# Stored data for newform 2352.4.a.ba, downloaded from the LMFDB on 23 April 2024.
{"label": "2352.4.a.ba", "space_label": "2352.4.a", "level": 2352, "weight": 4, "hecke_orbit": 27, "hecke_orbit_code": 117093590378744112, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 113157687255425720, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [2, 1]], [11, [-8, 1]]], "qexp_display": "q+3q^{3}-2q^{5}+9q^{9}+8q^{11}+42q^{13}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 37632, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 138.77249233350193, "hecke_ring_index": 1, "level_radical": 42, "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": [2352, 1, [1471, 1765, 785, 2257], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "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": "0.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.896", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.669", "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], [7, -1]], "trace_display": [0, 3, -2, 0], "traces": [0, 1, 0, 3, 0, -2, 0, 0, 0, 9, 0, 8, 0, 42, 0, -6, 0, 2, 0, -124, 0, 0, 0, -76, 0, -121, 0, 27, 0, 254, 0, -72, 0, 24, 0, 0, 0, 398, 0, 126, 0, -462, 0, -212, 0, -18, 0, -264, 0, 0, 0, 6, 0, -162, 0, -16, 0, -372, 0, -772, 0, -30, 0, 0, 0, -84, 0, 764, 0, -228, 0, 236, 0, -418, 0, -363, 0, 0, 0, -552, 0, 81, 0, 1036, 0, -4, 0, 762, 0, -30, 0, 0, 0, -216, 0, 248, 0, 1190, 0, 72, 0, -1370, 0, 464, 0, 0, 0, 2136, 0, -1226, 0, 1194, 0, 338, 0, 152, 0, 378, 0, 0, 0, -1267, 0, -1386, 0, 492, 0, -2088, 0, -636, 0, -292, 0, 0, 0, -54, 0, 818, 0, -2156, 0, -792, 0, 336, 0, -508, 0, 0, 0, -2850, 0, -1672, 0, 18, 0, 144, 0, -446, 0, -486, 0, 0, 0, -2708, 0, -48, 0, 896, 0, -433, 0, -1116, 0, -4034, 0, 0, 0, -2316, 0, 3480, 0, 2898, 0, -90, 0, -796, 0, 16, 0, 0, 0, -2652, 0, 146, 0, -252, 0, -2546, 0, -2536, 0, 2292, 0, 0, 0, 924, 0, -684, 0, -992, 0, 1300, 0, 708, 0, 424, 0, 0, 0, -1254, 0, 84, 0, 2576, 0, -1089, 0, -1836, 0, 1874, 0, 0, 0, 3730, 0, 528, 0, -1656, 0, -2004, 0, 646, 0, 243, 0, 0, 0, -5208, 0, 3108, 0, 1260, 0, -608, 0, -12, 0, -5910, 0, 0, 0, 2286, 0, -2988, 0, 324, 0, -90, 0, 1318, 0, -5640, 0, 0, 0, -968, 0, 6446, 0, -648, 0, 4930, 0, -6260, 0, 744, 0, 0, 0, -4909, 0, 3570, 0, 2310, 0, 1544, 0, 216, 0, -3192, 0, 0, 0, -4110, 0, 60, 0, 196, 0, 1392, 0, -6736, 0, -394, 0, 0, 0, -6714, 0, 2032, 0, 6408, 0, -248, 0, -5082, 0, -3678, 0, 0, 0, -692, 0, 3582, 0, -1528, 0, -1566, 0, 1014, 0, -576, 0, 0, 0, 456, 0, 5328, 0, -11326, 0, 1134, 0, 2130, 0, -472, 0, 0, 0, -3044, 0, 8517, 0, -3801, 0, 836, 0, 12416, 0, -4158, 0, 0, 0, -7442, 0, 1476, 0, 10668, 0, -100, 0, -6264, 0, 8080, 0, 0, 0, -1908, 0, -5482, 0, -152, 0, -876, 0, 1104, 0, -10446, 0, 0, 0, -11334, 0, -3024, 0, -162, 0, 3184, 0, -8594, 0, 2454, 0, 0, 0, -2072, 0, -6468, 0, 10500, 0, -12066, 0, -2376, 0, -242, 0, 0, 0, 1008, 0, -4332, 0, 1918, 0, -1524, 0, 9424, 0, -7992, 0, 0, 0, -3184, 0, 60, 0, -8550, 0, 11426, 0, -3696, 0, -5016, 0, 0, 0, -16934, 0, 54, 0, 17038, 0, 13592, 0, 432, 0, 8612, 0, 0, 0, -1338, 0, -1696, 0, 15004, 0, -1458, 0, 7432, 0, 16716, 0, 0, 0, -2380, 0, 6616, 0, -8124, 0, -17040, 0, 508, 0, -144, 0, 0, 0, 2948, 0, 2688, 0, 17304, 0, 2740, 0, -1299, 0, -4650, 0, 0, 0, -3348, 0, -928, 0, -2112, 0, -12102, 0, -16854, 0, -124, 0, 0, 0, -144, 0, -6391, 0, -6948, 0, -19404, 0, -4272, 0, 10440, 0, 0, 0, 5382, 0, 8694, 0, 2452, 0, -17460, 0, -270, 0, -31496, 0, 0, 0, -2388, 0, -9514, 0, -8904, 0, 48, 0, 3988, 0, -676, 0, 0, 0, 11346, 0, 8436, 0, -7956, 0, 9196, 0, -2098, 0, 438, 0, 0, 0, -1296, 0, -756, 0, 9436, 0, 8928, 0, -7638, 0, 1314, 0, 0, 0, -7608, 0, 8940, 0, -16058, 0, 6876, 0, 2534, 0, 3936, 0, 0, 0, -11088, 0, 174, 0, 2772, 0, 16018, 0, -3068, 0, -2052, 0, 0, 0, 14141, 0, -2976, 0, 796, 0, -24656, 0, 3900, 0, 4176, 0, 0, 0, 2124, 0, 7594, 0, -3724, 0, 1272, 0, 3792, 0, -6176, 0, 0, 0, 24702, 0, 584, 0, -3762, 0, 20144, 0, 2522, 0, 252, 0, 0, 0, -19304, 0, 7728, 0, -240, 0, -10414, 0, -3267, 0, 22230, 0, 0, 0, -5508, 0, -18192, 0, -1636, 0, 5622, 0, -6804, 0, 8108, 0, 0, 0, 4312, 0, -924, 0, 11190, 0, -5794, 0, -49352, 0, 1584, 0, 0, 0, -1954, 0, -4968, 0, 5472, 0, -672, 0, -6012, 0, -32016, 0, 0, 0, 1938, 0, -30734, 0, -23072, 0, 729, 0, -424, 0, -31782, 0, 0, 0, 6112, 0, 24396, 0, -15624, 0, 32604, 0, 5700, 0, 9324, 0, 0, 0, 7680, 0, 3780, 0, 3344, 0, 366, 0, -1824, 0, -29374, 0, 0, 0, -36, 0, -32424, 0, 38990, 0, -17730, 0, 20470, 0, 8712, 0, 0, 0, 57288, 0, 1888, 0, 6858, 0, 892, 0, 29916, 0, -8964, 0, 0, 0, -1260, 0, 972, 0, -4914, 0, -528, 0, -270, 0, -3344, 0, 0, 0, 3954, 0, 34250, 0, -41804, 0, -16920, 0, 5416, 0, 26288, 0, 0, 0, 30862, 0, -10576, 0, -2904, 0, 10680, 0, 1178, 0, 19338, 0, 0, 0, -1792, 0, -1944, 0, -5600, 0, 40127, 0, 14790, 0, 866, 0, 0, 0, -18780, 0, -30248, 0, 826, 0, 2232, 0, -45918, 0, 42380, 0, 0, 0, 26524, 0, 8068, 0, -14727, 0, -4416, 0, 32088, 0, 10710, 0, 0, 0, 20614, 0, 6930, 0, 23730, 0, 9028, 0, 4632, 0, 37200, 0, 0, 0, 648, 0, 32736, 0, -6960, 0, -9576, 0, -18288, 0, -324, 0, 0, 0, -5796, 0, -23988, 0, -12330, 0, -15276, 0, 8288, 0, 180, 0, 0, 0, 10760, 0, 588, 0, 9912, 0, -48158, 0, 4176, 0, 52890, 0, 0, 0, -20208, 0, -32, 0, 6118, 0, -1182, 0, 32230, 0, 35112, 0, 0, 0, 18544, 0, -17556, 0, -20142, 0, 25930, 0, 5304, 0, 6096, 0, 0, 0, -24607, 0, 19224, 0, -292, 0, -8192, 0, -744, 0, -54444, 0, 0, 0, -15246, 0, -25446, 0, -240, 0, -11034, 0, 33192, 0, 5092, 0, 0, 0, 16112, 0, -11024, 0, -2076, 0, 5072, 0, 40714, 0, 10746, 0, 0, 0, -1544, 0, -4584, 0, 20088, 0, 28226, 0, -4698, 0, -48330, 0, 0, 0, 3042, 0, -44456, 0, -61054, 0, -1728, 0, 55902, 0, -23184, 0, 0, 0, 3900, 0, -32166, 0, 1368, 0, -60, 0, 27984, 0, 15984, 0, 0, 0, 1984, 0, -33978, 0, 11242, 0, -7548, 0, 3402, 0, -2600, 0, 0, 0, 6390, 0, -22730, 0, 16688, 0, -1416, 0, 9520, 0, 24946, 0, 0, 0, 101092, 0, 25652, 0, -9132, 0, 43512, 0, 20064, 0, 25551, 0, 0, 0, 2136, 0, -11403, 0, 39676, 0, -62690, 0, 2508, 0, 17386, 0, 0, 0, 37248, 0, 62140, 0, -168, 0, -12474, 0, 27078, 0, -10960, 0, 0, 0, -5152, 0, 2022, 0, -22326, 0, 95728, 0, -36052, 0, 4428, 0, 0, 0, 32346, 0, 32004, 0, 3712, 0, 3672, 0, -300, 0, 1528, 0, 0, 0, -18792, 0, -3748, 0, -28656, 0, 24240, 0, 65280, 0, 13718, 0, 0, 0, -1260, 0, 3720, 0, -5724, 0, 70824, 0, -7460, 0, -16446, 0, 0, 0, 28484, 0, -456, 0, 31944, 0, 17088, 0, -2628, 0, 5150, 0, 0, 0, 3312, 0, 14736, 0, -117348, 0, -31338, 0, 27386, 0, 4008, 0, 0, 0, -9808, 0, 16610, 0, -34002, 0, -1292, 0, 472, 0, -9072, 0, 0, 0, 24646, 0, -486, 0, 77658, 0, 12312, 0, 9552, 0, 33840, 0, 0, 0, -25782, 0, -58122, 0, 17472, 0, 7362, 0, 10416, 0, 36706, 0, 0, 0, -836, 0, 2704, 0, -6216, 0, -53848, 0, -76410, 0, -19404, 0, 0, 0, -2520, 0, 31500, 0, -73164, 0, 49980, 0, -36198, 0, 1216, 0, 0, 0, -7128, 0, 33264, 0, -94736, 0, -726, 0, -35922, 0, 9872, 0, 0, 0, 52704, 0, 11820, 0, 3024, 0, 25482, 0, 30140, 0, -12996, 0, 0, 0, -75118, 0, 5754, 0, 18046, 0, -8472, 0, -4572, 0, -23980, 0, 0, 0, 28272, 0, -57540, 0, 5976, 0, -23976, 0, -27792, 0, 74086, 0, 0, 0, 19602, 0, -29056, 0, -9552, 0, -20784, 0, 15264, 0, 180, 0, 0, 0, 19488, 0, -25650, 0, -1104, 0, -2636, 0, 34278, 0, -29264, 0, 0, 0, -11088, 0, 11280, 0, 58672, 0, -15048, 0, -24526, 0, -67056, 0, 0, 0, 62084, 0, 107751, 0, -50802, 0, -42530, 0, 3936, 0, 162, 0, 0, 0, -7778, 0, 51114, 0, -12892, 0, 51832, 0, 40776, 0, 89712, 0, 0, 0, 1296, 0, -16704, 0, -35840, 0, 25836, 0, 2280, 0, -9860, 0, 0, 0, -42414, 0, 2072, 0, -4014, 0, 12520, 0, -51492, 0, -5088, 0, 0, 0, 95264, 0, 45012, 0, 68796, 0, -56866, 0, -4374, 0, 49250, 0, 0, 0, 22296, 0, -106196, 0, -2336, 0, 50148, 0, 9818, 0, 54336, 0, 0, 0, -20208, 0, -11754, 0, -7140, 0, 19008, 0, 25828, 0, 19848, 0, 0, 0, -4620, 0, -24372, 0, 14196, 0, 14096, 0, -51120, 0, 93412, 0, 0, 0, 1524, 0, -36870, 0, 52556, 0, -432, 0, 27312, 0, -79018, 0, 0, 0, 56622, 0, 6384, 0, 8844, 0, -38880, 0, 68448, 0, 8064, 0, 0, 0, 6544, 0, 51912, 0, 46760, 0, -60, 0, 8220, 0, -183876, 0, 0, 0, -3897, 0, -48712, 0, 3630, 0, -13950, 0, -17248, 0, -75388, 0, 0, 0, -392, 0, -41148, 0, -10044, 0, -58064, 0, -2872, 0, -2784, 0, 0, 0, 39990, 0, -6336, 0, 28490, 0, 13472, 0, -36306, 0, -92160, 0, 0, 0, -50562, 0, 788, 0, -24360, 0, -372, 0, -12140, 0, -53214, 0, 0, 0, -128464, 0, -1532, 0, -432, 0, 9084, 0, 13428, 0, -19173, 0, 0, 0, -84376, 0, -20844, 0, -4064, 0, -125018, 0, -58212, 0, 44658, 0, 0, 0, -12816, 0, 3564, 0, 120638, 0, 31320, 0, 56702, 0, 496, 0, 0, 0, -19984, 0, 3758, 0, 16146, 0, 20664, 0, 9420, 0, 26082, 0, 0, 0, -17936, 0, 7356, 0, -14378, 0, -22800, 0, -52380, 0, 11664, 0, 0, 0, -810, 0, 2380, 0, -87696, 0, -94488, 0, 1384, 0, 94582, 0, 0, 0, -13376, 0, 22184, 0, -7164, 0, -94376, 0, -68878, 0, -28542, 0, 0, 0, -92444, 0, -26712, 0, 31768, 0, 144523, 0, 144, 0, 3132, 0, 0, 0, 11964, 0, 3720, 0, -34846, 0, -2028, 0, 107298, 0, 109132, 0, 0, 0, -12264, 0, 1152, 0, 34038, 0, 27414, 0, -196088, 0, 25308, 0, 0, 0, -2740, 0, -23868, 0, 42490, 0, -75196, 0, 27588, 0, -3568, 0, 0, 0, -6294, 0, 44022, 0, -10656, 0, 1314, 0, -105072, 0, -43710, 0, 0, 0, 22652, 0, -69404, 0, -3888, 0, 928, 0, -51378, 0, -2268, 0, 0, 0, -120224, 0, 28308, 0, 97944, 0, -4260, 0, 26784, 0, -7620, 0, 0, 0, -22914, 0, -28556, 0, 47894, 0, 3942, 0, 34356, 0, -18912, 0, 0, 0, 69560, 0, -45690, 0, -22824, 0, -21664, 0, 6088, 0, 26820, 0, 0, 0, 90250, 0, -48174, 0, -17034, 0, -90552, 0, 20628, 0, -139452, 0, 0, 0, 7602, 0, 41952, 0, 4272, 0, 11808, 0, -22752, 0, 50578, 0, 0, 0, 55584, 0, 83616, 0, -33264, 0, -24832, 0, 7168, 0, 522, 0, 0, 0, -147560, 0, 8316, 0, -40824, 0, -34563, 0, 48054, 0, -2452, 0, 0, 0, -9204, 0, -3464, 0, 69034, 0, -6156, 0, 14884, 0, 9732, 0, 0, 0, -95500, 0, 94674, 0, 42423, 0, 17950, 0, 26864, 0, -8928, 0, 0, 0, -21336, 0, 2388, 0, 93450, 0, 2160, 0, -73968, 0, 200, 0, 0, 0, 11700, 0, 13110, 0, -32272, 0, 12528, 0, -47028, 0, -78736, 0, 0, 0, -56190, 0, -16160, 0, 6372, 0, 169880, 0, 676, 0, 22782, 0, 0, 0, 121968, 0, -11172, 0, 101948, 0, -21418, 0, 3816, 0, -119700, 0, 0, 0, 11376, 0, 194056, 0, 10964, 0, -18528, 0, -131346, 0, -114784, 0, 0, 0, 304, 0, -57536, 0, 74106, 0, -64476, 0, -70224, 0, 1752, 0, 0, 0, 27840, 0, -11286, 0, -161154, 0, 66792, 0, 60432, 0, -13956, 0, 0, 0, 7566, 0, 20892, 0, -67620, 0, 756, 0, 23184, 0, -32650, 0, 0, 0, -55266, 0, 41336, 0, -57912, 0, -51648, 0, 22668, 0, 23184, 0, 0, 0, -55628, 0, -720, 0, 6048, 0, 73586, 0, -31242, 0, 55968, 0, 0, 0, -9801, 0, -6656, 0, 137242, 0, 66690, 0, -264864, 0, -6368, 0, 0, 0, 28652, 0, -18732, 0, -16524, 0, 17188, 0, 2280, 0, -54576, 0, 0, 0, -98050, 0, -4908, 0, -2534, 0, 59944, 0, 16866, 0, 113808, 0, 0, 0, -20412, 0, 125894, 0, 152024, 0, 24324, 0, -125356, 0, -55008, 0, 0, 0, -78310, 0, 73396, 0, 12936, 0, 110164, 0, 11230, 0, -2772, 0, 0, 0, -21000, 0, 33570, 0, 20412, 0, -21216, 0, -17382, 0, 24132, 0, 0, 0, -148056, 0, 30556, 0, -21770, 0, 4752, 0, -106172, 0, -113736, 0, 0, 0, 1168, 0, 984, 0, -5862, 0, 60090, 0, 107924, 0, -14904, 0, 0, 0, -149318, 0, 16416, 0, -8610, 0, -118288, 0, -2016, 0, -41912, 0, 0, 0, -18036, 0, 14762, 0, 8664, 0, -96048, 0, -4176, 0, -118442, 0, 0, 0, -3836, 0, -20368, 0, 5814, 0, 37632, 0, 74844, 0, -92202, 0, 0, 0, 121276, 0, -69216, 0, -307256, 0, -18848, 0, 2187, 0, -20288, 0, 0, 0, -1272, 0, 15984, 0, -110460, 0, -95346, 0, -16992, 0, 135004, 0, 0, 0, -92476, 0, -34127, 0, 18336, 0, -41690, 0, 6368, 0, 73188, 0, 0, 0, -56554, 0, -46872, 0, 3630, 0, -584, 0, 97812, 0, -90440, 0, 0, 0, 17100, 0, -45074, 0, -31416, 0, 27972, 0, 201892, 0, -22852, 0, 0, 0, -169428, 0, -52828, 0, 23040, 0, 7392, 0, -11940, 0, 11340, 0, 0, 0, 30096, 0, 10032, 0, -44884, 0, -17610, 0, 1098, 0, 81226, 0, 0, 0, -5472, 0, 34344, 0, 36526, 0, -88122, 0, 33868, 0, -488, 0, 0, 0, -140208, 0, 141518, 0, -108, 0, 79746, 0, 157108, 0, -97272, 0, 0, 0, -34076, 0, 116970, 0, -176274, 0, -152952, 0, -53190, 0, -27184, 0, 0, 0, 61410, 0, 10400, 0, 104120, 0, 26136, 0, 146160, 0, 1636, 0, 0, 0, 80814, 0, -17224, 0, 171864, 0, -63408, 0, -29678, 0, 5664, 0, 0, 0, -71924, 0, 20574, 0, 10080, 0, 121716, 0, 2676, 0, -96714, 0, 0, 0, 89748, 0, -4312, 0, 3392, 0, -26892, 0, -35264, 0, -61276, 0, 0, 0, -61008, 0, 23498, 0, -3780, 0, -117738, 0, -93312, 0, 2916, 0, 0, 0, -70610, 0, -14742, 0, 136010, 0, -14864, 0, -1584, 0, -5920, 0, 0, 0, -810, 0, -33432, 0, 263144, 0, -10032, 0, -172524, 0, 258912, 0, 0, 0, 71602, 0, 356664, 0, 11862, 0, -173812, 0, -143990, 0, 102750, 0, 0, 0, 672, 0, -125412, 0, -13232, 0, -51266, 0, -50760, 0, 83522, 0, 0, 0, 16248, 0, 2836, 0, 39744, 0, 78864, 0, 20608, 0, 34080, 0, 0, 0, -51400, 0, -162336, 0, 92586, 0, -1016, 0, -38180, 0, -31728, 0, 0, 0, -133750, 0, -8712, 0, 60438, 0, 304072, 0, 32040, 0, -111384, 0, 0, 0, 3534, 0, 36208, 0, 42768, 0, 58014, 0, -5896, 0, -14688, 0, 0, 0, 13860, 0, -145872, 0, -5376, 0, 93176, 0, 6132, 0, -5832, 0, 0, 0, -34608, 0, -16800, 0, 14992, 0, -122246, 0, 120381, 0, 165770, 0, 0, 0, 44370, 0, -11416, 0, -5700, 0, 2598, 0, 163664, 0, 62764, 0, 0, 0, -208284, 0, 9300, 0, -56340, 0, 65774, 0, -118736, 0, -90744, 0, 0, 0, 40102, 0, 2478, 0, -106932, 0, 29840, 0, 6696, 0, -3344, 0, 0, 0, -137754, 0, -74592, 0, -56144, 0, 127140, 0, -114900, 0, -7620, 0, 0, 0, 4224, 0, -106512, 0, 79572, 0, -40084, 0, 243854, 0, 24204, 0, 0, 0, -25688, 0, -44181, 0, -101432, 0, 33708, 0, -13248, 0, 96290, 0, 0, 0, 96264, 0, 248, 0, -249074, 0, 32130, 0, 116958, 0, 6360, 0, 0, 0, 93928, 0, -16032, 0, 61842, 0, -202774, 0, 288, 0, 20790, 0, 0, 0, 267344, 0, 71190, 0, 12782, 0, -17320, 0, 27084, 0, 5168, 0, 0, 0, 13896, 0, 126930, 0, 158284, 0, 111600, 0, 27032, 0, 38808, 0, 0, 0, -892, 0, -243536, 0, 1944, 0, -258456, 0, -104494, 0, 98208, 0, 0, 0, 178340, 0, -20880, 0, -66584, 0, -178078, 0, -28728, 0, -64962, 0, 0, 0, -54864, 0, -80296, 0, -166364, 0, -972, 0, -10764, 0, -86140, 0, 0, 0, -92420, 0, 47802, 0, -17388, 0, -41664, 0, 149056, 0, -71964, 0, 0, 0, 148346, 0, -36990, 0, -129766, 0, 53940, 0, -45828, 0, 34920, 0, 0, 0, 24864, 0, 121078, 0, 54600, 0, 540, 0, -352968, 0, -143054, 0, 0, 0, 41922, 0, 62992, 0, 32280, 0, 2160, 0, 10080, 0, 1764, 0, 0, 0, -67864, 0, 29736, 0, -5416, 0, 203808, 0, -144474, 0, -11678, 0, 0, 0, 12528, 0, 96292, 0, 19028, 0, 158670, 0, 71934, 0, -5752, 0, 0, 0, 17808, 0, 157366, 0, -60624, 0, -208542, 0, 39212, 0, -96, 0, 0, 0, -122633, 0, 18354, 0, 302260, 0, -7976, 0, -3546, 0, 201028, 0, 0, 0, 96690, 0, -40898, 0, -47280, 0, 105336, 0, 353400, 0, 48830, 0, 0, 0, -252218, 0, 1792, 0, 55632, 0, -120304, 0, -22692, 0, -52668, 0, 0, 0, 251364, 0, -60426, 0, -16872, 0, 77786, 0, 77790, 0, 56726, 0, 0, 0, 15912, 0, 7920, 0, 207328, 0, 18288, 0, -866, 0, -37392, 0, 0, 0, -119860, 0, -161968, 0, -73821, 0, 4196, 0, 22048, 0, 57672, 0, 0, 0, -23904, 0, -876, 0, -271950, 0, 108192, 0, -24576, 0, -293536, 0, 0, 0, -2232, 0, 167950, 0, -109032, 0, -163332, 0, 2592, 0, -150278, 0, 0, 0, 158688, 0, -219696, 0, -45738, 0, 183524, 0, -347980, 0, -76338, 0, 0, 0, -18872, 0, -720, 0, -178332, 0, -8068, 0, -33102, 0, -17856, 0, 0, 0, 99576, 0, -77112, 0, 203350, 0, 15276, 0, -156098, 0, 10544, 0, 0, 0, 233752, 0, -2628, 0, 48336, 0, 190290, 0, -315660, 0, -33072, 0, 0, 0, 78708, 0, -6228, 0, -45120, 0, 55304, 0, 15216, 0, 117856, 0, 0, 0, 122142, 0, 193116, 0, -17880, 0, 32238, 0, 191056, 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": "42.4.a.b", "char_is_minimal": false, "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], [-2], [0], [0], [0], [9], [0], [8], [0], [42], [0], [-6], [0], [2], [0], [-124], [0], [0], [0], [-76], [0], [-121], [0], [27], [0], [254], [0], [-72], [0], [24], [0], [0], [0], [398], [0], [126], [0], [-462], [0], [-212], [0], [-18], [0], [-264], [0], [0], [0], [6], [0], [-162], [0], [-16], [0], [-372], [0], [-772], [0], [-30], [0], [0], [0], [-84], [0], [764], [0], [-228], [0], [236], [0], [-418], [0], [-363], [0], [0], [0], [-552], [0], [81], [0], [1036], [0], [-4], [0], [762], [0], [-30], [0], [0], [0], [-216], [0], [248], [0], [1190], [0], [72], [0]]}