{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP example: Correlation functions and spectrum of a atom-cavity system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.R. Johansson and P.D. Nation\n", "\n", "For more information about QuTiP see [http://qutip.org](http://qutip.org)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model and parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the Jaynes-Cumming model of a single two-level atom interacting with a single-mode cavity via a dipole interaction and under the rotating wave approximation." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "kappa = 2\n", "gamma = 0.2\n", "g = 5\n", "wc = 0 \n", "w0 = 0 \n", "wl = 0\n", "N = 5 \n", "E = 0.5\n", "\n", "tlist = np.linspace(0,10.0,500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation functions and spectrum using `eseries`" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def probcorr(E,kappa,gamma,g,wc,w0,wl,N):\n", " #\n", " # returns the two-time correlation and covariance of the intracavity \n", " # field as exponential series for the problem of a coherently driven \n", " # cavity with a two-level atom\n", " #\n", " # E = amplitude of driving field, kappa = mirror coupling,\n", " # gamma = spontaneous emission rate, g = atom-field coupling,\n", " # wc = cavity frequency, w0 = atomic frequency, wl = driving field frequency,\n", " # N = size of Hilbert space for intracavity field (zero to N-1 photons)\n", " # \n", "\n", " # Hamiltonian\n", " a = tensor(destroy(N),qeye(2))\n", " sm = tensor(qeye(N),destroy(2))\n", " H = (w0-wl)*sm.dag()*sm + (wc-wl)*a.dag()*a + 1j*g*(a.dag()*sm - sm.dag()*a) \\\n", " + E*(a.dag()+a)\n", "\n", " # collapse operators\n", " C1 = np.sqrt(2*kappa) * a\n", " C2 = np.sqrt(gamma) * sm.dag()\n", " c_op_list = [C1, C2]\n", "\n", " # Calculate the Liouvillian\n", " L = liouvillian(H, c_op_list)\n", "\n", " # Find steady state density matrix and field\n", " rhoss = steadystate(L);\n", "\n", " ass = expect(a,rhoss);\n", " \n", " # Initial condition for regression theorem\n", " arho = a*rhoss;\n", "\n", " # Solve differential equation with this initial condition\n", " solES = ode2es(L,arho);\n", " \n", " # Find trace(a' * solution)\n", " corrES = expect(a.dag(),solES);\n", "\n", " # Calculate the covariance by subtracting product of means\n", " covES = corrES - np.real(np.conjugate(ass) * ass)\n", "\n", " return corrES, covES" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "corrES, covES = probcorr(E, kappa, gamma, g, wc, w0, wl, N)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "corr= esval(corrES, tlist)\n", "cov = esval(covES, tlist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlation function" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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rIdirVThFREREMl08d8b/H/BB4PzYfifRInqsjgLWOufWO+cGgCXA2bu0ORu43UU9DxSb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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(12, 6))\n", "\n", "ax.plot(tlist, np.real(corr))\n", "ax.plot(tlist, np.real(cov))\n", "ax.set_xlabel('Time')\n", "ax.set_ylabel('Correlation and covariance')\n", "ax.legend((\"corr\", \"cov\"));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spectrum" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "wlist = np.linspace(-10,10,200)\n", "Ps = esspec(covES, wlist)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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xxrEMVQWp+C0cb9dVMokuKrRFQkxt2yC5KXFkJsU6lsEYQ3VJJjvre7BWfdoi4aqlb5Tm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\nFXt56C8FfGniIO65cLTX5YiIiJxSXHQUT940lZy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(12, 6))\n", "ax.plot(wlist, np.real(Ps))\n", "ax.set_xlabel('Frequency')\n", "ax.set_ylabel('Spectral amplitude');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison: Correlation function using `correlation_ss` with `mesolve` and `eseries`" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def calc_correlation(E, kappa, gamma, g, wc, w0, wl, N, tlist):\n", " #\n", " # returns the two-time correlation of the intracavity field as exponential\n", " # series for the problem of a coherently driven cavity with a two-level atom\n", " #\n", " # E = amplitude of driving field, kappa = mirror coupling,\n", " # gamma = spontaneous emission rate, g = atom-field coupling,\n", " # wc = cavity frequency, w0 = atomic frequency, wl = driving field frequency,\n", " # N = size of Hilbert space for intracavity field (zero to N-1 photons)\n", " # \n", "\n", " # Define cavity field and atomic operators\n", " a = tensor(destroy(N),qeye(2))\n", " sm = tensor(qeye(N),sigmam())\n", "\n", " # Hamiltonian\n", " H = (w0-wl)*sm.dag()*sm + (wc-wl)*a.dag()*a + 1j*g*(a.dag()*sm - sm.dag()*a) \\\n", " + E*(a.dag()+a)\n", "\n", " # collapse operators\n", " C1 = np.sqrt(2*kappa)*a\n", " C2 = np.sqrt(gamma)*sm.dag()\n", "\n", " A = a \n", "\n", " corr_ode = correlation_2op_1t(H, None, tlist, [C1, C2], A.dag(), A, solver=\"me\")\n", " corr_es = correlation_2op_1t(H, None, tlist, [C1, C2], A.dag(), A, solver=\"es\")\n", "\n", " print(\"real corr at 0 [me]:\", corr_ode[0])\n", " print(\"real corr at 0 [es] :\", corr_es[0])\n", "\n", " return corr_ode, corr_es" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "real corr at 0 [me]: (0.0499554840591+0j)\n", "real corr at 0 [es] : (0.0499554840591-8.67361737988e-19j)\n" ] } ], "source": [ "corr1, corr2 = calc_correlation(E, kappa, gamma, g, wc, w0, wl, N, tlist)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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B/mBmdwH7EhXG3UeAq4D7gO3Abe6+1cyuNLMrY6fdC+wGdgHfBz5y+PNm9gtG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\n0S+IztIXREVEREROWEqnuLwcd28FLjr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(12, 6))\n", "\n", "ax.plot(tlist, np.real(corr1),\n", " tlist, np.real(corr2))\n", "ax.set_xlabel('Time')\n", "ax.set_ylabel(r'Correlation $\\langle a^\\dag(t)a(0)\\rangle$')\n", "ax.legend((\"me\", \"es\"));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation functions and spectrum at two different coupling strengths" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def calc_spectrum(N, wc, wa, g, kappa, gamma, tlist, wlist):\n", "\n", " # Hamiltonian\n", " a = tensor(destroy(N), qeye(2))\n", " sm = tensor(qeye(N), destroy(2))\n", " H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n", " \n", " # collapse operators\n", " c_op_list = []\n", "\n", " n_th_a = 0.5\n", " rate = kappa * (1 + n_th_a)\n", " if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * a)\n", "\n", " rate = kappa * n_th_a\n", " if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * a.dag())\n", "\n", " rate = gamma\n", " if rate > 0.0:\n", " c_op_list.append(np.sqrt(rate) * sm)\n", "\n", " A = a.dag() + a\n", " B = A\n", "\n", " # calculate the power spectrum\n", " corr = correlation_2op_1t(H, None, tlist, c_op_list, A, B, solver='es')\n", "\n", " # calculate the power spectrum\n", " spec = spectrum(H, wlist, c_op_list, A, B)\n", "\n", " return corr, spec" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "N = 4 # number of cavity fock states\n", "wc = 1.00 * 2 * np.pi # cavity frequency\n", "wa = 1.00 * 2 * np.pi # atom frequency\n", "g = 0.10 * 2 * np.pi # coupling strength\n", "kappa = 1.0 # cavity dissipation rate\n", "gamma = 0.2 # atom dissipation rate\n", "\n", "wlist = np.linspace(0, 4 * np.pi, 200)\n", "tlist = np.linspace(0, 15, 500)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "corr1, spec1 = calc_spectrum(N, wc, wa, g, kappa, gamma, tlist, wlist)\n", "corr2, spec2 = calc_spectrum(N, wc, wa, 0, kappa, gamma, tlist, wlist)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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GGAXuHLPeEF4SkIwXpoBlTzrPdSfCwWc5r1e9WphaRERERAYgBe4cs96w8yJWoJlKPngS\nhk6F4hooGgRlI2H1vMLUIiIiIjIAKXDnmq+AgTsZd9pHRh+zbdvww6D+DfVxi4iIiOSJAneOma7A\nHe/I/8UbPoJUAgYdtG1b7XRoXQfN9fmvR0RERGQAUuDOMbffCdzxztb8X3zTEue5evy2bbXTnef6\n1/Nfj4iIiMgApMCdY+5AMQCRjpb8X3zTUsBA1QHbtg2eBC4PrH8v//WIiIiIDEAK3DnmDRQBEG0v\n0Ah32QjwhbZtc3uhfBQ0fJj/ekREREQGIAXuHPOEnMAdi7Tl/+KblsKgA3fdXlnn9HeLiIiISM4p\ncOeYP+i0lMTy3VKSTEDDsh37t7tU1kHjR5BK5bcmERERkQFIgTvHAuESABL5HuFuWgXJ2I79210q\nx0IiAi1r8luTiIiIyACkwJ1jgZAzwp2M5Hke7ubVznPZyF33VY5zntXHLSIiIpJzCtw5FgqFSVpD\nKprnEe6uebZLh2GtJZHcrn2kss55VuAWERERyTkF7hwLB7x0EMDme6XJ5nS7SMkw/u1vC6n7rzmc\ncePLROJJKB4M3rACt4iIiEgeKHDnWJHfQwf+/C/t3rwawoNY2ZTg0bfXMnVEGe/UN/PQW2vAGKgY\nA43L81uTiIiIyACkwJ1jfo+LTuvH5Dtwt6yB0lrueHUlHpfhlvMP5aAhJdz28gqstVA2fNsouIiI\niIjkjAJ3jhlj6HQFMYmO/F64uR5bMowHFtQza9IQBpUEuOSo0Szb2Mabq7ZAybBtfd4iIiIikjMK\n3HkQMwHc+Qzc1kLzGpp8NbRGEhw9rhqAEyYMAmDeikYorYVoM0QKsOS8iIiIyACiwJ0HUVcQT7Iz\nfxfs3ALxdlbFKwA4ZHgZABVhH3WDipi/Mh24QXNxi4iIiOSYAnceJNxBvPkM3OkQ/X57McUBD2Oq\nwlt3TR9VzvxVW0iVpAO32kpEREREckqBOw8S7hC+VB4DdzpEv74lxCHDy3C5zNZd00ZW0BpJsDxe\ntsOxIiIiIpIbCtx5kPSE8OczcLeuA+CNhsDWdpIu00c5bSbzNnrBuBW4RURERHJMgTsPrDeI30by\nd8G2jQBsTBVz8NDSHXYNrwhSHPCweGMHlAxV4BYRERHJMQXuPLDeMAFikErm54JtG4l5S0ngYUx1\neIddxhjGDSpi2YY2Z2pA3TQpIiIiklMK3PngS4feeJ6mBmzfSKu3EmNgREVol90H1BSzbGObM1NJ\n08f5qUlERERkgFLgzgOTDtyJztb8XLBtE42UMqQkQMDr3mX3uJpiGttjdAYGQet6Z95uEREREckJ\nBe48cPmdwN3ZkafA3b6R9ckSRlWFu909blARABtsGSSjEGnKT10iIiIiA5ACdx64A8UARNvzN8L9\ncTS828B9QI1Tz+p4ibOhdUN+6hIREREZgBS488AdcIJvNB8tJfFOiLWyJl7MqMpd+7cBakr8FAc8\nfNCeDuRt63Nfl4iIiMgApcCdB970CHcsHy0l6SkBN1HKqMruR7iNMYytLmJxW9DZoBFuERERkZxR\n4M4Db9DpmY7nY4S7fRMAm23pbltKAEZWhninJT0CrhFuERERkZxR4M4DX8jplU5E2nJ/sTZntHqT\nLWVoWXC3h42oCPFRs8F6wxrhFhEREckhBe48CIScEe5kNB+B22kpifgrKfJ7dnvYiIoQyZQlERq0\ndSl4EREREck+Be488KdHuFP5GOFOt5T4Sgb1eFjXgjgdvqqto+IiIiIikn0K3HkQCjs3TdpYe+4v\n1r6JVlNEVVlJj4eNTN9QucVd4Sx+IyIiIiI5ocCdB6GAlw7rz0/g7mhgiy1mcIm/x8MGFfvxeVxs\ntGUa4RYRERHJIQXuPPC5XXTix8Q7cn6tVHsDm1JFDC7d/Q2TAC6XYURFiPp4KcTaIB/95SIiIiID\nkAJ3Hhhj6DQBTDz3I9yJtga22CKGlAZ6PXZERYjlka7FbzTKLSIiIpILBQ3cxphTjDFLjTEfGmN+\n0M3+44wxzcaYhenH/xSizmyImADuRGfuL9TVUpJB4B5eHmRZR3okvH1zjgsTERERGZh2P29cjhlj\n3MBNwIlAPfCGMeZRa+2inQ59yVp7Wt4LzLKoCeJO5L6lxB1pZAvFTMogcA8pCzI/WgR+ts5uUjCp\nFKx/GwZPBpe7sLWIiIiIZFFGgdsY4wfOAUZt/x5r7U/7ce3DgA+ttcvT17gXOBPYOXDvF+LuAOFk\njke4Yx24kxG22GKGlPTcww0wpDTAZpuezaSQgbtzCzx4OSz7J4w4Aj57G5QMKVw9IiIiIlmUaUvJ\nIzhhOAG0b/foj2HA6u2+rk9v29kRxph3jDFzjDEH7+5kxpjLjTHzjTHzN20q8GhtN+KuEL5kjke4\nOxsBaHMXUxLs/bPU0LIgjXQF7gK2lDx7NXz0LEy/DNYthLm7dBeJiIiI7LMybSmptdaektNKurcA\nGGGtbTPGzAIeBsZ1d6C19lbgVoBp06bZ/JWYmYQ7iC8eye1FOpzAnQpUYozp9fAhpQHieIh5ivEV\naoS7vQHeugumnAufvg4CJfDSr2HTUqgeX5iaRERERLIo0xHuV40xk7J87TXA8O2+rk1v28pa22Kt\nbUu/fgLwGmOqslxHXiS9Ifw2xy0lHQ0AmFB5RofXlAQwBto85YVrKZl/GyQ64fBvOF/P/Bp4Q/DK\nbwtTj4iIiEiWZRq4jwLeTM8o8o4x5l1jzDv9vPYbwDhjzGhjjA84F3h0+wOMMYNNeqjWGHNYut6G\nfl63IFKeEH6b4xHudEuJuyizzyRet4tBxX6aXGWFC9zvPwQjj4JBE5yvw5Vw8Gdg8eOQjBemJhER\nEZEsyrSl5NRsX9hamzDGfB14EnADt1lr3zfGXJHefwvwWeBKY0wC6ATOtdbude0imbDeMEGiYC1k\n0O6xR9ItJf6S6ozfMqQ0yOa2YsYUooe7dT1sfB8+9eMdt48/FRb+FVa9CmOOzX9dIiIiIlmUUeC2\n1q4yxkwBjk5vesla+3Z/L55uE3lip223bPf6RuDG/l5nb2C9IVxYiHeCL5STayTbG3ADodLMA/fQ\nsgDrtxRD+9Kc1NSjj551nsd+csftY48Htx+WzlHgFhERkX1eRi0lxphvAXcBg9KPvxpjvpHLwvY3\nJh2yY52tObtGtHkjLTZEZUnmgX5IaZDVsTC2owFSyZzV1q2PnoVwNdRM3HG7LwxjjoMP5uS3HhER\nEZEcyLSH+1JghrX2f6y1/wPMBC7LXVn7H+MvAiDSnrvAHWtroNEWU1Xkz/g9Q0oDrE8WY7BbW1Ly\nwlpY8aITrF3d/DEccxxsWQnNa3bdJyIiIrIPyTRwG2D74c9keptkyB0IAxDpaMnZNVJtm2miiKri\nzAP30LIgDYVY/KZlLbRtgNrp3e8fMcN5Xj0vfzWJiIiI5ECmN03eDswzxjyU/vos4P/lpqT9k8df\nDEA0h4HbdG5hiy1iVB9HuBtsqfNFPgP3uoXpAg7pfv/gyeAJOoF74tn5q0tEREQkyzK9afLXxpjn\ncaYHBLjYWvtWzqraD3kCTktJvLMtZ9dwR5toYhRVRb6M3zOsLEgDzoeBvAbutQvBuGDwbqZ3d3th\n2KEa4RYREZF9Xo+B2xhTYq1tMcZUACvTj659FdbaPDb97tu8QSfUxjpy18PtjbfQaoop8mf6gwuo\nKvLT4uoa4c7j1IDrFkL1hJ5nbBkxA16+HmLtzo2UIiIiIvug3pLZ3cBpwJvA9vNfm/TXY3JU137H\nH3JGuBORHI1wp5IEk60kvCUZLevexeUy+IurSEVcuPI1wm2tM8Jd96mej6s9DGwS1r0DIw/PT20i\nIiIiWdZj4LbWnpZ+Hp2fcvZfvnTgTkbbc3OBSDMAqUBZn986pCxMy8ZSyvIVuFvXQ/tGGDKll8Im\nO8/rFbhFRERk35XpPNzPZLJNdi8Qcto2UtEcjXBHmpzn4J4E7oAzU0m+Wko2LXGeBx3Y83HFQyBU\n5Yxwi4iIiOyjeuvhDgAhoMoYU862qQBLgGE5rm2/Ego7U++loh25uUDnFgBcofI+v3VIaZD1yWLG\ntG/Kz1yPmz9wnqsn9HycMc4o9/p+L2oqIiIiUjC9jXB/Bad/e0L6uevxCPvJkuv5EgwGiFk3xHMz\nwm07nRFub7jvgXtoWYDNtoRk68Zsl9W9TUsgUApFg3o/dvBk2LgEErHc1yUiIiKSAz0Gbmvtb9P9\n29+x1o6x1o5OP6ZYaxW4+8DncdFBAGK5GeGOtTkTxviKq/r83iGlzuI3piNfLSUfQNV4ZwS7N0Mm\nQyoOmxbnvi4RERGRHMh0Hu7fGWMmAgcBge2235mrwvZHERPAlchN4O5o3owfCBZX9vm9Q0oDvGVL\ncMfbIN4J3mD2C9ze5qVwwMmZHTs4fWPl+nd7v8lSREREZC+UUeA2xvwIOA4ncD8BnAq8DChw90HU\nBDDx3ATuaKszwh0u25MR7gANbDcXd9nwbJa2o45GZ4GdqvGZHV8+Ctx+2LQ0dzWJiIiI5FBGs5QA\nnwU+Cay31l4MTIGuhCaZipoAnhyNcMfbG+m0PspKivr83oqwj2aTp+Xdt94wmWHgdnugapwCt4iI\niOyzMl2SsNNamzLGJIwxJcBGIIfDoPunmCuIJ9mZk3Mn27fQTJjyUObLuncxxmDDVRAl91MDNnzo\nPFfWZf6e6vFQPz839WSqoxFeu9lZiGfCaTBsamHrERERkX1GpoF7vjGmDPgjziwlbcC/clbVfiru\nDhJINeXm5J1baLZhasJ9D9wA3uKadODO8Qh343Iwbigbkfl7qifAew8Wbon3zcvgtlOgsxEw8Orv\n4Ow/wsFn5b8WERER2edk1FJirf2qtbbJWnsLcCJwYbq1RPog6Q7iT+VmhNsVbaaFMCUB7x69P1Be\n47zIeeBe4fSIu/tQZ/V4wDrBN98SUbj/ErApuPwF+N5HMHQqPHApbNTMKSIiItK7HgO3MWbqzg+g\nAvCkX0sfJDwhfKlITs7tjTXT7irG5dqzpWsqysrptD5sW47n4t6yAirG9O09XQvkFKKP+7XfO0vL\nn3mTM0VhsBzOvQv8JfDYtyCVyn9NIiIisk/praXkVz3ss8AJWaxlv5fyhAjY3ARuf6KFqLcPbRo7\nGVwapIESqls24c9iXbtoXAET+/hZrWIMuDzbloTPl3gE/vV7GHsCTJi1bXu4Ck78KTz6dVjyOBx0\nRn7rEhERkX1Kj4HbWnt8vgoZCKw3SIBoTs4dTLaSCO75xDGDSwM02BLKWjbkLnB3NEKkCSpG77Ir\nmbK4dzc67/ZCxdhtM5zky9v3QPtGOPLfdt035Tx46Tp49QY48PTMFvERERGRASmjHm5jTMgY80Nj\nzK3pr8cZY07LbWn7H+srwk8cm4xn98TJOEHbSdJfssen6ArcqVzOUrJlhfNcvi1w/+OddZz0mxc4\n8L/nctmd81nTtJse9+rx+R/hXvBnGDwJRh+z6z63Bw7/OtS/AR+/lt+6REREZJ+S6TzctwMx4Ij0\n12uAq3NS0f7MGwIg1tmW3fNGWpznYNken2JIOnC7O3MYuBvTgTvdwz33vfV8454FeFwuPj+9ltc+\nauBzN7/Kqob2Xd9bPcGZ4SSRm58Q7KLhI1j7Fkw+d/ej14fMBn+pE8xFREREdiPTwD3WWvt/QBzA\nWtsB6GfofeTyO1Padba3ZvW8NtIMgLsfgbu6yE8jJfijW8DabJW2o60j3KPY3BblP+5byJThZdx/\n5eFcfdYk7v3KTDriSb529wJiiZ1uRqwe78wU0jWPd669ez9gYOLZuz/GF3KmBlz0KESz/CFKRERE\n9huZBu6YMSaIc6MkxpixkKNm5P1YV+COtDdn9bwdrQ0AeEJ7Hrg9bhdRfwUeG4Nodj8QbLVlFYQH\ngS/E755ZRiSR4rrPTSHkc24lOHhoKdeePZn31rRw47M7TQG4daaSPLWVvP8gjDwSSob2fNwhX4R4\nOyx+ND91iYiIyD4n08D9I2AuMNwYcxfwDPC9nFW1n3IHnGXXox3ZHQ3taNkCgDdc3q/zpIKV6RPm\nqK2k6WMoH8n65gh3zfuYL0wfztjqHZeiP2XiYM48ZCi3vLh8x37uyjowrvxMDbhllRPsJ3y692OH\nz3B60t/vwLVrAAAgAElEQVS9P/d1iYiIyD6p18BtjDHAEuBs4CLgHmCatfb5nFa2H/KmA3e2e7g7\nWxoB8Bf1L3C7iqqdF7m6cbLpYygdzgML6kmkLJcf3f183N87xRnN/tWT24Vrb8AJtvkY4f7wKed5\n3Em9H2uMM0vJihe39dKLiIiIbKfXwG2ttcAT1toGa+0/rLWPW2tzeGfd/qsrcMc7s9uyEWtzRriD\nJRX9Ok+gNIerTaZS0FyPLRvB3+evZsboCkZVdb9M+7CyIBcfMYqHFq5hxebtbqCsHp+fEe5lT0H5\nKKgcm9nxEz4Nqfi2oF4IyQQsfgyeu8aZO7xlbVZOm0pZIvEkqVSO+vpFREQGgExbShYYY6bntJIB\nwBdypu2LR7I7wh3raAIgXNK/Ee5g+WAAIs05WG2ybT2k4qxKVrKyoYPPTRve4+GXHj0ar9vFrS8u\n37ax6gBnppJkIvv1dUlEndHqcSdlPrd27XQIV8OSf+Surp40fAQ3Hw5/Ox9euBaevAqunwQvX7/H\nK2G2RxNcM2cxU69+ign/PZeZ1zzDr5/6gGgimeXiRURE9n+9rTTZZQYw2xizCmjHmaHEWmsn56yy\n/ZAv5IxwJ7McuJMdTaSsoaSsfyPcpVVDAGhvXEcgG4Vtr2k1AP9qCONzuzhl4uAeDx9UHOCcqbU8\nsKCeb584jkHFASdwJ2PQtCrz0ee+WrMA4h0w+tjM3+Nyw/hT4b2HnMDuyWzpoNZInDnvrmdFQztD\nSgOcMGEQteWhvtW76QO47SSnv/3zd8L4Tzvfn6d/DE//yHn96V/3aWGetU2dXHz7Gyzb2MopEwdz\n8NBSFqzawg3PLOO5JRu5/eLpVBXldD1SERGR/UqmgfvknFYxQATTI9zJaDfzTPeD7WymjSClof6F\noOryMtpsgGguRribPgbgyTU+ZoypoMjf+x+9y48Zw71vfMwdr6x0+rqrDnB2bF6Wu8D98b+c5xGH\n9+19E06DBXfCypeg7lO9Hv7ggnp+8tgimjvjuF2GZMpy9T8W843j6/j6CXWYTAJypAXu/SIYN3z5\nqa3zm1M51gnfT/8IXvktFA+FY7+b0S+jJRLnottfZ11ThD9fchhHj6veuu/J99fzrXvf4qLbX+ee\ny2ZSHPBmdE4REZGBLpObJt3Ak9baVTs/8lDffiVQVAxAKstzNptoC62ECHrd/TpP1+I3idZcBG7n\nj8u8xhCfOrAmo7eMrgpz6sTB/OW1VbRG4lBV5+zI5RLvH/8LqsZDuLJv7xt9LHjDGbWV/OqfS/n3\n+95mfE0xD331CD64+lSe+85xnHhQDb966gN+8MC7mfVMP/U/0PgRfP7P28J2F2PgUz+BSZ+H538O\nK1/u9XTWWv7jvrdZvqmdP3zp0B3CNsDJBw/m97OnsnhdK1c9+C42V/O190FzR5z31zazcnP7XlGP\niIhIdzK5aTIJLDXGjMhDPfu1UMgJ3MSyO8LtijXTbsKZjYr2YHBpgEZKcjNLSfNqOr3ldOK0TmTq\nK8eMpTWS4N7XV0Ow3JnHO1eBO5WEj+fByD6OboMzi0rdJ2HJEz32Tf/hhY/43bMf8oVpw7nrshl8\nYkQ5bpdhdFWYG8/7BN84oY6/zV/NDTvPQ76z+vnw5h0w40oYdVT3xxgDp/3Gmd3lwa/0+ufuobfW\n8NSiDXzvlPEcUVfV7TEnTKjh258ax+PvrOPBBWt6rjGHlqxv4aLbX2fq1U/x6Rte5rjrnufIa5/l\ntpdX7LpokoiISIFletNkOfC+MeYZY8yjXY9cFrY/8ng8dFqf0yOcRd54GxF39zN+9EXA66bZVYo3\n0pCFqnbS9DHrTTVjqsMMr8i8T3nK8DJmjqng9ldWEE+mnLaSzb2E0T21cTFEm/veTtJlwqedm0PX\nLex29/NLN3Lt3CV8evIQrjl7El73jv/7GWP49xMP4Oypw7j+6WW8+MFuZouxFp78TyiqgeOv6rkm\nfxGc9XtoqYcXr9vtYU0dMX76+CIOHVnOpUd1P11jlyuPq2P6qHJ+9o9FNLbHer7+zpIJiDT3azXT\nu+d9zKdveJmFq5u44tgx3HL+VH7+mUmMqAzx08cX8blbXqV+S3b/HxMREemPTAP3fwOnAT8FfrXd\nQ/ooYvyYLAduX6KVqLs4K+eK+ioIxrdk5Vzbs031LIuWc/iYPrZq4PRyr22O8I931kHVuNyNcO9p\n/3aXuk8BxplWcCcbWyJ8+28LGV9TzHWfnYLL1f1PI4wx/PwzkxhbHeaqB9+lLdrNjCwfPgOr58Gx\n3wN/Br/vI2bClPPg1d/B5g+7PeS3zyyjpTPO1WdNxL2b2rq4XYarz5pEWyTBL+ZkMC96vBNeuxn+\ncCz8rBKuHQHXjnRmVfno2T6F7z+88BH/+dC7HD2uiuf+4zi+e/IETpk4hC/OGMG9lx/OzbOnsnxT\nO2f//lU+3JijFVNFRET6KKPAba19AWfxm+L0Y3F6m/RRpwniynLgDiTbiHuzE7jjgUqKkk39GoHc\nhbWkmutZnaxg5h4E7uMOGETdoCJufXE5tmocdDZCew5G4Ve9CiXDoGwPu6fCVTDsUFj2zx02W2v5\n4cPv0RFLctPsqQR9PffaB7xufnHOZNY2d3L9Uzt9uLDW6ckuGwGf+FLmtX3qJ+ANwpzv7fJ7u7qx\ng7/8axVfmD6CA4eUZHS68YOLueiIUdz35mqWru8h2H48D246DOb+wJnN5Zjvwok/g4mfgY9fg798\nBv56DjTX93rNh99awzVzlnDa5CH86YJplId9uxxz6qQh3H/lEaQsnPfHeTuuVioiIlIgGQVuY8zn\ngdeBzwGfB+YZYz6by8L2V1ETwJ3IbuAOpdpJ+rITuE24Eg9JiDRl5XwARJpwJzpYayuYMabvUxe6\nXIbLjh7NonUtLIqnpxPM9ii3tc4I94iZfZpCbxfjToI1b+7QB//Eu+v556INfPvEA3ZZyn53po2q\n4HOH1nLnv1axunG7Py8f/8s5/5HfAs+ugXO3imvguKvgo2dg6Zwddt38wke4jOHfPjUu8/MBXz+h\njiK/h18+uZvFiN6+F24/FTBwwaNw2bNwwg/hyG/C6b+Fb78PJ1/jBO+bj4Dlu/8Mv2R9Cz948B1m\njK7gV5+fgse9+7+6xg8u5p7LZhCJJbn0jje6/ylBjnXGksx9bz0/f2IxX7t7AV+7ewE/f2Ixc99b\nV5B6RESksDJtKfkvYLq19kJr7QXAYThtJtJHcVcAdzKLo27WErbtpPylWTmdu9iZQSTWksWZSpqd\nm+tSxcOc+bT3wJmHDKOqyM+fFqenE8x24G5aBa3r9rydpMsBJwEWPnwagC3tMX706HtMGlbKl48a\n3adT/dunDsAY+M32o9yv/g6CFTDli32v7bDLoHKcM11gevGg9c0R7p9fz+em1VJT0rffm7KQjyuO\nHcvTizcwf2XjjjsX3g0PfQVGHQlXvARjupnX3OOHw78KV77sTF3413Ng4T27HBaJJ/n63W9RHPDy\nuy9+Ar+n99l4xtUU8/vzp7JsYxvfuHsBiWQvN1K2boB374dnfgqPfQv+8R/wwi9h6VyIZf4BuT2a\n4Nf/XMqMnz/NFX99kzteXcnitS0sWtvCHa+u5Iq/LuCw/32a/3zoXdZq9F1EZMDIdB5ul7V2+wTW\nQOZhfbeMMacAvwXcwJ+stdfutN+k988COoCLrLUL+nvdQoq5Q3izGLgTnS14jMUEMmsF6E2gzAnc\nWzatpaZmfFbOmWqqxwVUDe35Zrwe6/K6ufSo0fzf3EX8KuzHle3Avaqf/dtdBk9xZlL54EmYci4/\nfXwRTR1x/nLpjB5HZbsztCzIRUeO4tYXl/Plo8dwUKDBGZ0+5jvg6+MCOQBuL5z4E2fu7gV/humX\ncuuLy0layxXH7tm85hcfOYo7Xl3JL+Yu4b6vHO7MlLP8eXj0G85UiV+8z5nBpScVY+CSuXDfl+Dh\nK5wPPkf/+9bdv37qAz7c2MadlxzWpw9sR4+r5idnHMwPH36PX/5zKVedeuCOB1jrrCr6yvXw0XOA\nBZfHmQ0nlXRalwA8QRh7PEy90PkJhqv738eXl23mu/e/zbrmCKccPJjzZ45kxpiKrTfHxpMp3ly1\nhYcWrOH++fXc/2Y9F8wcyTdOGEdpSHOai4jszzIN3HONMU8CXcNPXwCe6M+F0/N73wScCNQDbxhj\nHrXWLtrusFOBcenHDODm9PM+K+EOEky0ZO18bc2NlAGuYFlWzldc4bRstDSsJ7PZsnvXsG451cDw\n0XX9Os8Fh4/kjy8tZ7VrGCOzHbjrXwd/CQw6qH/ncblg3Imw5HGeX7SWh95awzc/OS7j3uidffXY\nOu6Z9zG/mLuEP4+Y47S7HHrxntc3fhaMOAKev4aGsWdx9+urOOuQYX2aOWZ7IZ+Hb35yHP/98Hs8\nv3QTx1c0wN8ucEbSv/CX3sN2l2AZzH4AHvkqPPMTZ0XRY7/Pu2ta+NNLy/nijBEcc0B17+fZyfkz\nR7JoXQt/eGE5nxhexikTndVU2fC+M5Jd/4bzAenY7zurhdYc7HwwAWcaxdWvOx9yFj8GS59wZsk5\n4psw5dytx1lruem5D/nVUx8wtrqIB648gkNHlu9Si9ftYuaYSmaOqeQbn6zjt08v47ZXVvDQW2v4\nz1kHcvbUYd1P7blllVNHwzJo+AiiLZCMO6uLFtVA8WCongBDD4HKOqdXvgfWWja2Rlm5uZ3G9hjN\nnXE8bhcBr4uKkI/a8hBDygK7zKIjIiJ7rsfAbYypA2qstd81xpwNdE34+y/grn5e+zDgQ2vt8vS1\n7gXOBLYP3GcCd1pnRYvXjDFlxpgh1tp1/bx2wSTdQXypSNbO19biBG5vODuBu6xqKACdW9Zn5XwA\nm9esoMy6ObCubz3COwv7PXzlmDG88/QgBq1bQjBL9QFOX/SwqbsdveyTcSfBwru458EHOaBmEl87\nfs9XxSwNefnq8XVcN+c94pvuxDvuZCgdtue1GQMnXQ1/OoGlD1xNNPEpvtqP+gDOnT6cP764nN/P\nXcBx5vsYbwBm/x0CfWxz8vjgM38Atw+ev4ZUIsYPFx9PZZGfH5w6YY/r+9HpB/H+2ha+8/d3qKsK\nUffRHfDs1U59p/3Gac/p7oOBL+yMbI89Hk7+X3j/YXj1t/Do1+HlX8NxV5E66Gx++sRS7nh1JWcd\nMpRrzp7c602xALXlIX75uSlcdOQofvjwe/zH39/mb/NXc/VZEzlgUBGsXQBv/825AXfLCudNxgWl\nwyFUAS4vpBKwaakzFWUq3RceKHV+sjD2BOdRPhJwWoeeWbKB55ZsYuHqJja3RXusz+MyjKspZuLQ\nEiYOK2XisBIOHFJCyLfdPxnJhNPatXGRs5Js82roaIRoKyQiTr0uNwTKIFztPIoGQdlwKBsFpbWZ\nfyDrr1iH80El1u48EhFSFmIpg3W58HgDeEKlmECZ8/vezzUN+spaS3NnnIb2GB3RJB2xBJ3xJMmU\nxeN24XEZPC5DccBLRdhHWchLoJ8Lne2JSDxJRyxJJJ4kmkiRSKZwuQxuY3C7DAGvm+KApyC1iezt\nehvhvh64CsBa+yDwIIAxZlJ63+n9uPYwYPV2X9ez6+h1d8cMA/bZwJ3yBPHb7AXujmZntg5f0a4j\nanuiqsYJ3LHmDVk5H0CkYRWbKGdsTf/7zC88YhR3vzQSf9s8EtEOPP6+jcxG4kkefXstj729lnfq\nm2mNxBkWhucT77HqwMsYlbK7nbIvY2OPJ4mbQ6Lz+OqF52fUc9yTCw4fyUcv3I23czMcelH/agOo\nPZTYhLM4ZPFdnDfh1Ixv5Nwdr9vFt06ow//IpVjPaszFc5xQtSdcbjjjRnC5cb38K2YlljD4nP+j\npB/LyPs9bm6ePZXLb3iAjj+eAslFcODpcNr1zswymXB7YfLnYNJnnRHv534OD17Ghsf/lw1tZ3Lp\nkZ/nvz59cJ//7Bw8tJQHrjiC++av5rY5r/DI7+7g4qLXqIqsBLffCc0zrnAWN6oa5/S976wr+K5b\n6My089GzsNhZJqE1PJJX7SQebhrLa6kDKaqo4ZgDqpg0rJS6QUVUhv2Uhrwkk5ZIIsnmtij1jZ2s\naGhn0doWnl2ykb+/WY+POONdqzmueB3TA6s5ILWc6vZluFPbBfdguROq/cVOG04qiU1EsU310L4Z\nV3TXG7HbfNVs8Q5mk2cw680gNnoGs9kzmM2eGrZ4BpE0HoxxwqYrHTq7wp3bZQjaTsqSmylLNlAa\n30wgspFQdBPh2GaK4o2UJBooTTUSsru28bmA7uJ+wrpoNyHaXUV0uEuIekuJ+8pI+ssgWIErXI47\nXEmgpJJQMEw4FCTg9+Py+HB7PLhtgli0k3ikg1i0k2iknfbWVjrbm4m2txLvbCUZaXVWHI6140p0\n4El0ECBCmCgVJsJwIriwJHHt8EjhotO6acJHwnhJuXzg8WE8flzeAG5vAI8vgM8fwB8I4g+E8AeC\nuL0B3D4/bm8A6/aTTFmSiSiJWIRIxHlEo53Eo1FisQiJWIR4LEYyESMZj5JMxLHJOK5UHA9JvCaB\nN11RChcJ3E6N1qnTGjfG7cbl8mDcHlxur/O98XjxeLx4vV48Xi9erw+v14dxuTFuD7g8uIwLY1Mk\nk4ntHknnObHtdSKRJJVKkEymSKW3pVIpUqkkqWQSbBKDxYXFjXMPhzHgNgbjcuEy4HK5cBuDywUu\n48LtMhhjcBmDcTnPLrPdNgMpC848TwZrLSkMYLEWUtZgsaRs+jgLKdLPFlLWbt22836TPj/GhUkX\na3C2Y5x6t21zru88tn0+tBi2/g20y4dGp7Yu3U1EZnf8z0472OH9PUqfvLvPraaHc/T0t2dP7+vi\nmXgGkz91fq/HFUpvgbvGWvvuzhutte8aY0blpKI9ZIy5HLgcYMSIvXdRzJQ3TLCbv/z3VLTN6TMN\nFPV99o/ulBSFabEhkm3ZW23S1bqWVn8NQ/sbZHF6uaceehiueX/jvqde4NzTTs3ofdZaHlywhl8+\nuZT1LRHGVIWZNWkIFWEvvnXzca9Mcs3bIdZvfIVrz5nEwUP3/MPBMysihFMHcE7xIgYN7/9PHkI+\nD98sfZm1jRWs909jar/PCHcXXcQXeYzv+h4ATur3+T6T+icu9zxu9V3IpbWH0a+PGC4XDcf/H08t\n2MBXPP/ArquFQ36x56OO1jL0o/t4xHUVHfEUfx58FRd87nuYPflphjEwYRado0/ktj9ez0kbb+dm\n32+x9c9glnzfadlxZ9qpB0RacC1+jHMX/40v2BcxHsvrHeP5o+9Kps+6mE9+4oDeV5B1e6DmIKg5\nCDvlPOavbOTFV18ltvQpZrS8zTHupznZ97jzrSieiPF/AtwTwdSBqwZcVeD1grUc4G0D3yYIrYXA\nUmzxEhLrF+Fu/BCXTUAU2qIh3k2O4jH7Sd5LjWKxHclaqkmlwngjLrxuF8Y4M7W0xxJb/2H3kqCK\nZmrNJmrNJoabTQxPbGSEezMjzEKm0LA1GAEkcdFoKogaPwncxHFjsARtJyHbSZAIAXZdeKmdII2u\nCppcFazwjqXVM50ObwVxbynWG8L6ghhfCJ/Lhd8NLlKYZBRXrBVvvAVPvA1XtAV3rBlfvJlApJnK\njtUU21bKTGarBPvTj+6krKHDBIiaIHF3kIQvhA2HwVeOy18EvjAdvjButxsXKUglMakk7mSCVCKO\nicfwxiO441FsPIpNRiHWhKszijsVx2fi+EjgI46fOD7iuM22sGJw/uH3pGvsWjItZt3E8BLH4wRo\n48W6PFiXF7xeTMCLcXvBHQC31wnIxg02XaNNYFNJUskENhknlYpAytlGLImJJDA2icsmcJPCTRIP\nSdyktj57TXLr96jrA8a2DxvbtqVwOVHaOA+2f7jcGLfz2pquYw0Yg7VgbSoddlOkUs6/DdbadBh2\nAnHCWrpC9Pb/920LfXbr93LnfS5jcWPAgAsLGFym63jndVde7tq/w3nTgdcCJl3H9vvsTtfb0a51\ndXesE717+/u05/19f/92Yb+H9/a8r2erNk7p5YjC6u1fhp7SQn9/or8G2H4YrDa9ra/HAGCtvRW4\nFWDatGlZnEQ6u6w3RJAoNpXas3/wdxJrd0aNQiXZGeE2xtDiKsXdmZ3A3RlLUhbfQGf1IVk5H8CU\nQ6bDPHjltX9x0CGHM7m251C7pqmTqx58lxc/2MQhw8v49eencPjYym1B5rXnYCV85rQz+PFzDXzm\nplf53injueTI0X0esdzSHuOqB9/l8tBMZnbc7swvXVq7h7/StMYVDN/yGre4Ps9rzy3njoszHJXd\njfZogusXxBlaehYnfXAfbPiWE9j21Pp3cT15FRtrjuaaVSdS+dYazjm0f7/ma+d+wEOxCzllWi1l\nr/8BOrfAGTc4c4n3ResGeOyb8MFc3KOP4ZHB3+dHzzUTf2UlXz56z27ibe6Ic+mf3+DNNQdRceY/\nGBd8HfP8Nc5Nn0U1Tn/3uJOcOdm7q3fLKlj1itMusnSO035RPhpz7Pdgyrm4W8t44aH3+MN9H3Lo\nvAZmzxjBrElDdvtjemstH25s4/F31vHgW/Wsbuwk5PPy6UmXUjJ9OIHaImf0e8ULmJWvOL3ob/0l\no1+rKRuJt3oCHHgqDJkCQ6ZQVDaKibEkpY2djGnuZFpzhA3NESLxJImUJZZMYa0l5PMQ9rkJ+T0U\nBzyUBLyUBr2UBL2UBDyUBr0UB7z4POm/B5NxaFnjtKdsWYW7aRXVzWuc708qnp5Zxzoj6L4iZxXV\nUBUUD4GSIc5z8WDC/mLC7PgPRzZYa2ntjNKyZTPtTZvobNlMe0c77Z1R4rEopGLYZIIYXlwePx5f\nEI8/gM8fpLi0nNLSUsrLyikvKaXI7aJ/P1fqXjJl2dIRY1NrlM1tUTa1RmnujDuj1fEoyVgEL3F8\nHhcurw+PN0BxUYjScJiKsJ+ykJfysI8yn7v3D3p7yFpLeyxJc2ec5o44bdEEiVSKZMqSSKZIJi3W\nGAJeFwGvG7/HeQ543IT9bor8HvweV87q27nWWDJFLJEinrQkU9b56crWUXHnJy3OSDhbR8ilMPrR\nbJkXvQXu+caYy6y1f9x+ozHmy8Cb/bz2G8A4Y8xonBB9LrDzXGePAl9P93fPAJr35f5tAOML4zEp\nItEIgeCe3ai2vUSHE7iLSvu+oMzutHvL8UUbez8wA4vXNXEwjaytzN5PHUyl0ws+yb+BS/88nweu\nOIIRlbt+LxPJFHf+axW/fuoDUtbykzMO5kszR+4aouvnQ8kwZh3xCWZOifH9B97h6n8s5sVlm7n+\nC4dQ0c0CK91JpizfvPctmjriHHvuF+GB251VJ6f14yZHgAV3gnERnHERzz/v9OAe0o+R87vmraKp\nI07Nef8NDzwNT/0PnH//np0s2gZ/vwhCFVSdfzsH3b6E65/5gNOnDN0WpPpo/spG/v5mPVccO5ay\nU2ZB5RB47mrYvBS+cFdm7SqpFLzzN3jyPyHeAaf8Ag67nNnG8NLGN7lmzhLGDiri+PGD+lTbxpYI\nF9z2Oss3tXPTF6cya9IQYDRMPMcJ0G/9BV69EV75rdNnXTnW6WH2Bp252VvqnQ8P4ITFT3wJJn8B\naqdtHcE/tAIe/8ZR3DXvY25/ZQX/ft/b/OiR95kxpoIJg0uoLPKRTFk2pds/Xl/ZyKbWKMbAUXVV\n/PuJB3DywYN37LcefpjzOOa7zo972zZC43Jo3+jUZdMjy96Q02ddNMi5AdMXpjvFARcHDfVy0NDs\nzI4EOG075aOcR99m0MwLYwzFoQDFoVoY1s8P0TnidhmqivxUFe1ufL3wjDEU+T0U+T0MK8vqnThZ\nZ4zB73H3uy1QBHoP3P8GPGSMmc22gD0N8AGf6c+FrbUJY8zXgSdxpgW8zVr7vjHmivT+W3BmQpkF\nfIgzLWA/k0vhGb/zD1hHW0tWAneqoxmAkrLsBe6Yr4Jw+8dZOdeHK1Yy1SQoH5LFf0F9ISgdwbmD\nItz0YYqzb36F//vsZI4fPwhjDKmU5ZWPNvPzJ5aweF0LxxxQzf+eNXH3M3F03TAJVIR93PqlQ7lr\n3sf89LFFnHbDS/z+/EN7DbjWWn72+CJeWraZa86exLiJw+Hp4c70gP0J3Mk4vPVXGHcy5xw/g9+8\n/iw3PLOM2y6avken64wlufXFFRxZV8mUcaPh6O/AU//t1HnAyX07mbXO9H+Ny+HCx3AVV/OdkywX\n3/EG981fzfkzR/a5vlgixX899B5DSwN885N1Tgg99rsweCI8cBnccpQzteEh5+++daN+Psy9ypl5\npnY6nHkTVDtTXBrgus9N4dxbX+PKv77JnZfM4LDRmbVjvbemmcvvnE9zZ5zbL57OkXXb/aTB7YEJ\ns5xHR6Mzq8jHr26bVSTa6tzsOnw6VB/ozE9efeBub9L1uF1ceMQoLjh8JP9a3sBjb69l3opGnlu6\n6f+3d+dhcpVl3se/d1V1V/W+pJfsG4RACIRADCSggiKDoASZcUFE3MZx13EWnXHGcd53xmV0xvF1\nV0T0lVEZQUXBhU1hFBSMZCNAQgJJdzpJJ71Ud9fS1VXP/HGqQyfp7lR3LaeL/D7X1Vdtp6pvzkXI\nj7uecz+kM94XeJXBAG31Ydaf4k0+uXh5K3MacggwZt5GSHWFmkMkIiInMmngds4dANab2SXAyuzT\ndzrn7ivEL3fO3cUx4wWzQXv0vgPeXYjfNVNYtmOUiEWB2Xl/nkv0k3AVRMKF6xRkqmdRP7DlyNdn\n+di/dycADe2LC1DZGC3LqB/czQ/esY533bKRt9z8KAubq5nbGGFX9xAHB5LMaYjw5evO5fKVsyf+\nmi/W402BOO+GI0+ZGW+4YBFnz2/gnd/ZyKu/8lv+8RUruP6CReN+Tibj+NQvnuDm3z7DWy5cwrVr\ns9385Vd4866HhybsFJ7Qk3d5Xcg1b6Y2HOJtFy3hM798is0dfSdcSjOebz30DIcGk3z50uxK8PP/\nAn1dbiYAACAASURBVB67BX76QXj3w97X9bl66Auw7Xa49GPeRX3AxctbOW9RE5+/bwevWj2PmvAU\n1jMDX/7V0zx5YICb3rTm6A7t8pfD23/lLQ/5yfvhwf/wlm4sON+7UC8Zha5N8PiPYe/vvOc2fAlW\nXXtcqK2LVHDzm9fy2q89xBtv+h1fuu5cXnL65OHzZ1u6+OCtm2iqruD7f7GOlfMmWeNf3QzLL/d+\n8mRmrD+lhfWneOE+lc4QjacIBQLUV4X09bWISJnI6Ttf59z9zrnPZ38KErZPVqGIt3IvGRssyOfZ\ncJRBm2aYm0Cgto1mohyM5r8Fff/+ZwCwfNcxH6vlNDi0g2WtNfzkvRfxb392Nstn15FKO9adMovP\nvnYV9//1xbz8rDmTh5LO7D5K88477qWz5zdy5/su4qJTW/joj7fxhm/8jk17j560sOdwjLd9+1G+\n+utdXHf+Qv7hyjGbq5zxCm/9aXbXyWl59CaonwenXgp4U1oaqiqO3n0yR9FEiq/8+mlefForL1ic\n7eqGwnDV5721sz/7UO4ftuvX3lKUM66CCz9w5Gkz4++vOJ0D0SRfuH/nlOrbcWCAL9y/g6tWzR0/\nALecCm+6E173X9C4EB74NHznGvjqC+HmK73lI8kBuOxf4b0bYfV1E3aQW+vC3PoX6zi1rZa33Pwo\nn7hr+7hbrh+IJvirWzfxzls2csacOn70ngsnD9tFVhEMMKvWmyyisC0iUj6m1n6SvB0J3PGBwnze\n8ADxQGEDd6SxjaA5DuzvYk7j9DerSY6kcf2d3r9lBQ/cy7y1uQP7iDTM5zVrFvCaNdO4TKrzD4DB\nnPEv6mysruQbN7yAW373LJ/+xZNs+OJvWNpaw9KWWg4NJtnU0UckFORjr1zBDesXHx2CFq73tmHf\n/lNYsWHqtR3a6e3aeMk/HNnMpC5SwTtefAqf+vkTPLzrMBcszX0p0U3/s5u+WIq/vuyYHUQXrPV2\nr3zg07BoPaw+wVilg9vhv2/w1vhe/aXjpoect6iZPz13Pjc+uItXrZ7Hae0n7pqnM44P3baZ2nCI\nf3rlJBdwmsHpV3o/sR5vA5t4r/cNQtsZUD/3hL9rVEttmB+8Yz3//JNtfPWBXdz66F6uOGsOy2fX\nMTySYeOeXu55/CAZ53jPJafy3peeqrWcIiIyLQrcJVZR5YWPVKwwgbsiFSURnMIygBzUNnu78R3u\n3genTz9wP7V/kHYOkQ6ECVYXbo054HW4wZs/nE+Y7/yDt0tfZOKLvwIB4/p1i7l69Txu39jJgzu6\n6eiNUR+p4H0vWca1axcyu2Gcib7BkLesZPsdkEpMfZOPR7/hXXh37huPevrNFy7m2w89w8fv2s6P\n3nVhTpNUeoeGufHB3Vx+5mzOmj9Oh/bFH4Y9D3vLNWpnw7JLx/+gA9vg/1/jbU7z+u9PuATl7644\nnfufPMgHb32MH77rwhPuWvi5e3ewcU8f//nac5iV6wVf1c2w5IW5HTuBSEWQT1xzNq99wUK+/uAu\nbt/YSTzljSZrrw/zurULeNtFS8e9KFdERCRXCtwlVpHtcKcShVlSEk4PMlxZwEkBQFOrF7ijh/Ib\nCLN1Xz9z7TCZurkEC/3192jg7n7K2xxkOpzzAneOFwvWRSq4Yf1ibli/OPffsfIaeOw73gSLFVfl\n/r7hIfjjLd57jrm4LVIR5G8vX85ffn8T33tkL68//8QTYP797ieJDY/wwctOG/+AYAhed4u3NON7\n18IVn4Zzbxizo4KDrbfBT//Sm2Rx/Y+geeKxei21YT7+qpW84zsb+fhd2/mnV5454bF3P36Az9+3\ngz87bz5Xr/ZnsNM5Cxr54uvPJZNxHBpMEg4FtUZaREQKpgD7WMtUhKu9juBIgQJ3VXqQkYrCBu5I\ng3cxZ7wvv90mt3b2Mz/YS6ipCCO0atu8cWvd26f/Gb3PQOyQN5KtWJa8GGravBF1U7H1Nkj2wwve\nNu7LV58zj/OXNPOpnz/BgejkO5f+4dlebvndHt60fsnkyzsiDfDGO2DRhV6n+2svhvv+1dtV8euX\nwG1v9ZaRvO2enOZ2X75yDm+5cAnf/M0z3PjgrnGP+Z8dh3j3f23k7HkN/N8NK8c9ppQCAaOtPqI1\n0iIiUlAK3CUWqfECTzqZ245lJ1LtYmTChQ3c1LQCkIoezOtjtnb2syDYU/gLJsHrvLaf6a0nnq6O\nR73b+dMbsZeTYOi5Gc2xHGebOwe//zq0rYCF68Y9xMz4+DVnMTyS4QPfe+zIqLhj9cdSfOD7f2RO\nfWTi7vZY1c3whtu8CR+ZDDz4Gfj1v3mbjlz5H17YnsK27R+58gxevnI2/3Lndv7hR1voi3k7A8aH\n03zpVzu54Zu/Z/Gsar755rVUVWp9tIiIPD9pSUmJRWq8cOwK0OFOpNLUM0RHoQN3dXaCRWz6u02m\n0hme3N9Pc6jHm7JRDG0rvM6xc9Pb9rvjEaio8eYhF9M5r4fffRk2fRfW5TDl8tnfwv7NcOW/T/rP\ndUprLf+84Uz+9geb+eiPt/IvV688qiubSKV5z3c3sr8/wffevo7aXEf0BYLehI/V10EqDoGQtynJ\nNAQDxhdefy4fv2s7N/1mN7c+0sHCWdV09cUZGk5z2Yp2/v01q6iLTO/zRUREyoECd4lVZZeUuOH8\nR+5FBwZpsxRWVeAxZcEKYsF6KuKHcc5N66v1nQcHaRw5TCCU9jb8KIa2M7z5y/17vTFxU9XxiLfh\nzUQbqBTKnLNh/lp45EY4/50Tjqo74sHPeLsQrjp249Xjvfq8+ezqHuIrv36a/niKj111Ji21YXYf\nGuJDt23m97t7+NSfnsV5i5qmV/tUt1IfRzBg/OMrVvDqNfO5fWMnu7qHWH/KLK48aw7nT2HKioiI\nSLlS4C6xYGUVaWeQyn9JyUB/D21AqLrwc4GHw800DPfRG0vlvLX5WFs7vQsmAagv0jbI7dkL8Q5u\nn3rgTiVg/xZY/57C1zWetX8Ot/85PH0vLHvZxMd1/gGevs/bTKbyxJMxzIwPXb6cukiIz979FHdt\n6aK9PsL+aILqiiD/+dpzfLsQ8Vinz67n768o8LcxIiIiZUCBu9TMiFukIIF7KOoF2oqaaXYvJ5Gp\nbmHW4ACdvfFpBe5t+6Isqej1HhRjDTd4HW7wRtVNdVvy/Zshkyru+u2xVmyAe/4ZfvUJbxOb8b41\ncA5+8RGvu73mrTl/tJnx7ktO5U/ObOeOTV3s7YmxtKWG161dSGtdjiP2REREpGgUuH2QIEIglf+S\nkviAF2jDtYUP3KHaVmYd7OKpntj4c5tPYGtnP1c1DMIAxVtSEmmAhgVw8PGpv7fjEe92XhEnlIwV\nCsPFH4Y73gNP/BTOeOXxx2y9DfY8BK/83KRzwSdyalsdH3xZYWeyi4iISP40pcQHyUCE4Eg8/88Z\n9AJ3dV1z3p91rKqmdpotyrM9U+/EpzOObfuinBaJQmWdF4yLZfZZ0LV56u/reAQaFh4347qoVl3r\nbbJz19/A0OGjX+t9Fu78IMxdDauvL11NIiIiUnQK3D4YDlQRTOff4U6NBu76wl94VlHfTpMNsvfQ\n1HfE3H1okHgqzYJgb/G626PmrPJ2m0xOcepLx6PFnb89nmAIrvk6xA57W6Mn+r3n+zvhu9d6S0r+\n7KYj27iLiIjI84MCtw9SgQihAnS40/E+AGrqC7+khOoWAjgOd++f8lu3dkYBaE53F28k4Kg55wAO\nDmzN/T3RLm+ySanWb48152x45f/zlo58aR18/3r48nro2wOv+fakuzeKiIhIeVLg9kEqWE1lJv/A\n7eJehzRQ3Zj3Zx2npgWAWM/Ut3ff2tlPOBQgEusqTYcbYN9jub9ndP22H4Eb4Jxr4YafeBd9dm6E\nU18Kb7sbTrnEn3pERESkqHTRpA9GQjXUJfLbNh2AZJQ0AYKVtfl/1rGyu026oW6SI2nCodyXOWzu\n7OfsOVVY98HijQQcVT8HatuhawqBe89DEIp43Wa/LFrv/YiIiMjznjrcPkiHqom4RN6fE0hGiVn1\n9HZZPJG62QC00sfenty78emMY2tnPxe1eVt4F73DDd6ykql0uJ95EBas9SaHiIiIiBSZArcPXGUN\nVQUI3BWpKPFAEbrb4HWNgVbrY88UJpXsPDhIbDjN6obse4q9hhtg3nnQ/cRzFyFOJt4L+7fCoouK\nX5eIiIgICtz+qKyhmgTDI5n8PmZkkGSoSIE7XIcLVdFmfTxzKPeJKps6vAs5T6vyLpws2qY3Yy28\nAHCw9/cnPvbZh7xjFytwi4iISGkocPvAKmsJW4qhWH4XTkbSg6QqirTRiRnUtTMv1M/O7txH7m3a\n20ddOERbptt7ohQd7vlrIBCCZ3974mOfedBbvz3vvOLXJSIiIoICty8s7HWlhwZzWAIxAeccVZkh\n0sUK3IDVzmZBxSA7D+YeuDd39HPW/AYC/Xu8Cy8rq4tW3xGVNd60kj0Pn/jYnffAwnVQESl+XSIi\nIiIocPsiGPFCcjI29U1lRg0mR6izGJlwEXdxrG2jPdCXc+BOpNI8sT/K2fMbvTnXDQuKV9uxFq6D\nzj9AapK18T27vU1yTvuT0tUlIiIiJz0Fbh8EI16HOzEUnfZn9MdT1BPDirltet1sGtKH6Rka5vBg\n8oSHb++Kkko7Vs1v8DZyaVxYvNqOtfiFkE56I/8msvMe73bZZaWpSURERAQFbl9UVnkd7uGh6S8p\n6RtKUkucQFUxO9zthEcGCTPMjhy63Js7vH+eVfProW8vNJaww73kRd7a7Cd/NvExT/3C28lx1iml\nq0tEREROegrcPqiszgbu+PSXlAxFewmYI1RThF0mR40ZDZhL4N7U0UdLbZg5oQGv29y4qHi1Hauy\nGpZeAk/9DJw7/vWhQ7Drfjj9ytLVJCIiIoICty8qq+sBSOUVuHu8zypm4M5ufrOoIsrOAyeudXNH\nP6vmN2B9e70nSrmGG2D55d5SloOPH//alh9AZgRWXVvamkREROSkp8Dtg0iNtwwknZh+4E4O9gJQ\nVddckJrGle1wn92Y5PGuydebRxMpnu4ezF4wucd7spRruAGWX+GNB/zjLce/tum7MPtsaD+ztDWJ\niIjISU+B2wdVtV6HO5PMfQfHYw0PZQN3ffED98qGBFs6+xlJT7xRz6PP9OAcvGBxk9dlhtKu4Qao\nbYMzXwUbvw2JMf+DsPsB6HoMVr+htPWIiIiIoMDti3B2DTfJ6Xe4U0Pejo7hmqZClDS+mlYIhDg1\nEiWRyky6jvuhpw9TGQxw7qIm74LJqiYIF29G+ITOfycMD8Cj3/AeOwd3f9TbgOfcN5a+HhERETnp\nhfwu4GRkldnt2Ien3+HOxL3AbcWcUhIIQN1c5ga89eKb9vZxxpz6cQ99aNdhzlnYSKQi6HW4S71+\ne9T887ylJff9CzQt9rZy3/dH2PAlqKjypyYRERE5qanD7YdAkASVkJp+4CaRHSlYzI1vAOrnUps4\nQH0kxKaO8ccY9sdTbNsXZd3SWdkn9pZ+/fZYr/oKNJ8C//0m+P1X4YJ362JJERER8Y063D6JWxWB\nPAK3JbNrlCPjd5wLpn4u1vUYZ89v5LG9feMe8tDTh3EOLlg6y1vC0bcHTnlJceuaTKQB/vxer7sd\nqoSlF/tXi4iIiJz01OH2SdKqCI1MP3AHhwdIWgSCFQWsahz1cyG6j/MXN7G9K0r3wPE7Tv5y234a\nqipYs7gJYochFfO3ww3e+vHTLlPYFhEREd8pcPskGawmNBKb9vsrUgMkgrUFrGgCDfNhJMHLlnrB\n/v4nDx718vBIhnu2H+DSM9qpCAbGTCjxOXCLiIiIzBAK3D5JBauoTMen/f7wyADDoRIE7vq5ACyv\nijKnIcJ9248O3A/vOkw0McLlK71Nco4Ebr8umhQRERGZYRS4fTISrKYyM73AnUpnqM4Mkqos8vpt\n8MbpARbt4iWnt/Hgjm4SqfSRl7//6F5qwyFeuKzFe6I/u8ukOtwiIiIigAK3b9KhGiJuektKovEU\n9RYjU1nkCSVwpMNNtJMN58xjaDjNdx5+FoCnuwe5a0sX169b5I0DBK/DHa6HqiJuOS8iIiJSRhS4\nfZKpqCHiEjjnpvzevniKBoZwkRIE7tp2sCBEO1m7pJmLTm3hS796mq7+OP9653bCoQBvvWjJmOJ8\nHgkoIiIiMsMocPvEVdZQTYLkyMTbpU+kL+Z1uAOl6CIHglA3G/o7AfibP1lONJ5i3Sfu474nDvKh\ny0+npTY8pjgfN70RERERmYF8mcNtZs3A94HFwDPAa5xzveMc9wwwAKSBEefcmtJVWVyBcA01xIkm\nR55bjpGj/liCeoZIFnNb97EaFx65GHLVgkbuev8L+eZvdvOiZa28/Kw5zx3nHPTuhiUvKk1dIiIi\nImXArw73h4F7nXPLgHuzjydyiXPunOdT2AawcD2VlmZgaOqzuAej/QTNUVmqwN20BHqfOfLwtPY6\nPnHN2UeHbYCBLm8Gd8uppalLREREpAz4Fbg3AN/K3v8WcLVPdfgmWFUHQDw6/u6Nk4kP9AAQri1V\n4F4MA/sglZj8uMM7vdtZCtwiIiIio/wK3O3Oua7s/f1A+wTHOeAeM/uDmb29NKWVRqjKu+AxPjT1\nwD086AXuSP2sgtY0oabF3u3ojO2JjAbu5lOKWo6IiIhIOSnaGm4zuweYPc5LHxn7wDnnzGyiUR0X\nOec6zawNuNvMnnDOPTDB73s78HaAhQtn/pSMympvhnZyqH/K7x3JhvRgqUbvNWenkPTuhtbTJj7u\n8NMQihyZ3S0iIiIiRQzczrlLJ3rNzA6Y2RznXJeZzQEOjnecc64ze3vQzH4IrAXGDdzOua8BXwNY\ns2bN1GftlVhljdfhHh6KTvm9mZjX4S7ZrOvRDveYddzjOrzT624HNPxGREREZJRfyegO4Ibs/RuA\nHx97gJnVmFnd6H3gMmBrySossqpaL3CPxKfe4XaJ7HtKMYcboKYVKmpyC9yztJxEREREZCy/Avcn\ngZeZ2Q7g0uxjzGyumd2VPaYd+B8z2wT8HrjTOfdzX6otgqo6rzudTgxM+b12JHCXqMNt5nW5Jwvc\n6RHvdV0wKSIiInIUX+ZwO+cOAy8d5/l9wBXZ+7uAVSUurWQqsxdNZhJTX1ISGo6SwQiE6wtd1sSa\nFkPProlf73kaMiPQsqxkJYmIiIiUAy229UvYGwvoptHhrhyJkgzUlHatdMsyb8lIOjX+6/u3eLft\nK0tXk4iIiEgZUOD2S2UtAIHhwSm9LZNxhEcGGK6oK0ZVE2s/EzKp50b/HevANgiEoHV5aesSERER\nmeEUuP0SCBCjikBqah3uweER6oiRqijhchKAthXe7YFt479+YCu0LIdQuHQ1iYiIiJQBBW4fJQLV\nBFNT29q9P5aiwYbIhEs0oWRUy2leB/vg4+O/vn8rzNZyEhEREZFjKXD7KBmspmJkaoG7L5ainhiu\nVCMBR4UqYdYyODBO4I71eFu/a/22iIiIyHEUuH00HKyhMj3FDnfc63AHqpqKVNUk2leMv6Rk/2bv\nVh1uERERkeMocPtoJFRDJBOb0nv64sPUM0SwpkQzuMdqWwH9eyDed/Tzzz4EFoC555a+JhEREZEZ\nToHbR+mKWiKZGM7lvhN9/2CMGktSWeNDh3vB+d7ts789+vndD8Ccc0q31byIiIhIGVHg9pGrrKXW\n4iRHMjm/JzHQC0C4trlYZU1swVqoqIZdv3ruueEh6HgElryw9PWIiIiIlAEFbh+5ylpqSBBNTLCZ\nzDiSgz0AVPjR4Q6FYdF62HX/c8/tedibz73kRaWvR0RERKQMKHD7yCJ11BJnMJ574E4PeYHbt+Ub\nSy+BQ09Bf6f3+MmfQaACFlzgTz0iIiIiM5wCt4+CkXoqLM3AUO6TStKxfu9OqccCjjr1Uu9247e8\ncYCP3QJnvRrCtf7UIyIiIjLDhfwu4GRWUe3tFhkb6ANm5/Qel8hOCIn41OFuOx3OvAZ+8zmv052K\nwYXv96cWERERkTKgDrePKrOj/bzAnZtAwucON8DL/o83BnDbD+HcG7wQLiIiIiLjUofbR1W1XmhO\nDvbm/J5QKhu4/RzB17gA3vWwdxFlXW6deREREZGTlQK3j6rrvNF+w0O5d7grUgOMBCsIhSLFKis3\nTYv8/f0iIiIiZUJLSnxUkV1Skj5258YJJFJpajODDIfqwKyYpYmIiIhIgShw+8iyy0Iy8f6cju+P\np6i3GKnK+mKWJSIiIiIFpMDtp9ELHxO5Be6eoWHqGSIT9vGCSRERERGZEgVuP4W9TnUgGc3p8J6h\nYeptCPNrJKCIiIiITJkCt58CQeJWTSg1hcBNjEC1AreIiIhIuVDg9lkiWEtFajCnY3uGhmmwISpq\nmopclYiIiIgUigK3z5KhOiLpgZyO7RlMUk+McK0Ct4iIiEi5UOD22UhlHVWZITIZd8JjBwf6qbA0\nAT83vRERERGRKVHg9lmmsp56hhhIjpzw2MTojpR+busuIiIiIlOiwO2zTLieOmJE46kTHjsyeMi7\nU91c5KpEREREpFAUuH1mkUbqLUZ/DoHbxXq8O9WzilyViIiIiBSKArfPgtWNXoc7ljzxsYls4K5S\nh1tERESkXChw+yxU00jQHEMDk+826ZyjItnnPVCHW0RERKRsKHD7bHTEX3ygd9LjookRGlx2g5wq\njQUUERERKRcK3D6rrvOWh8QGDk96XM/QME02SCpUA6HKUpQmIiIiIgWgwO2z0Q538gQd7p6hYRpt\nkJGwutsiIiIi5USB22/ZmdqpoRMH7mYGcLpgUkRERKSsKHD7LRu40/HJL5o8NJik0QYI1OiCSRER\nEZFyosDtt4i3TbvF+yY9rHsgSTMDVNS1lKIqERERESkQBW6/VTWSwQglJ19S0j2QpCkwSFAdbhER\nEZGyosDtt0CQRLCOcGryDveh6CB1xLXpjYiIiEiZUeCeAYYrm6h3UWLDIxMek+zv9u5UK3CLiIiI\nlBMF7hlgJNxIEwMcHhye8JjUYHZOtwK3iIiISFnxJXCb2avNbJuZZcxszSTHXW5mT5rZTjP7cClr\nLCVX1UyTDdIzNH7gds7hhkYDt9Zwi4iIiJQTvzrcW4FrgAcmOsDMgsAXgZcDK4BrzWxFacorrUDt\nLJpsYMLAHU2MUJMZ3dZdHW4RERGRchLy45c657YDmNlkh60FdjrndmWP/R6wAXi86AWWWKh2FtUM\ncniCwN09kKTFsoG7prWElYmIiIhIvmbyGu55wN4xjzuyz43LzN5uZo+a2aPd3d1FL66QIvVtVNkw\n/dHxJ5UcHEjQQnZjnBrN4RYREREpJ0UL3GZ2j5ltHednQzF+n3Pua865Nc65Na2t5dUFrsxuZhPv\nPzTu690DSVqtj3SkGYIVpSxNRERERPJUtCUlzrlL8/yITmDBmMfzs88971h2M5vh6Pid+e6BJPMt\nCrVtpSxLRERERApgJi8peQRYZmZLzKwSeB1wh881FUf2QshkdPwO98GBJG2BfgJ1CtwiIiIi5cav\nsYCvMrMOYB1wp5n9Ivv8XDO7C8A5NwK8B/gFsB241Tm3zY96iy476m9kcPwOd2dfnNmBKFbbXsqq\nRERERKQA/JpS8kPgh+M8vw+4Yszju4C7SliaP0Y3s4n14pw7bnpLR2+cZvqgRh1uERERkXIzk5eU\nnDyqmgCoTffTH08d93JPz2EiLqE13CIiIiJlSIF7JghWkKqoo9EG2deXOOql+HAai2XXditwi4iI\niJQdBe4ZIl3VQqv109UfP+r5jt7YczO4FbhFREREyo4C9wwRqJ9Dm/Wyr//oDndHb5xWG930RoFb\nREREpNwocM8Qoca5zLZeuvqO73C3WnYHSnW4RURERMqOAvcMEaifQ/u4gTtOezCKw6Ba27qLiIiI\nlBsF7pmibi5hUvT3Hj2Lu6M3ztLKKFbTCkFfpjiKiIiISB4UuGeKutkAJA93HPX07kNDLAwdhsYF\n471LRERERGY4Be6Zon4uAMHYfnqGhgFIjqTZcXCAuRyCxoV+ViciIiIi06TAPVNkO9zt1svj+6IA\nPLV/kJF0msbh/dCgDreIiIhIOVLgninq5gDQTi/b9nljALd09tNClGBmWB1uERERkTKlwD1ThMJQ\n1czScJRt2Q73ls5+lkeyIwEVuEVERETKkgL3TFI/lyWRAR7v8gL31s5+zm8e8F7TkhIRERGRsqTA\nPZPUzWau9bKre5Ctnf08sT/Kypps4NaUEhEREZGypMA9kzQtpjXVQShgvParDwFwXsMAVDVBuM7n\n4kRERERkOhS4Z5LW0wkMD/CBtTUMDae5/oLF1Ce7tJxEREREpIxp68KZpO0MAN66PEl9+0quXj0P\nvvwkzF3tc2EiIiIiMl3qcM8kracDEO7dwRsuWERtOgp9zypwi4iIiJQxBe6ZpKYFqlvg4Hbv8b4/\nercK3CIiIiJlS4F7pmk7A7qf8O53PebdzlnlXz0iIiIikhcF7pmm9XTofhKc8zrczUuhqtHvqkRE\nRERkmhS4Z5p550IyCs/+Bjr/qOUkIiIiImVOgXumWXE1VDXD7W+HaAcsvdjvikREREQkDwrcM01l\nNbzgbRDthEUXwjnX+V2RiIiIiORBc7hnogveCfFeuPB9EAj6XY2IiIiI5EGBeyaqboYrP+N3FSIi\nIiJSAFpSIiIiIiJSRArcIiIiIiJFpMAtIiIiIlJECtwiIiIiIkWkwC0iIiIiUkQK3CIiIiIiRaTA\nLSIiIiJSRArcIiIiIiJFpMAtIiIiIlJECtwiIiIiIkWkwC0iIiIiUkQK3CIiIiIiRaTALSIiIiJS\nROac87uGgjOzbuBZH351C3DIh9/7fKJzmD+dw8LQecyfzmH+dA7zp3OYP53DiS1yzrWe6KDnZeD2\ni5k96pxb43cd5UznMH86h4Wh85g/ncP86RzmT+cwfzqH+dOSEhERERGRIlLgFhEREREpIgXuUoAk\nPgAABXFJREFUwvqa3wU8D+gc5k/nsDB0HvOnc5g/ncP86RzmT+cwT1rDLSIiIiJSROpwi4iIiIgU\nkQJ3AZjZ5Wb2pJntNLMP+11POTKzBWZ2v5k9bmbbzOz9ftdUrswsaGZ/NLOf+l1LOTKzRjP7gZk9\nYWbbzWyd3zWVGzP7y+yf461m9l0zi/hdUzkws5vM7KCZbR3zXLOZ3W1mO7K3TX7WONNNcA4/nf3z\nvNnMfmhmjX7WONONdw7HvPZXZubMrMWP2sqZAneezCwIfBF4ObACuNbMVvhbVVkaAf7KObcCuAB4\nt87jtL0f2O53EWXsc8DPnXOnA6vQuZwSM5sHvA9Y45xbCQSB1/lbVdm4Gbj8mOc+DNzrnFsG3Jt9\nLBO7mePP4d3ASufc2cBTwN+VuqgyczPHn0PMbAFwGbCn1AU9Hyhw528tsNM5t8s5Nwx8D9jgc01l\nxznX5ZzbmL0/gBdy5vlbVfkxs/nAlcCNftdSjsysAXgR8A0A59ywc67P36rKUgioMrMQUA3s87me\nsuCcewDoOebpDcC3sve/BVxd0qLKzHjn0Dn3S+fcSPbhw8D8khdWRib49xDgs8DfArr4bxoUuPM3\nD9g75nEHCop5MbPFwGrgd/5WUpb+E+8/iBm/CylTS4Bu4JvZZTk3mlmN30WVE+dcJ/AZvC5YF9Dv\nnPulv1WVtXbnXFf2/n6g3c9ingfeAvzM7yLKjZltADqdc5v8rqVcKXDLjGJmtcBtwAecc1G/6ykn\nZvYK4KBz7g9+11LGQsC5wJedc6uBIfQV/pRk1xhvwPufl7lAjZm9wd+qnh+cN1ZM3cVpMrOP4C1f\nvMXvWsqJmVUDfw981O9aypkCd/46gQVjHs/PPidTZGYVeGH7Fufc7X7XU4YuBK4ys2fwlja9xMy+\n429JZacD6HDOjX678gO8AC65uxTY7Zzrds6lgNuB9T7XVM4OmNkcgOztQZ/rKUtm9ibgFcB1TvOQ\np+oUvP+B3pT9+2U+sNHMZvtaVZlR4M7fI8AyM1tiZpV4Fwfd4XNNZcfMDG/d7Hbn3H/4XU85cs79\nnXNuvnNuMd6/h/c559RZnALn3H5gr5ktzz71UuBxH0sqR3uAC8ysOvvn+qXowtN83AHckL1/A/Bj\nH2spS2Z2Od5Su6ucczG/6yk3zrktzrk259zi7N8vHcC52f9eSo4UuPOUvRDjPcAv8P5SudU5t83f\nqsrShcD1eF3Zx7I/V/hdlJyU3gvcYmabgXOAj/tcT1nJfjvwA2AjsAXv7xntUpcDM/su8BCw3Mw6\nzOytwCeBl5nZDrxvDz7pZ40z3QTn8AtAHXB39u+Wr/ha5Aw3wTmUPGmnSRERERGRIlKHW0RERESk\niBS4RURERESKSIFbRERERKSIFLhFRERERIpIgVtEREREpIhCfhcgIiKFZ2azgHuzD2cDabxt6wFi\nzjltRiMiUiIaCygi8jxnZh8DBp1zn/G7FhGRk5GWlIiInGTMbDB7e7GZ/drMfmxmu8zsk2Z2nZn9\n3sy2mNkp2eNazew2M3sk+3Ohv/8EIiLlRYFbROTktgp4B3AG3m6vpznn1gI34u26CfA54LPOuRcA\nf5p9TUREcqQ13CIiJ7dHnHNdAGb2NPDL7PNbgEuy9y8FVpjZ6HvqzazWOTdY0kpFRMqUAreIyMkt\nOeZ+ZszjDM/9HREALnDOJUpZmIjI84WWlIiIyIn8kueWl2Bm5/hYi4hI2VHgFhGRE3kfsMbMNpvZ\n43hrvkVEJEcaCygiIiIiUkTqcIuIiIiIFJECt4iIiIhIESlwi4iIiIgUkQK3iIiIiEgRKXCLiIiI\niBSRAreIiIiISBEpcIuIiIiIFJECt4iIiIhIEf0vxsLIuz2+/4IAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(12,6))\n", "ax.plot(tlist, np.real(corr1),\n", " tlist, np.real(corr2))\n", "ax.set_xlabel('Time')\n", "ax.set_ylabel('Correlation')\n", "ax.legend((\"g = 0.1\", \"g = 0.0\"));" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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hPjvpQ20fIiKeqKAWEQl1NfsgOgGSswP/2an5EBGlI8hFRLxQQS0iEuqq90J6AUQE4Z/s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\npmnDT2HbnyAYhTOW+T95N8+vdJVFKmvLfXDfP0D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Ra0zMQm5mV5rZKjNb1d7eXunqiIiI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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(12,6))\n", "ax.plot(wlist/(2*np.pi), abs(spec1), \n", " wlist/(2*np.pi), abs(spec2))\n", "ax.set_xlabel('Frequency')\n", "ax.set_ylabel('Power spectrum')\n", "ax.legend((\"g = 0.1\", \"g = 0.0\"));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Versions" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.2.0
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Wed Jul 19 21:55:51 2017 MDT
" ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }