# Stored data for newform 1150.4.a.b, downloaded from the LMFDB on 25 April 2024. {"label": "1150.4.a.b", "space_label": "1150.4.a", "level": 1150, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694480510, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1776546685338618634, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [1, 1]], [7, [-18, 1]]], "qexp_display": "q-2q^{2}-q^{3}+4q^{4}+2q^{6}+18q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 18400, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 67.8521965066017, "hecke_ring_index": 1, "level_radical": 230, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1150, 1, [277, 51], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5, 23], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.975", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.916", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, 1], [23, -1]], "trace_display": [-2, -1, 0, 18], "traces": [0, 1, -2, -1, 4, 0, 2, 18, -8, -26, 0, -32, -4, 47, -36, 0, 16, -20, 52, 36, 0, -18, 64, 23, 8, 0, -94, 53, 72, -27, 0, -33, -32, 32, 40, 0, -104, -56, -72, -47, 0, -157, 36, -18, -128, 0, -46, -65, -16, -19, 0, 20, 188, 14, -106, 0, -144, -36, 54, -744, 0, 552, 66, -468, 64, 0, -64, 156, -80, -23, 0, 699, 208, 609, 112, 0, 144, -576, 94, -644, 0, 649, 314, -512, -72, 0, 36, 27, 256, -102, 0, 846, 92, 33, 130, 0, 32, -578, 38, 832, 0, -6, -40, 160, -376, 0, -28, -380, 212, 250, 0, 56, 288, 390, 72, 0, -108, -1222, 1488, -360, 0, -307, -1104, 157, -132, 0, 936, 769, -128, 18, 0, -213, 128, 648, -312, 0, 160, -2836, 46, -1631, 0, 65, -1398, -1504, -416, 0, -1218, 19, -224, -1966, 0, 35, -288, 520, 1152, 0, -188, -1702, 1288, -14, 0, 414, -1298, 2045, -628, 0, 1024, -1016, 144, 12, 0, -936, -72, -598, -54, 0, -512, 744, 204, -4607, 0, -1212, -1692, -552, -184, 0, -66, 640, -260, 954, 0, -1058, -64, -1047, 1156, 0, -76, -251, -1664, -3508, 0, -156, 12, -486, 80, 0, -320, -598, 752, -1152, 0, -3296, 56, -699, 760, 0, -424, -594, -500, -609, 0, -940, -112, 2720, -576, 0, -780, 4134, -144, -4510, 0, 576, 216, 5003, 2444, 0, -2976, 644, 720, -6309, 0, 3038, 614, -2080, 2208, 0, -314, 1692, 264, 512, 0, -1332, -1872, -736, -1538, 0, 256, -3301, -36, -1008, 0, 702, 426, -2072, -256, 0, -1296, 102, 624, 5721, 0, -5900, -320, -846, 5672, 0, -92, -6371, 3262, 858, 0, 3190, -130, 4226, 2796, 0, 3008, -2826, 832, -4513, 0, 578, 2436, -6048, -38, 0, 448, -1696, 3932, 1081, 0, -324, -70, 6, 576, 0, -1040, -8628, -2304, -160, 0, 8247, 376, -2620, 3404, 0, -2576, -9906, 28, 864, 0, 380, -828, -720, 2596, 0, -4090, -250, 1256, -1170, 0, -8115, -2048, 1456, 2032, 0, -288, 7586, -24, -390, 0, 1056, 1872, -6516, 144, 0, 1196, -1356, 108, 6649, 0, 2491, 1024, -10691, -1488, 0, -408, 360, 9214, -6420, 0, -5563, 2424, 307, 3384, 0, 1104, 524, 368, 4082, 0, 252, 132, -5566, -1280, 0, 520, -1269, -1908, 2240, 0, -769, 2116, -8778, 128, 0, 2094, 468, -2312, 4056, 0, -460, 152, 213, 502, 0, 3328, 9151, 7016, -648, 0, 15930, 312, -1551, -24, 0, 972, 1792, -160, -5891, 0, 2836, 640, -13392, 1196, 0, -1504, 1631, 2304, 15282, 0, -10934, 6592, 1690, -112, 0, 1398, 9936, -1520, 1504, 0, -2794, 848, 15062, 1188, 0, 1000, 828, 1218, 261, 0, 494, 1880, 7083, 224, 0, -5440, 1966, 1152, -10370, 0, 5024, 1560, -35, -8268, 0, 288, 10496, 9020, -1060, 0, 18021, -1152, 17188, -432, 0, -10006, 15246, -4888, 2808, 0, 1702, 5952, 576, -1288, 0, -1440, -364, 12618, -8556, 0, -2632, -6076, -414, -1228, 0, 4160, 1805, -4416, -2045, 0, 5245, 628, 540, -3384, 0, -528, 12582, -1024, 9027, 0, 1016, 2664, -3522, 3744, 0, 1472, -12, 3076, 3949, 0, 10962, -512, 1908, 6602, 0, 72, 2080, 2016, 598, 0, 3236, -1404, -12394, -852, 0, 4144, 660, 512, 529, 0, 19344, 2592, -7379, -204, 0, -1248, 4607, -11442, 608, 0, -7159, 11800, 1212, 640, 0, 1692, 19761, -11344, -14352, 0, -972, 184, -11592, 12742, 0, -6524, -18010, -1716, -846, 0, -640, -6380, 2648, 260, 0, -8452, 11682, -5592, -1566, 0, 2864, -6016, 1058, 5652, 0, -1664, 929, 9026, 1047, 0, -9216, -1156, -448, -4872, 0, 12096, 19499, 76, -1188, 0, 251, -896, -6570, 3392, 0, -7864, 3508, -2162, 1880, 0, 3701, 648, -4056, 140, 0, -12, 3080, -1152, 486, 0, -3055, 2080, -24004, 17256, 0, 4608, -780, 320, 21892, 0, 1219, -16494, -1836, -752, 0, 5240, 1152, -6808, 1120, 0, 8050, 5152, 3296, 19812, 0, -56, -893, -1728, -18174, 0, -25890, -760, -4774, 1656, 0, 1440, -3349, -5192, 23808, 0, 594, 8180, -24813, 500, 0, -2512, -15834, 2340, 18180, 0, -29250, 16230, 940, 4096, 0, -2912, -621, -4064, -2720, 0, -17664, 576, 23027, -15172, 0, 48, -20106, 780, -10404, 0, -4134, -2112, 18745, -3744, 0, 13032, 4510, -288, 658, 0, 24424, -2392, 14976, 2712, 0, -216, 3140, -13298, -5003, 0, -27278, -4982, -2016, -2048, 0, 21382, -108, 2976, 12214, 0, 16744, 816, -759, -720, 0, -18428, 6309, 12840, 12932, 0, 2880, 11126, -3038, -4848, 0, -614, -10046, -6768, -15443, 0, 360, -2208, 5924, -1048, 0, -736, -4992, -8164, 829, 0, -1692, -504, -7072, -264, 0, 11132, 13312, 2560, -6840, 0, 16234, -1040, 1332, 2538, 0, 3816, -9128, -4480, 736, 0, 165, 1538, 4500, -4232, 0, 17556, -34968, -256, -20834, 0, 3301, -4188, 31782, -936, 0, 4624, 1008, -8112, -5652, 0, -22368, 920, -1431, -304, 0, -426, -33104, -1004, 2072, 0, 7020, -6656, 25944, -18302, 0, -14032, -4736, 1296, 1300, 0, 2652, -31860, -19488, -624, 0, 3102, -5721, 48, -7470, 0, 19919, -1944, 5900, -3584, 0, 320, -648, 11782, -21996, 0, -22694, -5672, 31907, -1280, 0, 26784, 15236, -2392, 27286, 0, 6371, 3008, 380, -3262, 0, -4608, -1749, -30564, 23054, 0, -23660, 21868, -3190, -13184, 0, -3380, -5526, 224, -4226, 0, -1288, -2796, 34506, -19872, 0, 3040, 22263, -3008, 12851, 0, 2826, 5588, -15723, -1696, 0, -30124, 4513, -2376, 20608, 0, 7332, -2000, 15028, -1656, 0, -2436, 886, -522, 6048, 0, -37120, -988, 7524, -3760, 0, -14166, -9221, -448, 13842, 0, -20768, 10880, -2340, -3932, 0, -2304, -1081, 20740, 891, 0, -280, -10048, 324, -3120, 0, 70, -29116, 16536, 156, 0, 11440, -576, 16384, -20992, 0, -18040, -3834, 2120, 2958, 0, 8628, -36042, 32853, 2304, 0, -34376, -4160, 864, 20907, 0, -684, 20012, -8247, -30492, 0, 9776, -9748, -5616, 2620, 0, 19624, -3404, -3611, -11904, 0, -1152, 41859, 2576, 28623, 0, 9906, 2880, -29226, 728, 0, -25236, -864, 17112, -51048, 0, -28702, 5264, 9880, 12152, 0, 828, 29849, 2456, 720, 0, -9390, -8320, -29358, -3610, 0, 8832, -33536, 4090, 3264, 0, -6500, -10490, -28994, -1256, 0, -1080, 1170, 6768, -414, 0, 11272, 1056, 8115, -25164, 0, 2048, -61186, -18054, -2968, 0, -27072, -2032, 14880, -5328, 0, 7044, 504, -7488, -23172, 0, -7586, -2944, 5651, 24, 0, -6152, -10140, -7898, -29844, 0, 32253, -21924, -1056, 1024, 0, -3816, -30268, -13204, 6516, 0, -51684, -144, -14464, -4160, 0, -4032, -11040, -1196, -34455, 0, 1356, -6472, -35388, 2808, 0, 24788, -6649, 1704, -57722, 0, 20165, -8288, 30503, -1320, 0, -1024, 630, -1058, 10691, 0, 13187, -38688, 31952, -5184, 0, 14758, 18496, 408, 60652, 0, 9360, 2496, 1512, -9214, 0, 22884, 6420, -1216, -24064, 0, -1495, 14318, 5563, -23600, 0, -2424, -44435, -1280, 7982, 0, 9882, -3384, -3743, -39522, 0, 22688, 31554, 28704, -30636, 0, -524, 1944, -18086, -368, 0, 23184, -8321, -25484, 20940, 0, 192, 13048, -252, 36020, 0, 3432, -54778, 1692, 5566, 0, -26784, 1280, 11288, 12760, 0, -5296, -437, -520, 27905, 0, 1269, 16904, -5120, -23364, 0, 11184, -2240, 3132, -3120, 0, 36810, -5728, -19994, 12032, 0, -2116, 1848, -11304, 8778, 0, 55120, 3328, 4343, -1858, 0, -18052, -4794, -2094, 19872, 0, -954, 18432, -58256, 2312, 0, 896, -4056, 9744, -18288, 0, 33434, -24192, 460, -38998, 0, -152, 12160, 2376, 5538, 0, 23850, -502, 216, 1792, 0, 13140, 22954, -6784, 4239, 0, -9151, 15728, 57546, -7016, 0, 4324, -16848, -3760, -8000, 0, 3632, -7402, -15930, -1296, 0, 8112, -13980, -280, 1551, 0, -10764, 24, 62448, -6160, 0, 2304, 58868, -972, 322, 0, -1792, 6110, 14553, -4160, 0, 48008, 5891, -34512, -1340, 0, -46480, -9216, 73736, 1560, 0, -640, 37233, -43784, 13392, 0, -12180, -2438, -12480, 32988, 0, 3672, 486, 1504, -30772, 0, 42406, -10480, -82926, -2304, 0, 13616, -15282, -2240, 18816, 0, -27166, -16100, 10934, -10304, 0, -6592, -21816, -39624, -3445, 0, 5181, 112, 5616, 1786, 0, 3456, -24307, 36348, 42140, 0, -9936, 51780, 63019, 1520, 0, 9548, 39104, -3312, -34881, 0, 1673, -2880, 2794, 6698, 0, 10384, -8237, -47616, -15062, 0, -22989, -1188, 69070, -16360, 0, 49626, 85010, -1000, 11520, 0, -828, 5024, -282, 31668, 0, -4680, -261, -36360, 22332, 0, -79230, 58500, -1007, -32460, 0, -1880, 9803, -8192, -7083, 0, 52416, 5824, 594, 1242, 0, 8128, -19044, 5440, 7520, 0, 51116, 35328, 12880, -1152, 0, -46054, 10370, 30344, 25164, 0, -18846, -96, -5024, 40212, 0, -1560, -17112, 20808, -910, 0, -64395, 8268, 1755, 4224, 0, -37490, 77126, 7488, -47517, 0, -10496, -26064, 32827, -9020, 0, 576, -12980, -1316, -4518, 0, 59715, -48848, -18021, 4784, 0, -29952, 21924, -5424, -17188, 0, -17860, 432, -63144, -6280, 0, 26596, -24608, 10006, -25720, 0, -15246, 54556, 12696, 9964, 0, 4032, -2808, 4096, -17335, 0, 10240, -42764, 44252, 216, 0, -5952, 11750, -24428, -576, 0, 513, -33488, 79042, -1632, 0, 1518, -6057, 1440, 3983, 0, 742, 36856, -59252, -12618, 0, -25680, 8556, -25864, -36175, 0, 6816, -5760, 2632, -22252, 0, 6076, 25786, 9696, -10764, 0, -76572, 1228, 40326, 20092, 0, 13536, 2145, 30886, 7630, 0, -1805, -720, -20736, 4416, 0, -11848, -53170, 2096, 18330, 0, -42094, 1472, -5245, 9984, 0, 16328, -59328, -1658, -540, 0, 2026, 3384, 81436, 1008, 0, 14144, 104418, 528, 102788, 0, -12582, -22264, -85128, -26624, 0, -5120, -9027, 13680, -59597, 0, -23184, -32468, 26416, 2080, 0, -2664, 90752, -5076, 3522, 0, -49271, -7632, 2040, 18256, 0, 8960, 8792, -1472, 627, 0, -312, -330, -87144, -3076, 0, -9000, -3949, 8464, 52192, 0, 71615, -35112, -10962, 69936, 0, 512, -378, 41668, 23364, 0, 3588, -6602, 24479, 8376, 0, -63564, -16920, 1872, -38985, 0, -2080, -9248, -57866, -2016, 0, 16224, 15548, 11304, 82103, 0, 48960, 44736, -3236, -1840, 0, 2862, 15083, 608, 12394, 0, -4254, 852, -14429, 66208, 0, 2008, -18432, -4144, -24002, 0, -660, -14040, -210, 13312, 0, -51888, -529, 36604, 74412, 0, 1008, 28064, -39432, 9472, 0, -2592, 15856, -2600, 7379, 0, 77550, -5304, -81180, 63720, 0, 38976, 61106, 1248, 33494, 0, 119782, -6204, -77670, 11442, 0, -96, -608, 14940, 62925, 0, -28560, -39838, 7159, 3888, 0, -11800, -44290, 7168, 31512, 0, 90054, -640, 16077, 1296, 0, -23564, -29151, 43992, 62912, 0, -19761, 45388, -462, 11344, 0, -63814, 29256, 2560, 11560, 0, 36143, -53568, 972, -30472, 0, 4784, 49969, -54572, 11592, 0, -1120, -12742, 14180, -6016, 0, -760, 48890, 6524, 61766, 0, 18010, 9216, -113562, 3498, 0, 61128, 846, -46108, 14007, 0, -44272, 47320, -16640, -43736, 0, 6380, 54684, 26368, -2648, 0, -3672, 6760, -29594, 11052, 0, -448, -119586, 8452, -83068, 0, -37440, 2576, -10011, 5592, 0, -69012, 1566, 39744, 14120, 0, 20088, -6080, -2864, -44526, 0, 6016, 120, -25702, 27508, 0, 14734, -5652, 89028, -11176, 0, 31446, 54464, 3392, 30456, 0, -929, 60248, -22735, -9026, 0, 4752, 27222, -41216, 3640, 0, 26293, -14664, 9216, 4000, 0, -30056, 4930, 3312, 448, 0, -3200, 4872, -62314, -1772, 0, 1044, -23976, -12096, -125926, 0, -19499, 74240, 2826, 1976, 0, -15048, 1188, 7520, -14904, 0, -13248, 28332, 6526, 18442, 0, 896, -40419, -27684, 6570, 0, -133292, 41536, -143489, -21760, 0, 4680, 53268, 7864, 95174, 0, 91208, 4608, -65440, 2162, 0, -41480, -1880, -1782, -59418, 0, -150298, 560, -3701, 20096, 0, -648, -76657, 6240, 8268, 0, 37840, -140, 1064, 58232, 0, -33072, -14812, -312, 7600, 0, -3080, -22880, -59175, 1152, 0, -32768, 12636, 41984, 24552, 0, 112682, 36080, 3055, 7668, 0, -4240, 32512, -5916, 24004, 0, -37296, -17256, -20808, 72084, 0, -65706, 49028, -4608, -79183, 0, 780, 68752, -5000, 8320, 0, -1728, -21892, -41814, -384, 0, -47862, 1368, 14927, -40024, 0, 16494, -146944, 60984, 1836, 0, -70488, -19552, -130578, 19496, 0, 11232, -26996, -5240, -1652, 0, 29952, -39248, 102978, 6808, 0, 7222, -1120, 23808, -98766, 0, -18216, 2304, -8050, -83718, 0, -5152, -106200, -57246, 85696, 0, 44962, -19812, 19136, -5760, 0, 58452, 80752, -1456, -11776, 0, 893, 50472, 18774, 1728, 0, -34224, 37047, 102096, -216, 0, -7800, 57404, 25890, -10528, 0, -19760, 10205, -24304, 4774, 0, -55608, -1656, 134093, -59698, 0, -4912, -92402, -1440, -114678, 0, 3349, 18780, -4212, 16640, 0, 58716, -23808, 7220, -32826, 0, 6500, -17664, 15444, 67072, 0, -8180, 5760, -6528, 24813, 0, -784, 13000, 1645, 20980, 0, 57988, 57420, 2512, 147424, 0, 32277, 2160, -141, -2340, 0, -13536, -18180, 828, -129307, 0, 76068, -22544, 29250, -2112, 0, -16230, -27223, 50328, 24440, 0, 38784, -4096, 66706, 122372, 0, 36108, 155468, 5936, -104304, 0, 621, 54144, 97269, 4064, 0, -29760, -70720, 10656, 2983, 0, -63692, -14088, 17664, -1008, 0, 14976, 86371, 46344, -23027, 0, 1170, 15172, -81234, 5888, 0, -11302, -81484, -48, 5272, 0, 20106, 12304, -13680, 20280, 0, 15796, 10404, 59688, -77154, 0, -79994, -64506, -107484, 43848, 0, 2112, -2346, -2048, -18745, 0, -108864, 7632, -62114, 60536, 0, 26408, 6140, -13032, -18873, 0, 117260, 103368, 49343, 288, 0, 28928, -658, 8320, -15328, 0, 9000, 8064, -24424, 22080, 0, 2392, -5148, 68910, -30528, 0, 117676, -2712, 20765, 12944, 0, 70776, 23116, -5616, -116222, 0, -3140, -49576, 19458, 13298, 0, -3408, -130078, 115444, -106503, 0, 33856, -40330, 27278, 16576, 0, -61006, 342, 2640, 2016, 0, 76531, 2048, 109508, -1260, 0, 2116, -16443, -21382, 96115, 0, 108, -26374, 33504, 77376, 0, -63904, -12214, 10368, 80719, 0, 108082, -29516, -34132, -36992, 0, -816, 134686, -121304, 759, 0, -147293, -18720, -113472, -4992, 0, -3024, 14040, 18428, -155304, 0, 164034, -45768, -15606, -12840, 0, 2432, -12932, 48128, -15380, 0, 7448, 2990, -2880, -28636, 0, -11126, 8032, 47200, -78988, 0, -47752, 4848, -2198, 88870, 0, 2560, 148446, -15964, -67918, 0, 10046, -19764, 41664, 6768, 0, 7486, 71603, 79044, 112256, 0, -47160, -45376, -360, -63108, 0, -57408, -102695, 61272, -5924, 0, -23067, 1048, 29957, -3888, 0, 36172, -52480, 736, -99598, 0, 4992, -46368, -16480, 16642, 0, 50968, -829, -41880, -178308, 0, -108655, -384, -43992, -26096, 0, 504, 4260, -72040, 7072, 0, -13294, -6864, 15552, 109556, 0, -3384, 138875, -11132, -132851, 0, -27136, 53568, -146751, -2560, 0, -22576, 6840, -25520, -28106, 0, 138636, 10592, -16234, 874, 0, 1040, -30912, -55810, 34632, 0, -12960, -2538, -20097, -33808, 0, 10240, 28873, 46728, -96298, 0, 9128, -22368, 34842, 4480, 0, -6264, 19136, 6240, -252, 0, -8161, -73620, -165, 11456, 0, 39988, 10310, -24064, -4500, 0, 17388, 4232, -36557, -3696, 0, 22608, -49290, -17556, -11052, 0, 34968, -110240, 1235, -6656, 0, -8686, 20834, 3716, -88238, 0, 175998, 36104, 85826, 9588, 0, 4188, -146070, -39744, -31782, 0, 105472, 1908, -138, -36864, 0, 116512, -216529, -4624, 56720, 0, 26208, -1792, 171910, 8112, 0, -19488, 5652, 36576, -38092, 0, -30265, -66868, 22368, 48384, 0, -920, 14008, 77996, -17523, 0, -182038, 304, -56964, -24320, 0, -4752, 65610, -11076, 136548, 0, 33104, -47700, 32620, 1004, 0, -432, 53872, -3584, 3680, 0, -15373, -26280, -7020, -45908, 0, 13568, 65589, -8478, -25944, 0, 166702, 18302, -139362, -31456, 0, -115092, 19008, 14032, -192324, 0, 4736, -8648, 180226, 33696, 0, 7520, -1300, 16000, 58372, 0, -110771, -7264, -5406, 14804, 0, 31860, 13824, 2592, 19488, 0, 51646, -16224, 27684, 27960, 0, 560, -129351, -3102, 116808, 0, -148746, 21528, 135384, -48, 0, -124896, 7470, 12320, -24408, 0, 30080, -4608, -19919, -117736, 0, 1944, -842, -644, 153400, 0, 44769, 3584, 119682, -12220, 0, -29106, 55073, 8320, 21252, 0, 648, -96016, -87040, -11782, 0, 69024, 44838, 2680, -53870, 0, -8740, 92960, 22694, 18432, 0, -147472, -212799, -3120, -31907, 0, -192438, 1280, -101111, -74466, 0, 87568, -96465, -26784, -8736, 0, -15236, 24360, -49726, 4876, 0, 24960, -27286, -65976, -7668, 0, -910, -7344, 165646, -972, 0, -3008, -132288, 61544, -380, 0, -86664, -84812, -116552, 20960, 0, 165852, 5750, 4608, -49209, 0, -21417, -27232, -115560, 30564, 0, 4480, -23054, -37632, 144320, 0, 241394, 54332, 23660, 32200, 0, -21868, -100134, 20608, -82940, 0, 237881, 13184, 39320, 43632, 0, 79248, 13392, 6890, 168596, 0, 5526, -10362, -11205, -224, 0, -11232, -109876, -3572, 133340, 0, -85672, -6912, 1288, 48614, 0, -72696, -30213, -84280, -34506, 0, -11797, 19872, -160096, -103560, 0, -126038, -700, -3040, 9432, 0, -22263, -19096, 16896, -78208, 0, 6624, -12851, 69762, 38265, 0, 2754, -3346, 73476, 5760, 0, -5588, -164876, -13396, 15723, 0, -153372, -20768, -116298, 16474, 0, 95232, -266, 30124, 8970, 0, 117338, 45978, -102096, 2376, 0, -138140, -20608, 32720, -206380, 0, -100188, -99252, -7332, -170020, 0, 2000, -4849, -23040, -30634, 0, -117782, 1656, -9936, -10048, 0, 564, -39144, -63336, 201888, 0, -886, 9360, 115968, 522, 0, 72720, 157248, -44664, -22842, 0, -58716, 158460, 37120, -117000, 0, 2014, -179536, 64920, -7524, 0, -97216, 3760, 40320, -19606, 0, 16384, -150513, 14166, -56782, 0, 9221, -104832, -129059, -11648, 0, -1188, -13842, -2484, 34040, 0, -44911, -16256, 66560, 38088, 0, -10880, 155334, -15040, 2340, 0, -158004, -102232, -23906, -70656, 0, -25760, 43356, 2304, -163924, 0, -28106, 92108, 13502, -20740, 0, -60688, -891, -50328, -142825, 0, -34104, 37692, 280, 192, 0, 10048, -1916, -80424, 8424, 0, 218154, 3120, -144962, 34224, 0, -41616, -54144, 1820, 148274, 0, 29116, 128790, 73008, -16536, 0, -3510, -318, -8448, -90758, 0, -215984, 74980, -11440, -154252, 0, -14976, -8280, 95034, -16384, 0, -276806, 20992, -154912, 52128, 0, -65654, -24492, 18040, -10617, 0, 3834, -1152, 113069, 25960, 0, 2632, -2958, 9036, 3366, 0, 42624, -119430, 224328, 97696, 0, 36042, 223302, -9568, -32853, 0, -40900, 59904, 48360, -43848, 0, 10848, -268836, 34376, 164718, 0, 8480, 35720, -7061, -864, 0, 126288, -20907, 12560, -31201, 0, -204281, -53192, 684, 49216, 0, -20012, -43980, 51440, -214422, 0, 281609, 30492, -24086, -109112, 0, -25392, 286740, -19928, -148681, 0, 9748, -8064, 15606, 5616, 0, -8192, 68120, 34670, 108772, 0, -27918, -20480, -19624, 85528, 0, -88504, 105632, -432, 3611, 0, -70776, 11904, 211163, -23500, 0, 48856, 185635, 1152, 20320, 0, -41859, -1026, -46436, 66976, 0, -158084, -28623, 3264, 32256, 0, 73534, -3036, 257556, 12114, 0, -2880, 45308, -7966, 29226, 0, -65127, -1484, -106038, -73712, 0, 118504, -35880, 25236, 1260, 0, -22464, 51360, -240, -17112, 0, 51728, 51048, 72350, 5440, 0, -2808, -13632, 28702, 11520, 0, -5264, -41480, 44504, -20140, 0, 14136, -12152, 66304, -51572, 0, -19392, -121442, 21528, 127840, 0, -29849, 153144, -55878, -2456, 0, -80652, 18720, -40184, -57634, 0, -109743, -27072, 9390, -4290, 0, -61772, 156194, -15260, 29358, 0, 17687, 3610, 36064, 1440, 0, 41472, -197744, -8832, 162, 0, 33536, 23696, 275076, 106340, 0, -4192, -3264, -36660, 15804, 0, 11960, 84188, 13250, -2944, 0, 10490, -196812, -19968, 28994, 0, 194298, -32656, -290691, 118656, 0, 3316, -219961, 1080, -183072, 0, 30420, -4052, -146152, -6768, 0, -162872, 414, -2016, 122766, 0, -267025, -28288, -11272, -208836, 0, -1056, -211970, -205576, 210990, 0, 188800, 25164, -61272, 44528, 0, 170256, -4320, 53248, -10488, 0, 61186, 10240, -95613, 18054, 0, -27360, -36344, 119194, 148359, 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": "230.4.a.e", "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], [-2], [-1], [4], [0], [2], [18], [-8], [-26], [0], [-32], [-4], [47], [-36], [0], [16], [-20], [52], [36], [0], [-18], [64], [23], [8], [0], [-94], [53], [72], [-27], [0], [-33], [-32], [32], [40], [0], [-104], [-56], [-72], [-47], [0], [-157], [36], [-18], [-128], [0], [-46], [-65], [-16], [-19], [0], [20], [188], [14], [-106], [0], [-144], [-36], [54], [-744], [0], [552], [66], [-468], [64], [0], [-64], [156], [-80], [-23], [0], [699], [208], [609], [112], [0], [144], [-576], [94], [-644], [0], [649], [314], [-512], [-72], [0], [36], [27], [256], [-102], [0], [846], [92], [33], [130], [0], [32], [-578], [38], [832], [0]]}