
_data := [
          // degree 2
          \[ -1, -1, 1 ],
          // degree 3
          \[ 1, -2, -1, 1 ],
          \[ 1, -3, -1, 1 ],
          // degree 4
          \[ 1, 4, -4, -1, 1 ],
          \[ 4, 0, -6, 0, 1 ],
          \[ 1, 1, -3, -1, 1 ],
          \[ 9, 2, -7, -1, 1 ],
          \[ 1, -1, -4, 0, 1 ],
          // degree 5
          \[ -1, 3, 3, -4, -1, 1 ],
          \[ -1, 3, 4, -5, -1, 1 ],
          \[ 12, 17, -4, -9, 0, 1 ],
          \[ 9, 18, -5, -11, 0, 1 ],
          \[ -1, 0, 6, -3, -2, 1 ],
          // degree 6
          \[ -1, -2, 7, 2, -7, -1, 1 ],
          \[ 1, -5, 0, 9, -2, -3, 1 ],
          \[ -1, -3, 12, 1, -10, -1, 1 ],
          \[ -169, 0, 104, 0, -19, 0, 1 ],
          \[ 1, -5, 4, 7, -6, -1, 1 ],
          \[ -1, -2, 4, 5, -4, -2, 1 ],
          \[ -1, 0, 8, 0, -6, 0, 1 ],
          \[ 3, -54, 42, 15, -14, -1, 1 ],
          \[ 1, 14, 32, 8, -10, -2, 1 ],
          \[ 99, -198, 99, 21, -21, 0, 1 ],
          \[ 1, -4, -1, 9, -2, -3, 1 ],
          \[ 3, 14, 15, -7, -10, 0, 1 ],
          \[ 1, -7, -1, 10, -2, -3, 1 ],
          \[ -69, -70, 90, 9, -18, 0, 1 ],
          \[ -10, -3, 27, 14, -9, -3, 1 ],
          \[ -1, -2, 5, 4, -5, -1, 1 ],
          // degree 7
          \[ -1, -9, -14, 28, 7, -12, -1, 1 ],
          \[ 1, -1, -10, 13, 10, -7, -2, 1 ],
          \[ -2, -6, 6, 16, -2, -8, 0, 1 ],
          \[ 5, -21, -26, 37, 9, -12, -1, 1 ],
          \[ -2, -6, 4, 15, -2, -8, 0, 1 ],
          \[ 2, -11, -14, 16, 11, -7, -2, 1 ],
          \[ 1, -2, -5, 8, 5, -6, -1, 1 ],
          // degree 8
          \[ 1, 4, -10, -10, 15, 6, -7, -1, 1 ],
          \[ 1, 0, -8, 0, 14, 0, -7, 0, 1 ],
          \[ 1, 0, -12, 0, 23, 0, -12, 0, 1 ],
          \[ 1, 11, -29, -51, 38, 27, -11, -3, 1 ],
          \[ 9, 0, -36, 0, 36, 0, -12, 0, 1 ],
          \[ 1, 2, -15, -14, 22, 10, -9, -2, 1 ],
          \[ 5, 0, -20, 0, 25, 0, -10, 0, 1 ],
          \[ 1, -5, -14, 15, 31, -10, -14, 0, 1 ],
          \[ 1, -4, -12, 8, 21, -4, -10, 0, 1 ],
          \[ 1, 0, -17, 0, 44, 0, -13, 0, 1 ],
          \[ -1, 4, 2, -18, 4, 16, -7, -2, 1 ],
          \[ -1, 11, -4, -34, 9, 24, -8, -3, 1 ],
          \[ 1, 4, -12, -28, 13, 24, -6, -4, 1 ],
          \[ -19, -82, -26, 202, 143, -18, -24, 0, 1 ],
          \[ -5, 15, 8, -37, -3, 23, -3, -4, 1 ],
          \[ 1, 3, -37, -39, 35, 21, -12, -2, 1 ],
          \[ -1, 2, 7, -12, -8, 14, 0, -4, 1 ],
          \[ 1, 0, -15, 0, 57, 0, -15, 0, 1 ],
          \[ 4, 0, -28, 0, 36, 0, -14, 0, 1 ],
          \[ 1, 6, -20, -36, 14, 24, -5, -4, 1 ],
          \[ 8, 0, -32, 0, 39, 0, -14, 0, 1 ],
          \[ -41, -124, -56, 96, 73, -12, -16, 0, 1 ],
          \[ 1, 31, 0, -52, 2, 26, -4, -4, 1 ],
          \[ 1, 1, -13, 4, 23, -4, -12, 0, 1 ],
          \[ 7, -50, -112, 26, 102, 10, -20, -2, 1 ],
          \[ 33, 0, -66, 0, 45, 0, -12, 0, 1 ],
          \[ 1, 8, 6, -21, -6, 17, -1, -4, 1 ],
          \[ 5, 0, -20, 0, 24, 0, -9, 0, 1 ],
          \[ 4, 0, -22, 0, 25, 0, -9, 0, 1 ],
          \[ 1, 15, 13, -46, -1, 26, -4, -4, 1 ],
          \[ -1, 6, -3, -20, 8, 18, -4, -4, 1 ],
          \[ -2, 35, 263, 272, -3, -93, -27, 2, 1 ],
          \[ -19, 78, -53, -72, 62, 15, -15, -1, 1 ],
          \[ -11, -203, -100, 277, 202, -13, -28, -1, 1 ],
          \[ -1, 5, -2, -16, 8, 14, -5, -3, 1 ],
          \[ -17, -132, -292, -80, 194, 12, -28, 0, 1 ],
          \[ 151, 309, -728, -357, 252, 63, -28, -3, 1 ],
          \[ 4, 2, -31, -17, 42, 18, -13, -3, 1 ],
          \[ 1, -1, -11, 1, 24, 1, -11, -1, 1 ],
          \[ -1, -3, 10, 18, -10, -20, -2, 4, 1 ],
          \[ -2, -12, -14, 20, 28, -4, -10, 0, 1 ],
          \[ -1, -24, -80, -26, 52, 16, -12, -2, 1 ],
          \[ 6, -556, -462, 308, 308, 0, -35, -2, 1 ],
          \[ -1, 4, 4, -16, -3, 15, -1, -4, 1 ],
          \[ 16, 24, -63, -25, 62, -3, -14, 1, 1 ],
          \[ -191, 0, 382, 131, -200, -131, -10, 7, 1 ],
          \[ 1, 2, -10, -7, 15, 5, -7, -1, 1 ],
          \[ -1, -8, -10, 20, 27, -4, -10, 0, 1 ],
          \[ 3, 1, -22, -2, 30, 6, -11, -2, 1 ],
          \[ 1, 0, -9, -3, 15, 4, -7, -1, 1 ],
          // degree 9
          \[ -1, 5, 10, -20, -15, 21, 7, -8, -1, 1 ],
          \[ 1, 6, -9, -38, 12, 54, -4, -15, 0, 1 ],
          \[ -392, 904, 940, -3137, 1211, 699, -226, -67, 3, 1 ],
          \[ 1, 5, 1, -20, -13, 22, 13, -8, -3, 1 ],
          \[ 64, 288, -864, -2652, 180, 756, -12, -54, 0, 1 ],
          \[ 7, 189, -63, -273, 42, 126, -7, -21, 0, 1 ],
          \[ -8, -132, 204, 81, -219, 39, 51, -15, -3, 1 ],
          \[ 1, 4, -16, -37, 20, 48, -7, -16, 0, 1 ],
          \[ 1339, 819, -1404, -858, 459, 297, -45, -36, 0, 1 ],
          \[ -4, 12, 48, -92, -120, 62, 44, -14, -4, 1 ],
          \[ -42, -126, 378, -21, -378, 189, 30, -27, 0, 1 ],
          \[ 2727, -7401, 6301, -473, -1857, 695, 68, -54, 1, 1 ],
          \[ 104, 716, 998, -247, -680, 79, 142, -30, -4, 1 ],
          \[ -1434, 4673, 4936, -4012, -1808, 980, 120, -60, -2, 1 ],
          \[ -2560, -2064, 13440, -8928, -960, 1464, 0, -72, 0, 1 ],
          \[ -1, 5, 0, -21, 5, 25, -3, -10, 0, 1 ],
          \[ 1, -5, 2, 20, -22, -14, 22, -2, -4, 1 ],
          \[ 16, 144, 384, 136, -480, -24, 167, -39, -3, 1 ],
          \[ -29, 255, 616, -616, -558, 298, 80, -32, -3, 1 ],
          \[ -1, 0, 15, 4, -31, -1, 22, -4, -4, 1 ],
          \[ -25, 291, -952, 1316, -766, 56, 118, -36, -1, 1 ],
          \[ -232, -1044, -1566, -659, 372, 279, -20, -30, 0, 1 ],
          \[ 5714, -4931, -14194, -2711, 3614, 1022, -196, -66, 2, 1 ],
          \[ -193, 36, 379, -161, -183, 90, 33, -17, -2, 1 ],
          \[ -83, -317, -313, 147, 355, 87, -63, -20, 3, 1 ],
          \[ -480, 972, 180, -1116, 90, 441, -30, -60, 0, 1 ],
          \[ -128, -27, 36, 0, 0, -18, -12, 0, 0, 1 ],
          \[ 1, 3, -11, -24, 13, 31, -4, -11, 0, 1 ],
          \[ -2, 14, -22, -21, 42, 17, -21, -7, 3, 1 ],
          \[ 9, 15, -53, -46, 73, 53, -24, -19, 0, 1 ],
          \[ -1, 4, 5, -17, -9, 22, 6, -9, -1, 1 ],
          \[ 1, 9, 26, 28, 0, 0, 0, -4, -1, 1 ],
          \[ 8570672, 12709796, 2985984, -1327104, -103680, 33984, 1152, -320, -4, 1 ],
          \[ -1, 2, 7, -10, -15, 15, 11, -7, -2, 1 ],
          // degree 10
          \[ 1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1 ],
          \[ -1, -2, 20, 2, -69, -1, 69, 2, -20, -2, 1 ],
          \[ -1, -3, 21, 8, -68, -19, 58, 11, -16, -1, 1 ],
          \[ 1, 5, -5, -30, 5, 53, 5, -30, -5, 5, 1 ],
          \[ 1, 24, 192, 608, 871, 542, 62, -74, -23, 2, 1 ],
          \[ 1, 5, -5, -50, -40, 53, 55, -10, -15, 0, 1 ],
          \[ 19, -19, -189, 207, 125, -188, -1, 51, -9, -4, 1 ],
          \[ -529, 0, 851, 0, -519, 0, 149, 0, -20, 0, 1 ],
          \[ 1, 2, -582, -1164, 2493, 5561, 739, -2326, -572, 6, 1 ],
          \[ 144, -1080, -620, 4870, -2485, -1611, 560, 165, -40, -5, 1 ],
          \[ -45, 0, 156, 0, -188, 0, 93, 0, -18, 0, 1 ],
          \[ -39868, 18388, 32052, -8960, -9936, 1192, 1334, -28, -72, -2, 1 ],
          \[ 1, -1, -15, 22, 31, -53, -10, 31, -3, -5, 1 ],
          \[ -23, 0, 80, 0, -96, 0, 51, 0, -12, 0, 1 ],
          \[ 27, -84, 8, 170, -85, -110, 62, 26, -14, -2, 1 ],
          \[ 83, 503, -3032, -5930, 14669, -9457, 1931, 212, -103, 2, 1 ],
          \[ -507, 0, 4225, 390, -2600, -48, 515, 0, -40, 0, 1 ],
          \[ -416, 704, 816, -1152, -800, 476, 288, -56, -32, 2, 1 ],
          \[ 6655, 11495, 869, -6208, -1843, 1106, 419, -80, -35, 2, 1 ],
          \[ -125, 978, -1939, 72, 3299, -3142, 691, 272, -101, -2, 1 ],
          \[ 4, 20, 16, -52, -68, 42, 66, -12, -18, 2, 1 ],
          \[ -1, 3, 12, -17, -46, 16, 46, -4, -15, 0, 1 ],
          \[ 1, 3, -26, -21, 70, 64, -30, -38, -2, 5, 1 ],
          \[ -4, 0, 40, 0, -90, 0, 56, 0, -13, 0, 1 ],
          \[ -125, 0, 395, 0, -400, 0, 160, 0, -25, 0, 1 ],
          \[ -115, -1243, 568, 3042, -1392, -806, 375, 71, -34, -2, 1 ],
          \[ 62, -320, 400, 160, -400, -16, 140, 0, -20, 0, 1 ],
          \[ -2871, -14082, -25799, -22200, -8071, 390, 1043, 136, -45, -6, 1 ],
          \[ -1, -10, 15, 60, -50, -98, 60, 40, -25, 0, 1 ],
          \[ -19051686375736, -13218507706544, -2586378241944, -90110140792, 
             20274710780, 1803173448, 26192194, -912608, -20520, -4, 1 ],
          \[ -200, 400, -200, 0, 0, 0, 0, 0, 9, -2, 1 ],
          \[ -4, -21, 79, 191, -153, -186, 87, 52, -18, -4, 1 ],
          \[ -191404, -171560, 133265, 77375, -46865, -3913, 4095, -90, -120, 5, 1 ],
          \[ -1, 0, 46, 0, -97, 0, 61, 0, -14, 0, 1 ],
          \[ -2268, 6264, 17620, -60064, 54884, -20104, 1996, 496, -103, -2, 1 ],
          \[ -4, -8, 43, 63, -118, -49, 96, -3, -18, 1, 1 ],
          \[ -1, 0, 12, 0, -31, 0, 27, 0, -9, 0, 1 ],
          \[ -22, 0, 122, 0, -146, 0, 69, 0, -14, 0, 1 ],
          \[ 1, -1, -18, 27, 27, -46, -8, 25, -3, -4, 1 ],
          \[ 28400, -198800, 552380, -766800, 546984, -183592, 21464, 1584, -396, 0, 1 ],
          \[ 7520800, 52645600, 127289540, 128605680, 59903172, 12146016, 721861, 
             -13680, -1746, 0, 1 ],
          \[ 2508800, -12544000, 21465600, -11827200, -3224464, 2957296, 737644, 13152, 
             -1584, -20, 1 ],
          \[ 1, -13, 20, 28, -46, -23, 34, 8, -10, -1, 1 ],
          \[ -188664187576370688, -916929518523200, 683878885063920, 0, -588906693648, 
             0, 182446992, 0, -22932, 0, 1 ],
          \[ 1, 0, -18, 21, 30, -40, -11, 23, -2, -4, 1 ],
          // degree 11
          \[ -1, -6, 15, 35, -35, -56, 28, 36, -9, -10, 1, 1 ],
          \[ -5, 56, 29, -222, 69, 208, -127, -53, 54, -4, -5, 1 ],
          \[ -243, -2673, 0, 4455, 0, -2079, 0, 396, 0, -33, 0, 1 ],
          \[ -3279, 19909, -36219, 20673, 5784, -7812, 28, 996, -31, -53, 1, 1 ],
          \[ 579, -847, -1586, 1805, 1574, -1010, -562, 237, 81, -25, -4, 1 ],
          \[ -57600, -82100, 56000, -22500, 0, -210, 540, -75, 0, 0, -4, 1 ],
          \[ -1, -1, 0, -2, 1, 2, -1, 1, 0, -1, 0, 1 ],
          \[ -1, 5, 2, -40, 40, 48, -67, -9, 30, -4, -4, 1 ],
          // degree 12
          \[ 1, 8, -40, -46, 110, 71, -113, -43, 54, 11, -12, -1, 1 ],
          \[ 1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1 ],
          \[ 1, 5, -25, -36, 121, 73, -168, -73, 85, 30, -15, -3, 1 ],
          \[ 3136, 0, 0, 0, -560, 0, 48, 0, 24, 0, 4, 0, 1 ],
          \[ -17, 4165, -4913, -9622, 6512, 6884, -3048, -1789, 638, 152, -46, -4, 1 ],
          \[ 64, 0, -512, 0, 800, 0, -503, 0, 148, 0, -20, 0, 1 ],
          \[ 1, 0, -39, 0, 321, 0, -345, 0, 135, 0, -21, 0, 1 ],
          \[ -1, -1, -1, -8, 4, 3, 1, -8, -2, -2, -2, 0, 1 ],
          \[ 4, 0, -288, 0, 1124, 0, -784, 0, 209, 0, -24, 0, 1 ],
          \[ 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1 ],
          \[ 2312, 0, -4232, 0, 3089, 0, -1152, 0, 232, 0, -24, 0, 1 ],
          \[ -1, 0, 0, -3, 0, 0, 4, 0, 0, -2, 0, 0, 1 ],
          \[ -3, 0, 0, 0, 3, 0, 0, 0, -9, 0, 0, 0, 1 ],
          \[ 1352, 0, -3008, 0, 2552, 0, -1056, 0, 226, 0, -24, 0, 1 ],
          \[ 48, 0, -1152, 0, 1680, 0, -896, 0, 216, 0, -24, 0, 1 ],
          \[ 4, -104, 38, 720, -1109, 52, 878, -536, -15, 92, -16, -4, 1 ],
          \[ 376, 2880, 6744, 3456, -5625, -6528, -484, 1848, 636, -72, -48, 0, 1 ],
          \[ 1, -4, 7, -6, 2, 0, 3, -8, 1, 6, 0, -2, 1 ],
          \[ 1, 84, -63, -654, 112, 798, -107, -362, 62, 68, -15, -4, 1 ],
          \[ 8, 228, 420, -2511, 1254, 2034, -1171, -603, 303, 73, -30, -3, 1 ],
          \[ 4, 0, -90, 0, 243, 0, -215, 0, 84, 0, -15, 0, 1 ],
          \[ 1, -57, 23, 9, -125, -18, 7, 0, -5, -9, 0, 0, 1 ],
          \[ 1, 0, -35, 0, 120, 0, -148, 0, 75, 0, -15, 0, 1 ],
          \[ 1, -2, 2, -2, 3, -2, 0, 2, 3, -8, 8, -4, 1 ],
          \[ 1, 0, -12, 0, 48, 0, -77, 0, 48, 0, -12, 0, 1 ],
          \[ 1, 0, 2, 0, -5, 0, -4, 0, -5, 0, 2, 0, 1 ],
          \[ -8, 144, -16, -816, 524, 880, -496, -384, 154, 68, -20, -4, 1 ],
          \[ -1, 0, 0, -5, 0, 0, -4, 0, 0, 0, 0, 0, 1 ],
          \[ 325, 0, -975, 0, 1144, 0, -663, 0, 195, 0, -26, 0, 1 ],
          \[ 37, 0, -296, 0, 527, 0, -384, 0, 131, 0, -20, 0, 1 ],
          \[ 169, 0, -2028, 0, 3679, 0, -2106, 0, 450, 0, -38, 0, 1 ],
          \[ 64, 0, -752, 0, 2584, 0, -2800, 0, 646, 0, -47, 0, 1 ],
          \[ 1, -4, 2, 0, 19, -12, -4, -12, 19, 0, 2, -4, 1 ],
          \[ 16, 0, -36, 0, 57, 0, 104, 0, 54, 0, 12, 0, 1 ],
          \[ 433, 0, -8, 0, 164, 0, -51, 0, 12, 0, -4, 0, 1 ],
          \[ 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1 ],
          \[ 256, 0, -5056, 0, 5360, 0, -2127, 0, 384, 0, -32, 0, 1 ],
          \[ 6534, 0, -13608, 0, 9585, 0, -3084, 0, 486, 0, -36, 0, 1 ],
          \[ 8, 0, -8, 0, 17, 0, -32, 0, 24, 0, -8, 0, 1 ],
          \[ 1600, 0, -1280, 0, 416, 0, 8, 0, -36, 0, 2, 0, 1 ],
          \[ 1, 0, 0, 3, 0, 0, -1, 0, 0, -3, 0, 0, 1 ],
          \[ 1, -3, 8, -12, 12, -9, 6, 0, -1, 0, -2, 0, 1 ],
          \[ 4, 0, 24, 32, 0, 36, 0, 0, 18, -28, 18, -6, 1 ],
          \[ -6, 0, 0, -10, 0, 0, -6, 0, 0, 0, 0, 0, 1 ],
          \[ -1, -2, 1, 1, 26, -5, -11, 0, -13, -4, 0, 0, 1 ],
          \[ 16, -180, 549, -573, 447, -513, 169, -171, 54, -19, 12, 0, 1 ],
          \[ 49, 0, -4602, 10080, 28917, -74304, 11624, 31488, 6213, -480, -162, 0, 1 ],
          \[ 4, 0, -120, 0, 270, 0, -224, 0, 85, 0, -15, 0, 1 ],
          \[ -2, 4, 4, -12, 0, 4, 12, -4, -14, 6, 4, -4, 1 ],
          \[ 24, 0, -1584, 0, 1986, 0, -954, 0, 219, 0, -24, 0, 1 ],
          \[ 27, 0, -279, 0, 588, 0, -422, 0, 133, 0, -19, 0, 1 ],
          \[ -7, -16, -32, -34, -23, -12, 12, 12, -5, 0, 0, -2, 1 ],
          \[ -4, -36, -19, 73, 78, -48, -90, 12, 46, -1, -11, 0, 1 ],
          \[ -1, 0, -3, 0, -2, 0, -1, 0, 2, 0, -3, 0, 1 ],
          \[ 169, 0, -8788, 0, 9659, 0, -3458, 0, 538, 0, -38, 0, 1 ],
          \[ 1, 0, -35, 0, 132, 0, -150, 0, 70, 0, -14, 0, 1 ],
          \[ 1545049, 0, 960267, 0, 134691, 0, -7571, 0, -2091, 0, -69, 0, 1 ],
          \[ 25, 0, -160, 0, 372, 0, -378, 0, 158, 0, -23, 0, 1 ],
          \[ 1, 14, 23, -82, -89, 188, 69, -164, 5, 48, -9, -4, 1 ],
          \[ 4, 0, 0, 0, -7, 0, 0, 0, -14, 0, 0, 0, 1 ],
          \[ -16, 0, 0, 0, 30, 0, 0, 0, -11, 0, 0, 0, 1 ],
          \[ 1, 0, -16, 0, 73, 0, -109, 0, 59, 0, -13, 0, 1 ],
          \[ 4, 0, 18, 0, 93, 0, 104, 0, 0, 0, -6, 0, 1 ],
          \[ -1, 0, 0, 0, 9, 0, 0, 0, -1, 0, 0, 0, 1 ],
          \[ 676, 0, -2016, 0, 2108, 0, -976, 0, 221, 0, -24, 0, 1 ],
          \[ 27, 0, -27, 0, -9, 0, 6, 0, -3, 0, -3, 0, 1 ],
          \[ 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1 ],
          \[ 1, 0, 1, 0, 6, 0, 3, 0, 6, 0, 1, 0, 1 ],
          \[ 1, 0, -5, 0, 0, 0, 9, 0, -2, 0, -3, 0, 1 ],
          \[ 9, 0, 0, -18, 0, 0, 9, 0, 0, 0, 0, 0, 1 ],
          \[ 4, 0, 0, -10, 0, 0, 11, 0, 0, -5, 0, 0, 1 ],
          \[ 2744, 4704, 7056, -7448, 8001, -6552, 3388, -1416, 414, -40, 12, 0, 1 ],
          \[ 164511, -335799, 358551, -219057, 122109, -41958, 16135, -3580, 1073, -163, 
             38, -4, 1 ],
          \[ 1, 0, -3, 0, -3, 0, 4, 0, 2, 0, -1, 0, 1 ],
          \[ 1, 0, -8, 0, 7, 0, 0, 0, 7, 0, 0, 0, 1 ],
          \[ -1, -4, 18, 35, -128, 13, 160, -74, -58, 40, 3, -6, 1 ],
          \[ 4, 0, -6, 0, 5, 0, -2, 0, -1, 0, -2, 0, 1 ],
          \[ -16, 0, 36, 0, 57, 0, -104, 0, 54, 0, -12, 0, 1 ],
          \[ 2, 0, -64, 0, 288, 0, -260, 0, 96, 0, -16, 0, 1 ],
          \[ -8, 96, -72, -128, 210, 0, -136, -24, -36, -16, 0, 0, 1 ],
          \[ 200, 0, -1368, 0, 1752, 0, -902, 0, 216, 0, -24, 0, 1 ],
          \[ 1, -4, 0, 9, 0, -30, 67, -84, 72, -45, 20, -6, 1 ],
          \[ -3, 0, 0, 1, 0, 0, 3, 0, 0, -3, 0, 0, 1 ],
          \[ 4, 8, 4, -8, -6, 0, 16, 0, -20, 12, 2, -4, 1 ],
          \[ 48, 198, -30, -128, -30, 15, 29, -33, -15, 15, -3, -3, 1 ],
          \[ 891, 0, -2691, 0, 2473, 0, -1044, 0, 225, 0, -24, 0, 1 ],
          \[ 169, 0, -2535, 0, 3662, 0, -1821, 0, 393, 0, -36, 0, 1 ],
          \[ 216, 0, -2376, 0, 2862, 0, -1313, 0, 276, 0, -27, 0, 1 ],
          \[ 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 1 ],
          \[ 1, 0, -17, 0, 85, 0, -116, 0, 60, 0, -13, 0, 1 ],
          \[ 10884540241, 0, -2021896020, 0, 143348046, 0, -4839186, 0, 78489, 0, -534, 
             0, 1 ],
          \[ -25, 0, 0, 0, 35, 0, 0, 0, -12, 0, 0, 0, 1 ],
          \[ 323, 0, -1938, 0, 3096, 0, -1566, 0, 327, 0, -30, 0, 1 ],
          \[ 181, 0, -543, 0, 644, 0, -383, 0, 119, 0, -18, 0, 1 ],
          \[ 1, 0, -22, 0, 112, 0, -196, 0, 107, 0, -20, 0, 1 ],
          \[ -4, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 81, 0, -5622, 0, 5951, 0, -2248, 0, 391, 0, -32, 0, 1 ],
          \[ 8560357, 0, -52237562, 0, -72912385, 0, 46928284, 0, -5541749, 0, -14210, 
             0, 1 ],
          \[ 8, 0, -144, 0, 228, 0, -160, 0, 60, 0, -12, 0, 1 ],
          \[ 1, 9, -11, -1, 21, -51, 74, -78, 63, -40, 19, -6, 1 ],
          \[ 49, 0, -220, 0, 344, 0, -245, 0, 87, 0, -15, 0, 1 ],
          \[ 208, 0, -280, 0, 145, 0, -70, 0, 20, 0, -5, 0, 1 ],
          \[ 64, 0, -48, 0, -68, 0, -25, 0, -17, 0, -3, 0, 1 ],
          \[ -1, 0, 6, 0, -3, 0, -8, 0, 12, 0, -6, 0, 1 ],
          \[ -5, 0, 69, -34, -186, 97, 174, -104, -58, 45, 2, -6, 1 ],
          \[ 23104, 0, -30096, 0, 15126, 0, -3826, 0, 519, 0, -36, 0, 1 ],
          \[ 5, 0, -30, 0, -21, 0, 28, 0, 3, 0, -6, 0, 1 ],
          \[ 4, 0, 6, 0, -25, 0, 8, 0, 13, 0, -8, 0, 1 ],
          \[ 25, 0, -170, 0, 309, 0, -235, 0, 86, 0, -15, 0, 1 ],
          \[ 27, 0, -611, 0, 891, 0, -509, 0, 141, 0, -19, 0, 1 ],
          \[ -14, 0, 6, 0, -46, 0, -28, 0, -34, 0, 0, 0, 1 ],
          \[ 16, 0, 0, 0, -8, 0, 0, 0, -18, 0, 0, 0, 1 ],
          \[ 4, 0, -12, 0, 13, 0, -6, 0, -3, 0, 4, 0, 1 ],
          \[ 2, 0, -27, 0, 105, 0, -125, 0, 61, 0, -13, 0, 1 ],
          \[ -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1 ],
          \[ 3, 0, 0, -3, 0, 0, 3, 0, 0, -3, 0, 0, 1 ],
          \[ -2, 0, 0, 4, 0, 0, 2, 0, 0, -4, 0, 0, 1 ],
          \[ -1, 0, 0, 3, 0, 0, -2, 0, 0, -2, 0, 0, 1 ],
          \[ 1, 0, 0, 4, 0, 0, -4, 0, 0, -1, 0, 0, 1 ],
          \[ -2, 0, 0, -8, 0, 0, -12, 0, 0, -2, 0, 0, 1 ],
          \[ 1, 0, 0, -2, 0, 0, 2, 0, 0, -1, 0, 0, 1 ],
          \[ 80, -1468, -5433, 31758, 35725, -16814, -15840, 3233, 2069, -190, -85, 3, 1 
             ],
          \[ 1, 0, -28, 0, 135, 0, -156, 0, 71, 0, -14, 0, 1 ],
          \[ -1, 4, -4, 0, 0, 1, -4, 4, 5, -15, 14, -6, 1 ],
          \[ 2, 0, -34, 0, 98, 0, -107, 0, 53, 0, -12, 0, 1 ],
          \[ 1, 0, -13, 0, 54, 0, -80, 0, 48, 0, -12, 0, 1 ],
          \[ 1775, -22518, 17484, -13176, -22005, 3996, 4372, 0, -315, -54, 0, 0, 1 ],
          \[ -6776, -28424, -8716, 58784, 45009, -13376, -13572, 1024, 1450, -24, -64, 
             0, 1 ],
          \[ -73, 1380, 8780, 12320, -4455, -14872, -5232, 1984, 1114, -48, -62, 0, 1 ],
          \[ 4, 0, 0, -8, 0, 0, 5, 0, 0, -1, 0, 0, 1 ],
          \[ 9616, -43272, -21636, 102474, 49953, -27216, -14530, 2466, 1566, -72, -69, 
             0, 1 ],
          \[ 6882575909, 2972896206, -2074843638, -264799046, 148490544, 9070833, 
             -4461428, -150879, 63891, 1162, -423, -3, 1 ],
          \[ 35969, -213274, 380622, -228636, -43306, 92583, -18568, -8429, 2631, 262, 
             -103, -3, 1 ],
          \[ -1, 54, 93, -152, -216, 187, 172, -128, -52, 45, 2, -6, 1 ],
          \[ 67, 0, -265, 0, 378, 0, -255, 0, 88, 0, -15, 0, 1 ],
          \[ 64, 0, -848, 0, 1300, 0, -750, 0, 195, 0, -23, 0, 1 ],
          \[ 48, 0, -276, 0, 489, 0, -362, 0, 120, 0, -18, 0, 1 ],
          \[ 1, 0, -17, 0, 72, 0, -99, 0, 56, 0, -13, 0, 1 ],
          \[ 4, 0, -54, 0, 195, 0, -197, 0, 82, 0, -15, 0, 1 ],
          \[ 308, 0, -898, 0, 973, 0, -512, 0, 140, 0, -19, 0, 1 ],
          \[ -13, 0, 0, 0, 19, 0, 0, 0, -8, 0, 0, 0, 1 ],
          \[ 8, 0, -120, 0, 258, 0, -217, 0, 84, 0, -15, 0, 1 ],
          \[ 539, 0, -1365, 0, 1316, 0, -628, 0, 158, 0, -20, 0, 1 ],
          \[ 5184, 0, -13104, 0, 9852, 0, -3237, 0, 508, 0, -37, 0, 1 ],
          \[ 101, 0, -505, 0, 724, 0, -447, 0, 134, 0, -19, 0, 1 ],
          \[ 63, 0, -322, 0, 497, 0, -342, 0, 115, 0, -18, 0, 1 ],
          \[ 6, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 2, 14, 8, -74, -56, 148, 77, -142, -21, 60, -11, -4, 1 ],
          \[ -6, 0, 0, 0, 18, 0, 0, 0, -9, 0, 0, 0, 1 ],
          \[ 1, 5, -15, -70, 25, 197, -10, -181, 9, 54, -7, -5, 1 ],
          \[ -2, 0, 0, 0, 9, 0, 0, 0, -12, 0, 0, 0, 1 ],
          \[ -1, 0, 0, 0, 4, 0, -2, 0, -4, 0, 0, 0, 1 ],
          \[ 2, 0, 2, 0, 5, 0, -16, 0, 12, 0, -10, 0, 1 ],
          \[ -12, 0, 12, 0, -8, 0, 9, 0, -1, 0, -3, 0, 1 ],
          \[ 5, 0, -95, 0, 244, 0, -215, 0, 84, 0, -15, 0, 1 ],
          \[ 144, 864, 1944, 1920, 621, -162, -101, -60, -45, -2, -3, 0, 1 ],
          \[ 2389, -864, -17855, -1208, 16143, 1485, -5571, -482, 847, 53, -53, -1, 1 ],
          \[ 49, 0, -217, 0, 334, 0, -239, 0, 86, 0, -15, 0, 1 ],
          \[ 5, 0, -25, 0, 14, 0, 14, 0, -8, 0, -2, 0, 1 ],
          \[ 2, 0, 4, 0, 6, 0, 0, 0, -1, 0, 2, 0, 1 ],
          \[ 4, 0, -8, 0, -20, 0, 20, 0, 10, 0, -8, 0, 1 ],
          \[ 1, 0, -12, 0, -1, 0, 9, 0, -1, 0, -2, 0, 1 ],
          \[ 1, 0, -16, 0, 79, 0, -133, 0, 74, 0, -15, 0, 1 ],
          \[ 64, 192, 300, 272, 192, 180, 155, 54, -30, -33, -6, 3, 1 ],
          \[ -108, 432, -576, 256, 0, 0, 0, 0, 12, -16, 0, 0, 1 ],
          \[ 729, 0, -270, -512, 63, 0, 348, 0, 135, 0, 18, 0, 1 ],
          \[ 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -2, 0, 0, -12, 0, 0, -10, 0, 0, 0, 0, 0, 1 ],
          \[ -3, 0, 0, 6, 0, 0, -2, 0, 0, -1, 0, 0, 1 ],
          \[ 2, 0, 0, -16, 0, 0, 20, 0, 0, -8, 0, 0, 1 ],
          \[ 64, 0, -144, 64, 81, -72, 0, 0, -36, -8, 0, 0, 1 ],
          \[ 6119045, -9324460, -11780111, 2062468, 2798428, -109816, -246953, -1630, 
             9372, 162, -159, -2, 1 ],
          \[ 128, 0, -288, 0, 162, 0, -32, -48, -36, 0, 0, 0, 1 ],
          \[ -32, -96, 72, 248, 273, 144, 8, -48, -36, -8, 0, 0, 1 ],
          \[ 1, 2, -21, -19, 82, 56, -118, -58, 73, 21, -17, -2, 1 ],
          \[ 1, 0, 0, -14, 0, 0, 23, 0, 0, -9, 0, 0, 1 ],
          \[ 2, 0, 0, 4, 0, 0, 0, 0, 0, -4, 0, 0, 1 ],
          \[ 1, 0, 0, -18, 0, 0, -11, 0, 0, 0, 0, 0, 1 ],
          \[ 2336832, -211968, 278784, -69696, 52272, 0, 2112, -1056, 396, 0, 0, -4, 1 ],
          \[ 1, -4, 11, -15, 5, 21, -39, 21, 5, -15, 11, -4, 1 ],
          \[ 1, 20, 94, 36, 77, 8, 92, -24, 33, -20, 2, -4, 1 ],
          \[ 49, -196, -56, 476, -215, -256, 224, 0, -63, 28, 0, -4, 1 ],
          \[ 1028196, 0, -773344, 0, 167648, 0, -20228, 0, 1472, 0, -60, 0, 1 ],
          \[ 1, 0, 10, 0, -29, 0, 16, 0, 6, 0, -6, 0, 1 ],
          \[ -2, 0, 0, 0, 12, 0, 0, 0, -7, 0, 0, 0, 1 ],
          \[ 3, 0, -51, 0, 133, 0, -134, 0, 62, 0, -13, 0, 1 ],
          \[ 4, 0, -50, 0, 160, 0, -165, 0, 72, 0, -14, 0, 1 ],
          \[ 8, 0, -102, 0, 371, 0, -486, 0, 185, 0, -24, 0, 1 ],
          \[ 194, 0, -884, 0, 1065, 0, -570, 0, 153, 0, -20, 0, 1 ],
          \[ 2932, 0, -5131, 0, 3599, 0, -1293, 0, 251, 0, -25, 0, 1 ],
          \[ 1, 0, -11, 0, 4, 0, 13, 0, -4, 0, -3, 0, 1 ],
          \[ 18, 0, -28, 0, -30, 0, 36, 0, 1, 0, -6, 0, 1 ],
          \[ -2, 32, 72, -96, -178, 132, 153, -102, -51, 40, 3, -6, 1 ],
          \[ 9, 39, -134, -662, 387, 3152, 674, -3159, 363, 435, -75, -5, 1 ],
          \[ 64, 0, -399, 0, 612, 0, -397, 0, 123, 0, -18, 0, 1 ],
          \[ 57, 0, -114, 0, -219, 0, 74, 0, 30, 0, -12, 0, 1 ],
          \[ 5, 0, -50, 0, 144, 0, -152, 0, 70, 0, -14, 0, 1 ],
          \[ 5, 0, 50, 0, 65, 0, -135, 0, 69, 0, -14, 0, 1 ],
          \[ 144, 0, -576, 0, 840, 0, -552, 0, 167, 0, -22, 0, 1 ],
          \[ -729, 0, -1458, 0, -243, 0, 540, 0, 135, 0, 18, 0, 1 ],
          \[ 13, 0, 35, 0, 4, 0, -27, 0, -6, 0, 6, 0, 1 ],
          \[ 4, 0, 2, 0, -6, 0, -3, 0, 0, 0, -2, 0, 1 ],
          \[ 1, 0, -18, 0, 63, 0, -85, 0, 49, 0, -12, 0, 1 ],
          \[ 125, 0, -900, -32, 2133, 108, -780, -648, 63, 260, 0, 0, 1 ],
          \[ -1, 12, 6, -64, -99, -48, 40, 48, 12, -12, -6, 0, 1 ],
          \[ 729, -2916, 2592, 1728, 162, -540, 0, 0, 27, -12, 0, 0, 1 ],
          \[ -793, -1848, -1494, -256, 207, 0, -60, 0, 9, -8, -6, 0, 1 ],
          \[ -1, 9, 129, -114, -276, 212, 201, -154, -53, 50, 1, -6, 1 ],
          \[ -8, -48, 0, -16, -33, 0, 24, -24, 18, -8, 0, 0, 1 ],
          \[ 9, -36, 90, -120, 105, -36, 8, 0, 0, -4, 0, 0, 1 ],
          \[ 80, 480, 1080, 1160, 765, 540, 210, -180, -135, 0, 0, 0, 1 ],
          \[ 2, 24, -108, -232, 45, -24, -28, -24, -24, 0, 0, 0, 1 ],
          \[ -9, -56, -124, -134, -70, 46, 41, -8, 5, 4, 1, -4, 1 ],
          \[ -32, 0, 288, -32, -402, -72, 164, 96, 18, -16, -12, 0, 1 ],
          \[ -304, -528, 684, 1572, 57, -1332, -186, 276, 99, -16, -18, 0, 1 ],
          \[ -1, -6, 9, 55, -84, -27, 51, 21, -18, -3, 3, 0, 1 ],
          \[ -4, 0, 0, -8, 0, 0, -6, 0, 0, 0, 0, 0, 1 ],
          \[ -88, -928, -44, 704, -143, -352, 220, 0, -22, 0, 0, 0, 1 ],
          \[ 1, 0, -2, 0, 2, 0, -4, 0, 1, 0, 2, 0, 1 ],
          \[ 16, -96, 216, -232, 126, 0, -96, 72, 0, -4, 6, 0, 1 ],
          \[ 212, 0, -657, 0, 768, 0, -434, 0, 126, 0, -18, 0, 1 ],
          \[ 1, 12, 47, 42, -155, -376, -170, 188, 141, -16, -22, 0, 1 ],
          \[ 37, 0, -185, 0, 312, 0, -235, 0, 86, 0, -15, 0, 1 ],
          \[ 31, 0, -175, 0, 310, 0, -235, 0, 86, 0, -15, 0, 1 ],
          \[ -3, 0, 0, 0, 2, 0, 2, 0, 0, 0, -3, 0, 1 ],
          \[ 1, 0, -27, 0, 99, 0, -131, 0, 72, 0, -16, 0, 1 ],
          \[ -1, 32, 72, -96, -178, 132, 153, -102, -51, 40, 3, -6, 1 ],
          \[ 12609, -19728, 16896, -6992, 1974, -912, 786, 96, -15, -24, -6, 0, 1 ],
          \[ 9, -144, 900, -2672, 3942, -2736, 1110, -576, 333, -24, 36, 0, 1 ],
          \[ 441, 0, -3676, 0, 4345, 0, -1800, 0, 340, 0, -30, 0, 1 ],
          \[ 81, 243, -3240, -756, 13527, 810, -7488, -324, 1287, 27, -72, 0, 1 ],
          \[ 14201, 67782, 113355, 59390, -37695, -53496, -13643, 4668, 2097, -96, -84, 
             0, 1 ],
          \[ 3, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 1 ],
          \[ -2, -8, -12, -1, 19, 21, 10, 6, 3, -6, -6, 0, 1 ],
          \[ -2, 0, 5, 0, 1, 0, -5, 0, -2, 0, 0, 0, 1 ],
          \[ 4, 0, -46, 0, 135, 0, -139, 0, 63, 0, -13, 0, 1 ],
          \[ 5, 0, -45, 0, 129, 0, -134, 0, 62, 0, -13, 0, 1 ],
          \[ -2, 0, 4, 0, 2, 0, 4, 0, -3, 0, -2, 0, 1 ],
          \[ -16, 0, 136, -80, -108, 64, 70, -84, 28, 12, 0, -4, 1 ],
          \[ 5, 50, 94, -136, -242, 190, 199, -146, -55, 50, 1, -6, 1 ],
          \[ 1219, 0, -2943, 0, 2535, 0, -1049, 0, 225, 0, -24, 0, 1 ],
          \[ 1, 12, 18, -112, -198, -36, 114, 36, 18, -4, -12, 0, 1 ],
          \[ 160, 960, 2160, 2224, 1098, 432, 168, -144, -108, -8, -12, 0, 1 ],
          \[ -16, -96, -216, -184, 63, 216, 116, 24, 18, -8, -12, 0, 1 ],
          \[ 16, 96, 216, 248, 225, 216, 92, -48, -36, -2, -3, 0, 1 ],
          \[ -144, -288, 720, 960, -399, -864, -28, 288, 54, -32, -12, 0, 1 ],
          \[ 32, 0, 144, 0, 162, 0, 8, -24, -18, 0, 0, 0, 1 ],
          \[ -112, -384, 504, 992, -255, -864, -52, 288, 54, -32, -12, 0, 1 ],
          \[ 8, 24, 0, -8, 81, 0, -108, 0, 54, 0, -12, 0, 1 ],
          \[ 23, 142, 107, -304, -258, 296, 187, -166, -50, 50, 1, -6, 1 ],
          \[ -27, 108, -144, 64, 27, -72, 48, 0, 0, 0, 0, 0, 1 ],
          \[ 3, -12, 45, -94, 124, -112, 79, -48, 36, -22, 13, -4, 1 ],
          \[ 27, 108, 144, 64, -18, -48, -32, 0, -3, -4, 0, 0, 1 ],
          \[ -11943, -32640, -48664, -52184, -42490, -26260, -11742, -2760, 381, 316, 
             -2, -12, 1 ],
          \[ -5, 2, 55, -27, -154, 73, 154, -86, -55, 40, 3, -6, 1 ],
          \[ -4, 8, 32, -86, 44, 39, -82, 60, -9, -15, 14, -6, 1 ],
          \[ 1, 0, 12, 0, 15, 0, -60, 0, 45, 0, -12, 0, 1 ],
          \[ 3, -36, -78, 10, 75, 28, -22, 4, -27, 12, 8, -6, 1 ],
          \[ 76396, 70872, -62658, -61429, 22593, 20775, -4892, -3348, 657, 245, -45, 
             -6, 1 ],
          \[ 1, 80, 124, -226, -268, 264, 193, -162, -51, 50, 1, -6, 1 ],
          \[ -1, 4, 10, -28, -48, 0, 68, -32, -32, 24, 2, -4, 1 ],
          \[ 16, 96, 216, 248, 225, 216, 108, 0, 0, -8, -12, 0, 1 ],
          \[ -8, -60, -126, -88, -57, 36, 70, 48, 72, -16, 0, 0, 1 ],
          \[ 2, 8, -12, 8, 14, -40, 32, -8, -17, 20, -2, -4, 1 ],
          \[ 13257, -16848, 10812, -1232, -762, -912, 498, 96, 21, -24, -6, 0, 1 ],
          \[ -16, -96, -216, -120, 351, 648, 316, -24, -18, -8, -12, 0, 1 ],
          \[ -16, -60, -9, 155, 87, -135, -109, 45, 54, -5, -12, 0, 1 ],
          \[ 27, 0, -48, -64, 0, 24, 48, 0, -3, -12, 0, 0, 1 ],
          \[ -29, 70, 4, -20, -21, -60, -3, -5, -11, 0, -5, 0, 1 ],
          \[ 1, -12, 27, 30, -120, 12, 151, -66, -60, 40, 3, -6, 1 ],
          \[ 64, -72, -468, 186, 393, -162, -160, 54, 54, -6, -12, 0, 1 ],
          \[ -41, 89, -64, -255, 415, 88, -392, -8, 145, 15, -16, -1, 1 ],
          \[ 27, 108, 144, 64, -27, -72, -48, 0, 0, 0, 0, 0, 1 ],
          \[ 16, 96, 216, 224, 117, 54, 15, -36, -27, -2, -3, 0, 1 ],
          \[ 2, 4, 18, 20, 6, 60, 16, -10, 66, -22, 14, -6, 1 ],
          \[ -108, 432, -576, 256, 108, -288, 192, 0, 0, 0, 0, 0, 1 ],
          \[ 169, 0, -570, 0, 712, 0, -421, 0, 125, 0, -18, 0, 1 ],
          \[ 800, 1280, -912, -320, 50, 0, -80, 0, 20, 0, 0, 0, 1 ],
          \[ 48, 96, 112, 50, 25, 0, 20, 0, 10, 0, 4, -2, 1 ],
          \[ 1, -2, -40, -67, 20, 65, -8, -14, 17, 0, -8, 0, 1 ],
          \[ 1, -4, -6, 14, -6, -10, 41, -47, 46, -27, 14, -4, 1 ],
          \[ -8, 40, 24, -16, -16, -16, -1, 16, 7, -8, -7, 0, 1 ],
          \[ -3, 10, 13, -28, -18, 6, 25, 4, -4, -6, -1, 0, 1 ],
          \[ 27, 108, 144, 64, 0, 0, 0, 0, -9, -12, 0, 0, 1 ],
          \[ 4, 0, -43, 0, 110, 0, -113, 0, 54, 0, -12, 0, 1 ],
          \[ 13, 0, -495, 0, 803, 0, -486, 0, 139, 0, -19, 0, 1 ],
          \[ 2, 0, 2, 0, 2, 0, 0, 0, -3, 0, -3, 0, 1 ],
          \[ -8, 48, -112, 120, -50, 0, 0, 0, 0, 0, 4, -4, 1 ],
          \[ 16, 96, 216, 200, 9, -108, -66, -36, -27, 0, 0, 0, 1 ],
          \[ -2, -4, 6, 24, 21, -2, -11, -2, 2, -3, -3, 0, 1 ],
          \[ -108, -432, -576, -256, 0, 0, 0, 0, -9, -12, 0, 0, 1 ],
          \[ 1, 0, 0, 0, -3, -6, 2, 3, -3, 5, 0, -3, 1 ],
          \[ 7, 0, -86, 0, 181, 0, -156, 0, 65, 0, -13, 0, 1 ],
          \[ 1, -8, -10, 9, -9, -8, 27, -2, -11, 9, -1, -3, 1 ],
          \[ -20, 30, 120, -250, 15, 240, -60, -120, 60, 50, -6, -6, 1 ],
          \[ 9768751, 0, 0, 0, 0, -37506, 6251, 0, 0, 0, 36, -12, 1 ],
          \[ -6614975, 240, 1026, 2560, 4095, 4320, 2940, 1152, 135, -80, -30, 0, 1 ],
          \[ -125, -300, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 1, 2, 2, 3, 2, 1, 0, 0, -1, -1, 0, -1, 1 ],
          \[ 833611, 1839798, 2384844, 1398122, 625185, -88704, 99330, -17028, 5841, 
             -814, 198, -6, 1 ],
          \[ 2, 8, -40, -46, 110, 71, -113, -43, 54, 11, -12, -1, 1 ],
          // degree 13
          \[ -1, 10, 68, -291, -215, 738, 246, -601, -116, 190, 19, -24, -1, 1 ],
          \[ 4, 304, -2759, 1835, 13442, 3890, -9319, -5045, 943, 857, -6, -50, -1, 1 ],
          \[ 3, 0, -234, -624, 1443, 2886, -507, -1989, 0, 468, 0, -39, 0, 1 ],
          \[ -99005292450, -10720383375, 21836871550, -557344775, -1553609850, 
             152496175, 39456950, -5556850, -393900, 76895, 1300, -455, 0, 1 ],
          \[ -1875, -5850, 51948, 191178, 216723, 68328, -33813, -21255, 1326, 1989, 0, 
             -78, 0, 1 ],
          \[ 69500, 203125, 0, -284375, 0, 113750, 0, -19500, 0, 1625, 0, -65, 0, 1 ],
          \[ -9, -21, -9, 9, 66, -18, 63, -99, 36, -24, 13, 3, -3, 1 ],
          \[ -3888, 4212, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -1, 0, 0, 0, 0, 1, 3, -1, 0, 0, 0, -1, -1, 1 ],
          // degree 14
          \[ 1, 0, 53, 0, 686, 0, 1194, 0, 767, 0, 214, 0, 25, 0, 1 ],
          \[ 8591, 0, 5415, 0, 731, 0, 1251, 0, 333, 0, 53, 0, 9, 0, 1 ],
          \[ -911, 943, 1018, 422, 782, 401, -282, -255, 33, 26, -19, 5, 16, 7, 1 ],
          \[ 8, -4, 1, 14, -22, 4, 13, -14, 26, -34, 26, -14, 8, -4, 1 ],
          \[ 484, 0, 3136, 0, 6272, 0, 4704, 0, 1680, 0, 308, 0, 28, 0, 1 ],
          \[ -1, 0, -56, 0, 406, 0, -322, 0, -245, 0, 56, 0, 28, 0, 1 ],
          \[ -3, 0, 1, 0, -6, 0, 0, 0, -1, 0, 3, 0, 3, 0, 1 ],
          \[ 823, 896, -532, -546, 336, 196, 147, 360, 140, -28, 28, 28, 0, 0, 1 ],
          \[ -7, 0, 0, 0, 294, 0, 588, 0, -245, 0, -49, 0, 7, 0, 1 ],
          \[ -112, -196, 133, -147, -2072, -3668, -2905, -894, 371, 455, 119, -35, -21, 
             0, 1 ],
          \[ -1, 0, 85, 0, -379, 0, 611, 0, -463, 0, 171, 0, -27, 0, 1 ],
          \[ -577916, 739662, -123305, -272986, 330764, -251559, 129262, -48856, 15953, 
             -4004, 756, -189, 28, 0, 1 ],
          \[ 2432, 6304, 7064, 31142, 96637, 128405, 92188, 46467, 18163, 3498, -352, 
             -222, -29, -2, 1 ],
          \[ 656356768, 0, 0, 0, 0, 0, 0, -31958, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 336238208, 348280352, 197804880, 95169270, 42847770, 12260920, 570164, 
             -607634, -94150, 19838, 5271, -147, -105, 0, 1 ],
          \[ 93084845681, -351070982458, 334176753379, 7649980758, -26524109654, 
             299534410, 768587344, -9963017, -12009193, 102858, 106400, -364, -504, 0, 1 
             ],
          \[ 3495368, 0, -3987152, 0, 1736792, 0, -353912, 0, 32592, 0, -964, 0, -18, 0, 
             1 ],
          \[ 1, 0, -17, 0, 23, 0, 27, 0, -25, 0, -11, 0, 5, 0, 1 ],
          \[ -17, 0, 257, 0, -650, 0, 699, 0, -386, 0, 114, 0, -17, 0, 1 ],
          \[ -59618052726016, 4701085568256, -3146649429952, 138886748224, -28570776528, 
             6022284016, 1002627612, -27661364, 7977046, -534016, 63455, -3164, 210, 0, 
             1 ],
          \[ -49, 0, 112, 0, 136, 0, -227, 0, 75, 0, 9, 0, -8, 0, 1 ],
          \[ 91264986397629, 7429846568445, 17926524826973, 4638317668005, 
             -335941176396, -117366985106, 2085856500, 859373823, -17922660, -708246, 
             118671, -9555, -63, 0, 1 ],
          \[ -1494810659, 704643912, 478963261, 48481531, 12092913, 1229802, -1470049, 
             -257782, -24528, -1372, 2534, 245, -56, 0, 1 ],
          \[ 4, -252, 49, -504, 196, -252, 294, -36, 210, 0, 77, 0, 14, 0, 1 ],
          \[ 7702, -5544, 18753, -3416, 22358, -6384, 7987, -5008, 1834, -840, 371, -56, 
             42, 0, 1 ],
          \[ 3694092486327, -939301493970, 453056529394, 9534071757, 5374837503, 
             2646742063, 492620814, 16294977, 4599168, 1459962, 80241, -5243, -546, 0, 1 
             ],
          \[ 151, 0, -79, 0, -9, 0, -16, 0, 25, 0, 3, 0, 5, 0, 1 ],
          \[ -1, 0, 2, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1 ],
          \[ -1, 9, -23, 0, 77, -100, 9, 97, -121, 59, 8, -29, 20, -7, 1 ],
          \[ 35152, 70304, 0, 0, 17576, 0, 0, 0, 845, -338, 0, 0, 13, -6, 1 ],
          \[ -13275, -20370, 21322, -31885, 27853, -13391, 9114, -1885, 1680, -21, 259, 
             -7, 14, 0, 1 ],
          \[ -736, -1120, -392, -448, 0, -560, 392, -16, 0, 0, -42, 0, 0, 0, 1 ],
          \[ -746496, 0, 43964424, 0, 2314872, 0, 359730, 0, 11872, 0, 1848, 0, 84, 0, 1 
             ],
          \[ -36, 0, 8, 0, 68, 0, -12, 0, -36, 0, 4, 0, 4, 0, 1 ],
          \[ -16, 0, 661, 0, -2194, 0, 2632, 0, -1328, 0, 289, 0, -28, 0, 1 ],
          \[ 551872, -1751568, 2804872, -2714152, 1918966, -706293, 120393, 5510, 5068, 
             -2282, 399, -147, -7, 0, 1 ],
          \[ 252, 252, 819, 546, 1267, 980, 1127, 466, 196, -56, -35, -28, 0, 0, 1 ],
          \[ -1, 4, -12, 23, -37, 39, -30, 28, -16, -2, 3, -4, 7, -4, 1 ],
          \[ -108, -648, -1404, 0, 0, 234, 585, 0, 0, 0, -78, 0, 0, -2, 1 ],
          \[ 12, 0, 49, 0, 91, 0, 70, 0, 35, 0, 7, 0, 0, 0, 1 ],
          \[ -1, 0, 4, 0, 10, 0, 17, 0, 13, 0, 9, 0, 3, 0, 1 ],
          \[ -859963392, 0, 446777856, 0, -62338248, 0, 650916, 0, 110376, 0, -2268, 0, 
             -42, 0, 1 ],
          \[ -1, 12, -49, 104, -173, 208, -195, 138, -70, 38, -14, 4, 3, -2, 1 ],
          \[ -107, 0, 889, 0, -1827, 0, 1631, 0, -735, 0, 175, 0, -21, 0, 1 ],
          \[ 9153, -3294, 11915, -484, -3310, 4052, -5118, 2984, 277, -442, 239, -120, 
             29, -6, 1 ],
          \[ 112, -784, 1792, -560, -4480, 8848, -7560, 3024, -252, -140, -28, 28, 7, 
             -7, 1 ],
          \[ -5, 0, 35, 0, -85, 0, 114, 0, -90, 0, 41, 0, -10, 0, 1 ],
          \[ 1, -3, -8, 31, 21, -122, -15, 219, -15, -122, 21, 31, -8, -3, 1 ],
          \[ 1, 0, 1, -2, 2, -3, 3, -3, 3, -3, 2, -2, 1, 0, 1 ],
          \[ -1, 0, -2, 0, -3, 0, 4, 0, 3, 0, 0, 0, -3, 0, 1 ],
          \[ 1, -5, 7, -4, 6, 12, -35, 1, 10, -2, 11, 5, -8, -1, 1 ],
          \[ 1218738478092, 350406522166, 209844613155, 32364129844, 11161212803, 
             589502440, 242006399, -19131448, 4628975, -143740, 93997, -406, 490, 0, 1 ],
          \[ -1, 3, 2, -22, 57, -114, 184, -241, 253, -211, 139, -71, 27, -7, 1 ],
          \[ -37, 42, 444, -499, 717, 772, -605, -300, 418, -108, -133, 73, -10, -2, 1 ],
          \[ -1, -1, 0, 1, 1, 1, -4, 1, 1, 0, 6, -15, 14, -6, 1 ],
          \[ 1, 0, 3, 0, -24, 0, 44, 0, -42, 0, 22, 0, -7, 0, 1 ],
          \[ -1, -2, 3, 3, -10, 5, -1, 0, 7, -9, 13, -13, 10, -5, 1 ],
          \[ 2556, -5964, 3479, 0, 0, 0, 0, 138, -161, 0, 0, 0, 0, 0, 1 ],
          \[ 562500, 0, -153125, 0, 0, 0, 0, -1500, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 36, 84, 49, 0, 0, 0, 0, -6, -7, 0, 0, 0, 0, 0, 1 ],
          \[ 36, 84, 49, 0, 0, 0, 0, -18, -21, 0, 0, 0, 0, 0, 1 ],
          \[ -5061888, -1053696, 0, 0, 0, -52416, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          // degree 15
          \[ 1, 1, -65, 60, 508, -525, -1112, 918, 885, -614, -300, 182, 42, -23, -2, 1 ],
          \[ -22825, 162804, -478177, 775903, -707345, 95751, 192039, -50961, -23852, 
             6364, 875, -188, 138, 17, -1, 1 ],
          \[ 1, 0, -6, -22, -47, -39, 37, 37, -2, 37, -12, -2, 0, 2, 2, 1 ],
          \[ 1, 0, 15, 42, 35, 97, -32, 79, -58, -5, -24, -18, 1, -4, 1, 1 ],
          \[ 9, 72, 288, 687, 1026, 894, 276, -201, -282, -121, -39, 72, 24, -12, -3, 1 ],
          \[ -2, 0, 0, 0, 0, -3708, 0, 0, 0, 0, -30, 0, 0, 0, 0, 1 ],
          \[ 1, 0, 2, 6, -3, -3, 5, 1, 2, 7, 6, -2, 0, 2, -2, 1 ],
          \[ -8, 0, 0, 0, 0, -228, 0, 0, 0, 0, 32, 0, 0, 0, 0, 1 ],
          \[ 4461221029, -7998223215, -5452953875, 7178878600, 717324725, -1542190154, 
             25284495, 119761820, -3714805, -4292700, 85357, 71840, -305, -470, 0, 1 ],
          \[ 1547, -5195, 6335, -1690, -3670, 3450, 400, -1925, 505, 550, -301, -55, 65, 
             -5, -5, 1 ],
          \[ 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -9179941, -6362585, 20087950, 19171805, -8278925, -11702794, 708890, 
             2876560, 112750, -325950, -14493, 15930, 70, -235, 0, 1 ],
          \[ -92889, -192375, -246465, -386555, -335025, 12810, 177525, 59640, -26775, 
             -14450, 1224, 1095, -90, -60, 0, 1 ],
          \[ 1432484, -5090420, 9369840, -9360980, 7033715, -3389737, 1127980, -156480, 
             -2815, 7935, 1142, 970, 220, 50, 5, 1 ],
          \[ -101738531, -165940785, -145749015, -53305596, -239988, -1001076, -2539227, 
             50352, 318432, 11178, -13272, 426, 277, -54, -3, 1 ],
          \[ 1, -2, -13, -8, 46, -32, -90, 140, -3, -40, -17, 36, 8, 3, -1, 1 ],
          \[ -450, -2250, 0, -1375, 0, 7305, 1800, 9000, 1350, 3625, 162, 630, 0, 45, 0, 
             1 ],
          \[ 1, -25, -160, -460, -875, -1153, -1105, -740, -165, 150, 149, 55, -15, -15, 
             0, 1 ],
          \[ -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ],
          \[ -1, -9, 0, 77, -24, 162, 22, 153, 54, 134, 18, 54, 2, 12, 0, 1 ],
          \[ 26273539, 57236934, -8511147, -80656366, 46961715, 2066256, -6975764, 
             821655, 487485, -109799, -13182, 5031, 59, -96, 0, 1 ],
          \[ -138979, -101025, 195837, 185503, -215697, -358221, -95461, 100197, 83334, 
             15172, -4800, -1818, -65, 27, 6, 1 ],
          \[ 1, -2, 0, 5, -3, -2, 7, -2, 7, -3, 0, 8, 7, 8, 5, 1 ],
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          \[ -57107, 8415, 263540, -33660, -436445, 13487, 333260, 31690, -114730, 
             -24280, 13297, 3330, -470, -110, 5, 1 ],
          \[ 23255, 93525, -3750, -247825, -119280, 214578, 161150, -60675, -73410, 
             -1700, 12366, 2400, -520, -150, 0, 1 ],
          \[ -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 64, -112, -712, 1034, 1032, 26, -312, -987, -64, 316, 64, -32, -8, -6, 0, 1 
             ],
          \[ 2, 0, 0, 4, 0, 0, 6, 0, 0, 6, 0, 0, 4, 0, 0, 1 ],
          \[ -377, -3200, -9555, -8695, 13270, 35952, 23050, -8030, -14270, -1980, 2791, 
             700, -220, -55, 5, 1 ],
          \[ 674662192576472, -201477388078380, -52551636276610, 8058450933185, 
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             -1724326, 196335, 8650, -615, 0, 1 ],
          \[ -1, 15, -42, 79, -117, 150, -190, 63, 72, 14, -60, -3, 26, -9, -3, 1 ],
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          \[ -1, -12, -16, -11, -12, 10, 48, 52, 53, 67, 44, 6, 0, 7, 5, 1 ],
          \[ 27, 279, 1350, 3487, 4868, 2690, -1543, -3994, -482, 1017, 382, -55, -73, 
             -8, 5, 1 ],
          \[ -1, -12, -15, 248, 813, -282, -4330, -6093, -1494, 3061, 2424, 330, -194, 
             -48, 3, 1 ],
          \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1 ],
          \[ 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, -5, 0, 0, 0, 0, 1 ],
          \[ 1313680000, 2535100000, 1343230000, -135052500, -281431250, -63158850, 
             -21372125, -11798025, 3236100, 4157575, 1101150, 83550, -5500, -675, 5, 1 ],
          \[ 9378358624, 10724525400, 5043879720, 981089960, -73095900, -29685606, 
             7999460, 794220, -455490, -36275, 2880, 75, -30, -15, 0, 1 ],
          \[ -512, 26880, 28160, -281600, -474720, 276592, 686640, -14160, -266000, 
             -62800, 19755, 7685, 130, -150, -5, 1 ],
          \[ 1, -2670, -774, 4043, -372, 11790, 8818, 5670, -54, -674, -270, 0, 31, -6, 
             0, 1 ],
          \[ 8, 0, 0, 0, 0, 0, 12, 0, 0, 11, 0, 0, 5, 0, 0, 1 ],
          \[ -43, 0, 0, -105, 0, 0, 285, 0, 0, -100, 0, 0, 5, 0, 0, 1 ],
          \[ 777069, -2726259, 4387594, -2852755, 97666, 681292, 95861, -119521, 24160, 
             14373, 508, -17, 133, 28, -6, 1 ],
          \[ -121, -495, 612, -360, 468, 252, -436, -81, 18, -43, -3, 27, 1, -9, 0, 1 ],
          \[ -28454, 80509, -108581, 53515, 43297, -91720, 59365, -6962, -15872, 12741, 
             -4627, 823, -18, -6, -2, 1 ],
          \[ 1760792336076600478279, 760206096328309516732, 130572572437690038271, 
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             35036846, 418640, -15544, -18, 1 ],
          \[ -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -7279, -39745, -58420, -28890, 5450, 16836, 6980, -1950, -1670, 50, 139, 0, 
             -10, -5, 0, 1 ],
          \[ 1024, -48320, 126420, -150040, 136600, -156072, 142500, -55090, -12230, 
             9150, 266, 330, -5, -50, 0, 1 ],
          \[ -8, 0, 0, 27, 0, 0, 19, 0, 0, 11, 0, 0, 5, 0, 0, 1 ],
          \[ 3, 0, -24, -15, 21, 36, 102, 198, 198, 133, 90, 67, 44, 22, 7, 1 ],
          \[ -5989054, -6410634, -135012, 2415630, 2170494, -295140, -1326320, -428418, 
             136296, 90400, 5454, -4950, -1074, -60, 6, 1 ],
          \[ 4, 0, 0, -1, 0, 0, 6, 0, 0, 3, 0, 0, 0, 0, 0, 1 ],
          \[ -1, -45, 815, -7105, 30185, -42329, -44395, 20595, 15625, -4375, -2399, 
             525, 175, -35, -5, 1 ],
          \[ 612968886770859386964763021, 338165560497864890767793817, 
             -5767418822154378301922100, -5086537813630840677351345, 
             -151310638511676685186017, 2235951723532365786373, 111386427537228333570, 
             268871342200307043, -22599650147469301, -183592676667989, 850215157784, 
             10447793997, -7490711, -185929, -6, 1 ],
          \[ 14578, -30480, 38780, -12005, -7825, 21707, -6605, 2355, 4870, 525, 986, 
             255, 45, 30, 0, 1 ],
          \[ 2059, 225, -1150, 1825, -1025, -1009, -245, -75, -275, 250, -53, 125, 0, 
             20, 0, 1 ],
          \[ 32722, -63825, 70990, -10400, -19075, 34680, -7470, 5730, 7630, 725, 1454, 
             255, 65, 30, 0, 1 ],
          \[ -1, 0, 0, 2, 0, 0, -5, 0, 0, 2, 0, 0, 0, 0, 0, 1 ],
          \[ 27, 0, 0, -27, 0, 0, 18, 0, 0, 130, 0, 0, 23, 0, 0, 1 ],
          \[ 146, -63, -180, -600, 120, 378, -20, 198, 0, -247, 0, 90, 0, -15, 0, 1 ],
          \[ 4, 0, 0, -1, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 1 ],
          \[ -102487167144832305896578849873538581080313524947316321767424, 
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             136771384654763125975628635944913787162688, 
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             -477582096907660950523117014816, -20251674921386743233089664, 
             1982470037108913200760, 248667491445971640, -1133827391276, -777124356, -9, 
             1 ],
          \[ -1302222456532760256406916223259306960561657428777814196224, 
             2266657182908547570648245464215192357802047101628186624, 
             -397561412445066919545461762354884631501806174863360, 
             -617589777108203716232396372453619309554471256064, 
             33516684438303088018217308253251277376159744, 
             15975069142211276963134599495014990639616, 
             -1142953506821390914419260564494304768, -178273077248353369941327628479552, 
             14153948932132918272984150384, 2604584980442264028744009, 
             -141524337796433387826, -35114805704965233, 1247857228852, 282185319, -114, 
             1 ],
          \[ -13824, 34560, 36864, -151552, -210144, 645456, -465624, -22668, 130602, 
             -21029, -11358, 2640, -76, 27, 0, 1 ],
          \[ -13824, 34560, -23040, -21760, 32800, -8272, -12880, 9000, 1120, -2560, 
             148, 370, -30, -25, 0, 1 ],
          \[ 41, 1590, -5937, 7351, -4926, 4068, -2736, 1410, -1137, 239, -279, 57, -45, 
             9, -3, 1 ],
          \[ 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 7303, -4551, -24117, 13966, 29238, -14886, -16690, 6717, 5289, -1662, 
             -1011, 414, 18, -33, 3, 1 ],
          \[ 7288, -36216, 59864, -18504, -42844, 28484, 3724, 1548, -3878, -1650, 906, 
             394, -81, -37, 1, 1 ],
          \[ 10942, -24180, 25520, -2705, -14800, 17912, -4070, -2295, 3580, 150, 674, 
             255, 30, 30, 0, 1 ],
          \[ -13824, 34560, -33408, 704, 22144, -9712, -12856, 11508, 1282, -3304, 1, 
             478, -6, -34, 0, 1 ],
          \[ -13824, 34560, 36864, -151552, -210144, 1041264, -1243408, 505608, 3720, 
             -24088, -7368, 1842, 190, 27, 0, 1 ],
          \[ 2, 0, 0, -1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 1 ],
          \[ 369608289704, 0, 0, 3418039096, 0, 0, -8487340, 0, 0, -512732, 0, 0, -952, 
             0, 0, 1 ],
          \[ 19, 136, 374, 443, 55, -415, -493, -467, -499, -214, 118, 65, -46, -20, 2, 
             1 ],
          \[ 29, -69, 59, 43, -111, 77, 31, -73, 42, 16, -28, 10, 7, -5, 0, 1 ],
          \[ -1, 5, 0, -20, 36, 0, -60, 64, -1, -39, 17, 13, 4, 8, 5, 1 ],
          \[ 1, 0, -10, 0, 10, -31, 0, 10, -30, 5, 0, -10, 5, 0, 0, 1 ],
          \[ -13824, 34560, -35712, 5696, 17664, -6528, -14352, 11112, 2232, -3526, 
             -138, 522, 0, -36, 0, 1 ],
          \[ 2, 0, 0, 3, 0, 0, -5, 0, 0, -4, 0, 0, 2, 0, 0, 1 ],
          \[ -154, -2310, -13860, -41395, -60150, -27432, 20060, 15705, 2160, 2075, 
             -510, -765, 0, 0, 0, 1 ],
          \[ 5, -23, -10, 36, 23, -40, -22, 44, 18, -23, -12, 10, 3, -5, 0, 1 ],
          \[ 12, 60, 120, 100, -20, -108, -65, 25, 45, 15, 0, 0, 0, 0, 0, 1 ],
          \[ 12, 60, 120, 120, 60, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 1, -13, -5, -53, 19, 45, 9, 13, -23, -5, 31, 7, -5, 5, 5, 1 ],
          \[ -51840, 0, 97200, -117000, 44550, 31995, -46360, 16665, 3330, -3385, 240, 
             225, -10, -15, 0, 1 ],
          \[ 2, 10, 20, 19, 6, -4, -6, -7, -6, 0, 4, 2, 0, 0, 0, 1 ],
          \[ -512, 3840, -11520, 16960, -11040, -432, 4320, -1620, 0, 0, 0, 0, 0, 0, 0, 
             1 ],
          \[ 4544, -17040, 21300, -8875, 0, 2688, -6720, 4200, 0, 0, -108, 135, 0, 0, 0, 
             1 ],
          \[ 1, -5, 10, -8, -3, 11, -8, 2, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 832, -3120, 3900, -1625, 0, 240, -600, 375, 0, 0, 24, -30, 0, 0, 0, 1 ],
          \[ 64, -240, 300, -125, 0, 0, 0, 0, 0, 0, -12, 15, 0, 0, 0, 1 ],
          \[ 7744, -29040, 36300, -15125, 0, 3888, -9720, 6075, 0, 0, -8, 10, 0, 0, 0, 1 
             ],
          \[ -256, 960, -1200, 500, 0, 64, -160, 100, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -4096, 15360, -19200, 8000, 0, -704, 1760, -1100, 0, 0, 4, -5, 0, 0, 0, 1 ],
          \[ -475136, -3563520, -12472320, -27023360, -40089600, -42316800, -31923200, 
             -16704000, -5572800, -940960, -14448, -8520, -320, 240, 30, 1 ],
          \[ -704, 2640, -3300, 1375, 0, 80, -200, 125, 0, 0, -12, 15, 0, 0, 0, 1 ],
          \[ 1216, -4560, 5700, -2375, 0, -912, 2280, -1425, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -64, 240, -300, 125, 0, 64, -160, 100, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ 224, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
          \[ -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
          ];

_last := \[0, 1, 3, 8, 13, 29, 36, 86, 120, 165, 173, 474, 483, 546, 650];

_maxdeg := #_last;

_check_degree := procedure(d)
    error if Type(d) ne RngIntElt, "Degree must be an integer";
    error if d le 1, "Degree must be at least 2";
    error if d gt _maxdeg,
        "Degree must not exceed " cat IntegerToString(_maxdeg);
end procedure;

_check_args := procedure(d, n)
    _check_degree(d);
    error if Type(n) ne RngIntElt, "Label must be an integer";
    error if n lt 1, "Number must be positive";
    error if n gt _last[d] - _last[d - 1],
        "There are only " cat i2s(_last[d] - _last[d - 1]) cat
        " transitive groups of degree " cat i2s(d)
        where i2s is IntegerToString;
end procedure;

_dn_to_i_check := function(d, n)
    _check_args(d, n);
    return _last[d - 1] + n;
end function;


PolynomialWithGaloisGroup := function(d, n)
    P := PolynomialRing(Integers());
    return P!_data[_dn_to_i_check(d, n)];
end function;

delete _data, _last, _maxdeg, _check_degree, _check_args, _dn_to_i_check;
