d_uprange.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from KRZmetric import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.01940541  0.06231897]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=199998.049416, spin=0.299982, aimomgr=0.019405, aimomgphi=0.062319\n",
      "e=0.500000, p=6.000000, M=199998.049696, spin=0.299982, aimomgr=0.019405, aimomgphi=0.062319\n",
      "[1e-10, 0.29998213921237654, 199998.04969550887]\n",
      "[ 0.02382669  0.05466113]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=196224.423927, spin=0.370452, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=199077.598110, spin=0.405466, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200273.716716, spin=0.428931, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200491.229012, spin=0.432786, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200503.882582, spin=0.433084, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200503.907870, spin=0.433083, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200503.909496, spin=0.433083, aimomgr=0.023827, aimomgphi=0.054661\n",
      "e=0.500000, p=6.000000, M=200503.909572, spin=0.433083, aimomgr=0.023827, aimomgphi=0.054661\n",
      "[0.10000000000000001, 0.43308339004826135, 200503.90957168996]\n",
      "[ 0.0264307   0.05171792]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=191005.299297, spin=0.406904, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=197090.463005, spin=0.475243, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=199586.422416, spin=0.546432, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200402.127189, spin=0.562629, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200483.586178, spin=0.565807, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200481.183670, spin=0.565704, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200481.189989, spin=0.565704, aimomgr=0.026431, aimomgphi=0.051718\n",
      "e=0.500000, p=6.000000, M=200481.190093, spin=0.565704, aimomgr=0.026431, aimomgphi=0.051718\n",
      "[0.20000000000000001, 0.56570391182137425, 200481.19009285219]\n",
      "[ 0.02846579  0.0498765 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=186049.226078, spin=0.433913, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=195361.361540, spin=0.528273, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=198418.692321, spin=0.659607, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200006.501458, spin=0.689754, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200207.632492, spin=0.701358, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200182.791740, spin=0.700220, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200182.210221, spin=0.700186, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200182.225485, spin=0.700187, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200182.225689, spin=0.700187, aimomgr=0.028466, aimomgphi=0.049876\n",
      "e=0.500000, p=6.000000, M=200182.225689, spin=0.700187, aimomgr=0.028466, aimomgphi=0.049876\n",
      "[0.30000000000000004, 0.700186523430821, 200182.22568908162]\n",
      "[ 0.03017631  0.0485316 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=181495.712391, spin=0.455961, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=194045.239694, spin=0.570947, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=196876.692921, spin=0.773762, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199416.630396, spin=0.814119, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199815.850386, spin=0.844906, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199697.046809, spin=0.837995, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199693.384394, spin=0.837666, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199693.591668, spin=0.837680, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199693.596844, spin=0.837680, aimomgr=0.030176, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=199693.596905, spin=0.837680, aimomgr=0.030176, aimomgphi=0.048532\n",
      "[0.40000000000000002, 0.83768024968003396, 199693.59690503494]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24df963f160>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299], 'e': [0.5], 'p': [6], 'spin': [0.29999999999999999]}\n",
      "[ 0.02156562  0.05818384]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.350000, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=199998.420140, spin=0.349990, aimomgr=0.021566, aimomgphi=0.058184\n",
      "e=0.500000, p=6.000000, M=199998.420178, spin=0.349990, aimomgr=0.021566, aimomgphi=0.058184\n",
      "[1e-10, 0.34999018980828833, 199998.42017797922]\n",
      "[ 0.02482482  0.05351731]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.350000, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=198360.788778, spin=0.439746, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=199901.872436, spin=0.466595, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200304.131680, spin=0.477034, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200335.761943, spin=0.477763, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200336.300606, spin=0.477781, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200336.300846, spin=0.477781, aimomgr=0.024825, aimomgphi=0.053517\n",
      "e=0.500000, p=6.000000, M=200336.300855, spin=0.477781, aimomgr=0.024825, aimomgphi=0.053517\n",
      "[0.10000000000000001, 0.4777811605093118, 200336.30085493889]\n",
      "[ 0.0271031   0.05113423]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.350000, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=195349.169405, spin=0.496627, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=198971.067064, spin=0.559607, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200081.149043, spin=0.600124, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200251.493376, spin=0.605233, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200258.066673, spin=0.605599, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200258.004026, spin=0.605593, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200258.005081, spin=0.605593, aimomgr=0.027103, aimomgphi=0.051134\n",
      "e=0.500000, p=6.000000, M=200258.005085, spin=0.605593, aimomgr=0.027103, aimomgphi=0.051134\n",
      "[0.20000000000000001, 0.60559291033602458, 200258.00508541806]\n",
      "[ 0.02894986  0.04952931]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.350000, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=192213.814270, spin=0.540555, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=197900.050798, spin=0.636872, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199550.335025, spin=0.720253, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199920.170796, spin=0.733451, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199938.528374, spin=0.735200, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199937.770121, spin=0.735137, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199937.766351, spin=0.735136, aimomgr=0.028950, aimomgphi=0.049529\n",
      "e=0.500000, p=6.000000, M=199937.766371, spin=0.735136, aimomgr=0.028950, aimomgphi=0.049529\n",
      "[0.30000000000000004, 0.73513624496381458, 199937.76637104162]\n",
      "[ 0.03052759  0.04831638]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.350000, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.350000, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=189199.251772, spin=0.577029, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=196899.813327, spin=0.702918, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=198822.232727, spin=0.838895, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199419.633524, spin=0.862685, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199449.785255, spin=0.867683, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199446.447491, spin=0.867390, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199446.379541, spin=0.867381, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199446.380547, spin=0.867382, aimomgr=0.030528, aimomgphi=0.048316\n",
      "e=0.500000, p=6.000000, M=199446.380551, spin=0.867382, aimomgr=0.030528, aimomgphi=0.048316\n",
      "[0.40000000000000002, 0.86738155259493266, 199446.38055119984]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d830315f8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407], 'e': [0.5, 0.5], 'p': [6, 6], 'spin': [0.29999999999999999, 0.34999999999999998]}\n",
      "[ 0.02306283  0.05589861]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.400000, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=199999.346803, spin=0.399992, aimomgr=0.023063, aimomgphi=0.055899\n",
      "e=0.500000, p=6.000000, M=199999.346812, spin=0.399992, aimomgr=0.023063, aimomgphi=0.055899\n",
      "[1e-10, 0.39999222766379694, 199999.34681236825]\n",
      "[ 0.02570373  0.05259125]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.400000, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=199138.825243, spin=0.495881, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200024.873095, spin=0.516400, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200191.032992, spin=0.521948, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200198.354870, spin=0.522160, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200198.403377, spin=0.522163, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200198.403475, spin=0.522163, aimomgr=0.025704, aimomgphi=0.052591\n",
      "e=0.500000, p=6.000000, M=200198.403474, spin=0.522163, aimomgr=0.025704, aimomgphi=0.052591\n",
      "[0.10000000000000001, 0.52216265689399632, 200198.40347418748]\n",
      "[ 0.0277145   0.05061971]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.400000, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=197242.503254, spin=0.563491, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=199479.603177, spin=0.617392, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200016.144083, spin=0.642538, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200066.156012, spin=0.644580, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200067.116577, spin=0.644653, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200067.114459, spin=0.644652, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200067.114509, spin=0.644652, aimomgr=0.027715, aimomgphi=0.050620\n",
      "e=0.500000, p=6.000000, M=200067.114510, spin=0.644652, aimomgr=0.027715, aimomgphi=0.050620\n",
      "[0.20000000000000001, 0.64465193831576761, 200067.11450954573]\n",
      "[ 0.02939049  0.04921393]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.400000, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=195122.650424, spin=0.617499, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=198735.893137, spin=0.705724, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199606.597997, spin=0.761875, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199724.210241, spin=0.768310, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199727.188977, spin=0.768739, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199727.144238, spin=0.768731, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199727.144425, spin=0.768731, aimomgr=0.029390, aimomgphi=0.049214\n",
      "e=0.500000, p=6.000000, M=199727.144425, spin=0.768731, aimomgr=0.029390, aimomgphi=0.049214\n",
      "[0.30000000000000004, 0.76873053442954464, 199727.14442519579]\n",
      "[ 0.03084266  0.04811984]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.400000, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.400000, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=193004.485097, spin=0.663069, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=197959.246504, spin=0.784065, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199041.756570, spin=0.880310, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199232.267564, spin=0.893837, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199236.075588, spin=0.895241, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199235.840694, spin=0.895200, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199235.838627, spin=0.895199, aimomgr=0.030843, aimomgphi=0.048120\n",
      "e=0.500000, p=6.000000, M=199235.838639, spin=0.895199, aimomgr=0.030843, aimomgphi=0.048120\n",
      "[0.40000000000000002, 0.89519921814842796, 199235.83863873503]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24dfdb24da0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473], 'e': [0.5, 0.5, 0.5], 'p': [6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997]}\n",
      "[ 0.0242728   0.05431541]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.450000, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.498532, spin=0.449992, aimomgr=0.024273, aimomgphi=0.054315\n",
      "e=0.500000, p=6.000000, M=200000.498538, spin=0.449992, aimomgr=0.024273, aimomgphi=0.054315\n",
      "[1e-10, 0.44999235368521384, 200000.49853757315]\n",
      "[ 0.02649122  0.05181174]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.450000, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=199479.088629, spin=0.546904, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200007.419901, spin=0.562874, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200083.546456, spin=0.566121, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200085.633935, spin=0.566197, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200085.639915, spin=0.566197, aimomgr=0.026491, aimomgphi=0.051812\n",
      "e=0.500000, p=6.000000, M=200085.639937, spin=0.566197, aimomgr=0.026491, aimomgphi=0.051812\n",
      "[0.10000000000000001, 0.56619705902769879, 200085.63993741124]\n",
      "[ 0.02827324  0.05015855]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.450000, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=198209.078395, spin=0.620106, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199616.247688, spin=0.665521, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199889.457801, spin=0.681952, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199906.357488, spin=0.682869, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199906.537918, spin=0.682887, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199906.538081, spin=0.682887, aimomgr=0.028273, aimomgphi=0.050159\n",
      "e=0.500000, p=6.000000, M=199906.538081, spin=0.682887, aimomgr=0.028273, aimomgphi=0.050159\n",
      "[0.20000000000000001, 0.68288734677762364, 199906.53808077436]\n",
      "[ 0.02979189  0.04892401]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.450000, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=196712.215314, spin=0.680227, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199040.893355, spin=0.758409, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199508.631085, spin=0.797533, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199550.562996, spin=0.800879, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199551.171753, spin=0.801007, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199551.170070, spin=0.801005, aimomgr=0.029792, aimomgphi=0.048924\n",
      "e=0.500000, p=6.000000, M=199551.170090, spin=0.801005, aimomgr=0.029792, aimomgphi=0.048924\n",
      "[0.30000000000000004, 0.80100517835244844, 199551.17009019793]\n",
      "[ 0.03112489  0.04793869]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.450000, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.450000, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=195164.616624, spin=0.731723, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=198397.368295, spin=0.842940, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=198994.680690, spin=0.912908, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=199061.038703, spin=0.920754, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=199061.474302, spin=0.921225, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=199061.460404, spin=0.921216, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=199061.460379, spin=0.921216, aimomgr=0.031125, aimomgphi=0.047939\n",
      "e=0.500000, p=6.000000, M=199061.460379, spin=0.921216, aimomgr=0.031125, aimomgphi=0.047939\n",
      "[0.40000000000000002, 0.92121642395145709, 199061.46037947349]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d83ee6898>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871], 'e': [0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996]}\n",
      "[ 0.02281305  0.0564012 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=198738.388935, spin=0.363139, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=200005.584097, spin=0.397334, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=199700.047669, spin=0.390031, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=199664.904231, spin=0.389359, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=199665.576915, spin=0.389375, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=199665.572300, spin=0.389375, aimomgr=0.022813, aimomgphi=0.056401\n",
      "e=0.500000, p=6.000000, M=199665.572241, spin=0.389375, aimomgr=0.022813, aimomgphi=0.056401\n",
      "[-0.10000000000000001, 0.38937529493405004, 199665.57224123389]\n",
      "[ 0.02531011  0.05310284]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.034310, spin=0.499995, aimomgr=0.025310, aimomgphi=0.053103\n",
      "e=0.500000, p=6.000000, M=200000.034312, spin=0.499995, aimomgr=0.025310, aimomgphi=0.053103\n",
      "[1e-10, 0.49999503136059575, 200000.0343115268]\n",
      "[ 0.02720541  0.05113753]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199634.251870, spin=0.595243, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199954.633285, spin=0.607835, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199991.428327, spin=0.609846, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199992.094470, spin=0.609877, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199992.095307, spin=0.609877, aimomgr=0.027205, aimomgphi=0.051138\n",
      "e=0.500000, p=6.000000, M=199992.095313, spin=0.609877, aimomgr=0.027205, aimomgphi=0.051138\n",
      "[0.10000000000000001, 0.6098766466413581, 199992.09531255029]\n",
      "[ 0.02878603  0.04973981]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=198735.884161, spin=0.670810, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199624.924997, spin=0.708811, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199767.158118, spin=0.719871, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199773.275661, spin=0.720311, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199773.314029, spin=0.720316, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199773.314121, spin=0.720316, aimomgr=0.028786, aimomgphi=0.049740\n",
      "e=0.500000, p=6.000000, M=199773.314120, spin=0.720316, aimomgr=0.028786, aimomgphi=0.049740\n",
      "[0.20000000000000004, 0.72031644903949188, 199773.31412033783]\n",
      "[ 0.03015874  0.04865578]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=197636.424104, spin=0.734355, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199137.622814, spin=0.802422, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199388.955429, spin=0.830179, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199404.587596, spin=0.831983, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199404.725638, spin=0.832024, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199404.726147, spin=0.832024, aimomgr=0.030159, aimomgphi=0.048656\n",
      "e=0.500000, p=6.000000, M=199404.726144, spin=0.832024, aimomgr=0.030159, aimomgphi=0.048656\n",
      "[0.30000000000000004, 0.83202396042877891, 199404.72614428186]\n",
      "[ 0.0313774   0.04777047]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.500000, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.500000, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=196470.818026, spin=0.789534, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198576.900755, spin=0.889249, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198898.527586, spin=0.940737, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198921.673100, spin=0.945351, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198921.653213, spin=0.945523, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198921.655192, spin=0.945521, aimomgr=0.031377, aimomgphi=0.047770\n",
      "e=0.500000, p=6.000000, M=198921.655188, spin=0.945521, aimomgr=0.031377, aimomgphi=0.047770\n",
      "[0.40000000000000002, 0.94552071567978702, 198921.65518755448]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d81497dd8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218], 'e': [0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994]}\n",
      "[ 0.02421554  0.05445606]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199366.319576, spin=0.429178, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199943.393727, spin=0.450005, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199839.244618, spin=0.446658, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199834.182373, spin=0.446529, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199834.205962, spin=0.446530, aimomgr=0.024216, aimomgphi=0.054456\n",
      "e=0.500000, p=6.000000, M=199834.205765, spin=0.446530, aimomgr=0.024216, aimomgphi=0.054456\n",
      "[-0.10000000000000001, 0.44653037313856503, 199834.2057649105]\n",
      "[ 0.02622643  0.05211766]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.161056, spin=0.549997, aimomgr=0.026226, aimomgphi=0.052118\n",
      "e=0.500000, p=6.000000, M=200000.161056, spin=0.549997, aimomgr=0.026226, aimomgphi=0.052118\n",
      "[1e-10, 0.54999689751440106, 200000.16105613619]\n",
      "[ 0.02785833  0.05054193]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199702.978777, spin=0.641904, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199897.583676, spin=0.651894, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199915.763508, spin=0.653181, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199915.989515, spin=0.653194, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199915.989624, spin=0.653194, aimomgr=0.027858, aimomgphi=0.050542\n",
      "e=0.500000, p=6.000000, M=199915.989625, spin=0.653194, aimomgr=0.027858, aimomgphi=0.050542\n",
      "[0.10000000000000001, 0.6531943216607724, 199915.98962543631]\n",
      "[ 0.02925818  0.04935545]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199031.583161, spin=0.717592, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199589.120801, spin=0.749179, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199663.056353, spin=0.756737, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199665.335280, spin=0.756956, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199665.343823, spin=0.756958, aimomgr=0.029258, aimomgphi=0.049355\n",
      "e=0.500000, p=6.000000, M=199665.343852, spin=0.756958, aimomgr=0.029258, aimomgphi=0.049355\n",
      "[0.20000000000000004, 0.75695756193354546, 199665.34385165523]\n",
      "[ 0.03049361  0.04840493]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=198195.537440, spin=0.782547, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199152.265961, spin=0.840990, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199284.479938, spin=0.860812, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199290.307982, spin=0.861801, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199290.340149, spin=0.861816, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199290.340388, spin=0.861815, aimomgr=0.030494, aimomgphi=0.048405\n",
      "e=0.500000, p=6.000000, M=199290.340387, spin=0.861815, aimomgr=0.030494, aimomgphi=0.048405\n",
      "[0.30000000000000004, 0.86181548475852587, 199290.3403866908]\n",
      "[ 0.0316027   0.04761302]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.550000, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.550000, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=197290.201855, spin=0.839689, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198643.704157, spin=0.927435, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198808.491179, spin=0.965404, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198815.915571, spin=0.968125, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198815.867006, spin=0.968189, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198815.868359, spin=0.968189, aimomgr=0.031603, aimomgphi=0.047613\n",
      "e=0.500000, p=6.000000, M=198815.868352, spin=0.968189, aimomgr=0.031603, aimomgphi=0.047613\n",
      "[0.40000000000000002, 0.96818891629856962, 198815.8683524348]\n"
     ]
    },
    {
     "data": {
      "image/png": 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5/Z92B+iVcn93RHxLkqr/fFfOeTplWNLVmuPF6ljDORFxTdJrkt7ZlXSdkWXNqWl1zR+T9DcdTdR5mdZs+1dtf0MbhffJLmXrhKbrtT0qaW9EdGQbedt8WYftZyS9p8Fdj3U7S44anYHXn71kmdNLUltPFpnXbPsXJBUl3dfRRJ2Xac0RcUbSGds/L+lTkj7a6WAdcsv12n6TpM9KerRTAbZNuUfEAze7z/a3bd8VEd+yfZek73QxWjctStpbc7xH0vJN5izavkPS2yR9rzvxOiLLmlOTac22H9DGyc19EfGDLmXrlFZ/z+ck/VFHE3VWs/XeKen9kp6r7qq+R9KM7SMRMduOAL2yLTOj//8b/KOSvphjlk66IOmA7f22d2njgulM3ZzaP4uHJX0lqldmelSWNaem6Zqr/8v+J5KOREQKJzNZ1nyg5vCnJH29i/na7ZbrjYjXImJ3ROyLiH3auK7StmLffJJt/6ONPeXz2vhln5f0jup4UdKf1cz7qqQVSRVt/M05lnf2Laz1IUmvaONK+2PVsdPVX7wkvVnSX0lakPTPkt6bd+YurPnHq7/P/5L0qqRLeWfuwpqfkfRtSS9Uf2byztyFNf+BpEvV9T4r6UfzztzJ9dbNfU5tfrUM71AFgAT1yrYMAKAFlDsAJIhyB4AEUe4AkCDKHQASRLkDQIIodwBIEOUOAAn6P0wmuW725GE/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d830732e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993]}\n",
      "[ 0.02538925  0.05303063]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=199712.832222, spin=0.491669, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=200002.481789, spin=0.505608, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=199962.207087, spin=0.503870, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=199961.184253, spin=0.503835, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=199961.185470, spin=0.503835, aimomgr=0.025389, aimomgphi=0.053031\n",
      "e=0.500000, p=6.000000, M=199961.185451, spin=0.503835, aimomgr=0.025389, aimomgphi=0.053031\n",
      "[-0.10000000000000001, 0.50383545263793439, 199961.18545131542]\n",
      "[ 0.02705053  0.05128556]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200001.130256, spin=0.599997, aimomgr=0.027051, aimomgphi=0.051286\n",
      "e=0.500000, p=6.000000, M=200001.130263, spin=0.599997, aimomgr=0.027051, aimomgphi=0.051286\n",
      "[1e-10, 0.59999667527237477, 200001.13026298795]\n",
      "[ 0.02845844  0.05000677]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=199731.473869, spin=0.687373, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=199848.233051, spin=0.695299, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=199857.189712, spin=0.696136, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=199857.268392, spin=0.696141, aimomgr=0.028458, aimomgphi=0.050007\n",
      "e=0.500000, p=6.000000, M=199857.268397, spin=0.696141, aimomgr=0.028458, aimomgphi=0.050007\n",
      "[0.10000000000000001, 0.69614139911297235, 199857.26839698516]\n",
      "[ 0.02969391  0.04899935]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199200.128170, spin=0.761509, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199542.984850, spin=0.787530, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199580.493290, spin=0.792715, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199581.340565, spin=0.792825, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199581.342407, spin=0.792826, aimomgr=0.029694, aimomgphi=0.048999\n",
      "e=0.500000, p=6.000000, M=199581.342416, spin=0.792826, aimomgr=0.029694, aimomgphi=0.048999\n",
      "[0.20000000000000004, 0.79282573515901156, 199581.34241550061]\n",
      "[ 0.03079962  0.04816902]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=198541.515282, spin=0.826280, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=199136.968274, spin=0.875758, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=199203.193820, spin=0.889878, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=199205.276068, spin=0.890421, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=199205.283208, spin=0.890426, aimomgr=0.030800, aimomgphi=0.048169\n",
      "e=0.500000, p=6.000000, M=199205.283281, spin=0.890426, aimomgr=0.030800, aimomgphi=0.048169\n",
      "[0.30000000000000004, 0.89042645818984334, 199205.2832812152]\n",
      "[ 0.03180298  0.04746464]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.600000, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.600000, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=197817.813109, spin=0.883969, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198664.837510, spin=0.959846, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198741.440593, spin=0.987676, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198743.249963, spin=0.989265, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198743.221863, spin=0.989289, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198743.222335, spin=0.989289, aimomgr=0.031803, aimomgphi=0.047465\n",
      "e=0.500000, p=6.000000, M=198743.222331, spin=0.989289, aimomgr=0.031803, aimomgphi=0.047465\n",
      "[0.40000000000000002, 0.98928924999194867, 198743.22233134843]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24dfdaeb940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987]}\n",
      "[ 0.02476375  0.05376204]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199134.887047, spin=0.429991, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=200245.542180, spin=0.484889, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199951.193805, spin=0.473302, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199915.023524, spin=0.472284, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199915.641169, spin=0.472310, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199915.635538, spin=0.472310, aimomgr=0.024764, aimomgphi=0.053762\n",
      "e=0.500000, p=6.000000, M=199915.635454, spin=0.472310, aimomgr=0.024764, aimomgphi=0.053762\n",
      "[-0.20000000000000001, 0.47230989011814906, 199915.63545431464]\n",
      "[ 0.02641426  0.05190231]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=199921.910959, spin=0.552622, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200071.885284, spin=0.562362, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200055.434115, spin=0.561398, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200055.191951, spin=0.561387, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200055.191988, spin=0.561387, aimomgr=0.026414, aimomgphi=0.051902\n",
      "e=0.500000, p=6.000000, M=200055.191986, spin=0.561387, aimomgr=0.026414, aimomgphi=0.051902\n",
      "[-0.10000000000000001, 0.56138742855617185, 200055.19198591341]\n",
      "[ 0.0278006   0.05056335]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200001.909495, spin=0.649997, aimomgr=0.027801, aimomgphi=0.050563\n",
      "e=0.500000, p=6.000000, M=200001.909513, spin=0.649997, aimomgr=0.027801, aimomgphi=0.050563\n",
      "[1e-10, 0.64999686885737318, 200001.90951316917]\n",
      "[ 0.02901264  0.0495199 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=199740.697162, spin=0.731922, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=199808.848446, spin=0.738171, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=199813.139431, spin=0.738717, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=199813.166740, spin=0.738719, aimomgr=0.029013, aimomgphi=0.049520\n",
      "e=0.500000, p=6.000000, M=199813.166735, spin=0.738719, aimomgr=0.029013, aimomgphi=0.049520\n",
      "[0.10000000000000003, 0.7387191856910843, 199813.16673459261]\n",
      "[ 0.03009635  0.04866658]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199299.679046, spin=0.803163, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199503.341873, spin=0.824333, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199521.395280, spin=0.827867, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199521.699957, spin=0.827923, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199521.700290, spin=0.827923, aimomgr=0.030096, aimomgphi=0.048667\n",
      "e=0.500000, p=6.000000, M=199521.700292, spin=0.827923, aimomgr=0.030096, aimomgphi=0.048667\n",
      "[0.20000000000000001, 0.82792319347844678, 199521.70029246109]\n",
      "[ 0.03107913  0.0479459 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.650000, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.650000, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=198761.290196, spin=0.866429, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=199117.557784, spin=0.907642, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=199147.747459, spin=0.917590, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=199148.416606, spin=0.917884, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=199148.417892, spin=0.917885, aimomgr=0.031079, aimomgphi=0.047946\n",
      "e=0.500000, p=6.000000, M=199148.417911, spin=0.917885, aimomgr=0.031079, aimomgphi=0.047946\n",
      "[0.29999999999999999, 0.91788546924364878, 199148.41791066184]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d81505668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991]}\n",
      "[ 0.02600636  0.05230215]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=199726.884862, spin=0.509127, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200227.572991, spin=0.544480, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200121.403845, spin=0.538556, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200114.947774, spin=0.538304, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200114.981943, spin=0.538307, aimomgr=0.026006, aimomgphi=0.052302\n",
      "e=0.500000, p=6.000000, M=200114.981581, spin=0.538307, aimomgr=0.026006, aimomgphi=0.052302\n",
      "[-0.20000000000000001, 0.53830709278717825, 200114.98158076761]\n",
      "[ 0.02733029  0.05096494]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200054.675158, spin=0.612868, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200131.719425, spin=0.619791, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200124.955219, spin=0.619241, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200124.893972, spin=0.619237, aimomgr=0.027330, aimomgphi=0.050965\n",
      "e=0.500000, p=6.000000, M=200124.893958, spin=0.619237, aimomgr=0.027330, aimomgphi=0.050965\n",
      "[-0.10000000000000001, 0.61923717087081875, 200124.89395831132]\n",
      "[ 0.0284889   0.04992362]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200002.388180, spin=0.699998, aimomgr=0.028489, aimomgphi=0.049924\n",
      "e=0.500000, p=6.000000, M=200002.388208, spin=0.699998, aimomgr=0.028489, aimomgphi=0.049924\n",
      "[1e-10, 0.69999815344853022, 200002.3882082708]\n",
      "[ 0.02952611  0.04907238]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=199742.551948, spin=0.775702, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=199780.472960, spin=0.780568, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=199782.408738, spin=0.780920, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=199782.417917, spin=0.780921, aimomgr=0.029526, aimomgphi=0.049072\n",
      "e=0.500000, p=6.000000, M=199782.417913, spin=0.780921, aimomgr=0.029526, aimomgphi=0.049072\n",
      "[0.10000000000000003, 0.78092139517077597, 199782.41791250982]\n",
      "[ 0.03046863  0.048354  ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199361.350926, spin=0.842930, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199475.731317, spin=0.859857, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199483.601854, spin=0.862227, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199483.703817, spin=0.862255, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199483.703836, spin=0.862255, aimomgr=0.030469, aimomgphi=0.048354\n",
      "e=0.500000, p=6.000000, M=199483.703837, spin=0.862255, aimomgr=0.030469, aimomgphi=0.048354\n",
      "[0.20000000000000001, 0.86225468734038757, 199483.70383739489]\n",
      "[ 0.03133401  0.04773398]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.700000, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.700000, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=198907.251041, spin=0.903534, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=199107.323419, spin=0.937178, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=199118.611596, spin=0.944045, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=199118.778179, spin=0.944200, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=199118.778214, spin=0.944200, aimomgr=0.031334, aimomgphi=0.047734\n",
      "e=0.500000, p=6.000000, M=199118.778218, spin=0.944200, aimomgr=0.031334, aimomgphi=0.047734\n",
      "[0.29999999999999999, 0.94420039072917594, 199118.77821827473]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d8e74dd30>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996]}\n",
      "[ 0.02709276  0.05114732]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200062.394249, spin=0.584528, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200290.312653, spin=0.608073, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200251.613282, spin=0.604931, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200250.302495, spin=0.604859, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200250.304298, spin=0.604860, aimomgr=0.027093, aimomgphi=0.051147\n",
      "e=0.500000, p=6.000000, M=200250.304260, spin=0.604860, aimomgr=0.027093, aimomgphi=0.051147\n",
      "[-0.20000000000000001, 0.60485990919416754, 200250.30425983923]\n",
      "[ 0.02816168  0.05016102]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200135.720346, spin=0.672844, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200173.566190, spin=0.677759, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200170.889203, spin=0.677444, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200170.873756, spin=0.677443, aimomgr=0.028162, aimomgphi=0.050161\n",
      "e=0.500000, p=6.000000, M=200170.873750, spin=0.677443, aimomgr=0.028162, aimomgphi=0.050161\n",
      "[-0.10000000000000001, 0.67744253775220853, 200170.87375048691]\n",
      "[ 0.02912418  0.04934792]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200002.972655, spin=0.749999, aimomgr=0.029124, aimomgphi=0.049348\n",
      "e=0.500000, p=6.000000, M=200002.972699, spin=0.749999, aimomgr=0.029124, aimomgphi=0.049348\n",
      "[1e-10, 0.74999924486082414, 200002.97269886135]\n",
      "[ 0.03000306  0.04865777]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=199743.129229, spin=0.818800, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=199762.604369, spin=0.822512, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=199763.383451, spin=0.822734, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=199763.386339, spin=0.822735, aimomgr=0.030003, aimomgphi=0.048658\n",
      "e=0.500000, p=6.000000, M=199763.386337, spin=0.822735, aimomgr=0.030003, aimomgphi=0.048658\n",
      "[0.10000000000000003, 0.82273480213392269, 199763.38633733118]\n",
      "[ 0.03081262  0.04805871]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=199406.646800, spin=0.881018, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=199465.152479, spin=0.894230, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=199467.953394, spin=0.895775, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=199467.983143, spin=0.895788, aimomgr=0.030813, aimomgphi=0.048059\n",
      "e=0.500000, p=6.000000, M=199467.983118, spin=0.895788, aimomgr=0.030813, aimomgphi=0.048059\n",
      "[0.20000000000000001, 0.89578765498895785, 199467.98311817562]\n",
      "[ 0.03156436  0.04753108]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.750000, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.750000, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199018.279760, spin=0.937887, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199119.136616, spin=0.964640, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199121.312153, spin=0.969232, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199121.322824, spin=0.969310, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199121.322681, spin=0.969310, aimomgr=0.031564, aimomgphi=0.047531\n",
      "e=0.500000, p=6.000000, M=199121.322682, spin=0.969310, aimomgr=0.031564, aimomgphi=0.047531\n",
      "[0.29999999999999999, 0.96930974985277318, 199121.32268236385]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d8e815c50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236, 0.7285771749567741], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999989]}\n",
      "[ 0.02486167  0.05352408]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=198912.371995, spin=0.358404, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=201905.515841, spin=0.544371, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200780.999736, spin=0.494047, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200167.023658, spin=0.476885, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200217.918218, spin=0.478896, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200215.950275, spin=0.478851, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200215.931738, spin=0.478851, aimomgr=0.024862, aimomgphi=0.053524\n",
      "e=0.500000, p=6.000000, M=200215.931430, spin=0.478851, aimomgr=0.024862, aimomgphi=0.053524\n",
      "[-0.5, 0.47885066213005423, 200215.93142990459]\n",
      "[ 0.02607027  0.0521338 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=199768.052975, spin=0.476055, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200742.474117, spin=0.565825, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200423.372906, spin=0.545855, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200368.692929, spin=0.543731, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200369.860831, spin=0.543807, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200369.846395, spin=0.543808, aimomgr=0.026070, aimomgphi=0.052134\n",
      "e=0.500000, p=6.000000, M=200369.846175, spin=0.543808, aimomgr=0.026070, aimomgphi=0.052134\n",
      "[-0.40000000000000002, 0.54380765007098941, 200369.8461746026]\n",
      "[ 0.0271235   0.05106011]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200146.607640, spin=0.573778, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200480.071184, spin=0.615167, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200402.753946, spin=0.608398, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200397.924755, spin=0.608133, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200397.944568, spin=0.608136, aimomgr=0.027123, aimomgphi=0.051060\n",
      "e=0.500000, p=6.000000, M=200397.944262, spin=0.608136, aimomgr=0.027123, aimomgphi=0.051060\n",
      "[-0.30000000000000004, 0.60813584478173632, 200397.94426245993]\n",
      "[ 0.02806573  0.05018741]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200251.371001, spin=0.658141, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200349.159317, spin=0.673829, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200335.806689, spin=0.672166, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200335.538355, spin=0.672144, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200335.538298, spin=0.672144, aimomgr=0.028066, aimomgphi=0.050187\n",
      "e=0.500000, p=6.000000, M=200335.538294, spin=0.672144, aimomgr=0.028066, aimomgphi=0.050187\n",
      "[-0.20000000000000007, 0.67214439261034797, 200335.53829355861]\n",
      "[ 0.02892359  0.04945446]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200182.695618, spin=0.732803, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200199.584053, spin=0.736230, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200198.623282, spin=0.736054, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200198.619667, spin=0.736053, aimomgr=0.028924, aimomgphi=0.049454\n",
      "e=0.500000, p=6.000000, M=200198.619665, spin=0.736053, aimomgr=0.028924, aimomgphi=0.049454\n",
      "[-0.10000000000000009, 0.73605312655096222, 200198.61966522678]\n",
      "[ 0.02971325  0.04882358]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.800000, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.800000, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200002.812853, spin=0.800004, aimomgr=0.029713, aimomgphi=0.048824\n",
      "e=0.500000, p=6.000000, M=200002.812893, spin=0.800004, aimomgr=0.029713, aimomgphi=0.048824\n",
      "[1e-10, 0.80000379152125123, 200002.8128929442]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d8a975940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236, 0.7285771749567741, 0.6418601782580009], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999989, 0.79999999999999982]}\n",
      "[ 0.02658224  0.05152749]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200114.475314, spin=0.503711, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200889.429987, spin=0.598319, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200620.567081, spin=0.577599, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200574.746011, spin=0.575529, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200575.611731, spin=0.575602, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200575.599847, spin=0.575602, aimomgr=0.026582, aimomgphi=0.051527\n",
      "e=0.500000, p=6.000000, M=200575.599659, spin=0.575602, aimomgr=0.026582, aimomgphi=0.051527\n",
      "[-0.5, 0.57560226220670907, 200575.59965850774]\n",
      "[ 0.02744135  0.05068676]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200346.421695, spin=0.588272, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200661.834322, spin=0.640085, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200576.512476, spin=0.631124, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200569.820679, spin=0.630714, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200569.854031, spin=0.630720, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200569.853424, spin=0.630720, aimomgr=0.027441, aimomgphi=0.050687\n",
      "e=0.500000, p=6.000000, M=200569.853417, spin=0.630720, aimomgr=0.027441, aimomgphi=0.050687\n",
      "[-0.40000000000000002, 0.6307202575600962, 200569.85341660352]\n",
      "[ 0.0282266  0.0499764]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200403.351753, spin=0.663343, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200521.595029, spin=0.688935, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200499.353808, spin=0.685678, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200498.589386, spin=0.685613, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200498.589481, spin=0.685613, aimomgr=0.028227, aimomgphi=0.049976\n",
      "e=0.500000, p=6.000000, M=200498.589453, spin=0.685613, aimomgr=0.028227, aimomgphi=0.049976\n",
      "[-0.30000000000000004, 0.68561302764521337, 200498.5894525139]\n",
      "[ 0.02895188  0.04936204]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200344.416240, spin=0.731086, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200380.252192, spin=0.741247, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200376.286749, spin=0.740401, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200376.237299, spin=0.740395, aimomgr=0.028952, aimomgphi=0.049362\n",
      "e=0.500000, p=6.000000, M=200376.237247, spin=0.740395, aimomgr=0.028952, aimomgphi=0.049362\n",
      "[-0.20000000000000007, 0.74039501838299804, 200376.23724749501]\n",
      "[ 0.02962762  0.04882201]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200203.085464, spin=0.792965, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200209.233928, spin=0.795262, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200208.955483, spin=0.795168, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200208.954782, spin=0.795168, aimomgr=0.029628, aimomgphi=0.048822\n",
      "e=0.500000, p=6.000000, M=200208.954782, spin=0.795168, aimomgr=0.029628, aimomgphi=0.048822\n",
      "[-0.10000000000000009, 0.79516784080485936, 200208.95478182266]\n",
      "[ 0.03026102  0.04834098]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.850000, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.850000, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200003.447045, spin=0.850005, aimomgr=0.030261, aimomgphi=0.048341\n",
      "e=0.500000, p=6.000000, M=200003.447104, spin=0.850005, aimomgr=0.030261, aimomgphi=0.048341\n",
      "[1e-10, 0.85000526816650945, 200003.44710441231]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d823c3630>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236, 0.7285771749567741, 0.6418601782580009, 0.54861136285618495], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999989, 0.79999999999999982, 0.84999999999999987]}\n",
      "[ 0.02805134  0.0500494 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200603.536436, spin=0.633768, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200793.700829, spin=0.683670, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200738.051526, spin=0.675469, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200733.935052, spin=0.675147, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200733.946195, spin=0.675152, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200733.945796, spin=0.675152, aimomgr=0.028051, aimomgphi=0.050049\n",
      "e=0.500000, p=6.000000, M=200733.945792, spin=0.675152, aimomgr=0.028051, aimomgphi=0.050049\n",
      "[-0.5, 0.67515161157116654, 200733.94579150886]\n",
      "[ 0.02865889  0.04952528]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200583.591343, spin=0.695001, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200665.159327, spin=0.724008, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200646.639079, spin=0.720241, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200645.888229, spin=0.720162, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200645.887774, spin=0.720163, aimomgr=0.028659, aimomgphi=0.049525\n",
      "e=0.500000, p=6.000000, M=200645.887734, spin=0.720163, aimomgr=0.028659, aimomgphi=0.049525\n",
      "[-0.40000000000000002, 0.72016267009881507, 200645.88773418881]\n",
      "[ 0.02923058  0.04905655]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200499.425747, spin=0.751602, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200529.649149, spin=0.766565, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200524.807895, spin=0.765126, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200524.709112, spin=0.765112, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200524.708940, spin=0.765112, aimomgr=0.029231, aimomgphi=0.049057\n",
      "e=0.500000, p=6.000000, M=200524.708938, spin=0.765112, aimomgr=0.029231, aimomgphi=0.049057\n",
      "[-0.30000000000000004, 0.76511177335565417, 200524.70893755989]\n",
      "[ 0.029771    0.04863306]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200367.474308, spin=0.804290, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200375.921094, spin=0.810435, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200375.118188, spin=0.810046, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200375.111375, spin=0.810044, aimomgr=0.029771, aimomgphi=0.048633\n",
      "e=0.500000, p=6.000000, M=200375.111363, spin=0.810044, aimomgr=0.029771, aimomgphi=0.048633\n",
      "[-0.20000000000000007, 0.81004406147282138, 200375.1113634418]\n",
      "[ 0.03028377  0.04824725]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200199.479128, spin=0.853615, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200200.678490, spin=0.855043, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200200.635509, spin=0.854998, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200200.635425, spin=0.854998, aimomgr=0.030284, aimomgphi=0.048247\n",
      "e=0.500000, p=6.000000, M=200200.635424, spin=0.854998, aimomgr=0.030284, aimomgphi=0.048247\n",
      "[-0.10000000000000009, 0.85499794535086437, 200200.63542441808]\n",
      "[ 0.03077166  0.04789321]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.900000, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.900000, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200004.761159, spin=0.900003, aimomgr=0.030772, aimomgphi=0.047893\n",
      "e=0.500000, p=6.000000, M=200004.761272, spin=0.900003, aimomgr=0.030772, aimomgphi=0.047893\n",
      "[1e-10, 0.90000331020087732, 200004.76127182881]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d83db7390>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236, 0.7285771749567741, 0.6418601782580009, 0.54861136285618495, 0.44962760194202839], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999989, 0.79999999999999982, 0.84999999999999987, 0.89999999999999991]}\n",
      "[ 0.02938577  0.04884355]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200711.205343, spin=0.760122, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200731.498699, spin=0.783478, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200724.957519, spin=0.780812, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200724.710380, spin=0.780772, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200724.709702, spin=0.780772, aimomgr=0.029386, aimomgphi=0.048844\n",
      "e=0.500000, p=6.000000, M=200724.709688, spin=0.780772, aimomgr=0.029386, aimomgphi=0.048844\n",
      "[-0.5, 0.78077208342024051, 200724.70968760658]\n",
      "[ 0.0297871   0.04853204]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200603.979072, spin=0.801783, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200609.637723, spin=0.815885, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200607.699025, spin=0.814607, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200607.649216, spin=0.814595, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200607.649053, spin=0.814596, aimomgr=0.029787, aimomgphi=0.048532\n",
      "e=0.500000, p=6.000000, M=200607.649051, spin=0.814596, aimomgr=0.029787, aimomgphi=0.048532\n",
      "[-0.40000000000000002, 0.81459550997999375, 200607.64905147647]\n",
      "[ 0.03017299  0.04824184]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200475.953669, spin=0.841419, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200475.932658, spin=0.848928, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200475.581508, spin=0.848421, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200475.574827, spin=0.848418, aimomgr=0.030173, aimomgphi=0.048242\n",
      "e=0.500000, p=6.000000, M=200475.574805, spin=0.848418, aimomgr=0.030173, aimomgphi=0.048242\n",
      "[-0.30000000000000004, 0.84841846698343337, 200475.5748046035]\n",
      "[ 0.03054468  0.04797042]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200331.005365, spin=0.879229, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200329.880168, spin=0.882397, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200329.885115, spin=0.882256, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200329.884733, spin=0.882255, aimomgr=0.030545, aimomgphi=0.047970\n",
      "e=0.500000, p=6.000000, M=200329.884732, spin=0.882255, aimomgr=0.030545, aimomgphi=0.047970\n",
      "[-0.20000000000000007, 0.88225539462296509, 200329.88473184058]\n",
      "[ 0.03090283  0.04771531]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200174.164285, spin=0.915372, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200173.667249, spin=0.916126, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200173.678719, spin=0.916109, aimomgr=0.030903, aimomgphi=0.047715\n",
      "e=0.500000, p=6.000000, M=200173.678722, spin=0.916109, aimomgr=0.030903, aimomgphi=0.047715\n",
      "[-0.10000000000000009, 0.91610913742472999, 200173.67872165344]\n",
      "[ 0.03124873  0.0474751 ]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200006.187441, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "e=0.500000, p=6.000000, M=200006.187633, spin=0.950000, aimomgr=0.031249, aimomgphi=0.047475\n",
      "[1e-10, 0.95000032981318283, 200006.18763278486]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d81497dd8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.359881689293299, 1.3089432112945407, 1.2369818587534473, 1.177256260093871, 1.1106439124758218, 1.0421462051766355, 0.97006933481706126, 0.89034500209048162, 0.81126922312044236, 0.7285771749567741, 0.6418601782580009, 0.54861136285618495, 0.44962760194202839, 0.33843401193408845], 'e': [0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999989, 0.79999999999999982, 0.84999999999999987, 0.89999999999999991, 0.94999999999999996]}\n"
     ]
    }
   ],
   "source": [
    "Ml=[]\n",
    "spinl=[]\n",
    "dic={'a_d2':[],'e':[],'p':[],'spin':[]}\n",
    "M=2e5\n",
    "spin=0.8\n",
    "e=0.5\n",
    "p=6\n",
    "d1=0\n",
    "d3=0\n",
    "for spin in np.arange(0.300,0.955,0.05):\n",
    "    dlist=[]\n",
    "    Mlist=[]\n",
    "    spinlist=[]\n",
    "    d2up=0.5\n",
    "    if spin<0.47:\n",
    "        d2down=0\n",
    "    elif spin<0.63:\n",
    "        d2down=-0.1\n",
    "    elif spin<0.77:\n",
    "        d2down=-0.2\n",
    "        d2up=0.35\n",
    "    else:\n",
    "        d2down=-0.5\n",
    "        d2up=0.1\n",
    "    for d2 in np.arange(d2down,d2up,0.1):\n",
    "        if np.abs(d2-0.0)<1e-5:\n",
    "            d2=1e-10\n",
    "        filename='C:\\\\Users\\\\HP\\\\Documents\\\\Visual Studio 2015\\\\Projects\\\\multiple_d\\\\multiple_d\\\\trace_M%.0f_spin%.6f_e%.6f_p%.6f_d1%.6f_d2%.6f_d3%.6f.dat'%(M,spin,e,p,d1,d2,d3)\n",
    "        index, tau,t,r,th,phi,ut,ur,uth,uphi,F_t,F_r,F_th,F_phi=np.loadtxt(filename,unpack=True)\n",
    "\n",
    "        if np.abs(e-0.0)>1e-8:\n",
    "            avgomgsec=getfreq_sec_frommaxi(t,r,phi,M)\n",
    "            print(avgomgsec)\n",
    "            avgomgr=avgomgsec[0]\n",
    "            avgomgphi=avgomgsec[1]\n",
    "\n",
    "            def fun(x):\n",
    "                #print('called')\n",
    "                M=x[0]\n",
    "                spin=x[1]\n",
    "                print('e=%f, p=%f, M=%f, spin=%f, aimomgr=%f, aimomgphi=%f'%(e,p,M,spin,avgomgr,avgomgphi))\n",
    "\n",
    "                omgr,omgphi=getfreq_sec_fromepma(e,p,M,spin)\n",
    "                avgomgsec=np.array([avgomgr,avgomgphi])\n",
    "                omgsec=np.array([omgr,omgphi])\n",
    "                return (omgsec-avgomgsec)/avgomgsec\n",
    "\n",
    "\n",
    "            from scipy.optimize import root,fsolve\n",
    "            (myM,myspin)=fsolve(fun,[M,spin])\n",
    "\n",
    "            getfreq_sec_fromepma(e,p,myM,myspin)\n",
    "        else:\n",
    "            avgomgsec=circfreq_sec_fromtrace(t,phi,M)\n",
    "            def circfun(x):\n",
    "                spin=x\n",
    "                omgsec=circfreq_sec_fromrma(p,M,spin)\n",
    "                #print('e=%f, p=%f, M=%f, spin=%.10f, omg=%.10f, aim=%.10f'%(e,p,M,spin,omgsec,avgomgsec))\n",
    "                return (omgsec-avgomgsec)/avgomgsec\n",
    "            (myspin)=fsolve(fun,spin)\n",
    "            myspin=myspin[0]\n",
    "            myM=M\n",
    "            circfreq_sec_fromrma(p,myM,myspin)\n",
    "        dlist.append(d2)\n",
    "        spinlist.append(myspin)\n",
    "        Mlist.append(myM)\n",
    "\n",
    "        #for i in range(len(dlist)):\n",
    "        print([dlist[-1],spinlist[-1],Mlist[-1]])\n",
    "    plt.figure()\n",
    "    plt.plot(dlist,spinlist,'o')\n",
    "    plt.show()\n",
    "    spinl.append(spinlist)\n",
    "    Ml.append(Mlist)\n",
    "    if spin>0.36:\n",
    "        dic['a_d2'].append(np.polyfit(dlist[0:6],spinlist[0:6],1)[0])\n",
    "    else:\n",
    "        dic['a_d2'].append(np.polyfit(dlist[2:6],spinlist[2:6],1)[0])\n",
    "    dic['e'].append(e)\n",
    "    dic['p'].append(p)\n",
    "    dic['spin'].append(spin)\n",
    "    print(dic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o4urWVBeXiJSpSnHE4ZzLNrPRwHR8l+P+3Tm30syeBBY65z4H7jGzK4BsYA8wyrOCS1FU7TD6tW5Av9YNAN8AZJv3HGHJln35j3fmbeKtuRsAXxdXlyZRdMs7KulcSBeXTr6LSHnw/D6OslBRjzgC/cOemZ3Lqm0H8oNk6ZZ9rN91GPi5i6tL3vmSrk2jGPrXb/OPaEREAlUpTo6XlYoaHKXhbF1cACN6xXN5p1h6NqtPcJC6tkTEfwqOKhocp3ppxhpemZV62vJaoUFc070JQzrFcl6zc3SyXUSKpOCoJsFRUOLYySQ/OYjZq3cyZcU2vlq1g6NZOdQPD2NQx0Zc3jGWXs0VIiJSuEpxclxKX+2wEN8ovp1jOZqZw9drdjB5+TY+XZzOez9s5pzwMAZ1iOHyTrH0bl5fISIiAVNwVCH3XtzqpNe1woK5rFMsl3Xyhcg3KTuYvHw7ny3Zyvs/bqFe7VAGdWjkC5EW9QlViIiIH9RVVQ0dy8rh6zU7mbJ8G7NWZXA4M4eo2qEMat+IyzvHcn4hIaJLfUWqPp3jUHD45VhWDt+k7GTq8m3MXLWDQ8eziaodyqXtfd1ZfVpGExocdNLNiyJSNekch/ilZmgwgzo0YlCHRhzLymHu2l1MWb6Nqcu38+HCNOrW8oUIwPHsHGqEBHtcsYh4TUccUqjj2Tk8+OFSvli27bR1l3VsxPPXddbgjCJVjLqqFByl5nh2Dm0encZN5zVlRnIGuw5lEhYcRJ+W9bm0QyMuaRdDg8gaXpcpIiWkriopNSe6p/50TWfGXeVYtHkv01dsZ3rydmb/dzkP23KSEurld3k1Pae2xxWLSFnSEYf4pbCrqpxzrNp2kOkrtzN95XZWbz8IQLvYOgzqEMOl7RvRLjZSo/qKVBLqqlJwlLvNu4/wZbIvRBZu2otzEH9ObS5tH8Ogjo3oHl9P42eJVGAKDgWHp3YePM7MVRlMX7md71N3k5mTS3REGJe0i2FQh0ac37L+SVdo6T4REe8pOBQcFcbBY1l8vWYn01du5+s1Ozl0PJuIGiH0b9OAQR0a0b9NAzo98aXuExHxmE6OS4URWTOUYV3iGNYljuPZOXyfupvpK7czIzmDScu2EZZ3l/pnS9K5pF0M4TX0YylSkek3VMpVjZBgLmrbkIvaNqRh5Bpe/SqVzJxcAO6duASAlg3DuX9gGwa0bUjNUN1wKFLRqKtKKoTEsZP58K7eTFq2lSnLt7HrUCbhYcFc0j6GYZ3j6Ns6Wneti5QxdVVJpXNes3M4r9k5/GFoe37YsIdJy7YydYVvNN/ImiEM6tCIYV3iCh2EUUTKj4JDKoSCQ8KHBAfRp2U0fVpG8+SVHfk2dRdfLN3K9BXb+einNOrVDuWyTrEM7awpckW8oK4qqTROjOQ7adk2ZiZncDQrhwaRNRjSKZZhXWLp1rQeQQoRkWLT5bgKjirtSGY2X63ewaSl2/hqzQ4ys3OJq1uTIZ1jGdYljk6N6+bfsa57RET8o+BQcFQbB49lMXNVBl8s3cbctTvJynHEn1ObYV1iGdo5jstemat7RET8oOBQcFRL+45kMn3ldiYt28Z3qbvIzfvx/u2gNlzZNY4m9TQAo8iZ+BscujRFqpSo2mHceG483ePr5YcGwAvT13DBc7Pp8+wsPliwmf1Hs7wrUqSS0xGHVHmJYycz57cX8emSdD5ZnM6GXYcJCwliYLsYrurWmH6tGxAWon9Dieg+DpEC4uvX5p6LWzFmQEuWpu3nk0VpfLFsG5OXb6Ne7VCGdo7j6u6N6dY0SsPAixRBwSFVXsF7RMyMrk2j6No0ikeHtmdOyk4+WZzOhwu38O/5m0isX5urujXm6m6NSagf7mHVIhWXuqpEgAPHspi2YjufLEpn/obdOAfd46O4unsThnaKpV54mNclipQ5XVWl4JBi2rrvKJ8t2coni9NIyThEaLDRr3VDrune+LSBF3WPiFQlCg4Fh5SQc47kbQf4dHE6ny3Zyo6Dx4msGcKQTrFc3a0x5yaeQ/OHp+geEakydHJcpITMjA5xdekQV5exl7Xju9RdfLo4nc+XbmXigi00jqoFwNqMg7SKifS4WpHyoyMOkQA9P201b3y97rTlfVtF8+fruxBTp6YHVYmUnLqqFBxSDhLHTuaxoe35bEk6y9L2YwZ9WkRzZdc4BndsRGTNUK9LFPFbpblz3MwGm9kaM0s1s7FnaXedmTkzK/JLiZSn2y9oxuejL2DWA/0Yc1FLNu85wm8/WkbSuJn8+r1FzEjOIDM71+syRUqNp+c4zCwYeB0YCKQBC8zsc+dc8intIoF7gB/Kv0qRMyt4j0iLBhHcf2kb7hvYmkWb9/HZknS+WLqVycu2EVU7NP+keo+EerrJUCo1T7uqzKw38IRzblDe64cAnHN/OqXdy8BM4EHgQefcWfuh1FUlFUVWTi5z1+7kk8VbmZG8nWNZuTQ9pxZXdmnMVd3iaNlQJ9Wl4qgsV1U1BrYUeJ0G9CzYwMy6AU2dc5PM7MHyLE6kpEKDgxjQNoYBbWM4dDybL1du55PF6bzxdSqvzU6lY+M6XNW1MVd0iaOhTqpLJeF1cBR2vJ5/CGRmQcBLwKgiN2R2J3AnQHx8fCmVJ1J6ImqEcE33JlzTvQk7Dh7ji6Xb+GxJOuMmr+KZKas4v0U0V3VrzKAOMfkn1XWDoVREFbqryszqAuuAQ3lvaQTsAa44W3eVuqqkMlm38xCfLU7n0yVb2bznCDVCghjYPoarujbml/9aqBsMpdxUistxzSwESAEuBtKBBcDNzrmVZ2j/NTrHIVWUc+6kk+p7j/jmDHlgYGtu7hlP/YgaHlcoVV2luBzXOZcNjAamA6uAD51zK83sSTO7wsvaRMqbmdEjoR71aoflhwbAX2ak0GPcTC5/ZQ7JWw94WKGIj24AFKnAEsdOZub9F/LP7zfy8U/pHM3KoWezc/hFn0QGtm9EcJAu65XSUymOOESkaC0bRjLuqk7Mf+hiHr68LWl7j3L3hEVc+Pxsxs9Zx/4jmgZXypeOOEQqsMKuqsrJdcxIzuAf323ghw17qBUazLU9GjPq/Ga0bBjhUaVSFVSKk+NlRcEh1cXKrfv553cb+WzpVjKzc7mwdQN+0SeRfq0aEKRuLAmQgkPBIdXI7kPHee+Hzfx7/iZ2HDxO8+hwRp6fyLU9mhBRw+vbtaSyUHAoOKQayszOZeqKbfz9u40s3bKPyBoh3HBuU0b2TiS+fm2vy5MKTsGh4JBqbvHmvfzju41MWb6NHOe4pF0Mv+iTSO/m9TEz3ZUup1FwKDhEANi+/xgT5m/ivR83s+dwJm0bRTLq/ETG/ne57kqXk+hyXBEBoFHdmjw4qA3fjx3A89d2BmDsf5cD8MbXqRw6nu1leVIJKThEqomaocGk7zvK6u0H85c9P20NHR+fzs1vzefgMd0PIv5RcIhUI/cNbM3GZ4fkd1F9+us+DGjbkO/X7eaC52bz6qy1HFCASBEUHCLVWNemUfx91Ll8ProP5ybW48UZKVzw7Fe8PDOF/UcVIFK4YgeHmTUzs1lmtt7MXjSzmgXW/Vg65YlIWSk47W3nJlG8PfJcJo25gF7N6/PyzLVc8OxXvPjlGvYdyfSwSqmIin1VlZlNBSYB84ExQCtgsHPuoJktds51K70yA6OrqkRKZuXW/fx1VirTVm4nokYIo85P5PYLmlEvPMzr0qQMlfnluGa2yDnXvcDrh4CrgYHA7ILrypuCQ6R0rN5+gL/OSmXKim3UDg3mtvMTuaNvc85RgFRJ5THn+Emzyjjn/mRmWcAsILIE2xWRCqJtozq8fkt3UjIO8uqstfzfN+t45/uN3No7gTv7NtfkUtVUSU6Op5jZwIILnHN/Bt4DWpSoKhGpUFrHRPLazd358jcXMrB9DG/NWc8Fz83m6cnJ7Dx43OvypJyVpKuqBuCcc6edOTOzxs659JIWV1zqqhIpW+t2HuK1r1L5bEk6YSFB3NIzgbv6NadhZP41MhrSpBIqtTvHzewFM3ugwOueZjYB+Az4q5kNMrPggu/xMjREpOy1aBDBSzd2Zeb9/RjSKY5/fr+Rvs/N5o9frCTjwDEAXpm11uMqpaz4c47jRuA+ADNrA8wEwoANwHnAHUCymV3rnFtTVoWKSMXTvEEEf7mhC2MGtOT12an8a94m3v1hMzed29Tr0qQM+XOOoyGwLe/5aGAd0MQ519Y5dw5wIXAQmG9mzcumTBGpyBKjw3nh+i7c2iuBzOxc3pm3ybd87GQSx07mpRkpHlcopcmf4DjIz1dQDQGecc7tPLHSOfctcAGQDPyx1CsUkUrjiSs6sPHZIcx+sH/+subR4XSLj/KuKCl1/gTHcmComfUCEvAFxEmccznAS8Cg0i1PRCqjZtHhAPxj1Lk4YNQ/FvDLdxawcddhbwuTUuFPcLwI/Ab4DtgOPGVmhd39k4Pu3xCRPPde3IqL2jZk+m8u5KHL2jJv3W4ufWkOz09bzWEN5V6p+XU5rpn1Bi4BJuALkUvwBcosfGHSFvgnkOOc61FWxfpLl+OKVDw7Dhzj2Wmr+e+idGLq1ODhy9txRZc4zMzr0iRPmQ05Yr7/y08DD3DyVVlZwBXOuS8D2mAZUHCIVFw/bdrLE5+vZHn6fpIS6vHEFR3o2Liu12UJ5TNWVSxwGRCP7wT6p865dcXaWClTcIhUbLm5jv/8tIXnp61hz5FMbjovngcvbaMxsDymOccVHCIV3v6jWbw6ay3//H4j4WHBPHBpG27pGU9IsKYK8oLmHBeRCq9urVAeG9qeaff2pXOTKB7/fCVDXv2W79ft8ro0OQsFh4h4rlVMJP++/TzevLUHhzOzufmtH/j1u4tI33fU69KkEAoOEakQzIxBHRox8/5+PDCwNbNWZ3DxX77mlZlrOZaV43V5UoCCQ0QqlJqhwYy5uBWzHujPJe1ieGlmChf/5RumrdjGiXOyGsLEWwoOEamQGkfV4rWbuzPxzl5E1gzh7gmLGPG3H0jJOKiRdz2m4BCRCq1X8/pMGnMBT13ZgRXpB7jslbkA6r7yUEmmjhURKRchwUHsOpTJ/qNZ+cvaPjYN8A1togmjypeOOESkUrhvYGs2PjuEjc8OAaBBZA3CgoOIrBlCbm7Vux+tIvM8OMxssJmtMbNUMxtbyPq7zWy5mS0xs2/NrL0XdYpIxTLt3r70a9OAcZNXMfIfP+bPPChlz9PgyJty9nV8Q5e0B24qJBjec851cs51BZ7HN7iiiFRj917civoRNRh/aw+euboTCzfuZfDLc5i2YrvXpVULXh9xnAekOufWO+cygYnAlQUbOOcOFHgZDuiYVKSaO3FOw8y4uWc8k+65gCb1anP3hJ8Y+/EyDdtexrwOjsbAlgKv0/KWncTMfm1m6/AdcdxT2IbM7E4zW2hmC3fu3FlYExGpolo0iODjX53P//RvwQcLtzD0r9+ydMs+r8uqsrwOjsIG4j/tiMI597pzrgXwe+DRwjbknBvvnEtyziU1aNCglMsUkYouLCSI3w1uy/t39OJ4Vg7X/u/3vD47lRydOC91XgdHGtC0wOsmwNaztJ8IXFWmFYlIpdareX2m3nshgzs24oXpa7hp/HzS9h7xuqwqxevgWAC0MrNmedPRDgc+L9jAzFoVeDkE0C2jInJWdWuH8tebuvHiDV1I3ua7afCzJelel1VleBoczrlsYDQwHVgFfOicW2lmT5rZFXnNRpvZSjNbAtwPjPSoXBGpRMyMa7o3Yeq9fWkdE8m9E5fwm4mLOXAsq+g3y1lpIicRqfKyc3J54+t1vDJrLY3q1OTl4V05N/Ecr8uqcDSRk4hInpDgIO65uBX/ubs3IcHGjW/O4y9friErJ9fr0iolBYeIVBvd4+sx+Z6+XNu9CX/9KpXr/m8eG3Yd9rqsSkfBISLVSkSNEF64vgtv3NKdjbsOM+TVuXywYDNVsdu+rCg4RKRaurxTLNN+05euTaP4/cfL+dWERew9nAlooqiiKDhEpNqKrVuLCbf35OHL2zJrdQaDX5nDt2t3aaKoIig4RKRaCwoy7rywBZ/8Tx8ia4Yy4m8/eF1ShaeJnEREgBnJGaTuOJT/OnHsZEATRRVGRxwiIvw8UVQn++joAAAOPUlEQVTq05flL7urX3N+c0mrs7yrelJwiIgUEBLs+7M4olc8b36znsc+W6EZBk+hrioRkVPce3ErfnNJKyJqhPJ/36zjyPEcnr+uc36oVHcKDhGRU5w4pzH2srZE1gzhhelrOJyZzas3daNGSLDH1XlP8Skicha/vqgljw9rz/SVGfzynYUczczxuiTPKThERIrwiz7NeP7aznyXuovb/v5DtR9hV8EhIuKHG85tyqs3dWPx5n3c8tYP+XeZV0cKDhERPw3tHMf423qQknGQG8fPY8eBY16X5AkFh4hIAAa0jeGfvziP9L1Huf7NeWzZU/2mpVVwiIgEqHeL+kz4ZU/2Hs7khjfnsW7noaLfVIUoOEREiqFbfD0+uKs3WTm53PjmPJK3HvC6pHKj4BARKaZ2sXX44K7ehAYHMXz8PBZt3ut1SeVCwSEiUgItGkTwn7t7Uy88jBFv/8D363Z5XVKZU3CIiJRQk3q1+c9dvWlSrxa/+McCvlqd4XVJZUrBISJSChrWqckHd/amTaNI7vzXT0xattXrksqMgkNEpJTUCw/j3V/2pHt8Pe55fzEfLtjidUllQsEhIlKKImuG8s7/O48+LaP53cfL+Md3G7wuqdQpOERESlmtsGDeHpnE4A6N+OMXybz21Vqcqzpzeig4RETKQI2QYF67uRvXdGvMn79M4dlpq3HO8dKMFK9LKzHNxyEiUkZCgoP48/VdqF0jmDe/Wc/h49lMmL+50s9hruAQESlDQUHGU1d2JLxGCG9+s97rckqFgkNEpIy9PHPtSaGROHYy4JuitjIefVhVOmFzQlJSklu4cKHXZYiInCQrJ5dWj0ylbq1Qpt7bl7ioWl6XdBIz+8k5l1RUO50cFxEpJ6HBvj+52Tm5/OaDJeTkVs5/uCs4RETK0b0Xt+Kpqzry44Y9vDE71etyikXnOEREytGJcxpzUnby8qy1nN8ymh4J9TyuKjA64hAR8cBTV3UkLqom905czIFjWV6XExDPg8PMBpvZGjNLNbOxhay/38ySzWyZmc0yswQv6hQRKU2RNUN5ZXg3tu0/xqOfrKhUd5Z7GhxmFgy8DlwGtAduMrP2pzRbDCQ55zoDHwHPl2+VIiJlo3t8Pe67pBWfL93Kx4vSvS7Hb14fcZwHpDrn1jvnMoGJwJUFGzjnZjvnTswGPx9oUs41ioiUmV/1b0mv5ufwh89WsHHXYa/L8YvXwdEYKDjucFresjO5HZhaphWJiJSj4CDjpRu7EhocxD0TF5OZnet1SUXyOjiskGWFdvSZ2QggCXjhDOvvNLOFZrZw586dpViiiEjZiq1bi+eu7cyytP28WAkGQfQ6ONKApgVeNwFOmzbLzC4BHgGucM4dL2xDzrnxzrkk51xSgwYNyqRYEZGyMrhjI27uGc+bc9bxXWrFnrfc6+BYALQys2ZmFgYMBz4v2MDMugFv4guNHR7UKCJSLh4b0p4WDSK474Ml7Dmc6XU5Z+RpcDjnsoHRwHRgFfChc26lmT1pZlfkNXsBiAD+Y2ZLzOzzM2xORKRSqxUWzKvDu7HvSBa/+2hphb1E1/M7x51zU4Appyz7Q4Hnl5R7USIiHmkfV4exl7XlyUnJ/Hv+Jm7rneh1SafxuqtKRERO8Ys+iVzUpgHjJq9izfaDXpdzGgWHiEgFY2a8cH0X6tQMZcz7iziWleN1SSdRcIiIVEDRETV48YYupGQc4pkpq7wu5yQKDhGRCurC1g24o28z/jVvEzOSM7wuJ5+CQ0SkAntwUBs6xNXhdx8tZfv+Y16XAyg4REQqtBohwbx6UzeOZeVy/4dLyK0AswYqOEREKrgWDSJ44or2fL9uN2/OWe91OQoOEZHK4IakpgzpFMtfvlzD0i37PK1FwSEiUgmYGc9c3YmYOjW5Z+JiDh3P9qwWBYeISCVRt3YoLw/vypY9R/jDZys8q0PBISJSiZybeA5jBrTiv4vS+WyJN7MGKjhERCqZMQNakpRQj0c/WcGWPUeKfkMpU3CIiFQyIcFBvDy8KxjcM3Ex2TnlO2uggkNEpBJqUq82z1zdicWb9/HKrLXl+tkKDhGRSmpYlziu79GE12anMn/9bl4qp2lnFRwiIpXYE1d0ILF+OPd9sKTcjjwUHCIilVh4jRBeHd6NXYeOA5TLrIGezwAoIiLF99KMlJOONJo95JtQ9d6LW3HfwNZl8plWUee0LYmkpCS3cOFCr8sQESk3ubmO5g9PYeOzQ4q9DTP7yTmXVFQ7dVWJiFQBQUFWfp9Vbp8kIiJl6t6LW5XL5yg4RESqiLI6p3EqBYeIiAREwSEiIgFRcIiISEAUHCIiEhAFh4iIBETBISIiAVFwiIhIQBQcIiISEAWHiIgERMEhIiIBUXCIiEhAFBwiIhIQBYeIiATE8+Aws8FmtsbMUs1sbCHrLzSzRWaWbWbXeVGjiIj8zNPgMLNg4HXgMqA9cJOZtT+l2WZgFPBe+VYnIiKF8XrO8fOAVOfcegAzmwhcCSSfaOCc25i3LteLAkVE5GReB0djYEuB12lAz+JsyMzuBO7Me3nIzNYUs6ZoYFcx3+s11V7+KmvdoNq9UpFrT/CnkdfBUdgkua44G3LOjQfGl6wcMLOF/kzWXhGp9vJXWesG1e6Vylz7CV6fHE8DmhZ43QTY6lEtIiLiB6+DYwHQysyamVkYMBz43OOaRETkLDwNDudcNjAamA6sAj50zq00syfN7AoAMzvXzNKA64E3zWxlGZdV4u4uD6n28ldZ6wbV7pXKXDsA5lyxTimIiEg15XVXlYiIVDIKDhERCUi1DQ4/hjq528yWm9kSM/u2kDvaPVNU7QXaXWdmzswqxKV/fuzzUWa2M2+fLzGzX3pRZ2H82edmdoOZJZvZSjOrMCMd+LHfXyqwz1PMbJ8XdRbGj9rjzWy2mS02s2VmdrkXdRbGj9oTzGxWXt1fm1kTL+osFudctXsAwcA6oDkQBiwF2p/Spk6B51cA07yu29/a89pFAnOA+UBSZagb39Ayr3ldazFrbwUsBurlvW7odd2B/LwUaD8G+LvXdQew38cDv8p73h7Y6HXdAdT+H2Bk3vMBwL+9rtvfR3U94sgf6sQ5lwmcGOokn3PuQIGX4RTzxsQyUGTteZ4CngeOlWdxZ+Fv3RWRP7XfAbzunNsL4JzbUc41nkmg+/0m4P1yqaxo/tTugDp5z+tSce4D86f29sCsvOezC1lfYVXX4ChsqJPGpzYys1+b2Tp8f4DvKafailJk7WbWDWjqnJtUnoUVwa99Dlybd+j+kZk1LWS9F/ypvTXQ2sy+M7P5Zja43Ko7O3/3O2aWADQDviqHuvzhT+1PACPyLtmfgu+IqSLwp/alwLV5z68GIs2sfjnUVmLVNTj8GurEOfe6c64F8Hvg0TKvyj9nrd3MgoCXgAfKrSL/+LPPvwASnXOdgZnAO2VelX/8qT0EX3dVf3z/an/bzKLKuC5/BDKsz3DgI+dcThnWEwh/ar8J+KdzrglwOfDvvN8Br/lT+4NAPzNbDPQD0oHssi6sNFSEHeyFQIc6mQhcVaYV+a+o2iOBjsDXZrYR6AV8XgFOkBe5z51zu51zx/NevgX0KKfaiuLPz0sa8JlzLss5twFYgy9IvBbIz/pwKk43FfhX++3AhwDOuXlATXyDCHrNn5/3rc65a5xz3YBH8pbtL78SS8DrkyxePPD963A9vsPyEyeuOpzSplWB58OAhV7X7W/tp7T/mopxctyffR5b4PnVwHyv6w6g9sHAO3nPo/F1U9SvDLXntWsDbCTvpuCK8PBzv08FRuU9b4fvj7Pn38HP2qOBoLznTwNPel23v49qecTh/BjqBBidd1nlEuB+YKRH5Z7Ez9orHD/rvidvny/Fd05plDfVnszP2qcDu80sGd+Jzt8653Z7U/HPAvh5uQmY6PL+ilUEftb+AHBH3s/M+/hCxPPv4Gft/YE1ZpYCxOALj0pBQ46IiEhAquURh4iIFJ+CQ0REAqLgEBGRgCg4REQkIAoOEREJiIJDREQCouAQKQYzG2hmk8ws3cyOmdkWM/uzmYV6XZtIWQvxugCRSqoLvpFN3wAOA93xjUi8B3jGw7pEypxuABQpITMLxjeo3cdAiHNuiMcliZQpdVWJBMjMQvJmK5xnZrvwjWiahW/Cr0N5bc4zs60F3tPBzFaZ2W8LrD+SN+veajP73sxa5q17osCMfCcex81sbvl/W5HTKThEAvce8Fd8A0iOxDcCcX98w2avyGvTA/gJfFPKApOA0c65Fwqsn+mc6+qca4tvgMHHAJxzT+Qt7+qc6wr8G9iFbyRYEc/pHIdIAMysK3A9cItz7r0Cy6/D1121OG9RD2Cpmf0Z31wL/ZxzmwtsqgewssDrVCCukM97AN9Afhc551JK87uIFJeOOEQCE5/33zUnFphZODAu7+WivP/2AO7GFwZ9TwmNE+tX5r0/EegLPFuwgZndz8+hsQaRCkInx0UCkDedbSrwHfAnoBHwO3zz0oc752LMrAZwEHgb39VXA9zPE1RRYP16fEcpzYEbnHOfFGhzX952L3LOrS6P7ybiLx1xiATAObcFuAVIAD4Hfo3vD3wqP3dTdQb2OOf+B9gE/OOUzXQGjgLtnHNtgCcpcLRRIDQGKDSkItIRh0gpM7O7gaHOuaFmVhPfSfTpzrnHC6y/1jk3MO91BLAD6A1cBIzFFxrJXtQvUhSdHBcpfflXVDnnjpnZVcAPZpbinHs3b/38E42dc4fMbAq+ee2fALYD75lZwW2+6Zz733KqX+SsdMQhIiIB0TkOEREJiIJDREQCouAQEZGAKDhERCQgCg4REQmIgkNERAKi4BARkYAoOEREJCAKDhERCcj/B8DDNhv3Ma44AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d86d08da0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dic['spin'],(1-np.array(dic['spin']))/np.array(dic['a_d2']) ,marker='+',label='e=%f, p=%f, M=$2\\\\times 10^5$'%(e,p) )\n",
    "plt.xlabel('$a_{KRZ}$',fontsize=16)\n",
    "plt.ylabel('$\\\\delta_2$',fontsize=16)\n",
    "#plt.text(0.3,0.3,'e=0.1, p=6, M=$2\\\\times 10^5$',fontsize=16)\n",
    "plt.legend(fontsize=12)\n",
    "plt.ylim(0.1,0.6)\n",
    "plt.savefig('limit_d2_e0.5_p6.png',dpi=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pickle.dump(dic,open('range_d2_e%.6f_p%.6f.p','wb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.5, 0.58157771302194172, 201394.59911492976]\n",
      "[-0.40000000000000002, 0.63430356171178692, 201149.28116077985]\n",
      "[-0.30000000000000004, 0.68747437617654639, 200887.24756641683]\n",
      "[-0.20000000000000007, 0.74113577733970382, 200608.01119010712]\n",
      "[-0.10000000000000009, 0.79530615302307428, 200312.0967782597]\n",
      "[1e-10, 0.85000999648627218, 199999.7252575582]\n",
      "[0.099999999999999867, 0.90529319385725404, 199670.42538087649]\n",
      "[0.19999999999999984, 0.96115681825953903, 199325.15707089895]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24dfd99b9e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.3513385592515752, 1.3209755064821875, 1.2850665639327952, 1.2437488113647626, 1.1675490448006107, 1.1184029193093827, 1.0645578227941437, 1.0060313935797862, 0.94283914632187071, 0.8749487127123089, 0.8023399513523094, 0.72482338014552405, 0.64198434039501484, 0.53680874061484363], 'e': [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.20000000000000001, 0.25, 0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999978, 0.79999999999999982, 0.84999999999999998]}\n",
      "[-0.5, 0.67753179205306835, 201266.02458352037]\n",
      "[-0.40000000000000002, 0.72135129304524614, 201035.66877942014]\n",
      "[-0.30000000000000004, 0.76551803372147131, 200792.91185776715]\n",
      "[-0.20000000000000007, 0.8100073824281725, 200539.30295684899]\n",
      "[-0.10000000000000009, 0.85482324235313778, 200275.22293272518]\n",
      "[1e-10, 0.90000205455336368, 199999.98970199254]\n",
      "[0.099999999999999867, 0.94558446265642471, 199712.90285910844]\n",
      "[0.19999999999999984, 0.99155235959895238, 199415.07441291193]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d82fa24a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.3513385592515752, 1.3209755064821875, 1.2850665639327952, 1.2437488113647626, 1.1675490448006107, 1.1184029193093827, 1.0645578227941437, 1.0060313935797862, 0.94283914632187071, 0.8749487127123089, 0.8023399513523094, 0.72482338014552405, 0.64198434039501484, 0.53680874061484363, 0.44493043111729114], 'e': [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.20000000000000001, 0.25, 0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999978, 0.79999999999999982, 0.84999999999999998, 0.90000000000000002]}\n",
      "[-0.5, 0.78078010865429981, 201047.60129376262]\n",
      "[-0.40000000000000002, 0.81425145484464778, 200850.27626496746]\n",
      "[-0.30000000000000004, 0.8478944048896031, 200647.12455726214]\n",
      "[-0.20000000000000007, 0.88173816658080484, 200437.40557216739]\n",
      "[-0.10000000000000009, 0.91577787335739913, 200221.51199731277]\n",
      "[1e-10, 0.95001427602138411, 199999.6297984003]\n",
      "[0.099999999999999867, 0.98446658180821078, 199771.39171057817]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\Documents\\GitHub\\KRZwave\\KRZmetric.py:342: RuntimeWarning: invalid value encountered in sqrt\n",
      "  r0 = 1 + sqrt(1 - sqspin);\n",
      "D:\\ProgramFiles\\lib\\site-packages\\scipy\\integrate\\quadpack.py:364: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n",
      "  the requested tolerance from being achieved.  The error may be \n",
      "  underestimated.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.19999999999999984, 0.95000000000000007, 200000.0]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramFiles\\lib\\site-packages\\scipy\\optimize\\minpack.py:161: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d83491160>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a_d2': [1.3513385592515752, 1.3209755064821875, 1.2850665639327952, 1.2437488113647626, 1.1675490448006107, 1.1184029193093827, 1.0645578227941437, 1.0060313935797862, 0.94283914632187071, 0.8749487127123089, 0.8023399513523094, 0.72482338014552405, 0.64198434039501484, 0.53680874061484363, 0.44493043111729114, 0.33845538682751553], 'e': [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1], 'p': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 'spin': [0.20000000000000001, 0.25, 0.29999999999999999, 0.34999999999999998, 0.39999999999999997, 0.44999999999999996, 0.49999999999999994, 0.54999999999999993, 0.59999999999999987, 0.64999999999999991, 0.69999999999999996, 0.74999999999999978, 0.79999999999999982, 0.84999999999999998, 0.90000000000000002, 0.95000000000000007]}\n"
     ]
    }
   ],
   "source": [
    "for spin in np.arange(0.850,0.955,0.05):\n",
    "    dlist=[]\n",
    "    Mlist=[]\n",
    "    spinlist=[]\n",
    "    if spin>0.77:\n",
    "        d2down=-0.5\n",
    "    else:\n",
    "        d2down=-0.2\n",
    "    for d2 in np.arange(d2down,0.3,0.1):\n",
    "        if np.abs(d2-0.0)<1e-5:\n",
    "            d2=1e-10\n",
    "        filename='C:\\\\Users\\\\HP\\\\Documents\\\\Visual Studio 2015\\\\Projects\\\\multiple_d\\\\multiple_d\\\\trace_M%.0f_spin%.6f_e%.6f_p%.6f_d1%.6f_d2%.6f_d3%.6f.dat'%(M,spin,e,p,d1,d2,d3)\n",
    "        index, tau,t,r,th,phi,ut,ur,uth,uphi,F_t,F_r,F_th,F_phi=np.loadtxt(filename,unpack=True)\n",
    "        \n",
    "        if np.abs(e-0.0)>1e-8:\n",
    "            avgomgsec=getfreq_sec_frommaxi(t,r,phi,M)\n",
    "            #print(avgomgsec)\n",
    "            avgomgr=avgomgsec[0]\n",
    "            avgomgphi=avgomgsec[1]\n",
    "\n",
    "            def fun(x):\n",
    "                #print('called')\n",
    "                M=x[0]\n",
    "                spin=x[1]\n",
    "                #print('e=%f, p=%f, M=%f, spin=%f, aimomgr=%f, aimomgphi=%f'%(e,p,M,spin,avgomgr,avgomgphi))\n",
    "\n",
    "                omgr,omgphi=getfreq_sec_fromepma(e,p,M,spin)\n",
    "                avgomgsec=np.array([avgomgr,avgomgphi])\n",
    "                omgsec=np.array([omgr,omgphi])\n",
    "                return (omgsec-avgomgsec)/avgomgsec\n",
    "\n",
    "\n",
    "            from scipy.optimize import root,fsolve\n",
    "            (myM,myspin)=fsolve(fun,[M,spin])\n",
    "\n",
    "            getfreq_sec_fromepma(e,p,myM,myspin)\n",
    "        else:\n",
    "            avgomgsec=circfreq_sec_fromtrace(t,phi,M)\n",
    "            def circfun(x):\n",
    "                spin=x\n",
    "                omgsec=circfreq_sec_fromrma(p,M,spin)\n",
    "                #print('e=%f, p=%f, M=%f, spin=%.10f, omg=%.10f, aim=%.10f'%(e,p,M,spin,omgsec,avgomgsec))\n",
    "                return (omgsec-avgomgsec)/avgomgsec\n",
    "            (myspin)=fsolve(fun,spin)\n",
    "            myspin=myspin[0]\n",
    "            myM=M\n",
    "            circfreq_sec_fromrma(p,myM,myspin)\n",
    "        dlist.append(d2)\n",
    "        spinlist.append(myspin)\n",
    "        Mlist.append(myM)\n",
    "\n",
    "        #for i in range(len(dlist)):\n",
    "        print([dlist[-1],spinlist[-1],Mlist[-1]])\n",
    "    plt.figure()\n",
    "    plt.plot(dlist,spinlist,'o')\n",
    "    plt.show()\n",
    "    spinl.append(spinlist)\n",
    "    Ml.append(Mlist)\n",
    "    if spin>0.36:\n",
    "        dic['a_d2'].append(np.polyfit(dlist[0:6],spinlist[0:6],1)[0])\n",
    "    else:\n",
    "        dic['a_d2'].append(np.polyfit(dlist[2:6],spinlist[2:6],1)[0])\n",
    "    dic['e'].append(e)\n",
    "    dic['p'].append(p)\n",
    "    dic['spin'].append(spin)\n",
    "    print(dic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.02076884  0.04346978]\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=200000.002980, spin=0.300000, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=200000.000000, spin=0.300000, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=230362.405867, spin=0.374877, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=238960.680466, spin=0.424796, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=243617.401154, spin=0.475260, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244235.105957, spin=0.496064, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244159.994451, spin=0.501385, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244122.476384, spin=0.501999, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244116.742786, spin=0.502053, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244116.213259, spin=0.502057, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244116.199864, spin=0.502057, aimomgr=0.020769, aimomgphi=0.043470\n",
      "e=0.500000, p=6.000000, M=244116.199834, spin=0.502057, aimomgr=0.020769, aimomgphi=0.043470\n"
     ]
    }
   ],
   "source": [
    "spin=0.3\n",
    "d2=-0.2\n",
    "filename='C:\\\\Users\\\\HP\\\\Documents\\\\Visual Studio 2015\\\\Projects\\\\multiple_d\\\\multiple_d\\\\trace_M%.0f_spin%.6f_e%.6f_p%.6f_d1%.6f_d2%.6f_d3%.6f.dat'%(M,spin,e,p,d1,d2,d3)\n",
    "index, tau,t,r,th,phi,ut,ur,uth,uphi,F_t,F_r,F_th,F_phi=np.loadtxt(filename,unpack=True)\n",
    "\n",
    "if np.abs(e-0.0)>1e-8:\n",
    "    avgomgsec=getfreq_sec_frommaxi(t,r,phi,M)\n",
    "    print(avgomgsec)\n",
    "    avgomgr=avgomgsec[0]\n",
    "    avgomgphi=avgomgsec[1]\n",
    "\n",
    "    def fun(x):\n",
    "        #print('called')\n",
    "        M=x[0]\n",
    "        spin=x[1]\n",
    "        print('e=%f, p=%f, M=%f, spin=%f, aimomgr=%f, aimomgphi=%f'%(e,p,M,spin,avgomgr,avgomgphi))\n",
    "\n",
    "        omgr,omgphi=getfreq_sec_fromepma(e,p,M,spin)\n",
    "        avgomgsec=np.array([avgomgr,avgomgphi])\n",
    "        omgsec=np.array([omgr,omgphi])\n",
    "        return (omgsec-avgomgsec)/avgomgsec\n",
    "\n",
    "\n",
    "    from scipy.optimize import root,fsolve\n",
    "    (myM,myspin)=fsolve(fun,[M,spin])\n",
    "\n",
    "    getfreq_sec_fromepma(e,p,myM,myspin)\n",
    "else:\n",
    "    avgomgsec=circfreq_sec_fromtrace(t,phi,M)\n",
    "    def circfun(x):\n",
    "        spin=x\n",
    "        omgsec=circfreq_sec_fromrma(p,M,spin)\n",
    "        #print('e=%f, p=%f, M=%f, spin=%.10f, omg=%.10f, aim=%.10f'%(e,p,M,spin,omgsec,avgomgsec))\n",
    "        return (omgsec-avgomgsec)/avgomgsec\n",
    "    (myspin)=fsolve(fun,spin)\n",
    "    myspin=myspin[0]\n",
    "    myM=M\n",
    "    circfreq_sec_fromrma(p,myM,myspin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "244116.1998337011"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.50205707376478403"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myspin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "krzwave=getwave(filename,np.pi/4,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filenamekerr='C:\\\\Users\\\\HP\\\\Documents\\\\Visual Studio 2015\\\\Projects\\\\multiple_d\\\\multiple_d\\\\trace_M%.0f_spin%.6f_e%.6f_p%.6f_d1%.6f_d2%.6f_d3%.6f.dat'%(myM,myspin,e,p,0,0,0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kerrwave=getwave(filenamekerr,np.pi/4,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramFiles\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 2000)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d83a23940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[20,5])\n",
    "plt.plot(np.arange(100000),kerrwave[1])\n",
    "plt.plot(np.arange(100000),krzwave[1])\n",
    "plt.xlim(0,2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filename='C:\\\\Users\\\\HP\\\\Documents\\\\Visual Studio 2015\\\\Projects\\\\multiple_d\\\\multiple_d\\\\trace_M200000_spin0.300000_e0.500000_p6.000000_d10.000000_d2-0.200000_d30.000000.dat'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.74018337798222689"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bracket(kerrwave[1],krzwave[1],1)/np.sqrt( bracket(kerrwave[1],kerrwave[1],1)*bracket(krzwave[1],krzwave[1],1) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "index, tau,t,r,th,phi,ut,ur,uth,uphi,F_t,F_r,F_th,F_phi=np.loadtxt(filename,unpack=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2000)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IjTeivtIU1OsKIfDn9Zthsc7hiZN9Qb02adMb7SOYsDuD0iNyqYf3FcOUEovvvXIh6Ncm7Zl1uvFc0wAOb81FSpwxqNcuzkrEJ3YV4LH3e9E/ySb7tH5PnepDSpwBt1cEPw/45oHNGLQ58PgHvUG9NmnLugtRQgg9gB8BOASgEsAnhRCVS972eQCTUsoyAN8H8I8AIKV8VEq5TUq5DcBnAHRLKRsX/d6nAz+XUo6sN1aKPE+c7ENuahxuLF//PvulEmIM+OotpTjRNYGT3VwVRevzUusQZubdeCAEgyUA+OotZfBK4GdvXwrJ9Uk7rLNOvNI2jHu25wel385S+8uzsKc4Az8+1gkXe0TQOj11qh/ZybHYH4S+e0vFGfX40o2l+KB7Ag3MA2idXmzx5QEP7gr+5CkA/PGt5ZCQ7BlJ6zblcOGltiHctS0vJHnAvrIs7CpKx0/fvsQ8gNYsGCui9gDokFJ2SSmdAB4HcPeS99wN4Of+vz8F4Dbx0Y3VnwTwqyDEQ1Fiwu7EOx1juHtbPvS64OyzX+qh3RuQnmDEj49xqTOtz3+f7seGjATsKckIyfUL0hNwd20efvVBLybtPDmH1u6l1iE4PV7ctyM0RVMhBL5ycykGbA482zgQks8gbRifmccb50dw7/Z8GPSh6Rbx0J5CpCcY8a/MA2idnmkaQGFGfMjygLy0eHx8Wz6eaOjD+Ax7RtLavdA8CIfLi/t3hqZoCgB/dEspLNY5PMM8gNYoGE/9fACL1+f3+19b9j1SSjcAG4DMJe95EB8tRP2Hf1veXy1TuAIACCG+KIRoEEI0jI6OrvW/gRTwctsQPF6JO2tyQ/YZ8TF6PLyvGK+fH0H70HTIPofUbXxmHsc7x3H3trygNSddzpdvLsWcy4OfH+8O2WeQ+j3fMoiizARU5wenOelybt6cjS3mZPzbW53wemXIPofU7ZWzw3B7Je7etjRtDJ6EGAN+/2MleP38CM4PTYXsc0jdJu1OvNcxhju2hjYP+NJNG+FwefHz4z0h+wxSv+dbBlGcmYDagtSQfcYtm3OwxZyMH7/JPIDWJhiFqOXuxku/jVd9jxDiOgCzUsrWRT//tJRyK4D9/j+fWe7DpZQ/kVLuklLuys4O/vYuCp0X/DfJqrzQDZYA4OG9xYg36vETLnWmNXrl7DC8EjhYbQ7p52wyJeP2ChP+871uzDrdIf0sUqdJuxPvdY7j8NbckA6WhBD40k0bcWF4Bm+0c+c8rU0gD6jITQ7p53x2bxESY/RcHU1r9srZIbi9EndsDd3kKQCU5fjygF8c74Z9nnkArV4gDzgUhjzgKzeXomNkBq+eGw7Z55B6BaMQ1Q9g8bq/AgBL1+gtvEcIYQCQCmDxZv2HsGQ1lJTS4v/nNIDH4NsCSCoxPjOP9zrHcUdNaG+SAJCeGIMHdxfimUYLG0HTmrzgX2FSmRvaoikAfOXmUlhnXfh1Q3/IP4vUJ7DSNNSDJQC4syYP+Wnx+PGbHNzT6llnnTjeOY6D1aHPA9ISYvDJPRvwXPMg8wBak+dbhrAhI7QrTQO+cvNGWGddPBCC1uTVc8PweCUOV4c+D7hjay42ZCTgZ29zsp9WLxiFqJMAyoUQJUKIGPiKSs8uec+zAB72//1+AEellBIAhBA6AA/A11sK/tcMQogs/9+NAO4E0ApSjZfbhv2DpeAef3slf7i/BF4p8csTXOpMqxMYLB0Kw2AJAHYWpaO2MA0/P97Npc60as+HaaUpABj1OvzBDSU42T2Jln5byD+P1OVV/7a8w1tDu9I04OF9xZBS4tH3mQfQ6lhnfdvyQr3SNGBnUQZ2FqUzD6A1eal1CAXp8WEpmhr0Onx2bxFOdk+i1cI8gFZn3YUof8+nrwF4GcA5AE9KKduEEN8RQtzlf9sjADKFEB0Avg7gW4sucSOAfinl4lJqLICXhRDNABoBWAD8dL2xUuR4/dwwNmSEfjl+QEF6Am6vMOHxk31wuDxh+UxSh3APlgDgc/uK0DVqxzsdY2H7TIp+0w4XjneO40C1OSyDJQC4f2cBEmL0+MXx7rB8HqnHi61DyE+Lx9b80PUwWawwIwG3VZjwqw+YB9DqvNE+ArdX4lCIt+cv9tm9RegZn8WbF9n/llZuyuHC2xdHcSiMecADuwoRb9Tj5+91h+XzSD2CckSJlPIFKeUmKWWplPLv/a/9tZTyWf/fHVLKB6SUZVLKPYuLTlLKY1LK65dczy6l3CmlrJFSVkkp/0RKyaxBJRwuD97tHMOtW3LCdpMEfLOhE3Ynnm8eDNtnUvQ7en4EppTYsA2WAODw1lxkJcXwoU6r8m7HGNxeiVs354TtM1Pjjbhnez6ebRrgaY+0YnNOD97pGENdpSmsecDn/HnA75gH0CocPT+KrKTw5gGHqnORnRyLXzAPoFV4+8IYXB6JA1XhK5qmxhtx7458PNM0gAnmAbQKoTkrl+gqjneNw+Hy4ubN4W0uv680E6XZifgFt+fRCrk8XrxzcQy3bA5v0TTWoMen9mzA0fYR9I7Phu1zKbodPT+C5DgDdhalh/VzP7u3GPNuL55sYD8TWpkTXeNwur24ZUv4iqaALw8oz0nCz9/rhr9DBNFVuT1evHVhFDdvzoZOF748IMagw6f2bMCxC6PoHrOH7XMpur3RPoLUeCO2bwhvHvDwvmI43V48frI3rJ9L0Y2FKAq7Y+dHEG/U4/qNmWH9XCEEPru3GE19VjT2WcP62RSdTvVMYnreHfaiKQB86roi6IXglidaESkl3mgfxY2bsmHQh/fRvtmcjOtKMvBfJ3rgYT8TWoFj7SOIM+pwXUlGWD9XCIHP7itGi8WG073MA+jaGvussM25cGuYi6YA8KnrNkAvBPub0op4vRJvXhjF/vIs6MNYNAV8pz7vK83EL4/3wO3xhvWzKXqxEEVhJaXE0fYRfKwsE3FGfdg//94d+UhkPxNaoWPtozDoBD5WlhX2zzanxuFAtRlPNPRh1skjnOnq2gamMDo9H9ZteYs9vK8Y/ZNzeOP8iCKfT9Hl2IVR7CvNUiYP2J6P5FgDtz7Tihw9PwK9TuCG8vDnAaaUOBysNuNJ5gG0AmcHfXnAzQrmAQM2B147N6zI51P0YSGKwqpzdAZ9E3OK3SST44y4b2cBftc0yH3MdE3H2kewqzgdyXFGRT7/4b3FmHa42c+ErumN8yMQArhJgdV7AFBXaYI5JY5bn+maLo3Z0TM+q8hKUwBIjDXgvp0FeKl1iHkAXdMb7aPYVZSOFKXygH3FmHK48WzjgCKfT9HjzQu+xvY3bVLm3np7hQm5qXF47ANu06eVYSGKwuqN876bZLj7Qiz26euK4PR48fTpfsVioMg3ZHPg/NA0blGoaAoAu4vTsTE7EU+c5EOdru5o+whqCtKQlRSryOcb9To8uLsQb18cRf8k+5rRlR1r962au3mTcvfWh/YUwunx4jdnLIrFQJFv0DaHc4NTimzLC9hVlI7ynCQ8zjyAruFY+wiq81OQnaxMHqDXCTywi3kArRwLURRWb7SPYLMpGflp8YrFsNmcjG2FaXiyoY/NSumK3rzgHywpWIgSQuCh3YU41TOJi8PTisVBkW3C7kRjnxW3KLTCJOCBXQUAgF83sMhPV3asfRQbsxOxITNBsRi2mFOwrTANT5zsZR5AV3SsXfnJUyEEHtxdiMY+K9qHmAfQ8mxzLpzutSpa4AeATzAPoFVgIYrCxuHyoKFnEvsV2Ge/1IO7C3FheAZn2LScruBY+yhyU+OwyZSkaBz37iiAQSe4Koqu6ETXOKQE9pcrW4gqSE/ADWVZ+HVDH5uW07IcLg9OdI0rPlgCgIf8eQCbltOVvNMxBnNKHMpzlM8DjHrmAXRl71wcg8crFdvyHFCQnoD95dnMA2hFWIiisDndMwmn24t9ZeE9LW85d9bkIt6ox5N8qNMyvF6J413juKEsC0KE9+SRpbKSYlFXacLTZyyYd3sUjYUi03udY0iKNaC2IFXpUPDg7kIM2Bx4p2NM6VAoAjV0T2Le7cX+TcpPSN1Zm4eEGD2e4HHjtAyvV+JE5zj2lWYqngdkJMagvtKMp8/0Mw+gZb3TMYbkWAO2FaYpHQoe8ucBb10cVToUinAsRFHYvNc5Dr1OYHdxeI9rXk5ynBF31uTiuaYB2Od5Egl92LmhKVhnXdhbqnzRFPAN7ifsTrx6lieR0Ee91zmOPSUZMOiVf6TXVZqQnmDk4J6WdbxrLGLygKRYA47U5OG5pkFMO1xKh0MR5sLINMbtzojJAz6xuxDWWRdeaWMeQB91oity8oDbK0zITIzBE2xaTteg/LeVNOO9zjHUFKQqdgLZUg/uLoTd6cHzPJGMljjeOQ4AEZOA7i/PRn5aPJfl00cM2RzoGrVj78bI+K7GGvS4Z3sBXj07jPGZeaXDoQhzvHMcNQWpSIo1KB0KAODBPYWYc3l4Mil9RKTlATeUZSE/LR5PNjAPoA8bsjlwacyO6yMkD4gx6HDfzgK8dm4Yo9PMA+jKWIiisJiZd6Op34Z9EfJAB4CdRb4TyR7nzD0tcaJrHMWZCchNVa6p/mJ6ncD9Owvw9sUxWKxzSodDEeR4l28LXKQMlgBfkd/lkTyRjD7EPu9Gc78tYoqmALC9MA2bTEkc3NNHvNc5jqLMBBSkK9dUfzHfiWS+PKBvgieS0WUnuiKraAoAn9hVCLdX4plG5gF0ZSxEUVic7J6Axyuxr1T5vhABQgg8uKsQp3ut6BqdUTocihAer8T7lyYi6oEOAPft8J1E8lsO7mmR9zrGkRpvRGVuitKhLNhsTkZtYRqeOsVTc+iyk90TcHtlRN1bhRC4b0cBzvRacWnMrnQ4FCE8XokTXeMRNXkKAPfv9OUBLPLTYsc7x5ESZ0BFBOUBZTlJqC1Mw3+f5neVroyFKAqL453jiNHrsLMoXelQPuTubfkQgoN7uqxtwIZphztiljgHbMhMwO7idDx9up/HjdOC413j2LsxEzqdss10l7p3ez7OD03j3OCU0qFQhDjeNQ6jXkRsHvCb0yyckk+k5gEF6Qm4riQDvzljYR5AC453jeO6jZnQR2AecG5winkAXRELURQW73WOYUdRGuKMeqVD+RBzahxuKMvC02cs8PKYUcKivhARloACviOcO0ftaLHYlA6FIkDfxCz6J+ci4iTSpY7U5sGgE5y5pwUnOsdRW5CGhJjI6A8VwDyAlnovwvpDLXbvjnxcGrOjsc+qdCgUASzWOfROzEZc0RRgHkDXxkIUhZxt1oW2gSns3Rg52/IWu2d7Pvon59DQM6l0KBQBjneNozQ7ETkpcUqH8hGHt+YixqDD01zqTIjsomlGYgxu3pyD356xwMPBveZNOVxosdgicmAP+Ab3zAMo4HjnOMpykpCTHHl5wKGtuYg16Di4JwCRnwfcsiUHvzljgdvjVTocikAsRFHIne6dhJTA7pLIWo4fcKDKjHijHr85w2X5Wuf2eHEyAvtDBaTGG1FXYcKzTQNw8aGueR90TyA9wYiynCSlQ1nWvTvyMTI9j3c7xpQOhRTW0D0Br4zMwRLgywMSYvR4mtvzNM/jlTjVM4nrSjKUDmVZKXFG1FX68gCnm3mA1p3oGkd6ghFbzMlKh7Ks+3bkY3R6Hu/6C2ZEi7EQRSF3snsCBp3AtsI0pUNZVmKsAQerzfhd8yAcLo/S4ZCCzg1Ow+70YE9JZA6WAN/gfsLuxJvto0qHQgo71TOJnUUZECKy+kIE3LolB8lxBs7cEz64NAmDTmD7hsickEqI8eUBzzMP0Lz2oWnMzLuxuzgyC1GALw+wzrpwrH1E6VBIYR9cmsDu4oyI6xMZcMuWHKTGG1nkp2WxEEUh19Aziaq8lIjrC7HYPdvzMe1w4+h5PtS1rKFnAgCwK8Ka6S5246ZsZCbG4Gmu4NO00el5XBqzY3dx5H5X44x63FmTi5dah2CfdysdDinoVM8EqvJTER8TWX0iF7tvRwGm59149eyw0qGQggJ5QKQ11V9sf7kvD2CRX9tGph3onZjFrgjOA2INvjzg5bYhTDtcSodDEYaFKAqpebcHTX1W7IrgmSUA+FhZFnKSY9l7R+MaeiaRlxqHvLR4pUO5IqNehyO1eXiJutKfAAAgAElEQVTt3Ahss3yoa9Upfy+bSE5AAV+D/TmXBy+3DSkdCilk3u1BU78togv8AHD9xkzkpsZxcK9xDd2TMKfEoSA9svOAu7bl4XXmAZp22p8H7CyK7DHWvTsK4HB58WIr8wD6MBaiKKRaLVOYd3sjetYeAPQ6gY9vz8ex9hFM2J1Kh0MKkFLiVPckdkZ40RTwLct3ur14vmVQ6VBIIQ3dE4gx6FCdn6p0KFe1qygdhRnxHNxrWKtlCk63N+ILUYE84M0LoxibmVc6HFJIQ/cEdhanR+yW54B7txfA6WEeoGUN3ZP+PCBF6VCuaseGNBRnJuC3zANoCRaiKKROLSxxjvzB/T3b8+H2SjzfPKB0KKQAi3UOQ1OOiB8sAcDW/FRszErEc038rmpVQ88kagtSEWuI3K1OACCEwD3b8vFOxxhGphxKh0MKWMgDInxCCgDu3pYHj1fiRQ7uNWnAOocBmwO7oyAPqM5PQVlOEgf3GhZNecBdtXk43jXOPIA+hIUoCqmT3ZMozkxAdnKs0qFcU0VuCjaZkvBcExNQLTq1sMQ58hNQIQSO1ObhxKVxDPOhrjlzTg9aLbaI3/IccNe2PEgJztxrVEP3JDZkJCAnOU7pUK5psykZ5TnMA7SqYWHLc+TfWwOD+5M9Exi0zSkdDoWZw+VB24AtKib6AeYBtDwWoihkpPQdgRsND/SAO2vy8EE3H+pa1NA9icQYfcQegbvUkVr/Q72ZD3Wtaeq3wu2VEb/lOaAsJxkVuSlcwadBC3lAFBT4gcuD+w+6JzBgZR6gNQ3dE1GVB9xZk8s8QKOa+qxweWTU3FuZB9ByWIiikOkas2PC7oyamyTge6gDfKhrUUPPJLZvSIdBHx23xbKcJFTmpuBZPtQ1p6Hbt9Vpx4boubceqc3F6V4r+iZmlQ6FwqhnfBbjdmdUbMsLOFKbB4B5gBY1dEdXHrAxOwnV+Rzca9Gp3uhZxR/APICWio47LUWlwGApmlZELTzUmYBqyrTDhfahqah6oAO+AVNjHx/qWnOyexKbTElIS4hROpQVO1LjH9xzWb6mLGx1ipLtIwBQnJWImoJUFvk1ZtrhwvmhqYg/iXSpu2rz0NRvQ8+4XelQKIxOdU+iNDsR6YnRlwf8jmMs8mMhikKmoXsS6QlGlGYnKh3KqhypyUNTnxW94xzca8WZXiu8ElGXgAZW8HHApB0er8Tp3smo6QsRUJiRgG2FaXi2kd9VLTnVM4GUOAPKc5KUDmVVjtTkocViw6UxDu61YiEPiLJ76x0c3GuO1ytxqncy6r6rhRkJ2L4hjTkrLQhKIUoIcVAI0S6E6BBCfGuZn8cKIZ7w//x9IUSx//ViIcScEKLR/+fHi35npxCixf87/1dE+jmq9BGneiaxsyjyj8Bd6g7/4P45np6nGQ09k9AJYHsUbXUCfA/1HRvSuCxfQy4MT2Pa4Y6qLc8BR2rzcHZwCh0jM0qHQmHS0D2JHUXp0OmiKw+4s9afB/DeqhkNPZPQ6wS2bUhTOpRVyU+Lx66idBb5NaRrbAbWWVdUbXkOuKs2D+cGp9AxMq10KBQB1l2IEkLoAfwIwCEAlQA+KYSoXPK2zwOYlFKWAfg+gH9c9LNOKeU2/58vL3r9XwF8EUC5/8/B9cZK4WOddaJrzB51A3sAKEhPwM6idCagGnKqZwJbzClIijUoHcqq3VWbh/ND07g4zIe6FjT2WQFEV1+IgDtrciEE8DsW+TXBOuvExZGZqCya5qbGY09xBp5tGoCUUulwKAzO9E5isyk5KvOAI7V5aB+eRvsQ8wAtaOgObHmOvnvrHVtzoRPAszyZlBCcFVF7AHRIKbuklE4AjwO4e8l77gbwc//fnwJw29VWOAkhcgGkSCmPS18G8AsAHw9CrBQmTf02AMD2wuiaWQo4UpPLwb1GeLwSTX22qBzYA8DhGt9DnYVTbWjstSItwYiizASlQ1k1U0ocrivJwHMc3GvCGX/RdEeU3luPbMtDx8gMznNwr3per0RjnzXqVkMFHPYP7lnk14bTvb7WJyVZ0dX6BAByUuJw/cZM/I55ACE4hah8AH2L/r3f/9qy75FSugHYAGT6f1YihDgjhHhTCLF/0fv7r3FNimCNvVYIAWwtSFU6lDVZGNxzz73qdY7OYGbejW1RWjTNSY7D3tJMztxrRGOfFbUFaVG35TngSG0eOkftODfIwb3aNfX58oCagui8tx6uNkOvE+xnogFdY3ZMO6I3D8hOjsW+0iwW+TWisc+KbYXRnQd0jdnRNjCldCiksGAUopb7f8HSu+CV3jMIYIOUcjuArwN4TAiRssJr+i4sxBeFEA1CiIbR0dFVhE2h1Ng3ibLsJCTHGZUOZU1ykuNwXUkmftfMh7raNfb6Zu1rozQBBXyNdbvHZ9FisSkdCoXQzLwbF0amo3awBACHqnM5uNeIxj4rNuVE51YnAMhMisXHyji414LAludoXcUPAEdqc9E9PotWCwf3ajYz78bFkRlsK4zOlaYAcKjaDKOeeQAFpxDVD6Bw0b8XAFj6zVp4jxDCACAVwISUcl5KOQ4AUspTADoBbPK/v+Aa14T/934ipdwlpdyVnZ0dhP8cWi8p5UK1Ppodqc1D16gdZwf5UFezxn4rkuMM2BiFS5wDDlabYdAJPN/CFXxq1tJvg5SI6ntrRmIMbuDgXvWklGjqs6K2MDpXRQccqclF/+QcmvtZ5Fezxr5JJMcaUJodXac7LnagKjC4tygdCoVQc7/VlwdE6TZSAEhL8OUBL7QMMg/QuGAUok4CKBdClAghYgA8BODZJe95FsDD/r/fD+ColFIKIbL9zc4hhNgIX1PyLinlIIBpIcT1/l5SnwXwTBBipTDom5jD5Kwrqm+SwOXB/XNsqKdqjb2+omm0neq0WFpCDD5WloUXW4b4UFexwKx9NK/eA3xNyy1WDu7VrHdi1pcHRPGsPQDUVZpg0Am80Mo8QM0a+6yoKUyN+jxgf3k2XmAeoGoLeUCUtj4JOLzVV+TnSn5tW3chyt/z6WsAXgZwDsCTUso2IcR3hBB3+d/2CIBMIUQHfFvwvuV//UYAzUKIJviamH9ZSjnh/9lXAPwMQAd8K6VeXG+sFB5n+nynOdRGaV+IgIzEGNxQzpl7NZtzetA+PB3131UAOLzVjN6JWe65V7GmPiuKMhOQkRijdCjrwsG9+gUGS9G8eg+4XOTnzL16OVwenB9URx5wqNrMIr/KNfVZUZKViLQEleQBLUNKh0IKCsaKKEgpX5BSbpJSlkop/97/2l9LKZ/1/90hpXxASlkmpdwjpezyv/7fUsoqKWWtlHKHlPK5RddskFJW+6/5NckMIGo09lkRZ9RhizlZ6VDW7fBW38w9K/bq1Dpgg8cro36wBAB1lb7Gui9we55qBRqVR7u0hBjs4wo+VTvTa0W8UY9Npujd6hRweKsZfRNzLPKrVNuADW7V5AEs8qudLw+I7tVQAIv85BOUQhTRYk19VmzNT4VBH/1fr3r/Q/3FVlbs1UgNjcoDMhJjsK80kw91lRqyOTA05VDFYAkA7uAKPlVr6ldTHsAiv5qd8ecB0d5OAmCRX+2GbA4MT82rJg/gSn6K/gyBIorT7UXrwJRqbpJpCTHYW5qJFzm4V6XGPivy0+KRnRyrdChBcajad2rOucFppUOhIFvY6qSCwRJweQXfi5y5Vx2n24u2gamob1QekM4iv6oF8oCc5DilQwkKFvnVqzHQ+kQlYywW+YmFKAqq80NTcLq9qrlJAhzcq1ljn1U1A3sAOFBlgk6Ag3sVauyzwqgXqMxNUTqUoMhIjMHejZlsrKtCgTwg2huVL8Y8QL3UcMrzYizyq9eZQB6Qp448gEV+YiGKgkotDUoXq/cP7l/iQ11VRqfnYbHOYbuKvquZSbG4fmMmnudDXXUa+yZRkZuCOKNe6VCC5tBWMy6N2XF+iIN7NVHb6j3gcpGfM/fqMjYzj/7JOVXlrCzyq1dTnxWVuSmINagnDzi8lUV+LWMhioKqsc+KrKRY5KfFKx1K0GQlxeK6kky8wD5RqrJwBK6KElDA91DvGrXjwvCM0qFQkHi8Ei39NlUNlgDgQJXZt4KPg3tVaez15QF5qerY6gRcLvJz5l5dGlXUH2qxw1tzWeRXGbXmAfWVJm7P0zAWoiioAkuchRBKhxJUh7aa0TEyg4vDfKirRVOfFXqdQHWeOvqYBByoMkMI4Hk+1FWjY2QGdqdHdQkoi/zq1Nivzjzg8NZcdI2xyK8mjSrNAwIr+VnkV49AHqC2yVNfkT+DRX6NYiGKgsY260LXqB3bVNKgdLHA4J6n56lHY58VW8zJiI9RzxJnAMhOjsWe4gwmoCqitgalix1mkV9VAnnAdpWtMAEur+BjkV89Gvus2GxSXx7AIr/6BPIAtU1IAb4efF1jdrQzD9AcFqIoaJotgf5Q6mlQGmBKicOuonQuHVUJr1eiqc+qyoE9ANxRk4uLHNyrRmOfDSlxBpRkJiodStAdqOYKPjVp6vdveS5Q3701OzkWe0pY5FcLr1eiqV9dB5YsFijyX2AeoAqNfVZfHpClwjzAX+R/oYWFU61hIYqCJrDXvkaFK6IAX8X+/NA0Lo3ZlQ6F1qlrzI7pebcqZ5YA4KB/BR8f6urQ6C+a6nTq2uoEADnJcdhdnIEX+V1VhaY+K4RQbx5weCuL/GrRPW7HtMON2gJ1flcDRX5OoKpDY58NtSrc8gxcLvLzu6o9LERR0DT2WVGanYiUOKPSoYTEwWozAPBIXBVoVvGsPQDkpMRhd1EGv6sqMOt0o31oSlWnOy51uNqM9uFpdIyw9060a+q3oSRLxXkAi/yq0WKxAQC25qvz3soiv3rMOT24MDyt2slTwFfk5zZ97WEhioJCSommfptqtzoBQF5aPLYVpvGhrgItFhvijXqUZqtviXPAoa1mnB+aRucoB/fRrG1gCl4J1Ki0aAoAB6tzAQAvsXAa9VotNtTkq3OFCcAiv5q0WmyIMehQbkpSOpSQYZFfHc4OTsHjldiq4nvrQR60o0ksRFFQDE/NY2xmXtUJKODbc99isaFvYlbpUGgdWi02VOalwKBX7y3wkH9wz34m0a253zdrX6PS7SMAYE6Nw86idK4yiXIj0w4MTTmwVcVFU4BFfrVo7rehMjcFRhXnAQeZB6hCa2D1norzgECR/yU22NcU9d59KawCW53UfJMELg/ueaOMXh6vRKtlStUzS4BvcL99QxpebhtWOhRah1aLDaaUWOSkxCkdSkgdqjbj7OAUesbZgy9aLQyWVH5vPVDl26b/chvzgGjl9Uq0DWgjD9hZlM4Tn6Ncc78NWUkxMKs8DzhQ7Svyd7MXr2awEEVB0WqxQSeAylx1P9QLMxJQnZ+CF7gsP2p1jc5gzuVRfQIK+AZMLRYbLNY5pUOhNWrut2rmuwpwcB/NmvttEAKoyktROpSQykuLR21BKov8UezSuB0z825N3FsPVvmK/FzJH71aLTZszU9VZaPyxeorTQCYB2gJC1EUFM0WG8pzkhEfo1c6lJA7VJ2LM71WDNo4uI9Gga1Oal+9Bywa3HM2NCrNzLvRNWZXbTPdxQozElCVl8LVplGs1WJDaXYSEmMNSocScvVVZjT1MQ+IVlrY6hTAIn90m3N6cHFkWhNF08BkP7+r2sFCFK2blNJXrdfAAx3wbSEBwKblUepyo3L1NigNKMlKxGZTMh/qUerswBSkBLYWqHuFScDBKjNO91oxMuVQOhRagxb/rL0WBE7RfYWroqJSc78NsQYdynPUnwdsyEzAFjPzgGh1dtAGrwSqNXJvPVDpywOGmQdoAgtRtG5DUw6MzTg1k4BuzE7i4D6KtVpsqMpLgV6n7iXOAQeqTDjZPYHxmXmlQ6FVCvTe00wCGhjcn+XgPtqMTDkwPDWvme9qaXYSynKSmAdEqRYNHFiy2MFqMxp6JjE6zTwg2rQsHFii/pXRwKIiP/MATdDGHZhCKrDVSSsJKMDBfbTy+BuUauq7Wm2GVwKvneNDPdq0Wmwwp8QhJ1ndDUoDynOSUJKVyMF9FGqxqP90x6UOVJnw/qUJTNqdSodCq+D1SrRpaPUe4NueJ5kHRKVmiw1ZSbEwpcQqHUpYlOUkYWNWIl5hHqAJLETRurVabNDrBCpztbF9BPD1h/BK4PVzI0qHQqvQ6W9UrqXBUmVuCgrS49l7Jwq1WGyaKpoKIVBfZcLxznHYZl1Kh0Or0GLxNSrXUh5wsCoXHq/k4D7KdI3ZYXdq48CSgC3mZGzISGCRPwq1WmyoKVB/o/IAXx5gZh6gESxE0bq1WGwoz0nSRKPygKq8FOSnxfOhHmUCS5y1lIAKIXCgyox3O8Yx7eBDPVpcblSune8q4OsT5fZKHG3n4D6atPRrp1F5QHU+84BopKVG5QFCCBysNuPdjjFMMQ+IGrNONzpGZjQ1IQX4tue5vRKvn2ceoHYsRNG6SCnR0q+tWXvg8sz92x1jmJl3Kx0OrVCLxYaEGD02aqBR+WIHq81werw41j6qdCi0Qm0WG6TU1lYnAKgtSIMpJZYr+KJMi8WGGo3mAW9dHIOdeUDUaO63Ic6oQ5nG8oADVSa4PBJvnOdK/mhxdmAKXqmtyVMAqMlPhTkljnmABrAQResyaHNg3O7U3GAJ8O25d7q9eOsCB/fRokVjjcoDdmxIR1ZSDF7izH3UCPTc0VqRX6cTqK80480Lo5hzepQOh1ZgeMqBkWntNCpfLJAHvMk8IGq0WmyozNVOo/KA7YXpyE6O5UmPUUSLvfcAXx5woMqEty4yD1A7bd2FKei0OlgCgN3FGchIjOGy/Cjh9nhxVmONygP0OoG6SjOOnR+Bw8WHejRosdiQmxqH7GRtNChd7GC1GQ6XF29d5OA+GixsedbYYAm4nAdw5j46eLwSrQPaalQeoNMJ1FWa8EY784Bo0WKxITs5FqYUbRxYstiBKl8ewCK/urEQRevS0q+9RuUBep3A7RU5OHp+BE63V+lw6Bo6R+2Yc2mrQeliB6pMsDs9eLdjTOlQaAW01qh8sT0lGUiNN+JlDu6jQovFBp3GGpUH6HUCdRUmvHF+BPNuDu4j3aWxGcw6PdhakKZ0KIo4WGXGrNODdy4yD4gGLf3aLJoCvjwgLcHIyX6VYyGK1iXQqDzOqJ1G5YvVV5ox7XDjeNe40qHQNWh1iXPAvtIsJMca+FCPAtMOFy5psFF5gFGvw20VOXjt3DBcHhb5I12LRXuNyhc7UG3C9Lwb73UyD4h0gTxAq/fW6zdmIjmOeUA0mHW60Tk6o9nvqkGvw+0VJrzOPEDVWIiiNZNSosWi3Wo9ANxQnoWEGD0f6lGgpd+KhBg9SrK01aA0IMagw60VOXjt3AjcfKhHtLaBKUipza1OAQeqzJhyuPF+14TSodA1aD0P2FeahcQYPV5hHhDxAo3KS7MTlQ5FETEGHW7b4ivyMw+IbFptVL5YIA84wcl+1WIhitZswObAhN2p6cFSnFGPmzdn49Wzw/B6pdLh0FW0WGyozkvVXKPyxQ5UmTFhd+Jk96TSodBVtGp81h4AbizPRrxRj5faBpUOha5ieMqB0el5zecBt2zJwSttw/AwD4horRYbqvJSNdeofLGD1WZMzrrwQTeL/JGsWcO99wL2+yf72YNPvYJyJxZCHBRCtAshOoQQ31rm57FCiCf8P39fCFHsf71OCHFKCNHi/+eti37nmP+ajf4/OcGIlYJnoUGphgdLgG9wPzo9jzN9VqVDoStwe7w4O6jNRuWL3bQpGzEGHVfwRbjmfl+j8qwk7TUqD4iP0eOmTdl4pY1F/kjWzDwAgC8PGLc7caqHRf5I5fFKtFqmNP9dvXFTNmINOp6eF+FaLTbkaLRReUBgsv8VTvar1roLUUIIPYAfATgEoBLAJ4UQlUve9nkAk1LKMgDfB/CP/tfHAByRUm4F8DCA/1rye5+WUm7z/xlZb6wUXC0WK/Q6gQoNNihd7JYtOTDqBZflR7CO0Rk4XF5sLdD2dzUx1oAby7PxStsQpORDPVK1anyrU8CBahNGpufR2M8if6RaaFSep+176y1bchCj13HmPoJ1jc5o+sCSgIQYA27clI2XmQdENK1veQ64PNnPIr8aBWNF1B4AHVLKLimlE8DjAO5e8p67Afzc//enANwmhBBSyjNSygH/620A4oQQ2p0CjjItlilNNyoPSIkz4vqNmXyoR7DLq/e0eVLOYgeqTBiwORaatlJkmXa40KXhRuWL3brFBINO8PS8CNZqsaEsJwkJMdpsVB6QFGvADeVZzAMiGLc6XXagyoxBm2PhfxOKLPZ5NzpGZzS/ih+4PNn/MlfwqVIwClH5APoW/Xu//7Vl3yOldAOwAchc8p77AJyRUs4veu0//Nvy/koIsWxjFyHEF4UQDUKIhtHR0fX8d9AqSCnRarFp9gSypQ5UmdE9PosLwzNKh0LLaLXYkBijx8YsbTYoXez2ChP0OsGZ+wjVapkCAFTz3orUeCP2lrLIH6mklGjut3Gw5HegygSLdQ5tA1NKh0LLaLHYEG/UozRbmweWLHZ7RQ70OsFt+hHq7KDvwBKOsXyT/ftKWeRXq2AUopYrEC39plz1PUKIKvi2631p0c8/7d+yt9//5zPLfbiU8idSyl1Syl3Z2dmrCpzWzmKd8zUqZwIKAKivNEEI8KEeoZr9DUp1Gm5UHpCeGIPrSjL4XY1QbFT+YSzyR67hqXmMzcyjht9VAL4iv455QMTyNSpP0fSBJQFpCTG4fiPzgEjFHrwfdrDajJ7xWZwfmlY6FAqyYBSi+gEULvr3AgADV3qPEMIAIBXAhP/fCwD8BsBnpZSdgV+QUlr8/5wG8Bh8WwApQiwMlgq41QkAclLisL0wjQ/1COT2eHF2YIrL8Rc5UGVG56gdHSN8qEeaFosNeRpvVL5YoMjPFXyRp8XCrU6LZSbFYndxBr+rEcjjlWgb4IElizEPiFwt/kblORpuVL7Y7RWc7FerYBSiTgIoF0KUCCFiADwE4Nkl73kWvmbkAHA/gKNSSimESAPwPIBvSynfDbxZCGEQQmT5/24EcCeA1iDESkHSYrHBoBPYYk5WOpSIcaDKjLaBKfRNzCodCi1ycWQG824vZ5YWqa8yAQBeOcs995GmxcKtTovlpMRhx4Z0JqARqKXf6mtUnsvva8CBKjMujsyge8yudCi0SKe/UTm3Ol1WX2kGAPbeiUAtbH3yIdnJsdi5IZ0nParQugtR/p5PXwPwMoBzAJ6UUrYJIb4jhLjL/7ZHAGQKIToAfB3At/yvfw1AGYC/8veCahRC5ACIBfCyEKIZQCMAC4CfrjdWCp7mfhvKTcmab1S+WH2V76H+Kgf3ESUwa8/B/WW5qfGoKUjlQz3CTDlcuDRmZwK6RH2lCWcHp9A/ySJ/JGmx2FCek4z4GOYBAXWVviI/84DI0sytTh9hTo1DbWEaJ6QizMy8G51sVP4R9VXMA9QoGCuiIKV8QUq5SUpZKqX8e/9rfy2lfNb/d4eU8gEpZZmUco+Ussv/+t9JKROllNsW/RmRUtqllDullDVSyiop5Z9IKT3BiJXWb6FROW+SH1KSlYhNpiTO3EcYNipfXl2FCY19VoxMOZQOhfzaAo3KeW/9EBb5I4+Ukqv3llGYkYCK3BS8cpZ5QCRptdiQEKPHRjYq/5D6ShOa+qwYZh4QMc4O+BqVs2j6YXWVzAPUKCiFKNIWi3UOk7Munuq0jANVZpzsnsD4zPy130xh0dxvQ1U+G5UvVeffnvfqOT7UI0WLxQqACehSJVmJKMtJYgIaQYamHBibcWJrforSoUScukoTTvVMYox5QMRoYaPyZdVzBV/EaeGBJcsqyUpEOfMA1WEhilaNpzlc2YEqM7wSeP3ciNKhEHyNys8NTnH13jI2m5KxISOBD/UI0mKZQn5aPDLZqPwj6ipNeP/SBKyzTqVDISzKA3hgyUfUV5rglcBR5gERwe3xom2Aq/eWU5aThOJM5gGRpKXfClMKG5Uvh3mA+rAQRavGRuVXVpWXgvy0eG7PixALjcq5eu8jhBCoqzThvY5xzMy7lQ6H4Ns+Us0VJsuqrzTB45V4o52D+0jQYrH5G5Xz+7pUIA9g753I0Dlqh8PlZe+9ZQghUF9lxnudY5h2uJQOh+C7t3Kif3n1VWbmASrDQhStWovFhk1sVL6swOD+7Y4x2Dm4V1xg1p4zocurrzTB6fHizfZRpUPRvECjciagy6stSENOcixn7iMEG5Vf2UIecHEUs07mAUpr7ueW56upqzTB5ZF48wLzAKXNzLvRNWbH1nyuNF1OTX4qcpJjedCOirAQRasSaFDKB/qVHagyw+n24i0+1BXXYrEhKdaAkkw2Kl/OzqJ0pCcY8Sob6yqu1cKtTlej0wncXmnCsfZROFw8u0RJgQNLuNL0yuoqTZh3e/H2xTGlQ9G8wIElJVlsVL6cHRvSkZkYw8F9BGiz2HyNygu40nQ5Op2vyP/mBeYBasFCFK1K/+QcrLMuJqBXsbs4HWkJRi7LjwCBBqVsVL48g16H2ypMOHp+BC6PV+lwNK2VDUqvqa7ShFmnB8c7x5UORdMGbYFG5fyuXsmekgykxBm4gi8CNFtsqMpLZaPyK9DrBG6ryMEb7SNwupkHKCnQqJyr+K+MeYC6sBBFq8LTHK7NoNfhti0mvH5umIN7Bbk8XpwdnOJ39RrqKk2YcrjxwaUJpUPRtOZ+G/LT4pGRGKN0KBFrX2kmEmP0eIUr+BTFwdK1GfU63LolB6+fG4abeYBiAgeWcPL06uoqzZh2uPH+JQ7uldRqscGcEoecZDYqv5K9pZlIijUwD1AJFqJoVQKNyjezUflV1VdxcK+0i8MzcLJR+TXdWJ6NOKMOr7DBvqJaueX5mmINety8OQevnRuB1yuVDkezWi026HWCjcqvoa7SjMlZF4cOI6wAACAASURBVE71TCodimZ1jM7A4fLy3noN+8uzEG/UcwWfwpotPN3xWmINety0ORuvnmUeoAYsRNGqtFps2Gxmo/JrCQzueXqeclosbFC6EvExetxQlo1Xzw5DSj7UlWCbc6F7fJZF0xWoqzRhdHoejf4GxBR+zf02lOcksVH5Ndy0ORsxeh236SuomQeWrEicUY/95VnMAxQ0M+/GpTE7T3dcgfpKE8Zm5nGmj3lAtGMhilZMSonmfs7ar0R8jB43lmfjlTY+1JUSaFRezEbl11RfZcKAzYG2gSmlQ9GkNm51WrFbNufAoBNsrKuQhUbl/K5eU1KsAfvKMjm4V1CgUfnGLOYB11JfZcagzYFWC/MAJSw0Kue99Zpu9ucBXMEX/ViIohXrn5yDbc7FwdIK1VeZMTTlWOinQeHVYplCdT4bla/EbVtyoBPgzL1C2Htv5VITjLhuYwZPelTIgM2BcbuTq/dWqL7SjN6JWbQPTysdiiY199tQlZ/KPGAFbvXnAby3KoO991YuNd6IvaWZ7BOlAixE0YoFbpJcNroyC4N7ztyHnSvQoJQP9BXJTIrFrqIMzi4ppNnCRuWrUV9pRueoHZ2jM0qHojkt3Oq0KrdX5AAAXmUeEHaBPKCG39UVyUiMwe7iDE5IKaTFYkNuahyyk2OVDiUq1FWa0DVqR8cI84BoxkIUrVhzvw1GPRuVr1R6Ygz2lGSwYq+AC8PTcLq9HCytQl2lCecGp9A3Mat0KJrDrU6rc3ulCQBYOFUAG5WvTk5KHLZvSOPgXgEXh2cwzwNLVqWu0oTzQ9PoHWceEG4tbFS+KrdXMA9QAxaiaMUCjcpjDWxQulL1lWZcGJ7BpTG70qFoSuvC6r00hSOJHnUc3CvCNutCDxuVr0p+Wjyq8lL4XVVAs8XXqJwHlqxcXaUJLRYbBm1zSoeiKa3c8rxq9ZVmAOAEaphNO1zoGrXzu7oKeWnx2Jqfyq2kUY6FKFoRKSVaOGu/apcH97xRhlNzvw3JsQYUZSQoHUrUKM5KxCZTEhPQMGsd4GBpLeorzTjdO4nR6XmlQ9EMNipfm8Dg/jUWTsOKB5as3obMBGwxJ7PIH2aBg2I4IbU6dZUmnOmzYmTaoXQotEYsRNGK9E2wUflaFGYkoDI3hX2iwqzVv8SZDUpXp67ShJPdk7DOOpUORTPYqHxt6ipNkBJ4/RzvreEyYHNgwu5kn8hVKstJwsasRG7PC7Nmiw1VeTywZLV8ecAEJuzMA8Il0HuPecDq1FcF8oARpUOhNWIhilZkoVF5Prc6rVZ9lQmnOHMfNk63F+eGpjmztAb1lWZ4vBJHz/OhHi4tFhsK0uORzkblq1KRm4yC9HgO7sOopd8KgI3K16KuyoTjneOwzbmUDkUTFhqVMw9YtfpKM7wSzAPCKNCoPCuJjcpXY7MpGYUZ8XiljSv5w+Wl1sGgXo+FKFqRZosVRr3AJnOS0qFEnQNVZs7chxEbla/d1vxUmFJiuYIvjFr6udVpLYQQqKs04Z2OMdjn3UqHowkt/kblFWxUvmr1lSa4vRLH2jm4DwfmAWtXnZ+C3NQ4tpQII255XhshBOorzXi3cxwzzAPC4nSvNajXYyGKVoSNytdui9lXsX+ZFfuwWGhUzof6qul0vsH9WxdH4XB5lA5H9WyzLvROsFH5WtVXmuF0e/H2xVGlQ9GEFssUNpmS2ah8DbYVpiMrKZa9d8KEB5asXaDI/9aFMeYBYTDlcKFrjI3K16qu0gSn24u3LjAPCIfANtJgYSGKrklK6Z+15wN9LRYq9h2s2IdDs8WG5DgDijLZqHwt6irNmHV68G7HmNKhqB4bla/P7uJ0pCUYuYIvDHx5gBVb87kaai30OoHbK3JwrH0U824O7kONB5asT12lCXMuD965yDwg1Nosvkbl1ZyQWpNdRelITzCyyB8GUsqFvDVYWIiia+qdmMWUw83B0jrUV5rg9HjxZjsr9qHWarGhOi8VQrBB6Vrs3ZiJ5FgDH+ph0OyfWarO4711LQx6HW7dnIPXz4/A7fEqHY6qWaxzmJx1MQ9Yh/oqE2bm3TjRNaF0KKrXarGhKp+NytfqupJMJMcZeIpuGLTywJJ1Meh1uHWLCUfPj8DFPCCkesZnMe0I7oIKFqLomniq0/rtLEpHRmIMH+oh5nR7cX5wmg1K1yHGoMNNm7Px2rlheLxS6XBUrdViQ2EGG5WvR32VCbY5Fz7o5uA+lBZOdeJWpzXbV5qFhBg9e++EWODAEm7LW7sYgw63bM7B6+dGmAeEWLPFhjw2Kl+XQB5w8hLzgFAK1AOCiYUouqYWiw0xeh0bla+DQa/DbVtycPT8CJxuVuxD5cLwNJweNihdr/oqM8ZmnGjsm1Q6FFVrtlhZ4F+n/eXZiDHouIIvxFosNhh0AlvMyUqHErXijHrctCkbr54dhpeD+5Bho/LgqK8yYdzuxOle5gGh1Gqx8bu6TvvLsxBr0PEU3RBr9dcDgomFKLqmln42Kg+G+iozph1uvH9pXOlQVIur94Lj5s3ZMOoFH+ohZJ11om9ijgnoOiXGGrC/LOv/Z+/Oo9u87jvhfy92gjtBEuC+SyRAUbtkbd4kQlIsW3YW23kzibK4mU77Nt0y7yRn5p3MSdoz6TJt33ZmOknTJG7TJI4dx3ZsS9Zqy5ZkbZS4SCRFUtxAcQcB7gQB3PcPANRiSiKJB3i23+ccHokUCFydg4Pnd3/Pvd+LY9cHwTlN7mOlsc9LQeUCqLVbMTg+F5M7yySEDiwRxmOrQnUANfljZ3x2Hp0jU7SKP0pmgw67KrKoDoixxj4vKnOEvRlFjSjyQJxzNFK3XhC7KjKRoNdSsG4MNVJQuSBSTHo8UmrBMXqvxkxTOKC0hg6BiFqt3QrX2Aya+yfEHooiReoAavBH78nKbGg1jLbpxxAdWCKMZJMe28oycfTaAE3uYyTSNKU5VvScdiv6PDO43j8u9lAUiXMek9V71IgiDxQJJqNuffRoWX7shU53pKByITjtVtwcmUL70KTYQ1Gkhj4PAKCaTiGL2u4qKxgD3bmPEdfYDDzT83SqkwDSzAZsKc6g92oMNfVRHSAUp92KrtFpqgNihILKhbO7KhsaBrrZHyORg8uEPlyHGlHkgWirk7CcDisGxmdpWX4MzPkDaBkYxxqaLAlij90KAHTnPkYiQeVpZgoqj1ZWshEbCtPpvRojtNVJWLV2K24MTqJrZErsoShO5MASqlmFUbtQB9DkPhYa+8aRl5YACwWVR82SZMTGonRq8sdIrPoBgjSiGGP7GGOtjLF2xti3Fvl3I2PslfC/n2eMFd/xb98O/7yVMbZ3qc9J4iMSTLbKSgGlQogsy3/vGk2YhHZjYBLzAU4FqEByUhNQk59KF/UYaezz0rY8AdXarbh2axx9nhmxh6I4DeGg8tUUVC6IyOSePluFRweWCMuaYsLagjRqRMVIo8tDq6IF5LTbcL1/HL3uabGHojiNfV7otUzwg8uibkQxxrQA/heA/QDsAD7PGLPf87CvARjjnJcD+FsAfxH+XTuAFwE4AOwD8L8ZY9olPieJgwZXKJjMoKPFc0JIMxuwtSSDLuoxQKv3hFdbZcWVHg+GxmfFHoqijE1RULnQnOHJ/XH6bBVcEwWVC6ogw4yqnBRqRMVApA6gOAnhOO1W1Pd6MEh1gKC8M/PoGp1GTT7dkBJKpMl/vJk+W4XW1Bebg8uE6C5sAdDOOb/JOfcB+CWAg/c85iCAl8N/fw3AbhbavH0QwC8553Oc804A7eHnW8pzfkLXKC1zFhLnHE23KKhcaE67Fe1Dk+gYpj33Qmrs8yLFpENhBgWUCsXpsAEAjjcPiTwSZWm6RU1ToZVmJaEsK5G25wksElROE3thOe1WXOp2Y3RyTuyhKEqDi+oAoTlpBV9MXKOgcsEVZyaiIjuJcqIEFgoqH49JzSpEIyoPQO8d37vCP1v0MZxzPwAvAMsDfncpzwkAYIx9nTF2iTF2aWLWD+/0fBT/FXKnSFA5TZaEVRue3NNFXViNfR6syaeAUiGtsiahMMOMYzS5FxSt3osNp8OG8zfdVAcIaCGonN6rgqq1WxHkwIkWavILqanPS3WAwMqzk1BsMVPNKjCqA2LD6bDiQpcbnmmf2ENRjF73DLwzsakDhGhELfZpf++RYPd7zHJ//skfcv5DzvkmzvkmADjVShd1oTTQh2RM5KUloDovBUcpJ0owc/4AWgcmaLIkMMYYnHYrzrSPYnLOL/ZwFKPR5UVhhhmpZr3YQ1GUWrsV/iCnOkBANFmKDUduCvLSEujOvYAiB5ZQHSAsxhicDhvOdoxgYpaa/EJp7PMiLy0BGYl0YImQau02BIIcJ6nJL5hY1gFCNKJcAAru+D4fwK37PYYxpgOQCsD9gN9dynN+gk7DaFm+gCioPHacdhuu9FL2jlAiQeUU/iy8WrsVvkAQp28Miz0UxWgMHy9OhLUuPw1ZyUa6cy+gBlcooLQyh+oAITHGUGu34qP2Ycz4AmIPRxHowJLYqbVbMR/g+IDqAMFQHRAbNXmpsKZQHSCkSFB5LA4sEaIRdRFABWOshDFmQCh8/K17HvMWgEPhv38WwEnOOQ///MXwqXolACoAXFjic35CSoIe77cOY3aeLupCaKSg8pjZ67CBc8reEUpDnwcA3bWPhY1F6chINNAKPoGMTfngGqOg8ljQaBj2VFnxfusQ5vxUBwghElQudEApCWXvzM4HcbqNJvdCoDogdjYUpsOSaKDJvUC8M/PoHp3GGsreE1ykDvjgBvUDhBLLOiDqDkM48+n/BvAegGYAv+KcX2OMfZcx9kz4Yf8MwMIYawfwJwC+Ff7dawB+BeA6gCMAfp9zHrjfcz5sLCkmPaZ9AZztGIn2v6V6wSAP7bWnC3pMrLImochiphV8Amnq8yI1QY+CjASxh6I4Oq0GT1Zm42TLEOYDQbGHI3t0qlNsOe1WTPkCONsxKvZQZC8SVE51QGxsLslAiklH2/MEEqkDKKhceFoNw+4qqgOEco22PMeU02HDtC+AM+3UD4hWrOsAQZa6cM7f5Zyv4pyXcc7/PPyz/8o5fyv891nO+ec45+Wc8y2c85t3/O6fh39vNef88IOe82GSjDokGemiLoRu9zQm5iioPFYi2Ttn20dpz70AIh+SFFAaG067FeOzflzodIs9FNmLNKKqc+mzNRa2lVmQaNDSnXsBRAJK6a59bOi1GuyusuJkyyD8NLmPWmOfF9V5KVQHxEit3YaJWT8+vklN/mhRBm9sbSu1INmoozpAAK6x2AWVAwI1oqSCMeDx1Vk43jyIQHDRbHOyRI10rGjMOR02+AJBvN9Ky/KjQUHlsberIgsmvYYu6gJo6qOg8lgy6bV4bHUWjl0fRJDqgKhQUHnsOe1WjE3P43L3mNhDkTWqA2JvV0UmEvTU5BdCJKg8nYLKY8Kg0+DxymzqBwgg1qv4FdWIAkKT+5FJH6720kU9GhRUHnuRPfdH6aIeldaBCQoojbEEgxaPVmTh6LUBhOL9yErRVqfYc9ptGJ6YQ73LI/ZQZC2WAaUk5NFVWTDoNFQHRIkOLIk9k16LR1dl4ui1QaoDotTU56Xt+TFWa7dSP0AAsa4DFNeIenx1FvRaRtvzokRB5bGnDQfqnWqhYN1oNLgocycenA4bbnlnce3WuNhDka1IUDltdYqtJ1Znh0/RpTogGo19Hgoqj7FEow67yjNx9Do1+aNBQeXx4bTbMDA+u7BKgiyfdzoUVE6r92KL+gHCaHTF9sASxXUZUkx6bCvLxHt0537FKKg8fpwOKybn/Pj4JmXvrFQkoDQ/nYLKY+nJymxoGOj0vCjQVqf4SDXr8Uiphd6rUeCco6lvnBr8cVBrt6LXPYOWgQmxhyJbdGBJfDxZmQ2thib30Wi6RXVAPFA/IHrxOLBEcY0oIHRR7xqdRvvQpNhDkSUKKo+fHeWZMBu0NGGKAgWVx0dGogGbizNolUkUKKg8fpwOKzqGp6gOWKFIUDndtY+93VVWMAaa3EeBgsrjIz3RgC3FGXTicxTohlT8OKkfEJVYB5UDSm1EVVkBgCZMK0RB5fFj0mvx2CoK1l2pOX8ANwYnaKtTnDgdNrQMTKB7dErsocgSBZXHz55wHUDBuiuzEFBKmTsxl5VsxMbCdJrcrxAFlceX02HFjcFJdI5QHbASjX1e5KdTUHk81NqpHxCNWAeVAwptRNlSTVhbkEZvvBWioPL42uuwYYiCdVeEgsrjy2mnyX00KKg8fnLTElCTn0qT+xVq6PNAr2VYZUsSeyiq4HRYce3WOFxj02IPRXYoqDy+ahfqAPpsXYlGF9UB8WJNMWFdQRrtOlmheBxYoshGFBCaMNX3ejDgnRV7KLJDQeXxRcG6KxcJKqeLenwUZJhRlZNCW0hWgILK489pt+JKjwdD41QHLFdTnxerbRRUHi+1dhsAavKvBAWVx1d+uhmOXKoDVsI7PY8eNwWVx5PTYUW9y4t+74zYQ5GdWAeVAwpuRO11hDv2zfRBuRzBIEfTLerWxxMF664cBZXHn9NuxaVuN0Ym58QeiqxQLkT8OR3hyT3VAcsSCSqn92r8lGQmYpU1iSb3K0BB5fHntNtwuWeM6oBligSV0yEQ8eMMN/mPU5N/WeIRVA4ouBFVlpWE0sxEmtwvU7d7GhOzFFQebxSsuzKNfV7U5FNQeTw5HVYEOXCyeUjsocgKBZXHX0V2EoosZprcL1MkqHwNbXWKK6fdhgtdboxN+cQeiqxQUHn8OR1WcA6coCb/slAdEH/l2UkozUqkXSfLFI+gckDBjSjGGGrtVnx8cxTjs/NiD0c2KKhcHHsWAvapcbpUs/OhoHJ6r8aXPScFeWkJ9F5dJgoqjz/GGJx2K852jGCC6oAlo61O4nA6rAgEOU62UJN/qSioXByVtmQUZCRQk3+ZGl0UVC6GWrsV5zpG4Z2hOmCp4hFUDii4EQWELurzAY73W4fFHopsUFC5OBaCdemivmQUVC4OxhicDis+bBvBtM8v9nBkg4LKxeF02KgOWKZIQCkFlcfXmrxU2FJMlBO1DBRULo5Qk9+GD9tHMDVHdcBSUR0gDqfdBn+Q4/1WavIvVTyCygGFN6LWFaQjM8lI2/OWgYLKxeO0W3G114NBCtZdEsrcEY/TbsOcP4jTN0bEHoosUFC5eDYUpsOSaKBl+ctAQeXiiKzk/+DGMGbnA2IPRxaoDhBPrd0Knz+I0zeoyb8UkaByqgPib31BWqgfQHXAksUjqBxQeCNKq2GotWfj/dZhzPnpov4wFFQuroVgXfqgXJKmPi/SzBRULobNxelIM+tpe94SRQJK6bM1/rQahj1VVpxqGaI6YAk45+HjxWmFiRicDitm5gP4qI2a/EvR2OehoHKRbCpKR7pZT5P7JaI6QDwaTajJ/z7VAUsSr6ByQOGNKCB0535yzo9zHaNiD0XyKKhcXBXZSSjJpEC9pYp8SFJAafzptBo8WZmNE81D8AeCYg9H8hpcFFAqJqfDisk5Pz6+6RZ7KJLX457GONUBotlaYkGySUdN/iWioHLx6LQa7K6y4kTzIOapDngoqgPE5XRYMeUL4Cz1Ax4qXkHlgAoaUdvKLDAbtDS5XwIKKhdXJFj3XMcIBew/xOw8BZSKzWm3wTszjwtdNLl/GAoqF9eO8sxQHUDb9B+KtjqJy6ALNfmPNw8hEORiD0fSKKhcfE67FeOzflzopDrgYZr6KKhcTNvLLEg0aCmLdwniFVQOqKARZdJr8fjqLBy7PoggXdQfiILKxUcB+0vTOjABf5CCysX06KpMGHUauqgvAQWUisuk1+KxVVQHLAUFlYvPabfBPeXD5e4xsYciaRRULr5dFVkw6TXU5F+Cxj5vXCb2ZHFGnRaPV2ZTHbAE8QoqB1TQiAJCF/XhiTnUuzxiD0XSKKhcfBSwvzR01158ZoMOuypCk3vO6aJ+PxRULg1OhxVDVAc8VFOfF5W2FAoqF9Fjq7Ng0NLk/mGoDhBfgkGLRyuycJTqgAeKBJXT6j1xOe1WjEzO4Uov1QEPEq+gckAljagnVmdDp2G0Pe8BOKegcimggP2loaByaXA6rOjzzODarXGxhyJZFFAqDU+utkJLdcADRYLKabIkriSjDjvKLTS5fwgKKpcGp8OGfu8smvqoDrgfappKwxOV2dBrGWXwPUA8g8oBlTSiUs16PFJqobtLD9A9SkHlUhEJ2KdAvftrcFFQuRTsrsyGhoEm9w9AAaXSEKoDMqgOeAAKKpcOp8OGHvc0WgcnxB6KZFFQuTTcrgPos/V+FjJ4qQ4QVYop0g+gJv/9RILK47WKXxWNKACotVvRMTyF9qFJsYciSQ0UVC4Z2yhQ74Fm5wO4MUgBpVJgSTJiUzFN7h+Egsqlw2m3UR3wAHTXXjp2V2WDMVAdcB8UVC4d6YkGbCnJoPfqAzT1eVGQQUHlUuC0W9E5MoWOYaoDFhPvOkBVjSgAOEZ37hdFQeXSEQrYp0C9+4kElddQASoJTrsVLQMT6BmdFnsokkRB5dJBdcCDNUbqAAoqF112sgkbCtNplcl9UFC5tDjtNrQOTqBrZErsoUgS1QHSsSdcB9BK/sXFM6gcUFEjKjctAWvyUumifh8UVC4tTgcF6t1PI63ekxSn3QaAluUvhoLKpYXqgAdr6vNitS0+AaXk4WrtVjT1jeOWZ0bsoUgOrd6TFmry359n2kdB5RKSk5qAtfmptILvPpr64hdUDqioEQWE7txf7fVgaHxW7KFICgWVSw8F6t0fBZVLS6HFjEpbMt1dWgQFlUuP027FlR6qA+5FQeXS46TJ/X1RULm0FGSYYc9JoZp1EZEQd6oDpMPpsOFqrweDVAfchXO+kMEbL+pqRDls4Bw43jwk9lAkhYLKpYcC9e6Pgsqlx2m34lKXG+4pn9hDkRQKKpcepyO0gu9YM03u70RB5dJTmpWE8uwkmtwvgoLKpcfpsOJS9xhGJufEHoqk0Oo96aEm/+LiHVQOqKwRtcqahCKLmS7q96CtTtLkdNgoUO8ekaByuqBLi9NhQ5ADJ2hyfxcKKpeehTqAluXfJVIH1NA2Uklx2q34+KYb3ul5sYciGRRULk1Oe+hmP9UBd4sElaeZKahcKsqzk1CSmUgr+e8hRtM0qkYUYyyDMXaMMdYW/jP9Po87FH5MG2PsUPhnZsbYO4yxFsbYNcbY9+94/JcZY8OMsavhr5eiGecdz4vaKivOto9iYpYu6hGNFFQuSbVVoY79ezRhWhAJKqdGlLQ4clOQm2qii/o9KKBUehhjcNqtONsxQnXAHagOkCanw4ZAkONkK322RlBQuTRV5SQjPz2Bmvz3aOjzUB0gMZE64FzHCMapDlgQ76ByIPoVUd8CcIJzXgHgRPj7uzDGMgB8B8BWAFsAfOeOhtVfc84rAawHsIMxtv+OX32Fc74u/PWjKMe5wOmwwRcI4oMbw0I9pexRULk02VJNWFuQRpP7O9DqPWlijMHpsOHDtmHM+AJiD0cSKKhcupwOG+YDHO+3Uh0Q0egKBZVTHSAtNXmpsKYYaXJ/B9rqJE2hyb0NH7aPYGrOL/ZwJMEz7UOve4ZqVglyOqxUB9wj3kHlQPSNqIMAXg7//WUAzy7ymL0AjnHO3ZzzMQDHAOzjnE9zzk8BAOfcB6AOQH6U43mojUXpyEg00EU9jILKpc1pt6K+14MBLwXqAaHJEgWVS5PTbsXsfBCn2+iiDlBQuZRtKEyHJdFATf4wzjma+iioXIo0GoZauxUf3BjG7Dw1+YFQI4qCyqXJ6bDC5w/iNN3sB3A7qJxW70nPuoJ0ZCYZcfQaxfUA4gSVA9E3oqyc834ACP+Zvchj8gD03vG9K/yzBYyxNABPI7SqKuIzjLEGxthrjLGC+w2AMfZ1xtglxtil4eGHf/BpNQx7qrJxqnUIPn/woY9XOgoql7a9jkigHn1QAre3OlFAqfRsLslAaoKemvxhC6v3KKhcckJ1gBWnWoYw56fJfSSonPKhpMlpt2HaF8CZ9hGxhyIJjX0eCiqXqE1F6Ugz66nJH3Z7FX+KyCMh94r0A95vHaY6AOIElQNLaEQxxo4zxpoW+Tq4xNdY7EqxcAwYY0wH4BcA/p5zfjP8498CKOac1wA4jturrj75RJz/kHO+iXO+KSsra0kDctptmJj143zn6BL/C8pFW52krTw7GaVZFKgHUFC51Om1GuyuzMaJlkH4A9Tkb3RRULmUOR1WTM758fFNt9hDER1tdZK2R0otSDbqqMkPCiqXOp1Wg92VVpxoHsQ81QFo7PNQULmEReqAcx3UDxCrDnhoI4pzvodzXr3I15sABhljOQAQ/nNokadwAbhzRVM+gFt3fP9DAG2c87+74zVHOeeR8z//CcDG5f23HmxnRSYS9Fq6qIMCSuXAabfhXMcovDPqDtSjoHLpczqs8EzP42LXmNhDER0FlUvbjvJMmA1aWpaPUNOU6gDpMug0eLwyG8ebBxEI8of/goJRULn0OR1WjM/6caGTmvxUB0jb9rJQHXCMbvaLElQORL817y0Ah8J/PwTgzUUe8x4AJ2MsPRxS7gz/DIyxPwOQCuCP7vyFSHMr7BkAzVGO8y4mvRaPrsrEseuDCKr8ok5B5dLndFjhD3K837pYn1c9Gmj1nuQ9uioLRp0GR1W+lZSCyqXPpNfisVVZVAcgVIBSULm0Oe1WjE75UNej7iY/rd6TvkcrsmDSa1Q/uY8Ela+hpqlkmfRaPL6a6gBAnKByIPpG1PcB1DLG2gDUhr8HY2wTY+xHAMA5dwP4HoCL4a/vcs7djLF8AP8ZgB1AHWPsKmPspfDzfoMxdo0xVg/gGwC+HOU4P8Fpt2FgfHbhoqZGFFQuD+vy05CVTKfmNLm8SKegckkzG3TYWZ6Jo9cGwbl6L+oUVC4PTocVQxNzqHd5xB6KaCJBGVInxQAAIABJREFU5dQ0lbbHV2dBr2Wqn9xTULn0JRi02FWRhaPXBtRdB4SDyqkOkDan3UZ1gEhB5UCUjajwFrrdnPOK8J/u8M8vcc5fuuNxP+acl4e/fhL+mYtzzjjnVZzzdeGvSPPq25xzB+d8Lef8Cc55SzTjXMyTldnQapiq79xTULk8RE7Neb91SNWn5jSGT3WigFJpczqs6PPM4Hr/uNhDEQ0FlcvDk6ut4TpAvZP7SFA51QHSlmzSY3tZJt5T+eSegsrlwWm34pZ3FtduqbcOaOgLNTYoqFzanlidDZ3K6wCxgsqB6FdEyVZ6ogFbijNUfXeJgsrlw2m3YsoXUG2gHgWVy8fuKisYg6pX8FFQuTykmvV4pDRD1TlRtNVJPpwOK7pHp9E2NCn2UERBQeXysbvKCg2Dqj9bm/pCdQAFlUtbqA6wqPq9KmYdoNpGFBC6qN8YnETnyJTYQxFFEwWVy8a2MguSjDrVruBroaBy2chMMmJTUbrqm/z0XpUHp92GjuEptKt0ck9B5fJRW2UFoN7JPQWVy0dGogGbizNUvcqE6gD5cDqs6q4DRAoqB1TeiKq1q/ui3kBB5bJh1N0O1FPjqTkL3XrKMZEFp92G6/3j6BmdFnsocUdB5fISqQPU2jht7KM6QC6yU0xYX5iGIyqtWWn1nrw4HTa0DEyge1R9N/sjQeW0ek8eInXAeyr9bBUrqBxQeSMqP92M6rwUHG5S3xuPgsrlx+mwYWTShysqPDUnElSel0YBpXKwr9oGQJ0XdQoql5fctASsyUtV5Xs1ElROkyX52OewoalvHL1u9TX5KahcXpwqntxT01ReclITsLYgTZXvVTGDygGVN6IAYH91Dq72etDvnRF7KHFFQeXy80T41Bw1LnWmoHJ5Kcgww5GbgsNN/WIPJe4oqFx+9lXbVFkHUFC5/OyvzgGg1sk9BZXLSUGGem/2UyNKfvZX29Dg8sI1pq4mv5hB5QA1om7fuVfZB2UDbXWSHbWemkNB5fK0v9qGuh4PBryzYg8lrhpdXhRZKKhcTvaH64AjaqsDXDRZkptCixn2HPVN7imoXJ72V+fgSo/6mvyRoHKqA+Rjn0OddYDYTVPVN6LKspJQkZ2kuot6Q68HRh0FlMqNGk/NoaByeYo0+dUWsF/f60FNPoXpyklpVhJWWdVXB9CBJfK0r9qGy91jGBpXT5O/pX8C8wGOdfTZKit7Heq82U9B5fJTnJmISluy6lab1rs8MGg1qLSliPL6qm9EAaG7oRe73BiZnBN7KHFT7/LAkZsCvZbeAnKixlNzGlweAMDaAipA5aQ8Oxnl2Uk43Kie9+rwxBxueWexllaays6+6hxc7HJjeEJddUAVBZXLzn4VZvDVh+uAGqoDZKU8W303+91ToaBy2nEiP/urc3CpewxDE+pp8tf3ilsHUPWBUAEa5Oo5NccfCKKpb5zu2stQ5NQcNeVEXe31IDPJiJxUk9hDIcu0v9qG852jGFVJkz/SNKXPVvnZX20D5+pZwRcIcjT1jVODX4YqrMkoy0pU1eS+vteLzCQDcqkOkB213eyPNE3XUh0gO/vCdcB719QxxwqG6wAxa1ZqRAGoyklGYYZZNRf19uFJzMwHsLaAuvVy5LSHAvVuedSx577B5cXafAoql6O9Dpuqmvz1Li80DKjOE2eJM1m5Slsyii1m1eRD3ByexOScn5qmMrWv2obznW64p3xiDyUuGlyhLc9UB8iP2m72N/R6wRhl8MrRKmsSSjMTVbOV9OZIpA4Q771KjSgAjDHsr7bhbPsIvNPzYg8n5hp6Q8FkVIDKk9MR2p53vFn5F/XJOT86hifpvSpTjtwUFGQk4IhKtpA0uDyoyE6G2aATeyhkmRhj2Fedg3Mdo6qoA+rDQeW0jVSe9lfnIBDkOK6Cyf3knB/tw5OiTpbIylXlJKPIop6b/Q0uD8qykpBkpDpAbkJ1gA3nbo5iTAVN/vpwP0DMldHUiArbV22DP8hxokX5F/V6lwfJRh1KLIliD4WsQFlWEsqyElWRD9Ho8oJzoIZW78lSqMmfgzPtI/DOKHtyzzlHg8tLkyUZ2x+uA46poMnf4PIg0aBFaVaS2EMhK+DITUF+egION/WLPZSYa+oL1QG01UmeGGPY51DHzX7OOepdHnqvyti+ahsCKqoDzAYtykSsA6gRFbY2Pw22FJMqOvYNLi/W5KdCo6ElznK112HDxzfdir+o0157+dvrsGE+wHFS4U1+19gM3FM+CtOVsZr8VOSmmnBEBZP7+l4P1uSnQkt1gCxFJvcftY9gfFbZdcDt7D1q8stV5Ga/0lfy3/LOYmTSR9EnMrYmLxV5aQmq2J5X7/KiOk/cOoAaUWEaTWg53ukbw5ia84s9nJiZ8wfQMkBB5XLndIQ69idblX1Rb3B5UJCRgIxEg9hDISu0viAN1hSj4rN3Gmirk+wxxrC32obTbSOYVHAd4PMH0dw/QQ1+mdu/JtTkP9UyJPZQYqre5UVeWgIsSUaxh0JWaG1+GnJSlX+zv6GXDiyRu8j2vA/bRjCh4Ca/zx/E9f5x0WtWakTdYV+1DXP+IE61Kvei3tw/gfkAF/2NR6JTk5cKa4oRRxV+skN9r5cu6DKn0YTu3H9wYxjTPuVO7htcHhi0GlTaKKhczvZX58DnD+Kkgif3LQPj8AWC9Nkqc+sL0pGdbMThRoVP7l0eWmEicxoNw16HDafblH2z/6rLA72WoSonWeyhkCjsq7bBF1B2HdA6MAGfX/w6gBpRd9hcnAFLokHRd+4XljjT9hFZ02gYau1WfHBjGLPzAbGHExMjk3Po88xQ01QB9lbbMDsfxPutw2IPJWbqXR5U5STDoKPLqpxtLEpHZpJR0cvy63tpq5MSRCb3798YUmyTf3RyDr3uGdEnSyR6+6tt8Cn8Zn9DrxdVOSkw6rRiD4VEYWNhOrKSjYrO4o1En6wTuR9AFfMdtBoGp8OKUy1Dip3c1/d6kZlkQG6qSeyhkCg57TZM+wI40z4i9lBiooHyoRRjS3EGMhTc5A8GOZr6aMuzEmg1DHsdVpxqVXAd4PLCkmhAfnqC2EMhUdofbvKfvqHMJn9DX+SUZ2qayt2m4gxkJhkUuz0vVAfQgSVKoInUAS3DmPEpsw5ocHmQbtaLXgdQI+oe+6pzMOUL4MM25U7ua/LTwBgFlMrdI6UWJJt0ir2o1/d6oWFAdR5d1OVOp9XAabfiZMsQ5vzKu6jfHJnE5JyfClCF2F+dg2lfAB8odXLv8qAmP5XqAAXYUpKBdLNesXVAQ68XjIUChIm8aTUMtXabYm/23xyZwsScn25IKcQ+Rw5m5pVcB3gl0Q+gRtQ9tpVakGLSKfLO/eScH+3DkzRZUgiDToNauxVHrw3A5w+KPRzBNbg8KM9OQqJRJ/ZQiAD2VtswOefHRwps8l/tDQeV05ZnRdhamoHUBL1i64C2oUmaLCmEThuqA042K7PJ3+DyoCwrCckmvdhDIQLYXx1aya/EFXyRLc9ib3UiwthamoE0s16R2/OmfX7cGJyQRPQJNaLuYdBpsKfKiuPNg5gPKGty39TnBee01UlJnlqTg/FZP850KGtyzzlHvYuCypVkR1mmYlfwNbg8MBu0KMtKEnsoRAD68OT+ePOg4pr8C3UAhT8rxv7qHEzM+XG2fVTsoQjqdh1A71Wl2Fam3Jv9VAcoi157ux+gtDrg2q1xBLk0TnekRtQi9lXb4J2Zx7kOZV3UF4LK6aKuGDsrQpP7dxr6xR6KoFxjM3BP+WiFiYIouclf7/KiOi8VWg1tdVKK/dU2TCiwyX+7DqDPVqXYXm5BslGHw03KqgP6vbMYmZyjm6cKotdqsEehTX6qA5RHqXXAwoElErghRY2oRTy6Kgtmg1Zxd+7re73IS0uAJcko9lCIQIw6rSK35zW4wludqGmqKPuqbfBMz+Pjm8pp8vv8QTTfGqf3qsLsrMhEklGnuNPz6l2hOiCT6gDFMOq0eLIqG0evK6vJTzdPlWl/dWgl/zmF1QHXqQ5QnEgdcLhRWU3+epcXOakmZCeLf3AZNaIWYdJr8WRlNt67NgC/gi7q9S4PLcdXoAM1ytue1+DywKDVoNKWIvZQiIAeW5WFRINWUSv4Wgcm4AsEaYWJwhh1Cq0DeqkOUKKn1uTAMz2PswpayV/v8kKnYajKoTpASXZVZCLRoMW7CqwDaBW/skRu9r93TVkr+CIHlkgBNaLu40BNLtxTPsVc1N1TPrjGZmiypEA7y7MUtz3vaq8HVTnJMOjoI0pJTHot9titOHJtQDF37uvDd+1p+4jyPFWTgzEFTe5HJ+fgGpuh96oCPboqC8lGHd6uvyX2UATT4PKgMicZJr1W7KEQAUXqgPeuUx1ApO+pNTnwzszjTLsybvZ7pn3oHp2WTD+AZnn38fjqLCQZdXi7QRkX9ch+UPqQVB6lnZ4XCHI09XnpzpJCHajJhWdaORf1+l4P0s16FGQkiD0UIrDHVoXqAKU0+Rv6QluepVKAEuGY9JE798qoA4JBjoZeOrBEqSJ1wEcKqwPy06kOUJpdq0JZvG8rpQ5YiD6RxmcrNaLu4/ZFXRnL8ep6xqBhdFKOUi1sz1PARb1jeBJTvgAVoAr16KrM0J17hVzUr/R6sL4wHYxRQKnSROqAIwqZ3Nf3esAYUJ1HW52U6MDaUB3wUfuw2EOJWsfwJCbm/FhPN6QUKVIHKKbJHz7lmeoA5THqtHDabTh6fQBz/oDYw4nalZ5QHSCVfgA1oh5AScvxrvR4UGlLgdmgE3soJAYWtucpIFDvSs8YAGB9IRWgSmTUaVHrCN25l/tF3Ts9j/ahSWyg96piHahRVh2wKjsZySa92EMhMbCzPAspJh3erpd/HVAXrgM2FKWLPBISC0qqAyZm53FjaALrqGmqWAfW5mBi1o8Pb8i/DqjrGZNUHRBVI4oxlsEYO8YYawv/uegVgzF2KPyYNsbYoTt+/j5jrJUxdjX8lR3+uZEx9gpjrJ0xdp4xVhzNOFcqshzvtzLfnhcIclzt9dDEXsEMOk2oY6+AO/d13R6kmfUozUwUeygkRp6uyVXERf1qOBdifSFNlpRqZ4UyluUHgxxXesaoDlAwg06DvQ4bjl0fxOy8vCf3V3o8SE3Qo8RCdYBSReqAj9rkXQfU93rBOTVNlWxneSZSE/Syj+sJSrAfEO2KqG8BOME5rwBwIvz9XRhjGQC+A2ArgC0AvnNPw+oLnPN14a+h8M++BmCMc14O4G8B/EWU41wRo04buqhfG5R1x759aBKTc35soMmSoj1VY1PE9ry6njGsL6Alzkq2I3xRl/sKvrrusfASZ+lc1ImwInWA3Jfl3xyZxPgs1QFKd2BtLibm/Dh9Q97b8+rCTVONhuoApdqxMLmXeR0QXr1HK6KUS6/VYJ8Cmvw3R6bgnZmXVB0QbSPqIICXw39/GcCzizxmL4BjnHM353wMwDEA+5bxvK8B2M1EmpUeqMkJX9TlO7mnrU7qENmeJ+eLundmHm1Dk7TCROFCd+6tsr+oX+n1YLU1GUlG2vKsZE/VhJbly7kOqOsOrd7bUER1gJJtL7Mg3Szvyf34bLgOKKA6QMmUUgfU9YyhIjsJqQnS2OpEYuPA2hxM+QJ4v1W+TX4p9gOibURZOef9ABD+M3uRx+QB6L3je1f4ZxE/CW/L+3/vaDYt/A7n3A/AC8Cy2AAYY19njF1ijF0aHhb+zbGjPBNpZnkvx7vSE9rqVEJbnRRtYXvedfluz4uc7iilbj2JjQM1uZic88v2oh4MclztGaOmqQrsDNcB78i4DqjrGUOKSYfSzCSxh0JiSK/VYF+1Dceb5Tu5r+/1hLc6SWeyRGIjUgd8INMVfKEtzx6qWVVgW6kFGYkGWa/kr+vxINmkQ1mWdOqAhzaiGGPHGWNNi3wdXOJrLLaSiYf//ALnfA2AXeGvLy7hd+7+Iec/5Jxv4pxvysrKWuKQli6yHO+4jDv2V3ppq5NaHAjfuZfrqTl1PWOSOs2BxE7kzr1cL+qRrU5SurNEYkMJy/Kv9IROd6StTsp3oCYX074ATrUMPfzBEnT7VCf6bFU6ua/gW9jqRE1TxdOFm/wnmgcx45NrHTCGdQXS2vL80EYU53wP57x6ka83AQwyxnIAIPznYlc9F4CCO77PB3Ar/Nx94T8nAPwcoQypu36HMaYDkArAvZL/oBAO1OSGl+PJ76K+sMSZuvWqsKM8M3Rqjkwv6nU9oa1OUjnNgcRO6KKeI9uLel1PZPUeFaBq8FRNjqzrgBtDE3TXXiW2lmTAkmiQbR1wJbzVKYXqAMWTex0Q2epEn63qcKAmB9O+AE7KsMk/OefHjUHp1QHRbs17C0DkFLxDAN5c5DHvAXAyxtLDIeVOAO8xxnSMsUwAYIzpARwA0LTI834WwEnO+aIrouLhkdLQRf23MryoLyxxltgbj8SGQafB/uocHL0mvzv3t091oveqWjwt44v6lR4PbXVSkW2lFtlO7mmrk7rotBrsX2PDiZZBTPv8Yg9nWTjnuNLroXwoFYnUAadk2OSvC9cBUtrqRGJna4kFmUlGvNMov236Db0eBLm08qGA6BtR3wdQyxhrA1Ab/h6MsU2MsR8BAOfcDeB7AC6Gv74b/pkRoYZUA4CrAPoA/FP4ef8ZgIUx1g7gT7DIaXzxFFmOd7J5SHYX9cgS5xra6qQaB9eF9tyfaJbXRf3myCQmaKuTqmwtle9F/UrPGNbRVifVuL0sX351QF03bXVSm6fW5GJ2Pii7OqBzZAqeadrqpCahOsAgyyxeqgPURath+NQaG062DGFqTmZ1QCSoXGJN/qgaUZzzUc75bs55RfhPd/jnlzjnL93xuB9zzsvDXz8J/2yKc76Rc17DOXdwzv+Qcx4I/9ss5/xz4cdv4ZzfjGacQjhQk4uZefndua+jJc6qs7XUguxkI9682if2UJZl4VQnWhGlGnK9qE/O+dE6OEHb8lTmqZoczMwHZDe5pzpAfbaUZCAr2Si7yX1kyzOtjFYPrYZhf3UOTrYMYVJGdcDE7DzVASp0oCbc5JdZP+BKjwdlWYlINUurDoh2RZRqRC7qv62Xz0Wdc46rvXSag9poNQxPr83F+63D8E7Piz2cJavrGUNqgh6ldLqjqjy1Jgez80Ecbx4UeyhLFtnqRJMlddlaYoE1xYg3r8qnDggGqQ5QI62G4ak1OTjVOozxWfnUAVd6xpBs1KGctjqpyjPrQpP7o9cGxB7KktX3ein6RIU2FaXDmmLEWzKqAyJbnqX4XqVG1BJpNQwHanJwqkU+k/v2ocnQEmcJvvFIbB1clwtfIIgj1+STZ1LXM4b1hdI6zYHE3ubiDOSkmvDGFfms4LvUFTrdcR1tdVIVrYbhmbW5+ODGEMamfGIPZ0kWTnWiOkB1nlmXC58/iCNN8pncX+4ewzqqA1RnY2E68tMT8IaMJveRrU605VldNDKsA7pGp+Ge8kny5ik1opbhufV58AWCeLdJHpP7i12hD8nNJRkij4TE25q8VJRkJsrmzr13OnS6I02W1EejYTi4Lg+n20YwMjkn9nCW5FK3G6utyUhNkNYSZxJ7z67Pw3yA451GedQBdd3hU50oc0d11hekochilk2T3zsd2uq0uZhqVrXRaBieXZeHj9qGMTQxK/ZwliSy5ZnqAPWRWx1wsdMNANhSIr05FjWilmFNXirKshLxG5lc1C92uZGZZESxxSz2UEicMRbq2J+7OYoBr/Qv6pe63eAcVICq1HPr8xAIcrwtg63P/kAQdd1j2EINflWy56SgIjtJNpP7C11uZCQa6FQnFWIsNLk/d3MU/d4ZsYfzUJd7qA5Qs2fX5yLIgd/WS39yHwhyXO4aoxv9KmXPScEqK9UBQqBG1DIwxvDc+jxc6HTDNTYt9nAe6kKnG1tK0sEYLXFWo4PrcsE5ZBFWeqHLDb2W0Yl5KrXaloyqnBT8RgYr+K73j2PKF6DJkkoxxvDs+jxc6h5Dr1sedcDmYqoD1OrZ9XngHLLIM7nQOUZ1gIqVZyejOi9FFgftNPePY2LOj63UiFKlO+uAnlHp1wEXu9zYVCTNOoAaUct0cF0eAEh+y9Mtzwz6PDPYVEQfkmpVmpWEmvxUyb9XgdCy0Zr8NJj0WrGHQkTy6fV5qO/14ObwpNhDeaALC0uc6bNVrQ6uywUAyU+YBryz6HFPU9NUxUoyE7GuIE0WK/kvdrmxJi+V6gAVe3ZdHhpcXnTIpA6gz1b1ut0PkPZn69D4LLpHpyVbs1IjapkKMszYXJyO31zpA+dc7OHc18UumiwR4Jm1uWjsk/ZFfcYXQIPLS+9VlXtmXS4Yg+TDSi92uVGYYYY1xST2UIhI8tPN2FKcIfk64EK4DthaYhF5JERMn96Qh5aBCTT3j4s9lPuanQ+gweWhrU4q9/TaXGgY8KbEG6cXu9zIT09AblqC2EMhIslLS8AjpRn4zVV51AFSbZpSI2oFnlufj/ahSVy7Jd2L+sUuN5KMOlTlpIg9FCKip9eGJvdSXhV1pXcM/iDHFol+SJL4sKaYsKMsE29IeHLPOcelrjHJXtBJ/Dy7Pg8dw1OSrgMudI4i0aBFVU6y2EMhInpqTQ50GoY3JHzn/mqvB/MBqgPUzppiwo7yTElP7jnn4egTeq+q3XPr83BzeAoNLq/YQ7mvi51umA1aOHKl2Q+gRtQKPLUmBwatRtJLnS92jmFDUTq0dASuqkUm97+54kIwKM2L+oVONxgDNhZL7zQHEl/Prs9Dj3t64VhkqekYnsLolE+SJ4+Q+JJLHbCxOAM6LZV6amZJMuKxVVl488otydYBF8N1AMVJkIPr8tDrnpF+HUBNU9XbV50Dg07adcCFrjFsKEyXbB0gzVFJXKpZjycqs/BW/S34A0Gxh/MJnmlf6AjcIposEeCzG/PR657B+fCedqm52OVGlS0FKSY6Alft9jqsMOmle1G/FF7ivIkKUNVLNevx+OpQHRCQ4OR+bCpUB1CYLgFCTf6B8Vl83Dkq9lAWdaHLjdXWZKSaqQ5Qu0gd8MYVaa7kp+gTEpGaoMeeqmz8tv4W5iXYD/DOzKNlYFzSq/ipEbVCz63Pw/DEHM52SO+ifrErdBeB9toTANjrsCHJqMNrl11iD+UT5gNB1HV76IJOAADJJj1q7Ta83dAPn196F/ULnW5kJhlQmpko9lCIBETqgDPtI2IP5RMudYfrAAkXoCR+9lRZkWTUSfK4cX8giLpu2vJMQm7XAbckXAcYUUJ1AEEoYH90yoePJFgH1HWPgXNgs4RX8VMjaoWeqMxGikmH1+ukN7k/0z4Ck15DR+ASAECCQYsDNTk43NSPqTm/2MO5S2OfFzPzAWpEkQXPrc+FZ3oep1qHxB7KXTjnONMxgq2lFkkegUvi74nKbKQm6PGqBJv8FzpHYdBpUJOfKvZQiAQkGLTYV23Du40DmPEFxB7OXRr6vJjyBfBIKYXqk5BPb8jD2PQ8TjQPij2UTwjlQ6VTHUAAAI+vzkaaWY/X66TX5D/bMQKDToMNhdSIUhyjTotn1uXicNMAvDPzYg/nLmc7RrC5OANGHR2BS0I+uzEf074A3m3sF3sodzkbvoNABSiJeLQiC1nJRrx6qVfsodylY3gKg+Nz2FGWKfZQiESY9Fo8uy4X710bgGfaJ/Zw7nKmfRQbCtNg0lMdQEI+uzEfk3N+ydUBZ9pCdcC2MqoDSMijFVmwpZjwK4nVAd2jU+jzzNBJpGSBQafBwbXSrQM2FqZLug6gRlQUXthUiDl/EG/VS2cf89DELG4MTmI7TZbIHTYWpaMkM1Fy2/M+ah+BIzcFGYkGsYdCJEKn1eAzG/JxqnUYQ+OzYg9nwdmO0GRpRzkVoOS25zcXwOcPSupk0tHJOVzvH8euiiyxh0IkZGtJBootZrwiscn9mQ6qA8jdtBqGz27Mxwc3hjHglU4dENl+tbOC5ljktkgdIKWtz5E6QOo1KzWiolCdl4KqnBT86qJ0LurnwplVUn/jkfhiLHRRP9/pRs/otNjDAQBM+/yo6/ZgZzld0MndXthcgECQ4zUJbX0+0z6CvLQEFGaYxR4KkRBHbiqq81LwioTqgLMLdQB9tpLbGGN4fnMBLnS60TkyJfZwAAAzvgDquj30XiWf8LlN+Qhy4NcSqwNyU02UE0nuslAHXHKBc2kcXnLupjzqAGpERYExhhc25aOxz4trt7xiDwdA6EMyxaSDI5dyIcjdnlufB8Ygmcn9xa4x+AJByX9IkvgryUzElpIM/OpiryQu6oEgx7mOUewop3wo8knPbyrA9f5xNPVJpw5INumwJo/qAHK3z27Ih1bDJLPl6VK3G75AENtpWx65R5ElEY+UZuBXl3oRlMDJpIEgx9mOUewoz6Q6gHzCC5sL0dw/jqa+cbGHAiC0LS/ZKP06gBpRUXp2fR4MOo0kVkVxznGmfRTbyizQauhDktwtNy0BO8sz8evLLklc1M+0j8Cg1dBJOWRRL2wqQNfoNM53usUeCq7d8mJ81k9NU7Kog2vDdYAEJvecc3zYNoLtVAeQRWSnmPDE6iy8dtkFvwSOGz/TPgq9ltGBJWRRL2wuQPfoNC50SaMO8EzP07Y8sqhn1ubCqNPglxd7xB4KgNAca2upBTqttFs90h6dDKSZDdjnsOE3V/owOy/uSSQ97mn0eWZoskTu63ObCtDnmcGHEjhm9KO2EWwsSkeCQbohekQ8n1qTg2SjThJN/jPtoSXOFKZLFpNq1mOfw4Y3JFQH0JZncj/PbyrA8MQcTrUOiz0UnGkfwfqCdJgNOrGHQiRon0M6dUAkH4oyeMliUhP0+NSaHLx19ZboJ5P2uqfR457GThnE9FAjSgAvbC7A+Kwf710bEHUckckSfUiS+9nrsMKSaMC/fdwt6jjkEqJHxJNgCJ1M+k5jv+gnk57tGMEqaxKyk00Wr48oAAAgAElEQVSijoNIl1TqgA/bIqH6VAeQxT1RmY2sZKPouWaeaR+abnmxneoAch+ROuDdpn6Mz4pbB5xpH0GlLRlZyUZRx0Gk6/lNBZiY8+Nwk7gnk94+XEf6dQA1ogSwrdSCgowE0S/qp28MIyfVhLIsCtEjizPqtPjcpgKcaBlCv3dGtHFQmC5Zihc2F4h+MumML4ALnW56r5IH2lZqQX66+HVAJEy3hMJ0yX3oF04mHRL1ZNKzHaPgnOoA8mDPbyrA7Ly4J5POzgdwsWuM3qvkgR4pzUCRxSx6HfBh2wiyk40oz04SdRxLQY0oAWg0DM9vLMDZjlHRTiLx+YP4qH0Ej6/OphA98kD/15ZCBIJc1A/KD24MI4XCdMlDrMlLRVVOCn5xvke00PJzN0cw5w/iidXZorw+kQeNhuHzWwpxtmMU7UMTooxhPhDEmfYRCtMlDxU5mVTMOuBkyxBSE/RYX5Am2hiI9NXkh04k+9m5btHqgPOdbvj8QdryTB6IMYbnNxXgfKdbtDrAHwji9I1hPLYqSxZ1ADWiBPLC5gLoNAz/ek6cLU+XutyYnPPjidVZorw+kY9CixmPrsrCLy/0ihJWGgxynGoZwuOrsyUfokfExRjDFx8pwvX+cVzuHhNlDCdbhmA2aLG1lMJ0yYO9uLkABq1GtDrgcvcYxmf9eLKSmqbkwUoyE7GrIhP/dr5HtDrg/dYhPLYqi+oA8kCMMXzpkWK0Dk6IdnjJyeZBmPQayokkD/WCROqA3VXyqAPo018g2SkmfGpNDl691IupOX/cX/9kyxAMWg0tGyVL8oWthRgYn8XJlqG4v3a9y4PRKZ9sPiSJuJ5dn4sUkw4/PdsV99fmnONUyzB2lGfCqKNQffJgliQjDtTk4Nd1fZgUqQ7Qaxl2raIbUuThDm0rxsD4LI5eH4z7azf2eTEy6aOmKVmSp9fmIjVBL8rknnOOEy1D2FmeCZOe6gDyYJnhOuC1yy5MiJBrFqkDdlbIow6gRpSADm0vxsScH7+50hf31z7VOoStpRlINNLJI+Thdldmw5pixM/Ox/+Y0ZMtQ9Aw4DGaLJElMBt0eH5TAY40DWAwznkmNwYn0eeZockSWbIvbivC5Jwfv6lzxf21jzcP4pFSC5KoDiBL8ERlNvLTE/CyCE1+qgPIciQYtHhhcwGOXBvAgDf+dYBrbAZPVlrj+rpEvr60vRhTvgBer4t/P+BkyxC2lGTIpg6gRpSANhSmYU1eKv7lXFdc9zH3jE6jY3iKMkzIkum0GnxhaxFO3xiO+z7mE81D2FSUgTSzIa6vS+Tri9uKEOAc/xbnxmlkxSB9tpKlWlcQqgNejnOeSefIFG4OT2E3NU3JEmk1DF/aVoTznW4094/H9bVPtQ5hfWE60hOpDiBL8++2FiHIOX5+Ib51wImW0IpBWsVPlmpdQRrWFqTh5XPx7Qf0uqfRNjQpq5qVGlECYozh0PZi3BicxLnwqWDxEDkuek8VdevJ0n1hayGMOg3++aPOuL3mLc8MrveP0wWdLEuRJRFPrM7Gz8/3wOePX57J0esDcOSmwJZqittrEnljLDS5bx+axLmb8asDIk3T3VQHkGV4flMBTHoN/iWOW55ueWbQ4PLSSlOyLIUWMx5flRX3OuBE8xDW5KXCmkJ1AFm6Q9uKcHN4Ch+1j8TtNY9djzRN5VMHRNWIYoxlMMaOMcbawn+m3+dxh8KPaWOMHQr/LJkxdvWOrxHG2N+F/+3LjLHhO/7tpWjGGU8HanKQkWiIa57Ju039qM5LQaHFHLfXJPJnSTLiMxvz8eu6PoxMzsXlNY80hZumdvl8SBJpOLS9GCOTczjc1B+X17vlmcGVHg8+tSYnLq9HlOPptblIN+vx44+64vaaR5r6UWlLRkEG1QFk6dLMBjy7Lg9vXOmDdzo+eSaHw3UAfbaS5fpSuA54u+FWXF5vcHwWdT1jdPOULNtTNTmwJBriuvX53cZQHVCSmRi314xWtCuivgXgBOe8AsCJ8Pd3YYxlAPgOgK0AtgD4DmMsnXM+wTlfF/kC0A3g9Tt+9ZU7/v1HUY4zbkx6LT6/pQDHmwfROTIV89eLTJb2V9MFnSzfV3eUwOcP4mcfx+du6DuN/ajKSUFZVlJcXo8ox67yTJRlJeKHp2/GZalzZLK0v9oW89ciymLSa/HFbcU43jyI9qHJmL/egHcWF7vG8BRN7MkKHNpejJn5AH52Pj51wOFwHSCnyRKRhscqsrDKmhS/OqCxH5yHFhkQshxGnRZf2FqI481DcYlAGfDO4lL3mOwa/NE2og4CeDn895cBPLvIY/YCOMY5d3POxwAcA7DvzgcwxioAZAP4MMrxSMKXt5dAp9Xgh6c7Yv5aNFki0SjPTsLuymz867luzM4HYvpatzwzuNw9Rhd0siIaDcO/f7QM126N48O22C91Phy+s1RKTVOyAoe2FcGo0+CfTt+M+Wu92xhaJfgp+mwlK1CVk4LHV2fhxx91xrwOWJgsUc1KVkCjYfj6o2VoGZjABzeGY/56bzeE6oDy7OSYvxZRnkPbi2HSa/CDD2JfBxwJ7xZQWyPKyjnvB4Dwn4utXcwD0HvH967wz+70eYRWQN3Z3v4MY6yBMfYaY6wgynHGVVayEc9vysevL/fF/JQnmiyRaH1tVwlGp3wxP+1xYbIksw9JIh0H1+fClmLCP74f2yZ/ZLJEK0zISlmSjHh+UwF+cyX2dQCtNCXR+g+PlWF0yodXL8f2tMeFyRI1TckKPbM2VAfEenLf752hOoBExZJkxAubCvDG1T70e2di+lrvNg5gtTUZ5dnyqgMe2ohijB1njDUt8nVwia/BFvnZvespXwTwizu+/y2AYs55DYDjuL3qarHxfZ0xdokxdml4OPbd8aX6+q4y+INB/DiGQdA9o9O4RCtMSJS2lVpQnZeCH3zQAX8gdgGQ7zT2w5FLy/HJyhl1Wry0qwTnbo7iSs9YzF7nt/Wh/AmaLJFo/M6u0lAdcCZ2dQCtNCVC2FKSgQ2Fafjh6djWAW/W38JqazI1TcmKGXQafG1nqA6o7/XE7HXeaQg1TZ+iz1YShZd2lSLIgX/+MLZ1wMVuN/avkd9K04c2ojjnezjn1Yt8vQlgkDGWAwDhP4cWeQoXgDtXNOUDWEiZY4ytBaDjnF++4zVHOeeR9OR/ArDxAeP7Ied8E+d8U1ZW1sP+O3FTaDHjQE0ufvZxd8wCIF+rc4Ex4NMb8mPy/EQdGGP4xpMV6BqdxhtXYxMA2T40iSs9HjyzNjcmz0/U48UthUhN0ON/x2hVFOccv7rUi/WFaTRZIlEptJjxVE0ufnauG+4pX0xe4/W60AoWakSRaDDG8LuPlaHXPYO3G2JzIET70ASu9Hjw2Y1Us5LovLilACkmHf7hZHtMnp9zjtfr+uDITaEdJyQqBRlmPLM2Fz+/0IOxGNUBv77sAufAZ2TYD4h2a95bAA6F/34IwJuLPOY9AE7GWHr4VD1n+GcRn8fdq6EiTa2IZwA0RzlOUfzeE2WY8gXwgxhkRQWDHL++7MLO8kzkpiUI/vxEXWrtVjhyU/APJ9ticjf0V5d6odMwapqSqCUZdfjKjmIcuz6IBpfwd0PrXV60DU3icxtltSOcSNQf7i7HzHwAP/ggNnXAK5d6sa3UgiILrTQl0dlTZUWlLRl/d/wG5mNQB7x6yQWthuHZ9femcxCyPMkmPf79Y2U43jwYk9XRTX3juN4/jhc3Ux1Aovd7j5dhZj6A/xOjOuDVyy5sL7PI8tTcaBtR3wdQyxhrA1Ab/h6MsU2MsR8BAOfcDeB7AC6Gv74b/lnE87inEQXgG4yxa4yxegDfAPDlKMcpikpbCp5Zm4ufnOnC0ISwGRHnbo6izzNDd5aIIBhj+KM9q9A9Oi14VpTPH8SvL7uwuyobWclGQZ+bqNPXdpYg3azHX73XKvhzv3qpFya9BgfW0goTEr3y7GQ8uy4PL5/rwpDAWVHnbo6i1z2DF7fQZIlET6Nh+KZzNbpGp/GawFlR84Egfl3XhycrqQ4gwvjy9mJkJBrwN8duCP7cv7jYA5Neg2fWUdOURK/Cmozn1ufhp2e7MOAVtg443+lGj3saz2+SZx0QVSMqvIVuN+e8IvynO/zzS5zzl+543I855+Xhr5/c8xylnPOWe372bc65g3O+lnP+xL3/Lid/UrsK84Eg/qfAy0d/ebEXySYd9jrktx+USNOeqmxU56Xg70+2Yc4v3Mk5J1sGMTrlw4ubCwV7TqJuySY9fu/xcnzYNoJzHaOCPe/UnB9v1d/CPocNKSa9YM9L1O0P91TAH+D4X6eErwNSE/RUBxDB7K7KxobCNPx/x9sEPUHvVMsQRibn8Dm6eUoEkmjU4fceL8OHbSP4+KZwdcC0z4+3rt7Cp9bkIDWB6gAijD/eswpBzvEPJ9sEfd5XLvYg2aTDPpmeRBrtiijyEMWZiXhhcwF+caEHPaPTgjxnn2cG7zb244VNBTDptYI8JyGMMfzHvZXodc/gX852C/a8Pz3bhZxUEx5dJZ0MNyJ/X9xWBFuKCX/5XgvuPnB15V691IuJWT++uK1IkOcjBACKLIn43KYC/FzAOmBwfBbvNQ3gufV5VAcQwUTqgIHxWfzsY+HqgB991IncVBOeqFzscG1CVubfPVIEa4oRf3lEuDrgjSu3MDnnp5unRFAFGWa8uLkQr1zsRdfIlCDPOeCdxTuN/fjMhnzZ1gHUiIqDb+yugFbD8N8PCxN19ZPwSXxf2VkiyPMREvHYqiw8vjoLf3+yDaOTcw//hYe40jOGj2+68bWdJdBqFjtAk5CVMem1+OPaClzp8eC3AoTr+gNB/POZTmwsSsfGogwBRkjIbX+0pwJ6rQbfe+e6IM/344864Q8G8dUdVAcQYW0rs2BXRSb+/kQbRgSoA672enCh042v7iyBXkvTDiIck16LP3WuRl2PB29cjT5Wwh8I4genO1CTn4rNxekCjJCQ2/7gyXIYdBr82TsC9QPOdCIQ5PiajPsBdEWIA2uKCX/wZAUONw3ggxvDUT3X+Ow8fnmxF0+tyUEehZSTGPgvT1Vh2hfAXx+Nft/9//mgA6kJenx+C91ZIsL77MYC1OSn4s/evo6J2ehOJ33v2iB63TP4nV2lAo2OkNsidcCx64NR1wHe6Xn87ONuHKjJRaFFfuGkRPq+87QDM/MB/MXh6JMxfni6A8kmHV6kOoDEwGc35GNtfir++7stmJzzR/Vch5sG0D06jd97vAyM0c1TIqzsFBO+sbsCx5sHcaplKKrnmpidx8/P9+BTa3JkGVIeQY2oOHlpVwlKMxPxnTebotp3/9MzXZic89NkicRMeXYyvrK9GL+40BPVvvv2oQkcvT6IQ9uKkGjUCThCQkK0GobvHazG8OQc/vbYyvfdB4Mc//NUO0oyE1Frtwo4QkJu++rOYpSE64AZ38rrgH/9uAtTvgD+w+NlAo6OkNvKs5PwtZ2lePWyCxe73A//hftoH5rAkaYBfGFrEZKoDiAxoNEw/LdnHBiamMNfR3GACecc//h+B8qyEuG0yzNvh0jfV3eUoCwrEf/tt9eiqgP+5Vw3Jub8+Pqj8u4HUCMqTow6Lb57sBpdo9P4yyMr+6AcnZzDDz7owD6HDWvyUwUeISG3/YlzFQoyEvDt1xtX3Dj9/uFWJBp0OLS9WNjBEXKHtQVp+MLWQvzkbCfOr7Bx+mZ9H5r7x/FHeypoCymJGaNOiz9/LlQH/MWRla00GZmcww8+uIk9VdmoykkReISE3PYHT5YjPz0B33y1HlMrXGny/cOtMBt0+J1d8t06QqRvfWE6Dm0rwk/Pdq34AJO36m/hev84fv+JcmioDiAxYtBp8L1nq9EdRR0wOjmHf3y/A3uqslGTnybwCOOLGlFxtLMiE4e2FeHHZzrxYdvyl+b/9dFWzPqD+Obe1TEYHSG3mQ06fP/TNegcmcJ3315+pslHbSM43jyI33+iHJYkOqqZxNa391ehKMOMP/lVPcaXuUVvcs6PvzrSCkduCp6uyY3RCAkJ2V6WiS9vL8ZPz3bhTPvIsn//b47dwMx8AN/aXxWD0RFyW6JRh//xubXocU+vKNPkTHuoDvjdx0qpDiAx95/2V6LYYsZ/fG35dcC0z4/vH25BdV4Knl2XF6MREhKyvSwTX91Rgp+e7cLpFWzV/5tjNzDt8+Nb+ytjMLr4okZUnH1rfxXKs5Pwx6/UwzW29NNzPr45il9c6MVLO0tQnp0UwxESErKjPBO/+1gZfn6+B6/XuZb8e1Nzfnz7Nw0otpjxlR3FsRsgIWGJRh3+5oV1GBifxZ/+qh6B4NJPz/mrIy3oH5/Fdw9W011QEhf/aV8lyrIS8Qe/uIJe99LrgHMdo/j5+R58aVsx1QEkLraWWvD1R0vxiws9eO3y0uuAGV8A3369EcUWM16iKAkSB2aDDv/j+bUY8M7iD39xZVl1wF8eaUW/dxbfedpBdQCJi/9n32pUZCfhj1+5uqw64PzNUfzb+R58eXsJyrOTYzjC+KBGVJwlGLT4xy9swJw/gK/99NKSuvYjk3P441euoshixh/tWRWHURIS8k3nKjxSmoFvv964pLwozjn+65vX4BqbwV99bq1sjxMl8rOhMB3/5akqHLs+iO8v8YTSo9cG8PK5bhzaVoyNRXRCDomPBIMW//SlTZgPBPE7/3JpSUH7o5Nz+Oar9Si2mPHNvVQHkPj509rV2F5mwbdfb1jS9mfOOf7zG43ocU/j+5+poTqAxM3Gogx85xkHTrUO4y+XuO3pZMsgfnq2C1/ZUYzNxXRiLomP/7+9Ow+uqjzjOP59SEhIZFcIS4Jii1SlDRBaqNZqteIyLdROUSEoWp1qWynWzrS1nWnVTjttFR2tihWkdUVo1SnT2gri2o4gIaAIGDZRElO2QCALCUme/nFPJEBuzLXknOTe32eGSfLm5M57Z3485z3PPUuP7mk8dFUBhxqbuO7Rle3qB+ypquOWRW+R1z8radYBakRFYEROL+YUFrBlVxXXzH+Typr44auua+DGx1dRUV3PA9PGkpWhHbqEJz2tGw9MG8uw/tl8+88rP/ampQ++soVnikuZdcEI7dAldNeePZwZXzyZua+/x91LN+Ie/xPRt0v38aNFb/G53D5JcXqzdC2nDujJ/dPGsnlnFVfPf5PK2vjrgJr6Bm54fBW7q+q498oxZGfops8Snoz0bswpLCCvfzbXP1rUrnXAs8Vl3PzVEUw49cSQZikSc9WEk5k+YRh/fG0rs5eUtLkOeKeskh8sWMOZQ3rz44u0DpBwfWpATx6aXsDWXdXM+Jh+QE19A999ophdVXU8OK0gadYBakRF5EsjTuIPU8ewtqySyx78D2+X7jtmm9K9NRTOW8Hq7fu454rRjBqqG5RL+E7smcmT149nUO8eFM5dweNvbKPpqFOe6xoa+fU/1nPnCyVMHj2EH5w/IprJSsr7xdfPZEpBLvct28TMBatb3bEv27CDwnkr6JPdnYemF+gTe4nEuacN4P5pY3mnrJLJ9/877jpg2twVFH+wl9mX55Of17VvTCpdU5/s7jxx3XgG9M6kcN4KHnvj2HVAfUMTv3l+A3e+UMKkfK0DJDp3TBrF5eNy+cNLm7lpwWr2Vtcfs83LJTuZ+vByevdI55EZn9cH/RKJsz59Eg8UjmVd2X4mPfBv3tp+7DqgbF8t0+etoOj9CmZPyU+qB5ZZW53irmbcuHFeVFQU9TQSsmLrHmY9vYYdBw4y8Ywczj1tIFkZ3Sh+fx/PFJfSzYy7puRz8Sg9SlSiVVFdz6ynV/P6pt18ZlAvJo8eytB+WWyvqOGvq0p5b3c10ycM4/ZJo/TkMYlUU5Mz59Ut3L10I9kZaXyrIJf83L5U1zewZN0OXt24i9MH92bu1QXk9suOerqS4oq2VfC9J2OfdF54eg7njRxIdkYaxR/s/ei+PPdcMZqLztQ6QKJVUV3PDxeu4dWNuxiZ04vJY4aQ2y/7iHVA4fhh3D7pTNLT9Fm3RMc9tg6YvWQjPTPTuWzMUPLz+lBT38jS9Tt4pSSW4T9d+3mG9M2KerqS4lZuq2DmU6v57/6DXHhGDueNHEB2RhqrP9jHM8E64K4p+Vzy2cERzxTMbJW7jzsur6VGVPQqaw7x8OtbWLiylN1VdQBkpHXja/mDufmC0xh2og6UpHNwdxa/9SHzXn+PtWWVH42PHdaXmeeP4CufGRjh7ESOtKF8P/ct28Syd3dS39AEwIBemVxz1ilcf85wMtP1Cah0DgcOHmLOK1tYVHR4HZCZ3o1LRg3iRxNHktdf6wDpHJqanL+vLefh17bwTtn+j8ZH5/Vl5vmf5oLTcyKcnciRSv57gHuXbeTF9Tupb4ytAwb17kHh+GF859xTtQ6QTqOy9hBzX9vKwqLt7DpwuB9w6WcHccuFIztNP0CNqDi6aiOqWVOTU7avlrqGRvL6Z6s4SqdWUV3PrgN1DOyVSb8TMqKejkhctfWNlFfWkpHejaF9szDTGXvSOTU2OeWVtRw81ERuvyxdNiqd2p6qOvZU15PTqwd9srtHPR2RuA4eaqR0by09undjcJ8snbkvnVZn7weoERVHV29EiYiIiIiIiIh0NsezEaULuEVEREREREREJBRqRImIiIiIiIiISCjUiBIRERERERERkVCoESUiIiIiIiIiIqFQI0pEREREREREREKhRpSIiIiIiIiIiIRCjSgREREREREREQmFGlEiIiIiIiIiIhIKNaJERERERERERCQUakSJiIiIiIiIiEgozN2jnsNxY2YHgJKo5yFdxknA7qgnIV2CsiKJUF6kvZQVSYTyIu2lrEgilBdpr5Hu3ut4vFD68XiRTqTE3cdFPQnpGsysSHmR9lBWJBHKi7SXsiKJUF6kvZQVSYTyIu1lZkXH67V0aZ6IiIiIiIiIiIRCjSgREREREREREQlFsjWiHo56AtKlKC/SXsqKJEJ5kfZSViQRyou0l7IiiVBepL2OW1aS6mblIiIiIiIiIiLSeSXbGVEiIiIiIiIiItJJqRElIiIiIiIiIiKhSJpGlJldbGYlZrbZzH4a9XwkWmaWZ2Yvm9kGM1tnZrOC8dvMrMzM1gT/Lm3xN7cG+Skxs4uim72Ezcy2mdnaIBNFwVh/M1tqZpuCr/2CcTOz+4KsvG1mY6OdvYTJzEa2qB9rzGy/md2s2iLNzGy+me00s3dajCVcT8xsRrD9JjObEcV7kY4VJyt3mtm7QR6eM7O+wfgpZlbbosY81OJvCoJ92OYgTxbF+5GOFScvCe97dMyU/OJkZWGLnGwzszXBuGpLCmvjmLnD1y1JcY8oM0sDNgIXAqXASmCqu6+PdGISGTMbDAx292Iz6wWsAr4BXA5UuftdR21/BrAA+AIwBHgROM3dG8OduUTBzLYB49x9d4ux3wMV7v7bYKHWz91/EizyZgKXAuOBe919fBTzlmgF+54yYjm4FtUWAczsy0AV8Ji7jwrGEqonZtYfKALGAU5sH1bg7nsjeEvSQeJkZSLwkrs3mNnvAIKsnAL8vXm7o17nTWAWsBx4HrjP3f8ZzruQsMTJy20ksO8Jfq1jpiTXWlaO+v1soNLd71BtSW1tHDNfQwevW5LljKgvAJvdfau71wNPA5MjnpNEyN3L3b04+P4AsAEY2safTAaedvc6d38P2EwsV5K6JgOPBt8/SqwoN48/5jHLgb5BEZfUcwGwxd3fb2Mb1ZYU4+6vARVHDSdaTy4Clrp7RbCIWwpc3PGzlzC1lhV3X+LuDcGPy4Hctl4jyEtvd3/DY58uP8bhfEkSiVNb4om379ExUwpoKyvBWU2XE2tUxqXakhraOGbu8HVLsjSihgLbW/xcSttNB0khQad/DLAiGLopOJVwfvNphihDqc6BJWa2ysy+E4zluHs5xIo0MDAYV1ak2ZUcuZBTbZF4Eq0nyo0AfBtoefbBcDNbbWavmtk5wdhQYvlopqyknkT2Paotcg6ww903tRhTbZGjj5k7fN2SLI2o1q5X7frXHMr/zcx6As8AN7v7fmAO8ClgNFAOzG7etJU/V4ZSx9nuPha4BPh+cEpzPMqKYGYZwCTgL8GQaot8EvHyodykODP7OdAAPBkMlQPD3H0McAvwlJn1RllJdYnue5QXmcqRH6Kptkhrx8xxN21l7BPVlmRpRJUCeS1+zgU+jGgu0kmYWXdi/6GedPdnAdx9h7s3unsTMJfDl8goQynM3T8Mvu4EniOWix3Nl9wFX3cGmysrArGmZbG77wDVFvlYidYT5SaFBTd5/RpQGFwSQ3CJ1Z7g+1XAFmL3/CnlyMv3lJUU8gn2PaotKczM0oFvAgubx1RbpLVjZkJYtyRLI2olMMLMhgefUl8JLI54ThKh4PrnR4AN7n53i/GW9/K5DGh+msRi4EozyzSz4cAI4M2w5ivRMbMTgpvzYWYnABOJ5WIx0PzEhxnA34LvFwNXB0+NmEDsZo/lIU9bonfEJ4qqLfIxEq0nLwATzaxfcKnNxGBMkpyZXQz8BJjk7jUtxgcED0jAzE4lVku2Bnk5YGYTgrXP1RzOlyS5T7Dv0TFTavsq8K67f3TJnWpLaot3zEwI65b04/g+IhM8WeQmYm82DZjv7usinpZE62zgKmCtBY8nBX4GTDWz0cROFdwG3ADg7uvMbBGwntip8N/XU61SRg7wXKwOkw485e7/MrOVwCIzuw74AJgSbP88sSdFbAZqiD0tTVKImWUTe+LQDS2Gf6/aIgBmtgA4DzjJzEqBXwK/JYF64u4VZvYrYgeNAHe4e3tvUixdRJys3ApkAkuD/dJyd78R+DJwh5k1AI3AjS0y8V3gz0AWsXtK6alWSShOXs5LdN+jY6bk11pW3P0Rjr23Jai2pLp4x8wdvm6x4IxfERERERERERGRDpUsl+aJiIiIiIiIiEgnp5Pzq0oAAABOSURBVEaUiIiIiIiIiIiEQo0oEREREREREREJhRpRIiIiIiIiIiISCjWiREREREREREQkFGpEiYiIiIiIiIhIKNSIEhERERERERGRUPwPEcCF3Secf8UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d8e73d0b8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=[20,5])\n",
    "plt.plot(t,ur)\n",
    "plt.xlim(0,2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x=[];\n",
    "y=[];\n",
    "z=[];\n",
    "\n",
    "for i in np.arange(index.size):\n",
    "    x.append(np.sqrt(r[i]*r[i]+spin*spin)*np.sin(th[i])*np.cos(phi[i]));\n",
    "    y.append(np.sqrt(r[i]*r[i]+spin*spin)*np.sin(th[i])*np.sin(phi[i]));\n",
    "    z.append(np.sqrt(r[i]*r[i]+spin*spin)*np.cos(th[i]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24d83efa860>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24d841d9940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}