# Stored data for newform 441.4.a.l, downloaded from the LMFDB on 25 April 2024.
{"label": "441.4.a.l", "space_label": "441.4.a", "level": 441, "weight": 4, "hecke_orbit": 12, "hecke_orbit_code": 49539595968184761, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1286388623423422056, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-3, 1]], [5, [-3, 1]], [13, [64, 1]]], "qexp_display": "q+3q^{2}+q^{4}+3q^{5}-21q^{8}+9q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 7056, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 26.019842312531612, "hecke_ring_index": 1, "level_radical": 21, "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": [441, 1, [344, 199], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [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": "0.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.872", "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]], "trace_display": [3, 0, 3, 0], "traces": [0, 1, 3, 0, 1, 3, 0, 0, -21, 0, 9, 15, 0, -64, 0, 0, -71, -84, 0, -16, 3, 0, 45, 84, 0, -116, -192, 0, 0, 297, 0, -253, -45, 0, -252, 0, 0, -316, -48, 0, -63, -360, 0, 26, 15, 0, 252, 30, 0, 0, -348, 0, -64, -363, 0, 45, 0, 0, 891, 15, 0, -118, -759, 0, 433, -192, 0, -370, -84, 0, 0, 342, 0, 362, -948, 0, -16, 0, 0, 467, -213, 0, -1080, -477, 0, -252, 78, 0, -315, -906, 0, 0, 84, 0, 90, -48, 0, 503, 0, 0, -116, 1086, 0, 1736, 1344, 0, -1089, 1353, 0, -370, 135, 0, 0, 648, 0, 252, 297, 0, 45, 0, 0, -1106, -354, 0, -253, -723, 0, 377, 1659, 0, -576, 651, 0, 0, -1110, 0, 1764, 1770, 0, -1558, 0, 0, 1026, -960, 0, 891, 1086, 0, -316, -2454, 0, 1259, 336, 0, 0, -759, 0, -196, 1401, 0, -135, 0, 0, -1252, -360, 0, -1431, 2646, 0, 1899, -756, 0, 26, 786, 0, 0, -1065, 0, -2718, -2892, 0, 1352, 0, 0, -1764, -948, 0, -1260, 30, 0, -144, -3912, 0, 1493, 1509, 0, 0, 4086, 0, -3556, 2436, 0, 3258, 0, 0, -1080, 5208, 0, 4544, -240, 0, 1250, -363, 0, 4059, 78, 0, 0, -1110, 0, 45, 5376, 0, 425, 0, 0, 1944, -3855, 0, -2188, 756, 0, -6237, -852, 0, 90, 15, 0, 0, -5508, 0, 791, -3318, 0, -118, 0, 0, 1024, 5313, 0, -2169, -5265, 0, 1260, 1131, 0, 1513, 6870, 0, 0, -192, 0, 1953, 222, 0, -1089, 0, 0, -370, -7851, 0, 5183, 5964, 0, 5310, -1740, 0, -4960, -4674, 0, 0, 774, 0, 3698, 342, 0, -2880, 0, 0, 2143, 2673, 0, 362, 6273, 0, 45, 6636, 0, -7362, -5376, 0, 0, 3777, 0, 1136, -354, 0, -1684, 0, 0, -2277, 1320, 0, -8503, -588, 0, 467, 2577, 0, 4455, 1299, 0, 0, 1344, 0, 7424, -3756, 0, 7560, 0, 0, -484, -477, 0, 7938, -1110, 0, -8359, 5697, 0, -252, -3795, 0, 0, -546, 0, 2358, 1860, 0, -1918, 0, 0, -675, 3048, 0, 1026, -906, 0, -8676, 30, 0, -6603, 4056, 0, 0, 1086, 0, -11311, -5964, 0, -2844, 0, 0, 1208, -3780, 0, -630, -19008, 0, 7640, -48, 0, -11736, -12750, 0, 0, 4479, 0, 503, -3126, 0, -7056, 0, 0, 12258, 1401, 0, -5932, -10668, 0, 8236, -1608, 0, 16192, 1086, 0, 0, -4740, 0, -4465, -3240, 0, 1736, 0, 0, -1431, 2880, 0, -720, 1584, 0, -1330, 3750, 0, 7623, 9744, 0, 0, 1353, 0, 234, -9588, 0, 494, 0, 0, -370, -1344, 0, -16009, -945, 0, 16128, -7773, 0, -2718, 1275, 0, 0, -864, 0, -5400, 648, 0, -11565, 0, 0, 2519, -6564, 0, 252, 342, 0, -4336, -21087, 0, -2556, -18636, 0, 0, 270, 0, -315, 390, 0, 1856, 0, 0, -16524, -15078, 0, 20224, 2373, 0, -1106, 1509, 0, 6221, 2478, 0, 0, 7371, 0, -24948, 3072, 0, 17963, 0, 0, 4274, -723, 0, -15795, 2520, 0, 3258, 3780, 0, 377, 14277, 0, 0, -8733, 0, 20610, 5208, 0, 450, 0, 0, 4032, 6306, 0, 8072, 651, 0, 666, 21252, 0, -5111, -3267, 0, 0, 23040, 0, 4059, 7770, 0, -23553, 0, 0, -22858, 15549, 0, 3780, -1110, 0, -24724, 1770, 0, -5220, -4752, 0, 0, -14880, 0, -1558, 9843, 0, -1664, 0, 0, 2322, 13371, 0, 1944, 11094, 0, -7182, 5232, 0, -14398, -960, 0, 0, -9744, 0, 19871, 6429, 0, 891, 0, 0, -5445, -7602, 0, 18819, 16137, 0, 4048, 135, 0, 22436, 21324, 0, 0, -2454, 0, -16128, 8646, 0, 11195, 0, 0, 1259, -3318, 0, -8971, 720, 0, -1062, -1920, 0, -12772, -5052, 0, 0, -12762, 0, 12842, -759, 0, 3960, 0, 0, 12331, -25509, 0, -196, 26544, 0, 21365, -9807, 0, 7731, 1131, 0, 0, 13365, 0, 4977, -8274, 0, 27998, 0, 0, 4032, 17466, 0, 225, 22272, 0, -1252, -2157, 0, 1953, 25560, 0, 0, -19944, 0, 27506, -1452, 0, 10017, 0, 0, 24948, 2646, 0, -3330, -1770, 0, -19123, -25077, 0, 1899, -13857, 0, 0, 5292, 0, -11385, 22245, 0, 5310, 0, 0, -1846, 23232, 0, -640, 786, 0, 5580, -4674, 0, 30240, -5754, 0, 0, 15561, 0, 5056, 6495, 0, 9144, 0, 0, 5534, 3078, 0, 19026, -21252, 0, -2880, -2892, 0, 90, 21846, 0, 0, -19809, 0, 1352, -34452, 0, -11089, 0, 0, 3258, -2184, 0, 11762, -33933, 0, -3780, -5550, 0, -22726, -948, 0, 0, -6678, 0, -7362, 3624, 0, -1260, 0, 0, -19987, -2130, 0, -57024, 3777, 0, 314, 22920, 0, 1008, 11496, 0, 0, -3912, 0, -38250, -960, 0, 2765, 0, 0, 1493, 14046, 0, 29348, -10563, 0, -9378, 5760, 0, 5130, -21168, 0, 0, -588, 0, -18514, 4086, 0, 4203, 0, 0, 7552, -17796, 0, -3556, 27495, 0, -2520, 5220, 0, -4824, 5430, 0, 0, 48576, 0, -22806, 7944, 0, -28942, 0, 0, -14220, -3756, 0, -416, -13395, 0, -1080, -8187, 0, -280, -36456, 0, 0, -25317, 0, 15320, -4293, 0, -27712, 0, 0, 7938, -240, 0, 4752, -34092, 0, 63820, -3990, 0, 1250, 5697, 0, 0, 25773, 0, 29232, -26544, 0, -7378, 0, 0, -28413, 15594, 0, -30538, 78, 0, -28764, 822, 0, 2358, 1482, 0, 0, 7005, 0, 23680, 7770, 0, -4032, 0, 0, -41824, -48027, 0, -3195, 46098, 0, 21008, 5376, 0, -23319, -24036, 0, 0, -8154, 0, 425, -480, 0, -8676, 0, 0, -2592, -75141, 0, 30492, -16200, 0, -13608, 4056, 0, 13292, -3855, 0, 0, 9306, 0, -7155, 7557, 0, -2188, 0, 0, 16496, -5292, 0, 1026, -21888, 0, 36656, -13008, 0, -13365, -14154, 0, 0, -852, 0, -55908, -3780, 0, -3781, 0, 0, 90, 25863, 0, -30240, -1065, 0, 1170, 42384, 0, -23168, 5568, 0, 0, -10530, 0, -11736, -5508, 0, -45234, 0, 0, 34218, 60672, 0, 791, 4479, 0, -38341, 23226, 0, 4527, -1923, 0, 0, 18663, 0, 8378, -57090, 0, -13590, 0, 0, 22113, -5484, 0, 12258, -74844, 0, 1024, 2184, 0, -22465, 11385, 0, 0, -10668, 0, 29366, 12822, 0, 15183, 0, 0, -1260, -5265, 0, 7560, 5808, 0, -28009, 9774, 0, 1260, -35601, 0, 0, -7917, 0, 42831, 8313, 0, 20234, 0, 0, -38303, 41760, 0, -29888, 6870, 0, 15624, 59520, 0, -4075, 1350, 0, 0, 9912, 0, -17011, 13632, 0, 18918, 0, 0, -720, 24216, 0, -13671, -52236, 0, -55738, 222, 0, 63756, 3750, 0, 0, -15333, 0, -1089, -3729, 0, 51272, 0, 0, 69120, 7545, 0, 35918, 12177, 0, 26270, -93852, 0, -3016, -7851, 0, 0, 30528, 0, 2520, -68574, 0, 5183, 0, 0, 54947, -36372, 0, -3330, 22113, 0, 3590, -74172, 0, -37170, 51366, 0, 0, -1740, 0, -14256, 21426, 0, 16128, 0, 0, -4960, -16581, 0, 16290, 32718, 0, 29529, 1275, 0, -15958, -4992, 0, 0, -240, 0, 25058, 774, 0, 40113, 0, 0, 34667, 5832, 0, 3698, 26040, 0, -11565, -24282, 0, 15696, 31080, 0, 0, -43194, 0, 20160, -6564, 0, 79948, 0, 0, -29232, 5280, 0, -59983, 59613, 0, 2143, 57984, 0, 1888, -18711, 0, 0, -25047, 0, -2556, -16335, 0, -25702, 0, 0, -55576, 6273, 0, 48411, -3480, 0, 20295, 12144, 0, 45, 31386, 0, 0, 14220, 0, 63972, 75147, 0, -106920, 0, 0, 51534, 26826, 0, -16524, -5376, 0, 25938, -5550, 0, 66710, 33585, 0, 0, 2373, 0, -28728, -26439, 0, -9954, 0, 0, -28918, -26913, 0, -6928, -19350, 0, -30492, -354, 0, -5760, -62178, 0, 0, -38316, 0, -1684, 46347, 0, -33616, 0, 0, -38286, 3072, 0, 7550, 38526, 0, 15939, -30408, 0, 9720, 1320, 0, 0, 7722, 0, -81550, 36993, 0, -8503, 0, 0, -15795, 4116, 0, 79632, -36432, 0, -32192, 64095, 0, -33157, 3780, 0, 0, 2577, 0, 3393, 91080, 0, 5920, 0, 0, 4455, 8529, 0, -48376, 4539, 0, -24822, -23919, 0, 20610, 83994, 0, 0, 53460, 0, -6130, 1344, 0, 52398, 0, 0, -29854, 675, 0, 7424, 70263, 0, -35605, 26292, 0, -6471, -47823, 0, 0, 5859, 0, 16200, -69504, 0, 666, 0, 0, -59832, -35328, 0, 69650, 82518, 0, -484, 42108, 0, -44071, 33867, 0, 0, -36555, 0, -6578, 74844, 0, -55566, 0, 0, -111104, -1110, 0, -5310, -39228, 0, -23553, -57369, 0, -8359, -5472, 0, 0, -39879, 0, -41571, 15549, 0, 1260, 0, 0, 17892, -46812, 0, 8910, -3795, 0, 66735, -50190, 0, 49203, 15930, 0, 0, 8262, 0, -10845, -1170, 0, 69696, 0, 0, -45280, -1920, 0, -16506, -14880, 0, -5792, 1860, 0, -14022, -86592, 0, 0, 90720, 0, -1918, 5655, 0, -20872, 0, 0, 46683, -9912, 0, 2322, 15168, 0, 24885, -32874, 0, 40068, 3048, 0, 0, 11094, 0, 23680, 16602, 0, 1026, 0, 0, 95807, 64326, 0, -63756, 93717, 0, 60632, -8640, 0, 60732, 38442, 0, 0, 30, 0, 65538, -58980, 0, 9765, 0, 0, -6603, 6429, 0, -44089, -28392, 0, -103356, -55428, 0, 6662, -33267, 0, 0, -7590, 0, -107368, 1086, 0, -6552, 0, 0, 18819, 35286, 0, -11311, -41472, 0, 72107, 36372, 0, -16650, -1740, 0, 0, -68178, 0, 19908, -13890, 0, -26362, 0, 0, -20034, -86808, 0, 10955, -22086, 0, 1208, 13719, 0, -16128, 26460, 0, 0, -64116, 0, -7472, -59961, 0, -1350, 0, 0, 26550, -19008, 0, 11331, -95292, 0, 76104, 942, 0, 7640, 113760, 0, 0, 3408, 0, 34488, -35796, 0, 13688, 0, 0, 82152, -23370, 0, -17296, -12750, 0, -2880, -5052, 0, -107811, 8295, 0, 0, -31080, 0, 17705, -31353, 0, 42138, 0, 0, 92258, 88044, 0, -35713, -5976, 0, 3960, -3126, 0, 17280, -20508, 0, 0, 15390, 0, -7056, -25509, 0, -31285, 0, 0, -1764, 60036, 0, 70784, -55542, 0, -85806, 7632, 0, 80048, 1401, 0, 0, 37440, 0, 7731, 22656, 0, -5932, 0, 0, -8216, 74676, 0, 82485, 13365, 0, -100198, -7560, 0, -50228, -89970, 0, 0, -1608, 0, 16290, 6918, 0, 111410, 0, 0, 16192, -57459, 0, 4032, -77106, 0, 23832, 42735, 0, -38962, -86826, 0, 0, 46272, 0, 127628, -4740, 0, -11268, 0, 0, 28728, -1248, 0, -4465, -82251, 0, -36810, 22680, 0, -24561, 91839, 0, 0, -840, 0, -123256, -42252, 0, -24128, 0, 0, -75951, -1452, 0, -80395, 45960, 0, -1431, 18885, 0, 63992, -106176, 0, 0, 134379, 0, 47366, 23814, 0, 5040, 0, 0, 42920, 1584, 0, -102276, 30408, 0, 60679, 191460, 0, -1330, -25077, 0, 0, -26250, 0, 17091, 14496, 0, -102412, 0, 0, 16335, 40614, 0, 83186, 9744, 0, -79632, -41664, 0, -11385, -22134, 0, 0, 74871, 0, 4455, -96063, 0, 46782, 0, 0, -91224, -91614, 0, -1638, 59544, 0, 67268, -9588, 0, 2466, -2940, 0, 0, 7074, 0, 494, 89655, 0, 5580, 0, 0, 21015, -9480, 0, -54736, 71040, 0, 26270, -5754, 0, -133282, -1344, 0, 0, -145824, 0, -379, -125472, 0, -16009, 0, 0, -95491, -2025, 0, 138294, -9360, 0, 9144, 63024, 0, -112896, -35046, 0, 0, -7773, 0, -72108, -39672, 0, 65405, 0, 0, -2718, -113280, 0, -69904, -8925, 0, -1440, -55455, 0, -103924, -26028, 0, 0, -18780, 0, 90, -864, 0, -225423, 0, 0, 45782, 91476, 0, -5400, -19809, 0, 99712, -46008, 0, 12168, -30336, 0, 0, 39876, 0, 80955, 39228, 0, -113652, 0, 0, 27918, -105546, 0, -41992, -21465, 0, 2519, -3795, 0, 112175, 45948, 0, 0, -33933, 0, 39690, 49488, 0, -17892, 0, 0, -8048, 342, 0, -65664, -50832, 0, -78831, 109968, 0, -4336, 31080, 0, 0, 128601, 0, -42462, 28485, 0, -14356, 0, 0, 17892, 3624, 0, 42506, -18636, 0, -11340, 38460, 0, 113255, -11343, 0, 0, -76761, 0, 3365, -1890, 0, 77589, 0, 0, -57024, -90720, 0, -675, -129636, 0, 29854, 390, 0, 127152, 22920, 0, 0, -69504, 0, 1856, 36258, 0, 11790, 0, 0, -31590, 83409, 0, -40068, -35208, 0, 115668, -106116, 0, -38250, -15078, 0, 0, -17376, 0, -54432, 102654, 0, 20224, 0, 0, -10800, -16611, 0, 13437, 35172, 0, 21608, -115023, 0, 78526, 157056, 0, 0, 1509, 0, -5769, -109890, 0, -9378, 0, 0, 6221, 98079, 0, 94184, 5310, 0, -171270, -21168, 0, -27776, -40770, 0, 0, 114708, 0, -80576, 7371, 0, -16452, 0, 0, -43380, 36774, 0, -24948, 4914, 0, -54172, -21504, 0, 6552, -115764, 0, 0, -67395, 0, -109549, -17796, 0, 89342, 0, 0, -32004, 20280, 0, 111014, 88098, 0, 4274, 50223, 0, -121219, 51333, 0, 0, 114723, 0, -4824, -3780, 0, 110565, 0, 0, 147302, 2520, 0, 17424, 48576, 0, 49058, -84027, 0, 3258, 780, 0, 0, -26460, 0, -106803, 84507, 0, -61306, 0, 0, -26767, -21648, 0, -14220, 14277, 0, 24939, 22494, 0, 12544, 60702, 0, 0, -13395, 0, -76104, -45045, 0, 125280, 0, 0, -154186, -89664, 0, -144270, 92904, 0, 101574, 5208, 0, 178560, 46398, 0, 0, -12225, 0, 450, 101094, 0, 5920, 0, 0, 29736, 55332, 0, 93610, -51033, 0, 8640, -105936, 0, 160640, 6306, 0, 0, -70596, 0, 85526, -2160, 0, 8072, 0, 0, 4752, -46221, 0, -156708, 14967, 0, -58680, -167214, 0, -4662, -3990, 0, 0, 21252, 0, 11250, -167772, 0, 75653, 0, 0, -5111, 107514, 0, 80128, 22869, 0, -11187, 22395, 0, 60732, 153816, 0, 0, 158184, 0, -31480, 23040, 0, 22635, 0, 0, 48890, 107754, 0, 4059, 50841, 0, -16192, 16650, 0, -281556, -10368, 0, 0, -9048, 0, 164871, 38976, 0, -28764, 0, 0, 91584, -31668, 0, -123085, 7560, 0, -22858, 1482, 0, 61290, -108843, 0, 0, -169344, 0, 130680, 164841, 0, -139356, 0, 0, 23786, -1110, 0, 66339, -4740, 0, -4032, 10770, 0, -24724, -53340, 0, 0, -125670, 0, 154098, -48027, 0, 19072, 0, 0, 36540, -86526, 0, 81962, -4752, 0, 64278, 169266, 0, -102923, 48384, 0, 0, -100557, 0, -23319, 104160, 0, -49743, 0, 0, 87902, 48870, 0, 110618, 105096, 0, -54684, 9843, 0, 3825, 42252, 0, 0, -47874, 0, -1664, 2679, 0, 105536, 0, 0, -720, 13704, 0, -2592, 75174, 0, -16254, -50304, 0, 84806, 13371, 0, 0, -16200, 0, 37288, 104001, 0, 1944, 0, 0, -91586, -77658, 0, 78120, 141444, 0, -98560, -34695, 0, -15390, 51042, 0, 0, 5232, 0, 93240, -9438, 0, 120545, 0, 0, -14398, 7557, 0, 7937, 68160, 0, -19692, 138699, 0, -105670, 239844, 0, 0, -57384, 0, 17696, -9744, 0, 15840, 0, 0, 1026, -179949, 0, 19871, -51759, 0, -104767, -45003, 0, 173952, -13008, 0, 0, 5664, 0, -63261, 18750, 0, 91224, 0, 0, -75141, 185088, 0, -148680, -7668, 0, -5445, 124257, 0, -55908, -16290, 0, 0, 104949, 0, -162514, -166728, 0, -131733, 0, 0, 4754, 16137, 0, -10440, -22158, 0, -86528, 60885, 0, 4048, -13839, 0, 0, -945, 0, 94158, 130872, 0, 1170, 0, 0, -136828, 145824, 0, 137888, 21324, 0, 225441, 11568, 0, -104509, -320760, 0, 0, 6894, 0, 180173, 174234, 0, 80478, 0, 0, -24238, -49572, 0, 112896, 121158, 0, -45234, 8646, 0, -16650, 31854, 0, 0, 200130, 0, 11195, 60672, 0, -141669, 0, 0, 7119, 52071, 0, -6032, -86184, 0, -89389, 134868, 0, -5400, -3318, 0, 0, 202518, 0, -58348, -86754, 0, -8971, 0, 0, 80640, -26544, 0, -58050, 18663, 0, -114274, -91476, 0, 7434, -227832, 0, 0, -1920, 0, -186534, -223014, 0, -118151, 0, 0, -12772, 6375, 0, 22113, 35364, 0, 139041, -122028, 0, 113652, -100848, 0, 0, -74844, 0, 79748, -12762, 0, 9216, 0, 0, -72541, 22650, 0, 12842, -20754, 0, 116920, 53889, 0, -91224, 250368, 0, 0, 29160, 0, -27720, -10416, 0, -10890, 0, 0, 23166, 12822, 0, -57825, -244650, 0, 12331, 42480, 0, -188632, 178563, 0, 0, -31080, 0, -95552, -47385, 0, 13916, 0, 0, 7560, 26544, 0, -109296, -32820, 0, -72631, -96576, 0, 21365, -125976, 0, 0, -21015, 0, 11340, -196455, 0, 206136, 0, 0, -54117, 390, 0, -135856, 1131, 0, 273240, -76722, 0, 42831, 17760, 0, 0, -28719, 0, -74608, -93555, 0, 25587, 0, 0, 237860, -145128, 0, -26199, -261504, 0, -12780, -8274, 0, -71757, -105756, 0, 0, 61830, 0, 27998, 120681, 0, -201376, 0, 0, 160380, -260904, 0, -269082, -18390, 0, -28224, 1350, 0, 227584, 17466, 0, 0, -10296, 0, -179029, -89562, 0, 225, 0, 0, 54432, -155904, 0, 210789, -28320, 0, 18918, -106815, 0, 88892, 56226, 0, 0, -2157, 0, -143469, 24216, 0, -199186, 0, 0, 1953, -129270, 0, -3068, -155880, 0, -208512, -108072, 0, -82620, 1998, 0, 0, -201870, 0, 63756, -19944, 0, -105984, 0, 0, 24928, 208950, 0, 27506, -15333, 0, 124208, 10164, 0, 126324, 11865, 0, 0, -132213, 0, 21465, 150936, 0, 265310, 0, 0, -109665, 263382, 0, 69120, -19734, 0, 24948, 16464, 0, 79424, -187866, 0, 0, -156948, 0, 154628, -333312, 0, 23310, 0, 0, -50560, -1770, 0, -117684, -200592, 0, 183761, -70659, 0, -19123, 102378, 0, 0, 175539, 0, -16416, 205467, 0, -114392, 0, 0, -134829, -68574, 0, 27026, -13857, 0, 46647, 117966, 0, 18719, 3780, 0, 0, 15360, 0, 49589, 11340, 0, -140436, 0, 0, 42920, 26730, 0, 79695, -148590, 0, -100540, 22245, 0, -150570, -74172, 0, 0, 147609, 0, 5310, -146001, 0, -80000, 0, 0, 24786, 133200, 0, -177856, -32535, 0, 11258, 180732, 0, -14256, 23232, 0, 0, 229218, 0, -78975, -135840, 0, -640, 0, 0, -93292, -55806, 0, -44640, 105168, 0, 450, -17376, 0, -39060, -108078, 0, 0, -4674, 0, -259776, -92904, 0, 29529, 0, 0, 30240, -124707, 0, -182287, 40278, 0, 16965, -4992, 0, 155006, -62616, 0, 0, -59562, 0, -94330, 15561, 0, -29736, 0, 0, -17108, 6966, 0, 5056, 149391, 0, 40113, 22695, 0, -98622, 99363, 0, 0, 120204, 0, -64008, -75168, 0, 103050, 0, 0, 33282, 39264, 0, 163703, 71040, 0, 5534, 61491, 0, -222264, -21546, 0, 0, -45099, 0, 15696, 287421, 0, 40770, 0, 0, -138898, -21252, 0, 281151, -43194, 0, -23374, 181896, 0, -2880, -170403, 0, 0, 205332, 0, 115326, -3540, 0, -20144, 0, 0, -630, -159516, 0, -60732, 21846, 0, -176940, -199716, 0, -9620, 29295, 0, 0, 59613, 0, -112048, 138663, 0, 19287, 0, 0, 3330, -132267, 0, -95992, 169020, 0, -27200, -34452, 0, -166284, -298266, 0, 0, 19986, 0, -11089, -244029, 0, -123120, 0, 0, -22770, -16335, 0, 285542, -322104, 0, -22806, 31668, 0, -147572, -2184, 0, 0, 27486, 0, 322542, 56457, 0, 11762, 0, 0, 48411, 237531, 0, -124416, 225171, 0, -66024, 216321, 0, 139356, 12144, 0, 0, -5550, 0, -5220, 246720, 0, -9286, 0, 0, -22726, -161922, 0, -117765, 67308, 0, -41670, -31623, 0, 63972, -79086, 0, 0, -225468, 0, 248870, -6678, 0, -260424, 0, 0, 140032, 32865, 0, -7362, 77745, 0, 3136, -25368, 0, 41157, 515592, 0, 0, -48384, 0, 89460, -130320, 0, 25938, 0, 0, -192348, 181572, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "21.4.e.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], [3], [0], [1], [3], [0], [0], [-21], [0], [9], [15], [0], [-64], [0], [0], [-71], [-84], [0], [-16], [3], [0], [45], [84], [0], [-116], [-192], [0], [0], [297], [0], [-253], [-45], [0], [-252], [0], [0], [-316], [-48], [0], [-63], [-360], [0], [26], [15], [0], [252], [30], [0], [0], [-348], [0], [-64], [-363], [0], [45], [0], [0], [891], [15], [0], [-118], [-759], [0], [433], [-192], [0], [-370], [-84], [0], [0], [342], [0], [362], [-948], [0], [-16], [0], [0], [467], [-213], [0], [-1080], [-477], [0], [-252], [78], [0], [-315], [-906], [0], [0], [84], [0], [90], [-48], [0], [503], [0], [0], [-116]]}