# Stored data for newform 276.4.a.d, downloaded from the LMFDB on 03 May 2024.
{"label": "276.4.a.d", "space_label": "276.4.a", "level": 276, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220628, "dim": 2, "is_polredabs": true, "nf_label": "2.2.13.1", "trace_hash": 1254502320105848893, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-68, -14, 1]]], "qexp_display": "q+3q^{3}+(7+3\\beta )q^{5}+(-5+\\beta )q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4416, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 16.28452716158441, "hecke_ring_index": 2, "level_radical": 138, "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": 0, "analytic_rank_proved": true, "char_values": [276, 1, [139, 185, 97], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3, 23], "conrey_indexes": [1], "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.049", "prec": 17}, {"__RealLiteral__": 0, "data": "1.938", "prec": 17}, {"__RealLiteral__": 0, "data": "0.030", "prec": 17}, {"__RealLiteral__": 0, "data": "9.603", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.850", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [23, 1]], "trace_display": [0, 6, 14, -10], "traces": [0, 2, 0, 6, 0, 14, 0, -10, 0, 18, 0, -4, 0, 104, 0, 42, 0, 122, 0, 74, 0, -30, 0, -46, 0, 82, 0, 54, 0, 40, 0, 4, 0, -12, 0, 8, 0, 340, 0, 312, 0, 164, 0, -6, 0, 126, 0, 568, 0, -610, 0, 366, 0, 450, 0, -184, 0, 222, 0, 400, 0, 300, 0, -90, 0, 1196, 0, -530, 0, -138, 0, 120, 0, -468, 0, 246, 0, -32, 0, -1726, 0, 162, 0, 1380, 0, -316, 0, 120, 0, -522, 0, -364, 0, 12, 0, -1120, 0, 40, 0, -36, 0, 356, 0, -1518, 0, 24, 0, -2580, 0, -1096, 0, 1020, 0, 526, 0, -322, 0, 936, 0, -1000, 0, -2550, 0, 492, 0, 2100, 0, -3052, 0, -18, 0, -456, 0, -916, 0, 378, 0, 206, 0, -3744, 0, 1704, 0, -520, 0, -3932, 0, -1830, 0, -1050, 0, -2320, 0, 1098, 0, -3872, 0, 2324, 0, 1350, 0, 230, 0, -6012, 0, -552, 0, -4496, 0, 1950, 0, 666, 0, 5992, 0, 682, 0, 1200, 0, 1784, 0, 4384, 0, 900, 0, 3316, 0, 536, 0, -270, 0, 1772, 0, 2856, 0, 3588, 0, 776, 0, -1134, 0, -1590, 0, -1604, 0, 9260, 0, -414, 0, 944, 0, -380, 0, 360, 0, 8928, 0, -1320, 0, -1404, 0, 4004, 0, -4816, 0, 738, 0, -40, 0, 1448, 0, -96, 0, 1684, 0, -2264, 0, -5178, 0, 5112, 0, 7920, 0, 486, 0, -5050, 0, 572, 0, 4140, 0, 3576, 0, 92, 0, -948, 0, 364, 0, -1388, 0, 360, 0, 4956, 0, 4476, 0, -1566, 0, 2328, 0, 28, 0, -1092, 0, -2348, 0, 1028, 0, 36, 0, -14906, 0, -674, 0, -3360, 0, 1884, 0, 3466, 0, 120, 0, 3562, 0, 5920, 0, -108, 0, -2392, 0, 3020, 0, 1068, 0, -11628, 0, 5164, 0, -4554, 0, -7976, 0, 8340, 0, 72, 0, -6552, 0, 2728, 0, -7740, 0, 12704, 0, 10816, 0, -3288, 0, -4920, 0, 3028, 0, 3060, 0, 2608, 0, 7000, 0, 1578, 0, 2592, 0, 6220, 0, -966, 0, -9712, 0, -10648, 0, 2808, 0, -9056, 0, -5712, 0, -3000, 0, 10212, 0, 486, 0, -7650, 0, -15444, 0, 7506, 0, 1476, 0, -1808, 0, -4972, 0, 6300, 0, -6344, 0, -6270, 0, -9156, 0, -1132, 0, 400, 0, -54, 0, 2554, 0, -2806, 0, -1368, 0, -13096, 0, -10708, 0, -2748, 0, -9742, 0, -7592, 0, 1134, 0, -1304, 0, 5016, 0, 618, 0, -960, 0, 7944, 0, -11232, 0, -19884, 0, 6208, 0, 5112, 0, -11378, 0, -6076, 0, -1560, 0, 13512, 0, 14220, 0, -11796, 0, -1702, 0, 11856, 0, -5490, 0, -3200, 0, -22140, 0, -3150, 0, -25276, 0, -5736, 0, -6960, 0, -832, 0, -568, 0, 3294, 0, -3024, 0, 33832, 0, -11616, 0, 5824, 0, 4756, 0, 6972, 0, -5968, 0, -19898, 0, 4050, 0, 20752, 0, 19552, 0, 690, 0, 13228, 0, -21952, 0, -18036, 0, 4016, 0, 23500, 0, -1656, 0, -2784, 0, -25276, 0, -13488, 0, 13232, 0, 36500, 0, 5850, 0, 6336, 0, -1716, 0, 1998, 0, -5400, 0, 3024, 0, 17976, 0, 14766, 0, 17798, 0, 2046, 0, 19744, 0, 1058, 0, 3600, 0, 24752, 0, -7608, 0, 5352, 0, 1740, 0, -15688, 0, 13152, 0, -22492, 0, -24956, 0, 2700, 0, 30964, 0, 8292, 0, 9948, 0, -6142, 0, 17628, 0, 1608, 0, 14920, 0, -15116, 0, -810, 0, 23290, 0, -6666, 0, 5316, 0, -1886, 0, -13512, 0, 8568, 0, -7472, 0, -1784, 0, 10764, 0, -28696, 0, 27448, 0, 2328, 0, 13292, 0, 3608, 0, -3402, 0, 18616, 0, 39544, 0, -4770, 0, -17226, 0, 7256, 0, -4812, 0, 17056, 0, -32028, 0, 27780, 0, -11730, 0, 6726, 0, -1242, 0, -3552, 0, 7726, 0, 2832, 0, 16060, 0, 16490, 0, -1140, 0, -9664, 0, -33280, 0, 1080, 0, -8086, 0, 3002, 0, 26784, 0, 45680, 0, -2880, 0, -3960, 0, -36812, 0, -8808, 0, -4212, 0, 35968, 0, 15948, 0, 12012, 0, 4664, 0, -920, 0, -14448, 0, 8552, 0, -52112, 0, 2214, 0, -8330, 0, 4116, 0, -120, 0, -6080, 0, -30460, 0, 4344, 0, 26052, 0, -15284, 0, -288, 0, -52728, 0, -30556, 0, 5052, 0, 46182, 0, 6028, 0, -6792, 0, 9556, 0, 10848, 0, -15534, 0, -92, 0, -12688, 0, 15336, 0, 2736, 0, 9332, 0, 23760, 0, -57328, 0, -48426, 0, 1458, 0, -45216, 0, -10856, 0, -15150, 0, -3152, 0, 16880, 0, 1716, 0, -32172, 0, -13044, 0, 12420, 0, 16384, 0, -53978, 0, 10728, 0, 24944, 0, -35312, 0, 276, 0, 49392, 0, 540, 0, -2844, 0, 27040, 0, 16452, 0, 1092, 0, 43102, 0, -54436, 0, -4164, 0, -50716, 0, 4128, 0, 1080, 0, 17828, 0, -73526, 0, 14868, 0, -8896, 0, -11856, 0, 13428, 0, -81510, 0, 65848, 0, -4698, 0, 9048, 0, -184, 0, 6984, 0, 73376, 0, -18788, 0, 84, 0, -20712, 0, -63012, 0, -3276, 0, -62692, 0, -21380, 0, -7044, 0, 48624, 0, 3832, 0, 3084, 0, -33310, 0, -53312, 0, 108, 0, 30932, 0, 27838, 0, -44718, 0, 62322, 0, 12958, 0, -2022, 0, -7820, 0, -14788, 0, -10080, 0, -52212, 0, -41840, 0, 5652, 0, 7232, 0, 42724, 0, 10398, 0, 4128, 0, -14924, 0, 360, 0, -9408, 0, 15484, 0, 10686, 0, -26666, 0, 10540, 0, 17760, 0, 9888, 0, 19160, 0, -324, 0, 64696, 0, 24032, 0, -7176, 0, 70280, 0, 20820, 0, 9060, 0, -10652, 0, -25514, 0, 3204, 0, -13904, 0, -1616, 0, -34884, 0, 408, 0, 36186, 0, 15492, 0, -6864, 0, 27044, 0, -13662, 0, -42316, 0, -17110, 0, -23928, 0, -3424, 0, 31356, 0, 25020, 0, -3010, 0, -3772, 0, 216, 0, -98984, 0, -48672, 0, -19656, 0, 54290, 0, -57952, 0, 8184, 0, -11664, 0, 5426, 0, -23220, 0, 5172, 0, -39540, 0, 38112, 0, -67184, 0, 9880, 0, 32448, 0, -85738, 0, 13368, 0, -9864, 0, 41904, 0, 72980, 0, -14760, 0, 138, 0, 47516, 0, 9084, 0, -48264, 0, -11640, 0, 9180, 0, -416, 0, 8800, 0, 7824, 0, 7368, 0, 63480, 0, 21000, 0, -39348, 0, 11392, 0, 4734, 0, -7336, 0, 102828, 0, 7776, 0, 120292, 0, -91780, 0, 18660, 0, 18404, 0, 48672, 0, -2898, 0, 86940, 0, 39356, 0, -29136, 0, 3352, 0, 4112, 0, -31944, 0, 34578, 0, 45864, 0, 8424, 0, -38072, 0, 25328, 0, -27168, 0, 45380, 0, 30154, 0, -17136, 0, -8712, 0, 74244, 0, -9000, 0, -10048, 0, 125334, 0, 30636, 0, 68328, 0, -13064, 0, 1458, 0, 10416, 0, 372, 0, -22950, 0, 13016, 0, -26252, 0, -46332, 0, -45384, 0, -11100, 0, 22518, 0, 44560, 0, -4264, 0, 4428, 0, 18946, 0, -23384, 0, -5424, 0, -69904, 0, 8108, 0, -14916, 0, -7040, 0, 84866, 0, 18900, 0, 14030, 0, 81500, 0, -19032, 0, -448, 0, 110792, 0, -18810, 0, -63920, 0, 37184, 0, -27468, 0, 24020, 0, -14920, 0, -3396, 0, 17408, 0, 50452, 0, 1200, 0, -64116, 0, 107196, 0, -162, 0, 120064, 0, -56228, 0, 7662, 0, 15200, 0, 9394, 0, -8418, 0, -64072, 0, -1808, 0, -4104, 0, 9196, 0, 6474, 0, -39288, 0, -7484, 0, -142736, 0, -32124, 0, -79182, 0, 47952, 0, -8244, 0, 12072, 0, -15100, 0, -29226, 0, 56220, 0, 40080, 0, -22776, 0, -29700, 0, 40080, 0, 3402, 0, -48790, 0, -10350, 0, -3912, 0, -58088, 0, -35930, 0, 15048, 0, 41562, 0, -56116, 0, 1854, 0, -63856, 0, -138092, 0, -2880, 0, 32292, 0, 11480, 0, 23832, 0, -161580, 0, -33768, 0, -33696, 0, -5072, 0, 5064, 0, -59652, 0, -3388, 0, 27976, 0, 18624, 0, 4232, 0, -35700, 0, 15336, 0, -134872, 0, -63836, 0, -34134, 0, 32968, 0, 5782, 0, -18228, 0, 16752, 0, 9724, 0, -4680, 0, 6820, 0, 26924, 0, 40536, 0, -1136, 0, -111436, 0, 42660, 0, -3972, 0, -31914, 0, -35388, 0, -24340, 0, -5072, 0, -5106, 0, 86528, 0, 62928, 0, 35568, 0, 80984, 0, 22788, 0, -16470, 0, 37014, 0, 75176, 0, -9600, 0, 10008, 0, -149512, 0, -66420, 0, -32312, 0, -68484, 0, -9450, 0, -100216, 0, 123780, 0, -75828, 0, 50304, 0, -19220, 0, -17208, 0, 12832, 0, -9200, 0, -20880, 0, -36960, 0, 123680, 0, -2496, 0, -1152, 0, -39762, 0, -1704, 0, -77076, 0, -6384, 0, 9882, 0, 18636, 0, 66632, 0, -9072, 0, -134140, 0, 67860, 0, 101496, 0, -113256, 0, -7772, 0, -34848, 0, -1696, 0, 15222, 0, 17472, 0, -6900, 0, -119708, 0, 14268, 0, -161048, 0, 92760, 0, 20916, 0, 34048, 0, -86632, 0, -17904, 0, 1840, 0, -54662, 0, -59694, 0, 5544, 0, 44176, 0, 12150, 0, -68946, 0, -20976, 0, 62256, 0, 90960, 0, 4656, 0, 58656, 0, -118478, 0, -28794, 0, 2070, 0, -10800, 0, -62728, 0, 39684, 0, 105136, 0, 153998, 0, -65856, 0, -5552, 0, 49660, 0, -54108, 0, -10244, 0, 56318, 0, 12048, 0, 60080, 0, -9904, 0, 70500, 0, -21664, 0, 72870, 0, -4968, 0, 6288, 0, -24416, 0, -8352, 0, 45106, 0, -27508, 0, -75828, 0, 148920, 0, -56764, 0, -40464, 0, -23944, 0, 20856, 0, 39696, 0, -26224, 0, 60588, 0, 109500, 0, 60328, 0, 11780, 0, 17550, 0, -104480, 0, -179892, 0, 19008, 0, 25168, 0, -2388, 0, -5148, 0, -824, 0, -14868, 0, 5994, 0, 12190, 0, -9732, 0, -16200, 0, -30784, 0, -67120, 0, 9072, 0, -117820, 0, 32152, 0, 53928, 0, 82504, 0, 12016, 0, 44298, 0, 110172, 0, -20244, 0, 53394, 0, 76228, 0, -131352, 0, 6138, 0, 63072, 0, -1314, 0, 59232, 0, 132088, 0, -120588, 0, 3174, 0, 37224, 0, 34860, 0, 10800, 0, 24400, 0, -116184, 0, 74256, 0, 27922, 0, -2612, 0, -22824, 0, 32316, 0, -136608, 0, 16056, 0, 151692, 0, -54280, 0, 5220, 0, 14112, 0, 33912, 0, -47064, 0, 115752, 0, 22150, 0, 39456, 0, -31092, 0, -2760, 0, -67476, 0, -64632, 0, 5896, 0, -74868, 0, -21200, 0, 18912, 0, 8100, 0, -62300, 0, -135304, 0, 92892, 0, 239752, 0, 71864, 0, 24876, 0, -22816, 0, 206938, 0, 29844, 0, -76260, 0, -147788, 0, -18426, 0, -21504, 0, 66722, 0, 52884, 0, 10764, 0, 156822, 0, 4824, 0, 53836, 0, -39340, 0, 44760, 0, 110088, 0, 56564, 0, -45348, 0, 156372, 0, -22474, 0, -2430, 0, -34944, 0, 25632, 0, 69870, 0, 111706, 0, -48160, 0, -19998, 0, -3104, 0, -148324, 0, 15948, 0, -34102, 0, 156542, 0, -5658, 0, -5688, 0, -25480, 0, -40536, 0, -82144, 0, -33040, 0, 25704, 0, 71600, 0, 45068, 0, -22416, 0, -35380, 0, 131690, 0, -5352, 0, -118728, 0, -40832, 0, 32292, 0, -24536, 0, -4938, 0, -86088, 0, 310468, 0, -45140, 0, 82344, 0, 253104, 0, 736, 0, 6984, 0, -86808, 0, -46468, 0, 39876, 0, -53092, 0, -96576, 0, 10824, 0, 53560, 0, -56788, 0, -10206, 0, -2224, 0, 210480, 0, 55848, 0, 572, 0, 157132, 0, 118632, 0, -117810, 0, -247728, 0, -14310, 0, -94380, 0, -106820, 0, -51678, 0, 39698, 0, -209640, 0, 21768, 0, 65256, 0, -189540, 0, -14436, 0, -51200, 0, 23946, 0, 51168, 0, 103320, 0, 23552, 0, -96084, 0, -15368, 0, -89156, 0, 83340, 0, -71396, 0, 184854, 0, -35190, 0, 7244, 0, -1736, 0, 20178, 0, -36348, 0, -115852, 0, -3726, 0, 109652, 0, -121740, 0, -10656, 0, 34040, 0, -9936, 0, 23178, 0, 163794, 0, 27120, 0, 8496, 0, 24188, 0, -254072, 0, 48180, 0, -97856, 0, 229400, 0, 49470, 0, -269856, 0, 4072, 0, -3420, 0, 281166, 0, -12504, 0, -28992, 0, 90676, 0, -31740, 0, -99840, 0, -77504, 0, 45584, 0, 3240, 0, -224884, 0, 126076, 0, -24258, 0, 7424, 0, -169744, 0, 9006, 0, 180648, 0, 30600, 0, 80352, 0, -65988, 0, -52252, 0, 137040, 0, -124324, 0, 43228, 0, -8640, 0, -143602, 0, 9398, 0, -11880, 0, 7268, 0, -92748, 0, -110436, 0, 81804, 0, -38272, 0, -26424, 0, 69408, 0, -11264, 0, -12636, 0, 163732, 0, -84962, 0, 107904, 0, -220088, 0, 16292, 0, 47844, 0, -54988, 0, -8600, 0, 36036, 0, 18792, 0, 63116, 0, 13992, 0, -218974, 0, -250970, 0, -2760, 0, 80504, 0, -101500, 0, -43344, 0, -77060, 0, 85458, 0, 25656, 0, -255008, 0, 11192, 0, -156336, 0, -240904, 0, -64910, 0, 6642, 0, -101920, 0, 60552, 0, -24990, 0, -168624, 0, -37520, 0, 12348, 0, 48916, 0, 123968, 0, -360, 0, 189396, 0, 12006, 0, -18240, 0, -9568, 0, -33728, 0, -91380, 0, -158670, 0, 120336, 0, 13032, 0, -70576, 0, -6720, 0, 78156, 0, -112334, 0, 63188, 0, -45852, 0, 32556, 0, -106360, 0, -864, 0, -74914, 0, -70272, 0, -158184, 0, -67696, 0, 37224, 0, -91668, 0, 8372, 0, -242616, 0, 15156, 0, 22896, 0, 43360, 0, 138546, 0, -213788, 0, -28070, 0, 18084, 0, 2408, 0, 163376, 0, -20376, 0, 209664, 0, -269880, 0, 28668, 0, 4168, 0, 111720, 0, 32544, 0, -176876, 0, 1922, 0, -46602, 0, 37808, 0, 1332, 0, -276, 0, 103996, 0, 143136, 0, -38064, 0, 151048, 0, -38144, 0, 46008, 0, 157042, 0, 322032, 0, 8208, 0, -244672, 0, -158384, 0, 27996, 0, 8124, 0, -46584, 0, 71280, 0, -277472, 0, 82868, 0, -171984, 0, 69208, 0, -162462, 0, -145278, 0, 80480, 0, 25760, 0, 4374, 0, 29152, 0, -24436, 0, -135648, 0, 12480, 0, -29744, 0, -32568, 0, 109440, 0, -34360, 0, -45450, 0, 127048, 0, 120066, 0, -9456, 0, -159030, 0, 152632, 0, 50640, 0, 7852, 0, 68388, 0, 5148, 0, -280206, 0, 264, 0, -96516, 0, -920, 0, -11872, 0, -39132, 0, 156572, 0, -120424, 0, 37260, 0, 326272, 0, -211252, 0, 49152, 0, 313144, 0, 182278, 0, -161934, 0, -69168, 0, -3912, 0, 32184, 0, -111256, 0, 201864, 0, 74832, 0, 153920, 0, 208716, 0, -105936, 0, -229690, 0, 9100, 0, 828, 0, 49480, 0, 150376, 0, 148176, 0, 286028, 0, -73734, 0, 1620, 0, -16268, 0, 128144, 0, -8532, 0, 282730, 0, -98718, 0, 81120, 0, -152440, 0, 228276, 0, 49356, 0, -156180, 0, 310318, 0, 3276, 0, 258976, 0, 57712, 0, 129306, 0, 24368, 0, -8188, 0, -163308, 0, 115856, 0, 172076, 0, -12492, 0, 15598, 0, 326872, 0, -152148, 0, -45424, 0, 180888, 0, 12384, 0, -18968, 0, -170324, 0, 3240, 0, -169680, 0, 145288, 0, 53484, 0, 94978, 0, -33388, 0, -220578, 0, -95784, 0, -59248, 0, 44604, 0, 34914, 0, -103600, 0, -26688, 0, 54768, 0, 341000, 0, -35568, 0, 56776, 0, 85578, 0, 40284, 0, -10464, 0, 147076, 0, -244530, 0, -205896, 0, -43184, 0, 197544, 0, -69396, 0, 162582, 0, -14094, 0, 265096, 0, 58488, 0, 27144, 0, -250464, 0, -194824, 0, -552, 0, 227864, 0, 140960, 0, 20952, 0, 50272, 0, 182912, 0, 220128, 0, 60208, 0, 13520, 0, -56364, 0, -241648, 0, -137676, 0, 252, 0, -171048, 0, 66292, 0, -62136, 0, -37104, 0, 13448, 0, -189036, 0, 33760, 0, -147232, 0, -9828, 0, -37168, 0, 59340, 0, -188076, 0, -115832, 0, 334008, 0, -64140, 0, 51364, 0, 163460, 0, -21132, 0, 185108, 0, -64828, 0, 145872, 0, -48568, 0, 17952, 0, 11496, 0, 22440, 0, 92440, 0, 9252, 0, -160552, 0, -73968, 0, -99930, 0, -451304, 0, -112030, 0, -159936, 0, 25208, 0, 118872, 0, 324, 0, -4728, 0, -19072, 0, 92796, 0, -12152, 0, 223020, 0, 83514, 0, 490708, 0, -42834, 0, -134154, 0, -423232, 0, -35580, 0, 186966, 0, 118400, 0, -35444, 0, 38874, 0, 284600, 0, -26316, 0, -6066, 0, -182754, 0, 169490, 0, -23460, 0, 30576, 0, -10804, 0, -44364, 0, 175448, 0, 41976, 0, -30240, 0, -347440, 0, -20604, 0, -156636, 0, 31360, 0, 10926, 0, -125520, 0, -102368, 0, 322308, 0, 16956, 0, -10656, 0, -139620, 0, 21696, 0, 108552, 0, -61228, 0, 128172, 0, -141670, 0, -12098, 0, 31194, 0, 230936, 0, 281124, 0, 12384, 0, -229634, 0, 73012, 0, -44772, 0, 252896, 0, 173160, 0, 1080, 0, 32522, 0, -527140, 0, -28224, 0, -5808, 0, -18336, 0, 46452, 0, -361642, 0, -102032, 0, 32058, 0, -38168, 0, 47112, 0, -79998, 0, 7406, 0, -288452, 0, 31620, 0, -16360, 0, -43972, 0, 53280, 0, -77236, 0, -138382, 0, 29664, 0, 237104, 0, 633464, 0, 57480, 0, 133964, 0, -118380, 0, -972, 0, 40548, 0, 54004, 0, 194088, 0, 23496, 0, -327906, 0, 72096, 0, 2120, 0, -132160, 0, -21528, 0, 136208, 0, 61320, 0, 210840, 0, -236032, 0, -128232, 0, 62460, 0, 31676, 0, 185308, 0, 27180, 0, -391080, 0, -230856, 0, -31956, 0, 44096, 0, 295182, 0, -76542, 0, -4320, 0, -252416, 0, 9612, 0, 174942, 0, 82282, 0, -41712, 0, -263768, 0, 23000, 0, -4848, 0, -35004, 0, -90584, 0, -104652, 0, 175564, 0, -108564, 0, 1224, 0, -73672, 0, 28144, 0, 108558, 0, 307056, 0, 6160, 0, 46476, 0, -4200, 0, -43214, 0, -20592, 0, -473592, 0, 30400, 0, 81132, 0, -261574, 0, 60196, 0, -40986, 0, 58650, 0, 167372, 0, -126948, 0, -4964, 0, -14368, 0, -51330, 0, 588432, 0, -208488, 0, -71784, 0, 115296, 0, -413562, 0, -10272, 0, 37608, 0, -188990, 0, 94068, 0, -232264, 0, 460744, 0, 75060, 0, 72232, 0, -29328, 0, -9030, 0, -241606, 0, -5512, 0, -11316, 0, 1008, 0, -277472, 0, 648, 0, 376948, 0, -165056, 0, -296952, 0, -82948, 0, -147020, 0, -146016, 0, -2944, 0, -204002, 0, -58968, 0, -542352, 0, 519344, 0, 162870, 0, -169512, 0, 26348, 0, -173856, 0, 451280, 0, -374128, 0, 24552, 0, -124410, 0, -48300, 0, -34992, 0, -243256, 0, 243780, 0, 16278, 0, -289740, 0, 129484, 0, -69660, 0, -132400, 0, -28736, 0, 15516, 0, -446226, 0, -322816, 0, -118620, 0, 314276, 0, 10096, 0, 114336, 0, -495190, 0, -217296, 0, -201552, 0, -50240, 0, -267116, 0, 29640, 0, 70196, 0, -297476, 0, 97344, 0, 372920, 0, -605024, 0, -257214, 0, 64944, 0, -321304, 0, 40104, 0, 338112, 0, 361612, 0, -29592, 0, 44560, 0, -116788, 0, 125712, 0, 220064, 0, -145084, 0, 218940, 0, 457428, 0, -76312, 0, -44280, 0, -247760, 0, -279796, 0, 414, 0, 292532, 0, -292940, 0, 142548, 0, 107512, 0, 103064, 0, 27252, 0, -8480, 0, 75068, 0, -144792, 0, -124428, 0, -45740, 0, -34920, 0, -460200, 0, 378976, 0, 27540, 0, -96312, 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": "276.4.a.d", "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, 0], [1, 0], [0, 0], [3, 0], [0, 0], [7, 3], [0, 0], [-5, 1], [0, 0], [9, 0], [0, 0], [-2, -2], [0, 0], [52, 6], [0, 0], [21, 9], [0, 0], [61, -15], [0, 0], [37, -21], [0, 0], [-15, 3], [0, 0], [-23, 0], [0, 0], [41, 42], [0, 0], [27, 0], [0, 0], [20, -54], [0, 0], [2, -50], [0, 0], [-6, -6], [0, 0], [4, -8], [0, 0], [170, 12], [0, 0], [156, 18], [0, 0], [82, 104], [0, 0], [-3, 115], [0, 0], [63, 27], [0, 0], [284, -80], [0, 0], [-305, -10], [0, 0], [183, -45], [0, 0], [225, 17], [0, 0], [-92, -20], [0, 0], [111, -63], [0, 0], [200, 40], [0, 0], [150, -176], [0, 0], [-45, 9], [0, 0], [598, 198], [0, 0], [-265, 81], [0, 0], [-69, 0], [0, 0], [60, -84], [0, 0], [-234, -156], [0, 0], [123, 126], [0, 0], [-16, 8], [0, 0], [-863, -13], [0, 0], [81, 0], [0, 0], [690, -22], [0, 0], [-158, 78], [0, 0], [60, -162], [0, 0], [-261, -237], [0, 0], [-182, 22], [0, 0], [6, -150], [0, 0], [-560, -36], [0, 0], [20, 166], [0, 0], [-18, -18], [0, 0]]}