pyqm-week5/notebooks/pyqm-5.1-line-plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00000-8a10eae1-9991-495c-9495-90baa0cb8c2c",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "<center>\n",
    "\n",
    "# Python for Quantum Mechanics: \n",
    "# Line Plots\n",
    "\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"700\"\n",
       "            height=\"400\"\n",
       "            src=\"https://www.youtube.com/embed/D50f3tPYUiM\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fa055f9f550>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('D50f3tPYUiM',width=700, height=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00001-f02f37a2-f020-40b8-aad6-7e9f85e3970e",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "`matplotlib.pyplot` is a collection of functions like those in MATLAB for plotting in Python. Used in conjuction with `numpy`, useful visualisations of data can easily be created. We will import both libraries in the next cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cell_id": "00000-e6a63540-cafd-40c0-8903-5b27e5620237",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 1131,
    "execution_start": 1625473973323,
    "source_hash": "21e32291",
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-b1a5e0cb-0f64-4012-a13d-8c9ae46a0c37",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Lets create two NumPy arrays each containing the $x$- and $y$-coordinates respectively of a two points, $(0,1)$ and $(3,5)$. The `plt.plot()` function in Matplotlib can be used to plot the line between these two points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cell_id": "00004-9be3f12a-0785-4141-bc63-f2977e038538",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 259,
    "execution_start": 1625473974458,
    "source_hash": "8a9233b0",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_points = np.array([0,3])\n",
    "y_points = np.array([1,5])\n",
    "\n",
    "plt.plot(x_points, y_points)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00005-636ef9ba-ba68-41fa-9e66-15c82b11f5ec",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "The `plt.show()` isn't stricktly necessary for jupyter notebooks but is a good habit to be in going forward.\n",
    "\n",
    "We can also plot longer arrays or coordinates and we get a line connecting each point succesively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cell_id": "00007-9883c0f5-a9fb-497b-9922-be6a1050971c",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 182,
    "execution_start": 1625473974723,
    "source_hash": "d11e31c3",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_points = np.array([-9.5,0,2.0,3,10.2])\n",
    "y_points = np.array([1,5,3.3,1,-2.3])\n",
    "\n",
    "plt.plot(x_points, y_points)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00007-26c02732-e099-4a0e-861e-48689e7d5247",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Now we can define a function that returns a polinomial and plot that using `np.arange()` to sample the $x$-axis and plug this sample into a function to get a graph of that function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_id": "00008-b85e4f0f-a73f-4207-aa1c-bcf764105884",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 153,
    "execution_start": 1625473974913,
    "source_hash": "ffc1ef02",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    '''Docstring: This returns 5x^3+6x^2-6x-2'''\n",
    "    return 5*x**3 + 6*x**2 - 6*x -2\n",
    "\n",
    "x_points_rough = np.arange(-2,1.5,.5)\n",
    "y_points_rough = f(x_points_rough) # all of the operations are in f(x) are overloaded for NumPy arrays\n",
    "\n",
    "plt.plot(x_points_rough, y_points_rough)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00009-ec4fd47a-dfc4-45a5-8b6f-e5048414ccc8",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Here we have sampled the $x$-axis between $-2$ and $1.5$ (exluding $1.5$) in steps of $0.5$. This approximates the shape of a cubic, however if we sample more frequently (for example stelps of $0.1$ as seen below), we can achive something approximating a smooth curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cell_id": "00007-bdd7722f-8865-40d6-ac46-40e717c6a3a7",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 225,
    "execution_start": 1625473975069,
    "source_hash": "ba42448",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MT+vOz9/fxAPz11NzrMHpaBKk3lu/j7p6V1CfDD1Bhe4Fr2fuYV7WXu49fyDXB8mdUDytd3wMr985kZ9cPowlm0qY8eev2Fl62OlYEmRO3MRiXN94RvWJczqO16nQPezLvDJ+s3gLFw9P5uFvDHU6jl8LCzPcc/5A5t09ieqj9cz480o+yi12OpYEkcz8CnaVHeG2EDg6BxW6R+0sreH+N9czuGdXnrx5HGF+tFKiP5syMJEPHzqXoSndeGD+eh79aAsNjZqzLh03b3UB8Z0jA3ZpjfZSoXtIVe1x7n5tLZ0iwnhpdgZdO+ly9/ZIiYvm7TmTmT25H3/5cje3vLSa0sN1TseSAFZYWcvSzQe4KaOvX65e6g0qdA84MaOlqKqOF2+bQGr34LwC1NuiIsL4zYxRPDFrLLn7qrjq6a/I3lPpdCwJUM8szyM8zHDXtP5OR/EZFXoHWWv59aL/P6NlQj/NaOmomWelsvD+qcREhXPz3Cz+unK3pjZKuxRUHOHd9fu5ZWJa0K7b0hIVege9nlnAm6s1o8XThveKZdGD05g+NInfLN7Cj9/N1Vow4rZnlu8kIsxw//SBTkfxKRV6B6zYUcZvFm/WjBYviYuJZO5tGXz3wkEsyN7HbS+v5uCR407HEj+3p/wIC7/ez7cm9aNnCB2dgwr9jFXVHueHCzYwJLmbZrR4UViY4YeXDuXJWeP4em8VM59bSX5ZjdOxxI89s3wnkeGGe6cPcDqKz6nQz9DvPt5KVW09T8wapxktPnDtWX14a84kDtc1MPPZlazcWe50JPFDu8uPsPDrfdw6qR89u4XW0Tmo0M/IqvxyFmTv4zvnDWB4r1in44SMCf0SeP+BqaTERTP7lTXMX73X6UjiZ55ZlkdURBj3nB9aY+cnqNDbqa6+kZ8t3ES/Hp353kWDnY4TcvomdObd+6YwdVAiP124kf/+cIuW4hUA8stqeH/Dfm6fnE5St05Ox3GECr2d/rx8J7vLj/C7maND5mIFf9MtOpKXZ2dwx5R0Xv5qN3Nez9biXsIzy/LoFBHOnPNCb+z8BBV6O2wrOcQL/8zn+vGpTB2U6HSckBYRHsavrxnJf88YyRc7yrjh+VUUVR11OpY4ZGdpDYtyirh9Sj8Su4bm0Tmo0N3W6LI88u5GYmMi+fmVw52OI81um5zOX+84m/0HjzLzuZVsKdIt7kLR08vyiI4M557zQnPs/AQVupveXF3AhsIqfnnVCLp3iXI6jpzkvCFJvHPfZMKM4aYXM1mxo8zpSOJDeQcOszi3iNlT0kkI8f83VehuKK4+yuNLtnPekCRmjOvtdBxpwbCUWBbeP5XU7jF8+9W1LFhb6HQk8ZGnluXROTKcOeeG7tj5CSr0Nlhr+cX7m2lwuXj02lEhe0/QQJASF807905mysAePPxuLn/6x3atARPkdhw4zEcbi7ljarp+c0aF3qYlm0r4bOsBfnjJEPomaBVFf9ctOpJX7jibmzJSeXr5Tn70To7WgAliT32WR5eoCO6epqNzAF3ieBrVR+v51aLNjOwdy51TQ2cJzkAXGR7GY9ePIbV7Z/706Q5Kqut44bYJxEYH9w2CQ822kkN8tLGYBy8YpKPzZjpCP43Hl2yjvOYYf7huDBHh2lWBxBjDdy8azB9vHMua3ZXc+HympjUGmac+y6NbpwjuPlcHWyeopVqxdk8lb67ey51T+zM6NfhvLhusrp+Qymt3TqSoqmla4+aiaqcjiQesyi/nk00l3DmtP/GddXR+ggq9BdZafvXBZvrEx/DDS4c4HUc6aOqgRP5+35SmaY0vZPJPTWsMaHX1jfz0vY3069GZ+0JsvfO2qNBbsHTzAbYUH+JHlw6hc5ROMwSDoSndWHj/VNJ6dOHOV9fyt7Va2CtQ/Xn5TvZU1Gr5jRao0E/hclme/GwHAxK7cM1YzTkPJiemNU4dlMiP392oaY0BSMtvnJ4K/RRLN5ewreQw371osE6EBqGunSJ4eXYGszL6Nk1rXKBpjYFCy2+0TeMJJ2k6Os9jYFIXrtbRedCKDA/jD9ePJrV7DH/8dAclh+p4/tYJxMVoWqM/m5fVtPzGk7PGaZpiK3QIepJPNpWw/UDT0Xm4bikX1IwxPHTRYP50U/O0xhdWsV/TGv1WUdVRHl+yTctvtMEjhW6MucwYs90Ys9MY84gn3tPXXC7LU8t2MKhnV64aox+YUHHd+KZpjcVVdcx8diWb9mtao7+x1vLLDzbTaK2W32hDhwvdGBMOPAtcDowAvmmMGdHR9/W1jzYWs+NADd/T0XnIOTGtMTzMMOvFTJZtPeB0JDmJlt9wnyeO0CcCO621u6y1x4G3gRkeeF+faXRZnlqWx5Dkrlw5upfTccQBQ1O68f4DU+mf1IXvvJ7NS1/u0gwYP6DlN9rHE4XeBzh5rdJ9zc8FjA9zi9hZWsP3LhpCmI7OQ1ZybDQL7pnMpSNS+O1HW/npwk3UN2oGjJMe0/Ib7eKJPdRSA/7HoY0xZo4xJtsYk11W5j9X6jW6LE8vy2NocjcuH5XidBxxWOeoCJ771njunz6Qt9bs5Y6/rqG6tt7pWCFp7Z5K5q/ey13TtPyGuzxR6PuAvid9nQoUnfoia+1ca22GtTYjKSnJA5v1jMU5ReSXHeF7Fw/W0bkAEBZmePiyYfxv88JeM59byZ7yI07HCinHGhr5yXsb6RMfww8u0fIb7vJEoa8FBhtj+htjooCbgUUeeF+va2h08fSyPIaldOOykTo6l393w4RU5t01iYO1x7n2uZVk7apwOlLIeP6LfHaW1vDozFFafqMdOlzo1toG4EFgKbAVWGCt3dzR9/WFRTlF7Co/wvd1dC6tmDSgB+8/MJUeXaK47eXVLMjWre28bdXOcp5ZvpMZ43ozfWhPp+MEFI+cZbDWfmytHWKtHWitfdQT7+ltJ47Oh/eK5dIROjqX1vXr0YX37p/KOQN68PDfc/n9x1tpdGkGjDfsLj/CfW+uZ2BSF3577Sin4wSckD1t/P6GIvZU1OroXNwSF9N0a7tbz0njxRW7uOOva6g8ctzpWEGl+mg9d722ljADL91+Nt10h6l2C8lCb2h08czyPEb2juXSEclOx5EAERkexm+vHc0frhvN6t2VXP3MV+QUVjkdKyg0NLp4cP56CitreeHWCaT10AVEZyIkC33h1/spqKjl+xcP0WXE0m43T0zj7/dOBuDGFzJ5a81eXYTUQf/94Ra+zCvn0WtHM2lAD6fjBKyQK3RrLXNX7GJEr1guHq4TLnJmxqTGs/ihaUwakMBP3tvIj9/Npa6+0elYAemNrAJeyyzgO+f256az+7b9B6RVIVfoa3ZXkldawx1T03V0Lh2S0CWKV789ke9eOIgF2fu4/vlVFFbWOh0roKzcWc6vF23mwmE9eeRyrXHeUSFX6G9kFRAXE8nVWlFRPCA8zPDDS4fy8uwM9lbWctUzX/H59lKnYwWEXWU13N88o+Wpm8dpUTwPCKlCLz1cx5JNJdwwIZWYKN2LUDznouHJfPjQNHrHx3Dnq2t54tMdNGgdmFZV19Zz92vZhIcZXp6tGS2eElKFvmBtIQ0uy7cmpTkdRYJQvx5deO++Kcw8qw9PLcvjxhcz2a0lA/5DfaOLB+avp/Bg04wWLYnrOSFT6I0uy/zVe5k2KJEBSV2djiNBKiYqnD/dNI6nv3kWu8qOcPlTK3g9cw8uXYgENN1I5pcfbOarnU0zWib2T3A6UlAJmUJfvq2Uouo6bj2nn9NRJARcM7Y3S79/HhP79+CXH2xm9l/XUFwd2re4O3q8kQfmr+etNXu5b/pAzWjxgpAp9DeyCkiJjdZURfGZlLhoXvv22Tw6cxTZew5y6RMrWPj1vpCcs156uI6b52ayZHMJv7hqBA9/Y6jTkYJSSBT6nvIjrNhRxjcnpmmRfPEpYwzfmtSPT753LkOSu/GDv+Vw/5vrqag55nQ0n9lWcoiZz65ix4Ea5t6WwV3T+mvKsJeERLvNX7OXiDDDzRP1K544Iz2xCwvumcwjlw9j2dZSvvHkCpZuLgn6o/Uvtpdyw/OZNLhcvHPvZC7RUhteFfSFXlffyILsQi4dmUxybLTTcSSEhYcZ7j1/IB88OJXErp2454113PbyGrYWH3I6mle8kbmHO19dS1pCZ95/YCqj+uiuQ94W9IX+UW4xVbX1OhkqfmN4r1gWPTiNX109go37q7ni6S/58d9zKT1U53Q0j2h0Wf5r8RZ+8cFmLhjak3funUyvuBinY4WEoL8VyBtZBQxM6sJkLfgjfiQqIoxvT+3PzLP68MzynbyeuYfFuUXce/5AvnPugIC98O3IsQa+9/bXfLa1lG9PTefnV47QFaA+FNRH6Jv2V7OhsIpbz+mnkzDil+I7R/GLq0bw6Q/O57zBSfzp0x1c8L9f8O66fQE1d91ayz82l3D1n79i+bZS/mvGSH519UiVuY8FdaHPyyogJjKc68anOh1F5LTSE7vwwm0TWHDPZHrGduJH7+RwzbNf8VVeud+fOM3eU8mNL2Qy5411ALx+5yRun5zubKgQFbRDLtVH63l/w36uHdeHuBitEyGBYWL/BN6/fyqLcop4fMk2bn15NQOSunDLxDRumJBKfOcopyP+S96Bwzy+dDufbjlAz26d+P11o7lxQqqmBjsoaAv9vfX7qKt36WSoBJywMMO1Z/XhslEpfJhbzPzVBfz2o608vnQ7V43uxS2T0pjQr7tjw4jF1Ud58tM83llXSJeoCP7vN4Zy59T+ATvuH0yCstCttczLKmBc33hNlZKAFR0Zzg0TUrlhQipbiw8xf/VeFn69n/e+3s/Q5G58c2JfZo5P9dlvoFW1x3nhn7v468rdWAvfntqfBy4YREIX//mtIdQZJ8bnMjIybHZ2ttfef1V+Obf8ZTV/vHEs10/Q+LkEj9rjDSzOKeLN1XvJ3VdNdGQYFw1PZnxad8b1jWdk71iiIz1zpFx7vIHsPQdZlV9BZn45G/dXY4GZ4/rwg0uGaJVEBxhj1llrM1r7flAeoc/LKiC+cyRXjunldBQRj+ocFcGss9OYdXYam/ZX8+bqvXyxvZSPcosBiAw3DO8Vy7i+8f/66J/Yxa3hmbr6Rr7eW0XmrqYC31BYRX2jJSLMcFZaPA9eMIgrxvRiWEqst/+acoaCrtAPHKpj6eYD3DWtv8eOVET80ag+cfz+utFA08/913ur2FBYxYbCg/x93T5ezywAIC4mkr4JMVhL0wdNw5LWgsvaf3297+BRjjW4CDMwuk8cd00bwJSBPchI707nqKCriqAUdP+V3l5TSKNuYiEhJjk2mstGpXDZqBSg6WrNvNLDbGgu+dLDxzCAMU0Lhp14HGZM03MYzh/SkykDezBxQAKxuoNQQAqqQrfW8v6G/UwZ2IN+Pbo4HUfEMeFhhmEpsQxLieXmiTq4CRVBNWF00/5D7C4/wjVjdQNoEQk9QVXoi3OLiAw3//q1U0QklARNobtclsU5RZw3OMmvrqYTEfGVoCn0dXsPUlxdxzXjNNwiIqEpaAp9cU4R0ZFhXDxcd0QRkdAUFIXe0Oji443FXDQsmS6dgmrijoiI24Ki0DN3VVBec5yrNbtFREJYUBT64pwiunaKYPrQJKejiIg4JuAL/VhDI59sKuHSkcm61F9EQlrAF/qKHeUcrmvQxUQiEvICvtAX5RTRvXMkUwclOh1FRMRRAV3otccb+GzLAS4f3YtI3fZKREJch1rQGPNrY8x+Y8yG5o8rPBXMHcu2lnK0vlHDLSIieGa1xSestf/rgfdpt0U5RSTHduLs9AQnNi8i4lcCdpyi+mg9/9xexlVjehMe5szNckVE/IknCv1BY0yuMeYVY0x3D7yfW5ZuLuF4o0sXE4mINGuz0I0xnxljNrXwMQN4HhgIjAOKgT+e5n3mGGOyjTHZZWVlHQ6+OKeItITOjE2N6/B7iYgEgzbH0K21F7vzRsaYvwAfnuZ95gJzATIyMqy7AVtSXnOMVfkV3Hv+ALdufisiEgo6Osul10lfzgQ2dSyOez7ZWEyjy2q4RUTkJB2d5fK4MWYcTTcS3wPc09FA7licU8zgnl0ZmtzNF5sTEQkIHSp0a+1tngriruLqo6zZU8mPLhmi4RYRkZME3LTFD3OKAbhKwy0iIv8m4Ap9cW4Ro/vE0T+xi9NRRET8SkAV+u7yI+Tuq9al/iIiLQioQv8wpwiAK8f0auOVIiKhJ6AKPTkumpsyUukdH+N0FBERvxNQd1S+KaMvN2X0dTqGiIhfCqgjdBERaZ0KXUQkSKjQRUSChApdRCRIqNBFRIKECl1EJEio0EVEgoQKXUQkSBhrO3TzoDPbqDFlQMEZ/vFEoNyDcXxBmb0v0PKCMvtKoGU+Xd5+1tqk1v6gI4XeEcaYbGtthtM52kOZvS/Q8oIy+0qgZe5IXg25iIgECRW6iEiQCMRCn+t0gDOgzN4XaHlBmX0l0DKfcd6AG0MXEZGWBeIRuoiItECFLiISJPy+0I0x/2OM2WaMyTXGLDTGxLfyusuMMduNMTuNMY/4OOapWW40xmw2xriMMa1OPzLG7DHGbDTGbDDGZPsyYwtZ3M3sF/vZGJNgjPnUGJPX/Ll7K69zfB+3tc9Mk6ebv59rjBnvRM5TMrWVeboxprp5v24wxvzSiZwn5XnFGFNqjNnUyvf9cR+3lbn9+9ha69cfwKVARPPjx4DHWnhNOJAPDACigBxghIOZhwNDgS+AjNO8bg+Q6PQ+djezP+1n4HHgkebHj7T0c+EP+9idfQZcAXwCGOAcYLXDPwvuZJ4OfOhkzlPynAeMBza18n2/2sduZm73Pvb7I3Rr7T+stQ3NX2YBqS28bCKw01q7y1p7HHgbmOGrjKey1m611m53avtnws3M/rSfZwCvNT9+DbjWoRxtcWefzQBet02ygHhjjJN3Qven/85usdauACpP8xJ/28fuZG43vy/0U9xJ07+yp+oDFJ709b7m5/ydBf5hjFlnjJnjdBg3+NN+TrbWFgM0f+7Zyuuc3sfu7DN/2q/gfp7JxpgcY8wnxpiRvol2xvxtH7urXfvYL24SbYz5DEhp4Vs/s9Z+0PyanwENwJstvUULz3l1PqY7md0w1VpbZIzpCXxqjNnW/K+2V3ggs0/38+nytuNtfLqPW+DOPvP5z28b3MmznqZ1RWqMMVcA7wODvR2sA/xtH7uj3fvYLwrdWnvx6b5vjJkNXAVcZJsHl06xD+h70tepQJHnEv6ntjK7+R5FzZ9LjTELafpV12tl44HMPt3Pp8trjDlgjOllrS1u/tW5tJX38Ok+boE7+8znP79taDOPtfbQSY8/NsY8Z4xJtNb66yJY/raP23Qm+9jvh1yMMZcBPwausdbWtvKytcBgY0x/Y0wUcDOwyFcZz4QxposxptuJxzSd/G3xbLcf8af9vAiY3fx4NvAfv2H4yT52Z58tAm5vnolxDlB9YjjJIW1mNsakGGNM8+OJNHVJhc+Tus/f9nGbzmgfO32m140zwTtpGvva0PzxQvPzvYGPT3rdFcAOms7O/8zhzDNpOiI4BhwAlp6amaYZBDnNH5sDIbM/7WegB7AMyGv+nOCv+7ilfQbcC9zb/NgAzzZ/fyOnmRnlR5kfbN6nOTRNVpjicN63gGKgvvnn+K4A2MdtZW73Ptal/yIiQcLvh1xERMQ9KnQRkSChQhcRCRIqdBGRIKFCFxEJEip0EZEgoUIXEQkS/w8YCG+GDFxsIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_points_fine = np.arange(-2,1.5,.1)\n",
    "y_points_fine = f(x_points_fine)\n",
    "\n",
    "plt.plot(x_points_fine, y_points_fine)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00011-2c728e76-6e12-4ddf-b1b0-9764bccaa4df",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "We can plot both lines on the same graph by calling `plt.plot()` twice and have two plots on the graph which will automatically be set to differnt colours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_id": "00012-03709735-6c0f-4ff2-944d-71268da097b0",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 140,
    "execution_start": 1625473975295,
    "source_hash": "74cebfa8",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D/o/J3abCcY5th1mDYfjr0Pdhs6upNgl0E1nOniT9resILsxmhuVRzrcbzuAooyulRYi/2eXVusW70nn+xwRyzhUwdUg7pvduiM/SJ2HvImjRF8Z8aPSxC1HbfnoUds2HJ/dCvYZmV1NtMmzRLEUFnPx8PKGFGSyPnsWbw0fj5123WqQjujWhX5tGvPzzHt5blcSyhEDeGDuTazqOgsV/hQ+vgxtfMW6/dtGPwMIF5OfAzu+g+ziXDnNbuM/nfCejlzxNaNYG3q43jRG33F7nwrxYcH0f3r6rB3Mm9SL3fAFjPvydV4925/yUdcZwzV+ehO8mwoU8s0sV7mrH11CYD9GTza6k1kmg14ZNn6DiP+XDwlF0vOkhU8eKO4shHcNZ9udB3NWrJR/HHeTmOYfYdN2nxiySexcZNyRl7Te7TOFuihexaBYNTXuYXU2tk0C3twOr0UueZr1XH+Y3+BOjrmlqdkVOI8jPm1dv78ZXD/Sh0GLhzlkbeSF7KPnjv4f8U0ao71549R0JYatDcXAiCXo9YHYlDiGBbk9ZifDtJM4EteWBM1OYNrSDtM7L0b9dKMueGMQfB0Ty5YZUbvhes/HGhcZ0wd9NMu7mKyo0u0zhBrJjP0TXC650ag13IoFuL+dOwry70F4+PKqfIaxRI26V1nmF/H28eGFUF+Y/3A9fbw/umneYZ4Ne5ULPB2D9+/DlrcYiBEJU09bt22mYuoyNDUZUbXlGFyaBbg9FBcaFvdNpbO4zk9hMP6Zf3x4vF7jD02zXtgph8WMDeSSmLd9uz2RQws3s6vMvOLoVPh5kLIgtRBUdOXmOwz+8iEV50mXsM2aX4zCSODWltTGf+aE49Kh3eXlHAC1D/BndQ1rntvLz9uTp4R35YeoAgv19GLW2Ga81e58iLz/4/BbY8JFxnoWwwbmLhTw/ZxEjWUt+9wkEhtWdNYwl0Gtq0ycQ/xkMeILVvkNJOJrL9CHtpHVeDd2aN+Cn6dfx5LAOfJrsz5DclzgePhCWPg0/TYfCi2aXKJyc1pq/fLeDW3Lmojy9aTBshtklOZSkTk0krzLCJmoEeujzvLsqiRYh9RjTs5nZlbksHy8PHhvanp8fHUhwSCj9UiazqOF9xlww/x1jXKsQogIfrElmd8J2bvf6Dc9ekyEwwuySHEoCvbrOnTQm3ArrBLfPIjbxBDvTTjMtpp1LzI7o7KIiAlnwSH+eHdGZv2SP5BkepejIRvTsoZCdZHZ5wgmt2JPBm8sTeSNsGcrTx5jhs46R5KmuFX83xk7fPgvtE8A7q5Jo1rAet/dsbnZlbsPL04Mpg9qy5PGBHIy4hXH5z5GXcxLLJ0PhYKzZ5QknkpSRx5+/2c6NEXn0zluB6jUZAhubXZbDSaBXx6E4owug/6MQ0ZW1iVnsOJLDtCHt3GrWRGfRJiyAr6f0ZfStY7i98BUOnA/E8t+xWDbPMbs04QROnyvgwS/j8fP24J0mK1CevjDgcbPLMoWkT1UV5MOiJyC4NQx+Gq0171pb53dcK63z2uLhoZjQL5I5T9zBG81nElfYBY9fnuD0wr+Cpcjs8oRJCossTJ+3laM5+cwZ1RD/fd9D7wcgINzs0kwhgV5VcW/CyQMw6h3wrse6pGy2Hc7hkZi20jp3gBYh/sx6YAhZI79gLjfTYMcsUj8YTVF+rtmlCRO8sWw/65Kyefm2rnRLngVeftC/brbOQQK9ajJ2w2/vwDX3QJuYktZ5kwZ+jIuW1rmjKKUY16c1w578nLmNHqVZ9q8ceXMgx1LlYmldsnBbGrPiDnJ/31aMb30eEuZD7wchIMzs0kwjgW4rSxH89Bj4NYCb/gHAb8kn2JJ6iqkxbfH1qpvT45qpcZAf905/hU0DPqZRUQZec25kZ/yvZpclHGBnWg5PL9hF79YhPD+qM6x9Hbzq1enWOUig2y7+MzgaD8NfA/8Qa+s8kYggP+7s1cLs6uospRT9b7yTnLsXgVK0WXQHKxZ9hRkrcQnHyMw7z5QvtxAW4MuH9/bE+0QiJCyAPlOgfiOzyzOVBLotTh+FlS9B26HQbRwA6w+cYHPKKR6R1rlTaNGxF/5TYznl04Qh8dNYMPs1LhTKxVJ3c6GwiEfmbiUn/yKzJlxLowBfo3XuU99Yp7aOk0C/Gq1h8V/AUggj3ypZKu2dVUk0DvLlLmmdO42AsJY0ezKWIw17ccfR1/jp7Wlk5uabXZawE601L/y4my2pp3hz3DV0adoAMvcac+j3eQj8Q8wu0XQS6Fez9yfYv9hYqT44EjBa55sOneThwW3r7NJyzsqjXgNaP/YLR1qNZdzZeWx+5252pWaaXZawg7kbUvl68xGmDWnLyO7Wye9iXwOfAOg33dzinIQEemXyc2DxDIjoDn2nlmx+d1UiYYG+jO9dd2Zxcyme3rSY9CmZ0U9xiyWWM5+OZtGmvWZXJWpg/YETvLRoD0M7hvPUsChjY8Zu2PODtM5LkUCvzKqX4Gwm3PoeeHoBsPHgCTYclNa501OK8JHPk3fzTHp57KP9z+OYuTCWIotcLHU1R06eY9pXW2nVyJ+37+6BR/EqYLGvgW8Q9JtmboFORAK9IqnrjZEtfadC0z+UbH53VRKhAb7c20da564gsM8EuG8BkV4nGbd9Es9/PI/T5wrMLkvY6NzFQqb8dwsFRRY+mRBNkJ+38cKhOKM7tO9UaZ2XIoFeHq1hyV+hQUuj79xqc8pJfj9wgocHt5HWuQvxajcEv4dWElTPh2eP/5n/9+5MkjLyzC5LXIXWmr9+t5P9x3OZOf4PtAkLMF4oyIdFjxvTb1z3hKk1OhsJ9PLs+xmO74LrnzOGQ1m9tyqJ0AAf7u3TysTiRLU07oz/1Fg8GrXm1Quv8OUHr7B893GzqxKV+E/sAX7Zlc7TwzsSE1Vqbpa4N+HkwZLpN8QlEuhlWSxG31yjdtD1jpLNW1JPsS4pmymD2lDPR1rnLimoKf4PraCw1WBe8fiYvfOe4b2ViVikX93prNyTwZvL93Nbj6ZMGdTm0gtlpt8Ql5NAL2vfIshIgMFPl1wIBaPvPKS+D/f1lda5S/MNxG/CdxRecx+Pey2k2do/89j/NnL2QqHZlQmr5Mw8nvhmO12aBvH62O4o670f5U2/IS4ngV5aces8tAN0HVuyedvhU8QlZvHgwDb4+3hVsgPhEjy98Rr9PnrIc4z1/JV7kp5kwgfLOXLynNmV1XnG3OZb8PP2YNb90Zdfq9r86WXTb4grSaCXtvdHyNxjtM49Lv0hvbsqiWB/byb0k9a521AKNXgGjPmYvp77eT13Bg/OXMjvydlmV1ZnFVk0j369jbRT5/jwvmtp2rBU//jpNGMYcanpN8SV7BLoSqnhSqn9SqlkpdQz9tinw1ksEPs6hEZBlzElm7cfySF2fxYPDGxDfV9pnbuda+7G4/4FtPHJ4X/8H6/O+YbPfzskk3uZ4I2l+4hLzOLl27rSK7JUC1xrWGxdyKTU9BviSjUOdKWUJ/ABcDPQGRivlOpc0/063J6FkLUXYi5vnb+3KomG/t5M7B9pXm2idrWJwWPycoID/PjO5xXifpnLjPk7ZXIvB/ph21E+Lp7bvOwd2OVMvyHKZ48Wem8gWWt9UGt9EfgauM0O+3UcS5HROg/rBJ0vtc53puWwel8mD1zXmgBpnbu3xp3xeHA1vhEdmO3zFkHbZ3H3x+vJzD1vdmVuz5jbfOeluc1Lq2D6DVE+ewR6M+BIqe/TrNtcx+6FkL3f2jq/dEreW5VEg3rSOq8zgpqg/rgEj0638HfvuYzPfIvRM2PZdviU2ZW5rcy88zz03y2EFs9t7lkmkla+eMX0G6Ji9gj08jq0ruiAVEpNUUrFK6Xis7Ky7HBYO7EUGfMph3eGTpc+WCQcPc3KvZlMvq41gcW3Gwv351Mfxn0J1z3JnWoV7xX9gwc/Xsn8LWlmV+Z2iuc2P3Wu1NzmpaWuhy1zrph+Q1TMHoGeBpSeFLw5cKzsm7TWs7TW0Vrr6LAwJ1rzL2EBZCdaR7ZcOh3vrkoiyM+LSQMizatNmMPDA254AUZ/yLXs5ad6LzJz/jJeXrSHwiKL2dW5hXLnNi+t8IJxe3+Z6TdE5ewR6JuB9kqp1kopH+Bu4Cc77Lf2FRUarfPGXaHTrSWbdx87zYo9GfzputaXJgMSdU+Pe1ATfqSJ9zmW+L/I7t8XM3HOJk6dvWh2ZS6v3LnNS/v1baMbdOTbl02/ISpX40DXWhcC04FlwF7gW6317pru1yES5sOJ5Cta5++tSiLQz4s/DmhtYnHCKUQOQD24Cv/gCOb5vUqLlIXc9sFv7D8uk3tVV7lzm5d2cC2sfcMYb97+BscX6MLsMg5da71Ya91Ba91Wa+0a9+SWtM67QceRJZv3pueybHcGfxzQmgb1pHUugJA2MHkFHq0H8prXRzx4fg5j/7OOpQkyuVdVVTi3ebETB+DbCcbd2re8ZU6RLqzu3im661tjxraYZ65snft6MVla56K0eg3h3u8gejL3W35kru8bPDt3DW+vkMm9bFXh3ObF8nPgq7tAecD4eeAXZEqdrqxuBnpRofGRLqI7dLylZPO+47ksSTjOpAGRNPCX1rkow9PbuFNx1HtcY9nDqsAXWLN6KQ/P3cIZmdyrUhXObV6sqBC+mwSnUuCuuRAiDarqqJuBvvMbOHUIYp697DbimauSCfD1YvJ18sckKnHtRNSflhLs781Cv5cJTZzH7R/8SuqJs2ZX5rQqnNu82LJn4eAa4yJo5ADHF+gm6l6gaw2/vwcR3SDq5pLNiRl5LE5IZ2L/VjT09zGxQOESmvVETYnDs81A/uk1m0dy32HczNX8miSTe5VV4dzmxTbPhk2zoN906Hm/4wt0I3Uv0FN/h6x90Ofhy1rn761Kwt/bkweuK+cPTojy1G8E986HQTMYwxr+5/E8f/tsEbPXHZTJvawqnNu82MFY49b+9jfBsJdNqdGd1L1A3zwb/BpCl9tLNiVl5PHLrnQm9I8kuL60zkUVeHgaSxWO/4Z23tksqfd3fl0yj6e+28H5gro9uVelc5sDZCfDtxONES1jZ182KZ6onroV6HkZxsxtPe4FH/+Sze+vSaaetycPDpTWuaimqOGoh9biH9aKOT7/ouXOdxn/0a8cP103J/eqdG5zgPxTMO8uI8Tv+VpGtNhJ3Qr0bV+CpRCi/1Sy6UDWGRbtOMb9/VoRIq1zURMhbVCTV6CuuZsnvL7nheynmDrzW7ak1r3JvSqc2xygqMA6oiXVGNEiU+LaTd0JdEsRxH9uLCwb2q5k8/urk/H1kta5sBMffxjzEYz9lG5+mXxV+BQ/z36Jbzelml2Zw1Q6t7nFAov/YvSdj3wbWvU3pUZ3VXcCPXEZ5KZBrwdKNh3MOsOP249yX9+WhJad6U2Imuh2B57TNuDZegAveM4hYtG9vDV/DQVuPrlXpXObXzwH302ELZ/DdX+WES21oO4E+ubZENgUOlwaqvj+mmR8vDyYMqitiYUJtxXUFO8JCyka8RZ9vZN4YNc9zJr5KifPXDC7slpR6dzmeRnw+S2wdxHc9CoMfcG8Qt1Y3Qj0EwfgwCq4dlLJJPkp2Wf5cfsx7u3TirBAaZ2LWqIUnr0n4zPtdy6GdGBazhvseOs2Eg8eMrsyu6p0bvOM3TB7qDFc+O6voN9UWRe0ltSNQN8yBzy8oOeEkk3vr0nGy0Px0GDpOxcO0KgtoY+u5livZxlg2UzIF4OJ+2kOaSfPuvyY9UrnNk9aCZ/eZAxG+OMS6DjCvELrAPdf06kgH7bNNeZsCWoCQOqJsyzcdpQJ/VoRHuhncoGizvDwpOktz3Ci4zDOzJvMoK1PsG7zbB73nIhnRDc6NQmkU5MgOjUJIioi8Mpx206qwrnNN30CS2ZA4y4w/hto4ForU7oi9w/03T8YY15LXQz9YE0ynh6KhwdL37lwvEZtr6XBjA0cXvUfem99m+8KZrA6ZxgvH7udLy4a47E9FLQOrV8S8J2tj42DfK+829JE5c5tbimC5f8HG/4DHYbD2E/BN6DyHQm7cP9A3zzbuBMtciBgzMf8/daj3Ne3FY2DpHUuzOHl40fLm5+EwZMg7k1u2DSLob6/kdNvKpsi7mF3VgF70vPYdjiHn3eml/xcsL93Sch3jDBa9O0bB+Dr5fjWfLlzm184AwsegMQl0OcRuOkfcgeoA7l3oB/bDkfjYfjrJRdhPliTjIeS1rlwEv4hMPyf0GsyauULBG/8FzcF/o+bhj4PN9wFHh6czi9gX3oue9Nz2Xc8j73puczdkMqFQmMIpJeHom1YwGVdNp2aBNXqxf4r5jb39YJ9v8CKF+DkARjxJvR+sNaOL8rn3oEe/yl4+8M1dwNGi2L+ljTu6dOSiAbSOhdOpFFb467J1N9h2d/gh4dh44dww0s0aBNDnzaN6NOmUcnbiyyaQ9ln2WsN+r3puWw4eJIftl9anz00wJdOTQJLums6NQmiTVj9y4cTVkPpuc0/m9SLNvkJ8NkLcGQDNGoP930PbYfU6Biietw30PNzYOd30H2csdoMxpzMHkrxSIy0zoWTatUfHlhtrHe78iX472gjJKP/CNeMN1r0gKeHol14AO3CAxh1zaULkSfPXmRfei570nPZm2605uf8lsJF6w1NPp4etAsPsAb8pbCvyqR0xXObvz7Ih5itT8D+XyAgAka9Cz3uKxkaLBzPfc/8jq+hMB+iJwNwNCef+VuOcFevFjRpUO8qPyyEiTw8oPud0GkU7F4I8XOMVvvKl6DLGCPcW/Qpdyx3SH0f+rcLpX+70JJtBUUWDmSdsbbkjZBfm5jJgq1pJe+JCPK7osumdWh9PMus+blyTwZzl//OvMZL6Lt5KfgEwPV/h75TL5vwTpjDPQNda6O7pVk0NO0BwH/WJAPwSEy7Sn5QCCfiXQ963GN8HU8w7qfY8Q3s/BrCOxs3ynW/q+QTaIW78fSgY0QQHSOCGPOHS9uz8i5c1mWzNz2PdUnZFFrXSPXz9iCqcWDJBdgW9c6T8uOrxPouwecMqD6PwMCnjHnhhVNQZtzUEB0drePj42vvAIfi4ItRMPoj6DGeYzn5DP7XGsZFt+CfY7rV3nGFqG0Xz0LCAoj/DI5tA696EDUcmveG5tHGOrne1b8+dKGwiKQMozWfnJaJPryBiJMb6WnZRTd1CKXgfKex+N/4PAS3suMvJmyhlNqitY6u6HX3bKFvng31go2Pp8CHsQcAmCp958LV+dQ37njuOcEYxbVlDiStMLpmADy8IaKr8em0ebTx2KitbbfaF5zHN20zXVPW0fVQHKTFg6UA7eFFQdNrORJ8MwE97yC0bc9a/RVF9blfoOemw96fjfkivP1IP53PN5uPcMe1zWkeLH18wo007QFN3zWe56YbQ3TT4uHoFtj+FWz+xHjNr6HRmtYa0KABbbE+t1zannMYCs+D8oAmPaDfNGg9CNWyLz4+9Yl0/G8oqsj9An3rl6CLShax+Cj2ABatmSp958KdBTWBoFHGhVQw7tbM2mcN+HhjtkOlAGUEdnGLveS5gnY3QOtBxkgbvwYVHUk4MfcKdK1h5zfGH2VIGzJyzzNv8xHG9mxOixBpnYs6xMPTmEOlcRe4dqLZ1QgHca/ZFtO3G3epdb0DgI/WHqDIopk2RFrnQgj3516BnrDAuCjUaRSZuef5auNhbv9DM1o2kta5EML9uU+gWyyQ8D20Gwr+IXwcd5BCi2b69dI6F0LUDe4T6Ec2Qu5R6HoHWXkX+N/GVEb3aEarRvXNrkwIIRzCfQI9YYH1JoubmRV3gIuFFmmdCyHqFPcI9KJC2PMDdLiJ7AJv/rshldt6NKN1qLTOhRB1h3sEekocnM2CbnfwSdxBaZ0LIeok9wj0hAXgE8iJJoP4cn0qo65pStswWfJKCFG3uH6gF16APYug00g+WZ/O+cIiHpXWuRCiDnL9QE9eBRdOk9f+Nr5cn8LI7k1pFx5odlVCCOFwrh/oCfOhXggfH25BfkERj0nrXAhRR7l2oF88C/uXcKHDKOZsSGNEtya0byytcyFE3VSjQFdKvaiUOqqU2m79GmGvwmySuBQKzrGwoB9nLxbx2PXtHXp4IYRwJvaYbfFtrfWbdthP1e1agCUggn/ubsiIbuFERUjrXAhRd7lul0t+DiSvYFvgEHIvWHhsqLTOhRB1mz0CfbpSaqdS6jOlVLAd9mebfT9D0UXePNaN4V0i6BgR5LBDCyGEM7pqoCulViqlEsr5ug34EGgL9ADSgX9Xsp8pSql4pVR8VlZWzStPWECOXzPWX2glrXMhhMCGPnSt9Q227Egp9QnwcyX7mQXMAoiOjta2FliuM1nog2v5Vt/KjZ0j6NxUWudCCFHTUS5NSn07BkioWTk22vMDShex4EIfaZ0LIYRVTUe5vKGU6oGxjngK8FBNC7JF4c75pNCcFlHRdG0mi9kKIQTUMNC11vfbqxCbnT6KV9oGfigYx+M3dHD44YUQwlm53LDFCzvmA3Ai8ha6NZfWuRBCFLPHjUUOlbP5azIsrRl/8xCzSxFCCKfiUi30c+n7aZy3hz2NhtG9eUOzyxFCCKfiUoG+a9nnAHQdNsnUOoQQwhm5VKB7NGjKpoYj6Nq5i9mlCCGE03GpPvReYx4FHjW7DCGEcEou1UIXQghRMQl0IYRwExLoQgjhJiTQhRDCTUigCyGEm5BAF0IINyGBLoQQbkICXQgh3ITSumaLB1XroEplAanV/PFQINuO5TiC1Fz7XK1ekJodxdVqrqzeVlrrsIp+0JRArwmlVLzWOtrsOqpCaq59rlYvSM2O4mo116Re6XIRQgg3IYEuhBBuwhUDfZbZBVSD1Fz7XK1ekJodxdVqrna9LteHLoQQonyu2EIXQghRDgl0IYRwE04f6Eqpfyml9imldiqlFiqlGlbwvuFKqf1KqWSl1DMOLrNsLeOUUruVUhalVIXDj5RSKUqpXUqp7UqpeEfWWE4tttbsFOdZKRWilFqhlEqyPgZX8D7Tz/HVzpkyvGd9fadSqqcZdZap6Wo1xyilTlvP63al1PNm1Fmqns+UUplKqYQKXnfGc3y1mqt+jrXWTv0F3Ah4WZ+/Drxezns8gQNAG8AH2AF0NrHmTkAUEAtEV/K+FCDU7HNsa83OdJ6BN4BnrM+fKe/vwhnOsS3nDBgBLAEU0BfYaPLfgi01xwA/m1lnmXoGAT2BhAped6pzbGPNVT7HTt9C11ov11oXWr/dADQv5229gWSt9UGt9UXga+A2R9VYltZ6r9Z6v1nHrw4ba3am83wb8IX1+RfAaJPquBpbztltwJfasAFoqJRq4uhCS3Gm/8420VrHAScreYuznWNbaq4ypw/0Mv6E8a9sWc2AI6W+T7Nuc3YaWK6U2qKUmmJ2MTZwpvPcWGudDmB9DK/gfWafY1vOmTOdV7C9nn5KqR1KqSVKKWdfud3ZzrGtqnSOnWKRaKXUSiCinJee01r/aH3Pc0Ah8L/ydlHOtlodj2lLzTYYoLU+ppQKB1YopfZZ/9WuFXao2aHnubJ6q7Abh57jcthyzhz+93sVttSzFWNekTNKqRHAD0D72i6sBpztHNuiyufYKQJda31DZa8rpSYCI4Gh2tq5VEYa0KLU982BY/ar8EpXq9nGfRyzPmYqpRZifNSttbCxQ80OPc+V1auUylBKNdFap1s/OmdWsA+HnuNy2HLOHP73exVXrUdrnVvq+WKl1H+UUqFaa2edBMvZzvFVVeccO32Xi1JqOPA0cKvW+lwFb9sMtFdKtVZK+QB3Az85qsbqUErVV0oFFj/HuPhb7tVuJ+JM5/knYKL1+UTgik8YTnKObTlnPwETrCMx+gKni7uTTHLVmpVSEUopZX3eGyNLTji8Uts52zm+qmqdY7Ov9NpwJTgZo+9ru/XrI+v2psDiUu8bASRiXJ1/zuSax2C0CC4AGcCysjVjjCDYYf3a7Qo1O9N5BhoBq4Ak62OIs57j8s4Z8DDwsPW5Aj6wvr6LSkZGOVHN063ndAfGYIX+Jtc7D0gHCqx/x5Nd4BxfreYqn2O59V8IIdyE03e5CCGEsI0EuhBCuAkJdCGEcBMS6EII4SYk0IUQwk1IoAshhJuQQBdCCDfx/wHksvA+KXJuOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_points_rough, y_points_rough)\n",
    "plt.plot(x_points_fine, y_points_fine)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00014-fec484f3-f0d5-4fa1-81bb-7bff4603090c",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "Or we can graph multiple plots in the same `plt.plot()` call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_id": "00013-1efbd7a4-2021-420f-bdc0-82d0abde550d",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 159,
    "execution_start": 1625473975438,
    "source_hash": "e31bf9d0",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_points_rough, y_points_rough, x_points_fine, y_points_fine)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or prehaps more elegantly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    x_points_rough, y_points_rough, \n",
    "    x_points_fine, y_points_fine)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00002-667fd317-67be-4dd8-b27f-3e3a5c5d7de5",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-1d616e79-4c28-4c6b-879a-2bbc853cf564",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "In the following section we will look at ways of formatting lines in our plots. We will use the following during the demonstartion. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cell_id": "00003-949e301e-80ee-48c9-8f78-662aa8c57e82",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 1,
    "execution_start": 1625488961773,
    "source_hash": "5984e38f",
    "tags": []
   },
   "outputs": [],
   "source": [
    "x = np.arange(0,1,.05)\n",
    "\n",
    "ex = np.exp(x)\n",
    "e2x = np.exp(2*x)\n",
    "e3x = np.exp(3*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00005-be6ed847-95de-4da2-b52a-aa7c20f8fb9d",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Colour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00006-00433244-f1b9-4abd-9780-02c70b299dbd",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "To specify the colour of a line we can use the `color` or `c`, keyword when calling `plt.plot()`. We can use the following named colours (sourced [here](https://matplotlib.org/stable/gallery/color/named_colors.html)) or specify a Hex Color Code.\n",
    "\n",
    "![Base Colors](images/sphx_glr_named_colors_001.webp)\n",
    "\n",
    "![Tableau Palette](images/sphx_glr_named_colors_002.webp)\n",
    "\n",
    "![CSS Colors](images/sphx_glr_named_colors_003.webp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "cell_id": "00007-2f72ea02-7bd9-4418-90ca-b51b5a177117",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 206,
    "execution_start": 1625488961779,
    "source_hash": "26682362",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,1,.05)\n",
    "\n",
    "ex = np.exp(x)\n",
    "e2x = np.exp(2*x)\n",
    "e3x = np.exp(3*x)\n",
    "\n",
    "plt.plot(x, ex, c = 'hotpink')\n",
    "plt.plot(x, e2x, color = 'tab:brown')\n",
    "plt.plot(x, e3x, '#31AF3F')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00008-ccbbbfaa-792c-4354-81b2-71cc9793ccb1",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "If no colour is specified the 'Tableau Palette' will be cycled through as seen below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cell_id": "00008-54a02441-4e51-481e-8e5d-6fd194938eeb",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 169,
    "execution_start": 1625488962055,
    "source_hash": "2bc6465",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6d/+HQW/SmTHCVcBEIFyhUFQBf8c5deIFbHD9tWaHEOLhC3hOGRmZS5TqY7mse2sBTTVV9Jk4hYl3zcXbv3PiazXZ2fVlKYd+rsLbz4PJd2eTObLrjoHm/Hzq5s3DuH0HnsnJxL+1CL/x47vd5zZYDazIXcHyo8sxO8xcl3odjwx4hGj/6G5d70LRmSmU287w20svwFlkZGQuI6wmI5tXreDA+q8JDI/ghj//k6QBgzv1XiEERXvr2fKx0zGwz7hYRnbDMdCu09EwfwHNn3yCMiCAqL/8hZBbb0Gh7p7zoMVh4cNjH7Lk8BKaLc1MTZzK44MeJyUopVvXu9DIm5gyMjJdpuzAXta//RptukYGXXktY2+dg6d358yemuuMbFyVf8Ix8OH+RCV3zTFQslppWrGCxjcXIVkshNx5BxGPPooqOLgbnwbskp3Piz7nzYNvUmesY3TMaJ4c/CR9wvp063qn0VgEYanQy3PhsoDLyMh0GpOhjZ+Xv03uph8JjYnj1v95gdjMzs1S26wO9n1Xzr715XioVYy/NYM+47vmGCiEoG39BupfeglbZSX+EycS+cwzeKUkd+vzSEJiffl6Xt//OmWtZfQP78+/x/6b4dG9lGtZexA2vQR5X8DtH0PGtN65rgtZwGVkZDpFwY4t/PDOIsyGNkbMvoWR19/SafOpssONbPqwgDadmcwRGkbf0HXHQNPRo9Q/Nw/jnj14pacTv3QJ/mPGdOejIIRga81WFuxbQJ4+j7TgNOZfMZ8r4q/one3Jqr2w6QUo+A68AmH8HyCua97mnUEWcBkZmXNiaNLz4zuLKNy1jcjkVG748z+JTOpcT7hVZ2LL6kJKD7ocA387iNjMrjkG2urraXh1Pi1r1qAKCUHzj38QfOMNKLrgoXIyB+oP8Oq+V9lbt5dY/1j+PfbfXJ18NSpl17c7T6N8G2x8AUp+Ap8QuOKvMPwB8Anu+bXPgCzgMjIyZ0QIwdGfv+fnlUuwW62Mu/0ehl47G6Xq/EJ3mmPgbJdjoEfnV8wlsxn9smU0Ln4bYbMRet+9hD/8MKqAgG59nnx9Pgv3L2Rj1UbCvMP40/A/cVPGTahV3Xvg6UYIKPkZNr0I5VvBLwKm/A8Mux+8unfWziILuIyMzGm01Nex4e3XKD+0n9isPkx76ElCY2I79d6q/CY2rcp3OgYOjGDszV1zDBRC0PrNN9T/5z/Ya2oJmDqVyD88jWc3rTgqWyt57cBrfFv6Lf5qf54c9CR3ZN/R83AFIaBwg7NVUrUbAqLhynkw+G7w7N3ghrMhC7iMjIwbSXJwYN3XbFm1AhQKJt//KAOmXNkp86n2FgvbPi2iYJfTMfCax/qT1C+8S/c3HTxI3XPzMB04gFdONjHz5uE3vHsPFOuN9bx18C0+K/wMD6UH9/a9l/v63keQV1C3rudGkiD/a2fFXXsQghLgmpdh4B2g7rq1bU+QBVxGRgYAXVUl696aT23BMZIHDmHKA48RGB553vdJkuDIxmp2fl6M3S4x9JokhnTRMdBWW0v9y6/Q+uWXqCLCif6//yVo1iwUnWjXnEqLpYWlR5ayKm8VdsnODRk38FD/h4jw7b5lLACSA46ugc3/gfpcCEmGma/BgFuhp22YbiILuIzMfzkOu53dX3zKjk9Xofb24arHf0/22ImdmsbQlraw8YPuOwZKRiO6JUvRvfMOSBJhDz1E2AMPoPL36/LnMNqMvJ/3Pu8eeReDzcDVKVfz2IDHiA/svO/4GXHY4fDHTuHWFUJ4Jlz/NvS5HlS/rITKAi4j819MXUkR6958lYaKMjJGjWPyvQ/hGxR83veZ209yDAz07LJjoJAkWr74goaXX8FeX0/g1VcR+fvfo47tXJ/9ZGwOGx8XfMziQ4vRmXVMjJvIE4OfICOk+x4oANitcPAD2PwyNJdDVD+4aTlkz4RO+plfaGQBl5H5L8RmtbD9k1Xs+fIzfIOCmfn0X0gfNuq87xOS4NiOWrZ9VozFaGfA5HiGd9Ex0LhvH3X/fg7zkSN49+9P7Kuv4ju467FjDsnB16Vf88aBN6g2VDM0aiivXvEqAyMHdvlaHbCZYd8K2PoqtFZDzCDnw8nMq3p9k7KnyAIuI/NfRlXuEdYvXkBTbQ19r5jGhLvuw9vv/OZTjVUGNq3Kp7a4hejUICbc3jXHQGtVNfX/eYm2b7/DIyqKmBeeJ/DaazudznMcIQQ/Vv7Ia/tfc0eY/W3K3xgdM7pnSzjWdtjzLmxbAIY6iB8JMxdA6uRLTriPIwu4jMx/CRajkc2rlnNw/dcERUZx41//l8R+A8/7PqvZzq6vSjn0YxVevh5MmpNN1kgNik6uwDsM7egWL0a/bBkolYQ//jhh992L0rfro3a7ancxf998DjU6I8xemvASUxOn9izCzNwKu9+G7a+DUQfJ4+GGJZA07pIV7uPIAi4j819A6f49bHj7ddr0jQy++jrG3nIXau9zj7wddwzc+nEh7a1W+oyNYeSs1E47BgqHg+bPPqNh/gIcjY0EXTeTiN/+FrVG0+XzH208yvx989leu50o3yj+Z/T/MDN1Zs8izExNsPMt2PEmmJshbQqMfwYSRnT/mqdgc0h8c7iWd7eWMf/WgSSGdf3h7LmQBVxG5leMqa3VaT61+SfC4hK47Z8vEpORdd73NdcZ2fRhPpV5TYTH+3Plw/3QJHd+frp9x07q5s3DcuwYPoMGEfXG6/j079/l858aYfaHoX/glqxbehZh1t7orLZ3vQ3WNsi8BsY/DbGds8LtDC0mGx/trmDZ1jJqWsykRPhR32aRBVxGRub8CCHc5lOWdgMjb7iVEbNvweM8Ptl2q4O9xx0DPZRddgy0lpdT9+KLGL7/AXVMDLEv/4eAq67qcm+61lDLGwff4IviL/BWefPIgEeYkzOnZxFmbVrYthD2vAM2E/SZBeOeBk3f7l/zFCr1Rt7ZWsrq3ZW0Wx2MSgnjX7P6ckVmZJdcFzuLLOAyMr8yDHod3y99k+I9O4hKSWf6X/+XiMTz262WHW5k80cFtDaayRgRxejr0/AL6lyl62htpfHNRejfew+lWk3Eb39L6N1zUJ6nTXMqOpPOGWGW/xEKFNyRfQdz+83tWYRZSxVsnQ97l4Nkh343wbjfQURm9695CnvLm1i6pYTvjmhRKhTMGBDD/WOT6Rvbw63P89CZSLV3cIYX1wsh+rp+LxT4CEgCyoCbhRBNF+6YMjIy50MIwZGfNrBx5VIcNhvj77yPIVdfd17zqTa9mc0fFTgdAzW+XPfbQcR10jFQ2O00f/wxDQsW4mhuJuj62UQ89RTqyPNvcHY4g7WN5UeXszJ3JWaHmVlps3hkwCNo/LreL3ejL4Utr8CBDwABA25zCndo76Tr2B0S63PrWLK5hH0VzQR6e/Dg+FTuGZ2EJujirNR3pgJfBrwGrDjp9/4I/CCEmKdQKP7o+vdne/94MjIynaG5TsuGxQuoOHKIuJy+THvoSUI0Med8j8MucfCHSnZ/XQp03THQsGUr9c/Pw1JYhO+wYUT96Y945+R06dxmu5mP8j9yR5hNS5zG44MeJzmoewENADQWOpdvDn0EShUMuRvGPAXB3TPDOhWDxc7q3ZW8s7WUqiYTCaG+/M/MPtw4JA4/r4vb1OhMJuYmhUKRdMpvX4cz6BhgOfAzsoDLyFx0JMnB/m+/ZMtHK1EqlUyZ+xj9J08/72x1dX4TG12OgckDwhl7czqBYZ2LRLOUlFD3/PO0b9yEOiGB2IULCJgypUt9brtkZ23RWt48+Cb1xnrGxIzhicFP9CzCrC4XNr8ERz4DD28Y8RCMfhICeyeIuLrZxPJtZazaWUGbxc6wpBD+ek0OU3OiUF2A/nZn6O6PiyghRC2AEKJWoVCc9e9LCoXiQeBBgIRu2kHKyMicTmNlOesXLaC2KJ+UwcOYMvcxAsLO7f7X3mJh22dFFOysIyDMm2se7U9S/845Btqbmmh8/Q2aVq1C6eND5B/+QMhdd6LsZCoPuCLMytbz2oHXKG8tZ0DEAOaNm8cwzbBOX+M0ag44nQGPfQWe/s5qe9Tj4N9D8yoXh6qaWbK5lK8P1wJwVV8Nc8elMDA+uFeu3xMueL0vhFgMLAYYOnSouND3k5H5teOw29i19hN2fPYRXr6+XP3kH8gaPf6cFbAkCY5uqmbH5yXYbQ6GXp3E4CsTUXfCMVDYbDStWkXD628gtbURfPNNRDzxBB5hYZ0+sxCCLdVbWLh/oTvCbMEVC5gY3znTrDNSudsp3IXrwCvIOcM98hHw7cEDTxcOSfB9Xh1LN5eyq0yPv5cH945O4p4xScSFXByv787QXQGvUygU0a7qOxqo781DycjInBltUQHr3lpAY0UZWWMmcMU9D+IbeO5Jh7rSVjauyqehoo24rBDG35pBiOb888hCCAw//0z98y9gLSvDb/RoIp99Fu/MrplE9XqEWdlWZ4hCyc/O2LJJf4XhD4J3zyc+jFY7n+yt4p0tpZTpjMQG+/DXa7K5ZVg8Ad6/jGXsueiugH8B3A3Mc/36ea+dSEZG5jRsFjPbPv6AvV+txS8khFnP/I3UIefeGDS329ixtpijW2rwDfRk2tw+pA2J7FTFa84voP75ebRv245nUhJxb76B/8SuVcsnR5iF+4TzlxF/4Yb0G7oXYSaEM2dy44tQsc0ZWzb1nzD0fvDqwWy4i7pWM8u3lfH+zgpaTDYGxAfz2vRMruyjwUN1aTgPnonOjBGuwvnAMlyhUFQBf8cp3KsVCsX9QAVw04U8pIzMfzOVRw+xfvFCmrW19J9yJePvuBcv37NX0E7HQC3bPityOgZOcjkG+py/XrPr9TQsWEDz6o9RBgQQ9ec/EXLbbSjOswDU4bwnR5h5+vPU4Ke4Pev27kWYCQEF65ytkuo9EBADVz4Pg+f0SmzZ0ZoWlm4u5ctDNdglwfQcDQ+MT2ZwQkjvpNNfYDozhXLbWb40uZfPIiMjcxIWYzub3nuXQz98R3BUNDf97d8k9D33Orqu2sDGVfnUFrWgSQliwu0ZhMedP1hXslppWrmSxjcXIZlMhNxxBxGPPYoqOLjT5z05wkytUnN/v/u5p8893YswkyTnQ8lNL4L20InYskF3gkcP1uhxPg/4uaCeJZtL2Vasw9dTxR0jErl3TFKvr7oDtNjsfFLXxK2aUPw8utk2OgvyJqaMzCVI8d5dfL/kddqbmhg643pG33Q7aq+zL4d0cAz08eCKu7LIHhV9XsdAIQRt339P/QsvYqusxH/CBCKffQavlM4vu3SIMBN2bsy4kYcGPES4T9fyMIETsWWbXoKGPOfSzXWvQ/9behxbZrY5+GxfNUu3lFDc0I4m0Js/XpXFbcMSCPLt3f62EIL9bUZWVOv4vL4JkySI9FQzIzK4V+8jC7iMzCWEsbWFn5Yt5tjWjYTHJzLz938mOu3sK99CCIr3NbBldQHtLVZyxsYwalYq3v7nFyRzbi51z83DuHs3XulpxC9Zgv/YMZ0/q83Ie3nvsezIMgw2A9ekXMOjAx8lPqAbEWYOGxxa7Ywt0xf3amxZQ5uFlTvKeW9HOfp2K31jA3n1loFc0z8adS/3t9vtDj6rb2JFtY7DBhO+KiU3akK5KyaM/gG9P70iC7iMzCWAEIJj2zbx07tvYTEaGX3THQyfdSMqj7MLcXOdkU0fFVCZq3c6Bj7UD03K+dsVtvp6GubPp+WzNaiCgtD8/f8RfNNNKDw6JwdWh9UdYaY365kYP5EnBnUzwsxuca66b3ml12PL8rVtLN1Swtr9NVgdElOyI5k7LoURyaG93t/ONZhYXt3Ip3VNGBwSOX7ezMuI44aoEAJ6uW1yMrKAy8j8wrTpGvl+yeuU7NtNdFom0x5+kvD4xLO+3m51sHddOfvWOR0Dx92STt/xsSjPU01KZjP6ZcvRLV6MZLMRes89hD/yMKrAwE6d89QIs2GaYcwfNL97EWY2E+xbeVJs2WC46nnIuLJHIQpCCDYXNrJkSymbChrwViu5eVgc945JJjWi59MqJ2NySHzZ0MyK6kb2tBrxViqYGRnM3THhDA70vSgPQWUBl5H5hRCSxKEf1rHp/XeQHBIT58xl0FUzUJ5jPvpkx8D0YVGMufH8joFCCNq+/Zb6l/6DraYG/ymTifrDH/BMPPsPiVPff3KEWU5YDv9v5P9jVMyorouUtd1p57ptoTO2LGEUzFwIqZN6JNwWu4PP99ewZEsJBXUGIgK8eHpaBrePSCTUr/Obop2hsN3Myhodq7V6mu0O0ny9+GdaDDdpQglRX2JeKDIyMr1Pk7aGDW8tpDL3MAl9+zP1wScJjjq7816b3syW1YWUHGggOMqX634zkLis828cmg4dou65eZj278crK4uEf/8bv5GdT5zZWbuTBfsWuCPM/jPhP0xNnNp14T5jbNlSSBrbI+HWt1t5b0c5K7aX02iwkKUJ4KWbBjBjQDRevdi6sEoS3zS0sKJGx7ZmA2qFgqsjgpgTE8boYP9fbORQFnAZmYuI5HCw95vP2fbReyg9PJj64BP0mzTtrALQwTFQwMhZKQycknBex0CbVkv9yy/T+sWXqMLD0fzrnwRffz2K81jLHudI4xHm75vPjtodaPw0/HP0P5mROqPrEWamJtixCHa+CeYWSJsK4//Q49iyonoD72wt5dO9VVjsEhMzI5g7NoUxaWG9KqblJgvv1ehYVaun0WYnwduTv6REc2t0KBGev/xmpizgMjIXiYbyUtYtWkBdSSGpQ0cw+f5HCAg9+6hddUETG1cV0FTbTlL/cMbdnE5g+LkdAyWjEd3Sd9AtXQqSRNiDDxL24IOo/Ds331zSXMLC/Qv5vuJ7QrxCeGbYM9yceXPXI8zaG2H7a7BrSa/Flgkh2F6iY8nmUn48Vo+nh5LrB8Vy/9hk0qPOP+veWeyS4HtdK8trGvlZ34ZSAVPDArk7JpwJoQEoL6EFH1nAZWQuMHabjZ1rVrNr7Wq8/Py55qlnyBw17qyVorHVyrZPi8jfqSUgzJurH+1P8nkcA4Uk0frll9S//Ar2ujoCrrqSyN8/jWdcbKfOWGOo4Y0Db/BlyZf4ePjw6IBHmdNnDn7qLi62XIDYMqtd4qtDNSzZXEpubSthfp78Zko6d45MJNy/Z0s9J1NjtvJ+rY4PavXUWmxEe6n5fZKG26NDifHu3T56byELuIzMBaSm4Bjr31qArqqC7HFXMHHO3LOaT3VwDLQ6GHJVIkOuSjqvY6Bx3z7qnpuH+fBhvPv2Jfbl/+A7ZEinzqcz6Xj78Nuszl+NAgV3Zt/J3H5zCfHuXCKPm5Yq2PIq7FtxUmzZ7yGiG6OFLpqNVj7YVcHybWXUtVpIi/Rn3vX9mDUoFm917/S3JSH4Wd/GippG1je2IoCJoQE8lx7HlLBAPH4hn+/OIgu4jMwFwGY2s3X1SvZ+8wX+oWHM/uPfSRl0ds/r7jgGWquqqf/PS7R9+x0ekZFEz3uOoJkzzxvmACcizFbkrsDqsDIrbRYPD3i46xFm+lLY8jIcWAUIGHg7jP1tj2LLyhrbeWdrKR/vqcJkczA2LZx5N/RnQnpErwUDN1htfFirZ2WNjgqzlXC1B48nRHJHTBiJPr1X1V9oZAGXkellyg8fYMPihbTU1zFg6tWMu/0evHzPvIVnbrex4/MSjm6u7rRjoMPQjm7xYvTLloFSSfijjxI2936UZ7lHh/vZzXx47EOWHFlCi6WF6UnTeXzg4yQFJXXtQzYWOrcmD60+KbbsNxDcjS1MnP3t3WVNLNlcwoa8OjyUCmYOiGXuuGSyozs3p96Ze2xtNrCiRse3DS3YhGBMsD9/SY3mqvAgPHu4OHQurFYdanUICkXv3kMWcBmZXsLcbmDTe+9w+Mf1hETHcMvf5xGXc+berxCCY9tdjoHtNgZcEc/wGed2DBQOBy1r1lD/6nwcjY0EzphB5O9+izr6/JFhNsnG2qK1LDq4yBlhFjuGJwc9SU5Y1zIsqTvq9Ck5usYVW/YwjH6i27FlNofEt0e0LNlcwqGqFoJ91Tw2MY05oxKJDOydYOAmm53VWme1XWS0EOyh4r7YcO6MCSPd78KFDzscFhobv0erXYtOv5FBA1cQEjKyV+8hC7iMTC9QtHsH3y99A2NzM8Nm3sCom25H7Xnmv4p3dAwMZPxtA4mIP/cURfvOXdTNm4clLw+fgQOJev01fAYMOO+5To0wGxgxkOfHPc9QzdCufcBeji1rNdv4cFcFy7aWUdNiJjncj3/N6suNg+Pw6URK0PkQQrC31cjymka+rG/GLAmGBvqyIDuBGRHB+Fwgj28hJJpb9qKt/Yz6hm+x29vw8tKQED8Xb++4Xr+fLOAyMj2gvbmJH5ctpmD7ZiISkpj1h7+hSU0/42utZju7vyrlYBccA60VFdS/+CJtG77HIyaamP+8RODVV5931lkIwebqzSzcv5Bj+mOkh6Tz2qTXGB937ui106jc7Uy/KVzvjC2b8Kyz6u5mbFml3si7W8v4aHcF7VYHI1NC+ed1fZmUFdkr/e02u4NP65pYUd1IbrsZP5WSWzShzIkNp49/50Kbu4PRWEqtdi1a7VrM5ipUKl8iIqYTrZlNSMhIFIoL44ciC7iMTDcQQpC35Wd+WrYYm9nEmJvvZNh1N6I6gyGU2zHw40Lamy2dcgx0tLXR+OYi9CtXolCrifjNU4Tecw9K7/P/lX9f3T7m75vPvvp9xPnH8dy457g6+WqUXem/lm2BjS9A6UbwCe1xbNm+iiaWbi7l2yO1KBUKru0fzf1jU+gX1/MYNIDDbUZW1Oj4tK4Jo0Oir78PL2bGMTsyBP8LZCZlszVTV/c1tdo1tLbuB5SEho4hJeW3REZMQ6W68NmZsoDLyHSR1sZ6vn/7dUoP7CU6PZPpDz9FWFzCGV97mmPgg33P6Rgo7HaaP/mEhvkLcDQ3EzR7NhG/eQp1ZOR5z5Wvz2fB/gVsqtpEuE84fx3xV65Pv77zEWanxZZFwtR/wdD7uhVb5pAE649qeXtzCfsqmgnw9uCB8SncMzqJ6KCeV8NGh8Ta+iZWVuvY32bER6ngusgQ5sSGMSjgwphJSZKFRt3PaLVraWz8CSFs+PllkJb6LFGamXh7dXGKp4f0SMAVCsVvgbmAAA4D9wohzL1xMBmZSw0hSRz8/js2vf8uQkhccfcDDLzy2jOaT53qGDj25nT6TTi3Y6Bh61bq583DUliE79ChRP7pj/j06XPec1W0VrgjzAI9A/nN4N9we/bt+Hh0UiTPFFt21QvO2DJ114XWYLGzencl724rpVJvIiHUl7/PyOHmofH4efW8ZjzWbmJltY6P6/S02iXSfb343/RYbowKIfgCmEkJIWhtPUCtdi11dV9htzfj6RlOfNwcNJpZ+PtnX35eKAqFIhZ4EsgRQpgUCsVq4FZgWS+dTUbmkkFfU836txZQfewoCf0GMu3BxwmKPHO1VX5Ex6YP8zvtGGgpKaH++RcwbNyIOj6e2AXzCZh6fsOoemM9iw4uYk3hGtQqNQ/0e4B7+t5DoGcnx+4kCY596YotOwzBCXDtq85Z7m7EltU0m1i+rYwPdlXQZrYzNDGEv1ydzdQcDaoe9rctksTXDS2sqG5kR0s7ngoF10QEMSc2nJFBfhdEQE2mSrTatdRq12IylaFUehMRMdXV1x6Dsqu+MBeAnp7AA/BRKBQ2wBeo6fmRZGQuHSSHgz1frWH7xx+gUquZ9vCT9J14ZnFt05vZ8nEhJfs75xjoaG6m4fU3aFq1CqW3N5F/eJqQu+5C6Xnute0WSwtLDy/lg2Mf4BAObsq8iQf7P9j5CLPTYstS4bo3oP/N3YotO1TVzJLNpXx9uBYhBFf1i2bu2GQGJXRxm/MMlBotrKzR8aFWh97mIMnHk7+lxnCLJpRwz94XUJutlfqGb9HWrqG5ZTcAIcEjSUp8hMjI6Xh49J7nSm/Q7e+AEKJaoVC8hDOV3gSsF0KsP/V1CoXiQeBBgISEM/cJZWQuRerLSli3aD71pcWkDRvJ5PsewT807LTXORwSB7/vvGOgsNloWvUhDa+/jtTWRvBNNxHx5BN4hJ1+7ZM5HmH27pF3abe1MyN1Bo8MeIS4gE6Op50aWxaR5bR07TPbuYzTBSRJ8H1eHUu2lLKrVI+/lwf3jk7i7tFJxIf27OGdTRKs17WwolrHxqY2VAqYHhbE3bHhjAvx73UzKUmyoddvpla7hsbG75EkK76+qaSmPI1Gcx3e3jG9er/eRCGE6N4bFYoQ4FPgFqAZ+Bj4RAjx3tneM3ToULFnz55u3U9G5mJht9nY+dmH7Pr8E7z9A5h838Okjxhzxqr7ZMfA5AHhjL3p7I6BQggMGzdS//wLWEtL8Rs9ishn/4h35rn9Qk6NMLsi/gqeGPQE6SFnHlc8/QMdjy17GZorQNPPaemaNaPLsWVGq51P91axdEspZTojscE+3DsmiZuHxRPo3TN71SqzlfdrdHxQq6POaifGS82dMWHcHh2Gxqv3Q4fb2o5Qq11DXd2X2Gx61OpQoqKuJVozm4CAfr9YX/tMKBSKvUKI04b3e/J3kClAqRCiwXWDz4DRwFkFXEbmUqc6P4/1by1AX11JzvhJTJwzF5+A03vKXXUMtBQWUjfvedq3bsUzKYm4N9/Af+LEc6/MSw6+KvmKNw68QU17DcM1w3ly8JMMiDj/Ag/gii1bAVvnO2PLYofAVS9CxvQuhyjUtZpZsb2M93dW0Gy0MSAuiIW3DeKqvho8erAU4xCCn/RtrKhu5Hud00xqUmggL8aGMSm0982kzOYatNovqNWuwWgsQqn0JDx8ChrNLMJCx6NU/vIe312hJwJeAYxUKBS+OFsokwG5vJa5LLGaTWz5cAX7v/uKgLBwrv/T/5A88HRHv646Btr1ehoWLqR59cco/f2J+vOfCLn1VhTn6HMLIfix4kcW7l9IcUsxOWE5/H303xkV3ckIM4vhRGxZez0kjO52bFluTStLtpTw5cEa7JJgeo6GueOSGZIY0qMKtd5iY1WtnpW1jVSZbUR4evBkYhS3R4eS0MtmUna7gfqG79Bq19LUtAMQBAUNJSvz/4iMvBq1une8Vn4JetID36lQKD4B9gF2YD+wuLcOJiNzsSg7tJ8Ni1+jtaGOgdOvYdxtd+Ppc3oft66slY0fdM4xULJaaVr5Ho2LFiEZjYTceivhjz+GR8i5H+ztqN3Bgn0LONx4mOSgZF6e+DJTEqZ0TizNrbBrsTO2zKSH5Akw4V1nbFkXkCTBxoIGlmwpYWuRDl9PFbcPT+C+sckkhnXRH/zk6wrB1iYDy2sa+a6xBbuAcSH+/D01livDg1D3YrUtSXaamrZRq11DQ8N6JMmMj08iyclPEa25Dh+fi/M8zmg0kp+fT15eHldeeSWhod3bYD0bPXqMK4T4O/D3XjqLjMxFxWww8PPKJRz9+XtComO55R/ziMs+3XzK3G5j5+clHDnuGHh/H9KGntkxUAiB4YcfqHvhRWwVFfhNGE/UM8/glZp6zrMcaTzCq/teZWftzq5HmBn1sPOtE7Fl6dOcPe744Z3+XgCYbQ4+21fN0i0lFDe0ExXoxbNXZnH78ASCfLvfWtDb7Hzksm4tMVkIVauYGxfBXTFhpPr2rplUm+EY2trP0NZ9gdXagIdHENHR16PRzCIocPBF6WsbDAaOHTtGbm4uZWVlSJJEUFAQLS0tl5aAy8hcrhTu2sYPS9/E2NrC8Fk3MeqG2/A4pa0hhCB/h9Mx0Gw4v2OgOS+PuufmYdy1C8+0VOLffhv/ceeufoubi1m4fyE/VPzQ9QizU2PLsq51xpbFDOr09wGgoc3Cyh3lvLejHH27lT4xgbx6y0Cu7heN53myN8+GEILdLe2sqNHxZUMzFkkwIsiP3ydFcU1EMN69aCZlsdSjrfsCrXYNBsMxFAo14WET0WhmEx4+EaXywvt7t7a2kpeXR25uLhUVFQghCA0NZfTo0WRnZxMTE3NBfnjIAi7zX0V7cxM/vrOIgp1biUhKYfazfycqJe20153qGDjjybM7BtobGqifP5+WTz9DFRSE5u//j+CbbkJxBl+U45wWYTbwUebkdDLC7LTYstlO4Y46/9bmyRTUtbF0cylrDlRjtUtMyY7k/rEpjEwJ7bbYtNodfKzVs6JGR367mQCVkjuiw7grJozsXjSTcjiMNDRsoFa7Br1+KyARGDiQzIz/ISrqGtTqns+gn4+mpiZyc3PJy8ujqqoKgIiICMaPH09OTg6Rkef2de8NZAGX+a9ACEHuph/5efnb2KwWxt46h6Ezrj/NfMpqtrP76zIO/lCJp4/qnI6BksWCftlydG+9hWSzEXrPPYQ/8jCqwLM/FDs1wuyu7Lu4v9/9nYswOzW2rP/Nztiy8E6OE7q+D1uKGnl7cymbChrwViu5aUgc941NJjWi634nxznQamRFTSNr6poxSRIDAnx4OTOe66KC8VP1jpmUEBJNTTvQatdQ37AOh6Mdb+9YkpIeIVozG1/f5F65z7loaGhwV9parRaA6OhoJk2aRE5ODuHhnVym6iVkAZf51dPaUM+Gt1+j7OA+YjJzmPbQE4TFdkyOEUJQsr+BzatdjoFjohk5OxUf/9OnRYQQtH33HfUvvoStpgb/KZOJevppPJOSznqGNmsby44uY2Xuyq5HmHWILQMG3tbl2DKL3cHnB2pYurmU/Lo2wv29eHpaBrePSCTUr3uBve0OB2vrmlle08ihNhM+SiXXRwVzV0w4AwN7z4nP0F6I1mXVarFoUan8iYq8Bo1mNsHBQ3s95eZkhBDU1dW5RbuhoQGAuLg4pk6dSk5ODiHneTB9IZEFXOZXi5AkDqz/ms0fLAdg0r0PMXDaNadlRjbXG9n8YQEVuXrC4s7tGGg6fJi65+Zh2rcPr6wsEv79f/iNPHvKitluZtWxVSw9spQWSwtXJl3JYwMf61yEWUOBU7gPrQalBwy5xxmk0IXYMn27lfd3lLN8ezmNBgtZmgBevLE/MwfG4NVNm9U8g4kVNTo+0eppc0hk+Xnz7/RYbtSEEthL1q1WayPaui/RatfS1nYEhUJFaOg40tP+RHj4FFSqC5ekI4SgpqbG3R7R6/UoFAoSEhK46qqryMrKIiiod2xwe4os4DK/SvQ1VaxbtICa/FySBgxm6gOPExjR0ZLVbnOw77ty9q2rQOmhOKdjoE2rpeGVV2j5/AtUYWFo/vVPgq+/HsVZ2gM2ycaawjW8dfAt6k3OCLOnBj1Fdlj2+Q9/cmyZ2gdGPuJMv+lCbFlxg4GlW0r5dG8VFrvE+IwIHhiXzNi08G71Zc0OiS8bmllRrWN3azteSgUzIoK5OzacoYG9Y93qcJhpbPzB1dfehBAOAgL6kJ7+V6KiZuDleeHaE5IkUVlZSV5eHnl5ebS0tKBUKklOTmb06NFkZWXh79/9FtOFQhZwmV8VDrudPV9+xvZPV6H29OLKR39LzvhJpwlM+REdmz4qoLXBdE7HQMlkQrf0HXRLl4LdTtgDDxD20IOozvKHWRIS35V+x+sHXqeircIZYTa+kxFmNfudwn08tmzsb5zC7dc54RJCsL1Ex9LNpfxwrB5PDyWzB8Zy/7hkMqK6Z8JUbDSzokbH6lo9TXYHKT5e/CM1hpujQwntBetWISSam/eg1a6hrv4bHA6DO4LMadV6bpuBnuBwOCgvLyc3N5djx45hMBhQqVSkpqYyceJEMjMz8e1EUPQviSzgMr8a6kqLWb9oAfVlxWSMGMOk+x7GL7hjf7JNb2brx4UUuxwDZ/5mIPFncAwUkkTrV19R//Ir2LVaAq68ksinf49n3JmNo45HmC3Yt4D8pnwyQjI6H2FWuctp6Vq43pl4M+GPMOKhTseWWe0SXx+uYcnmUo7WtBLq58lTk9O5c2QiEQFdH6GzShLfNbayorqRLc0GPBRwZXgQ98SGMybYv1eqbWcE2Rq02s8vagSZ3W6ntLTULdomkwm1Wk1aWho5OTmkp6fj3YnUo0sFWcBlLnvsVivbP13F7i8+xScgkJm/+zPpI0Z3eI3DIXHwh0p2f10GkmDEdSkMmpKASn16u8S4bz918+ZhPnQI7z59iH3pRXyHnr2CPjXCbN64eVyVfNX5I8xOji3zDYPJ/w+Gze10bFmL0cYHuypYvq0MbauZ1Ag/nru+H7MHxeKt7roAVpgsvF+r54NaHQ1WO3Heav6UHM1t0aFE9oKZlM3WdFIE2QEuVgSZzWajqKiIvLw88vPzsVgseHp6kpmZSXZ2NmlpaXiex8L3UkUWcJnLmqpjR1m/aAFNtdX0mTiFiXfNxfuU9kZNodMxUF/TTlL/cMbdfGbHQFt1NfX/eZnWb77BIzKS6HnPETRz5mkPPY9zTH+MBfsWsLl6MxE+Efxt5N+YnT4b9bkMkYSA4h+drZLjsWXT/tcZW+bZuTX1cl0772wpZfWeKkw2B2PTwnnuhn5MSI/ocjCwQwh+0LWyvFrHj/pWFMCUsEDmxIZzRWgAqh5W2+4Isto1NOp+Rggb/n6ZpKX9EU3UTLy8onp0/bNhsVgoLCwkNzeXwsJCbDYb3t7eZGdnk5OTQ0pKCh7nmNO/XLj8P4HMfyVWk5HNq5ZzYN3XBEZEcsOf/0nSgMEdXmNstbLtsyLyd2gJCPXm6kf6kTwg4rRrOQzt6N5+G/2yZaBQEP7oo4TNvR/lWfqf5a3lvL7/db4t60KEmRBQ8J0rtmwvBMY6nQEH39Wp2DIhBHvKm1iyuYT1uXV4KBXMHBDL/WOTyYnpuhmT1mLjg1od79foqLbYiPL04DeJUdwRE0acd8+qUWcE2f6TIshaToogm01AQCce5HYDk8lEQUEBubm5FBcXY7fb8fPzo3///uTk5JCUlISql2bSu4JktGEubMY7MwSld+9KrizgMpcdZQf2sv7t12jTNTLoqhmMvXUOnt4nRFCSBLmbnY6BNouDIVcmMuTq0x0DhSTRsmYt9a++gqOhkcAZM4j83W9RR5952qOuvY5Fh5wRZp4qz85FmPUwtszukPj2iJYlW0o5WNlMkI+aRyemcveoJCIDu9arlYRgU1MbK2t0fNfYgkPAxJAA/pkey7SwnptJmUwV1Go/R6tdg8lU7oogm0a0ZtYFiyBrb2/n2LFj5OXlUVJSgiRJBAYGMmTIELKzs0lISEDZRc/zniIkga3GgDm/CXO+HmtlGwgIvSMb3369O0kjC7jMZYPJ0MbPy98md9OPhMbEcev/vEBsZsdqrr7c6RhYX95GbGYIE247s2Ng+65d1M2bhyU3D58BA4h67TV8BpzZZ7vZ3Mw7R95xR5jdnHnz+SPMJAcc+Qw2vwQNxyAsDWa9Cf1u6lRsWavZ5gwG3lpGdbOJpDBf/nVdH24YEodvF6PEGq12PtLqWVnTSJnJSqhaxcPxkdwZHUayb898Qmy2Vurrv6ZWu5aWFqebtDOC7NELFkHW1tbmHvcrKytDCEFwcDAjR44kJyeHmJiYiy7ajnYblsImp2gXNCG120AB6lh/AiYl4J0Zgmdc738vZAGXuSwo2LGFH95ZhNnQxojZtzDy+ls6mE91cAwM8GTq/TmkD406bWLCWlFB/Ysv0bZhAx7R0cT85yUCr776jJMVRpuRlbkrWXZ0WecjzE6LLcvuUmxZVZORd7eW8dHuSgwWOyOSQ/nHzD5MzorsUn9bCMGOlnZWVDfydUMLViEYGeTHs8nRXB0RhFcPBE6SbOj0m1x97R8uSgRZc3OzexuysrISgPDwcMaOHUtOTg4ajeaiJugISWCtasOc34SloAlrlbPKVvp54J0egldmKN7pwajOsMnbm8gCLnNJY2jS8+M7iyjctY3I5FRu+PM/iUw6sUIuhCB/p5ZtnzodA/tfEcfwGSl4neIY6Ghro3HRIppWrAS1moinniT03ntRnmFk7NQIs0nxk3hi0BOkhZxueuXGboED78OWV1yxZf3h5pVOh8BOiOX+iiaWbCnl28O1KBQKru0fzf1jk+kfF9zp7xVAs83OJ3VNLK9upNBoIdBDyZzYMO6KCSfTr/vjcc4IssOuCLKv3BFkMTG3XrAIMp1O5xbtmhpnXnpUVBQTJ050m0VdTBwGK+bCZsz5eiwFTUhGOyjAMz6AwMkJeGeGoo71P6NvzoVCFnCZSxIhBEd//p6fVy7BbrUy7vZ7GHrtbJQnPYTSVRvY9GEBNYXNRCWf2TFQ2O00f/IpDQsW4GhqImj2bCKeegp11Ol/+B2Sgy9LvuTNA2+6I8yeGvwU/SP6n/2gNhPsXe6MLWurgdihcPVLTk/u8wiaQxJsyNXy9uZS9pY3EeDtwQPjU7h7VBIxwZ137hNCsL/VyIoaHZ/XN2GSBIMDfXklK57rIkPw7YF1qzOC7HNqtWsvSgRZfX29e4W9rq4OgJiYGKZMmUJ2djZh5wl+7k2EJLBWtmHO12MuaMJWbXBW2f5qvDND8c4MwSs9BJXfLxfDJgu4zCVHS72W9Ytfo+LwAWKz+jDtoScJjYl1f91qtrPH5Rio9lFxxZ1ZZI8+3TGwfds26uY9j6WgAJ+hQ4j602J8+pxuuSqE4IeKH1i4fyElLSX0Cetz/gizU2PLEsfArDcgZeJ5hbvdYmf1nkre2VpKpd5EfKgPf5+Rw01D4/H36vwfSYPdwWd1Tayo0XHEYMJXpeQmTSh3xYTRL6D7M9V2exv19evQatfQ1LyTCxlBJoRAq9W6RbuxsRGAhIQEpk+fTnZ2NsHBwb12v/PhaLNiLnA+fDQXNiNMrio7IZDAKYl4Z4agjrm4Vfa56JGAKxSKYGAJ0BcQwH1CiO29cC6Z/0IkycGBdV+zedVyFAolk+97hAFTr3LPYR93DNzycSGGJgvZY6IZdQbHQEtJKfUvvIDh559Rx8URO38+AdOmnlGMd9TuYP7e+RzRHelchJm5xRVb9oYztixlIoxfBkljzvv5altMLNtWxgc7K2gz2xmSGMKfr8pmWh8Nqi4IwlGDieXVjXxa10S7QyLHz5vnM+K4PiqEgG6aSTkjyLa6Isg2XNAIMkmSqK6udrdHmpubUSgUJCUlMXz4cLKzswkI6P0HfmdCOATWylb3xIitph0AZYAan5wwvDND8E4LRtmDRKILSU8r8PnAd0KIGxUKhSdwaRsHyFyy6KoqWffWfGoLjpE8cAhTHniMwPATbY7meiObPyqg4qiesFh/ps3tS3Rqx41FR0sLjW+8gf79D1B6eRH5h6cJuesulGfYsjvccJj5++ezs3Yn0X7R548wM+ph5yLnP+YWSJ/uii0bdt7PdqS6hbc3l/D1oVokIbiqn7O/PTih8zakRofEF/VNrKzRsbfViLdSwczIYO6OCWdwN82khBAYDHlOq9a6z7FaG10RZDcQrZlFYOCgXutrS5JERUWFW7Tb2tpQKpWkpKQwfvx4MjMz8fPrft5mV3C0WJxVdkET5sImhNkBSleVPT3JWWVH+13Uh6LdpdsCrlAoAoHxwD0AQggrYO2dY8n8t+Cw29n9xafs+HQVam8frnr892SPnej+w2O3Odi3roJ935U7HQNvSqffxI6OgcJmo+nDj2h87TUcbW0E33gjEU8+gccZzPVPjjAL9Q7l2WHPcnPmzXiqzjItYGhwxpbtXgJWgyu27A8QM/Ccn0uSBD8cq2fJ5hJ2lurx81Rx9+gk7hmdRHxo5+ucwnYzK2t0fKTV02J3kO7rxT/TYrhJE0pIN82kLJY6tNrP0WrXYmjPv2ARZA6Hg7KyMrfvSHt7OyqVyu07kpGRgY9P76X0nA3hkLCWH6+ym7BpnVW2KtATn77hzn52enCvL9lcDHpy4hSgAXhXoVAMAPYCTwkh2k9+kUKheBB4EJx9LRmZ49SVFLHuzVdpqCgjY9Q4Jt/7EL5Bwe6vlx/VselDp2Ng2tBIxt6Yjl/wCXERQtC+aRN1z7+AtaQE31EjifrjH/HOzDztXtWGat448AZflXyFr4cvjw18jLty7jp7hFlr7YnYMrsZ+l4P456GqJxzfiaT1cEn+6p4Z0sppY3txAR585ers7lleDyB3p37a7hFkvi2oYXlNY1sb25HrVBwdUQQd8eEMyq4e5Whw2GkvmE92to16Ju2caEiyOx2O8XFxW7fkeNmUenp6W6zKC+vC59RaW+2YC7QO8f8ipoRFgcoFXglBRJ0VRLemaF4RPWODe4viUII0b03KhRDgR3AGCHEToVCMR9oFUL87WzvGTp0qNizZ0/3Tirzq8FmtbD94w/Y89UafIOCmXz/I6QPG+X+uqHJzJaPCyne53QMHH9rBvHZHZ35LIWF1D3/Au1btuCZmEjks8/if8XE0/5ANpoaefvQ26wuWI1KoeK2rNu4v+/9BHsHn/lwzRXOiZJ9K12xZbfAuN+dN7asvtXMiu3lvLeznGajjQFxQcwdl8JVfTV4dHIKpNxkYWWNjlW1enQ2OwnentwVE8at0aFEeHa9ByuEg6amHa6+9jocDiPe3nFoNLOI1szqtQgyq9XawSzKarXi5eXVwSxKrb6wPWRhl7CUtbpF215nBEAV5OXsY2eE4JV2eVbZAAqFYq8Q4jRHtZ58miqgSgix0/XvnwB/7MH1ZP4LqMo9wvrFC2iqraHfpGmMv/M+vP2c5lMOh8ShH6vY9VUpQhKMmJnCoKkdHQPtej0NCxfSvPpjlH5+RP3pj4TcdhuKU/rcbdY23j3yLu/lvde5CDN9CWx+GQ6uAhTOVfexv4XQc4tcXm0rS7eU8sWBGmySxLScKOaOS2FoYkinqju7JNiga2FFjY6f9G2oFDAtLIg5MWFMCA1A2Y0K0WAoQKtdg7bui5MiyK5FE309wUFDeiWCzGw2u82iioqKsNls+Pj40KdPH3JyckhOTr7gZlH2JrP74aOluBlhlUClwCs5CL8hUXhnhuAReWlU2Q67DYVSibITy1xdodvfYSGEVqFQVCoUikwhRD4wGcjtvaPJ/JqwGI1s/mAZBzd8Q1BkFDf+9X9J7DfQ/fWawmY2rsp3Ogb2C2PcLRkdHAOF1Yr+/Q9ofOMNJKORkFtvJfzxx/A4JY/QZDc5I8wOL6XV2nr+CLOGAufW5OGPnbFlQ+9zxpYFnX3bUgjBxoIGlmwuZUtRIz5qFbcNj+feMckkhXfuQVyN2cr7tTrer9GjtdqI9lLzdJKG26NDiemGmZTF2khd3Zdoa9fQZjiKQqEiLHQC6Wl/Jjx8cq9EkBmNRvLz88nLy6O4uBiHw4G/vz8DBgwgJyeHxMTEC2oWJWwSlrIWt2jbG0wAqEK88B0c5ayyU4NRel18w6pTsVktaAvzqco7SlXeEWoKj3Hjn/9FbNa5W3Bdpac/Ip8A3ndNoJQA9/b8SDK/Nkr372HD26/Tpm9kyDXXMebmu1C7NiCNrVa2f1bEsR1a/EO9TnMMFEJg+OEH6l58EVt5BX7jxxH1zDN4pXXcijw1wmxs7FieHPTk2SPMtEecPiVH156ILRv9BAScPWTYbHPw+YFqlmwupbDeQFSgF89emcXtwxMI6sSYmSQEP+vbWFHTyPrGVgRwRWgAz8fGMTk0EI+uWsE6zDQ0bkCrXYtev9kVQdaX9PS/oomagWcvRJAZDAaOHTtGbm4uZWVlbrOoYcOGkZ2dTXx8/AX1HbHrTK657CZnlW1zVdkpQfgNj3ZW2RE+v3iVbTWbqMnPcwn2YbRFBTjsdlAoiEhMpt+kaXj79/5oZLd74N1B7oH/d2FsbeHnFUvI2/wTYXEJTHvoSWIysgCXY+CWGnasLcZmcTBwagJDr0pCfVL1ZM7Lo27e8xh37sQzNZWoZ5/Bf/z4Dvc4NcJsUOQgnhr8FEOihpz5UNX7nF7c+V+DZwAMfwBGPXbO2DKdwcLKHeWs3F6Ort1KTnQgD4xP5pp+MXh6nF+8Gqw2PqzVs6JGR6XZSrjag9ujQ7kjJoxEn6490HNGkO2mVruG+vpv3RFkGs0sZwSZ37l79Z2htbXVPe5XUVGBEIKQkBBycnLIzs4mNjb2ggmmsDmwlLS4TaHsja4qO9Tb2cvODMUrJQil5y9bZZsNBqrzj7or7LqSIoQkoVAqiUpJIy67L3HZfYnNzDnNn747XIgeuIzMGRFCuM2nLO0GRt5wGyNm34yH60FWR8fAYMbfmklo9InWg72hgYYFC2j+5FNUQUFE/e2vhNxyC4qTeqpnijB7ffLrjIsdd2ZxqdgJm16Aou+diTcT/+SMLfM5+/RFUX2bMxh4XzVWu8TkrEjmjkthZEroeQVMCMHWZgMranR829CCTQjGBPvz19RorgoPwrOLVWt7e4mrr/05ZnM1KpUfkRHT0WhmExIyoscRZE1NTe5tyKqqKgAiIiIYN24cOTk5REWdbgzWW9gaTc7Nx/wmLCUtYJfAQ+msskdF450Rgkf4L1tlG1uaqTp2lKrcI1TlHaGhogyEQOXhgSYtk+HX3URcTl9iMrI6WBtfaGQBl+lVDHod3y99k+I9O4hKSWf6X/+XiETng0CL0ekYeHhTNT4Bnky9L4f0YSeEQbJY0C9bju6tt5CsVkLnzCH80UdQBXVc2Nlbt5cF+xawr34f8QHxPD/uea5MvvL0CDMhnLFlm16A0k2u2LK/u2LLzrwOLoRgW7GOtzeX8HN+A14eSm4cEsd9Y5JJizx/JdVks7Naq2dljY4io4VgDxX3xYZzZ0wY6V00k7Ja9dTVf41Wu4bW1oMcjyBLTfk9ERFTexxB1tjY6Bbt2tpaADQaDZMmTSI7O5uIiNPDL3oDyXq8ynZ6jDh0ZgA8wn3wH65xeoykBKHoRixcb9Gma6QqzynWVblH0Nc4f6h5eHkRk5HN6JtuJy67L9FpmR1cMS82soDL9ApCCA7/uJ5N772Dw2Zjwp33Mfjq61CqVM6KfFcdWz8pxGyw0W9iHCNmnnAMFELQtm4d9S++hK26Gv9Jk4j8w9N4JXecAOl0hJkQUPwDbHwRKneAfxRM+z8Yeu9ZY8ssdgdfHqxlyeYSjmnbCPf34vdTM7hjZCKhfuf+AyqEYG+rkeU1jXxR34xFEgwN9GVBdgIzIoLx6YKZlCRZaGz8iVrtGnS6nxHCjr9/liuC7Dq8vLrvwCeEoK6uzt0eaWhoACA2NpapU6eSnZ1NaGjngpS7el97g8nVFtFjKW0Bu0ChVuKVGkzA2FhnlR128SrXU8/XUl/nFuuqY0doqdMC4OnjS2xWDn0mTiEuuy9RKamoPC6dtXpZwGV6THOdlg2LF1Bx5BBxOX2Z9tCThGicntD6mnY2rso/4Rj4xEAiEk48zDEdPkLdvHmY9u7FKzOThHffwW/UqA7XPzXC7LdDfsttWbedHmEmBOR/60y/qdkHgXFOZ8BBd4H6zNVvU7vVHQxc32YhMyqAF27sz3UDY/A6j69Im93Bp3VNrKhuJLfdjL9KyW3RYcyJCSPHv2tugi2t+9DWrqGu/htXBFkE8XF39ziCTAhBTU2NW7T1ej0AiYmJXHnllWRnZxMU1LkQ5a4gWRxYiptPVNlNFgA8InzwHxnjrLKTglCcIVT6QiOEQF9ddaLCzjuCQa8DwDsgkLisPgyaPoO47D5EJCX3+uhfbyILuEy3kSQH+7/9ki0frkSpUjL1gcfpN2kaCqUSm8XBnm9KObChErW3iol3ZJIzJsbt4marq6Ph5Vdo+fxzVGFhaP75PwTfcAOKk8bQOh1hJkmQ94Xz4WTdYQhJghkLYMBt4HHm6rm00RkM/PHeSsw2ifEZEfzn5mTGpoWft9d6uM1p3fppXRNGh0Q/fx9eyoxndmQwfl0wk3JGkK11RZBVoFR6u/raswgJGd3tCDJJkqiqqnK3R1paWlAoFCQnJzN69GiysrLw74UHaycjhMBeb3Q/fLSUtoBDoPB0VdkT4vDOCMUjtOfjjF0+myTRUFF2kmAfxdTaAoBfcIjzgWNOP+Ky+xAWG3/WEOtLEVnAZbpFY0UZ699aSG1RPimDhzFl7mMEhIW7HQM3ry5wOgaOdjkGBjiFVDKZ0L3zDrolS8FuJ+yBuYQ99BCqkwSl2dzM0iNLWXVsFQ7h4JbMW3ig/wOnR5g57HD0M6dwN+a7YssWuWLLTv9fWwjBzlI9SzaX8sOxOtRKJbMHxXLf2GQyNece8TI6JNbWN7GyWsf+NiM+SgWzokKYExPOwIDOP2Cz2Vqor/+GWu0aWlr2AgpCQkaSnPQ4ERHT8fDonrA6HA4qKircom0wGFCpVKSmpjJx4kQyMzPxPUtIc3eRzHZXle0UbUezq8qO8sV/TIxzLjspCEUnJnV69VwOB3WlRe4JkepjR7G0Ox0+AiMiSR44xCXafQmOiv7FRxB7gizgMl3CYbexc83H7FyzGi9fX65+8g9kjR6PQqGgpcHE5o8KKD+iczoG3t+H6LRgwFkFtX71FfUvv4JdqyVg+nQin/49nvHx7msbbUZW5K5g+dHlGO1Grk25lkcHPkqsf+wph7DBoY9csWUlEJkDN74DObPOGFtmc0h8c7iWJZtLOVzdQqifJ09MSueukYlEBJx7jO9Yu4mV1To+rtPTapfI9PPm/9JjuTEqhKBOmkmdOYIsjdSUP6DRzOx2BJndbqe0tJS8vDyOHTuG0WjEw8OD9PR0srOzycjIwPsMiUPdRQiBvc54YmKkrBUkgcJLhVdaMAGT4p297OCLW2XbbTa0xQXuCZGa/DxsFueD0ZDoWDJGjHGP9QVGXNwUnwuNLOAynUZbVMC6RfNprCwna8wErrjnQXwDg7DbHOxfX8He78pRKk93DDTu30/dc/MwHzqEd04OsS+9iO/QEyOtVoeV1fmrefvw2+jNeiYnTOaJQU+QGpza8QB2C+x/D7a8Ci2u2LJb3oPMa84YW9ZisvHhrgqWbSujtsVMaoQfz13fj9mDYvE+x4SDRZL4uqGFFdWN7Ghpx1Oh4NrIYO6OCWN4UOfMpM4WQRYbczsazSwCAvp2q/Kz2WwdzKLMZjOenp5kZGSQk5NDWloanr04FSGZ7R1ixBytTsNRtcaPgHGxeGWE4JUYeFGrbJvZTE3hMffSTG1hPg6bDYDwhCT6TJzsFmy/4N4x6bpUkQVc5rzYLGa2rn6ffV9/jl9ICLOe+RupQ0YAUJHrdAxsqXc6Bo65IR3/EGdVa6uupv4/L9P6zTd4REQQ/dxzBF03091jPB5h9saBN6htr2VE9AieGvQU/SL6nXKAU2LL4obBNf+B9KlnTL+p0Bl5Z2spq/dUYrQ6GJMWxv/N7svEjHMHA5cYLaysaeQjrR69zUGyjyf/LzWGWzShhHUyCd4ZQbbWFUFW7I4gi9bMJjR0XLciyKxWq9t3pLCwEKvVire3N5mZmeTk5JCSktJrZlFCCGy17e51dWtFK0ig8Fbhne40hfLOCEEVdOEdBY9jMbZTk59HpauHXVdciORwoFAoiUxOYeC0a5xLM1k5+AT0XlrQ5YAs4DLnpPLoIda/tZDmulr6T7mS8Xfci5evH4Ymi8sxsJ6gSB9mPjmQ+BznCJrU3k7j22+jf3cZAOGPPkLY/fejdBn2nxph1jesL/8z+n8YFdNx+sQZW7bUFVvWcN7Ysr3lzv72uqNaVEoFMwbEcP/YZPrEnH3KwiYJ1jW2sKKmkU1NBjwUMD3cad06NsS/U2ZSxyPIarWf0dzs9HYLDh5OQsL9REZc1a0IMrPZTEFBgdssym634+vrS79+/cjOziY5ObnXfEckow1zUbN7zE9qc1az6hg/AiY42yKeCQEoepCt2RVMba1UHTtKdd4RKnOP0FBWihASSpUHmtR0hl47m7jsvsRk5uDVy3393sRuc9BYZaChvI36ijaGTE8kOKp3zysLuMwZsRjb2fTeuxz64TuCo6K56W//JqFvfxwOiQPfV7Dry1IkSTBiZjKDpiaiUisRkkTLmrXUv/oKjoZGAq+9lsjf/RZ1zIke7/aa7SzYt4AjuiOkBKXwysRXmJwwuWM7wdwCOxfDjtfB1AQpVzhDFM4QW2Z3SKw7WseSLSXsr2gmyEfNwxNSuXt0ElGBZ+/FVpmtvF+j4/1aHfVWO7Feav6YrOG26DCivDrhayLZ0TdtQatde1IEWRIpyb9Fo7kOH5/4817jVIxGI8eOHXObRUmSREBAAIMHDyY7O5vExMRe8R0RksBWY3A/fLRWtIIAhbcH3hnBeGeEOqvswIuzoGJo0runQ6rzjtBYWQ6Ah9qT6PRMRlx/C3HZfYjJyELtdfGnWDqDwy6hqzZQX95GQ3kr9RVt6KvbkSSnVYlPgJqMYVGygMtceIr37uT7t1+nvbmZoTOuZ/RNt6P28qamqJlNq/LRVbeT2C+McTdnEBThnHc27t7t7HPn5uI9oD/xCxfiM3Cg+5qHGg6xYN8CdmqdEWb/GvMvZqTMQHXyQ0ejHna8CTvfAksLZFzpFO640ywgaDPb+Gh3Je9uLaO62URSmC//uq4PNwyJw/cs7Q6HEPyoa2VFjY4fdE4zqSlhgcyJCWNSWCCqTqzHGwx5rr72F64IsmCio28kWjObwMABXe5rt7W1dTCLEkIQHBzMiBEjyMnJITY2tldE29Fuw1LY5I4SkwyuKjvWn4Ar4vHODMUzLgCF6sJPZLQ21FPlqq6rjx2hqbbGeRZvH2Izs8kaM4HY7D5oUjPc9guXEg6HRFNtO/XlbW7Bbqw2INmdYu3l50FkQgADpyUQmRhAZGIg/iFeF2TaRRZwGTfG1hZ+WraYY1s3Eh6fyMyn/0J0WiamNiubPsrj2LZa/EO9uOrhfiQPcM5LWysrqX/xJdrWr8cjOpqYF18k8Npr3P+zFjUVsXD/Qn6s/JFQ71D+OPyP3JRxU8cIM0MDbF8Iu5c6Y8uyZziFO3rAaWesbjaxbGspH+6qpM1iZ3hyKH+fkcPk7KizBgPXWWysqtWxskZHtcVGpKcHTyVGcXtMGPGdsG41W7TUab+gVruG9vYCZwRZ+BVEa2YTFjYRpbJrlWpzczN5eXnk5eVRUVEBQFhYGGPHjiU7O5vo6J6PtglJYKs2uBdprJVtIEDp64FXeog75EDlf2GrbCEEzdoap1jnHaEy7whtjc4NUC8/P2Kz+tB/8pXEZfclMjkV5QW0o+0OkiRo0rY72yDlbdSXt9JYZcBhkwDw9FYRkRjIgEnxRCYGEpkYQECY90UbTZTdCGUQQnBs60Z+XLYYq9HIyOtvYfisG1EqPcjdWsP2NcXYzC7HwKudjoEOgwHdokXol68ADw/nPPe996J0ZRwejzD7svhL/NR+3N3n7tMjzFprYOsC2LsMHBbocz2MfxoiT988PFjZzJItpXxz2OnZcU2/aOaOS6Z/XPAZP5MkBFuaDCyvaWRdYwt2AeND/JkTE8708CDU57FutdvbaWhY77RqbdoKCIICB6HRzCYq6uouR5Dp9Xr3jHZ1dTUAkZGRboe/yMjIHv+hdxisJyZGCpuQ2u2gAHVcgPPhY2aIs8ruom1tVxCShK6qwvXA0dkSaW9uAsA3KJi4rD7EZvclPqcv4fGJl9TSjJAEzfVGV1XdRn1FKw2VBuwWBwBqLxURCQFEJAY4K+uEQIIifC7o9/M4shuhzBlp0zXy/ZLXKdm3G01aBtMfepLwhCQaKtr4+YN86staic1wOQbG+CEcDpo+Wk3D/Pk49HqCZs0i4re/RR3lnK9tNDWy+NBiPi74GJVCxT197uG+vvd1jDBrroAtrzhHAiUHDLgVxv4Owjt6fDskwfd5dSzZXMLusiYCvDy4f2wy94xOIib4zKvqOqudj7R6VtY0UmqyEqpW8UBcBHfFhJPie+7JiRMRZJ/R0LDeFUEWT3LS42g013U5gqy+vt69wl5XVwdAdHQ0kydPJjs7m/AzhC53BSEJrJVt7irbVm1wVtl+amcfOzMEr/QQVH4Xrg0hORw0lJee1BI5itnQBoB/WDgJfQe4JkT6EBobd8kszQghaG00dWiD1Fe0YTM7xdpDrSQ8PoCc0dFEJgYQkRBIsMb3nFNMvwSygP+XIiSJQz+sY9P77yA5JCbOmcugq2ZgM0ts+rCAIxur8A7wZMq9OWQMdzoGtm/fTt2857Hk5+MzZAhRb72FT7++ALRaW1l2ZJk7wuz69Ot5qP9DRPlFnbiprhi2vAwHPwQUMOgOZ2xZSFKHs7Vb7Hyyt4p3tpZSrjMSF+LD367N4ZZh8fh7nXnDcldLOytqdHxZ34xVCEYE+fF0koZrIoLxPs/0hMGQj1a71h1B5uERQFTUDKI11xMUNKTToiOEQKvVuivtxsZGAOLj45k2bRrZ2dmEhHStcj8VR5vV3ce2FDYhGZ1Vtmd8AIFTEvHOCEEd63/BqkKH3Ya2uMi54Zh3hOr8XKwmp2d3cFQ0qUNHEO9aSw+MuHAWtF1BCEGbzuwU6opW169tWIx2AJQeCsLjAsgcoXH3rEM0vu49hksZWcD/C2nS1rDhrYVU5h4mvk9/pj34BEFRGqdj4KdFmNus9J0Yx4gZyXj5qrGWlVH3wosYfvwRdWwssa++SsD0aSgUitMizK5KuorHBj1GYmDiiRs25DvX3Y98AipPGHq/K7as44altsXMsm1lfLCznFazncEJwTx7ZRbTcqLOGAzcanfwsdYZlJDfbiZApeTOmDDuigkj+zxmUhZrI3XaL9Bq17oiyDwICx1PevpfCA+bjErVuTlnIQTV1dVu0W5qakKhUJCYmMjw4cPJysoiMLD7s8nCIbBWtronRmzVBgCU/mq8s1xVdtqFq7KPR4Mdf+BYU5CP3epcmQ+LSyB77ERnhZ3dh4DQnicA9RQhBO3NFne/+njv2tzufGirVCoIi/MndUgkkQlOsQ6N8UN1kdf9e4se98AVTif5PUC1EOLac71W7oH/skgOB3u/+ZxtH72H0sODCXfdT79J02jSGtm0Kp/qgmYikwKZeHsmEQkBOFpaaHzjTfTvv4/S05OwRx4mdM4clF5e7gizRQcX0WBqYFzsOJ4c/CRZoVknbqg97HQGzP3CGVs27H4Y9QQERHU415HqFpZuKeXLgzVIQnBlXw33j01hSOKZq9UDrUZW1DSypq4ZkyQxMMCXOTFhXBcVjN85HoKdiCBbg16/xRVB1o9ozSyioq7tdASZJElUVFS4H0S2traiVCpJSUkhOzubrKws/Pw6l415xnO2WtwxYubCZoTZDkrwTAh09bJDUUf7XZAq22oyOqPBjh2lMvcI2qICJIczGiwyMYW47D5uwfYN7H0Xw67S3mJxibSzBVJf3obJtS2qUCoIjfZztUACiEwKJCzWD49f0Ge8u1zIHvhTQB7w37UCdZnRUFHG+kXz0RYXkjp0BJPvfwRvvxB2rC0+zTEQhx39e+/T+NprOFpaCL7xRiKeehKP8HAkIfF1yde8fuB1KtsqGRw5mBcnvNgxwqx6ryu27BtnbNm438HIx8AvzP0SSRL8lF/Pks2lbC/R4eepYs6oJO4dk0R86Omzsu12B2vrm1le08ihNhM+SiU3RIVwV2wYAwLOPlvrjCDbRa12bYcIsoSEB4nWzMLPL+2s7z0Zh8NBWVmZW7Tb29tRqVSkpaUxadIkMjMz8fHpnp+1cEhYy1vdom2rdRovKQM88ekT5pwYSQtG2Yncza5iNhicSTOulkhdabE7GkyTks6Qa65zLc1k4+3Xuw6GXcXUZqW+wtWvdlXW7S4DLRQQovEjISfU3QYJi/NH/QtHr11oeiTgCoUiDrgG+D/gd71yIplexW6zsXPNanatXY2Xnz/XPPUMGSPHUnZIx+bVOzDoLWSNjma0yzHQsHkzdfOex1pcjO/IkUT98Vm8s7KcSeyVG1mwfwEFTQVkhmSeHmFWsQM2vuAMU/AOhol/hhEPdogtM1kdfLa/iqVbSilpaCc6yJs/X53FrcMTCPQ+XaDyDCaW1+j4VKunzSGR5efNcxlx3BAVQuA5rFvb24udEWTazzFbalwRZFe6rFpHojg1vedM3zu7nZKSEnJzc8nPz8dkMqFWq0lPTycnJ4f09HS8vLq3Um5vsTinRfKbMBc1IywOUCrwTAwg8MokZy87unO+K12hvbmJald1XZ13hIbKcmc0mFpNdFomI2bdRFx2P6IzMi9qNNipmNttNFR0bIO06c3urwdH+RKbEUxkYiARiQGEx/nj6f3f1xHu6Sd+FXgGOKsXp0KheBB4ECAhIaGHt5PpCrWF+axbNB9dVQXZYycy8e4HsFk8+ebNw5Qf1hEW68fUp/sQkxaMpaiIit+9QPvmzagTE4h743X8r7gChULB3rq9zN83n/31+0kISOCF8S8wPWm6M8JMCGdc2cYXoGwz+IbDlH84+9wnxZbVt5lZub2c93aU02S00T8uiAW3DeKqvhrUp/S3TQ6JrxqaWVGtY3drO15KBTMigrk7Npyhgb5nFTVnBNlXaLVrO0aQpf6BiIgpnYogs1qtFBcXk5ubS0FBARaLBS8vrw5mUd3xHRF2CUvZ8Spbj73OCIAq0BPf/hGuXnYwyl4WoTZdI1W5h93WqqdGg40ZOZa47L5o0jJ+sWgwq8nuEmvn6F59eRutDSb31wMjfIhKDqTfxDgiEwMITwhwpzn9t9PtHrhCobgWuFoI8ahCoZgIPC33wC8NbGYzW1evZO83X+AfGsbUBx4jse8Q9m8oZ8+3TsfA4TOS6XdFHKK1hcaFr9H00UcofX0Jf+xRQm+/HYWnJ3m6PObvn8/W6q1E+kTy8MCHmZU2yxlhJgQU/eDscVfuAH8NjHkShtzTIbbsmLaVpZtL+fxADTZJYmp2FHPHpTAsKeQ0IS4ymllZo2N1rZ4mu4NUHy/uignj5uhQQs9i3XrmCLJsZ0p71MxORZBZLBYKCgrIy8ujsLAQm82Gj48PWVlZZGdnk5KSgodH1wXD3mR2t0UsRc0IqwNUCrySAt1jfh5RZ/+B1FWEELTUaTskzbTUO8cXPX18icvuQ2xWH+Jz+hGZnIqqG5+pp1jNdhorDc7K2iXaza4fZgABYd5EumetA4lICMD7Ao5BXmiccXINWIuL8c7JOS3ftbNciB74GGCmQqG4GvAGAhUKxXtCiDt7cE2ZHlJ++AAbFi+kpb6OAVOvZtzt91BfbmbVv3Y6HQOHRDLmxnT8/BToV66g8fU3kIxGQm65hfAnHscjJITy1nJe2/4a35V9R5BXEL8b8jtuy7oNbw9vp3Af+8YZFFyz/4yxZUIINhU2smRzCZsLG/FRq7hlWDz3jU0mObzjwz2rJPFtYwsrqnVsbXaaSV0dEcycmDDGBPufUdyEELS07EWrXUtd/dfY7a14ekYSH3+PM4LMP+u095yKyWQiPz+fvLw8ioqKcDgc+Pv7M2DAAHJyckhMTOyyWZSwS1hKW9ymUPZ6ZxWpCvbCd1AE3hmheKUFoTzDKGR3cEaDVbp9RM4UDTb4qpnEZvclIjHpokeD2awOdFVOsT7es27StoOrZvQP8SIi4cT4XkRiAD4XeDP0QiEkCVtNLdaSYixFxVhKirEWFWMpKUFqbQUg/q1F+E+Y0Kv37ZVNTLkC/+UxtxvY9N47HP5xPSHRMUx78EmCo9PZ+mkhRXvqCYrwYfxtGcRnh2L48UfqX3gRa3k5fuPGEfXsM3ilpaFt17Lo4CLWFq3FU+XJXTl3cU+fewjwDHDFln3uii074pzdHvu7DrFlZpuDzw9Us3RLKQV1BqICvbh7dBK3D08g2LfjH8xyk4X3a3R8UKun0WYnzlvNnJhwbtWEEnkWMymjsdw1r73WFUHmQ2TENDSa2YSGjsY5EHV22tvb3b4jpaWlSJJEYGAg2dnZ5OTkEB8f32XfEbvOdKLKLm5G2CRnlZ0c5Hz4mBmKR0TnE3vOhSQ5aKwo79ASMbU5xcEvJNTtgR2f05fQmLiLuuXosEk0Vhs6PGDU17Yjjps5BXoSlRhAhGvdPCIhAL+LaEnbWwi7HWtlJdbiYizFJViKi7AWl2ApKUGYTrR9VGFheKWm4pmagldqGl6pKXj37Ysq4NzJT2dD3sT8FVO0ewffL30DY0szw667kZGzbyF3awPfvLUDSRIMn5HMoGkJ2EuKqLj3aYw7duCZmkr84rfwHz+eJnMTC3e/xKpjqxAIbs26lbn95jojzBx2OLT6pNiy9NNiy3QGC+/tqGDljjIaDVayowN5+eYBXNs/Bs+T5mvtkuAHfSvLqxv5Sd+GApgaHsicmHAmhgac0UzKZmuhrv5rtNo1tLTswxlBNqrTEWStra1u0S4vL0cIQUhICKNGjSI7O5vY2NguiauwHa+ynak09kZXlR3qje+QKGcvOzUYZS9MPzjsdupLi93tkOpjuViMx6PBokgZPIxY11jfxYwGc9gl9DXt7tG9hvI2dNUGJIdTrL391UQmBpA8INw5vpcYiF+w5yWx1NNZJKsVa2nZaRW1tawM4QqPAPDQaPBKTSXk5pvwTEnFKy0Vz5QUPHq4sNVZZC+Uy5j25iZ+XLaYgu2biUhMZvrDTyFJ4WxcVYCu2kBi3zDG3ZKBn6KdhvkLaP70U1QBAYQ/8QQht9yMEas7wsxkNzEjZQaPDnyUGP8YsFudsWVbXj4RWzb+6Q6xZUX1bSzdUsZn+6qw2CUmZUUyd2wyo1LDOvxhrbVY+aBGz/u1OmosNjSeam6PCeWO6DBiz2AmJUlWdLqN1GrX0tj4I0I4I8iio69HEzUTb+/oc35fmpqa3ON+lZWVAISHh5OTk0NOTg5RUV3bELQ3mtzr6paSFmeV7aHAKyXY7THiEd7zKttutTqjwVzV9anRYHE5fV1Vdh8Cwy9ONJjkkNDXGk+aBjnFec/Xw9X+CHT3rgNCL56ZU0+RjEYsJaVYi4tcFXUx1uJirJWV4HCu1aNQoI6LwyvVJdCuitozJaVDluuF5GwVuCzglyFCCPK2/MxPyxZjM5sYecNt9J00g11flJO3rRb/EC/G3ZxBYnYATStXolv0FpLFQugddxD+6CPY/b1Znb+aJYeXnB5hZjPDgeOxZZVOR8Dxz0Dm1aBUIoRgW7GOJZtL+Cm/AS8PJdcPjuP+scmkRZ74n1kSgo36NlbU6Fiva8Eh4IrQAObEhDE1LAiPU5ZQhBC0th1CW7uGuvqvsNmaUKtD0UTN7FQEWWNjo9t3pLbWaXil0Wjc7ZGIiIhOf38lqwNLSYs7Rsyuc4qoR7iPM6g3MwSv5KAeV9k2s5magmNUHXNW2KdGgx1vicRl97ko0WCSJGjWGt2TIA3lrTRWGrB3cN5zmjgdf8gYGH55iLWjtdUtzidX1LaamhMv8vDAMzHxhFAfr6iTklD2YrZod5AF/FdCa2M937/9OqUH9hKdkcW0B5+krkzF9rXF2EwOBk6NZ8hVSZh//oH6l17CVlWF/6RJRP7haVSJ8XxZ/CVvHHwDbbuWkdEjeXLQk84IM6vR6Qq4bQG01Tpjy8Y/444ts9olvjxYw5ItpeTVthLu78mcUUncMSKBMP8TvcwGq40Pa/W8V6Oj3GwlTO3BbdGh3BkTRpLP6T1Pk6kabd1atNo1GI2lrgiyqa4IsrFnjSATQlBfX+9eYa+vrwcgNjbWLdqhoaGd+p4KIVxVtstjpKQZ7AKFWolXShDema6JkbCezUVbjO1U5+e6w3frSopOigZLdW455vRzRoP5d69X2lmEJGhpMJ30gLGj856Hl4qIeH+3RWpEQgDBkb4XxXmvuwghcOj1ToE+3pt2iba9ocH9OoWXF54pKU6hTk3BMzXV2a9OSEBxCfqPgyzglz1Ckji44Vs2fbAMhGDsbXcTmz2ezR8VUlfaSkx6MBNuy8RHX0bdvOcw7dmLV0YGUX/6I74jR/J9xfcs3L+Q0pZS+oX348nBTzIyeiRY2pw+3Ntfc8WWjYUJf4DkCaBQ0Gy08v7OCpZvK6O+zUJGlD9zx6Ywc2CMOxhYCMH25nZW1DTydUMLNiEYFezH3THhXBURhNcpD9OcEWTfUqtd2yGCLFozm8jIq/DwOLN4CSGora0lNzeX3Nxc9Ho94NwvOG7LGtTJMS3J6sBS1Ow2hnK4lkQ8Inzc6+peyUEo1N1/EGhsbaH62FF3S6RDNFhahnstPSYj+4JGg53svOe2SS1vw+py3lOplUTE+7sfMEZeos57xxFCYNdqsRQVn9SjLsFaVISjpcX9OqWfn1uc3UKdloY6JgbFJeY7fj5kAb+M0ddUs/6tBVQfO0pi/0FMuOth8ra3c+TnKrz91Yy5MZ3kRAWN8+fTsnYtqpAQIp56iqAbrmdH/S4W7FvAUd1RUoNSeWLQE0xKmITC3AK7FsOON07Elk14BhJHA1Da2M47W0r5ZG8VJpuDcenhzB2Xwvj0cPdfmZttdj7WNrGippFCo4UgDxU3a0K4KyacDL+Of+WUJDt6/WZqtWtobPweSbLg65uMJmoWGs0sfHzizvjZJUmiqqrK3dNubm5GoVCQlJRETk4OWVlZBHTiyb5zHtfkfvhoKW0Bh0DhqcQrNdgVcBCKR2j3/6ps0Os6jPTpqpxhDcejwZw97H5Ep2dcsGgwIQRtenOHAILTnPdi/d0bjJGJgYRGX5rOe8LhwFZV1XHaw1VRS8YTs+Oq4GA801Ld0x7HRduji886LmVkAb8MkRwO9ny1hm0fv4+HpycT7pqLp29ftn5ajKnNSr/xsQybHoPhw5XoliwFm43Qu+cQ9tBDHDWXMn/ffHZpdxHjF8OjAx/l2pRrUZmanaK9azFYWjvElgkh2FWqZ8mWUr7Pq0OtVDJrUAz3j00hU+MUSSEE+1uNLK/R8Xl9E2ZJMDjQaSY1MzIE35OEQAhBm+Goc/RP+wU2mw4Pj2A0UTPQaGadNYLM4XBQUVFBbm4ux44do62tDaVSSWpqKtnZ2WRmZnbKLEqy2LEUtWAucIq2w+Wb4RHp6xrxC8ErKQhFN5zohBDuaLDj/zRrnb13tbcPsVk5xGU5K+yo1PQLFg1maLKctBTjbIeYDSec90Jj/dwLMVFJl6bznrBasZaXny7UpaUIq9X9Oo/IyI696ZQUvNLS8Ohkq+xyRh4jvMyoLyth3aL51JcWkzZsFEOuvZs939ZTnZ9HZGIA1zzaH+8jm6m64RHstbUETJtG5B+eptzfzP/u/gs/Vf7UMcLM1Azf/8PZLrG1d4gtszkkvnHNbx+qaiHEV80TV6Rx56hEIgOclaLB7uDTuiZW1ug4YjDhp1JysyaUOTFh9D3FTMoZQfa5K4Ks8KQIsusJC5twxggyh8NBaWmpW7SNRiMeHh6kpaWRnZ1NRkbGec2ihBDY64zuRRpLWaurylbhlRbsyn4MwSO469WvEIKm2uoTFXbuEdp0zr6qt58/sdl9GTD1amc0WFLKBYkGM7Za3SJ9fN7aeIrzXlL/cLdNaljcpeW8J5lMzlZHSUmH9oe1oqLjxEdsLJ6pKfiNGYNXqrNX7ZmSgqoHtry/VuQK/BLDbrWy47OP2P3FJ3j7BzBxzkM0N8ZwYEMFai8VI2elkuxfT8Pzz2M6eBCvnGyi/vhHmrJjeOPAG3xV8hV+aj/u7Xsvd2bfia+pGbbOd8WWWTvElrWYbHy4q4Jl28qobTGTEuHH/WOTuX5QHD6uCYsjbUZW1Oj4tK6JdodEH39v7o4J5/qoEPxPMpNyRpCtc0WQbcMdQRZ9PVGRV6NWB5/2WW02G8XFxeTl5ZGfn4/ZbMbT09NtFpWWlnZesyjJbHf2sl2i7WhxCppa44tXpjNd3SsxsMtVtpAkGqsqOizNGFuaAVc0WHZf91hfeFxCry/NmAzW09oghqaOznuRx6O9LjHnPUdbm2vR5aRll+MTH8f1RqVyTXyknNSnTsUzOdkdyydzArmFchlQnZ/H+kXz0ddU0WfCZJIGzWLnlzVOx8CRGoaNDaBt0QJav/oKVUQ4kb/5LbbpY1h8ZAmfFH6CSqHi9qzbnRFmphZnbNmB952xZf1vgXG/h/A0KvVG3tlayurdlbRbHYxKCWPuuGSuyIxEqVRgdEh8Ud/Eihod+1qNeCsVzIwM5p6YcAadZCYlhAN903a0tWuob1iHJJnw9o4nWjPrrBFkVquVwsJC8vLyKCgowGq14u3tTWZmJtnZ2aSmpp7TLEoIga223b39aC1vBUmg8FLhnR7sfPiYEYJHF7f8JIeD+rKSE0szeUcxtzvDEwLCIlwTIs4edkh0TK/2Vs3tNhoq2074Wpe30abr6LznXIhxinV4/KXhvGfX67EUFbkr6uPtD7trIghA4enpbHWkpDj71MfbHwkJKH4h86zLEVnAL2GsZhNbVq1g/7qvCAgLZ8wtD1J22JeywzpCY/wYd30iXj+uRvfOuyAEoffeg+c9t7KiZDXv5b2HzWFjdvpsZ4SZ2QCbX4ZDp8eW7S1vYumWEr47okWpUDBjQAz3j02mb6xzcqOg3czKmkZWa5tosTtI9/ViTkw4N2lCCD7JTMpgyKdWu4Y67RdYrHV4eAQQGXkN0ZrZZ4wgM5vNFBQUkJubS1FREXa7HV9fX7KyssjJySEpKemcZlGSyY65sMk9MSK52gbqaD/niF9GCJ6JASi68CDOYbehLSp0Cvaxo9ScHA2miSYuu597SiQoMuo8V+s8VpOdhsq2Dm2QllOc9041c/olnfecbam6M85QO5qb3a9T+vqeGMc7vj6eloo6Nvaym/joLu22dmoMNc5/2muoNdR2+PXF8S8yVHOaBncKuQd+iVJ2cB8b3n6N1sYGBky5Gv+IK9j8sRaF0sro61NJbNuP7tFnaKuvJ/Dqqwn8zaOsbvmZd769wRlhlnwVjw98nASzEb7762mxZXb/aNYdrWPJqq3sr2gm0NuDhyakcveoJDRB3lgkibV1TSyvaWR7cztqhYJrIoKYExPOqOATftQWSwN1dV9Qq12LwZDrjCALm0C65m+Eh006LYLMaDSSn59Pbm4uJSUlbrOoQYMGkZOTQ0JCwlnNooTkqrJd24/WilaQQOHtgXdGsNPJLyMEVWDnKzibxUxtYQFVec6WSG3BMew25w8CZzTYFc4KO6sP/qFh57laZ+/p6FBZN1S00VRndJs5BYR6E5kYQPaY6F/ceU9IErbq6lMqatfER3u7+3WqoCA809IImDq1w1aih0bzq5n4OBNCCJotzScE2VBDbXst1YZqatud/95qbe3wHrVSTbRfNNH+0YyLHef0FOpl5Ar8F8JkaGPjiqUc3fg9ITFxDJx+N3nbFTTXGUkdHMGQTBOGBS9gPnoU7/79CXv2ab71K+GtQ2/RYGpgfNx4nhz0JJlW6xljywyeYXy0u5J3t5ZS1WQiMcyX+8Ykc+OQOPy8PCg3WVhZo2NVrR6dzU6ityd3xYRxS3QoEZ5OEXE4TDQ0uCLImrYihIPAgP5o3BFkHYXOYDC4x/1KS0sRQhAUFOSe0Y6LizurWZRktDmrbNcyjeSapFDH+rvX1T3jA1GoOicSVpOR6vw890PH06LBcvq67VV7IxrMbnXQWGXokHDeVNvubvn6BXkSmRTYYe3cJ+DitxCEzYa1ouJERX184qOkBGGxuF/nERHRsaJOScUrPQ1VaOivUqglIdFoajxnBW2ymzq8x9fDlxj/GKL9ok/7NdY/ljCfMKdnfi8gt1AuIQp2buWHpW9iamtl4LRZWKyDKNnfRGCED6OnhOL12Zu0rVuHR1QUEb//HVty4PWDb1JlqGJw5GCeGvwUg+2iY2zZiAdh5GNU23xZvq2MVTsraLPYGZYUwv1jU5iaE4UA1uuc1q0/N7WhUsD0sCDmxIYxPiQApUKBEBJNzTvRatdSX/+dK4IsGo1mFtGa2fj5pXb4LC0tLe4V9ooK59xzWFiYexsyOvrMJktCEtiqDSeq7Mo2EKD09cArPcQp2hkhqDopciZDG9XHcp2CnXuE+tJi19KMiqiUNLcPdm9EgzlsEroag/sBY315G/qak5z3AtROsXZNg0QkXnznPclsxlpWdsqySzHWsnKw292vU8fEdOxNpziXXrrrW32pYpNs1LXXuavlU0Va267FJtk6vCfIK4gYv5gO4hzjF0O0fzQxfjEEeQVdtB9msoBfArQ3N/HDO29SuHMbEYnJJA+5jbztNiS7YNCkaBKKv6ZlxTLw8CDs/vs5Oj2dBXmLKGwqJDMkk6cGP8VYhweKTS+eiC0b+SiMeJCDjQqWbCnlm8POWeSr+mqYOy6FgfHB1JitvFer44MaPVqrjRgvNXdEh3F7TCjRXk6BbG8vola7ljp3BJk/kZFXEq2ZTXDw8A4RZHq93i3a1dXVAERGRrpFOzIy8szz3e02LAUn9bLbbaBwVdmudXXPuIBOrWu3Nze5p0POFA3mbIf0JSYjC3UPfCwcDgl99Tmc9/zUbi/r42vnfsFeF88Z0NDuFOjikg6GTLbKyhMTH0olngkJzoo6JeVE6yM5CWUPwpcvJcx28xmr5uNi3WBqQBJSh/dE+ES4xfj4r8dFOsY/Bl/1hduO7SqygP+CCCE4uvEHNq5Ygs1qoe+k62moSkNfYyIhJ4QBgcWY334Vh05H0HXXUXPnFcyvfI8DDQdICEjg8YGPMV34oNz8nxOxZaMfxzHkfr4vMbJ0cym7yvQEeHlw6/B47h6dRHSwDz/r21hR08iGxlYEMCk0kLtjw5gUGoiHUoHVqqOu7itqtWtoazsMKAkLG4cmahYREVNRqU6MczU0NLhFW6vVAhAdHe1uj4SHn57oLiSBtarN3RaxVbmqbD8PvNNd6+rpwag6YeLf2thAdd4RKl0tkSZXNJjay5uYzGzn0kxOXzSp3Y8GkxwSTVpjhwACXZUBh91l5uTj4R7di0hwinVA2MUxc7I3NZ027WEpLsbu+m8BoFCr8UxKOq2i9kxOQnmZT3wYrIYO/WZ3/9kl1HqzvsPrVQoVUb5RHQQ61j/WXUlr/DR4qS4fP3JZwH8hWurr2PD2a5Qf2k90ejbBsddSetCBf4gXwwYKvD54CWt+Pj6DB2N89BYWmL5ha40rwmzAw8wiEPWW/0DlTndsmbHfnXxyuIl3tpRSpjMSG+zDvWOSuGVYPGYlrKrVs7JGR6XZSrjagztiwrgjOpQEHy8cDguNuh/Rateg0210RZDlEK2ZTVTUDLy8nK59Qgjq6urcZlENLjOguLg4t2iHnMHz2NFmdfeyLYVNSEY7KMAzLsAdcKCO9T9nlS2EoLmu1j3OV5l7hNYGZzSYl6+fc8vR5dTX3WgwSRI01xk7BBA0Vra5nffUXqoOo3sRCQEERfZOMMPZEEJgr284Y6qLQ6dzv07h4+Mcyztp2sMzJQXP+HgUv0BMWk8RQtBkaXJXy+42x0kPDNtsbR3e46n0PGP/+XgFHeEbgYfy8vtenA1ZwC8yQpLYv+5rtqxaDgoF6SNmUVUUh90s0XdYIHG7V2D+cT3qmBh47G4WhR1kXfl6gryCmNvnfm5VheC95dUTsWVjf0Nd2k0s26Xlg50VtJhsDIwP5oFxKUzLiWRnm5Hl1Tq+bWzGLmBssD9zYsO5MjwQtUJBS8tearVrqK//Gru9DS/PKKI0M4nWzMbfP9N5ZiGorq52V9pNTU0oFAoSExPJzs4mOzubwFO24YRDYK1sdc9l26qds9NKf7W7j+2VHoLqHNMVJ0eDHU9LNzQ5KyqfgEC3pWpcTj/CExK7HA3mdt5z26S20VDRhu24856n0inWbpvUC+u8547fcrc8TlTUUtsJoVIGBp6Yn3Z7UKeijom+qGk7PcUhOWgwNZxWNZ/8q9lh7vAeP7XfiZ7zcZE+qc0R6h3aaw8ILwdkAb+I6KorWf/WQmryc4nJ7I/CYxK6GiXRyf70NW/H8clSlGo1XvfdwYp+TXxW/iWeKk/mZN/F3aowAra9fiK2bNzvyY24iiXbqvnyUA0OSTC9j4a545JJig7gY61zvb3YZCHEQ8XN0aHcFRNGmq83RmOZy4fkc0xmVwRZ5HRnBFnIKBQKFZIkUVlZ6Z4eaWlpQalUkpycTHZ2NllZWfifYlrvaLW6+th6zIXNCJOryk4IdJlChaCOOXuVLUkOGsrLqD7J+Ol4NJh/SChxOSdmsENj47uWmCMEbTpzhweMDRVtWE3OB3cqtZLwuJNsUhMDCNH4XRDnPWG3Y62oPFFRH5/8KC3tGL8VHn6iN31yqktExGUx8WFz2NC2a90955Mr6BpDDXXtddiFvcN7QrxCTmtrnPxroGfgZfHZLxa9LuAKhSIeWAFoAAlYLISYf673/NoF3GG3s+fLz9j+yQd4eHkTmzWDmhINPv6eDIhpwH/1i0gtLfjMupYvJvmxXPsFAsEtGTcxVxVF2I43obEAwtKRxv2ejZ7jWbylku0lOnw9Vdw8NJ57xyRR7wHLqxv5sqEZiyQYFujHnNgwro0IxkNqpa7+G7S1n9HSuh9QEBoyGo1mliuCzA+Hw0F5ebnbd8RgMKBSqUhNTSUnJ4eMjAx8T7I3FQ4Ja4Wrl52vx1brnAtWBni6R/y804JR+p65yj4eDVaZe5jqY0c7RIMFRUadFFzQl6Cozs8TCyEwNFlObDC6DJ0s7S7nPZWC8Dh/99heZFIAIdF+qHrZec8dv1VcdMLatLgIS1k5nBy/FRPt7E0fH81LS8MrJQVVcHCvnqe3MdlNHR4KnlpJNxgbEJzQEQUKInwjTn846KqoNX6aS+oB4eXAhRDwaCBaCLFPoVAEAHuBWUKI3LO959cs4HWlxaxbNJ+GshKiM4ZgMo7GbFSTmaYk7ueFiMJcvIYNYesNGbxu/AaT3cTM5Gt5RK0hZudSaCqFyD5YR/+OT8yDWbK1gpKGdjSB3twzJolrB8eyodXAiupG8trN+KuU3OQyk8r0VbkiyNbQ2PgTQljx80t39bWdEWR2u72DWZTJZEKtVpOenu42izrZd8TRYnG1RfSYi5oRZgcowTMx0LlIkxmCOtrvjGJrt1rRFhU4WyJ5R6gpyMPumjEOiYkj3tUSic3uS2B455Ny2pstHarq+vJWTG2nOO8lnAjODYvxR9UDP+9TkdrbnfFbp1TU1spKZ+iz8yCo4+NOszb1TE5B5X9pTny0WltP6z+fPG7XZGnq8HoPhQdRflEdJjZOHrPT+GlQqy7NYITLlQveQlEoFJ8DrwkhNpztNb9GAbdbrWz/5AN2f/kZ3v6BBGqupKUhhnCNJ9k1X6Le9AUe8fEcu304L3pvpMnazJT4K3hCHUvKnpWu2LKBNA97incaslm5s5Imo42+sYE8MC6FuKQgPtDq+ayuGZMk0d/fh7tjw7kuIgiH8Qha7dqTIsjC0Lj72jnY7XaKiorcZlEWiwVPT0+370haWhqerukE4ZCwlDl72ZZ8PTat029ZFeiJlyvgwDs9GOUZPDhsZjPVBXnulkht0YlosIiEJGK7EQ123HnPKdROsTa6jKoUCgiN8TtRWfey856jpeW03rSluAh7Te2JF6nVeCYmdBTqtDRn/NZ5DLguJkIIdGbdaWN1te0n+s8Gm6HDe7xV3qeN151cSUf4RKDq4nMImZ5xQQVcoVAkAZuAvkKI1lO+9iDwIEBCQsKQ8vLyHt/vUqHq2FHWL1pAU201kSkjaGseitrLlxyvAkK+WoDK14fam8byfMIhqix1jPz/7Z15cCTlmeZ/X2VWZd0qqUpXSa3W0QfdXB7ABxiGNuAAY2zwrh1hj+3ZsCfCs7EzXs9/s+uY2N2I3Z3wxHo3jNcHYTDjgfGa8QHjMXgAAwZjDDZXA90S3WqppdZ9H6W6M/PbP7JUqlNdfejs/EV0qLoqS+TXap5+6/ne732a38dXtD1c8cYjudiy9zF61V9y79Befv7WBFnT5NbLmvncB/cy5hE8NDHHW7EkHofgnuZ6/l00wkHnvOVrT/1zLoJMozHyYVpa7qGh4SayWYP+/n56e3vp7+8nm83idrvzc0e6u7vzc0f0xfRaWO+pRWTaAIdA6wzmO0bUZm9ZlZ2Kr+QPzYz1HWfqdEk0WG5KX63RYKmVbNEG4/TwcvHkvWZvQZ+1NczpQifvSSkx5uaKuz0GrMfGzGz+OqFpaycRC2ZQu/bs2RbxW7qpM5OYKfefc48n4hOkjXTRewLOQNmmYKH/3ODenactNxwprRn78VlIzK19Tcxaj6/7IoR7zv59KrBhAi6E8AMvAP9TSvnoetfulgo8k0zw4o/+gaNPPYG3LoLT+2HSqVY6G+PsefYbOBcnWbnzev731eMcN0e4suEwX9E6eP/RRyExi+y8kbe7/5yvn2zixVNzuJ0OPnltOzf/UZRfp5P8ZHKemGFy0OfmT6Nh7ok4Sc8/XRJB9v5cBNkdZLNq0bAowzDw+XxFw6IURUHqJumhpXzHiD6Vq7LrtLWAg30hHFpxlZ1YXrLa+XJzRGaGT4OURdFgew5dQfTgIVye9b3NdCJbUFXHmDmzzPLsWgdCXZMnv8HYtDdAZE/ggibvSSnRJyYKKuq14+NmYfyW37/Wllcav7WFHR8ZI1NmaxR60FOJKQxpFL2nwd1Q0X9eFemNmMmxKzENK60qPrsmwolZSMyXPDe3JtglpznzqG749A9h323ndSsbIuBCCCfwOPCUlPL/nO363SDgp4++zq/u/xaxuVnqo9eTiF9DfZ2LAyf+H/4TL5G97nLuvznL865BeoKdfFnbyy1v/wKRWsTo/hAvNH+Br/WGODm1QmNA47Mf2EtDd5CfLSzz+6U4LiH4WFOIz7WG2Ke/weRUYQRZNy0t99DSfDemWc+7775LX18fg4ODmKZJMBjMt/t1dHTgcDjQ51N5Lzs9sIjMmKAItK66/Aak2lRcZcfmZxntO24dnOk9xvzYCACqSyN64CBtl1kVduuBgzhd1e2CTErPi3XFyXsRd/5AzGpwrlZlI/RsSMMgOzJCejUsIDePOjM4WBy/1dBQPtq0pwe1yunRjSaRTRT1PI/Fi9vsZpIzRdc7hINGT2PRpmChzdHqa8Wj2vO0K6KnC0R4DuJzJcJc8lxyAaiij+468IatQ3W+SO5xOPd49bmGtceuC9v/2IhNTAH8AzAvpfyrWt6zkwU8GVvm+YceoPc3z+Gta0E6bkFxtrI/+RrNL/0AsaeFn90R5McN/bT5WvkPWgcfPf40SnqZTM/tPOb/DP/ruJ/ZlQyXtQS4+/17mGhQ+enMIvNZgy6Pi8+3hrkzME1m7uf5CDKns57mprtoabkH6MpP+BseHkZKSX19ff4IezQaRRiQPr2UF209J5hKvZYfvar1hHBoa4HEyzNTjPYdt7pE+o6zOGV5vS6Ph+jB3KGZyy6nZd9+FLWywGbTBrO5MamrobmFk/f89VpBDqPVc+32n7tYm5kMmaGh8lSXoaHi+K3m5ly3Ry4sYFWoKxw+2iiklGsbhKX+c+65pfRS0XtUh2pVylX852ZfM07H1ls3W46UViB3YjYnuqViXFolz0MmVvl7CaVYbMvEOFwu1pu8SbsRAn4j8CLwDlYbIcBXpZS/rPaenSjgUkr6f/8Szz54H8lYDG/99ejGNbS5F+j8zTdxqxlevCPKd7oGCHkb+JLWzid7n8eVjbPSfScPKp/i230e0rrJzQcaueqqJl5Rsry4GEcVcHukjs9EBN2pp5ieWo0gcxGJ3EJryydQlKt5910rAGFkxKqEI5FI/jRkS0sLRr7KXrCq7KwJaq7Kzs0YUSPWKcJ8NFjvsfykvnw0mD9A22WXW5bI4Stp3NtVMRpMz1qT9woDCAon73mDBZP3cpuM3nMY/QpgJhLFHR85nzozMlIcv9XeXjyDuqfbit+qIej4QjGlyVxyruLsjVWRTuiJovd4VE9VcW71tdLobbykDqjkqWhXFFgTpRVyYs5KmKqE6q4uvHmBLnjOHYJtfjDKPshzHqwszPPs97/LqVdfxhNsw5C3EPSF2PfOwzRMHaX3yF6+fuUZRMDHF7Q2Pnvit3j0DLN77+LezMf5x0EvLtXB7Ve14u0J8q+pBNMZnTbNyWdbgtzmfAN99qcsLLwMSOrqrqGl5RM41es5edJKYh8fHwegubk5L9qN9WHSg0v5GSP6bK7KDrtztkgDWncdDpdiRYONDBelpRdFgxUcmqkUDWboJnNjxWNS58fimIWT93JHzVePnftCtXdhGMvLJaNNrc6PbG5IFgCqasVvlR4f7+rCcQGDqs6GbupMJaaq+s8T8YmyCXZBV7BopGjpKcKQFro0NgjXtSvmCirnGuwKrc6qkIsq4kj1Ktnls1qVdhG2gJ8DUkqOP/8Mzz/0ANl0BtV7PYrzj+iee5n2Yz9h+spmvn79DNNhlT9xtfJnp/5A0DAYbvsY/2PpDp6ZDtDgc/HBq1uYbtF4MZ5AAreFA3wiMMW++KPMzT6JaSbxuDtobrkbl/MmBgZi9Pb2Mp2LpGpra1s7wi69VsfIiQXSg0ugm6A6cPfU5UVbjXjOHg2Wm4NdKRrMMEwWJuJrG4zDy8yOrWDq1t8RzadaG4wFY1L99WefvCelxJifr5jqos+sebxC03B1da1ZHoXxWxvQ8ZE20kV+c+mwpKnEVNkEu4gnsu4Goc+5PXu9LwgpIbNS0l1R0mlRKtZV7QoHeErFeB0v2RsGdWcP4roY2AJeI0vTkzz9vW9x5p2juHwdoNxKs4zT8/oDGBGD79yU4K1Oyb9xNvHng2/SaMLx5o/xNzO3cTRWR1ejj+7DEd70S8Z1gyaXyqfCcIRnELM/zkWQBWlq+ihO9UaGh1V6e/uYyw0r6ujo4PDhwxzcdwD3LHnRNuatTg014sm3+GldQQxMpgb61wT7RB/ZlFWR17dGcxuOliUSbGzKr9M0JQuT8aLg3NnRFYzs2uS90mFOwcj6k/fy8VunBopGm2YGKsRv5U4hrnrTWs/Fj99aL+JqbGWMudRc0fWKUGjyNlXcHFz9upMm2FXFNK2Kd72KuOi5OShpRcyjaDX6xrmvO8Cu2I7YAn4WTNPg6JOP8+KPHsI0weG6EZ92gP3Hf0go9S7/dJPgl1dmuN0V5i+GjtFuKvy+4WP858kPMZQNcUVnCLU7yGtOHR3BjXUad7l72R97iFT8mBVB1nAzTucfMzISoq/vFIuLiwgh6Ozs5NChQ+xv6kQdyZI6OU/69BLoEuF0oPWE8jNGpF8w0X8ib4mURoPlLZGCaDBpShanE0UJ5zNnYuiZ4sl7hRuMdY2eqrNMpGHk4rcKwwIGq8ZvWYnj3dYM6n09qM3NF2wjlEZclVbPlSKuXA5XvlOjks3R5G3amRPs9MxZKuKSr8l5KPlkkccVWLMo8lVwQ0l3RcFzLv+usyu2I7aAr8Pc6Bmeuu+bTPS/i+ruRtFuYe/kG3QMP84L1wl++L407/XW8eUzJ9knVZ7x3cXfTH+IBUeIy/aHmWzVGHVBvarw8eACN+uPoi09AZgEAlehuW5mbCxKX98IsVgMh8NBd3c3hw4cotPZjGMoSerkAkbu8Ira5MkfV6fZycTgCUZ7rR7syYF+TENHCAeNnV1Wh8jhK2g7eBhvsA4prcl7hRuMMyMxsqnc5D2no0Csg+tO3pOZTC5+q/hUYub06fL4rcKJebmK+kLit0xpMpOYKRstutpmNxGfqBpxVS1B5WJGXG0YUkImfpaKuESQ08tVvplY667whsuFubTVzRsGdRd8wtiF2AJeAUPXefXnP+Xlnz0COFG0IzToXg72/iODexe5/6Y07WEfXxkb5ArDxaPOu/jawhGy7gZa9tdzMqyS0Rxc6zO4Q3mFg7G/RzEX0LQomnYzU5Od9PUtEI/HUVWVffv2caCtmz2ZMAzGSQ8tgyERLgVtXwj3gXpodzI5cSpfYRdFg/XszwcXtB08jMvjzU/emzmzNiMknchN3lMdRPb4i1LO61u8OEqGOZmpFJnTp8tmUGeGS+K32tpKwgK6LaEuGTFbC1nTmmBXLUFlMjGJbhZPsAtpobK5z4Ve9LacYGeakFqsUBFXan/LvVbVrnBVF+OyKjkMnnqwj7zvCmwBL2FyoJ8nv3svcyNDKK4DeLTr2d//BKZylPuPZJF7PfzHyRGuzWo8LD/Ct+K3oobCyE4/ExEnAZeD2z1n+GDqIZqyb6IoPjTtg8xMd9Pbq5NKWXNH9vfsY19dB9FYEPPUCsZSrspu9loVdtTJVHyI0ROWYM+eGQKwosH2H8xP6Wvdd5B0UhRN3psZjpGK54Y5KYJwm3/Ns94boCFaPHnPWFkp6/ZIDwyQHR1di99SlFz8VsmpxK4uHN7aJ8gl9WTZse7Cr9OJ6fIJdtUirnIV9baYYKdnLAtivXa3wio5MQ8lJyXzuPzlG3ZlwlzwnBaw7YpLFFvAc2QzaX734x/y2uOPIYQX1XMrHTPjNM/8kh/dEOf0FU7+Ym6KG9Ia92c+woOZW/G0RJiNuklFNC53J7iVX/Ge1D+hYaC53sPc/AH6el2kUiaaprG/o4duLUrLrA/zTBxMidCsKps2lRl9jJEhK3x3YcJql8tHg+WGPgUbO5kbT1me9XDx5D3hEDREfXmxLp28py8slHV7pAcHy+O3urrKZlC7OmuL34plYhU3CFdFujTiqnCCXam90eZro9nXjEvZgm6DTHydirj0QMgclBy8WUNYFW/VU3kVuiucG9cCabN1SCnJGCbJjEEya5DIGCQzBnvDXgLu8+umsgUcGOl9hye/fS/Ls5MorisJmd0cGPgZvz58hpfer/LFlVmOJNx8N30nPzJvRWlrYLbdgzukcsTZx43ph+mU/ahKN4tLl/FuX4Bk0oXX42VfcyedsonGcQ0Rsz76qy1eRLuLeaYYmnyH0XcrRIMdvpLGjoNIIsyOJvLte/GCyXv1rb78gZimvQEi7ZZY69Mzxakuq/Fb82viKbxeq9tjdROxx7I9nO3tVeO3pJTMp+ar5g9OrEyURVxpila+ObjZE+xW7YqyijgnxIXCvCrWJT56Hoez+ODH2apkTz0oO3AD9BJEN0ySWUtcC0U2VSi4Ba8Vfk1kDFLZ1et0klmTZEbPvb722Kwgqz/4wns5crCp/IUauKQFPJ1I8MLDD/LOc08iHHVo7j/mwPDrDNW9xBM3O/iEucCtcTf3pe7iMeUWEu0hknt8dPtjfMj4OR8wf4VPeIjFDnGqP0IsFsTv9dET2kNnMkJ4yonDdCDcCqLNxZJznuG5Ywz1HyW+Gg0WrKP90OU0dx/CG+winQoyM2Klna/Mr3meoWZvkQ0SiXphfrq8oh4YwFxZGwPqCAbL+qe1nh7Ulpbywzm5iKtK1fP4yjiT8cmyiCu/01+W3F0acXXR/WcjWy686w0SSsxVtyucvhLhrVARF4q1FrTtii3ANCVp3cyJoyWWqxVsIlsssqns2vPJTIHQVhVfnVTWJGNU6cBZB0114HUpeF0qbqcDj0vB61RxuxQ8TkfueQWvS8HjVPAUfPW6FNxOhWs66mkMnN8m8SUr4INvvsqT3/6/JGMLKNo1tC07ca78gp8ciXODf5nblj08kP44T2hHWOqoQ2lzc4PrDY4Yj7GPYZLxgwyebmZhvomgJ0i3p42OpRCNcR8CAREnK55lRpdP0D/wComY9RHbX99A68HLCTbuQ3G1E1/0MnMmVjx5r9GTi/UK0tjupY4l5OhgsU89eBqZWnuPEokUtOWtdX4okUheQDNGJh9xVWptVIu4anA3lAfErh7x9lsRVxdMJrFORVzhuVQ1uwKr4l33mHTJa057wNOFIqUka8giobREcU1ki0SzVFhrqHCT2Sr/AK+DUxFF4pl/nBdRFXdOgD0uFU/udbdLwVsitvnXCr6HW1U2JHLvXLjkBDyxvMSvvncfp159EeEIE3BcQ8f4Mzx+7SDte1a4bdHHw+m7eTx4M4nOOlqa49wif8FNvICSjHDmTJTZmT0EXWG6HC10LNYRMQMIl4NkIMlEcoB3h14hFp8FINjYTLj9AO5AJ6bZyuKMk6XptY/ngbDbsj+iXhq0FQLxMTizOjFv4OzxW6uteaEQiWxi3YDYmWTliKtK+YOrj895gp2UObuitCKuMkgoMQvZROXv5VDLhbfMvigQZE+DbVdUwDBlXghTZUKpk8yYxYJbIrKrFe7qa+Xfw8Co5A2sgxBY4rieQBZVrmsC63GWiOzqNQUC7HEqOC9yRN525JIRcCklfb99gWfu/y7ZdBLVdS1dMzMcbX8B8/IVbon5eSR9D09E/hij0891oTe5RT7Fvswk46MdTE934hdROjMR9qbCNEg/WW+W6ewI/eOvMbMyjEQSbIwSaOxBcbaTSjSyPKcWTd5rbPNS70tTp88QWBiAoX7SA6fIjoyuG7/l6u4m3R5hUi5VPaSymF4sWrPqUGnxtlT0n1v9rbR4a4i4MvSzd1eUDhMqafPL4/TWLsbesDWac5fbFVJa1kDhR/5igdSLNrwqiWd1L9b6mtHPzxrw5ETS7apQxTrXF1l3gU1Q6X2a6th+rZ07kEtCwGPzszz+jXsZP/EmQmmmKd1BTHma8WsnuSHj59HMv+XJ1psIdma5zf00H9RfJjlZz/RUN550J53JRjrNRgION3NykqGZtxhfGSAtk/gbongCnRhGK4mVRsCqWL0BlXA9hJQlgiujeCd6EQPH0Scqx2+5errJ7GlivsXHeBjGMzNlbXbxbLxoXYURV5UOqkQ8kfINwmzyLMekSzb5UovV/2Ar2RXVNva8YXBtg3a/cyRrmMW+akU7QK/oxZZ6tRXFN2twrv+rKQ6Rrz5LbQFviai6c56sx+Uor2JLRLawkt1qa8CmNna1gEspee2JJ/jtDx/ENE3c6tXULx+j79q3ucoZ5BfZT/Fcx/Vc0X6SDzuepmV2gdmpLpwLl9GZbWav2YiQKc4s9jERH2AxO427LopDbSeTbkY4ogiHG02DBm+Kuuw0/rlTeAZfR50aYvV/AeF24+ruwtwbJd7WwFyzh9EInPYlGUtN5kU6YxaPwQy4AlUTvFv9rdS7QohM7NyGCZX8I5BnB9oV5qo1UEMVmsqUV7WFnQLVRFa/AGug3HMtqE7LKldHzg5QK1oLhWJ9KVgDNrWxawV8fnyMx/72ayzOnMahtNGU0Djd9RzRiJun+Qyvd17Brc3Pc13sbbKT9SjTV7I3s4eoHmQpPsJEYpCp9AhoDRiyFeFow6FG0VSFkGOJQGwY3/hx/FPvoqUXLLH2+9A7WohF65hp1hgJw8m6JCedc0ympssirsLucHHuoLeZqOon6nATlQ78+V7kah0Xc9Wjmlbtikon8Sr1Il9ku2LVGjjbR/6yzoGziGyqwGpIn4c14FIdZVVoqchW8mXL7YCc0JZUtrY1YLOZ7DoBN02DX3//YY4+8xigEGA/K/6XcHZleNb1eeZ66rnN8xytEzGcE1fTnugmkDRYSJxhMnmGRVPBobTjUNtwqhFC2Tl8s/0EFgYJxoZxp+bQ63wsR4NMNzkZrjc5URenN7DMgp+8CDqEgyZPI1FPhKgrRKviJSqcRE1Ba1anNZPEnVwsrpCTC9UX5q4rmVdRaapb4ezj9e2KbK7ntbAyLW3BqmwHWJte1ubX+t0F51i85q0Bd6l4lmxOrWcBFL9HXRPj3DWKbQ3Y7CJ2lYCPHj/BY3/3t2TSc6jKHtwssLJ/iN80fA5P1wofWHmH8GgnjfMHcK3EmE2MMp3NYChNqI4WgokUdbERArFhgrEzGFqMqSaV0w06g6EMoxHBWBhWvAKnUGh1BmhVPLThpNWEaCZDazpJNLlEU2wOZzW7QigltkRxRWx6wmS0EClnPXG1noQSJGk6iivZ9arYog6DckshlTXIGuf+83Xn+lpL/dKiarWKF1vJRljtnbU8WgWnIuzq1cbmHNioUOM7gHsBBXhASvm19a6/UAHXMxke+ep/ZWrkOAiNgGxkqfMYf+j8GO2NM1w7ZhIc60Isx5hNJ4kZHgIZhfqVJQIrI+icYdo/zVhEMhoWjEYE82EHYU2l1ZBEM2laU3Gi2QxRXSeq64QNk1Un0lTcZN0NZLR60s56ks564mqIFSVETAmyJOpYIMg8QeZlgDndTUInZwfoZYcNUtnzsAYUx9pBgpLDA2VCWtCCdTaRXa1kNdVhb2zZ2Gwzqgn4ee9OCSEU4NvAh4FR4FUhxL9IKXvP/zar8/Nv38vgi7/HlMu4RBt6eIzfXRXhPY7r+XS/gf5mhJWVOIn4MIoxjamNshSaZKjJIFtv4gzoNKMT1Q3eq+t8XNep1zXkVJBl4WWBAHMywKwZ4JgZ4FnDz6wZYF4GmCfInAyQxA1Vim3rz4ScYKp4XDpeZyp/UqvRr1lVbRUPtlKPq7fguUup59XGxqY2LqS94H3AKSnlIIAQ4hHgbuCiC/g3P/9FspkZhPCieRoYuDbANePXcdtvdeL6JJOe1zCDo8ioSdzrxG16UbN+WjP7Cco65hNB5uMB+pQ63lBDJJ31pF0hnJq7qDtgtaL1OBVaXApdBZWr2+nA41QrdhusVr/2xpaNjc1mciEC3gaMFPx+FHh/6UVCiC8BXwIrLux8MF0Sp9FIostLMJHkUDaGcUWEwAc6Cfhuw+GLoPjq8WjO4ip2mx2HtbGxsbmYXIiAV1LDMkNdSvk94HtgeeDn8x/6q+///fm8zcbGxmZXcyGG6iiwp+D37cD4hd2OjY2NjU2tXIiAvwrsF0J0CSFcwKeBf7k4t2VjY2NjczbO20KRUupCiL8EnsJqI3xQSnn8ot2ZjY2Njc26XNCQCynlL4FfXqR7sbGxsbE5B+ymYhsbG5sdii3gNjY2NjsUW8BtbGxsdii2gNvY2NjsUDZ1GqEQYgYYPs+3R4DZi3g7Ow17/fb67fVfuuyVUjaWPrmpAn4hCCFeqzSN61LBXr+9fnv9l+76q2FbKDY2NjY7FFvAbWxsbHYoO0nAv7fVN7DF2Ou/tLHXb1PGjvHAbWxsbGyK2UkVuI2NjY1NAbaA29jY2OxQtp2ACyHuEEKcEEKcEkL8pwqvCyHEN3Ovvy2EuGYr7nOjqGH9n82t+20hxO+EEFdvxX1uFGdbf8F17xVCGEKIT27m/W00taxfCHFECHFUCHFcCPHCZt/jRlLD3/86IcQvhBBv5db/ha24z22DlHLb/MIaSzsAdAMu4C3gcMk1dwL/ipUI9AHg91t935u8/huA+tzjj1xq6y+47jmsSZif3Or73uSffwgrd7Yj9/umrb7vTV7/V4G/yz1uBOYB11bf+1b92m4VeD4oWUqZAVaDkgu5G3hIWrwChIQQrZt9oxvEWdcvpfydlHIh99tXsJKQdgu1/PwBvgz8DJjezJvbBGpZ/58Aj0opzwBIKXfTn0Et65dAQFjp4X4sAdc39za3D9tNwCsFJbedxzU7lXNd259hfRrZLZx1/UKINuATwH2beF+bRS0//wNAvRDieSHE60KIP920u9t4aln/t4BDWPGN7wBfkVKam3N7248LCnTYAGoJSq4pTHmHUvPahBAfwhLwGzf0jjaXWtb/DeCvpZSGVYTtKmpZvwpcC9wKeICXhRCvSClPbvTNbQK1rP924ChwC9AD/EoI8aKUcnmD721bst0EvJag5N0cplzT2oQQVwEPAB+RUs5t0r1tBrWs/zrgkZx4R4A7hRC6lPKfN+UON5Za//7PSinjQFwI8RvgamA3CHgt6/8C8DVpmeCnhBCngcuAP2zOLW4zttqEL9mgUIFBoIu1TYzLS675KMWbmH/Y6vve5PV3AKeAG7b6frdi/SXX/4DdtYlZy8//EPBs7lovcAy4YqvvfRPX/13gv+UeNwNjQGSr732rfm2rClxWCUoWQvz73Ov3YXUe3IklYgmsf5F3BTWu/78AYeA7uSpUl7tkSluN69+11LJ+KWWfEOJJ4G3ABB6QUh7buru+eNT48//vwA+EEO9gFXF/LaW8ZMfM2kfpbWxsbHYo260LxcbGxsamRmwBt7Gxsdmh2AJuY2Njs0OxBdzGxsZmh2ILuI2Njc0OxRZwGxsbmx2KLeA2NjY2O5T/D8bSAN62cVQWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    x, x, \n",
    "    x, 2*x, \n",
    "    x, 3*x,\n",
    "    x, 4*x, \n",
    "    x, 5*x, \n",
    "    x, 6*x, \n",
    "    x, 7*x, \n",
    "    x, 8*x, \n",
    "    x, 9*x, \n",
    "    x, 10*x, \n",
    "    x, 11*x, \n",
    "    x, 12*x, \n",
    "    x, 13*x, \n",
    "    x, 14*x, \n",
    "    x, 15*x, \n",
    "    x, 16*x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00008-882dbdc2-1778-439b-8817-95affa921c45",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Width"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00011-cb1dfb4d-74ff-4d19-bba1-f95ca6ca33f1",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "The line width can be specified with the keyword `linewidth` or `lw` and has default value of 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cell_id": "00012-27007769-375d-4899-8df0-8475f2655100",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 177,
    "execution_start": 1625488962242,
    "source_hash": "8b73273f",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, lw = '1.5')\n",
    "plt.plot(x, e2x, linewidth = '2.8')\n",
    "plt.plot(x, e3x, lw = '10')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-73b87486-aa71-4c6b-91c9-144dc6bddddd",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Line style"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00014-f26f1974-d6c1-40c8-9ba9-6e7f924ac6d1",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "The line's style can be specified with the keyword `linestyle` or `ls` and is defaulted to `'solid'`. The other options are \n",
    "\n",
    "<center>\n",
    "\n",
    "| Line | Name | Shortcut | \n",
    "| :-: | :-: | :-: | \n",
    "| ![solid](images/solid.png) | `'solid'` | `'-'` | \n",
    "| ![dashed](images/dashed.png) | `'dashed'` | `'--'` | \n",
    "| ![dotted](images/dotted.png) | `'dotted'` | `':'` | \n",
    "| ![dashdot](images/dashdot.png) | `'dashdot'` | `'-.'` | \n",
    "|  | `'None'` | `''` | \n",
    "\n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "cell_id": "00004-1fa26b7d-b6e0-4d76-907f-ca4fb3a828ba",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 138,
    "execution_start": 1625488962465,
    "source_hash": "bcad2aa9",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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50MsEeQeZXZY4Q41b4FrrbOAlYB+QAxRqreefeZ5SaoJSKl0plZ6fn1/zSoUQDeK4/TgPL3mYaRumcWXKlbx10VsS3k6qNl0oTYDLgBZALBCglLrhzPO01lO11mla67TISPn1Swhn99iyx/hxz4/c2/Venur9FF4WL7NLEmdRmy6Ui4DdWut8AKXUV0Af4OO6KEwIYY6/dfgbw5oPY3jicLNLEedRm1Eo+4BeSil/ZWwzPRTYUjdlCSEa0prcNbyx7g0AWoe1lvB2EbXpA18JfAmsBTZUvtbUOqpLCNGAFu9fzPw98ym2FptdirgASmvdYBdLS0vT6enpDXY9IcTZaa05VHaISP9I7A47pbZSebPSSSml1mit0848LjMxhWiEKuwVPPHbE1z33XUcLT+Kh8VDwtsFSYAL0cgUHi/k9oW3M3fnXK5qdRWhPqFmlyRqSFYjFKIRySrO4s5Fd7K/eD/P93ueMS3HmF2SqAUJcCEaiT/y/+Cun+/C5rAxddhUukd3N7skUUvShSJEI7Bg7wJu+ekW/D39+fiSjyW83YS0wIVwc+9kvMM769+hY2RHXh/yOmG+YWaXJOqItMCFcHMOHIxpOYZpF0+T8HYz0gIXwg0tyVqCr4cvPWJ6cGenOzEmSwt3IwEuhJuxOWy8uuZVovyj6BHTQ8LbjUmAC+EmDpQcINQnFH8vf94a+pZ0lzgDayms/RDCkqDVxXX+8tIHLoQbWLh3IVd9exWvrHkFgNjAWHw9ZYdD05QXwbJX4bWO8OPDsO37ermMtMCFcGHH7cd5Of1lPt36KanhqYxPHW92SQLg8A5Y+DS0HAoDHoDmferlMhLgQriovUV7eXDxg2w5soUb293IfV3vw8tDNl8wRUkeLH8TKsrgkv+DuK7w93SISKnXy0qAC+GC5u2axzPLn8HT4snrg19ncMJgs0tqnAqz4LfXYe0HYLdCh2tAa1Cq3sMbJMCFcClltjJeXPUis7fPpnNkZyYPmExMYIzZZTVOf8yCr+8ANHS6DvrdD+EtG7SEWgW4UioUmAa0BzRwi9Z6eR3UJYT4E9M2TGP29tnc1uE27ux8p+xX2dDythgt7KbtIKEXdPsr9L0bQhNMKadWGzoopT4AlmqtpymlvAF/rXXB2c6XDR2EuHBaa4qsRYT4hFBaUcrGQxvpEdPD7LIalwPrYMlLsPU7aH0JXP9pg17+bBs61LgFrpQKBgYAfwXQWlsBa01fTwjx555f+TyrD67m09Gf4u/lL+HdkHYsgqWvwN5l4BsCAx+GnrebXVWV2nShJAH5wPtKqU7AGuAerfWxU09SSk0AJgAkJJjza4YQrsahHdi1HS+LF4OaDSI2MBZvi7fZZTUO5YXg5Q8eXpCTAQX7YNizRneJb7DZ1Z2mxl0oSqk0YAXQV2u9Uin1GlCktX7ibN8jXShCnN+ugl08vfxpukd3564ud5ldTuNxeCesmgrrPoYxr0GHq4xhgRYv8DB3vEedd6EAWUBW5e70YOxQ/49avJ4QjZrVbmX6hum8t+E9/L38ubrV1WaX5P60ht1LYMU7kPkjWDyh/ViIams87+Vnbn3nUeMA11ofVErtV0q11lpvA4YCm+uuNCEaj4y8DJ76/Sl2Fe7ikhaX8FD3hwj3Cze7LPd1Yqw2wLwHofQQDHgQut8KQdHm1nYBavt7wV3AJ5UjUHYBN9e+JCEajxJrCVPWTuGLbV8QHRDN20Pfpn98f7PLcl9FOZA+HTZ+Bf+zBHwC4bpPIKQZeLne2jG1CnCtdQbwX/0yQojz+2XfL/xz5T/JL81nXNtx3NXlLvy9/M0uyz1lr4EV78Kmr8BhN4YClhcYAd4AMybri8zEFMIkc3bMIcQnhFcHvUrHyI5ml+O+8rfBe0PAOwi6/w16TjCWd3UDEuBCNBCtNXN2zCGtaRoJwQk82/dZ/D39ZQGquqQ1ZKXD2png6QujXobI1jB2GrQa7nTDAGtL1gMXooEcKT/CS6tfYlbmLABCfEIkvOtK6RFjJMk7fWD6RbBxjjGi5ISOV7tdeIO0wIWoVyXWEubunMv1ba4n3C+cj0d9TGJwotlluYcTc1iUgqUvG8u5xnYxxnC3vxJ8gsytrwFIgAtRDyocFXyZ+SXvrn+XI+VHaBvWlq5Nu5IU4h59r6YqyYf1/zG2KrvkJWg5GHrdAR2vhZjG9V6CBLgQdUhrzaJ9i5iydgp7i/bSPbo7b3d7m9SIVLNLc20OB+z6xVh3e+s8cFRAs17GdHeAkHjjo5GRABeijmTkZfBy+stk5GeQFJLEm0PeZED8ANkVvjbKjoJfE9AO+PpOY9OEHhOg600Q1cbs6kwnAS5ELe0t2stra19jwd4FRPhF8FTvp7g8+XI8LfLPq0aKc2HjbPjjcyjJhfs2GWuR3PgVhCeDp4/ZFToN+QkTopZW5qxkWfYy7ux0J+NTx8tknJrauxwWvwi7Fxst7pjO0OcusFeAxQOaSjfUmSTAhbhANoeNmZtmEukXyWXJlzE2ZSxDEoYQ4RdhdmmuxV5hrLcd2RrCWkDFMTiyC/pPMvaWjGxldoVOTwJciAvkoTxYmrWUFiEtuCz5MjwtnhLe1aU17F8FG74w1iMpO2IsIjXkcUgaAvesP7nIlDgvCXAhquH37N95Z/07vDLoFSL9I3l32Lv4eTr3UqNOx+GAd/tC3mZjlmTrS6DjNdByqPG8ReYVXigJcCHOQmvN0uylTNswjXV564gLjCPnWA6R/pES3uejtRHUW76F/K1w9UwjoDteA4FNoc1ot5wZ2dAkwIU4g81hY/6e+UzfOJ3Mo5nEBMTwaM9HuTLlSrw9ZFuzc8rPNCbZbP4GjuwEFCT0Busx8A6AfveZXaFbkQAXopLVbmXuzrm8v/F99hfvJykkief6PcfIFiPxssiaJX/KYYf9KyE8BQIjITsdfnsdWgyA3hONlnZQU7OrdFu1DnCllAeQDmRrrUfXviQhzPHCqhf4MvNL2oe3Z9KgSQxOGIxFSb/sf7FXwJ6lRvfIlu/gWB6M+Jcxnb3dZdBqBPiHmV1lo1AXLfB7gC2AdGgJl1JsLeaDTR8wInEEyU2SubHtjQxPHE7P6J4ye/JsrMdgSgcoPWzs3J4yDNpeaizVCkY3iXeAuTU2IrUKcKVUPDAKeA64v04qEqKe2R12PCwe2B12Ptr8EaE+oSQ3SSYpNImkUFlsqkpxLmyfb3wAXPuREc497zA2/U0e6vSb/rq72rbApwAPAe6/bqNwebsLdzNj4wx2F+7mo5EfEeobyk9X/kSob6jZpTmXdZ/AqqmQk2E8DoqFNqNObgQ88EFTyxMn1TjAlVKjgTyt9Rql1KBznDcBmACQkJBQ08sJUSNaazLyM/ho80cs3LsQHw8fxqaMxeqw4uPhI+FdVgA7f4btC2Dki8bQvtJDxnojQ54wukaatpfJNU5K6ROLol/oNyr1AnAjYAN8MfrAv9Ja33C270lLS9Pp6ek1up4QF6LYWsx3u77ji21fsKNgB0FeQVzX5jrGtR1HuF+42eWZqyQP1n8KmfNh33LQdvANhRu+gvhuJ1vawmkopdZorf9rA/kat8C11o8Aj1S++CDggXOFtxANoaC8gClrpzBv9zzKbGW0C2/HM32eYUTiiMa7yJT1GOz5zRjmF9vFeANywZNGy7rvPUYrOy7NWPEPJLxdiIwDFy6vtKKU/cX7aR3WmgCvAFbkrGBki5Fc0+qaxrmRwomNfXf9anzsX2lsgNDlBrjsLYhsA/dvgeBYsysVtVTjLpSakC4UUR/uWnQX245u44exP+Bh8cDmsDWutbi1hvxtULjfGNYH8FpnOLrH2GIsaRC0GAjN+4KXr4mFipqq8y4UIcxgtVtZuHchs7fP5oX+LxDlH8VtHW/D5rBVTbppFOFdlGNsMbZrsdHKLjkI/uHwwA5jzZGr34eQBAho5P39bq4R/KQLd7C/eD+zMmfx9favOXr8KM2CmnGg5ABR/lF0iuxkdnn1r6wA9iwz+qs9vIwd2Je/Cf4RkDTQaGEnDTy5ol9sF1PLFQ1DAlw4rYLyAubvnc8Pu38gPTcdD+XBoGaDuKbVNfSK7eXe09zLC43W9d7fYd/vcHCDsUvNLT9BQi/ofht0uh6i2skyrI2YBLhwOlprJi2exC/7fsGmbSQGJzKx80SuSL6CpgFuuDCS1lCwzxjS17Q9RLc3AvuLG8HTD+LTjE0PWgyE2K7G94S1MLdm4RQkwIVTWJO7ht+yf+PurnejlCLSL5Ib293IyBYjaRPWxv3WJrEdh3UfG6G993coyjaOD3jQCPC4NLh1gbEvpKcsYSv+nAS4MIVDO1iTu4bU8FT8vfzZkL+BWZmzuKndTYT6hvJIz0fMLrHu2KxGi3rf78ZaImm3gMULFj1jtLCb9zZGiCT0NrpEwBgt0qyHuXULpyfDCEWD0Vqz5cgW5u2axw97fiCvNI/n+z3PmJZjKLOV4ak88fJwo3W3l02BbfPgQAbYjxvHUi6GcbOMr0vyICBSJs6I85JhhMIUWmu2F2xn0d5FzNs9jz1Fe/C0eNIvrh8PpD3AwPiBAK67RdnxYshea2xkkLXG6Mu+fakRyid2pOnxN6MfO6E3BEWf/N7AKNPKFu5BAlzUC601k1dP5pf9v5Bdko1CkRadxvjU8QxrPowQnxCzS7xwDrsxYSYixRjKt/QVWPS/QOVvsWEtIb472MqNZVYvfcPUcoX7kwAXdWbx/sVsO7qNCR0noJRie8F2UkJTuLXDrQyMH0iUv4u1OI8dht2/Qs56OLAOsteBtRj+9gvEdTX6qAc+bLSu47rJLjSiwUmAixrRWrO7cDdLs5fyl7Z/wcviRXpuOvP3zOfm9jfjZfHivWHvucboEYcdDm03gjonA9pdDgk9IXcjfHkLeHgbby52utYYHdIk0fi+xH7GhxAmkQAX1VbhqGBd7jp+zfqVxfsXs694HwCdozrTKbITd3S6g/u63Vc1wcYpw9teYazO5xcKJfnw+ThjhEhFqfG8px9EtjYCPL47/M8SiGwrQ/nEf7HaHOQWlRMV7IOPpweZucV8t/4At/RrQai/N9//kcOz323mm7v6EhVUP2vQSICLczp47CArc1by24HfWJa9jGJrMV4WL3rE9OCmdjcxsNlAogOMN+accrnWvcuNlnTuRqOFnbvZWJVv9CtGl4eXH3T7K8R0Mj7CU04uq+rtbxwTjYbN7kADXh4WDpcc55dt+fRLjiA6xJeN2YU89/0Wnrq0HW2ig1mcmc/fPkznm7/3pWN8KLsPHePNX3Ywon0Mof7eNA32oX9KRNVbJPVBAlyc5kj5Ecpt5cQGxrKvaB+j5owCIMw3jKEJQxkUP4jesb2dK6ztFUYXSN5myN1khPLAh4zn5kwwRob4hhhh3HMCtBxiPGfxgJvmmle3aFDlFXZW7DpMy8hAmoX5k1dcznPfb+EvPRLomRTOlpwiLnl9Ke+M68aI9tEcKCjngVnr+feN3YgOicbTQ2FzODhe4QCgQ1wIk6/sSGyoMYJqSJsoMv85Ek8P4zfQtMQw0hLr930RCfBGrsRaQs6xHFKapKC15oq5V9Avrh/P9XuOZkHNeKznY3SJ6kJKkxTz1x7RGooOGIHcvLdx7Os74Y8vjPWuASyekDT45Pdc/YExXC84TsZbuxmtNel7jxIR6EOLiACsNgf//H4zA1tFMrRtU4rKKxgw+RfuHpLCLf1acOy4jb++v5qnx7Tjr31bYFGKdfsKGJ5q/AYZG+LH3UNSSIoMAKBVdCCLHxxEdIjR/dEmOphZt/epun50iC/XdG9W9djLo+H/fdRmS7VmwIdANOAApmqtXzvX98hEHvMdtx8nIy+DlTkrWXlwJZsObSIuMI7vx34PwIK9C4gPjKdteFvzijx1S68dC2HrPMjfarSuywvA0xcePWC0oFe9B4VZ0DTV+AhPkf5qF/ZHVgHenhbaRAcD8Mr8bSRFBnJ5lzgAhr78KxenRvPwiDZorWn75I/c1DuRRy9pi9aaHs8v4m/9WzBhQEscDs1T32xiRPto+iZH4HBo1u0/SouIQMICXOtnpD4m8tiASVrrtUqpIGCNUmqB1npzLV5T1LEyWxmbDm1iXd46VuasZF3eOqwOKx7Kg/YR7bml/S30iumF1hqlFMOaD2vYAkvyjN1jDm2D/MyTn+/JgIAIY3LMxi+NXWRSrzBC+sR0czAmyQincuJnCWBjdiHHbXa6NTe6Et5dvBNPi+K2/kkAXDd1OVFBvrx+vbH87b2fZdA2Npi3/mIs2jV/cy49W1RUBfiQNlG0jTHCXSnFzJt7EFfZhaGUYvVjF1XVYbEonr28/WmPT9ThLmqzJ2YOkFP5dbFSagsQB0iAm+hI+RFWHFjB0OZD8fHw4Z317/D+xvcBaN2kNde2uZZeMb3oGtWVQO/AhinKWmrMSszfBocyjc+DHzVGe2yfD3MnGucFxUBEK+h8PThsxrH+9xv92dL9YQqHQ1NitRHsayxxkLG/gNyi8qpuhxnLdpN1tIwnxxj/qd75yRoOFJTz9cS+APzrh62UWm18dafxOH3PUXw8T3Y1DGwVRYjfyeUTXrqmU9W1AH68d8Bp9Tw2qt1pj3slNe4NK+qkD1wplQh0AVbWxeuJ6jluP87mw5tZn7ee/vH9aRnakoy8DB5e+jAfBn5Il6guXJp0KV2jutIpshNNfJvUXzG248YWXod3GmHdYqCxndeeZTBz1CknKmMcdUmeEeApw+G2RcbsRt8/mZ3pTmujOIHC0gpyisqquijS9xxh7b6jTBjQEoCPVuxl4eZcPrjFWEjrsa83smBzLumPGy3b/6zcy+LM/KoAzy4oY2d+SdXrD2nTlOLyiqrHT4xux6ldw9PGn94LcMeglqc97ppQjz+jbqjWAa6UCgRmA/dqrYv+5PkJwASAhISE2l6uUTt47CAZeRmsz1/P+vz1bDmyBVtlS9XP04+WoS3pEd2DL0Z/QUqTFACSmyST3CS5bgqwVxhvIB7eCcExEN0BCrPh/RFGP7R2nDx3xL+MAI9oDYMfg/CWxtfhyafvyxgYaXyIaiuvsOPlYcHDosgpLGP9/kIGtY7E18uDlbsO83VGNk+Mboe/tydfrN7PlIWZLJo0CD9vDz5cvoeXF2SS+c+ReHtaWLbjEFMWbueWvi3w9LCgAIfWVd0gozrE0DYmqOra9w9rzd1DU6oePzH69BbxVd3iT3vcOjoIUX9qtRqhUsoL+A74SWv9yvnOlzcxq0drjdVhxcfDhxJrCY8ue5RNhzeRV5oHgK+HL+3C21VNoOkY2ZEIv4i6uXh5odGStnga/c0OO/znGjiyC47uBW03zut5O4x80Vgq9es7jIAOa1n5OUmmlVfTseM2MnOLaRkVSLCvF/sOlzI3I5ur0uKJCfEjfc8RJv+0jRev7EiLiADmZmRzz2cZLJo0kJaRgcxek8WkWetZ/OAgmocHMHtNFv/6cSvf/r0f0SG+LMnM55v1B3hyTDuCfb3YnlvM9rwSLmrbFG9PC2VWO0qBr5eH2X8U4hzq/E1MZbxLMR3YUp3wFn/OoR3sL95PwfGCqr0dx34zlvYR7Xm277MEeAWQV5pHt6bd6BTZic6RnWkV1govSw27FmxWY/dyW7kR0ADf3G1Mcjm6xxjlAdBmNFz3iTHSQzuM1nbqFSdDOqKVcZ6nN1w1vVZ/Bq6swu5g96FjRAT6EBbgTWFZBV+vy6ZvcjjJUUFkHS3l2e82M2FAEt2ah7Exu5Br/72cN8d1ZXDrKDbnFHH1u8v56NYe9E+JJKuglJcXZJKWGEZMiB8eFoXCmGACkBobwkMjWlf1Ew9uE8X3d/erGup2Zbd4rjylFTygVSQDWp38DSelaRApTU+2iv28JbhdWW26UPoCNwIblFIZlcce1VrPq3VVbqrCUcGugl1sPryZrUe2svXIVrYd3caximMkhSQx93JjUsnlyZdXzW5USvHZ6M8u4CLlRndGeSHEdzOO/foi7FlqtKCLKrs6YrvChF+M58sLjBEf8WkQ2tzoo45sc/I1b5xT+5t3UlprMnNLCPbzJCbED7tD85+Ve2kfF0KXhCaUV9iZNGs9l3aKZXhqNAWlVi56ZTH3DWvFuJ7NOXLMysWvLuG5K9ozrmdzSo7beOqbTUy+siPJUUZQ7jlUSlG50dUVFeTDtd0TiKkM3FZNg3j/r91JjTX6/3skhlV1bwB0SWjC5//Tu6re5KhAkqNOdomFBXi73JA4UXdkQ4d64NAO8krzqkJ45saZzNs9jx0FO6ionHDi5+lH6yataRPWhnbh7Wgb3pY2YW3O9bLG+OjSI1C4z3gTsNVw4/iyKbB5rtGyPpZvHAuIgge3G19/ew/kbTGC+cRHeAo0617Xt94gtNZY7Q58PI3W44asQrw9LVX9rR8t30N0iB/D2hn7Z973eQadm4Uyvk8iAH1eWMSYTrE8cokx1r3VYz9wS78W/GOkMba45aPzuHNQMg8Mb43doRn26mJu65fEX3omYLU5eObbTYzqEEOf5AisNgfzNx+kY1woCeH+2B2awrIKgn09q2bkCVFbsqFDPXBoB9kl2ewq2MWOgh1c1+Y6ArwCeDvjbaZtmMbqcavx8vCizFZGiE8IN7S9oSqoE4IS8LCc8uurw2EsrlR8wJhtWHQAutxodFGseg9WTTVa1icWXQJ4PA88fYx+ab9Qo5sjpBmENjM+nzDmnPOrGtyRY1bKKuxV43dX7DpMeYWdQa2N5WY/+H0PDq25ua+xce/DX/6Bn7cHT19qdPmMfG0pCWH+TL3J+Hm+9/N1tIkO5q1xxtjhact20yk+tCrADx+znjYy4oqucXSIOzni5c2/dKFFhDH7TinFqscuIsjX+KfhYVH8PGlQ1bnenhaeu6LDaY9Hd4yteuxhUdIiFg1GArwabA4bB0oOsLNgJzsLdxqfC3ayu3A35fbyqvN6xfQiNSKVwQmDiQ6Ixq7teOHFHR1ug5LcymDOhoM/GJ/73A1BTSF9BvzwMNitp184eajRWvYJNro0Ui6GkHgjnEPijTcaAfpPMj7qSXmFnZLjNiICfQDYkVdCdkEZAyv7Vn/Zmsf2vOKqoWjTl+1mS04RL11t9Ok/OmcDW3OKqsYCPzz7D7KOlvHDPf0B+PfinRwqsVYF+JLMfOynBHigr+dpY4fH90msCliAyVd1IviUxz/eM+C08z+85fS9JR8cfvpvOhenRp/2+MR9CuHsJMAr2Rw27NqOj4cPOSU5fLj5Q65MuZLkJsks2LuAh5Y8VHVudEA0LUNa0j26Oy1DW9LSJ4Kko1kE7VgCGbNILc4lteQgBCQZC/9vnguzbz39gp6+kDrWCPCoVOh1h7FeR1CM8Tk4BgIrg6XTtcZHNZVX2CksqyAi0AcPi+JAQRlbcoronxKJt6eFdfuOsjgzn4mDk/HysPDjxhy+XJPFv29Mw8OimL5sNzOW7WbZw4NRSvHqgkxm/r6Hbf8cCcB/Vu7ji/T9bHzG6ML5ZVse3/2RUxXgxeUVHC45XlVPp/iQ00Lx5j6JHLPaqx4/e3l7LKdM1Jn+19O7ds4cqnZ9j9OHo3ZrfvrYYXljTjQWjSrAT7Sk9xXvY1/RvqrP+4v3k1WSxaRuk7ih1dVUFO5nduYs0oKSSG6STBf/OP43uBMtrVaSSosJzMmDzC0w6mVIGWssWTrnDuMiFi8IbGoEc0WZcSy+O4yeUhnMsRAci/YNRaOwAGXRaezzbkdcEz8CfTzJKy7n9x2H6Z9SQXigDzvyipm1Jou/9kkkJsSP1XuO8Pqi7Tx/RQeahfnz48YcHpuzkTl39iUh3J+5Gdk8PHsDv/9jCLGhfizamscTX29k1WNDiQryJWN/AVMWbmd870SaBHhTVGbjQEE5x212/L09adbEj37JEdgdGk8PxcWpTYkP868aG3xz30SuqJzaDEbAPlPZvQFw70WtTvtzv7b76YHbJ/n0IY/xTZxoZUMhXIhbBrjWmnm75xEXGEfnqM4UlB1h3HfXcaAsD5s+2fLzs3jTPDSJlKDmXJS/j/bznoAvJtIMY0qpar4fgEivYC7bvAgd0BSP4GjsUakcCOuDt1ccTYHC0Lb8kPYZXdq1pXViArklVl6Yt4UbVXO6Abts4Uz8LZnHR7Wlb3QE6/cXcPnbPzBjfHcGt4liQ3Yh1/x7OR/f2pN+KRFszy3h3s8z+GxCL8IDfcg6Wsb7y/Ywsn1M1UiJkuM2KiqHlsWE+DGifTS+XieXsXxhbIeqbobhqU3pGBdCqJ/RN3tDr+bc1DsRD4vR6r2me7PTVlW7ODX6tG6Fbs3DTltDolmYP81OGeZtxipsQggXC/AKRwW5RfvJObyNrKM7yC4/Qq4yWtVZeZtpbwngZe94VOlh/uXYQ3+fBDr/5XuCvAJpl7eT4bYKmlXYSKiw0dxWwdEW40kZMwWbtZzlq67CN6YZdE+iwjece7/Lpn9pGtcDJT6xdCqexhMD23FrvxYcKT5O/+cW8mxSPDcCpfjwj2UOXoiy0DrJgs2hWbuvgEs6xADGJIm4UL+qftmYEF/uGpxMszCj5ZkSFcjb47pWjaLokhDKz5MGVq0zPLBVJJnPjaz6c+iVFM6cyv5kgE7NQunULLTqccvIQFpGnlznJCrI97QdQSRwhXAPLhPgY9/rzE4vG45T+kqVhkj/KGICY2hdVEAnaz54FkBABHcfiEBFG+OgPTy9IX8cTZKbc8XQ7hAYxYipmxibkEgK4OntywdxTzGmUyxtOsfh6dDEH95KYrLxplqAryeTr+pIl8qQbOLvxdyJfasCuGmQL1ufHVEV0HGhfix56OSa1LGhfqetAREV7Mv9F7euetwkwLsq7AH8vT1JOiWAnXJrMiGE6VxmHPhj0y/Dy1JBp6h4YgJi2X84kKZRHRnQ/2IAFm3OISrYnw7xxvCwzNxiQv28iAo2Wp7lFXZ8PC0ShkIIl3O2ceAuE+BCCNFYnS3ApTNUCCFclAS4EEK4KAlwIYRwURLgQgjhoiTAhRDCRUmACyGEi5IAF0IIFyUBLoQQLqpBJ/IopfKBvTX89gjgUB2W42rk/uX+5f4br+Za68gzDzZogNeGUir9z2YiNRZy/3L/cv+N9/7PRrpQhBDCRUmACyGEi3KlAJ9qdgEmk/tv3OT+xX9xmT5wIYQQp3OlFrgQQohTOF2AK6VGKKW2KaV2KKX+8SfPK6XU65XP/6GU6mpGnfWlGvc/rvK+/1BK/a6U6mRGnfXlfPd/ynndlVJ2pdRVDVlffavO/SulBimlMpRSm5RSixu6xvpUjZ//EKXUt0qp9ZX3f7MZdToNrbXTfAAewE4gCfAG1gPtzjjnEuAHQAG9gJVm193A998HaFL59cjGdv+nnPczMA+4yuy6G/jvPxTYDCRUPo4yu+4Gvv9HgRcrv44EjgDeZtdu1oeztcB7ADu01ru01lbgM+CyM865DPhQG1YAoUqpmDNfyEWd9/611r9rrY9WPlwBxDdwjfWpOn//AHcBs4G8hiyuAVTn/v8CfKW13gegtXanP4Pq3L8GgpSxN2IgRoDbGrZM5+FsAR4H7D/lcVblsQs9x1Vd6L3divHbiLs47/0rpeKAK4B3G7CuhlKdv/9WQBOl1K9KqTVKqZsarLr6V537fxNoCxwANgD3aK0dDVOe83G2Xen/bMfhM4fJVOccV1Xte1NKDcYI8H71WlHDqs79TwEe1lrb3XCD6urcvyfQDRgK+AHLlVIrtNaZ9V1cA6jO/Q8HMoAhQEtggVJqqda6qJ5rc0rOFuBZQLNTHsdj/E97oee4qmrdm1KqIzANGKm1PtxAtTWE6tx/GvBZZXhHAJcopWxa668bpML6Vd2f/0Na62PAMaXUEqAT4A4BXp37vxn4lzY6wXcopXYDbYBVDVOikzG7E/6MNyg8gV1AC06+iZF6xjmjOP1NzFVm193A958A7AD6mF2vGfd/xvkzca83Mavz998WWFR5rj+wEWhvdu0NeP/vAE9Xft0UyAYizK7drA+naoFrrW1Kqb8DP2G8Iz1Da71JKXV75fPvYow8uAQjxEox/kd2C9W8/yeBcODtylaoTbvJIj/VvH+3VZ3711pvUUr9CPwBOIBpWuuN5lVdd6r59/8sMFMptQGjEfew1rrRrlIoMzGFEMJFOdsoFCGEENUkAS6EEC5KAlwIIVyUBLgQQrgoCXAhhHBREuBCCOGiJMCFEMJFSYALIYSL+n9xodK5/nJ9gQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, linestyle = ':')\n",
    "plt.plot(x, e2x, ls = 'dashed')\n",
    "plt.plot(x, e3x, '-.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00016-1f53d6be-3448-45c4-bcdb-b27ca342837f",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "The `'None'` line style might seem pointless but it can be used when only the point markers are needed which we will seen next. A more complete description of the line style formatting options can be found [here](https://matplotlib.org/stable/gallery/lines_bars_and_markers/linestyles.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00002-6677a4e6-a695-4883-aef7-f7d8712406cf",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Marker Types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00018-ecbe5d8f-aa10-44fb-af19-8c353ab4cf1e",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "A marker type can be specified in a similar way to line styles with the keyword `'marker'`. A list of the marker types can be found [here](https://matplotlib.org/stable/api/markers_api.html). When the marker type specified without a keyword the the line style defaults to `'None'` showing only the data points without the connecting lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "cell_id": "00005-85a226cf-32a6-4b2a-ae58-a4037e5b4e82",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 297,
    "execution_start": 1625488962661,
    "source_hash": "a5f75b5c",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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M9XvxgTDFfcIcOPcrMO0fobhvrqOnABdJE82kTNJ1o6ClwyiSjQ+FZyuEzz0Fo6Zkpl1ZRAEukiaaSZmgxh1hve3hJ0H9uvbjhcUw9R/ggz/IqxuRyVCAi6SJdoXvgYONUPtfYSTJK4+GGZNjZ8L4M2Hr6rAx8OFDcFypwrsDBbiIZMbhZtj0CLzw61DXbnkLSitCXbvyMig7JYwiiXw6b0eRJEsBLnIM2tIsBTqOIhk8Kky0eeHXsO73YT2SAcNh1idCaE848+ip7Xk+iiRZCnCRY9BEnBRoW4vk7svg7b2w59UwK3LyRTDjo3Di+VBUnOlW5iQFuEgXNBEnCe5hFMnhDrssbn8uPBcUwdc2hYk2khSthSLSBW1p1kPusO0ZWPEv8JPZ7eHdtiZJ21okX1qv8E4R9cBFuqCJOHFoPRxq2rV/gtr7Yd9roYc98Vw4+wvhvTX3Rrcjy7+1SDIt6QA3s0KgGtjm7vOTb5JIdtBEnKjYqeyHm+HVv4XQfnF5GBlS2D/Ust/3LThlHgwcHn530yN5vRZJpqWiB34NUAsMScFniWQNTcSJapvK/sfPh1EkGx6At/aEFf9OngvTPgwnf6DzsohGkaRVsluqjQfuAL4PfLm7Hri2VJPepmGASYjdEKGNFcBl/wknXQD9BvR+u/qgtGypBvw78HVAdyQkK2kYYA+0tsLrz4Y1R1566J3hXVgMUz8MH7xedewskXCAm9l8oN7da8zsvGOcVwVUAZSXlyf6dSI9pmGAcXhrL7z8V9j4F9j4MDTtDD3s8WfA+f8bdqwJNycLi6NT2YcqvLNIMj3wc4APm9lFwHHAEDO7y92v6HiSuy8BlkAooSTxfSI9ovW4o2JnQja8GHrYGx+GLU+CH4YBw+Ck98PJHwylkbabkHm+IUKuSzjA3f2bwDcBoj3wr8aGt0gmaRhg1H9/P8yEvPPDcKgJ9m0Jx0dPh3OugVM+COMiUNhJHOgmZFbTOHDJW312GODhFnj9Gbj9QmhtaT/e8GJ4LiiCa9bA0D42miYPpSTA3X0lsDIVnyWSKn1mGKA7NGyAupXhsfnvcHB/eO+4Ujj0ZgjyogEwdT584PuqY+cJ9cAlqyUzDDBv1uOOnUgDsG9bWDe7biXUPQpv7gjHh50QNvSddB6c8B54ZDE8szQ6E/KgZkLmGQW4ZDUNA6R9Nb8/fBaGTwrBvfOl8N7AkTDpvdHAfi8Mqzj6dw/U6yZkHlOAS9bq08MA32yAm6aGzXvbvPxIeFhBKINMOg9GTYOCY6xJp5uQeU0BLlmrzwwDdIe9W8KQvs1/D73tXRvDe1YIeNhirLB/dE9ITaSRQAEuWStvhgHG1rBbW2HnBtj8RDS0n4D928K5xw2F8rNg1hVQcTY8uwyevbN9NT9NpJEOFOCSVsnchMybYYArfxB61fdeAYPKYMsTYTEogMFjQlBXnB2CO7Yk8vebVcOWLinAJa2SuQmZk8MA3cOa2Fur4b7PhFmObbY+HZ6tEC7+GVScFUaNdNwDMpZq2HIMCnBJm2RvQmbNMMDOhvG1OdgYFoDauhq21sC26vZecmF/6F8Kb++LjsM+LtSwNQ5bUkQBLmmTNzch29bDXnkDnLkwhHRbYDfUhhuMACNOgknvg/GR8Bg9HR74eodx2NqRRlJLAS5pk9M3IVtb4fujj96Ut+a28IAww3F8JPSox58B405vXwCqI43DljRSgMsx5cVNyGOVQCDs67hzI2x/vv2xY83R4Q1QUAjHz4a5i6H8XceuXbdRDVuAms17WFW3izmTRjC7YljKPlcBLseUFzch20ogj94IF94YFnVqC+rXn4M31kJzUzi3aACMmQ4zLoOxM2HjCnixw3rYYyqhYk7vtl8yLpkArtm8h0/csopDLa0UFxWw7DNzUhbiCnDpUs7fhIzdEqz61vBoUzwYxsyA0xeEsD7+NBhx8tHLqr70kEogfVyyAbyqbheHWlppdWhuaWVV3S4FuKRf1tyE7K4Ecrg5lEDq14fe9Bvr4Y1179wSzArCjcZ3LQrrhgyfdOxp6KASSB5ItnyRbADPmTSC4qICmlta6VdUwJxJI3rchq4owPNcMjXsrLkJeaQEcgOc+9VoUK8Lj/r1YSnVtjVDCopg5OQwxnrUtDDLcdMKKCoOQT/xXDjjqt5tvyQl0+WLZAN4dsUwln1mTnbVwM1sAnAnMAZoBZa4+82papikRjI17IzdhHSHxu1w84wQum2qbwuPNkPGwehTw1Zgo08NjxEnh7Bus60GIp9WCSSDMhnAqShfpCKAZ1cMS2lwt0mmB94CfMXdnzGzEqDGzB529/UpapskKdkadspuQnZVAjncAns3hx70zg3Q8FL7c/QfjaNYYahVn/sVmHhO2MexOyqBZFSmAzhV5Yt0BXCyktkTczuwPfpzo5nVAuMABXiWSLaGnbKbkP99fVgL5HdVYfhdw4awnvWuTUcP1SsZCyNPgdMuD89lk+HZu+GFe9tHgRw/K+wqI70mmR50pgM4neWLbJCSGriZTQRmAU+l4vOkXVbUsLu7iQjQchD2vBpCedfLsPtleOaOUA5p88rK8MDCRronvT+E9MjJUHZKWGkv1lO/1CiQJGWyhJENAZytvedUSDrAzWwwcB/wRXff38n7VUAVQHl5ebJf1+dkRQ37yFTyH8DZV4eA3rUphHRbWO/b2j6lHGDA8DBE7609sP/1sBZIYX+YMh/m/SD+6eQqgeR0DVkBnF5JBbiZ9SOE9zJ3/11n57j7EmAJQCQS8c7Okc6lrIZdMIAqL6Hy1Co2Hdx57Br2W3tDXXrPq/DbTx+9q3nN7eHRpv8QGHEijD8TZl4Ow08Mr4dPap9Wfv+Xjl4LZEBpn1sLJJcDOBU1ZAVw+iQzCsWAW4Fad++bXaM4JFMCSVkN+7++zNWba2HkY5w37wbYXdce0ntehT0dfn5779EfUtAvGuIehugdPwve/eWw/segkd1PJ8+DtUD6cgDnew051yXTAz8H+CTwgpk9Fz32LXd/IOlW5ZFkSiBHatinXcOlf/0spcUl3dewm98O5Yx9r8GyS47uQcfORIRwc7C0HEorYNzssCnusInhUVoBK74XetCF/aNTyWfAlIvi/wPIghKIAlgljHyVzCiUvwFxrObTdyVbAjlSw66+BYDCt8MthqktDrX3h6De+1oI67bQPtDQ9QdaYbhpOOuTYTjesIow8iNaG+9UFvSgFcAKYOmcZmJ2IyUlkKEn8eK+TSyrvQvoogTiDk27wt6I+7fD/m0s2vAkTQYVW/5EVclgKg/Ws6m4H+P+89L23+s3EIaOh6ETwkJLQydA6YT2Y3+7CZ65s30YXvlZcNbn4v8DSEEPWgGsAJb0UIB3I5RABjFt5b9S/pG7EiuB+HAuBUpbWmgCKndvg4e+HWYb7n89PBq3v2P50rkUQFF/ONzK1Xv3QUER55VOgfcuDCvmDZ0QbhYeqw59YCf1p3ycvw7+EOe/uZxRCfSgFcAKYMlOeR/gyfSg20sgB5hfcICFf15I3VuvtpdADh0IY6TffCM8Gt+AN3cceV7x1nroX0zjhvth7GgKm5ugXz+mPn070A+GHA8lx8OEd8GQsWFqeNuxIcfD4FGw/Kt4ze0cLiimsLUZGzcbTr8i7uuvOeunHQJ0fgjQHvz5KYAVwJK98j7Ae9yDbjkIB3bCgXpq75oPo4cz5eAhXuxfzLIDdVBQwLxtG+D68Z1P9y7oB4NHw+BRLOo/gaYD9Uxocar27GN6cysvjz6ZcQt/A6Mmx7UhwJ6GbTzQ+n6WHTqfTxT9lYvqt9KTKEk2QBXAItkr6wN8ed1yCt7ez4VP3QmXLGX1gS0J96A/ed9HqSvYzdiiElh5Y7hB92b9kcDmQEPYgDZqXekQABbv3MWl48Yy9HArTQUFVI6YBqfMCEFdMqbD85iwPkd0idK5QMM9n2PEG3ezcI9TTAunjp+GjZ4S9/XffcL1/OvGDbQ6fKf5SvaeMJnP9+DPL9kAVQCLZK+sD/BrH7+WQRQyddtWBtz/Pa4bsJW6/a+wYMTpIXibdkHTbmhq+3lX9PhuahtfhjGjjvSg72MnUMC8nVth4/VhtuCgslCqGFMJg0ZFX5fBoDJWrP0pHNjKfgujNIoI85CmXvwfUDI+rvbv3/U6fz58AXcfvoCPFz7C2bu2MaoH15/pAFUAi2Qvc++9yZGRSMSrq6vjPr/h+jGcP67syOuFe/bxH8OGMralhb+89nrM2RZ6vwNHhMegkfy8dRc/a97GPVvruXz8KMY2t7C9XxE3zbyGuZULoLDfMb//4c0P88qDP6Blewl3DSll7qHtDBxxkK8vXInFsx8i7TXktgBOZD3idO2nJyK5wcxq3D0Sezyre+C1l/4SnvhnJh88xIb+xSwbWgLAvBGz4Kwbjwprjis9eissYMWfPgJ7oCm66cqRHvSJ87oNbwgzGWsujIQA3tnKvUUFLPv4nLjDG9SDFZH0yeoAX3cg9LL/T8NuPjp+THsNetaV0GGp064smrmIpsdvYnDFuzincBAXFu6ggd09Ws9aASwi2SqrA7xtJuK2iR+AljVYv8HA23Gvpje3Yu6RoP9FEu1QAItINsrqAG9bTW/m8WdR9eK9ie8IIyKSh7L6JqaIiHR9E7MgE40REZHkKcBFRHKUAlxEJEcpwEVEcpQCXEQkR/XqKBQzawA2J/jrI4GdKWxOrtH16/p1/X1XhbuXxR7s1QBPhplVdzaMpq/Q9ev6df199/q7ohKKiEiOUoCLiOSoXArwJZluQIbp+vs2Xb+8Q87UwEVE5Gi51AMXEZEOsi7AzWyemW0ws01mdm0n75uZ/Tj6/hozOz0T7UyXOK7/E9HrXmNmT5jZzEy0M126u/4O551hZofN7JLebF+6xXP9ZnaemT1nZuvM7NHebmM6xfHf/1Azu9/Mno9e/5WZaGfWcPeseQCFwMvAJKAYeB6YFnPORcCDgAFzgKcy3e5evv6zgWHRny/sa9ff4by/Ag8Al2S63b38918KrAfKo69HZbrdvXz93wJujP5cBuwGijPd9kw9sq0Hfiawyd3r3P0Q8Cvg4phzLgbu9GAVUGpmY3u7oWnS7fW7+xPuvif6chUQ3+7KuSGev3+Aq4H7gPrebFwviOf6Pw78zt23ALh7Pv0ZxHP9DpRY2NdwMCHAW3q3mdkj2wJ8HPBah9dbo8d6ek6u6um1XUX4v5F80e31m9k44H+Q3CZL2Sqev/9TgGFmttLMaszsU73WuvSL5/p/CkwFXgdeAK5x99beaV72ybYdeTrbLTh2mEw85+SquK/NzN5HCPB3p7VFvSue6/934Bvufrgnm0vniHiuvwiYDVwADACeNLNV7v5SuhvXC+K5/g8CzwHnAycCD5vZ4+6+P81ty0rZFuBbgQkdXo8n/Evb03NyVVzXZmYzgFuAC919Vy+1rTfEc/0R4FfR8B4JXGRmLe7+h15pYXrF+9//Tnc/ABwws8eAmUA+BHg8138lcIOHIvgmM3sFmAI83TtNzDKZLsLH3KAoAuqAE2i/iXFqzDkf4uibmE9nut29fP3lwCbg7Ey3NxPXH3P+UvLrJmY8f/9TgUei5w4E1gLTM932Xrz+nwP/Ev15NLANGJnptmfqkVU9cHdvMbMvAA8R7kjf5u7rzGxR9P1fEEYeXEQIsSbCv8h5Ic7r/w4wAvhZtBfa4nmyyE+c15+34rl+d681sz8Da4BW4BZ3X5u5VqdOnH//i4GlZvYCoRP3DXfvs6sUaiamiEiOyrZRKCIiEicFuIhIjlKAi4jkKAW4iEiOUoCLiOQoBbiISI5SgIuI5CgFuIhIjvr/ZchXk95bFQsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0,1,.05)\n",
    "\n",
    "plt.plot(x, ex, '.') # dots\n",
    "plt.plot(x, e2x, marker = '*') # stars\n",
    "plt.plot(x, e3x, marker = '$hi$', ls = 'None')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-6a0362ce-dd0e-4a73-908a-69559e456a19",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "I should note that the keyword `markerfacecolor` and `markersize` exist and they do as you might expect. I will further note that we can assign colour and marker in a single compact form as seen below. This is useful for quick assignment but might get confusing and/or limit customisability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cell_id": "00004-968a4d33-fe68-4f5e-8f14-d87c8984796c",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 155,
    "execution_start": 1625488963004,
    "source_hash": "a19bb220",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, 'rx', x, e2x, 'bo', x, e3x, 'g--x')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00001-6bd63046-ccaa-446e-ad79-5166097d32a9",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00005-8cc35a06-e771-4ae9-996d-a5c9897f7083",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Limits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00027-48c3d5c5-3059-4960-b3ae-aca7ba498853",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "We have seen above that the size of our graph changes and rescales. You can set the $x$- and $y$-axis limit with `plt.xlim()`  and `plt.ylim()` as shown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "cell_id": "00028-acffecae-19bc-4a73-9722-4084572b43d0",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 142,
    "execution_start": 1625488963523,
    "source_hash": "da3053f8",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qbits = [0,1,2,3,4,5,6,7]\n",
    "probs = [.02,.23,.32,.03,.02,.13,.2,.05]\n",
    "\n",
    "plt.plot(qbits,probs,'_',markersize = 20)\n",
    "plt.ylim([0,.4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00008-c3cf9474-d7c7-44b2-b427-a646bf8dd5cf",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Ticks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00030-d882eb67-a968-46e9-a542-2d0fae755dcb",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "We can reformat the $x$ and $y$ ticks in the following way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "cell_id": "00030-18038216-85f7-4970-9ed3-24719bf4f016",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 143,
    "execution_start": 1625488963660,
    "source_hash": "8d58d1ba",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_ticks = [0,1,2,3,4,5,6,7]\n",
    "y_ticks = np.arange(0,1,.02)\n",
    "x_labels = ['000','001','010','011','100','101','110','111']\n",
    "\n",
    "plt.plot(qbits, probs, '_', markersize = 20)\n",
    "plt.xticks(ticks=x_ticks, labels=x_labels)\n",
    "plt.yticks(ticks=y_ticks)\n",
    "plt.ylim([0,.4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This effect is however better achieved by a histagram or bar chart that we will look at later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00009-b23ef526-b2f8-43f2-a98a-150aec0169d3",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often the clarity of demonstrating  the values of the points can be assisted by adding a grid of horizontal and verticle lines stretching from the ticks. This can be toggled on/off using `plt.grid()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "cell_id": "00033-a3a52748-47e2-4d83-94a5-6b0c93c6b2b9",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 160,
    "execution_start": 1625488963873,
    "source_hash": "e4e4cd1c",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(qbits,probs,'o')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00001-044021e5-6b15-4786-836e-35d6ae5c2ef4",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Lables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lables are a great way to explain what it is your are plotting. In the strings used to label a lot of $\\LaTeX$ is supported which can be very useful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00002-e3fd1edf-3bb9-49df-93be-4a701bbff813",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Title"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A title string can be added using `plt.title()`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "cell_id": "00036-4830282c-795f-4c2f-b80c-e818d6592867",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 159,
    "execution_start": 1625489494267,
    "source_hash": "f06e772c",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, ':')\n",
    "plt.plot(x, e2x, '--')\n",
    "plt.plot(x, e3x, '-.')\n",
    "\n",
    "plt.title('Exponentials')\n",
    "\n",
    "plt.xlim([0,1])\n",
    "plt.ylim([0,18])\n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-254ada92-0776-4813-a728-b809ad2bf6c2",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Axis Lables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, `plt.xlabel()` and `plt.ylabel()` can be used to add labels to the $x$- and $y$-axes respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "cell_id": "00038-b582bcac-514b-4fbd-bd2a-593856cbc543",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 154,
    "execution_start": 1625489565983,
    "source_hash": "db20f463",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, ':')\n",
    "plt.plot(x, e2x, '--')\n",
    "plt.plot(x, e3x, '-.')\n",
    "\n",
    "plt.title('Exponentials')\n",
    "plt.xlabel('this is the $x$-axis') \n",
    "plt.ylabel('this is the $y$-axis')\n",
    "\n",
    "plt.xlim([0,1])\n",
    "plt.ylim([0,18])\n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00004-bba463ac-f09b-4f57-9c6b-3c3f9a3ab477",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Legend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `plt.plot()` we can assign a name to what is being plotted using the `label` keyword. A legend displaying this can then be toggled on/off using `plt.legend()` with keyword `loc` to set a location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "cell_id": "00040-d563cf00-5002-4c4e-be89-422d1d6f5905",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 283,
    "execution_start": 1625489762120,
    "source_hash": "f98b5f7a",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ex, ':', label = '$e^x$')\n",
    "plt.plot(x, e2x, '--', label = '$e^{2x}$')\n",
    "plt.plot(x, e3x, '-.', label = '$e^{3x}$')\n",
    "\n",
    "plt.title('Exponentials')\n",
    "plt.xlabel('this is the $x$-axis') \n",
    "plt.ylabel('this is the $y$-axis')\n",
    "\n",
    "plt.xlim([0,1])\n",
    "plt.ylim([0,18])\n",
    "\n",
    "plt.grid()\n",
    "plt.legend(loc = 'upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00003-4965e725-227f-4ee5-a7aa-91efa6c6e29a",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Error Bars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00023-f60f33fa-14ed-44f7-b0a7-064fdbf4a9e4",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "If we call `plt.errorbar()` instead of `plt.plot()` we can add error bars in the $x$ and $y$ directions by specifying either a constant error or a list as the `xerr` and `yerr`. These error bars can be formatted in various ways as shown with `capsize` and [here](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.errorbar.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "cell_id": "00023-cfce6023-7fe6-42c7-b6c5-ef686e69983e",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 231,
    "execution_start": 1625488963190,
    "scrolled": true,
    "source_hash": "4292a7ca",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CLs/3ylNw2Q8qP8HYOddFNrBnK3fp5kLgTnd34EkzO8zM2tx95JMhIjUmSFZdNw8+BbHjeVj7zwdq7IV2z6hzJrSwN2MdeMjM1pnZ0hyfHw38IeP91tQ2kViqmwefgojZ8nxREjajP9vdt5nZFOBhM3ve3TOfbLAcx3iuL0r9oFgKMH369JDDEgkv6LJ+AMseX8bA8ABt49vonNupB5/SYrQ8X5SEyujdfVvq9x3AvcDpWbtsBY7JeD8N2Jbnu25x93Z3b29tbQ0zLJGqSsxKMKd1Du1HtvPQxQ/VdpCv9BJ91VieL31Tdcuayi1DWGMCZ/RmNh5ocPc3U687gC9m7XY/cJWZ3U3yJuzrqs9LFKR74QeGB+hY1RHfrDxI90zQm6rVWp4vRjdVgwpTujkSuDfZQck44C53f9DMrgRw9xXAAyRbKzeSbK8MNlm3SAWF7YWHCLRHhhH0pmrMlueLEks2xNSW9vZ27+npqfYwJEaK6YnP1QsP0NzQzJzWOQV/T2SC/W2pH16FZvRdhx68mIcPJ7P07c8lZ6Qs9fnCHlcnzGxd9rNMaZoCQSSLeuELoMU8IkVTIEhdKCa7jlwvvBbzkDEoo5fYK3Zu+Mj1wgddzCPoPO/VWMxDnTOhKKMXyVI3vfC5bqredUlyuoHRVOOmqjpnQlGgl1gL2iZZF4uA9K48+Kbqdz8Ew4NjTy2gKQkiR6Ubia18bZKaHz5D9k1ViSVl9BI5hdbbw04ZXPFMvhZuqpZbjKb+jRIFeomtyLVJVvIpVcj9pOpdlySPL1cZRrX2qlCgl8gpNNOOXJtkEEGfUoXcN1Uv+0Hyh4Tq7bGiGr1ERuzbJIMIM/XvvKtHBvSZ88f+n4BEjgK9REKQBbcTsxJ0ndVFc0MzkMzku87qKn+bZJAZIYP2tEN1nlJVX3ukqHQjNS/MJGNVaZMMUmsPU4KpxlOqqrVHigK9VFUhpZig3TPpwB6JenyunvbW2cntF63If1y1pv6VSFHpRmpe5LpnggpSgpkyO/lUanrf9FOqU2aXbZgSPcropaoKybar0j0TtKc9TLtjkBJM2KdU1ddeFxTopeKKXYu1c24nXWu76B/q37+t7N0zQersELzWrtWXpIxUupGKilT3TBBB2x1VgpEyUkYvFROZ7pkw5Rc4uNZ+6DGF1do1UVhN+frDL7L8kZdGbO889zg+c97xVRhROAr0UlKjddEE6Z7JDOqBAnyQWvvRc5NTARz+ruJbHaHy7Y6qs5fcZ847ns+cdzwf+dYTAHz/U2dWeUThBA70ZnYMcCcwFRgGbnH35Vn7LADuAzanNt3j7l8Mek6Jtqp0zwSptc+cD/veLr7VEapTa1edPa9iMvOvP/xiUdl6sftXU5iMfhD4nLs/ZWYTgXVm9rC7/y5rv1+6+wdCnEdqTPem7ryLcoyWdVe8eyZsCabY8gtUZ1GOmCu2jJIZgMfKzDP3Xf7ISyO+783+fbzRP8i6Lbs57dhJB32Wa/9aFTjQu3sf0Jd6/aaZbQCOBrIDvcRImDp7qO6ZICWYME+bAvhw8eWXMLX2mJdgggbsQsooQQN29r7pc6SP+V3fmwAsWrGW2VMnMrGlqZhLrhklqdGb2QzgVOBXOT4+08yeAbYB/8Xd15finFJ+uertxdbZMzP1UEv0BSnBBH3adPNqaDrkQI1erY4HCXqjsti6d3YQLia7LkXAfqN/cP/rYU++r9tAb2YTgB8BV7v7G1kfPwUc6+57zGwh8GPguDzfsxRYCjB9+vSww5IyCVtnT8xKFN8WGaYEE6QD5pWnktP1qvySUzEBO2zdO32OMNl1MQE781rWbdnNohVrGXZoaWpg+aWnHvQDZsa10VmpLFSgN7MmkkH+e+5+T/bnmYHf3R8ws2+a2WR335Vj31uAWwDa29s9zLikMKPV2iF3vT10nb3SJRg9bZpXJW5UlqruXWx2XWjAHi1Yn3bsJGZPncgb/YMjgnzUhOm6MeA7wAZ3/6c8+0wFtru7m9npJB/Q+mPQc0rpBK21h6qzr7kRZpwNL89Lvl/SfWAq3tEy86hN+FXBEkwUblSGKaOkxxQmuy40YHeeO7LYMLGliYktTTmPybV/rQqT0Z8N/D3wrJk9ndp2PTAdwN1XABcDnzazQeBt4FJ3V7ZeBdn19kJr7dlZemJWAtbfx/Ltv+TVcY1MHRyi8/BTCyvH5MrM77okWSYZS5ASTJgOmApn5fVyozJo3buY7LqYgJ25b+a1Zv99pH+QZP59RKXjBsJ13awBbIx9bgJuCnoOKUz3pm6WP7WcV/e+ytTxUwu6wRm41r7mRhKn/B2JXa+AA58sMCuH3Jn58GBhJZFKl2ACZuVByyFhA3Yt36gMWvfODtiFZtfFBOB8+6b/PuJCT8ZGXLoEky6l5CvBZGfmgWvtYVsWszPz1/8w9jEVLsFEoRwC0bxRWUxmXoqAXUhmXg8U6CMoswwzVgkmX9DuHH88XW/von943/5tLQ1NdI4f4x9/0Hp5WnZmXoBfvj6Zb/7pSp547eTkhhfe5MyGK/mH19/gfaMc9/WHX8Qeu4Grxx0owdw4eBH+/uvquhxSyRuVpah7hwnWccvMg1KgrxFByi8QvASTeHsQdr/J8omH8Ko5U1sm0bmjj8T4wVGPA4LVy4H1rQmm3n4ZV+27hifeOpkzG9bznaav0v3Du1i06LK8x71vyf/ifcD6/528iXvy9WuA3H822dk1593GR761FEgGuKtH2T9K5ZD09UBt36gsRd1bwTo8BfoaUGj5JS0zS+/43hn0De4dsU/buPGjl2B6V5I48hQSW1KZuW8rODNf/NL7uanpGf51KMHf/en/cdXOj7KyeeynRk9+z+lw9JV8fuX1wP3JgL35DBbluDk6op3v0Rs4eeDZ5OscN0dL1c4X93JINW9UKmBXjwJ9lS15cEng8gvAh/dM4l+a9/DnhgP3xd8x7Hx4z9g9vzO2XM9nxv2QTu5l+eCH+PqWRbzckj+zBmDOYlZuXMHmgcn89Ts2csTiu1j5wyvg3bnr5QcF7Fw3azNujo5aDjnnOhb2np03mJWqnS+tlsshoBuVUhwF+hIL1AEzNJCzf2lgaOynTT/Vt5ZpRx3P8oY9yXbHoSE6hyaQ6Fs7Yt/sLPnlT01k8I772dEwhc6/WE3noo/DHbn33/861bL41srrkzvlaFkcNWA/egP9/f08OXwi/cvaOe2cD+/PzFUOqWzA1o3K+qFAn0PQuTy+dtvH+B6/ZV9D8lGBvr19/I/HruP5x37A55bckfOY286/jY6759P3590jPmtreEfObD47YCeapnDels00sy9ZMz9sCvDiiH0PCqSpTpbHbS4/HzqVy+Yv4ISsTpbM/fe/nnf1qMF6xHnIDthn87uBOQA0GMzuncjEFw98nk/cyyGFyHcDWTcqZSyxDvSBJ1865AGO/9tBPr/hJwzaa7RNaKNzWgeJwZeA/L3Q97OOfQ0Hp+b7Gpyf2Xo+l2P/9OvO06+h67H/Rn/DgZUdWxw6d7yS8zwjsuQF1+B3XMQvfC5n979MU0aPeb6g+8E97+TZhs9yz9vTGKSR794HlxzxWf7D5k3c/63cgfdA/TpYsIZoBewoZNcK1lKI2AX6g7ouxgjYOUsTQPfW1XS9/SKDqaDdt7ePrg23wyHHk0j1beS6+bc7z+Njrw4fmC4gV5acmJWAH32Sf5p0ODvHGa3DDXzWJpHY+/ucx8GBoPvplnM59c7LuWrgczw+fApn7NvAzXdezm9bzuXmPAEb4P4Jizh8+1oGaWCYBhp9iNff+jP3H7lozD/jWq5fR7UcooAt5RS7QJ8ZEHMH7NvgxCUkyFOaAJbv2UB/08F/NP0NxvI9G/Y39eW6+Te1cYi+ppF/pFMHhw4qX2RKb//im5P44Z7X+dehc7m88RG+OnEpCZ7Oe1zaK00z+O2fj+Lx4ZMZpoFfDc/mVi5kSlNzzv0PDrqz+dmKteDQ1NTEJz/28VGz5CjUr1UOERkpdoEeDgTP3Y25AnYDn9/wE+585uy8x736jsac3/vquMZRA2/n7j9x/eQjGW4Y2r+tYbiRzt27uPMv8o/35D8/w1ENu/nUwNWsHT6FJ4ZP5pt7vsIvWs7Ne8yBgH0m67bs5v9mBOz5V3yJ046dxOWUZ3a+qLTzKbsWSYploE97dVzugD1or4163NTB/Jl5LvuD7j0XMvj7R/ifEw5nYNxbNA+O5wt7/kjiXReSuCi5T84sec2veGHzJTy1/jgaGeK3w+9mx7suYsHMmSyYl/u4TJUoa5Sifj1W4C11O58CtkhSLAN9OvB2fDt3wG6b0Mb3rzgzb2mi++4T6Xr7Rfozbqy2DDudE04kcekogXfKbC4Epj3dw5PD7+WMhg2c9t5zky2Jo5l3NSfMg1nLV+8P1icce1He3avR5ZF5LyPorH4KvCLVEctAn9Y5IU/Anjb6BFyJafNhK3x1z0v8cRwcMQj/dcLxye3Z58gMuqkHgv5xZ7K8859yzJFSK1myyhoi9cNqcXr49vZ27+npCXTsQT3ma26ke+tqlu/ZcGDu9AknJgP2vKvzdt2kFTqpVbZC18TM/K4gbaAiImlmts7d23N+FrdAn0ulAq8CtohUS90GegVeEakXdRvoRUTqxWiBviHXRhERiY9Qgd7MzjezF8xso5ldm+NzM7N/Tn3ea2Zzw5xPRESKFzjQm1kj8A3gAuAkYLGZnZS12wXAcalfS4Gbg55PRESCCZPRnw5sdPdN7j4A3A1cmLXPhcCdnvQkcJiZtYU4p4iIFClMoD8a+EPG+62pbcXuIyIiZRQm0OealDe7haeQfZI7mi01sx4z69m5c2eIYYmISKYwgX4rcEzG+2nAtgD7AODut7h7u7u3t7a2hhiWiIhkChPofwMcZ2YzzawZuBS4P2uf+4GPprpvzgBed/e+EOcUEZEiBZ7UzN0Hzewq4GdAI3Cru683sytTn68AHgAWAhuBt4AlhXz3unXrdpnZlqBjy2MysKvE31lrdI3xoGuMh0pf47H5PqjJJ2PLwcx68j01Fhe6xnjQNcZDLV2jnowVEYk5BXoRkZirp0B/S7UHUAG6xnjQNcZDzVxj3dToRUTqVT1l9CIidUmBXkQk5mIV6Oth2uQCrvHy1LX1mtlaM3tPNcYZxljXmLHffzSzITO7uJLjK5VCrtPMFpjZ02a23sweq/QYwyrg3+uhZvYTM3smdY0FPWtTK8zsVjPbYWbP5fm8NmKOu8fiF8mHtv4dmAU0A88AJ2XtsxD4Kck5eM4AflXtcZfhGs8CJqVeXxDHa8zY7+ckH8q7uNrjLtPf5WHA74DpqfdTqj3uMlzj9cBXUq9bgdeA5mqPvYhrnA/MBZ7L83lNxJw4ZfT1MG3ymNfo7mvdfXfq7ZMk5xeKkkL+HgH+M/AjYEclB1dChVznZcA97v57AHeP2rUWco0OTDQzAyaQDPSDlR1mcO6+muSY86mJmBOnQF8P0yYXO/5PkMwmomTMazSzo4EPASsqOK5SK+Tv8nhgkpn9wszWmdlHKza60ijkGm8CTiQ52eGzQKe7D1dmeBVREzEn8Fw3Naik0ybXqGKmfT6HZKCfV9YRlV4h13gjcI27DyUTwUgq5DrHAacB5wKHAE+Y2ZPu/mK5B1cihVzj3wBPA38FvAt42Mx+6e5vlHlslVITMSdOgb6k0ybXqILGb2ZzgG8DF7j7Hys0tlIp5BrbgbtTQX4ysNDMBt39xxUZYWkU+u91l7vvBfaa2WrgPUBUAn0h17gE+LInC9obzWwzMBv4dWWGWHY1EXPiVLqph2mTx7xGM5sO3AP8fYQyv0xjXqO7z3T3Ge4+A1gF/EPEgjwU9u/1PuB9ZjbOzN4J/CWwocLjDKOQa/w9yf+xYGZHAicAmyo6yvKqiZgTm4zeyzhtcq0o8BqXAUcA30xlvINeIzPoFaLAa4y8Qq7T3TeY2YNALzAMfNvdc7bx1aIC/y6/BNxuZs+SLHNc4+6Rmb7YzFYCC4DJZrYV+ALQBLUVczQFgohIzMWpdCMiIjko0IuIxJwCvYhIzCnQi4jEnAK9iEjMKdCLiMScAr2ISMz9f9JacZHL1V+HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(x, ex, ls = 'None',  marker = '.', xerr=.02, yerr=.4, capsize = 3)\n",
    "plt.errorbar(x, e2x, ls = 'None', marker = 'x', xerr=.01, yerr=.2*e2x, capsize = 2)\n",
    "plt.errorbar(x, e3x, ls = 'None', marker = 'o', xerr=x/10, yerr=x, capsize = 0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Asymptotes and Annotations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verticle and horizontal lines can be added using `plt.vlines()` and `plt.hlines` which takes in the value the line is at and the begining and end of the line as arugaments as shown. One can also have an array of vales for this which will give many lines.\n",
    "\n",
    "The function annotate `plt.annotate()` is ver useful when you want to draw attention to a particular point in your plot. It takes in a string that will be displayed and the point you are interested in. One can change the text colour as you might expect by calling the `c` keyword. The text can be put at different point to the point of intrest using `xytext` and an arrow can be generated between using `arrowprops` and giving a dictionary that will specify the features as shown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bOHwuzeg4QuTL6s3EoCCD0ghbpFA7mY+PYmyfWLTWPD9/I2aztECEZ8ppfVxzM/GllwxKI2yRQu0C1cuFMOqWRvy1+wwzVx8wOo4QVlndPU94JCnULtL/huq0q1uBMb9s58CZVKPjCJFH7qO4ri7Ut91mUBphixRqF1FK8W7vWPx8FCPnSgtEeJ4sa/OoH3vMoDTCFinULlQ1PJhXb2vEmv1n+fKvfUbHEeIaZms3E7t3NyiNsEUKtYv1aRbJTQ0qMu7XHew5dcnoOELksroyUXgkKdQuppTi7TubEOTvy7Nzk3M/OYQwWk7r45oedWSkQWmELVKo3aBiWBCjb2/MPwfPM2XFXqPjCAHkszLx+++NCSNskkLtJj3jqtKtcWU++G0nO46nGB1HCExmy8/XtD569TIki7BNCrWbKKV4844YSgX5MWLuBjJzPkuEMIjJbPk/eM3NxMOHDUojbJFC7UYVSgXyVq8YNh+5yORle4yOI0q4nLGCLHjxfA4XaqWUr1LqH6XUQlcGKu66N6lCz7iqTPrvLrYcvWB0HFGC/TuivuqDixYZE0bYVJAR9dPANlcFKUlG396YsqEBjPg2mYwsaYEIY5i0xtdHoa5ufUyebFwgkS+HCrVSKhK4BfjctXFKhvCQAN6+ownbj6cw8fddRscRJZTJbKXt8dNPxoQRNjk6ov4QeA7Id/inlBqilEpSSiWdOnXKGdmKtc6NKtG7aSSf/LGH5EPnjY4jSiCT2Yyvkv60N7BbqJVStwIntdbrbB2ntZ6itU7UWidGREQ4LWBx9uptjYgoFciIucmkZ5qMjiNKGKsj6jFjjAkjbHJkRN0G6KmU2g/MBjoppb52aaoSokywP+/2iWX3yUuM/22n0XFECWPO7lFfI12e9+mJ7BZqrfWLWutIrXUU0A/4r9b6XpcnKyE61Iug/w01+Ox/e1l34KzRcUQJkmU25y3Uo0cbE0bYJPOoPcCoWxpSLTyYZ+du5HKGtECEe5jM1y12ER6rQIVaa71ca32rq8KUVKUC/RjbJ5Z9p1N5d/F2o+OIEsJkNufdOe+uu4wJI2ySEbWHaF27Ave1qsm0v/ezcs8Zo+OIEsDqzcT+/Y0JI2ySQu1Bnu/egKjyIYycl8ylK1lGxxHFXJbZjJ/vdYX6jjuMCSNskkLtQUIC/HivbxxHzl9mzC+yCFS4VpZZy0MDvIQUag+TGFWOwW2jmbX6ICt2ysIh4TpZJjN+PteVgDp1jAkjbJJC7YFG3Fyf2hGhPD9/IxfTM42OI4qpLJPO2/qYPduYMMImKdQeKMjfl/fviufExXTe+Gmr0XFEMZVl1vj5XlcCunUzJoywSQq1h4qvHs7QDrWZu+4wv287YXQcUQxlWZued/q0MWGETVKoPdjTnevSoHJpXvhuE+fTMoyOI4qZTJPcTPQWUqg9WKCfL+/1jeNcagav/bjF6DiimDGZNf7Xtz6WLzcki7BNCrWHi6lWhic61eGHDUdZvPmY0XFEMZJlsrLXx1tvGRNG2CSF2gs8fmMdYqqFMWrBZs5cumJ0HFFMZJo0/tfP+vjtN2PCCJukUHsBf18f3u8bz8X0TF75YTNaa6MjiWLAZNZ551ELjyT/Sl6ifuXSPNO5Hr9sOs5PG6UFIoou02zG9/oR9fjxxoQRNkmh9iKPtK9FXPVwXv1hMydTZIN3UTRZJo3/9T3qYzII8ERSqL2In68P7/eN43KGiZe+2yQtEFEkJmsLXsaNMyaMsEkKtZepU7EUI7vWZ+m2k3y3/ojRcYQXyzRZWfAiPJIUai/0QJtomkeV5fWftnDswmWj4wgvZVlCfl2hHjTImDDCJinUXsjXRzGuTxxZJs3z86UFIgrH6u553bsbE0bYJIXaS0VVCOWF7g1YsfMUs9ceMjqO8EJW96OWJ7x4JCnUXmxgy5q0qlWeNxdu5dDZNKPjCC9j2eZUSoA3kH8lL+bjoxjbJxaA5+ZtxGyWFohwXJbZnHdlYkyMMWGETVKovVz1ciG8fGsjVu49w4xVB4yOI7yE2awxaysPt502zZA8wjYp1MVAv+bV6VAvgncWbWf/6VSj4wgvkGk2A+TdPa9DBwPSCHukUBcDSine6d0EP1/Fs3OTMUkLRNiR838kz83EVA/9Qj9mjP1jzp+HyZNdHsUIUqiLiSplgvlPz8YkHTjH5//ba3Qc4eEyTZZCnaf14amkUIvi4o6EanRtXIn3l+xkx/EUo+MID5Zlyqf1sWqV9Tf06gXNmkHjxjBlCphMcP/9lpuPTZrABx/Anj3QtOm/79m1y/IegKgoeOklaNUKEhNh/Xro2hVq14b/+z/LMcuXQ/v2cMcd0KgRDB0KZjO88AJcvgzx8TBggOXY8eMt146JgQ8/tHzshRcsGeLjYeRIy8fGjYPmzSE2Fl57rSh/ZcbSWjv9R7NmzbQwxqmUdN109BLdY8IKnZFlMjqO8FAnLlzWNZ9fqL9etf/aF555xvobzpyx/JyWpnXjxlonJWndufO/r587Z/m5Y0et//nH8usXX9R64kTLr2vW1Hry5H+v0aSJ1hcvan3ypNYREZaPL1umdWCg1nv2aJ2VZTn/3LmW10JD/71WUpLWMTFaX7qkdUqK1o0aab1+vdb79lmy5fj1V60fflhrs1lrk0nrW27R+o8/HP47cjcgSedTU+2OqJVSQUqpNUqpZKXUFqXUf9zw9UMUUoVSgbx1RxO2HL3IpP/uNjqO8FCZ+fWo//c/62+YOBHi4qBlSzh0CDIyYO9eePJJWLwYwsIsxw0eDFOnWkbcc+bAPff8e46ePS0/N2kCLVpA6dIQEQFBQZa2BcANN0CtWuDra1l88+efebP8+adl1B0aCqVKwZ13Ws+9ZInlR0KCZaS/fbtllO+FHGl9XAE6aa3jgHigm1KqpUtTiSLpFlOZOxOq8fGy3SQfOm90HOGBclofDj04YPlyWLoUVq6E5GRL4btyxfLrjh3h448tBRqgd29YtAgWLrS0PcqX//c8gYGWn318/v11zu+zsiy/Vtd94bj+9wCObpmgNbz4ImzYYPmxezc89JBj7/Uwdv+Vskfll7J/65/9Q6YVeLjXejYmolQgI+Ymk55pctt1J06cSMOGDRmQ00t0gv379zNr1qzc3yclJfHUU0857fwF8f3337N161ZDru1MWTkj6usXvFi7GXfhApQtCyEhllHpqlVw+rSlf9y7N7zxhqXnDJbRcdeu8Oij8MADBQ+2Zg3s22c595w50Lat5eP+/pCZafl1+/bw/feQlmaZpbJgAbRrZxmhp1x1b6ZrV/jyS7iUXb6OHIGTJwueyQM4dDNRKeWrlNoAnAR+01qvtnLMEKVUklIq6dSpU06OKQqqTLA/Y/vEsvvkJd77dYfbrjt58mR++eUXZs6c6bRzXl+oExMTmThxotPOXxDFplCbclof15WAbdvyHtytm2XEGxsLr7xiaX8cOWIZTcfHW24qvv32v8cPGGAZCd98c8GDtWpluSkYEwPR0ZYWB8CQIZbrDxhgaWPcf7+lTdKihWU0n5BgGb23aWN578iRluvfc4/lnE2aQJ8+1xZyb5Jf89raDyAcWAbE2DpObiZ6jlELNuqoFxbqlXtOu/xajzzyiPb399cxMTF6/Pjx+rXXXtPjxo3Lfb1x48Z63759et++fbpBgwZ68ODBulGjRrpLly46LS1Na631rl279E033aRjY2N1QkKC3r17t27RooUOCwvTcXFxevz48XrZsmX6lltu0VprfebMGX377bfrJk2a6BYtWujk5GSttdavvfaafuCBB3SHDh10dHS0njBhgtXMoaGh+qWXXtKxsbG6RYsW+vjx41prrffv3687deqkmzRpojt16qQPHDig//rrL122bFkdFRWl4+Li9O7du1351+lSmw6f1zWfX6gXbz527QvO+NwdN07rl18u+PuWLbPc8CuhKMrNxOuK+nlgOdDNuV8uhKu82L0hNcqFMHJeMpeuZLn0Wv/3f/9H1apVWbZsGcOGDbN57K5du3j88cfZsmUL4eHhzJ8/H4ABAwbw+OOPk5yczN9//02VKlV45513aNeuHRs2bMhz3tdee42EhAQ2btzImDFjGHTVfsrbt2/n119/Zc2aNfznP/8hM+db56ukpqbSsmVLkpOTad++PZ999hkATzzxBIMGDWLjxo0MGDCAp556itatW9OzZ0/GjRvHhg0bqF27dlH/ygyTs+Alz14fRXXHHTB9Ojz9tHPPW8I5MusjQikVnv3rYKAzsN3FuYSThAb68V7fOA6fu8xbP1v5ttYg0dHRxMfHA9CsWTP2799PSkoKR44c4Y7sb3eDgoIICQmxeZ4///yTgQMHAtCpUyfOnDnDhQsXALjlllsIDAykQoUKVKxYkRMnTuR5f0BAALfeeus1OQBWrlzJPdkzFgYOHMif1mYfeLGs7CXkvte3PoYMKdqJFyyAjRuhQoWCv7djR8tNSJGHIyPqKsAypdRGYC2WHrX8bXqR5lHlGNKuFt+sOciyHe67meLn54c5uyAApKf/+0DewKvu+vv6+pKVlVWoByBYe4/Knilg7RrX8/f3zz0+v2OuPmdxkbMyMc/DbVu1MiCNsMeRWR8btdYJWutYrXWM1nq0O4IJ5xrWpR71KpXi+XkbOZ+W4ZZrRkVFsT57NsD69evZt2+fzePDwsKIjIzk+++/B+DKlSukpaVRunRpUvK5CdS+ffvcG5fLly+nQoUKhOXM6S2C1q1bM3v2bABmzpxJ2+zZB7ayeJPcvT6uX5lYmJkawuVkCXkJEeTvy/i74jmbmsFrP25xyzV79+7N2bNniY+P55NPPqFevXp23zNjxgwmTpxIbGwsrVu35vjx48TGxuLn50dcXBwffPDBNce//vrrJCUlERsbywsvvMBXX33llOwTJ05k6tSpxMbGMmPGDCZMmABAv379GDduHAkJCezZs8cp1zJCpimn9VG8vlMorlRhvt20JzExUSclJTn9vKLoJizdxQdLdzJ5QFN6NKlidBxhkKVbTzB4ehI/PtGG2Mjwf1949FH45BPDcpVkSql1WutEa6/JiLqEeezG2sRGlmHUgk2cTEm3/wZRLOUueLn+ZqIUaY8khbqE8ff1YfxdcaRmmHjpu83yBPMSKmfWR56ViS1aGJBG2COFugSqU7E0z3Wtz9JtJ5i37rDRcYQBcnrUAdffTDS5b7sB4Tgp1CXUg22iuSG6HKN/2sqR85eNjpPHtGnTeOKJJ+wec/To0dzfDx482OHl3Y6cvzjLyMrej9rvuhLg62tAGmGPFOoSysdH8X7fOMxaM3Juslc+wfz6Qv3555/TqFEjt1zb5OUjz5xCnWdEvTrPNj7CA0ihLsFynmD+9x7nPcG8V69eNGvWjMaNGzNlypTcj5cqVYpRo0YRFxdHy5Ytc1cJ/vTTT7Ro0YKEhAQ6d+6cZ/VgSkoK0dHRucu/L168SFRUFHPnziUpKYkBAwYQHx/P5cuX6dixIzmzjRYvXkzTpk2Ji4vjpptuspr16NGjdOvWjbp16/Lcc8/lfnzJkiW0atWKpk2b0rdvXy5l774WFRXF6NGjadu2LXPnzs33OG+Qkb3gJeD6EfWjjxqQRtgjhbqE69e8Oh3rR/D2om3sPVX0QvPll1+ybt06kpKSmDhxImfOnAHy31Ojbdu2rFq1in/++Yd+/foxduzYa85XunRpOnbsyM8//wzA7Nmz6d27N3379iUxMZGZM2eyYcMGgoODc99z6tQpHn74YebPn09ycjJz5861mnXDhg3MmTOHTZs2MWfOHA4dOsTp06d58803Wbp0KevXrycxMZHx48fnvicoKIg///yTzp072zzO0+U7ol671oA0wh4/owMIYymleLd3LDd/sIIRc5OZN7R1kRZBTJw4kQULFgBw6NAhdu3aRfny5fPsqfHbb78BcPjwYe6++26OHTtGRkYG0dHRec45ePBgxo4dS69evZg6dWpukc/PqlWraN++fe65ypUrZ/W4m266iTJlygDQqFEjDhw4wPnz59m6dStt2rQBICMjg1ZXLau+++67c69h6zhPl1uorx9RC48khVpQKSyI0bc35unZG/h0xR4e61inUOdZvnw5S5cuZeXKlYSEhNCxY8fc/T3y21PjySefZPjw4fTs2ZPly5fz+uuv5zlvmzZt2L9/P3/88Qcmk4mYmBibObTWDu3Nkd9+I126dOGbb76x+p7Q0NDca9g6ztNlmsz4+qi8X5SnTjUmkLBJvpwKAHrGVeWWJlX44LedbDt2sVDnuHDhAmXLliUkJITt27ezKr8nWl/3nmrVqgHYXP49aNAg+vfvzwNX7UWR374brVq14o8//sjdW+Ts2bMO/xlatmzJX3/9xe7dludNpqWlsXPnzkIf56kyTGbrW5yuXOn+MMIuKdQCsLRA3ugVQ5ngAIZ/m5z7rXFBdOvWjaysLGJjY3nllVdo2dL+ozVff/11+vbtS7t27ahgY2vMAQMGcO7cOfr375/7sfvvv5+hQ4fm3kzMERERwZQpU7jzzjuJi4vLbVc4IiIigmnTptG/f39iY2Np2bIl27fn3dXX0eM8VUaWOW9/GuCqG8DCc8heH+IaOXtAPHFjHZ7tWt/oOLnmzZvHDz/8wIwZM4yOUiy8tGATS7YcJ+nlLte+kJgI8rlrCFt7fUiPWlyjc6NK9G0WyeTlu7mpYUUSapQ1OhJPPvkkixYt4pdffjE6SrGR74j6ySfdH0bYJa0PkccrtzWiSplgRnybzOUM4xd2TJo0id27dzu0TapwTEaW2fqMj4YN3R9G2CWFWuQRFuTPuD6x7D2dythfvafvKhyXaTLjb21E/dhj7g8j7JJCLaxqXacC97eOYupf+/l7z2mj4xSI1prNmzfn+/rOnTv54osv3JjI8+Q7ohYeSf6lRL6e79aA6AqhjJy7kZT0vE/w9lQpKSm0bds23y1cw8PDefnll4vdA2sLIsOUT6Fu1879YYRdUqhFvoIDfHn/rjiOXbjMmws95wnm9oSFhREUFHTNhk1Xq1ixIlOmTGHgwIG5TywvaTKy8ml9jBvn/jDCLinUwqamNcoytENt5iQd4r/bT9h/g4do1KiRzS1Pb7vtNrp27VpitzrNMJkJtDaidmDuu3A/KdTCrqc716VB5dI8P38T51Ld8wTzomrUqBFbtth+iO/777/PmjVrcp82XpLkOz1PeCT5lxJ2Bfr58sHd8ZxPy+Dl773j8V2NGze2+xCB0NBQZs2axVNPPcXBgwfdlMwz5DvrI3svE+FZpFALhzSsEsawLvX4edMxfthgvffrSey1PnI0a9aMYcOGMWjQIK9/GEBB5Dvr448/3B9G2CWFWjjskfa1SaxZlld+2MxRD3x819VyCrUjo//nnnsOs9nM+++/74ZkniHTpK0X6vvvd3sWYZ8UauEwXx/F+3fFYTJrnvXwx3dFRETg6+vL8ePH7R7r6+vLjBkzGDduHOvXr3dDOuNdyW/Wh43558I4UqhFgdQsH8qr2Y/vmvb3fqPj2ORInzpHzZo1+fDDDxkwYABpaWkuTma8jCyT9VkfwiPZ/ZdSSlVXSi1TSm1TSm1RSj3tjmDCc93dvDqdG1bk3cXb2X0y737QnsLRPnWOAQMGkJCQwMiRI12YyjPk2/rw0gchFHeOfEnNAkZorRsCLYHHlVLuedSz8EhKKd6+M5bQQD+embOhUHtXu0NBCzXA5MmTWbhwYbHfqS/fBwcsWuT+MMIuu4Vaa31Ma70++9cpwDagmquDCc8WUTqQMXc0YfORi0z67y6j41jlyFzq64WHhzN9+nQGDx7MyZMnXZTMWCazxmTWBPj65n1x+nT3BxJ2FahJpZSKAhKA1VZeG6KUSlJKJZ06dcpJ8YQn6xZTmd5NI/l42W7WHzxndJw8GjduzJYtWwo877tDhw7cd999PPTQQ14xZ7ygMk2W74D8/Qr/EGPhXg4XaqVUKWA+8IzWOs9D9bTWU7TWiVrrxIiICGdmFB7stZ6WvauHz9lAWkaW0XGuUbFiRQAKM3D4z3/+w9GjR/n000+dHctwVzKzn0BubdZHCejPeyOHCrVSyh9LkZ6ptf7OtZGENwkL8uf9u+I4cDaNMb941sZNSqlC9akBAgICmDlzJi+//LJXPQvREelZloU9Qf5WWh9Vqrg5jXCEI7M+FPAFsE1rPd71kYS3aVmrPIPbRvP1qoMs2+FZfd3C9KlzNGjQgDfeeIMBAwaQkeEde5w4ImdEbbVQDx/u5jTCEY6MqNsAA4FOSqkN2T96uDiX8DIjbq5P/UqleW7eRo/auKkgc6mtGTp0KFWrVuX11193XiiD/TuilnnU3sKRWR9/aq2V1jpWax2f/aN4z10SBRbk78v4u+M8buOmwrY+ciil+OKLL5g6dSorVqxwYjLjpGdmF2o/KyPqLl3yfkwYTr6kCqdpXLWMx23cVNRCDZabkp999hmDBg3i/PnzzglmoHRbrY9Ro9ycRjhCCrVwKk/buKlKlSpcuXKF06eL9tzHW2+9lR49evD44487KZlxckfU1lofHTu6N4xwiBRq4VSetnGTUqrIfeoc7733HuvXr2fWrFlOSGacfwu1lRG18EhSqIXT1SwfyisetHGTM9ofACEhIcycOZNnnnmGAwcOOCGZMdKzclofVj79K1RwcxrhCCnUwiX6Na/OTQ08Y+MmZxVqgKZNmzJixAivftBAzog60NrNxMWL3ZxGOEIKtXAJpRRv927iERs3ObNQAzz77LMopRjnpU/svmKr9dGvn5vTCEdIoRYuU7F0kEds3JSz54ez+Pr6Mn36dMaPH8+6deucdl53+XfWh5VP/9273ZxGOEIKtXApT9i4qVq1aqSmpnL27FmnnbNGjRpMmDDBKx80IDcTvY8UauFyRm/clLPnx7Ztzt2LpH///iQmJjJixAinntfV0rNM+Poo64/iWrDA/YGEXVKohct5wsZNzu5T5/j4449ZtGgRCxcudPq5XSU900xQfo/hkie8eCQp1MItjN64ydl96hxlypRhxowZPPzww5w4ccLp53eF9ExT/m2Pb791bxjhECnUwm2M3LjJVSNqgHbt2vHggw/y4IMPesweJ7akZ5qlP+1lpFALt7l646aXFmxya1FzZaEGeO211zhx4gSffPKJy67hLOlZJgLz2znv1VfdG0Y4RAq1cKvGVcswvEt9Fm0+zrx1h9123erVq3P+/HkuXLjgkvPnPGjg1VdfdfpNS2e7kmm2vnMeQFCQe8MIh0ihFm43pH0tbogux+s/buHgGfdMbfPx8aFhw4YuHVXXr1+ft956y+MfNHAly5T/XtQvveTeMMIhUqiF2/n6KD64Ox4fH8Uzc/4hy+SeVYvO2pzJliFDhlC9enVe9eAWgs2bicIjSaEWhqgWHsybvWJYf/A8k5fvccs1Xd2nBsuc7c8//5zp06ezfPlyl16rsNIyTIQE5FOob7vNvWGEQ6RQC8PcHl+N2+OrMuH3XfzjhlWL7ijUABEREXzxxRfcd999nDtnzGpMWyyF2s/6i4895t4wwiFSqIWhRt8eQ+WwIIbN2UDqFdeuWizKg24Lqnv37tx222089thjHjdlLy0jK/8Rdffu7g0jHCKFWhiqTPC/qxbfWOja0W5UVBRnzpzh4sWLLr1OjnHjxpGcnMzMmTPdcj1HpV2xMaIWHkkKtTBcy1rlGdqhNrPXHuLXLcdddh0fHx8aNGjA9u3bXXaNqwUHBzNr1iyGDRvG/v373XJNe7TWpGZkERqYz4g6MtK9gYRDpFALjzCscz1iqoXxwvyNnLyY7rLruKtPnSM+Pp7nnnvOYx40cCXLjFlDcH6tj++/d2se4Rgp1MIjBPj58OHdCVzONPHsvI0u6+u6s0+dY8SIEfj5+fHuu++69brWpGVYvliE5tf66NXLfWGEw6RQC49Rp2IpRvVoyIqdp/jKRc9adNXmTLb4+Pjw1Vdf8eGHH5KUlOTWa18v54ZtviPqw+5bLSocJ4VaeJR7W9bkxvoRvL1oOztPOP9Zi67Yl9oR1atXZ9KkSQwYMIDU1FS3Xz+H3RG18EhSqIVHUUoxtk8cpQL9eHr2Bq5kObevGx0dzYkTJwwplnfffTctWrQw9EEDqdkPbgjJ72biokVuTCMcJYVaeJyI0oG82zuWbccuMn7JTqee29fXl3r16hm2cdJHH33EkiVL+PHHHw25/uXsEXVIfkvIJ092YxrhKLuFWin1pVLqpFJqszsCCQHQuVEl7mlRgyn/28vfe0479dzu2PMjP2FhYUyfPp0hQ4Zw/LjrpiLmJ6dHHRqYT+vjp5/cmEY4ypER9TSgm4tzCJHHy7c0JLp8KCO+TeZCWqbTzuvuKXrXa9u2LYMHD+aBBx5w+6rFnB51visThUeyW6i11isA5z2+WQgHhQT48WG/eE6lXGHU98570IDRhRosDxo4c+YMH3/8sUPHn7l0hd0nL7H/dGqR+vb/Fup8RtRjxhT63MJ15Nav8GixkeEM61KPcb/u4KaGFbkjoegr54yYS309f39/vv76a1q3bk2nTp1o1KjRNa9rrVmz7yzfbzjC8h2nOHbh30VAAX4+tK1TgSHta9GyVvkCXTfN3s3EdNctNhKF57RCrZQaAgwBqFGjhrNOKwRDO9Rm+Y6TvPr9FhJrlqN6uZAina927docPXqUtLQ0QkKKdq6iqFevHm+//TYDBgxg1apVBAYGorVm2Y6TTFi6i+TDFwgJ8OXG+hVJqBFOxbAgMrLMbDl6gYUbj9FvyiruSoxk9O0xDu8vnXrFzs3E0aOhZ09n/RGFkzht1ofWeorWOlFrnRgREeGs0wqBr49i/F3xAAz/dgMmc9FaIH5+ftStW5cdO3Y4IV3RDB48mJo1a/LKK69w6GwaD05by4PTkjiTmsHbdzYh6eXOfDygKYPb1aJnXFX6NIvktdsa87/nbuTxG2vzbdJh7vtyTe5sDntS0jMJ9vfFz1cmfHkT+dcSXqF6uRDe6BXD2v3n+Oi/u4t8Pk/oU4Nl3viUKVP4fNp02jw9idX7zvLyLQ1Z9mxH+t9QI99ecpC/LyO7NmBCv3jW7D/Ls/OSHerhp6RnUTrIxjfSd91V2D+KcCFHpud9A6wE6iulDiulHnJ9LCHy6pVQjTsSqjHh950k7S/a/W1P6FMDXLqSxZu/H8G/42Oc+eUD5j4Yy+B2tfB3cMR7e3w1Rnatz88bjzFn7SG7x6dcybRdqPv3dzS6cCNHZn3011pX0Vr7a60jtdZfuCOYENaMvr0xkWVDeHr2Bi5cLvyUPU8YUe8/nUrPSX+ycONRXhnanwfv6cvo54cVeHbL0Pa1aRFdjncWb+dcqu2H6lpG1P75H3DHHQW6tnAPaX0Ir1I6yJ8J/eI5cTGdUQsKP2XPyEUvAGv3n+WOyX9xLi2DmYNb8kSnuowdO5YtW7bw9ddfF+hcPj6KN3rFkJKexcfLbLeFLtprfQiPJIVaeJ2EGmUZ1qUeCzceY+66wu32VqdOHQ4dOkS6AdPRfkw+yoDPVhMeEsCCx9rQqrZlil1wcDAzZ85k+PDh7Nu3r0DnrFepNLfHVWXm6oOctTGqvpSeSZitEXWdOgW6rnAPKdTCKw3tUJtWtcrz+o9b2HvqUoHf7+/vT61atdw+82PW6oM8Pfsf4quH892jrYmqEHrN63FxcTz//PMMHDiQrKyCPUPysRtrcznTxKzVB/I9xu7NxNmzC3RN4R5SqIVX8vVRfHB3PAF+Pjw9ewMZWeYCn8Pdfeov/tzHSws20bFeBNMfuoGyoQFWjxs+fDiBgYG88847BTp/nYqlaV27PHOSDmHOZwqj3ULdTXaL8ERSqIXXqlwmiLG9Y9l05ALvLSn4yNidhfrjZbt5Y+FWusdU5tOBiTYXqOQ8aGDSpEmsWbOmQNe5u3l1Dp29zKq9Z/K8lmkycznTRKlAG62P087dAEs4hxRq4dVublyZe1vWYMqKvazYeapA73XXDcWPl+1m3K87uCOhGpP6JxDgZ//TLjIyko8++ogBAwZw6ZLjrZ2ujSsTEuDLz5uO5XntUrqllSI3E72PFGrh9Ub1aETdiqUY/m0ypy9dcfh97hhRT/trH+N+3cHt8VV5r29cgVYE9u3blzZt2jB8+HCH3xPk70vH+hH8tvVEnvZHiiOFevlyh68l3EcKtfB6wQG+TLongYvpmYyc69gKPYC6deuyb98+rlxxvLgXxLdrD/H6T1vp2rgS7/eNw9dHFfgcEydOZOnSpXxfgKeDd21cmZMpV/jn0PlrPn4x3TLv3OY86rfeKnBG4XpSqEWx0KByGKN6NGTZjlNMc/DBuIGBgURFRbFr1y6n5/kp+SjPf7eR9vUimNg/odB7a4SFhTFjxgyGDh3KsWN52xnWdKgXgVLw565r+80XsxcIhYfYKNS//VaonMK1pFCLYmNQq5rc1KAib/+yna1HLzr0Hlf0qZfvOMmwORtoHlWOT+9tRqBf0Tbpb9OmDUOGDOGBBx7AbLY/uyU8JIDGVcPyPBnnbJplfnXZEOuzTYTnkkItig3Lg3FjCQ/x58lv1ju0o5yz+9Sbj1zgsZnrqVepNF/cl0iwk56k8sorr3Du3Dk++ugjh45vVas8/xw8f83fwbnsp+SUtTWiHj++SDmFa0ihFsVK+VKBjL8rnr2nU3njZ/sF2JmbMx06m8b9U9dSNiSAaQ80t90LLqCcBw2MHj3aobyta1cgw2Rm/cFzuR87n71iMdzWiNrB9opwLynUothpW9fy9JNZqw/yi5Vpaldz1oj6XGoG901dQ6bJzFcPNqdiWFCRz3m9unXr8s4773DPPffYvQGaUCMcgA1X3VA8l5ZJaICv7emB48Y5IalwNinUolga0aU+cdXDeX7eRg6eScv3uPr167N3714yMwu/E196ponB05M4fO4yn9+XSJ2KpQt9LnseeughatWqxahRo2weFx4SQM3yIWw8fD73Y+fTMmyPpoXHkkItiqUAPx8+6p8ACp78Zn2+S8yDgoKoXr06u3cX7mEEZrNm2JwNrD94jg/vjqd5VLmixLZLKcVnn33GN998w++//27z2LjIcDYevpD7+7NpGZTLZ9l6rkGDnBFTOJkUalFsVS8Xwrg+sSQfvsDYxdvzPa4ofer3luxg0ebjjOrRkB5NqhQ2aoFUqFCBqVOncv/993P2bP4PUIiNLMOxC+mcTLHsEHguLdP21DyA7t2dGVU4iRRqUax1i6nCfa1q8vmf+1i69YTVYwrbp17wz2EmL99D/xtq8FDb6KJGLZCbb76Z3r1788gjj+S7wCc2MhyALdlTFc+nZdifmidPePFIUqhFsfdij4Y0rhrGiLnJHDl/Oc/rhSnU6w+e4/n5m2hZqxyjb2+MUgVfdVhUb7/9Ntu2bWP69OlWX69XqRQAu06kAJYbnjan5gmPJYVaFHtB/r58dE9TskxmnvrmHzJN1/arC7ro5cj5ywyZvo7KYUF8MqCZw883dLbg4GBmzZrFs88+y969e/O8Hh4SQETpQHaduESWyczF9Cz7NxNjYlyUVhSFFGpRIkRXCGXMnU1Yd+AcH/y285rX6tevz65duxzaqD8tI4uHv0riSqaJL+5LzHdPaXeJjY3lxRdf5N5777Wav16lUuw8eYnz2cvH7d5MnDbNBSlFUUmhFiXG7fHV6Ne8OpOX7+GPq7ZEDQkJoWrVquzZs8fm+3NmeGw/fpGJ9yRQt5LrpuEVxDPPPENISAhjxozJ81rdiqXZfSIl96G3dm8mdujgioiiiKRQixLltdsaU79SaYbP2cDJi/8+L9GRPvWHv+/i1y0neKlHQ26sX9HVUR3m4+PDtGnT+Oijj1i1atU1r9WtVIrUDFPuTnoRpQNtnyw11UUpRVFIoRYlSnCALx/dk0BahomnZ2/AlL1n89V9amuzKH7beoKJv++id9NIt8/wcERkZCSTJ0/m3nvvveZBA7UjLDcUV++1TOOrWNr5KyaF60mhFiVO3UqlGX17Y1buPcO4hf+QlJSUO5d61qxZjBgx4prj9566xPA5G4ipFsZbd8QYMsPDEX369KFdu3Y888wzAEyYMIGyvpaWx9r92YU6zM6I+roRufAMUqhFidSnWSR3JlTj41830eXmbgQHB7N161Zmz55Ns2bNco9LvZLFIzPW4e/nw//d28zmsw49wcSJE1m2bBkLFixg4cKF7NnyD0H+Phw8m0aQvw+lA+08hmvkSPcEFQUihVqUSEop3ugVQ71aNQlrP5BXX/sPO3bsYPny5fTo0QOwtEBGzktmz6lLTOqfQGTZEINT26a1Zv369UybNo2hQ4cSGRnJzp07iSofCljaHna/G/jf/9yQVBSUPOVSlFihgX58cm8zep67zKVDyZjNu4iJiaFs2bIATFmxl182HefF7g1oU6eCwWntM5lMjB49mmPHjtGxY0dWrlxJYGAgNdu0ZfvxFCrZa3sIjyUjalGi1atUmrd7N4F2j2BGkZCQAMBfu0/z7uLt3NKkCkPa1zI4pWP8/PxYunQp7733Hlu3bmXv3r38/vvv14yo7Zo82cUpRWE4VKiVUt2UUjuUUruVUi+4OpQQ7nRHQiQDOzQi4r5JdHtwJIfPpfHErPXUqViKsX1iPfbmoTVKKXr06MGGDRsYM2YMVapUIaqCpVDbnZoHsG2bixOKwrBbqJVSvsDHQHegEdBfKdXI1cGEcKdXb21E0yYNGLFgG7dO+pMsk+bTgYmE2rv55qF8fX159tlnWbFiBTXLW3rrdmd8AEya5OJkojAcGVHfAOzWWu/VWmcAs4HbXRtLCPcK8vdl8j3NyMgycz4tkw/ujic6eyTq7epXKk2wvy8NK4cZHUUUkiPDhWrAoat+fxhocf1BSqkhwJDs315SSu0oejyrKgCn7R7luSS/sRzK3+VdNyQpnEL//Xd608EDXdvq8eb/P67OXjO/Fxwp1Nb+1fIs3dJaTwGmFCBUoSilkrTWia6+jqtIfmNJfmN5c34jszvS+jgMVL/q95HAUdfEEUIIcT1HCvVaoK5SKlopFQD0A350bSwhhBA57LY+tNZZSqkngF8BX+BLrXXhHjDnHC5vr7iY5DeW5DeWN+c3LLvK73lrQgghPIOsTBRCCA8nhVoIITyc1xZqpdST2cvatyilxhqdpzCUUs8qpbRSyvN3/LmKUmqcUmq7UmqjUmqBUirc6Ez2ePM2CEqp6kqpZUqpbdn/3582OlNhKKV8lVL/KKUWGp2loJRS4Uqpedn/77cppVq58/peWaiVUjdiWR0Zq7VuDLxncKQCU0pVB7oAB43OUgi/ATFa61hgJ/CiwXlsKgbbIGQBI7TWDYGWwONelj/H04C3biYyAVistW4AxOHmP4dXFmrgUeAdrfUVAK31SYPzFMYHwHNYWTzk6bTWS7TWOY+8XoVlbr0n8+ptELTWx7TW67N/nYKlSFQzNlXBKKUigVuAz43OUlBKqTCgPfAFgNY6Q2t93p0ZvLVQ1wPaKaVWK6X+UEo1NzpQQSilegJHtNbJRmdxggeBRUaHsMPaNgheVehyKKWigARgtcFRCupDLAMTs8E5CqMWcAqYmt26+Vwp5daNYDx2azCl1FKgspWXRmHJXRbLt4HNgW+VUrW0B801tJP/JeBm9yYqGFv5tdY/ZB8zCsu35TPdma0QHNoGwdMppUoB84FntNYXjc7jKKXUrcBJrfU6pVRHg+MUhh/QFHhSa71aKTUBeAF4xZ0BPJLWunN+rymlHgW+yy7Ma5RSZiwbppxyVz578suvlGoCRAPJ2fscRwLrlVI3aK2PuzGiTbb+/gGUUvcBtwI3edIXyHx4/TYISil/LEV6ptb6O6PzFFAboKdSqgcQBIQppb7WWt9rcC5HHQYOa61zvouZh6VQu423tj6+BzoBKKXqAQF4yY5cWutNWuuKWusorXUUlv8ETT2pSNujlOoGPA/01FqnGZ3HAV69DYKyfEX/AtimtR5vdJ6C0lq/qLWOzP7/3g/4rxcVabI/Nw8ppepnf+gmYKs7M3jsiNqOL4EvlVKbgQzgPi8Y1RUnHwGBwG/Z3xWs0loPNTZS/jxwG4SCagMMBDYppTZkf+wlrfUvxkUqcZ4EZmZ/od8LPODOi8sSciGE8HDe2voQQogSQwq1EEJ4OCnUQgjh4aRQCyGEh5NCLYQQHk4KtRBCeDgp1EII4eH+H5JTXmtx7nJVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(-7,7,.01)\n",
    "ys = np.abs(xs - 1/(3-xs))\n",
    "\n",
    "plt.xlim([-7,7])\n",
    "plt.ylim([0,6])\n",
    "\n",
    "\n",
    "plt.plot(xs,ys)\n",
    "\n",
    "plt.vlines(3,0,10,color='r',ls='dashed',lw=.8)\n",
    "\n",
    "\n",
    "plt.annotate('asymptote',(3.2,3),c='r')\n",
    "plt.annotate('function not\\nanalytic here',(2.6,0),c='w',xytext=(-1.7,2.5),arrowprops={'arrowstyle':'->', 'lw':1})\n",
    "plt.annotate('function not\\nanalytic here',(.35,0),xytext=(-1.7,2.5),arrowprops=dict(arrowstyle='->',lw=1))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00016-0454d782-9624-475e-ab93-1e21ec15de18",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Log Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Very often data is better displayed using logarithmic scaling on the axes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00042-166aaa7b-a80c-4312-a717-1eba740acbb0",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Log-log plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00043-6a00670e-ce31-4932-8810-fdc34e2b2043",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "One can make a log-log plot using `plt.loglog()` in the place of `plt.plot()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "cell_id": "00043-515d5e01-d18f-49b1-ab97-a6691173edcc",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 525,
    "execution_start": 1625490122908,
    "source_hash": "a3db383d",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0.1,20,.01)\n",
    "y = np.exp(x)\n",
    "\n",
    "plt.loglog(x,y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00043-deab9027-f11d-4742-8f7c-026491ababd9",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "### Semi-log plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also scale just one axis with a log scaling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "cell_id": "00046-426c6819-7ad7-410c-8a6c-3fa1d5f5ebd8",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 324,
    "execution_start": 1625490253691,
    "source_hash": "d792165",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0.1,20,.01)\n",
    "y = np.exp(x)\n",
    "\n",
    "plt.semilogy(x,y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0.1,20,.01)\n",
    "y = np.log(x)\n",
    "\n",
    "plt.semilogx(x,y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "00000-840e3183-be39-4a62-8462-448490e47bfe",
    "deepnote_cell_type": "markdown",
    "tags": []
   },
   "source": [
    "## Figure Object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far we have been plotting rather recklessly without looking into what objects we have been creating in our plots. This is fine when we only want to get a quick look at our data but for puplication or the like we will require more costomisability and to put this on more solid footing. \n",
    "\n",
    "One creates a figure object using the `plt.figure()` function. We can specify the figure dimensions in inches as a tupple using the `figsize` keyword. We then can add a a set of axes to this figure using the `.add_axes()` attribute funtion of the figure. This function takes in the argument of a list that specifies things about our axes. The list elements are taken as the `[left, bottom, width, height]` as fractions of the size height an width."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9,4))\n",
    "ax = fig.add_axes([0.1,0.1,.8,.8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then plot on this set of axes, now using the attribute of the axis we can plot in a similar way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9,4))\n",
    "ax = fig.add_axes([0,0,1,1])\n",
    "\n",
    "x = np.arange(0,10.2,.2)\n",
    "ax.plot(x, np.sin(x), c='green', lw=.5, ls='--', marker='*', label='$\\sin(x)$')\n",
    "ax.plot(x, np.cos(x), c='blue', lw=2, ls='-.', label='$\\cos(x)$')\n",
    "\n",
    "ax.set_xlim(0,10)\n",
    "ax.set_ylim(-1.03,1.03)\n",
    "ax.set_title('Trig Functions')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many of the functions act the same as before but now they are attributes of the axis object and have `set_` before them.\n",
    "\n",
    "We can also not save this image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig('first_image.png')"
   ]
  }
 ],
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