# Stored data for newform 1911.4.a.f, downloaded from the LMFDB on 25 April 2024.
{"label": "1911.4.a.f", "space_label": "1911.4.a", "level": 1911, "weight": 4, "hecke_orbit": 6, "hecke_orbit_code": 22517998203963255, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 551587985678945755, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [5, [-12, 1]]], "qexp_display": "q+3q^{3}-8q^{4}+12q^{5}+9q^{9}-6^{2}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 30576, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 112.75265002097031, "hecke_ring_index": 1, "level_radical": 273, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1911, 1, [638, 1522, 1471], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 7, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.945", "prec": 17}, {"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "1.843", "prec": 17}, {"__RealLiteral__": 0, "data": "0.148", "prec": 17}, {"__RealLiteral__": 0, "data": "4.515", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, -1], [13, 1]], "trace_display": [0, 3, 12, 0], "traces": [0, 1, 0, 3, -8, 12, 0, 0, 0, 9, 0, -36, -24, -13, 0, 36, 64, 78, 0, -74, -96, 0, 0, -96, 0, 19, 0, 27, 0, 18, 0, 214, 0, -108, 0, 0, -72, -286, 0, -39, 0, 384, 0, 524, 288, 108, 0, -300, 192, 0, 0, 234, 104, 558, 0, -432, 0, -222, 0, -576, -288, -74, 0, 0, -512, -156, 0, 38, -624, -288, 0, -456, 0, 682, 0, 57, 592, 0, 0, 704, 768, 81, 0, 888, 0, 936, 0, 54, 0, 1020, 0, 0, 768, 642, 0, -888, 0, -110, 0, -324, -152, 990, 0, -1208, 0, 0, 0, 996, -216, -1402, 0, -858, 0, 1926, 0, -1152, -144, -117, 0, 0, 0, -35, 0, 1152, -1712, -1272, 0, -988, 0, 1572, 0, 2100, 864, 0, 0, 324, 0, -2496, 0, 2464, 0, -900, 0, 468, 576, 216, 0, 0, 2288, 216, 0, -898, 0, 702, 0, 2568, 312, 1510, 0, 1674, 0, 0, 0, -394, -3072, -1296, 0, -84, 0, 169, 0, -666, -4192, -1194, 0, 0, -2304, -1728, 0, 3156, -864, 1078, 0, -222, 0, -3432, 0, -2808, 2400, 0, 0, 3192, -1536, 722, 0, -468, 0, 2796, 0, 340, 0, 114, 0, 0, -1872, 4608, 0, -864, -832, 2664, 0, -1924, -4464, -1368, 0, 6288, 0, 0, 0, 2046, 3456, -1014, 0, -5042, 0, 171, 0, 2676, 1776, 2410, 0, 0, 0, 3726, 0, -3600, 4608, 2112, 0, 1248, 2304, 4210, 0, 243, 592, 0, 0, 962, 0, 2664, 0, 7692, 0, 3456, 0, 2808, 4096, -1326, 0, 0, 1248, 162, 0, -6048, 0, 6696, 0, 3060, -304, -6474, 0, -5978, 4992, 0, 0, -684, 2304, 8750, 0, 1926, 0, 8976, 0, 592, 3648, -2664, 0, 0, 0, 1171, 0, -330, -5456, 4608, 0, -6912, 0, -972, 0, 1248, -456, 0, 0, 2970, -4736, -888, 0, 3166, 0, -3624, 0, -2472, 0, 3094, 0, 0, -5632, 2316, 0, -648, -6144, 2988, 0, -5772, -648, -247, 0, -4206, 0, 0, 0, -4426, -7104, -2574, 0, 456, 0, 866, 0, 5778, -7488, -7704, 0, 0, 0, -3456, 0, -2556, -432, 11014, 0, -351, 0, 9720, 0, -5472, -8160, 0, 0, -2988, 0, -1383, 0, -105, 0, 8184, 0, 2068, -6144, 3456, 0, 0, -5136, 902, 0, -3816, 0, -234, 0, 12818, 7104, -2964, 0, 1332, 0, 0, 0, 4716, 880, 3054, 0, -7488, 0, 6300, 0, 8448, 2592, -11162, 0, 0, 1216, -14820, 0, -2782, -7920, 972, 0, 10296, 0, 9682, 0, -7488, 9664, 0, 0, 10656, 0, 7392, 0, 348, 0, 2486, 0, -2700, 0, 1482, 0, 0, -7968, 1404, 0, -1812, 1728, 6226, 0, 648, 11216, 7104, 0, 12544, 0, 0, 0, -8556, 6864, 12240, 0, 648, 0, 4116, 0, -13824, -15408, -2694, 0, 0, 0, -6514, 0, 2106, 9216, -10500, 0, -5542, 1152, 7704, 0, 5220, 936, 0, 0, 4530, 0, -18864, 0, -1406, 0, 5022, 0, -11592, 0, 3718, 0, 0, 280, -1320, 0, 12170, 0, -1182, 0, 1812, -9216, 1404, 0, -3888, 13696, 0, 0, -1330, 10176, -252, 0, 2688, 0, 11880, 0, 507, 7904, -5124, 0, 0, 0, -1998, 0, -14496, -12576, 10800, 0, -3582, 0, 882, 0, 2320, -16800, 0, 0, 16692, -6912, -2951, 0, -5184, 0, -4992, 0, 11952, 0, 9468, 0, 0, -2592, 21422, 0, 3234, 0, -16824, 0, 7040, 19968, -666, 0, -1332, 0, 0, 0, -10296, -19712, -8400, 0, -6812, 0, -8424, 0, -19044, 7200, 23112, 0, 0, 0, -4698, 0, -8728, -3744, 9576, 0, -1824, -4608, -2018, 0, 2166, -1728, 0, 0, -20088, 0, -1404, 0, -11376, 0, -15836, 0, 8388, -18304, 25596, 0, 0, -1728, 1020, 0, 3480, 0, -10010, 0, 342, 7184, -420, 0, -3764, 0, 0, 0, 3900, -5616, 13610, 0, 13824, 0, 6408, 0, 6694, -20544, -2592, 0, 0, -2496, -17639, 0, 7992, -12080, -22308, 0, -27250, 0, -5772, 0, -11856, -13392, 0, 0, -4104, 0, -12630, 0, -14798, 0, 18864, 0, -26232, 0, 20736, 0, 0, 3152, -30390, 0, 25200, 24576, 6138, 0, -28740, 10368, 9214, 0, -3042, 0, 0, 0, -1728, 672, -15126, 0, 2664, 0, 16598, 0, 513, -1352, 8610, 0, 0, 0, 8028, 0, 804, 5328, -29952, 0, 7230, 33536, -7254, 0, -2270, 9552, 0, 0, 29568, 0, 29952, 0, 11178, 0, 1782, 0, 21164, 18432, -10800, 0, 0, 13824, -10690, 0, 6336, 0, -20544, 0, 5616, -25248, 3744, 0, -11568, 6912, 0, 0, 12630, -8624, 342, 0, 11644, 0, 729, 0, 40872, 1776, 15010, 0, 0, 0, -1368, 0, 33410, 27456, 2886, 0, -6504, 0, 2592, 0, 7992, 22464, 0, 0, -13912, -19200, 23076, 0, -10776, 0, -23974, 0, 10368, 0, 288, 0, 0, -25536, 8424, 0, 7488, 12288, -1514, 0, -3978, -5776, -15816, 0, 4066, 0, 0, 0, -28416, 3744, 16416, 0, 486, 0, 18120, 0, -10154, -22368, -18144, 0, 0, 0, 962, 0, 20088, -2720, 17442, 0, -23400, 0, 9180, 0, -24552, -912, 0, 0, -19422, 0, -8778, 0, 430, 0, -17934, 0, -4728, 14976, -38776, 0, 0, -36864, -32976, 0, -1168, 0, -2052, 0, -17172, 6912, -27146, 0, 26250, 6656, 0, 0, -1008, -21312, 5778, 0, -30696, 0, -24065, 0, 26928, 15392, 2028, 0, 0, 35712, 1776, 0, 27456, 10944, -24842, 0, -7992, 0, -11406, 0, -20540, -50304, 0, 0, 9108, 0, -14328, 0, 3513, 0, -25344, 0, -494, 0, -990, 0, 0, -16368, -24046, 0, 13824, -27648, -7998, 0, 24032, 8112, -20736, 0, 15648, 0, 0, 0, -2916, 40336, 22200, 0, 37872, 0, 3744, 0, 3852, -1368, 43524, 0, 0, 0, 12936, 0, -808, -21408, 8910, 0, 39144, -14208, -31968, 0, -2664, -19280, 0, 0, -38248, 0, 9498, 0, 5928, 0, -5434, 0, -10872, 0, 54264, 0, 0, -29808, -7416, 0, -33696, 0, -12206, 0, 9282, 28800, -17664, 0, -36864, -36864, 0, 0, -51984, -16896, -8866, 0, 6948, 0, 13782, 0, 38304, -9984, -1944, 0, 0, -18432, 16005, 0, 8964, -33680, 8664, 0, 14618, 0, -17316, 0, 18708, -1944, 0, 0, -741, -4736, -48804, 0, -36720, 0, -12618, 0, 44736, 0, 33552, 0, 0, -7696, -50304, 0, -21004, 0, -13278, 0, 4080, -21312, -9038, 0, -7722, 0, 0, 0, -44928, -61536, 1368, 0, -41292, 0, 59726, 0, 2598, -27648, -18258, 0, 0, 0, 17334, 0, -31884, -22464, -34706, 0, -23112, -32768, 7296, 0, -9152, 10608, 0, 0, 16920, 0, 50582, 0, -10368, 0, -5772, 0, 45520, -9984, -7668, 0, 0, -1296, 31968, 0, 33042, 0, 4950, 0, -11230, 48384, -1053, 0, -23088, 0, 0, 0, 29160, -53568, 25920, 0, 16216, 0, -16416, 0, 3960, -24480, -57134, 0, 0, 2432, -5148, 0, 9956, 51792, -8964, 0, -11544, 0, 28800, 0, -4149, 47824, 0, 0, -3670, -39936, -315, 0, -53004, 0, 50474, 0, 24552, 0, 32148, 0, 0, 5472, 6204, 0, 7644, -18432, -12168, 0, 10368, -70000, 34698, 0, -35640, 0, 0, 0, -60504, -15408, -33262, 0, 2706, 0, 42624, 0, 22246, -71808, -11448, 0, 0, 0, 1910, 0, -702, -4736, 43488, 0, 32112, -29184, 38454, 0, 2964, 21312, 0, 0, -8892, 0, 28920, 0, -61204, 0, 3996, 0, -47820, 0, 11842, 0, 0, -9368, -13260, 0, 5476, 0, 14148, 0, -16968, 2640, 44712, 0, 9162, 43648, 0, 0, -14416, -36864, -22464, 0, -5700, 0, -35856, 0, 18900, 55296, 60552, 0, 0, 0, 25344, 0, -23316, 7776, 6912, 0, -33486, 0, -65982, 0, 14976, -9984, 0, 0, 50472, 3648, -36430, 0, -44460, 0, 50520, 0, -35568, 0, -8346, 0, 0, -23760, -38554, 0, 2916, 37888, -68124, 0, -53568, 7104, 30888, 0, -40176, 0, 0, 0, 29046, -25328, -60372, 0, 41308, 0, -22464, 0, 11544, 28992, 10834, 0, 0, 0, 53196, 0, -69336, 19776, 31968, 0, 9432, 0, 5218, 0, 22176, -24752, 0, 0, 92304, 0, 1044, 0, -56184, 0, 1430, 0, 7458, 45056, 41472, 0, 0, -18528, -8100, 0, 82176, 0, -2812, 0, 4446, 5184, -12534, 0, -60266, 49152, 0, 0, 40932, -23904, -15912, 0, 4212, 0, 19836, 0, -73208, 46176, -5436, 0, 0, 5184, 80174, 0, 18678, 1976, 63570, 0, -55744, 0, 1944, 0, 26364, 33648, 0, 0, 21312, 0, -12870, 0, -72576, 0, 37632, 0, 78228, 0, 29086, 0, 0, 35408, 10602, 0, 53696, 56832, -25668, 0, 49176, 20592, 112136, 0, 36720, 0, 0, 0, 15704, -3648, 1944, 0, 54912, 0, -77688, 0, 12348, -6928, 33744, 0, 0, 0, -41472, 0, -71736, -46224, 55296, 0, -8082, 59904, -19410, 0, -5400, 61632, 0, 0, -80904, 0, 31143, 0, -19542, 0, 71304, 0, 45792, 0, 6318, 0, 0, 27648, -85570, 0, -31500, 0, 105000, 0, -50468, 20448, -16626, 0, -12948, 3456, 0, 0, 23112, -88112, 35568, 0, -39890, 0, 15660, 0, 7104, 2808, 107712, 0, 0, 0, 7620, 0, 69264, -77760, 13590, 0, 7104, 0, 18226, 0, -56592, 43776, 0, 0, 63146, 65280, -4218, 0, 6180, 0, 6374, 0, 15066, 0, -23274, 0, 0, 23904, -34776, 0, -10536, 0, -75600, 0, 11154, 11064, 14052, 0, 94228, 0, 0, 0, -30768, 840, 11234, 0, -3960, 0, -64200, 0, 69568, -65472, 36510, 0, 0, 0, 55296, 0, -3546, -16544, -25038, 0, 69302, 49152, 5436, 0, -10944, -27648, 0, 0, 4212, 0, 61746, 0, 95632, 0, -11664, 0, 33648, 41088, -32870, 0, 0, -7216, 5712, 0, 14976, 0, -3990, 0, 9036, 30528, -52096, 0, -756, 0, 0, 0, 89856, 1872, 8064, 0, 26040, 0, 79560, 0, 35640, -102544, -109824, 0, 0, -56832, 1521, 0, -22248, 23712, -1406, 0, -15372, 0, -88704, 0, -95096, -10656, 0, 0, 37992, 0, 10044, 0, -5994, 0, -3648, 0, 68416, 0, -43488, 0, 0, -37728, 118730, 0, 32400, -7040, -8028, 0, -29664, -24432, -10746, 0, 44808, 0, 0, 0, 2646, 59904, 37128, 0, 102670, 0, 6960, 0, 10968, -50400, 455, 0, 0, 0, -65712, 0, -40030, -67584, 50076, 0, 106440, -20736, 27792, 0, -8853, 89296, 0, 0, -149864, 0, -15552, 0, -7776, 0, -109042, 0, -14976, -9728, -60072, 0, 0, 118560, 35856, 0, 10608, 0, 123190, 0, 28404, 22256, -52194, 0, -69264, 63360, 0, 0, -24612, -7776, 34238, 0, 64266, 0, 16536, 0, -51266, -82368, 9702, 0, 0, 0, 43776, 0, -50472, -77456, -46566, 0, -7776, 0, 21120, 0, 119412, 59904, 0, 0, -1998, -77312, -8580, 0, 12844, 0, -3996, 0, -53112, 0, 85390, 0, 0, -85248, 32328, 0, 13268, 0, -30888, 0, 19332, -59136, -254, 0, -25200, 0, 0, 0, 722, -2784, -20436, 0, -65472, 0, 78535, 0, -25272, -19888, 10392, 0, 0, 0, -57132, 0, -75480, 21600, 72970, 0, 69336, 0, 56700, 0, -15284, -11856, 0, 0, -27300, 0, -92448, 0, -14094, 0, -95460, 0, -10368, 63744, -26184, 0, 0, -11232, 77220, 0, 28728, 0, -21648, 0, 103826, 14496, -5472, 0, -54360, -13824, 0, 0, -6054, -49808, 83610, 0, -30672, 0, 6498, 0, 85800, -5184, 29302, 0, 0, -89728, 132168, 0, 82982, -56832, -60264, 0, -94224, 0, 23794, 0, -4212, -100352, 0, 0, 60752, 0, -34128, 0, 201216, 0, 116640, 0, -47508, 0, -1332, 0, 0, 68448, 25164, 0, -8664, -54912, -94250, 0, 76788, -97920, 32448, 0, 18250, 0, 0, 0, -35748, -5184, 6050, 0, 3060, 0, 14184, 0, -35856, -32928, 10440, 0, 0, 0, -127510, 0, -30030, 110592, -16596, 0, -32032, 123264, 1026, 0, -110148, 21552, 0, 0, -1260, 0, -67584, 0, 77688, 0, -11292, 0, 123216, 0, 12958, 0, 0, 52112, -123264, 0, -143998, 0, 11700, 0, 24816, -16848, 3024, 0, 40830, -73728, 0, 0, 8140, 84000, 41472, 0, 109392, 0, 195069, 0, 19224, 44336, -109356, 0, 0, -9216, 20082, 0, -6084, -61632, 35566, 0, -7776, 0, 10824, 0, -24986, -41760, 0, 0, 45072, -7488, -73762, 0, -52917, 0, -122376, 0, -33014, 0, 23976, 0, 0, -36240, -2808, 0, -66924, 0, 45042, 0, -15836, 150912, -81750, 0, 153816, 0, 0, 0, -17316, 11248, 20862, 0, 42984, 0, -35568, 0, 61764, -40176, -85248, 0, 0, 0, 38964, 0, 15984, 92736, -12312, 0, -73260, 0, 150228, 0, -37890, -29744, 0, 0, -115200, 0, -44394, 0, -39168, 0, 132266, 0, 56592, -2240, -2808, 0, 0, 10560, -78696, 0, 684, 0, 36648, 0, 62208, -97360, -81798, 0, -28172, 0, 0, 0, -89856, 9456, 89392, 0, -91170, 0, -159588, 0, 11674, -14496, 75600, 0, 0, 73728, -113616, 0, 18414, -11232, -67950, 0, 13376, 0, -86220, 0, -134988, 31104, 0, 0, 27642, -109568, -133944, 0, 134494, 0, -9126, 0, -38808, 0, 31174, 0, 0, 10640, -77004, 0, -17728, -81408, -5184, 0, 146508, 2016, -177840, 0, -45378, 0, 0, 0, 52256, -21504, 7992, 0, -33384, 0, 14006, 0, 49794, -95040, -157200, 0, 0, 0, 1539, 0, -87540, -4056, -69590, 0, 25830, -63232, -73704, 0, 123552, 40992, 0, 0, 8832, 0, -19630, 0, 24084, 0, 116184, 0, -97920, 0, 2412, 0, 0, 15984, 134606, 0, -89856, 0, -2730, 0, -8208, 115968, 21690, 0, -105936, 100608, 0, 0, -21762, -86400, 117276, 0, 103748, 0, -6810, 0, 16872, 28656, 8132, 0, 0, 0, -98178, 0, 84908, -7056, 88704, 0, 66828, 0, 88846, 0, 89856, -18560, 0, 0, 4176, 134400, 33534, 0, -9564, 0, -114912, 0, 5346, 0, 29832, 0, 0, -133536, 63492, 0, 150540, 55296, -123662, 0, -32400, 23608, 12276, 0, 5122, 0, 0, 0, -25992, 41472, -99216, 0, -32070, 0, 2514, 0, -90884, 39936, 19008, 0, 0, 0, -67966, 0, -61632, -95616, 48642, 0, 14222, 0, 16848, 0, -142524, -75744, 0, 0, 11232, 0, 52428, 0, -21744, 0, -34704, 0, -77064, 20736, 128770, 0, 0, -171376, 74712, 0, -100656, 0, 37890, 0, 1092, -25872, 214272, 0, 1026, 0, 0, 0, 97166, 134592, 34932, 0, 164736, 0, 85248, 0, 2187, -56320, -12240, 0, 0, -159744, 122616, 0, 150528, 5328, -2197, 0, 45030, 0, -97584, 0, -139430, 10656, 0, 0, -112104, 0, -13823, 0, -4104, 0, -110118, 0, -102672, 0, 100230, 0, 0, 82368, 104582, 0, 8658, 157696, 19380, 0, 163800, 67200, -19512, 0, 10560, 0, 0, 0, 7776, 54496, 27978, 0, 5488, 0, 23976, 0, 156900, 67392, 49392, 0, 0, 0, 15522, 0, -9070, 152352, -41736, 0, -165888, -57600, 21164, 0, 69228, -184896, 0, 0, 145948, 0, -32328, 0, 41544, 0, -166318, 0, -71922, 0, 52368, 0, 0, 37584, 31104, 0, 292392, 0, 136690, 0, 864, 69824, -78168, 0, 21688, 29952, 0, 0, 12672, -76608, 100586, 0, 25272, 0, -127722, 0, 2590, 14592, 22464, 0, 0, 36864, -126000, 0, -4542, 16144, -29472, 0, 175016, 0, -11934, 0, -66504, -17328, 0, 0, -47448, 13824, 69264, 0, -95040, 0, 12198, 0, -41028, 0, -194688, 0, 0, 160704, 93948, 0, 62640, 0, -85248, 0, -206676, 11232, 96802, 0, 49248, 0, 0, 0, -108106, 91008, 1458, 0, -152748, 0, -14014, 0, 54360, 126688, 225618, 0, 0, 0, -30462, 0, 192192, -67104, -226368, 0, -54432, 146432, 115968, 0, 73978, -204768, 0, 0, 94128, 0, 129998, 0, 2886, 0, -129336, 0, 36700, 13824, 60264, 0, 0, -8160, -63790, 0, 52326, 0, 119034, 0, -139104, -27840, -70200, 0, -76716, 0, 0, 0, 27540, 80080, 44616, 0, 15984, 0, -73656, 0, 1428, -2736, 73112, 0, 0, -57472, -137730, 0, -221184, 3360, -58266, 0, 104196, 0, -2090, 0, -26334, 30112, 0, 0, 36504, 0, 1290, 0, 146040, 0, -83446, 0, -53802, 0, 171054, 0, 0, -31200, -14184, 0, -50304, 44928, 150656, 0, -116328, -108880, 181512, 0, 21744, 0, 0, 0, 144828, -110592, -95616, 0, -98928, 0, 16848, 0, -158204, -51264, -3504, 0, 0, 0, -168298, 0, -6156, -53552, 30684, 0, -10868, 164352, -51516, 0, -41496, 20736, 0, 0, -81438, 0, -155400, 0, -167400, 0, 78750, 0, -15960, 19968, -96336, 0, 0, 141112, -28416, 0, -164986, 0, -3024, 0, 134592, -63936, -9386, 0, 17334, 96640, 0, 0, 32256, 178464, -92088, 0, -86760, 0, -31282, 0, -72195, 218000, 18810, 0, 0, 0, 80784, 0, 126924, 46176, 16848, 0, 6084, 0, -301824, 0, 207988, 94848, 0, 0, -184188, 107136, -61488, 0, 5328, 0, 17310, 0, -113888, 0, 82368, 0, 0, 32832, 111206, 0, -74526, 0, -36348, 0, -134136, 101040, -23976, 0, -70044, 0, 0, 0, -34218, 118384, 190032, 0, -22952, 0, -61620, 0, -151440, -150912, 18360, 0, 0, 0, 129600, 0, -4420, 209856, 27324, 0, -102192, 0, -209234, 0, -42984, -165888, 0, 0, -184896, 0, 10539, 0, 184704, 0, 10584, 0, -76032, -25216, 85542, 0, 0, 243120, -1482, 0, 27840, 0, -158006, 0, -2970, -201600, -205248, 0, -38776, -196608, 0, 0, 130416, -49104, -44928, 0, -72138, 0, 63288, 0, 200304, 229920, 41472, 0, 0, -82944, -182336, 0, -23994, -73712, -35412, 0, 124418, 0, 72096, 0, -151560, 24336, 0, 0, -62208, 0, 79860, 0, -244766, 0, 46944, 0, 76512, 0, -59904, 0, 0, 13824, 117780, 0, 15230, -5376, -8748, 0, 18924, 121008, 84238, 0, 66600, 0, 0, 0, -95686, -21312, 113616, 0, -210384, 0, -65698, 0, 11232, -132784, 73656, 0, 0, 0, 11556, 0, 84348, -4104, -195052, 0, 130572, 10816, 257064, 0, -94628, -68880, 0, 0, -150060, 0, -73978, 0, 38808, 0, -34632, 0, 5794, 0, -2424, 0, 0, -64224, -26638, 0, 26730, 0, 193398, 0, -61324, -6432, 117432, 0, 84480, -42624, 0, 0, -95904, 239616, -180276, 0, 25012, 0, -7992, 0, 14592, -57840, -259130, 0, 0, -268288, -280974, 0, -15984, 58032, -114744, 0, 218280, 0, -276912, 0, 28494, 18160, 0, 0, 182378, -76416, 17784, 0, -30732, 0, 172800, 0, -16302, 0, -46788, 0, 0, -236544, -32616, 0, 3360, 0, -100800, 0, 162792, -239616, 121956, 0, -84224, 0, 0, 0, -81744, -89424, -247354, 0, -22248, 0, -222420, 0, 8566, -14256, -101088, 0, 0, 0, 162487, 0, -36618, -169312, -1980, 0, -228528, -147456, 27846, 0, -32364, 86400, 0, 0, -52992, 0, 36594, 0, 47736, 0, -110592, 0, -15984, -110592, 140830, 0, 0, 85520, 36126, 0, -6552, 0, -155952, 0, -111228, -50688, -56376, 0, -26598, 0, 0, 0, 135452, 164352, 20844, 0, -104736, 0, 71714, 0, 41346, -44928, -22662, 0, 0, 201984, 114912, 0, 22200, -29952, 66452, 0, -5832, 0, 13182, 0, 122112, 92544, 0, 0, -282768, -55296, 19912, 0, 48015, 0, -24216, 0, -117776, 0, 26892, 0, 0, -101040, 217728, 0, 25992, 68992, 6348, 0, 65546, -2736, 43854, 0, 183888, 0, 0, 0, -51948, -93152, 10674, 0, -175104, 0, 56124, 0, -241056, -5832, 42838, 0, 0, 0, 94848, 0, -201344, -326976, -2223, 0, -253080, -14208, 17820, 0, -146412, -120080, 0, 0, -136512, 0, -110160, 0, -162708, 0, -93132, 0, -37854, 0, -190032, 0, 0, 10944, 134208, 0, -34788, 0, -293906, 0, 100656, -267280, -111384, 0, 233064, -219648, 0, 0, -110148, -23088, 307152, 0, -150912, 0, 292356, 0, -235550, 52032, -63012, 0, 0, 0, -31330, 0, -39834, -20736, 215208, 0, -111740, 0, 12240, 0, -21744, -63936, 0, 0, -27114, -179712, 261888, 0, 41760, 0, -23166, 0, 80976, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "39.4.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [0], [3], [-8], [12], [0], [0], [0], [9], [0], [-36], [-24], [-13], [0], [36], [64], [78], [0], [-74], [-96], [0], [0], [-96], [0], [19], [0], [27], [0], [18], [0], [214], [0], [-108], [0], [0], [-72], [-286], [0], [-39], [0], [384], [0], [524], [288], [108], [0], [-300], [192], [0], [0], [234], [104], [558], [0], [-432], [0], [-222], [0], [-576], [-288], [-74], [0], [0], [-512], [-156], [0], [38], [-624], [-288], [0], [-456], [0], [682], [0], [57], [592], [0], [0], [704], [768], [81], [0], [888], [0], [936], [0], [54], [0], [1020], [0], [0], [768], [642], [0], [-888], [0], [-110], [0], [-324], [-152]]}