python/optimal_codes_sss_3_1_4b.ipynb

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    "# Linear codes for SSS-based polynomial masking\n",
    "\n",
    "### The SSS-based masking is a special case of GCM (Generalized Code-based masking)\n",
    "### $n=3$ shares, $t=1$, $\\ell=4$ bits: (3,1)-SSS (Shamir's Secret Sharing)"
   ]
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   "cell_type": "markdown",
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    "Parameters:\n",
    "\n",
    "- $Z=(X + \\alpha_1Y_1, X + \\alpha_2Y_1, X + \\alpha_3Y_1)=X\\mathbf{G} + Y\\mathbf{H}$ where $X, Y=(Y_1)$ and $Z$ are the sensitive variable, a mask and the protected variable, respectively, where $\\alpha_i$ for $1\\leq i\\leq 3$ are three public points in SSS-scheme\n",
    "- $\\mathbf{G} = [1, 1, 1]$ and $\\mathbf{H} = [\\alpha_1, \\alpha_2, \\alpha_3]$ are two generator matrices of codes $\\mathcal{C}$ and $\\mathcal{D}$, resp.\n",
    "- $\\alpha_i\\in \\mathbb{F}_{2^\\ell}\\backslash\\{0\\}$ and $\\alpha_1\\neq\\alpha_2\\neq\\alpha_3$, thus there are ${15}\\choose{3}$=455 linear codes for (3,1)-SSS\n",
    "- Each nonzero element over $\\mathbb{F}_{2^\\ell}$ can be denoted as $\\alpha^i$ where $i\\in\\{0, 1, \\ldots, 14\\}$, the corresponding irreducible polynomial is $g(\\alpha) = \\alpha^4 + \\alpha +1$\n",
    "- Due to equivalence of linear codes, we simplify the enumeration by choosing $(\\alpha_1, \\alpha_2, \\alpha_3)=(\\alpha^i, \\alpha^j,\\alpha^k)$ where $i=0$ and $0<j<k$. Therefore, we get 91 linear codes"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import re\n",
    "import pandas as pd # Pandas for tables\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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     "end_time": "2020-10-18T20:14:20.380033Z",
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    "def read_log(file_name):\n",
    "    \n",
    "    pow_ind = []\n",
    "    dim_all = []\n",
    "    d_orig_w = []\n",
    "    d_dual_w = []\n",
    "    d_dual_b = []\n",
    "    with open(file_name, 'r') as fp:\n",
    "        wd = fp.read().split(\"\\n\")[:]\n",
    "        len_all = 0\n",
    "        for i in range(len(wd)):\n",
    "            if wd[i].startswith(\"j, k =\"):\n",
    "                pow_ind.append([int(i) for i in re.findall(r\"\\d+\", wd[i])])\n",
    "                len_all = len_all + 1\n",
    "            elif wd[i].startswith(\"Dimension:\"):\n",
    "                dim_all.append([int(i) for i in re.findall(r\"\\d+\", wd[i])])\n",
    "            elif wd[i].startswith(\"WD orig D (word):\"):\n",
    "                d_orig_w.append([int(i) for i in re.findall(r\"\\d+\", wd[i])])\n",
    "            elif wd[i].startswith(\"WD dual D (word):\"):\n",
    "                d_dual_w.append([int(i) for i in re.findall(r\"\\d+\", wd[i])])\n",
    "            elif wd[i].startswith(\"WD dual D  (bit):\"):\n",
    "                d_dual_b.append([int(i) for i in re.findall(r\"\\d+\", wd[i]+wd[i+1])])\n",
    "            else:\n",
    "                continue\n",
    "    \n",
    "    return pow_ind, d_dual_b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Loading all weight enumerators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
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     "output_type": "stream",
     "text": [
      "91\n"
     ]
    }
   ],
   "source": [
    "pow_ind, d_dual_b = read_log(\"./magma_paper/gen_codes_sss_3_1_4b.log\") # indices and Weight distributions\n",
    "\n",
    "print(len(pow_ind)) # 91 entries: 91 for (3,1)-SSS\n",
    "#print(len(d_dual_b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Generating values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "source": [
    "alpha_all = np.array(['$\\\\alpha^{%d}$'%i for i in np.arange(15)])\n",
    "d_all = np.zeros(len(pow_ind))\n",
    "B_all = np.zeros(len(pow_ind))\n",
    "alpha_2 = np.zeros(len(pow_ind), dtype=int)\n",
    "alpha_3 = np.zeros(len(pow_ind), dtype=int)\n",
    "for i in range(len(pow_ind)):\n",
    "    d_all[i] = d_dual_b[i][2]\n",
    "    B_all[i] = d_dual_b[i][3]\n",
    "    alpha_2[i] = pow_ind[i][0]\n",
    "    alpha_3[i] = pow_ind[i][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Defining styles of dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
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    "ExecuteTime": {
     "end_time": "2020-10-18T20:14:35.707742Z",
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    "# Set properties for th, td and caption elements in dataframe\n",
    "th_props = [('font-size', '14px'), ('text-align', 'left'), ('font-weight', 'bold'), ('background-color', '#E0E0E0')]\n",
    "td_props = [('font-size', '13px'), ('text-align', 'left'), ('min-width', '80px')]\n",
    "cp_props = [('font-size', '16px'), ('text-align', 'center')]\n",
    "# Set table styles\n",
    "styles = [dict(selector=\"th\", props=th_props), dict(selector=\"td\", props=td_props), dict(selector=\"caption\", props=cp_props)]\n",
    "cm_1 = sns.light_palette(\"red\", as_cmap=True)\n",
    "cm_2 = sns.light_palette(\"purple\", as_cmap=True, reverse=True)"
   ]
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       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col3 {\n",
       "            background-color:  #ffbaba;\n",
       "            color:  #000000;\n",
       "            background-color:  #982b98;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col3 {\n",
       "            background-color:  #ff0e0e;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #f8d8f8;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col2 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col3 {\n",
       "            background-color:  #ff0000;\n",
       "            color:  #f1f1f1;\n",
       "            background-color:  #ffe5ff;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col3 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "            background-color:  #800080;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col3 {\n",
       "            background-color:  #ffd7d7;\n",
       "            color:  #000000;\n",
       "            background-color:  #880e88;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col3 {\n",
       "            background-color:  #ffc9c9;\n",
       "            color:  #000000;\n",
       "            background-color:  #901d90;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col3 {\n",
       "            background-color:  #ffbaba;\n",
       "            color:  #000000;\n",
       "            background-color:  #982b98;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col3 {\n",
       "            background-color:  #ffbaba;\n",
       "            color:  #000000;\n",
       "            background-color:  #982b98;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col3 {\n",
       "            background-color:  #ffbaba;\n",
       "            color:  #000000;\n",
       "            background-color:  #982b98;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col3 {\n",
       "            background-color:  #ff9e9e;\n",
       "            color:  #000000;\n",
       "            background-color:  #a848a8;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col3 {\n",
       "            background-color:  #ff9e9e;\n",
       "            color:  #000000;\n",
       "            background-color:  #a848a8;\n",
       "            color:  #f1f1f1;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col2 {\n",
       "            background-color:  #ffe5e5;\n",
       "            color:  #000000;\n",
       "        }    #T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col3 {\n",
       "            background-color:  #ff8181;\n",
       "            color:  #000000;\n",
       "            background-color:  #b865b8;\n",
       "            color:  #000000;\n",
       "        }</style><table id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77ae\" ><caption>Tab. I All linear codes for (3,1)-SSS-based masking with $n=3$ shares over $\\mathbb{F}_{2^4}$.</caption><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >$\\alpha_2$</th>        <th class=\"col_heading level0 col1\" >$\\alpha_3$</th>        <th class=\"col_heading level0 col2\" >$d_{\\mathcal{D}}^\\perp$</th>        <th class=\"col_heading level0 col3\" >$B_{d_{\\mathcal{D}}^\\perp}$</th>        <th class=\"col_heading level0 col4\" >Weight Enumerators</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow0_col0\" class=\"data row0 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow0_col1\" class=\"data row0 col1\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow0_col2\" class=\"data row0 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow0_col3\" class=\"data row0 col3\" >8</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow0_col4\" class=\"data row0 col4\" >[0, 1, 2, 8, 3, 10, 4, 28, 5, 50, 6, 50, 7, 62, 8, 35, 9, 6, 10, 6, 1, 3]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow1_col0\" class=\"data row1 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow1_col1\" class=\"data row1 col1\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow1_col2\" class=\"data row1 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow1_col3\" class=\"data row1 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow1_col4\" class=\"data row1 col4\" >[0, 1, 2, 6, 3, 14, 4, 22, 5, 52, 6, 64, 7, 48, 8, 33, 9, 12, 10, 2, 11, 2, 1, 4]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow2_col0\" class=\"data row2 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow2_col1\" class=\"data row2 col1\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow2_col2\" class=\"data row2 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow2_col3\" class=\"data row2 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow2_col4\" class=\"data row2 col4\" >[0, 1, 2, 4, 3, 16, 4, 23, 5, 48, 6, 72, 7, 48, 8, 23, 9, 16, 10, 4, 12, 1, 1, 5]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow3_col0\" class=\"data row3 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow3_col1\" class=\"data row3 col1\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow3_col2\" class=\"data row3 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow3_col3\" class=\"data row3 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow3_col4\" class=\"data row3 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 1, 6]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow4_col0\" class=\"data row4 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow4_col1\" class=\"data row4 col1\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow4_col2\" class=\"data row4 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow4_col3\" class=\"data row4 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow4_col4\" class=\"data row4 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 1, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow5_col0\" class=\"data row5 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow5_col1\" class=\"data row5 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow5_col2\" class=\"data row5 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow5_col3\" class=\"data row5 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow5_col4\" class=\"data row5 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 1, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow6_col0\" class=\"data row6 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow6_col1\" class=\"data row6 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow6_col2\" class=\"data row6 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow6_col3\" class=\"data row6 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow6_col4\" class=\"data row6 col4\" >[0, 1, 2, 3, 3, 14, 4, 30, 5, 52, 6, 58, 7, 48, 8, 33, 9, 12, 10, 3, 11, 2, 1, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow7_col0\" class=\"data row7 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow7_col1\" class=\"data row7 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow7_col2\" class=\"data row7 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow7_col3\" class=\"data row7 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow7_col4\" class=\"data row7 col4\" >[0, 1, 2, 3, 3, 13, 4, 30, 5, 56, 6, 58, 7, 42, 8, 33, 9, 16, 10, 3, 11, 1, 1, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow8_col0\" class=\"data row8 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow8_col1\" class=\"data row8 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow8_col2\" class=\"data row8 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow8_col3\" class=\"data row8 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow8_col4\" class=\"data row8 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 1, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow9_col0\" class=\"data row9 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow9_col1\" class=\"data row9 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow9_col2\" class=\"data row9 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow9_col3\" class=\"data row9 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow9_col4\" class=\"data row9 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 1, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow10_col0\" class=\"data row10 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow10_col1\" class=\"data row10 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow10_col2\" class=\"data row10 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow10_col3\" class=\"data row10 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow10_col4\" class=\"data row10 col4\" >[0, 1, 2, 4, 3, 12, 4, 28, 5, 58, 6, 58, 7, 42, 8, 35, 9, 14, 10, 2, 11, 2, 1, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow11_col0\" class=\"data row11 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow11_col1\" class=\"data row11 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow11_col2\" class=\"data row11 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow11_col3\" class=\"data row11 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow11_col4\" class=\"data row11 col4\" >[0, 1, 2, 6, 3, 12, 4, 26, 5, 52, 6, 60, 7, 52, 8, 29, 9, 12, 10, 6, 1, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow12_col0\" class=\"data row12 col0\" >$\\alpha^{1}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow12_col1\" class=\"data row12 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow12_col2\" class=\"data row12 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow12_col3\" class=\"data row12 col3\" >8</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow12_col4\" class=\"data row12 col4\" >[0, 1, 2, 8, 3, 10, 4, 28, 5, 50, 6, 50, 7, 62, 8, 35, 9, 6, 10, 6, 2, 3]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row13\" class=\"row_heading level0 row13\" >13</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow13_col0\" class=\"data row13 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow13_col1\" class=\"data row13 col1\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow13_col2\" class=\"data row13 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow13_col3\" class=\"data row13 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow13_col4\" class=\"data row13 col4\" >[0, 1, 2, 6, 3, 12, 4, 26, 5, 52, 6, 60, 7, 52, 8, 29, 9, 12, 10, 6, 2, 4]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row14\" class=\"row_heading level0 row14\" >14</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow14_col0\" class=\"data row14 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow14_col1\" class=\"data row14 col1\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow14_col2\" class=\"data row14 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow14_col3\" class=\"data row14 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow14_col4\" class=\"data row14 col4\" >[0, 1, 2, 4, 3, 14, 4, 26, 5, 52, 6, 64, 7, 48, 8, 29, 9, 12, 10, 4, 11, 2, 2, 5]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row15\" class=\"row_heading level0 row15\" >15</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow15_col0\" class=\"data row15 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow15_col1\" class=\"data row15 col1\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow15_col2\" class=\"data row15 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow15_col3\" class=\"data row15 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow15_col4\" class=\"data row15 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 2, 6]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row16\" class=\"row_heading level0 row16\" >16</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow16_col0\" class=\"data row16 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow16_col1\" class=\"data row16 col1\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow16_col2\" class=\"data row16 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow16_col3\" class=\"data row16 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow16_col4\" class=\"data row16 col4\" >[0, 1, 2, 2, 3, 16, 4, 30, 5, 48, 6, 64, 7, 48, 8, 25, 9, 16, 10, 6, 2, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row17\" class=\"row_heading level0 row17\" >17</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow17_col0\" class=\"data row17 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow17_col1\" class=\"data row17 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow17_col2\" class=\"data row17 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow17_col3\" class=\"data row17 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow17_col4\" class=\"data row17 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 2, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row18\" class=\"row_heading level0 row18\" >18</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow18_col0\" class=\"data row18 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow18_col1\" class=\"data row18 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow18_col2\" class=\"data row18 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow18_col3\" class=\"data row18 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow18_col4\" class=\"data row18 col4\" >[0, 1, 2, 2, 3, 16, 4, 31, 5, 48, 6, 60, 7, 48, 8, 31, 9, 16, 10, 2, 12, 1, 2, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row19\" class=\"row_heading level0 row19\" >19</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow19_col0\" class=\"data row19 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow19_col1\" class=\"data row19 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow19_col2\" class=\"data row19 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow19_col3\" class=\"data row19 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow19_col4\" class=\"data row19 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 2, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row20\" class=\"row_heading level0 row20\" >20</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow20_col0\" class=\"data row20 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow20_col1\" class=\"data row20 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow20_col2\" class=\"data row20 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow20_col3\" class=\"data row20 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow20_col4\" class=\"data row20 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 2, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row21\" class=\"row_heading level0 row21\" >21</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow21_col0\" class=\"data row21 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow21_col1\" class=\"data row21 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow21_col2\" class=\"data row21 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow21_col3\" class=\"data row21 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow21_col4\" class=\"data row21 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 2, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row22\" class=\"row_heading level0 row22\" >22</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow22_col0\" class=\"data row22 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow22_col1\" class=\"data row22 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow22_col2\" class=\"data row22 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow22_col3\" class=\"data row22 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow22_col4\" class=\"data row22 col4\" >[0, 1, 2, 3, 3, 12, 4, 34, 5, 52, 6, 54, 7, 52, 8, 29, 9, 12, 10, 7, 2, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row23\" class=\"row_heading level0 row23\" >23</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow23_col0\" class=\"data row23 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow23_col1\" class=\"data row23 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow23_col2\" class=\"data row23 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow23_col3\" class=\"data row23 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow23_col4\" class=\"data row23 col4\" >[0, 1, 2, 4, 3, 14, 4, 26, 5, 52, 6, 64, 7, 48, 8, 29, 9, 12, 10, 4, 11, 2, 2, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row24\" class=\"row_heading level0 row24\" >24</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow24_col0\" class=\"data row24 col0\" >$\\alpha^{2}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow24_col1\" class=\"data row24 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow24_col2\" class=\"data row24 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow24_col3\" class=\"data row24 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow24_col4\" class=\"data row24 col4\" >[0, 1, 2, 6, 3, 14, 4, 22, 5, 52, 6, 64, 7, 48, 8, 33, 9, 12, 10, 2, 11, 2, 3, 4]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row25\" class=\"row_heading level0 row25\" >25</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow25_col0\" class=\"data row25 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow25_col1\" class=\"data row25 col1\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow25_col2\" class=\"data row25 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow25_col3\" class=\"data row25 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow25_col4\" class=\"data row25 col4\" >[0, 1, 2, 4, 3, 12, 4, 28, 5, 58, 6, 58, 7, 42, 8, 35, 9, 14, 10, 2, 11, 2, 3, 5]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row26\" class=\"row_heading level0 row26\" >26</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow26_col0\" class=\"data row26 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow26_col1\" class=\"data row26 col1\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow26_col2\" class=\"data row26 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow26_col3\" class=\"data row26 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow26_col4\" class=\"data row26 col4\" >[0, 1, 2, 3, 3, 12, 4, 34, 5, 52, 6, 54, 7, 52, 8, 29, 9, 12, 10, 7, 3, 6]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row27\" class=\"row_heading level0 row27\" >27</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow27_col0\" class=\"data row27 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow27_col1\" class=\"data row27 col1\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow27_col2\" class=\"data row27 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow27_col3\" class=\"data row27 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow27_col4\" class=\"data row27 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 3, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row28\" class=\"row_heading level0 row28\" >28</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow28_col0\" class=\"data row28 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow28_col1\" class=\"data row28 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow28_col2\" class=\"data row28 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow28_col3\" class=\"data row28 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow28_col4\" class=\"data row28 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 3, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row29\" class=\"row_heading level0 row29\" >29</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col0\" class=\"data row29 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col1\" class=\"data row29 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col2\" class=\"data row29 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col3\" class=\"data row29 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow29_col4\" class=\"data row29 col4\" >[0, 1, 2, 1, 3, 16, 4, 36, 5, 46, 6, 52, 7, 54, 8, 35, 9, 10, 10, 3, 11, 2, 3, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row30\" class=\"row_heading level0 row30\" >30</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col0\" class=\"data row30 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col1\" class=\"data row30 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col2\" class=\"data row30 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col3\" class=\"data row30 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow30_col4\" class=\"data row30 col4\" >[0, 1, 2, 1, 3, 17, 4, 34, 5, 44, 6, 58, 7, 54, 8, 29, 9, 12, 10, 5, 11, 1, 3, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row31\" class=\"row_heading level0 row31\" >31</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col0\" class=\"data row31 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col1\" class=\"data row31 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col2\" class=\"data row31 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col3\" class=\"data row31 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow31_col4\" class=\"data row31 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 3, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row32\" class=\"row_heading level0 row32\" >32</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col0\" class=\"data row32 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col1\" class=\"data row32 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col2\" class=\"data row32 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col3\" class=\"data row32 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow32_col4\" class=\"data row32 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 3, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row33\" class=\"row_heading level0 row33\" >33</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col0\" class=\"data row33 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col1\" class=\"data row33 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col2\" class=\"data row33 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col3\" class=\"data row33 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow33_col4\" class=\"data row33 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 3, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row34\" class=\"row_heading level0 row34\" >34</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col0\" class=\"data row34 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col1\" class=\"data row34 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col2\" class=\"data row34 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col3\" class=\"data row34 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow34_col4\" class=\"data row34 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 3, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row35\" class=\"row_heading level0 row35\" >35</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col0\" class=\"data row35 col0\" >$\\alpha^{3}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col1\" class=\"data row35 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col2\" class=\"data row35 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col3\" class=\"data row35 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow35_col4\" class=\"data row35 col4\" >[0, 1, 2, 4, 3, 16, 4, 23, 5, 48, 6, 72, 7, 48, 8, 23, 9, 16, 10, 4, 12, 1, 4, 5]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row36\" class=\"row_heading level0 row36\" >36</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col0\" class=\"data row36 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col1\" class=\"data row36 col1\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col2\" class=\"data row36 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col3\" class=\"data row36 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow36_col4\" class=\"data row36 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 4, 6]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row37\" class=\"row_heading level0 row37\" >37</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col0\" class=\"data row37 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col1\" class=\"data row37 col1\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col2\" class=\"data row37 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col3\" class=\"data row37 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow37_col4\" class=\"data row37 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 4, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row38\" class=\"row_heading level0 row38\" >38</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col0\" class=\"data row38 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col1\" class=\"data row38 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col2\" class=\"data row38 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col3\" class=\"data row38 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow38_col4\" class=\"data row38 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 4, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row39\" class=\"row_heading level0 row39\" >39</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col0\" class=\"data row39 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col1\" class=\"data row39 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col2\" class=\"data row39 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col3\" class=\"data row39 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow39_col4\" class=\"data row39 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row40\" class=\"row_heading level0 row40\" >40</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col0\" class=\"data row40 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col1\" class=\"data row40 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col2\" class=\"data row40 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col3\" class=\"data row40 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow40_col4\" class=\"data row40 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row41\" class=\"row_heading level0 row41\" >41</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col0\" class=\"data row41 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col1\" class=\"data row41 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col2\" class=\"data row41 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col3\" class=\"data row41 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow41_col4\" class=\"data row41 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row42\" class=\"row_heading level0 row42\" >42</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col0\" class=\"data row42 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col1\" class=\"data row42 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col2\" class=\"data row42 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col3\" class=\"data row42 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow42_col4\" class=\"data row42 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row43\" class=\"row_heading level0 row43\" >43</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col0\" class=\"data row43 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col1\" class=\"data row43 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col2\" class=\"data row43 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col3\" class=\"data row43 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow43_col4\" class=\"data row43 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 4, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row44\" class=\"row_heading level0 row44\" >44</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col0\" class=\"data row44 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col1\" class=\"data row44 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col2\" class=\"data row44 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col3\" class=\"data row44 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow44_col4\" class=\"data row44 col4\" >[0, 1, 2, 2, 3, 16, 4, 30, 5, 48, 6, 64, 7, 48, 8, 25, 9, 16, 10, 6, 4, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row45\" class=\"row_heading level0 row45\" >45</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col0\" class=\"data row45 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col1\" class=\"data row45 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col2\" class=\"data row45 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col3\" class=\"data row45 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow45_col4\" class=\"data row45 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 5, 6]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row46\" class=\"row_heading level0 row46\" >46</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col0\" class=\"data row46 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col1\" class=\"data row46 col1\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col2\" class=\"data row46 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col3\" class=\"data row46 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow46_col4\" class=\"data row46 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 5, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row47\" class=\"row_heading level0 row47\" >47</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col0\" class=\"data row47 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col1\" class=\"data row47 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col2\" class=\"data row47 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col3\" class=\"data row47 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow47_col4\" class=\"data row47 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 5, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row48\" class=\"row_heading level0 row48\" >48</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col0\" class=\"data row48 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col1\" class=\"data row48 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col2\" class=\"data row48 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col3\" class=\"data row48 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow48_col4\" class=\"data row48 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 5, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row49\" class=\"row_heading level0 row49\" >49</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col0\" class=\"data row49 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col1\" class=\"data row49 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col2\" class=\"data row49 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col3\" class=\"data row49 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow49_col4\" class=\"data row49 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 5, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row50\" class=\"row_heading level0 row50\" >50</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col0\" class=\"data row50 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col1\" class=\"data row50 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col2\" class=\"data row50 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col3\" class=\"data row50 col3\" >16</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow50_col4\" class=\"data row50 col4\" >[0, 1, 3, 16, 4, 39, 5, 48, 6, 48, 7, 48, 8, 39, 9, 16, 12, 1, 5, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row51\" class=\"row_heading level0 row51\" >51</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col0\" class=\"data row51 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col1\" class=\"data row51 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col2\" class=\"data row51 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col3\" class=\"data row51 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow51_col4\" class=\"data row51 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 5, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row52\" class=\"row_heading level0 row52\" >52</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col0\" class=\"data row52 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col1\" class=\"data row52 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col2\" class=\"data row52 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col3\" class=\"data row52 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow52_col4\" class=\"data row52 col4\" >[0, 1, 2, 1, 3, 16, 4, 36, 5, 46, 6, 52, 7, 54, 8, 35, 9, 10, 10, 3, 11, 2, 5, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row53\" class=\"row_heading level0 row53\" >53</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col0\" class=\"data row53 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col1\" class=\"data row53 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col2\" class=\"data row53 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col3\" class=\"data row53 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow53_col4\" class=\"data row53 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 5, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row54\" class=\"row_heading level0 row54\" >54</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col0\" class=\"data row54 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col1\" class=\"data row54 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col2\" class=\"data row54 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col3\" class=\"data row54 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow54_col4\" class=\"data row54 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 6, 7]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row55\" class=\"row_heading level0 row55\" >55</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col0\" class=\"data row55 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col1\" class=\"data row55 col1\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col2\" class=\"data row55 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col3\" class=\"data row55 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow55_col4\" class=\"data row55 col4\" >[0, 1, 2, 3, 3, 13, 4, 30, 5, 56, 6, 58, 7, 42, 8, 33, 9, 16, 10, 3, 11, 1, 6, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row56\" class=\"row_heading level0 row56\" >56</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col0\" class=\"data row56 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col1\" class=\"data row56 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col2\" class=\"data row56 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col3\" class=\"data row56 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow56_col4\" class=\"data row56 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 6, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row57\" class=\"row_heading level0 row57\" >57</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col0\" class=\"data row57 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col1\" class=\"data row57 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col2\" class=\"data row57 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col3\" class=\"data row57 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow57_col4\" class=\"data row57 col4\" >[0, 1, 2, 1, 3, 17, 4, 34, 5, 44, 6, 58, 7, 54, 8, 29, 9, 12, 10, 5, 11, 1, 6, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row58\" class=\"row_heading level0 row58\" >58</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col0\" class=\"data row58 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col1\" class=\"data row58 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col2\" class=\"data row58 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col3\" class=\"data row58 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow58_col4\" class=\"data row58 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 6, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row59\" class=\"row_heading level0 row59\" >59</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col0\" class=\"data row59 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col1\" class=\"data row59 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col2\" class=\"data row59 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col3\" class=\"data row59 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow59_col4\" class=\"data row59 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 6, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row60\" class=\"row_heading level0 row60\" >60</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col0\" class=\"data row60 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col1\" class=\"data row60 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col2\" class=\"data row60 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col3\" class=\"data row60 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow60_col4\" class=\"data row60 col4\" >[0, 1, 2, 1, 3, 17, 4, 34, 5, 44, 6, 58, 7, 54, 8, 29, 9, 12, 10, 5, 11, 1, 6, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row61\" class=\"row_heading level0 row61\" >61</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col0\" class=\"data row61 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col1\" class=\"data row61 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col2\" class=\"data row61 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col3\" class=\"data row61 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow61_col4\" class=\"data row61 col4\" >[0, 1, 2, 2, 3, 16, 4, 31, 5, 48, 6, 60, 7, 48, 8, 31, 9, 16, 10, 2, 12, 1, 6, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row62\" class=\"row_heading level0 row62\" >62</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col0\" class=\"data row62 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col1\" class=\"data row62 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col2\" class=\"data row62 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col3\" class=\"data row62 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow62_col4\" class=\"data row62 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 7, 8]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row63\" class=\"row_heading level0 row63\" >63</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col0\" class=\"data row63 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col1\" class=\"data row63 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col2\" class=\"data row63 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col3\" class=\"data row63 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow63_col4\" class=\"data row63 col4\" >[0, 1, 2, 3, 3, 14, 4, 30, 5, 52, 6, 58, 7, 48, 8, 33, 9, 12, 10, 3, 11, 2, 7, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row64\" class=\"row_heading level0 row64\" >64</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col0\" class=\"data row64 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col1\" class=\"data row64 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col2\" class=\"data row64 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col3\" class=\"data row64 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow64_col4\" class=\"data row64 col4\" >[0, 1, 2, 2, 3, 16, 4, 31, 5, 48, 6, 60, 7, 48, 8, 31, 9, 16, 10, 2, 12, 1, 7, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row65\" class=\"row_heading level0 row65\" >65</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col0\" class=\"data row65 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col1\" class=\"data row65 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col2\" class=\"data row65 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col3\" class=\"data row65 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow65_col4\" class=\"data row65 col4\" >[0, 1, 2, 1, 3, 16, 4, 36, 5, 46, 6, 52, 7, 54, 8, 35, 9, 10, 10, 3, 11, 2, 7, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row66\" class=\"row_heading level0 row66\" >66</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col0\" class=\"data row66 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col1\" class=\"data row66 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col2\" class=\"data row66 col2\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col3\" class=\"data row66 col3\" >17</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow66_col4\" class=\"data row66 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 7, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row67\" class=\"row_heading level0 row67\" >67</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col0\" class=\"data row67 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col1\" class=\"data row67 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col2\" class=\"data row67 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col3\" class=\"data row67 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow67_col4\" class=\"data row67 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 7, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row68\" class=\"row_heading level0 row68\" >68</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col0\" class=\"data row68 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col1\" class=\"data row68 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col2\" class=\"data row68 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col3\" class=\"data row68 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow68_col4\" class=\"data row68 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 7, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row69\" class=\"row_heading level0 row69\" >69</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col0\" class=\"data row69 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col1\" class=\"data row69 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col2\" class=\"data row69 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col3\" class=\"data row69 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow69_col4\" class=\"data row69 col4\" >[0, 1, 2, 3, 3, 14, 4, 30, 5, 52, 6, 58, 7, 48, 8, 33, 9, 12, 10, 3, 11, 2, 8, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row70\" class=\"row_heading level0 row70\" >70</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col0\" class=\"data row70 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col1\" class=\"data row70 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col2\" class=\"data row70 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col3\" class=\"data row70 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow70_col4\" class=\"data row70 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 8, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row71\" class=\"row_heading level0 row71\" >71</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col0\" class=\"data row71 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col1\" class=\"data row71 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col2\" class=\"data row71 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col3\" class=\"data row71 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow71_col4\" class=\"data row71 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 8, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row72\" class=\"row_heading level0 row72\" >72</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col0\" class=\"data row72 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col1\" class=\"data row72 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col2\" class=\"data row72 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col3\" class=\"data row72 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow72_col4\" class=\"data row72 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 8, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row73\" class=\"row_heading level0 row73\" >73</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col0\" class=\"data row73 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col1\" class=\"data row73 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col2\" class=\"data row73 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col3\" class=\"data row73 col3\" >1</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow73_col4\" class=\"data row73 col4\" >[0, 1, 2, 1, 3, 16, 4, 34, 5, 48, 6, 58, 7, 48, 8, 29, 9, 16, 10, 5, 8, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row74\" class=\"row_heading level0 row74\" >74</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col0\" class=\"data row74 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col1\" class=\"data row74 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col2\" class=\"data row74 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col3\" class=\"data row74 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow74_col4\" class=\"data row74 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 8, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row75\" class=\"row_heading level0 row75\" >75</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col0\" class=\"data row75 col0\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col1\" class=\"data row75 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col2\" class=\"data row75 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col3\" class=\"data row75 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow75_col4\" class=\"data row75 col4\" >[0, 1, 2, 3, 3, 13, 4, 30, 5, 56, 6, 58, 7, 42, 8, 33, 9, 16, 10, 3, 11, 1, 9, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row76\" class=\"row_heading level0 row76\" >76</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col0\" class=\"data row76 col0\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col1\" class=\"data row76 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col2\" class=\"data row76 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col3\" class=\"data row76 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow76_col4\" class=\"data row76 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 9, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row77\" class=\"row_heading level0 row77\" >77</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col0\" class=\"data row77 col0\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col1\" class=\"data row77 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col2\" class=\"data row77 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col3\" class=\"data row77 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow77_col4\" class=\"data row77 col4\" >[0, 1, 2, 2, 3, 16, 4, 30, 5, 48, 6, 64, 7, 48, 8, 25, 9, 16, 10, 6, 9, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row78\" class=\"row_heading level0 row78\" >78</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col0\" class=\"data row78 col0\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col1\" class=\"data row78 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col2\" class=\"data row78 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col3\" class=\"data row78 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow78_col4\" class=\"data row78 col4\" >[0, 1, 2, 2, 3, 15, 4, 32, 5, 50, 6, 58, 7, 48, 8, 31, 9, 14, 10, 4, 11, 1, 9, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row79\" class=\"row_heading level0 row79\" >79</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col0\" class=\"data row79 col0\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col1\" class=\"data row79 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col2\" class=\"data row79 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col3\" class=\"data row79 col3\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow79_col4\" class=\"data row79 col4\" >[0, 1, 2, 2, 3, 13, 4, 34, 5, 56, 6, 52, 7, 42, 8, 37, 9, 16, 10, 2, 11, 1, 9, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row80\" class=\"row_heading level0 row80\" >80</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col0\" class=\"data row80 col0\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col1\" class=\"data row80 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col2\" class=\"data row80 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col3\" class=\"data row80 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow80_col4\" class=\"data row80 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 10, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row81\" class=\"row_heading level0 row81\" >81</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col0\" class=\"data row81 col0\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col1\" class=\"data row81 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col2\" class=\"data row81 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col3\" class=\"data row81 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow81_col4\" class=\"data row81 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 10, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row82\" class=\"row_heading level0 row82\" >82</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col0\" class=\"data row82 col0\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col1\" class=\"data row82 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col2\" class=\"data row82 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col3\" class=\"data row82 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow82_col4\" class=\"data row82 col4\" >[0, 1, 2, 3, 3, 15, 4, 28, 5, 50, 6, 64, 7, 48, 8, 27, 9, 14, 10, 5, 11, 1, 10, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row83\" class=\"row_heading level0 row83\" >83</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col0\" class=\"data row83 col0\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col1\" class=\"data row83 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col2\" class=\"data row83 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col3\" class=\"data row83 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow83_col4\" class=\"data row83 col4\" >[0, 1, 2, 3, 3, 12, 4, 34, 5, 52, 6, 54, 7, 52, 8, 29, 9, 12, 10, 7, 10, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row84\" class=\"row_heading level0 row84\" >84</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col0\" class=\"data row84 col0\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col1\" class=\"data row84 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col2\" class=\"data row84 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col3\" class=\"data row84 col3\" >3</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow84_col4\" class=\"data row84 col4\" >[0, 1, 2, 3, 3, 10, 4, 36, 5, 58, 6, 48, 7, 46, 8, 35, 9, 14, 10, 5, 11, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row85\" class=\"row_heading level0 row85\" >85</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col0\" class=\"data row85 col0\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col1\" class=\"data row85 col1\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col2\" class=\"data row85 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col3\" class=\"data row85 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow85_col4\" class=\"data row85 col4\" >[0, 1, 2, 4, 3, 16, 4, 23, 5, 48, 6, 72, 7, 48, 8, 23, 9, 16, 10, 4, 12, 1, 11, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row86\" class=\"row_heading level0 row86\" >86</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col0\" class=\"data row86 col0\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col1\" class=\"data row86 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col2\" class=\"data row86 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col3\" class=\"data row86 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow86_col4\" class=\"data row86 col4\" >[0, 1, 2, 4, 3, 14, 4, 26, 5, 52, 6, 64, 7, 48, 8, 29, 9, 12, 10, 4, 11, 2, 11, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row87\" class=\"row_heading level0 row87\" >87</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col0\" class=\"data row87 col0\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col1\" class=\"data row87 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col2\" class=\"data row87 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col3\" class=\"data row87 col3\" >4</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow87_col4\" class=\"data row87 col4\" >[0, 1, 2, 4, 3, 12, 4, 28, 5, 58, 6, 58, 7, 42, 8, 35, 9, 14, 10, 2, 11, 2, 12, 13]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row88\" class=\"row_heading level0 row88\" >88</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col0\" class=\"data row88 col0\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col1\" class=\"data row88 col1\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col2\" class=\"data row88 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col3\" class=\"data row88 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow88_col4\" class=\"data row88 col4\" >[0, 1, 2, 6, 3, 14, 4, 22, 5, 52, 6, 64, 7, 48, 8, 33, 9, 12, 10, 2, 11, 2, 12, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row89\" class=\"row_heading level0 row89\" >89</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col0\" class=\"data row89 col0\" >$\\alpha^{12}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col1\" class=\"data row89 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col2\" class=\"data row89 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col3\" class=\"data row89 col3\" >6</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow89_col4\" class=\"data row89 col4\" >[0, 1, 2, 6, 3, 12, 4, 26, 5, 52, 6, 60, 7, 52, 8, 29, 9, 12, 10, 6, 13, 14]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aelevel0_row90\" class=\"row_heading level0 row90\" >90</th>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col0\" class=\"data row90 col0\" >$\\alpha^{13}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col1\" class=\"data row90 col1\" >$\\alpha^{14}$</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col2\" class=\"data row90 col2\" >2</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col3\" class=\"data row90 col3\" >8</td>\n",
       "                        <td id=\"T_8d379dee_117e_11eb_bc3d_8c16459d77aerow90_col4\" class=\"data row90 col4\" >[0, 1, 2, 8, 3, 10, 4, 28, 5, 50, 6, 50, 7, 62, 8, 35, 9, 6, 10, 6]</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x2502ea1b898>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'$\\\\alpha_2$': alpha_all[alpha_2[:]], '$\\\\alpha_3$': alpha_all[alpha_3[:]], '$d_{\\mathcal{D}}^\\perp$': d_all[:], \n",
    "                   '$B_{d_{\\mathcal{D}}^\\perp}$': B_all[:], 'Weight Enumerators': d_dual_b[:]})\n",
    "\n",
    "pd.set_option('display.max_colwidth', 1000)\n",
    "pd.set_option('display.width', 800)\n",
    "(df.style\n",
    "    .background_gradient(cmap=cm_1, subset=['$d_{\\mathcal{D}}^\\perp$','$B_{d_{\\mathcal{D}}^\\perp}$' ])\n",
    "    .background_gradient(cmap=cm_2, subset=['$B_{d_{\\mathcal{D}}^\\perp}$' ])\n",
    "    .set_caption('Tab. I All linear codes for (3,1)-SSS-based masking with $n=3$ shares over $\\mathbb{F}_{2^4}$.')\n",
    "    .set_table_styles(styles))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Optimal linear codes for (3,1)-SSS-based masking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Linear codes with $d_{\\mathcal{D}}^\\perp=3$\n",
    "\n",
    "We focus on the the linear codes with greater $d_{\\mathcal{D}}^\\perp$, which are better in the sense of side-channel resistance (from our paper)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-18T20:14:48.353129Z",
     "start_time": "2020-10-18T20:14:48.339321Z"
    }
   },
   "outputs": [],
   "source": [
    "# Finding the indices of d_C=6\n",
    "d_index = []\n",
    "d_index_alpha_2 = []\n",
    "d_index_alpha_3 = []\n",
    "d_D_perp = 3\n",
    "for i in range(len(d_dual_b)):\n",
    "    if d_dual_b[i][2] == d_D_perp:\n",
    "        d_index.append(i)\n",
    "        d_index_alpha_2.append(pow_ind[i][0])\n",
    "        d_index_alpha_3.append(pow_ind[i][1])\n",
    "\n",
    "d_index = np.array(d_index)\n",
    "d_index_alpha_2 = np.array(d_index_alpha_2)\n",
    "d_index_alpha_3 = np.array(d_index_alpha_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-18T20:14:50.060052Z",
     "start_time": "2020-10-18T20:14:50.052829Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "[39 40 41 42 49 50 51 58 59 66]\n"
     ]
    }
   ],
   "source": [
    "print(len(d_index))\n",
    "print(d_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-18T20:14:52.634721Z",
     "start_time": "2020-10-18T20:14:52.620205Z"
    }
   },
   "outputs": [],
   "source": [
    "def highlight(s, threshold, column):\n",
    "    is_min = pd.Series(data=False, index=s.index)\n",
    "    is_min[column] = (s.loc[column] <= threshold)\n",
    "    return ['background-color: gold' if is_min.any() else '' for v in is_min]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-10-18T20:14:57.863683Z",
     "start_time": "2020-10-18T20:14:57.714339Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
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       "            color:  #000000;\n",
       "        }</style><table id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77ae\" ><caption>Tab. II Linear codes for (3,1)-SSS-based masking with $d_{\\mathcal{D}}^\\perp=3$.</caption><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >$\\alpha_2$</th>        <th class=\"col_heading level0 col1\" >$\\alpha_3$</th>        <th class=\"col_heading level0 col2\" >$d_{\\mathcal{D}}^\\perp$</th>        <th class=\"col_heading level0 col3\" >$B_{d_{\\mathcal{D}}^\\perp}$</th>        <th class=\"col_heading level0 col4\" >Weight Enumerators</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row0\" class=\"row_heading level0 row0\" >5</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow0_col0\" class=\"data row0 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow0_col1\" class=\"data row0 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow0_col2\" class=\"data row0 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow0_col3\" class=\"data row0 col3\" >16</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow0_col4\" class=\"data row0 col4\" >[0, 1, 3, 16, 4, 39, 5, 48, 6, 48, 7, 48, 8, 39, 9, 16, 12, 1, 5, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row1\" class=\"row_heading level0 row1\" >0</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow1_col0\" class=\"data row1 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow1_col1\" class=\"data row1 col1\" >$\\alpha^{8}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow1_col2\" class=\"data row1 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow1_col3\" class=\"data row1 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow1_col4\" class=\"data row1 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 9]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row2\" class=\"row_heading level0 row2\" >1</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow2_col0\" class=\"data row2 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow2_col1\" class=\"data row2 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow2_col2\" class=\"data row2 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow2_col3\" class=\"data row2 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow2_col4\" class=\"data row2 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row3\" class=\"row_heading level0 row3\" >2</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow3_col0\" class=\"data row3 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow3_col1\" class=\"data row3 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow3_col2\" class=\"data row3 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow3_col3\" class=\"data row3 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow3_col4\" class=\"data row3 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row4\" class=\"row_heading level0 row4\" >3</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow4_col0\" class=\"data row4 col0\" >$\\alpha^{4}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow4_col1\" class=\"data row4 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow4_col2\" class=\"data row4 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow4_col3\" class=\"data row4 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow4_col4\" class=\"data row4 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 4, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row5\" class=\"row_heading level0 row5\" >4</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow5_col0\" class=\"data row5 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow5_col1\" class=\"data row5 col1\" >$\\alpha^{9}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow5_col2\" class=\"data row5 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow5_col3\" class=\"data row5 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow5_col4\" class=\"data row5 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 5, 10]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow6_col0\" class=\"data row6 col0\" >$\\alpha^{5}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow6_col1\" class=\"data row6 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow6_col2\" class=\"data row6 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow6_col3\" class=\"data row6 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow6_col4\" class=\"data row6 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 5, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow7_col0\" class=\"data row7 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow7_col1\" class=\"data row7 col1\" >$\\alpha^{10}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow7_col2\" class=\"data row7 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow7_col3\" class=\"data row7 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow7_col4\" class=\"data row7 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 6, 11]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow8_col0\" class=\"data row8 col0\" >$\\alpha^{6}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow8_col1\" class=\"data row8 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow8_col2\" class=\"data row8 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow8_col3\" class=\"data row8 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow8_col4\" class=\"data row8 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 6, 12]</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aelevel0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow9_col0\" class=\"data row9 col0\" >$\\alpha^{7}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow9_col1\" class=\"data row9 col1\" >$\\alpha^{11}$</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow9_col2\" class=\"data row9 col2\" >3</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow9_col3\" class=\"data row9 col3\" >17</td>\n",
       "                        <td id=\"T_97fd47c6_117e_11eb_bd3b_8c16459d77aerow9_col4\" class=\"data row9 col4\" >[0, 1, 3, 17, 4, 38, 5, 44, 6, 52, 7, 54, 8, 33, 9, 12, 10, 4, 11, 1, 7, 12]</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x2502ac9d390>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_4 = pd.DataFrame({'$\\\\alpha_2$': np.array(alpha_all)[d_index_alpha_2], '$\\\\alpha_3$': np.array(alpha_all)[d_index_alpha_3], '$d_{\\mathcal{D}}^\\perp$': \n",
    "                     d_all[d_index], '$B_{d_{\\mathcal{D}}^\\perp}$': B_all[d_index], 'Weight Enumerators': np.array(d_dual_b)[d_index]})\n",
    "df_4 = df_4.sort_values(by=['$B_{d_{\\mathcal{D}}^\\perp}$'], ascending=True)\n",
    "\n",
    "(df_4.style\n",
    "    .apply(highlight, threshold=16, column=['$B_{d_{\\mathcal{D}}^\\perp}$'], axis=1)\n",
    "    .background_gradient(cmap=cm_2, subset=['$B_{d_{\\mathcal{D}}^\\perp}$' ])\n",
    "    .set_caption('Tab. II Linear codes for (3,1)-SSS-based masking with $d_{\\mathcal{D}}^\\perp=3$.')\n",
    "    .set_table_styles(styles))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Optimal codes for (3,1)-SSS-based masking\n",
    "\n",
    "As shown in our paper, the codes satifying two conditions are optimal:\n",
    "\n",
    "- Maximizing $d_{\\mathcal{D}}^\\perp$, here $\\max\\{d_{\\mathcal{D}}^\\perp\\} = 3$\n",
    "- Minimizing $B_{d_{\\mathcal{D}}^\\perp}$, here $\\min\\{B_{d_{\\mathcal{D}}^\\perp}\\} = 16$\n",
    "\n",
    "Note that we use two complementary metrics **SNR** (signal-to-noise ratio) and **MI** (mutual information) to assess the side-channel resistance of SSS-based masking with different codes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": false
   },
   "source": [
    "As a result of Tab. II, we conclude that the optimal codes for (3,1)-SSS based masking are generated by $\\mathbf{H}=[\\alpha_1, \\alpha_2,\\alpha_3]$ where $(\\alpha_1, \\alpha_2,\\alpha_3)\\in\\{(\\alpha^0, \\alpha^5, \\alpha^{10})\\}$. Note that permutation on three public points does not change the codes due to equivalence.\n",
    "\n",
    "The generator matrix of the code is: \n",
    "$$\n",
    "\\mathbf{H}_{optimal}=\\left( \\begin{matrix} \\alpha^0 & \\alpha^5 & \\alpha^{10} \\end{matrix} \\right) \\in \\mathbb{F}_{2^4}^{1\\times 3} \n",
    "= \\left(\n",
    " \\begin{matrix}\n",
    "    1&0&0&0&0&1&1&0&1&1&1&0 \\\\\n",
    "    0&1&0&0&0&0&1&1&0&1&1&1 \\\\\n",
    "    0&0&1&0&1&1&0&1&1&1&1&1 \\\\\n",
    "    0&0&0&1&1&0&1&0&1&0&1&1 \n",
    "  \\end{matrix} \n",
    "\\right) \\normalsize\\in \\mathbb{F}_2^{4\\times 12}\n",
    "$$ "
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