       "6. 1.54931623086441e-13\n",
       "7. -1.25843779841261e-13\n",
       "8. -3.56381590904675e-13\n",
       "9. -3.13471471002913e-13\n",
       "10. 2.92821322744885e-14\n",
       "11. 4.12527650928141e-13\n",
       "12. 4.77085385086617e-13\n",
       "13. 1.01075398051265e-13\n",
       "14. -4.30549693120064e-13\n",
       "15. -6.31903383785382e-13\n",
       "16. -2.60280512420774e-13\n",
       "17. 4.07683869302344e-13\n",
       "18. 7.70239557898456e-13\n",
       "19. 4.42364027353204e-13\n",
       "20. -3.42484070617322e-13\n",
       "21. -8.8439932460771e-13\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -2.055023e-13 -1.476597e-13  6.383782e-15  1.853656e-13  2.663147e-13\n",
       " [6]  1.549316e-13 -1.258438e-13 -3.563816e-13 -3.134715e-13  2.928213e-14\n",
       "[11]  4.125277e-13  4.770854e-13  1.010754e-13 -4.305497e-13 -6.319034e-13\n",
       "[16] -2.602805e-13  4.076839e-13  7.702396e-13  4.423640e-13 -3.424841e-13\n",
       "[21] -8.843993e-13"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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EBn9LXY3bt3r7y83MDAwM7OjmedAAAA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\nEgQ7AAAASfwPKuqcIkYe6oAAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "phi1 <- 0.243\n",
    "omega2 = 0.013\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- cos(omega*times)\n",
    "eiw2 <- cos(omega2*times) \n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ 0.5 * (\n",
    "    cos((omega-omega2)*T) * Q((omega-omega2)*T) + \n",
    "    cos((omega+omega2)*T) * Q((omega+omega2)*T))})\n",
    "\n",
    "\n",
    "plot(omegas, analytical_estimates)\n",
    "points(omegas, numeric_estimates, col='blue')\n",
    "analytical_estimates - numeric_estimates\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b677cd5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0</li><li>1.32949207198862e-13</li><li>-8.06577027390176e-14</li><li>-4.61963800546528e-13</li><li>-4.54525306281539e-13</li><li>1.68476343986868e-13</li><li>8.966577480507e-13</li><li>8.66806626476091e-13</li><li>-1.37639899477904e-13</li><li>-1.27853283515833e-12</li><li>-1.34907363058545e-12</li><li>-2.99352556631938e-14</li><li>1.58300456076788e-12</li><li>1.87798041006992e-12</li><li>3.28218680532844e-13</li><li>-1.7881165298439e-12</li><li>-2.42752172530114e-12</li><li>-7.50286985318205e-13</li><li>1.87518923999708e-12</li><li>2.97023169948396e-12</li><li>1.28455362666258e-12</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 1.32949207198862e-13\n",
       "\\item -8.06577027390176e-14\n",
       "\\item -4.61963800546528e-13\n",
       "\\item -4.54525306281539e-13\n",
       "\\item 1.68476343986868e-13\n",
       "\\item 8.966577480507e-13\n",
       "\\item 8.66806626476091e-13\n",
       "\\item -1.37639899477904e-13\n",
       "\\item -1.27853283515833e-12\n",
       "\\item -1.34907363058545e-12\n",
       "\\item -2.99352556631938e-14\n",
       "\\item 1.58300456076788e-12\n",
       "\\item 1.87798041006992e-12\n",
       "\\item 3.28218680532844e-13\n",
       "\\item -1.7881165298439e-12\n",
       "\\item -2.42752172530114e-12\n",
       "\\item -7.50286985318205e-13\n",
       "\\item 1.87518923999708e-12\n",
       "\\item 2.97023169948396e-12\n",
       "\\item 1.28455362666258e-12\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 1.32949207198862e-13\n",
       "3. -8.06577027390176e-14\n",
       "4. -4.61963800546528e-13\n",
       "5. -4.54525306281539e-13\n",
       "6. 1.68476343986868e-13\n",
       "7. 8.966577480507e-13\n",
       "8. 8.66806626476091e-13\n",
       "9. -1.37639899477904e-13\n",
       "10. -1.27853283515833e-12\n",
       "11. -1.34907363058545e-12\n",
       "12. -2.99352556631938e-14\n",
       "13. 1.58300456076788e-12\n",
       "14. 1.87798041006992e-12\n",
       "15. 3.28218680532844e-13\n",
       "16. -1.7881165298439e-12\n",
       "17. -2.42752172530114e-12\n",
       "18. -7.50286985318205e-13\n",
       "19. 1.87518923999708e-12\n",
       "20. 2.97023169948396e-12\n",
       "21. 1.28455362666258e-12\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  0.000000e+00  1.329492e-13 -8.065770e-14 -4.619638e-13 -4.545253e-13\n",
       " [6]  1.684763e-13  8.966577e-13  8.668066e-13 -1.376399e-13 -1.278533e-12\n",
       "[11] -1.349074e-12 -2.993526e-14  1.583005e-12  1.877980e-12  3.282187e-13\n",
       "[16] -1.788117e-12 -2.427522e-12 -7.502870e-13  1.875189e-12  2.970232e-12\n",
       "[21]  1.284554e-12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OwAAABkgmIHAAAgExQ7AAAAmaDYAQAA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\nAAAkQbADAACQxP8B1Rr7W5FE6XwAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "omega2 = 0.013\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- sin(omega*times)\n",
    "eiw2 <- sin(omega2*times) \n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ 0.5 * (\n",
    "    cos((omega-omega2)*T) * Q((omega-omega2)*T) -\n",
    "    cos((omega+omega2)*T) * Q((omega+omega2)*T))})\n",
    "\n",
    "\n",
    "plot(omegas, analytical_estimates)\n",
    "points(omegas, numeric_estimates, col='blue')\n",
    "analytical_estimates - numeric_estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "43830f81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0</li><li>-3.13415959851682e-13</li><li>-5.5122573172639e-13</li><li>-6.50146603220492e-13</li><li>-6.13398221105399e-13</li><li>-5.60218538225854e-13</li><li>-6.75792755089333e-13</li><li>-1.05501024583177e-12</li><li>-1.56860635591727e-12</li><li>-1.91854865327912e-12</li><li>-1.89048776633172e-12</li><li>-1.59111612774154e-12</li><li>-1.41435474443341e-12</li><li>-1.70886915729085e-12</li><li>-2.4249248442576e-12</li><li>-3.09527924124975e-12</li><li>-3.22750853820608e-12</li><li>-2.781651645134e-12</li><li>-2.27066976332679e-12</li><li>-2.33297062224302e-12</li><li>-3.12902048021924e-12</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item -3.13415959851682e-13\n",
       "\\item -5.5122573172639e-13\n",
       "\\item -6.50146603220492e-13\n",
       "\\item -6.13398221105399e-13\n",
       "\\item -5.60218538225854e-13\n",
       "\\item -6.75792755089333e-13\n",
       "\\item -1.05501024583177e-12\n",
       "\\item -1.56860635591727e-12\n",
       "\\item -1.91854865327912e-12\n",
       "\\item -1.89048776633172e-12\n",
       "\\item -1.59111612774154e-12\n",
       "\\item -1.41435474443341e-12\n",
       "\\item -1.70886915729085e-12\n",
       "\\item -2.4249248442576e-12\n",
       "\\item -3.09527924124975e-12\n",
       "\\item -3.22750853820608e-12\n",
       "\\item -2.781651645134e-12\n",
       "\\item -2.27066976332679e-12\n",
       "\\item -2.33297062224302e-12\n",
       "\\item -3.12902048021924e-12\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. -3.13415959851682e-13\n",
       "3. -5.5122573172639e-13\n",
       "4. -6.50146603220492e-13\n",
       "5. -6.13398221105399e-13\n",
       "6. -5.60218538225854e-13\n",
       "7. -6.75792755089333e-13\n",
       "8. -1.05501024583177e-12\n",
       "9. -1.56860635591727e-12\n",
       "10. -1.91854865327912e-12\n",
       "11. -1.89048776633172e-12\n",
       "12. -1.59111612774154e-12\n",
       "13. -1.41435474443341e-12\n",
       "14. -1.70886915729085e-12\n",
       "15. -2.4249248442576e-12\n",
       "16. -3.09527924124975e-12\n",
       "17. -3.22750853820608e-12\n",
       "18. -2.781651645134e-12\n",
       "19. -2.27066976332679e-12\n",
       "20. -2.33297062224302e-12\n",
       "21. -3.12902048021924e-12\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  0.000000e+00 -3.134160e-13 -5.512257e-13 -6.501466e-13 -6.133982e-13\n",
       " [6] -5.602185e-13 -6.757928e-13 -1.055010e-12 -1.568606e-12 -1.918549e-12\n",
       "[11] -1.890488e-12 -1.591116e-12 -1.414355e-12 -1.708869e-12 -2.424925e-12\n",
       "[16] -3.095279e-12 -3.227509e-12 -2.781652e-12 -2.270670e-12 -2.332971e-12\n",
       "[21] -3.129020e-12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CAJih0AAIAkKHYAAACSoNgBAABIgmIH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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "omega2 = 0.013\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- sin(omega*times)\n",
    "eiw2 <- cos(omega2*times) \n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ 0.5 * (\n",
    "    sin((omega-omega2)*T) * Q((omega-omega2)*T) +\n",
    "    sin((omega+omega2)*T) * Q((omega+omega2)*T))})\n",
    "\n",
    "\n",
    "plot(omegas, analytical_estimates)\n",
    "points(omegas, numeric_estimates, col='blue')\n",
    "analytical_estimates - numeric_estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bf3bccfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>-1.56430424169685e-13</li><li>-3.15691917052163e-13</li><li>-5.24080778774305e-13</li><li>-3.34877958696467e-13</li><li>2.30260255307257e-13</li><li>5.60163027074623e-13</li><li>1.01141317543352e-13</li><li>-9.03499497439952e-13</li><li>-1.47171858033701e-12</li><li>-8.39814329189892e-13</li><li>6.12648820563777e-13</li><li>1.52633461425467e-12</li><li>8.33621366380655e-13</li><li>-1.04968681316486e-12</li><li>-2.40263885176173e-12</li><li>-1.7717025763142e-12</li><li>4.99586483293513e-13</li><li>2.36803632258642e-12</li><li>1.92784416902514e-12</li><li>-6.63779900050279e-13</li><li>-3.10285044186065e-12</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -1.56430424169685e-13\n",
       "\\item -3.15691917052163e-13\n",
       "\\item -5.24080778774305e-13\n",
       "\\item -3.34877958696467e-13\n",
       "\\item 2.30260255307257e-13\n",
       "\\item 5.60163027074623e-13\n",
       "\\item 1.01141317543352e-13\n",
       "\\item -9.03499497439952e-13\n",
       "\\item -1.47171858033701e-12\n",
       "\\item -8.39814329189892e-13\n",
       "\\item 6.12648820563777e-13\n",
       "\\item 1.52633461425467e-12\n",
       "\\item 8.33621366380655e-13\n",
       "\\item -1.04968681316486e-12\n",
       "\\item -2.40263885176173e-12\n",
       "\\item -1.7717025763142e-12\n",
       "\\item 4.99586483293513e-13\n",
       "\\item 2.36803632258642e-12\n",
       "\\item 1.92784416902514e-12\n",
       "\\item -6.63779900050279e-13\n",
       "\\item -3.10285044186065e-12\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -1.56430424169685e-13\n",
       "2. -3.15691917052163e-13\n",
       "3. -5.24080778774305e-13\n",
       "4. -3.34877958696467e-13\n",
       "5. 2.30260255307257e-13\n",
       "6. 5.60163027074623e-13\n",
       "7. 1.01141317543352e-13\n",
       "8. -9.03499497439952e-13\n",
       "9. -1.47171858033701e-12\n",
       "10. -8.39814329189892e-13\n",
       "11. 6.12648820563777e-13\n",
       "12. 1.52633461425467e-12\n",
       "13. 8.33621366380655e-13\n",
       "14. -1.04968681316486e-12\n",
       "15. -2.40263885176173e-12\n",
       "16. -1.7717025763142e-12\n",
       "17. 4.99586483293513e-13\n",
       "18. 2.36803632258642e-12\n",
       "19. 1.92784416902514e-12\n",
       "20. -6.63779900050279e-13\n",
       "21. -3.10285044186065e-12\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -1.564304e-13 -3.156919e-13 -5.240808e-13 -3.348780e-13  2.302603e-13\n",
       " [6]  5.601630e-13  1.011413e-13 -9.034995e-13 -1.471719e-12 -8.398143e-13\n",
       "[11]  6.126488e-13  1.526335e-12  8.336214e-13 -1.049687e-12 -2.402639e-12\n",
       "[16] -1.771703e-12  4.995865e-13  2.368036e-12  1.927844e-12 -6.637799e-13\n",
       "[21] -3.102850e-12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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efy8vJnHLN3796lS5fWIhoAAIA+yKfY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\nhwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "omega2 = 0.013\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- cos(omega*times)\n",
    "eiw2 <- sin(omega2*times) \n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ 0.5 * (\n",
    "    -sin((omega-omega2)*T) * Q((omega-omega2)*T) +\n",
    "    sin((omega+omega2)*T) * Q((omega+omega2)*T))})\n",
    "\n",
    "\n",
    "plot(omegas, analytical_estimates)\n",
    "points(omegas, numeric_estimates, col='blue')\n",
    "analytical_estimates - numeric_estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "76775be8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>-1.98396854500515e-13</li><li>-1.2623235789988e-13</li><li>4.23550083894497e-14</li><li>2.14883666416199e-13</li><li>2.70505839949919e-13</li><li>1.44384504352502e-13</li><li>-1.12743148150685e-13</li><li>-2.90545365544403e-13</li><li>-2.11664019644786e-13</li><li>1.10703113342936e-13</li><li>4.30020602459891e-13</li><li>4.49184092699006e-13</li><li>1.00950497960994e-13</li><li>-3.41254802194157e-13</li><li>-4.68194493591367e-13</li><li>-1.10221727578352e-13</li><li>4.61401316459442e-13</li><li>7.33786946136017e-13</li><li>4.15677041398776e-13</li><li>-2.53649965614722e-13</li><li>-6.72045318700354e-13</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -1.98396854500515e-13\n",
       "\\item -1.2623235789988e-13\n",
       "\\item 4.23550083894497e-14\n",
       "\\item 2.14883666416199e-13\n",
       "\\item 2.70505839949919e-13\n",
       "\\item 1.44384504352502e-13\n",
       "\\item -1.12743148150685e-13\n",
       "\\item -2.90545365544403e-13\n",
       "\\item -2.11664019644786e-13\n",
       "\\item 1.10703113342936e-13\n",
       "\\item 4.30020602459891e-13\n",
       "\\item 4.49184092699006e-13\n",
       "\\item 1.00950497960994e-13\n",
       "\\item -3.41254802194157e-13\n",
       "\\item -4.68194493591367e-13\n",
       "\\item -1.10221727578352e-13\n",
       "\\item 4.61401316459442e-13\n",
       "\\item 7.33786946136017e-13\n",
       "\\item 4.15677041398776e-13\n",
       "\\item -2.53649965614722e-13\n",
       "\\item -6.72045318700354e-13\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -1.98396854500515e-13\n",
       "2. -1.2623235789988e-13\n",
       "3. 4.23550083894497e-14\n",
       "4. 2.14883666416199e-13\n",
       "5. 2.70505839949919e-13\n",
       "6. 1.44384504352502e-13\n",
       "7. -1.12743148150685e-13\n",
       "8. -2.90545365544403e-13\n",
       "9. -2.11664019644786e-13\n",
       "10. 1.10703113342936e-13\n",
       "11. 4.30020602459891e-13\n",
       "12. 4.49184092699006e-13\n",
       "13. 1.00950497960994e-13\n",
       "14. -3.41254802194157e-13\n",
       "15. -4.68194493591367e-13\n",
       "16. -1.10221727578352e-13\n",
       "17. 4.61401316459442e-13\n",
       "18. 7.33786946136017e-13\n",
       "19. 4.15677041398776e-13\n",
       "20. -2.53649965614722e-13\n",
       "21. -6.72045318700354e-13\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] -1.983969e-13 -1.262324e-13  4.235501e-14  2.148837e-13  2.705058e-13\n",
       " [6]  1.443845e-13 -1.127431e-13 -2.905454e-13 -2.116640e-13  1.107031e-13\n",
       "[11]  4.300206e-13  4.491841e-13  1.009505e-13 -3.412548e-13 -4.681945e-13\n",
       "[16] -1.102217e-13  4.614013e-13  7.337869e-13  4.156770e-13 -2.536500e-13\n",
       "[21] -6.720453e-13"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QoAAAATk0Kxmzdv3vbt202dAgAAwMSs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\n2AEAAEiCYAcAACAJgh0AAIAk/huKWx8U6PumhwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegas <- seq(0, 0.2, 0.01)\n",
    "phi1 <- 0.0243\n",
    "phi2 <- 0.0432\n",
    "omega2 = 0.013\n",
    "numeric_estimates <- sapply(omegas, function(omega) { \n",
    "eiw1 <- cos(omega*times + phi1)\n",
    "eiw2 <- cos(omega2*times + phi2) \n",
    "hprod(eiw1, eiw2, times)})\n",
    "analytical_estimates <- sapply(omegas, function (omega){ 0.5 * ( \n",
    "   (\n",
    "    cos(phi1-phi2)*cos((omega-omega2)*T) * Q((omega-omega2)*T)  + \n",
    "    cos(phi1+phi2)*cos((omega+omega2)*T) * Q((omega+omega2)*T)) -\n",
    "   (\n",
    "    sin(phi1-phi2)*sin((omega-omega2)*T) * Q((omega-omega2)*T) +\n",
    "    sin(phi1+phi2)*sin((omega+omega2)*T) * Q((omega+omega2)*T)))}) \n",
    "\n",
    "\n",
    "plot(omegas, analytical_estimates)\n",
    "points(omegas, numeric_estimates, col='blue')\n",
    "analytical_estimates - numeric_estimates\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c0120e",
   "metadata": {},
   "source": [
    "To derive any arbitrary formula, use simply that cos(x) = sin(\\pi/2-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c522181b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>-4.81212292235966e-15</li><li>-3.22131210594989e-13</li><li>-5.4634075041804e-13</li><li>-6.24500451351651e-13</li><li>-5.86752868514395e-13</li><li>-5.63438184997267e-13</li><li>-7.16759984698001e-13</li><li>-1.09876691078981e-12</li><li>-1.56677448792664e-12</li><li>-1.85940152164221e-12</li><li>-1.82057147135595e-12</li><li>-1.5779044737485e-12</li><li>-1.47937911920692e-12</li><li>-1.79719433779368e-12</li><li>-2.44892127410079e-12</li><li>-3.01873803731922e-12</li><li>-3.10937907366249e-12</li><li>-2.72963422698336e-12</li><li>-2.34013156075186e-12</li><li>-2.4659588607201e-12</li><li>-3.19884656957425e-12</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -4.81212292235966e-15\n",
       "\\item -3.22131210594989e-13\n",
       "\\item -5.4634075041804e-13\n",
       "\\item -6.24500451351651e-13\n",
       "\\item -5.86752868514395e-13\n",
       "\\item -5.63438184997267e-13\n",
       "\\item -7.16759984698001e-13\n",
       "\\item -1.09876691078981e-12\n",
       "\\item -1.56677448792664e-12\n",
       "\\item -1.85940152164221e-12\n",
       "\\item -1.82057147135595e-12\n",
       "\\item -1.5779044737485e-12\n",
       "\\item -1.47937911920692e-12\n",
       "\\item -1.79719433779368e-12\n",
       "\\item -2.44892127410079e-12\n",
       "\\item -3.01873803731922e-12\n",
       "\\item -3.10937907366249e-12\n",
       "\\item -2.72963422698336e-12\n",
       "\\item -2.34013156075186e-12\n",
       "\\item -2.4659588607201e-12\n",
       "\\item -3.19884656957425e-12\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -4.81212292235966e-15\n",
       "2. -3.22131210594989e-13\n",
       "3. -5.4634075041804e-13\n",
       "4. -6.24500451351651e-13\n",
       "5. -5.86752868514395e-13\n",
       "6. -5.63438184997267e-13\n",
       "7. -7.16759984698001e-13\n",
       "8. -1.09876691078981e-12\n",
       "9. -1.56677448792664e-12\n",
       "10. -1.85940152164221e-12\n",
       "11. -1.82057147135595e-12\n",
       "12. -1.5779044737485e-12\n",
       "13. -1.47937911920692e-12\n",