# Stored data for newform 1452.4.a.d, downloaded from the LMFDB on 19 April 2024.
{"label": "1452.4.a.d", "space_label": "1452.4.a", "level": 1452, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949221804, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1801945634695922685, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [18, 1]], [7, [8, 1]]], "qexp_display": "q+3q^{3}-18q^{5}-8q^{7}+9q^{9}+10q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 23232, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 85.67077332833537, "hecke_ring_index": 1, "level_radical": 66, "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": [1452, 1, [727, 485, 1333], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 11], "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": "0.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "1.933", "prec": 17}, {"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "4.790", "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], [3, -1], [11, -1]], "trace_display": [0, 3, -18, -8], "traces": [0, 1, 0, 3, 0, -18, 0, -8, 0, 9, 0, 0, 0, 10, 0, -54, 0, -18, 0, 100, 0, -24, 0, 72, 0, 199, 0, 27, 0, 234, 0, -16, 0, 0, 0, 144, 0, -226, 0, 30, 0, -90, 0, -452, 0, -162, 0, 432, 0, -279, 0, -54, 0, 414, 0, 0, 0, 300, 0, -684, 0, -422, 0, -72, 0, -180, 0, 332, 0, 216, 0, -360, 0, -26, 0, 597, 0, 0, 0, -512, 0, 81, 0, 1188, 0, 324, 0, 702, 0, -630, 0, -80, 0, -48, 0, -1800, 0, -1054, 0, 0, 0, -558, 0, 8, 0, 432, 0, -1764, 0, -1622, 0, -678, 0, -1134, 0, -1296, 0, 90, 0, 144, 0, 0, 0, -270, 0, -1332, 0, 592, 0, -1356, 0, 1908, 0, -800, 0, -486, 0, 954, 0, -2564, 0, 1296, 0, 0, 0, -4212, 0, -837, 0, 738, 0, 2440, 0, -162, 0, 288, 0, -2554, 0, 1242, 0, -576, 0, -820, 0, 0, 0, -1944, 0, -2097, 0, 900, 0, 1242, 0, -1592, 0, -2052, 0, 1116, 0, 1070, 0, -1266, 0, 4068, 0, 0, 0, -216, 0, -576, 0, 1342, 0, -540, 0, -1422, 0, 872, 0, 996, 0, -1872, 0, 1620, 0, 648, 0, 0, 0, -1340, 0, -1080, 0, 8136, 0, 128, 0, -78, 0, -180, 0, 4880, 0, 1791, 0, -2700, 0, 254, 0, 0, 0, -4410, 0, -7776, 0, -1536, 0, 3888, 0, -5138, 0, 243, 0, 5022, 0, 1000, 0, 3564, 0, 4788, 0, 0, 0, 972, 0, -5886, 0, 1808, 0, 2106, 0, -2232, 0, -7452, 0, -1890, 0, -666, 0, 5536, 0, -240, 0, 0, 0, -2126, 0, -144, 0, 2934, 0, -2036, 0, -5400, 0, 720, 0, -4589, 0, -3162, 0, -2286, 0, 12312, 0, 0, 0, 720, 0, 3616, 0, -1674, 0, 7596, 0, -1244, 0, 24, 0, 1224, 0, 1898, 0, 1296, 0, -9162, 0, 0, 0, -5292, 0, -1800, 0, 1990, 0, -4866, 0, -3456, 0, -4348, 0, -2034, 0, -5976, 0, -7154, 0, -3402, 0, 0, 0, 4976, 0, -3888, 0, 1836, 0, -5894, 0, 270, 0, 11106, 0, 6480, 0, 432, 0, -13176, 0, 3141, 0, 0, 0, 468, 0, -6112, 0, -810, 0, -3312, 0, 13618, 0, -3996, 0, 2340, 0, 692, 0, 1776, 0, -8064, 0, 0, 0, -4068, 0, 12654, 0, -1296, 0, 5724, 0, 9216, 0, -106, 0, -2400, 0, -4014, 0, -160, 0, -1458, 0, 0, 0, -3914, 0, 2862, 0, 5472, 0, -21384, 0, -7692, 0, 4428, 0, -15490, 0, 3888, 0, -3582, 0, 3376, 0, 0, 0, -6768, 0, 1298, 0, -12636, 0, 7200, 0, 2248, 0, -2511, 0, -9612, 0, 11340, 0, 2214, 0, 162, 0, 0, 0, 7320, 0, 1440, 0, -1370, 0, -486, 0, 15354, 0, -13024, 0, 864, 0, -14436, 0, -2656, 0, -7662, 0, 0, 0, 19900, 0, 3726, 0, -12096, 0, -2260, 0, -1728, 0, 18972, 0, 6056, 0, -2460, 0, -7524, 0, -4212, 0, 0, 0, 2880, 0, 5276, 0, -5832, 0, -4968, 0, 10044, 0, -6291, 0, 10998, 0, 208, 0, 2700, 0, -144, 0, 0, 0, 3726, 0, -8838, 0, -22436, 0, -4776, 0, 288, 0, -6983, 0, -6156, 0, -900, 0, 31752, 0, 3348, 0, 0, 0, 4762, 0, 3210, 0, 29196, 0, 6004, 0, -3798, 0, 23400, 0, 4096, 0, 12204, 0, 5274, 0, -4520, 0, 0, 0, 12420, 0, 20412, 0, -648, 0, 21366, 0, -21140, 0, -1728, 0, 14328, 0, 3266, 0, 4026, 0, -9504, 0, 0, 0, -1620, 0, 17028, 0, -1600, 0, -4266, 0, -9522, 0, -2592, 0, 2616, 0, -10296, 0, 3382, 0, 2988, 0, 0, 0, 20656, 0, -5616, 0, 4320, 0, 22114, 0, 4860, 0, 19962, 0, -604, 0, 1944, 0, 5040, 0, -899, 0, 0, 0, 4068, 0, 152, 0, -4020, 0, -10656, 0, -2790, 0, -3240, 0, 4194, 0, -7252, 0, 24408, 0, -6696, 0, 0, 0, 384, 0, 28422, 0, -34344, 0, -234, 0, 19908, 0, 14318, 0, -540, 0, 14400, 0, 16848, 0, 14640, 0, 0, 0, -30050, 0, 5373, 0, -22158, 0, 8432, 0, -8100, 0, -3132, 0, -17172, 0, 762, 0, 4140, 0, -20932, 0, 0, 0, 46152, 0, 1620, 0, -13230, 0, 21834, 0, -22600, 0, -23328, 0, 4464, 0, 12446, 0, -4608, 0, -1152, 0, 0, 0, 11664, 0, -12528, 0, -64, 0, -15414, 0, 46566, 0, 11576, 0, 729, 0, 8136, 0, 29338, 0, 15066, 0, 0, 0, -2540, 0, 3000, 0, 18792, 0, -13284, 0, 10692, 0, 14112, 0, 4832, 0, 14364, 0, -43920, 0, -20818, 0, 0, 0, -12042, 0, 12976, 0, 2916, 0, -6840, 0, -13058, 0, -17658, 0, -11826, 0, -3184, 0, 5424, 0, -9000, 0, 0, 0, 6318, 0, 45972, 0, -11996, 0, -6696, 0, 9072, 0, -4220, 0, -22356, 0, 6966, 0, -7776, 0, -5670, 0, 0, 0, 10368, 0, -1998, 0, 40806, 0, 17980, 0, 16608, 0, 14760, 0, -45200, 0, -720, 0, 12834, 0, -37864, 0, 0, 0, -42516, 0, 45638, 0, -6378, 0, 5022, 0, 34992, 0, -432, 0, 17496, 0, 30367, 0, 8802, 0, 37746, 0, 0, 0, -6108, 0, -16272, 0, -32174, 0, -16200, 0, 38934, 0, 29780, 0, 2160, 0, -48096, 0, -22356, 0, -13767, 0, 0, 0, 3320, 0, -9486, 0, 10656, 0, -21302, 0, -6858, 0, -7470, 0, 764, 0, 36936, 0, -32328, 0, -4736, 0, 0, 0, 43200, 0, -20088, 0, 2160, 0, -3744, 0, -7452, 0, 10848, 0, -19260, 0, -36316, 0, -5022, 0, -13392, 0, 0, 0, 22788, 0, -15264, 0, -38072, 0, -3732, 0, -3600, 0, -44974, 0, 72, 0, -12798, 0, -27900, 0, 3672, 0, 0, 0, -34874, 0, 5694, 0, -17190, 0, -6480, 0, 3888, 0, 40284, 0, -260, 0, -27486, 0, -15498, 0, 10368, 0, 0, 0, -7632, 0, -29535, 0, -15876, 0, -24156, 0, -37160, 0, -5400, 0, 18468, 0, 20512, 0, 5970, 0, 10386, 0, 0, 0, -14598, 0, 44136, 0, 25596, 0, -10368, 0, -32544, 0, -28432, 0, -13044, 0, -15696, 0, 39778, 0, -6102, 0, 0, 0, 12312, 0, -17928, 0, 41400, 0, 31726, 0, -21462, 0, -19458, 0, 33696, 0, -10206, 0, 2988, 0, 31142, 0, 0, 0, -17910, 0, -5120, 0, 14928, 0, 46728, 0, -42074, 0, -11664, 0, 7596, 0, -25984, 0, 5508, 0, -5904, 0, 0, 0, -17682, 0, -28278, 0, 50956, 0, 810, 0, 24120, 0, -19520, 0, 33318, 0, 26190, 0, 19000, 0, 19440, 0, 0, 0, 3274, 0, 1296, 0, -52884, 0, -89948, 0, -39528, 0, 11880, 0, 31104, 0, 9423, 0, -2304, 0, 38672, 0, 0, 0, 29844, 0, -48994, 0, 1404, 0, 21222, 0, 20432, 0, -18336, 0, 51120, 0, 3240, 0, -2430, 0, -59490, 0, 0, 0, -9936, 0, -87840, 0, 37018, 0, 40854, 0, -68400, 0, 53036, 0, -11988, 0, -20088, 0, 23878, 0, 7020, 0, 0, 0, 48600, 0, 2076, 0, -5976, 0, 6560, 0, 5328, 0, -4572, 0, 3616, 0, -24192, 0, -42624, 0, 38402, 0, 0, 0, -6300, 0, -42200, 0, -12204, 0, 11772, 0, 79380, 0, 37962, 0, 15552, 0, -38404, 0, -3888, 0, 85968, 0, 0, 0, 17172, 0, 28854, 0, 16776, 0, 27648, 0, -66924, 0, -21060, 0, -318, 0, -17478, 0, -69984, 0, -7200, 0, 0, 0, -42002, 0, -12042, 0, 92484, 0, 6480, 0, -480, 0, -9936, 0, 20870, 0, -4374, 0, 41022, 0, 29808, 0, 0, 0, -64440, 0, -55521, 0, -11742, 0, -6534, 0, -3104, 0, 8586, 0, -18000, 0, 43406, 0, 16416, 0, 468, 0, 0, 0, -64152, 0, -105768, 0, 22366, 0, -23076, 0, -8928, 0, -86184, 0, 13284, 0, -19836, 0, -10540, 0, -46470, 0, 0, 0, -8560, 0, 11664, 0, 1440, 0, 33200, 0, -10746, 0, -35082, 0, -38224, 0, 10128, 0, 6228, 0, 105948, 0, 0, 0, -52506, 0, 63908, 0, -20304, 0, -32544, 0, -44594, 0, 3894, 0, -50850, 0, 77912, 0, -37908, 0, -49932, 0, 0, 0, 21600, 0, -5580, 0, 40176, 0, 6744, 0, -6264, 0, -30790, 0, -7533, 0, 82386, 0, -34976, 0, -28836, 0, 0, 0, 7232, 0, 34020, 0, 4608, 0, 80, 0, 6642, 0, 9216, 0, 11988, 0, 486, 0, -36000, 0, -10736, 0, 0, 0, -99648, 0, -49248, 0, 21960, 0, 9774, 0, 101088, 0, 4320, 0, 3816, 0, 423, 0, -4110, 0, -12618, 0, 0, 0, -1458, 0, 11376, 0, 46018, 0, 46062, 0, 38268, 0, -2600, 0, -39072, 0, -17640, 0, -6976, 0, 2592, 0, 0, 0, -66296, 0, -43308, 0, -30384, 0, -52812, 0, -7968, 0, 50850, 0, -21384, 0, -22986, 0, 36648, 0, -16220, 0, 0, 0, -65286, 0, 44768, 0, 59700, 0, -35100, 0, -18926, 0, 11178, 0, -76086, 0, -12960, 0, -36288, 0, 67968, 0, 0, 0, -6780, 0, 82602, 0, -10376, 0, -5184, 0, -31140, 0, -8938, 0, 56916, 0, -6912, 0, -69500, 0, 18168, 0, 0, 0, 41148, 0, -7380, 0, -11340, 0, -63920, 0, -22572, 0, -136116, 0, 10720, 0, -12636, 0, -1818, 0, -32284, 0, 0, 0, 49968, 0, 13490, 0, 8640, 0, 3618, 0, -12960, 0, 15828, 0, -48492, 0, -51200, 0, -17496, 0, -65088, 0, 0, 0, -14904, 0, -115848, 0, 11340, 0, 30132, 0, 20340, 0, 4464, 0, -18873, 0, 18108, 0, -83978, 0, 32994, 0, 0, 0, -109268, 0, 624, 0, 22392, 0, 96876, 0, 8100, 0, 23904, 0, -100216, 0, -432, 0, 1440, 0, -17578, 0, 0, 0, 38862, 0, -22032, 0, 11178, 0, 14328, 0, -39040, 0, -26514, 0, -34164, 0, 18800, 0, -67308, 0, 42156, 0, 0, 0, -14328, 0, 118800, 0, 77020, 0, 864, 0, -70416, 0, 164916, 0, -20949, 0, 21600, 0, 102152, 0, -18468, 0, 0, 0, -51014, 0, -2700, 0, -56322, 0, -2032, 0, 95256, 0, -117864, 0, 84122, 0, 10044, 0, 77274, 0, 32400, 0, 0, 0, 59652, 0, -102898, 0, 14286, 0, -13320, 0, 54412, 0, 9630, 0, 35280, 0, -25920, 0, 87588, 0, 73710, 0, 0, 0, 18012, 0, -6624, 0, 62208, 0, -11394, 0, 18972, 0, 5920, 0, 70200, 0, 78264, 0, 31318, 0, 12288, 0, 0, 0, 40528, 0, 36612, 0, -75276, 0, 95842, 0, 15822, 0, -31104, 0, 66068, 0, -13560, 0, -1872, 0, -60821, 0, 0, 0, 128772, 0, 41104, 0, 37260, 0, -63000, 0, -101510, 0, 61236, 0, 82818, 0, -4948, 0, -1944, 0, 19080, 0, 0, 0, 64098, 0, -102042, 0, -160056, 0, -63420, 0, -89568, 0, 10044, 0, -5184, 0, -40662, 0, -14132, 0, 42984, 0, 0, 0, -8000, 0, 9798, 0, -78894, 0, -33048, 0, 12078, 0, -97632, 0, 99926, 0, -28512, 0, 106092, 0, -121348, 0, 0, 0, -144, 0, 134858, 0, -4860, 0, -38304, 0, -15344, 0, 51084, 0, 40680, 0, -199908, 0, -4800, 0, -98748, 0, 0, 0, -12798, 0, -71640, 0, -39890, 0, -28566, 0, 9540, 0, 51704, 0, -7776, 0, 130932, 0, -4070, 0, 7848, 0, 0, 0, 237168, 0, -30888, 0, 47088, 0, 103462, 0, 10146, 0, -56538, 0, -25640, 0, 8964, 0, 89028, 0, 63054, 0, 0, 0, -36864, 0, 31752, 0, 61968, 0, -50688, 0, -5174, 0, -16848, 0, 10944, 0, 41672, 0, 12960, 0, 110016, 0, 0, 0, 66342, 0, 17856, 0, -105400, 0, 14580, 0, -7272, 0, 124797, 0, 59886, 0, 29196, 0, 59616, 0, -1812, 0, 0, 0, -74942, 0, 5832, 0, -245124, 0, 141148, 0, 15120, 0, 29808, 0, -51022, 0, -2697, 0, -71838, 0, -83656, 0, 0, 0, 5328, 0, -42120, 0, 12204, 0, 11934, 0, 6752, 0, 456, 0, -12456, 0, -44288, 0, -12060, 0, 112806, 0, 0, 0, -31968, 0, 71964, 0, 85536, 0, -8370, 0, 65430, 0, 145152, 0, -9720, 0, -55800, 0, 20412, 0, 12582, 0, 0, 0, -38880, 0, -21756, 0, 87804, 0, -61526, 0, 73224, 0, 7380, 0, 17008, 0, -20088, 0, 77688, 0, -227772, 0, 0, 0, 152586, 0, 60560, 0, 1152, 0, 23328, 0, 800, 0, 85266, 0, -93564, 0, 24400, 0, -103032, 0, -23472, 0, 0, 0, -702, 0, 44190, 0, -101888, 0, 59724, 0, 42444, 0, 16288, 0, 42954, 0, 1908, 0, -106028, 0, -1620, 0, 0, 0, 109414, 0, 43200, 0, -73926, 0, 23488, 0, 50544, 0, -77508, 0, 72252, 0, 43920, 0, 25110, 0, -27244, 0, 0, 0, 2880, 0, 11234, 0, -90150, 0, -195264, 0, 36712, 0, 16119, 0, -87228, 0, 24470, 0, -66474, 0, -176400, 0, 0, 0, 25296, 0, 173736, 0, -25540, 0, -24300, 0, 70452, 0, -45360, 0, -9396, 0, 18288, 0, 36226, 0, -51516, 0, 0, 0, -84240, 0, 2286, 0, -87408, 0, -98496, 0, 12420, 0, -40770, 0, -162200, 0, -62796, 0, 236412, 0, -5312, 0, 0, 0, 183870, 0, 59660, 0, 138456, 0, -32472, 0, -1082, 0, 4860, 0, -5760, 0, -79704, 0, -39690, 0, 37404, 0, 0, 0, 65502, 0, 278820, 0, 126108, 0, -67800, 0, -69408, 0, -55870, 0, -69984, 0, -6084, 0, -8200, 0, 13392, 0, 0, 0, 23976, 0, 37338, 0, -194994, 0, 15940, 0, -13824, 0, -60768, 0, -53686, 0, -3456, 0, 33066, 0, -69712, 0, 0, 0, -113400, 0, 9952, 0, 34992, 0, -80154, 0, 121824, 0, -37584, 0, -10656, 0, 48914, 0, -192, 0, -23364, 0, 0, 0, -46242, 0, -19440, 0, -37260, 0, 139698, 0, -9792, 0, 170156, 0, 34728, 0, 154584, 0, -129600, 0, 2187, 0, 0, 0, -15184, 0, 24408, 0, -40464, 0, -42940, 0, 88014, 0, 5760, 0, -133036, 0, 45198, 0, -90720, 0, 82801, 0, 0, 0, 50994, 0, 173016, 0, -7620, 0, 73296, 0, 146026, 0, 9000, 0, -125370, 0, -34344, 0, 56376, 0, -75888, 0, 0, 0, -39852, 0, -117162, 0, 124624, 0, 32076, 0, 31860, 0, -2916, 0, 42336, 0, 12420, 0, -61508, 0, 14496, 0, 0, 0, 95372, 0, 43092, 0, 14400, 0, 416, 0, -131760, 0, -42732, 0, 1862, 0, -62454, 0, 175518, 0, -15920, 0, 0, 0, -187128, 0, 15482, 0, -36126, 0, 24660, 0, 102976, 0, 38928, 0, -119808, 0, 107918, 0, 8748, 0, -101430, 0, 0, 0, -20520, 0, -120528, 0, -276372, 0, -39174, 0, 44658, 0, -128728, 0, -52974, 0, 234432, 0, 34784, 0, -35478, 0, 0, 0, -40176, 0, -9552, 0, 11160, 0, -17172, 0, 16272, 0, -65322, 0, 259848, 0, -27000, 0, -122508, 0, 117182, 0, 0, 0, 47808, 0, 160292, 0, 18954, 0, -5040, 0, 10700, 0, 137916, 0, -60066, 0, 57232, 0, -35988, 0, 46152, 0, 0, 0, -20088, 0, 576, 0, 146260, 0, 27216, 0, -133200, 0, 38618, 0, -12660, 0, -22554, 0, 175264, 0, -67068, 0, 0, 0, 108370, 0, 20898, 0, -188874, 0, 217728, 0, -23328, 0, 135648, 0, 55889, 0, -17010, 0, 40680, 0, 277992, 0, 0, 0, 13212, 0, 59200, 0, 31104, 0, 14670, 0, 61560, 0, -5994, 0, -7416, 0, -209746, 0, 122418, 0, -14688, 0, 0, 0, 53940, 0, -109008, 0, 171586, 0, 49824, 0, -195354, 0, 47152, 0, 44280, 0, -222480, 0, 8192, 0, -135600, 0, 0, 0, 135432, 0, -2160, 0, 235692, 0, -127008, 0, 38502, 0, 75816, 0, 170540, 0, -113592, 0, -88848, 0, -19270, 0, 0, 0, -16326, 0, -75032, 0, -127548, 0, -5760, 0, -51840, 0, 136914, 0, 190800, 0, 178848, 0, -19134, 0, -94968, 0, 0, 0, 15066, 0, 37980, 0, 58744, 0, 104976, 0, -116784, 0, 13420, 0, -1296, 0, 105408, 0, 89424, 0, 52488, 0, 0, 0, -47690, 0, 91101, 0, -111042, 0, -25128, 0, 26406, 0, -164340, 0, -13284, 0, 113238, 0, 309168, 0, -46396, 0, 0, 0, -13968, 0, -197964, 0, -18324, 0, -45918, 0, 51688, 0, -48816, 0, -3744, 0, 208070, 0, -96522, 0, -14220, 0, 0, 0, -48600, 0, -43920, 0, 48896, 0, 116802, 0, -19008, 0, 1592, 0, 89340, 0, -99684, 0, -147420, 0, 6480, 0, 0, 0, 8720, 0, -144288, 0, -49248, 0, -4706, 0, -67068, 0, -115506, 0, -81648, 0, -41301, 0, 95400, 0, 159084, 0, 0, 0, 83790, 0, -108944, 0, 9960, 0, 403848, 0, -23210, 0, -28458, 0, 174294, 0, 190744, 0, 31968, 0, 81360, 0, 0, 0, -63906, 0, -26118, 0, -5184, 0, -20574, 0, -18720, 0, -256400, 0, -22410, 0, 125694, 0, 121672, 0, 2292, 0, 0, 0, -5536, 0, 110808, 0, -8226, 0, -71756, 0, -96984, 0, 125784, 0, 16200, 0, -14208, 0, 45972, 0, 108128, 0, 0, 0, -351036, 0, -219538, 0, 129600, 0, 64512, 0, -161684, 0, -60264, 0, -111456, 0, -147454, 0, 6480, 0, 156078, 0, 0, 0, -11232, 0, -27900, 0, 5876, 0, -22356, 0, -85716, 0, 89756, 0, 32544, 0, -109080, 0, -44234, 0, -57780, 0, 0, 0, 14320, 0, -108948, 0, -101232, 0, -322778, 0, -15066, 0, 187866, 0, -65788, 0, -40176, 0, -108072, 0, 10368, 0, 0, 0, 174978, 0, -13400, 0, 68364, 0, -29880, 0, 279898, 0, -45792, 0, 30690, 0, -421200, 0, -114216, 0, 10080, 0, 0, 0, -11196, 0, -73728, 0, -36704, 0, -10800, 0, 14760, 0, -295488, 0, -134922, 0, -197910, 0, 848, 0, 216, 0, 0, 0, -94932, 0, -38394, 0, 17874, 0, 168856, 0, -83700, 0, 81360, 0, 6614, 0, 11016, 0, -136818, 0, -18244, 0, 0, 0, 32112, 0, 22519, 0, -104622, 0, -246636, 0, -223560, 0, 17082, 0, 58284, 0, 1280, 0, -51570, 0, -225666, 0, 0, 0, -19440, 0, 73800, 0, 136654, 0, 11664, 0, 153378, 0, 34992, 0, 120852, 0, 26388, 0, -384588, 0, -780, 0, 0, 0, 104500, 0, -82458, 0, 380520, 0, -147770, 0, -46494, 0, -177210, 0, 31312, 0, 31104, 0, -182304, 0, 244000, 0, 0, 0, 37746, 0, -95904, 0, -22896, 0, -207936, 0, -150064, 0, -88605, 0, -58788, 0, 263816, 0, -47628, 0, 190836, 0, 0, 0, -72468, 0, 211986, 0, 48800, 0, -111480, 0, 223416, 0, 171072, 0, -16200, 0, -149706, 0, 32400, 0, 55404, 0, 0, 0, -43742, 0, 61536, 0, 42624, 0, 115712, 0, 17910, 0, -147888, 0, -130572, 0, 31158, 0, -35424, 0, -306504, 0, 0, 0, -266868, 0, -22356, 0, -43794, 0, 28800, 0, 123920, 0, 132408, 0, -27000, 0, -172582, 0, 76788, 0, 39654, 0, 0, 0, -31104, 0, -258084, 0, 171396, 0, -97632, 0, 48438, 0, 144020, 0, -85296, 0, 28656, 0, 2540, 0, -39132, 0, 0, 0, -255400, 0, -47088, 0, 1872, 0, 117738, 0, 119334, 0, 2340, 0, 185328, 0, -18306, 0, -256680, 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": "12.4.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], [0], [-18], [0], [-8], [0], [9], [0], [0], [0], [10], [0], [-54], [0], [-18], [0], [100], [0], [-24], [0], [72], [0], [199], [0], [27], [0], [234], [0], [-16], [0], [0], [0], [144], [0], [-226], [0], [30], [0], [-90], [0], [-452], [0], [-162], [0], [432], [0], [-279], [0], [-54], [0], [414], [0], [0], [0], [300], [0], [-684], [0], [-422], [0], [-72], [0], [-180], [0], [332], [0], [216], [0], [-360], [0], [-26], [0], [597], [0], [0], [0], [-512], [0], [81], [0], [1188], [0], [324], [0], [702], [0], [-630], [0], [-80], [0], [-48], [0], [-1800], [0], [-1054], [0], [0], [0]]}