# Stored data for newform 912.4.a.i, downloaded from the LMFDB on 01 May 2024.
{"label": "912.4.a.i", "space_label": "912.4.a", "level": 912, "weight": 4, "hecke_orbit": 9, "hecke_orbit_code": 36028797086073744, "dim": 2, "is_polredabs": true, "nf_label": "2.2.97.1", "trace_hash": 1018817927813846380, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [18, 13, 1]], [7, [-216, 3, 1]]], "qexp_display": "q-3q^{3}+(-6-\\beta )q^{5}-3\\beta q^{7}+9q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 14592, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 53.80974192523544, "hecke_ring_index": 1, "level_radical": 114, "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": [912, 1, [799, 229, 305, 97], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 19], "conrey_indexes": [1], "field_disc": 97, "field_disc_factorization": [[97, 1]], "field_poly": [-24, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "2.044", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.096", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "69.251", "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], [19, 1]], "trace_display": [0, -6, -13, -3], "traces": [0, 2, 0, -6, 0, -13, 0, -3, 0, 18, 0, 41, 0, 8, 0, 39, 0, -103, 0, -38, 0, 9, 0, 74, 0, -117, 0, -54, 0, -186, 0, 30, 0, -123, 0, 165, 0, -274, 0, -24, 0, -392, 0, 193, 0, -117, 0, 275, 0, -245, 0, 309, 0, -250, 0, -121, 0, 114, 0, 684, 0, 201, 0, -27, 0, 530, 0, 384, 0, -222, 0, 868, 0, 715, 0, 351, 0, 375, 0, -420, 0, 162, 0, 1198, 0, 815, 0, 558, 0, 210, 0, 1734, 0, -90, 0, 247, 0, 328, 0, 369, 0, 568, 0, -1438, 0, -495, 0, 2490, 0, 386, 0, 822, 0, -234, 0, 392, 0, 72, 0, 591, 0, -1385, 0, 1176, 0, 1755, 0, 422, 0, -579, 0, 2171, 0, 57, 0, 351, 0, -575, 0, -159, 0, -825, 0, 1910, 0, 2082, 0, 735, 0, 1973, 0, -2508, 0, -927, 0, 1454, 0, 5544, 0, 750, 0, 2508, 0, -2132, 0, 363, 0, 1802, 0, 2622, 0, -342, 0, 5422, 0, -1716, 0, -2052, 0, -2130, 0, 3292, 0, -603, 0, 132, 0, -1675, 0, 81, 0, 1165, 0, 1322, 0, -1590, 0, -56, 0, -6343, 0, -1152, 0, 2898, 0, 4488, 0, 666, 0, -779, 0, 380, 0, -2604, 0, -2855, 0, 4902, 0, -2145, 0, 1334, 0, -2852, 0, -1053, 0, 222, 0, 2871, 0, -1125, 0, 6199, 0, -2127, 0, 1260, 0, -3559, 0, 5298, 0, -486, 0, 1156, 0, -152, 0, -3594, 0, 10127, 0, 4136, 0, -2445, 0, -1908, 0, -4536, 0, -1674, 0, 2831, 0, 3274, 0, -630, 0, -3382, 0, -7216, 0, -5202, 0, -4290, 0, -4133, 0, 270, 0, -5762, 0, 3637, 0, -741, 0, 6408, 0, -4085, 0, -984, 0, -8756, 0, -6580, 0, -1107, 0, 10772, 0, -5091, 0, -1704, 0, -1549, 0, 2052, 0, 4314, 0, -7041, 0, 196, 0, 1485, 0, 3456, 0, -1194, 0, -7470, 0, 1957, 0, -8034, 0, -1158, 0, -1431, 0, -5860, 0, -2466, 0, -556, 0, -9636, 0, 702, 0, 5562, 0, 87, 0, -1176, 0, 5875, 0, -16241, 0, -216, 0, 6876, 0, 760, 0, -1773, 0, -695, 0, 722, 0, 4155, 0, 833, 0, -10892, 0, -3528, 0, 5322, 0, -16610, 0, -5265, 0, 9732, 0, -10550, 0, -1266, 0, 12366, 0, 327, 0, 1737, 0, 7611, 0, -1192, 0, -6513, 0, -956, 0, -6473, 0, -171, 0, -12304, 0, 19908, 0, -1053, 0, -10564, 0, -5936, 0, 1725, 0, -7428, 0, -12152, 0, 477, 0, 8538, 0, -16476, 0, 2475, 0, 4134, 0, -1029, 0, -5730, 0, -9046, 0, -9444, 0, -6246, 0, -1406, 0, 15538, 0, -2205, 0, 12455, 0, -9222, 0, -5919, 0, -8304, 0, -2216, 0, 7524, 0, -11562, 0, -303, 0, 2781, 0, 9589, 0, -693, 0, -4362, 0, 14739, 0, 5244, 0, -16632, 0, -845, 0, 2223, 0, -2250, 0, 8954, 0, -20884, 0, -7524, 0, -7370, 0, -10044, 0, 6396, 0, 1398, 0, 12198, 0, -1089, 0, 17904, 0, 2615, 0, -5406, 0, -12366, 0, -1170, 0, -7866, 0, -12806, 0, 15369, 0, 1026, 0, 6922, 0, 4619, 0, -16266, 0, 19360, 0, 22918, 0, 5148, 0, 3402, 0, -5882, 0, 6156, 0, 21712, 0, -8910, 0, 6390, 0, -6332, 0, -1435, 0, -9876, 0, 16988, 0, -22518, 0, 1809, 0, 3534, 0, -10428, 0, -396, 0, -19591, 0, -18434, 0, 5025, 0, 16344, 0, -12738, 0, -243, 0, 32102, 0, 24112, 0, -3495, 0, -15678, 0, -12255, 0, -3966, 0, -14892, 0, -178, 0, 4770, 0, 13047, 0, -570, 0, 168, 0, 3892, 0, -11553, 0, 19029, 0, 3244, 0, -38154, 0, 3456, 0, 14968, 0, -21014, 0, -8694, 0, -2974, 0, -11741, 0, -13464, 0, 46005, 0, 13168, 0, -1998, 0, -23886, 0, -1584, 0, 2337, 0, 9164, 0, -3503, 0, -1140, 0, 11710, 0, -6218, 0, 7812, 0, 7670, 0, 32425, 0, 8565, 0, -55015, 0, 7620, 0, -14706, 0, -22995, 0, -16391, 0, 6435, 0, -21454, 0, 37506, 0, -4002, 0, -3135, 0, 8832, 0, 8556, 0, 3393, 0, 10822, 0, 3159, 0, -7486, 0, -16206, 0, -666, 0, 3754, 0, 12807, 0, -8613, 0, 18788, 0, 30583, 0, 3375, 0, 597, 0, 26008, 0, -18597, 0, -14464, 0, 5206, 0, 6381, 0, 6714, 0, -32664, 0, -3780, 0, 30792, 0, 98, 0, 10677, 0, 8497, 0, -5118, 0, -15894, 0, -468, 0, -4837, 0, 1458, 0, -14741, 0, 5396, 0, -3468, 0, 13692, 0, 19569, 0, 456, 0, 22352, 0, 707, 0, 10782, 0, 18090, 0, 7184, 0, -30381, 0, 8348, 0, 13381, 0, -12408, 0, 44313, 0, 57912, 0, 7335, 0, -22872, 0, 36409, 0, 5724, 0, 39584, 0, -23192, 0, 13608, 0, 7448, 0, 37000, 0, 5022, 0, -39334, 0, -18444, 0, -8493, 0, -42426, 0, -2106, 0, -9822, 0, 7400, 0, -15181, 0, 1890, 0, 31099, 0, -12228, 0, 10146, 0, -7289, 0, 32246, 0, 21648, 0, 38496, 0, -3667, 0, 15606, 0, 17981, 0, 36981, 0, 12870, 0, 7688, 0, -28970, 0, 12399, 0, 11308, 0, -30822, 0, -810, 0, -7426, 0, -15766, 0, 17286, 0, -12387, 0, 19974, 0, -10911, 0, -39820, 0, 38240, 0, 2223, 0, 36748, 0, 80161, 0, -19224, 0, 6568, 0, -26610, 0, 12255, 0, -19668, 0, 24816, 0, 2952, 0, -17037, 0, -2584, 0, 26268, 0, -171, 0, 21105, 0, 19740, 0, 31712, 0, 42726, 0, 3321, 0, -5225, 0, 31014, 0, -32316, 0, 26892, 0, 17822, 0, 15273, 0, -47394, 0, 3550, 0, 5112, 0, -15378, 0, 11464, 0, 4647, 0, -10095, 0, 64512, 0, -6156, 0, 80296, 0, 37466, 0, -12942, 0, -37072, 0, 4655, 0, 21123, 0, 6377, 0, -61025, 0, -588, 0, -75558, 0, 20416, 0, -4455, 0, -5326, 0, 68626, 0, -10368, 0, -25872, 0, 13719, 0, 3582, 0, 28071, 0, -3066, 0, 22410, 0, -12764, 0, 5640, 0, -5871, 0, 36960, 0, -1071, 0, 24102, 0, 23454, 0, -19266, 0, 3474, 0, 19436, 0, -5262, 0, 4293, 0, -21668, 0, 75624, 0, 17580, 0, 28765, 0, 59499, 0, 7398, 0, 34674, 0, -41628, 0, 1668, 0, 4750, 0, -57218, 0, 28908, 0, -100075, 0, -33678, 0, -2106, 0, -76420, 0, 27940, 0, -16686, 0, -2288, 0, -45912, 0, -261, 0, 32814, 0, -10584, 0, 3528, 0, -11079, 0, -19802, 0, -17625, 0, 37635, 0, 2299, 0, 48723, 0, -80397, 0, 24, 0, 648, 0, 17512, 0, -20100, 0, -20628, 0, 5349, 0, -119204, 0, -2280, 0, -8990, 0, -61847, 0, 5319, 0, -4200, 0, 9516, 0, 2085, 0, -47588, 0, 4064, 0, -2166, 0, -32154, 0, -62313, 0, -12465, 0, -112186, 0, 49324, 0, -2499, 0, 12880, 0, -18210, 0, 32676, 0, -61339, 0, -38062, 0, 10584, 0, 5869, 0, 19210, 0, -15966, 0, -7652, 0, 35100, 0, 49830, 0, -12996, 0, -48844, 0, 15795, 0, -16922, 0, 12944, 0, -29196, 0, -36754, 0, -52950, 0, 31650, 0, -13956, 0, 77112, 0, 3798, 0, 13397, 0, -60176, 0, -37098, 0, 26254, 0, -8508, 0, -981, 0, -93444, 0, -3819, 0, -5211, 0, -41511, 0, -61391, 0, -22833, 0, -60030, 0, -102482, 0, 3576, 0, -11674, 0, 72870, 0, 19539, 0, -121996, 0, 10035, 0, 2868, 0, -94790, 0, 71376, 0, 19419, 0, 40186, 0, 39187, 0, 513, 0, 66404, 0, -59913, 0, 36912, 0, 7176, 0, -25496, 0, -59724, 0, 17766, 0, 56620, 0, 3159, 0, 90052, 0, 20432, 0, 31692, 0, -24537, 0, 20007, 0, 17808, 0, -133604, 0, -34456, 0, -5175, 0, -10070, 0, 114846, 0, 22284, 0, -20381, 0, -47574, 0, 36456, 0, -46758, 0, -49104, 0, -1431, 0, 54702, 0, -68687, 0, -25614, 0, -63702, 0, -61544, 0, 49428, 0, -3604, 0, -82926, 0, -7425, 0, 60080, 0, -7296, 0, -12402, 0, -65667, 0, 57231, 0, 3087, 0, -22608, 0, 62648, 0, 17190, 0, 78133, 0, -83190, 0, 27138, 0, 12024, 0, 3196, 0, 28332, 0, -29376, 0, 95321, 0, 18738, 0, -177444, 0, -11019, 0, 4218, 0, 32536, 0, 1241, 0, -46614, 0, -62406, 0, -46862, 0, 6615, 0, -6812, 0, -1012, 0, -37365, 0, -65067, 0, -51522, 0, 27666, 0, 62127, 0, -34852, 0, 17757, 0, 10572, 0, 22274, 0, 24912, 0, -16492, 0, -14496, 0, 6648, 0, 87644, 0, -13104, 0, -22572, 0, -53024, 0, -31686, 0, 34686, 0, -108614, 0, -7702, 0, 909, 0, -100345, 0, 21573, 0, -8343, 0, -16794, 0, 50822, 0, -28767, 0, 18377, 0, -13585, 0, 2079, 0, 97260, 0, -27879, 0, 13086, 0, 52010, 0, -9560, 0, -44217, 0, 3072, 0, 61994, 0, -15732, 0, -120578, 0, -74792, 0, 49896, 0, -88291, 0, 235508, 0, 2535, 0, 14928, 0, 107399, 0, -6669, 0, -15944, 0, -40867, 0, 6750, 0, 97300, 0, -73080, 0, -26862, 0, -31772, 0, 37667, 0, 62652, 0, 11566, 0, 112660, 0, 22572, 0, -73899, 0, 106101, 0, 22110, 0, -7418, 0, -95042, 0, 30132, 0, -7125, 0, 26844, 0, -19188, 0, -172044, 0, -59006, 0, -4194, 0, -12272, 0, 59376, 0, -36594, 0, 1456, 0, 27763, 0, 3267, 0, -98251, 0, -132701, 0, -53712, 0, 64139, 0, -44992, 0, -7845, 0, 105026, 0, 7980, 0, 16218, 0, 49533, 0, 15421, 0, 37098, 0, -30236, 0, -34386, 0, 3510, 0, -12256, 0, -18516, 0, 23598, 0, -4306, 0, -8606, 0, 38418, 0, -4569, 0, 106371, 0, -46107, 0, 11688, 0, 52932, 0, -3078, 0, 49128, 0, 66648, 0, -20766, 0, -90174, 0, -69998, 0, -13857, 0, -54738, 0, 82869, 0, 48798, 0, 16643, 0, -74292, 0, -58080, 0, -38910, 0, -102489, 0, -68754, 0, 70020, 0, 66046, 0, -15444, 0, -22762, 0, 56148, 0, -10206, 0, 105599, 0, -64368, 0, 17646, 0, -154854, 0, 27976, 0, -18468, 0, 12126, 0, 83920, 0, -65136, 0, 74043, 0, 91869, 0, 26730, 0, 8466, 0, -45454, 0, -19170, 0, -16445, 0, -15485, 0, 18996, 0, 10290, 0, -139657, 0, 4305, 0, -50598, 0, -98250, 0, 29628, 0, -72591, 0, 147352, 0, -50964, 0, -78600, 0, 81041, 0, 67554, 0, 52316, 0, 29817, 0, -5427, 0, -32606, 0, 175124, 0, -10602, 0, 96872, 0, 6624, 0, 31284, 0, -75276, 0, 165472, 0, 1188, 0, -45360, 0, -14255, 0, 58773, 0, 53499, 0, -47684, 0, 55302, 0, 125104, 0, 16590, 0, -15075, 0, 18402, 0, 116892, 0, -49032, 0, -3990, 0, -6516, 0, 38214, 0, 38279, 0, 88098, 0, 729, 0, -18670, 0, -166, 0, -96306, 0, -42494, 0, -102024, 0, -72336, 0, -67641, 0, -21686, 0, 10485, 0, 115815, 0, 1224, 0, 47034, 0, 103758, 0, -32946, 0, 36765, 0, -115145, 0, 30537, 0, 11898, 0, -26132, 0, -62352, 0, 44676, 0, 134133, 0, -136908, 0, 534, 0, 66782, 0, -37601, 0, -14310, 0, -23775, 0, 159709, 0, -39141, 0, -101848, 0, 9626, 0, 1710, 0, -23058, 0, 63636, 0, -504, 0, -134004, 0, -127726, 0, -11676, 0, 106534, 0, 273616, 0, 34659, 0, -49427, 0, -237432, 0, -57087, 0, 30208, 0, -7365, 0, -9732, 0, 153600, 0, 9266, 0, 114462, 0, -4693, 0, -5874, 0, -10368, 0, 28441, 0, 48406, 0, -44904, 0, -81888, 0, -106410, 0, 63042, 0, 161332, 0, -113074, 0, 26082, 0, -62296, 0, 236432, 0, 8922, 0, 21328, 0, -20386, 0, 35223, 0, 54681, 0, -6232, 0, 40392, 0, -3285, 0, -87573, 0, -138015, 0, 38612, 0, -55254, 0, -39504, 0, 67719, 0, 98262, 0, 5994, 0, 165292, 0, 38709, 0, 71658, 0, 93921, 0, 2789, 0, 4752, 0, -58934, 0, 102681, 0, -7011, 0, 5946, 0, -113892, 0, -27492, 0, 63550, 0, -5230, 0, 10509, 0, 62270, 0, 133044, 0, 3420, 0, 51976, 0, 137050, 0, -35130, 0, 130093, 0, -34244, 0, 18654, 0, 216146, 0, -76014, 0, -23436, 0, -10792, 0, -30726, 0, -23010, 0, -57876, 0, -67480, 0, -97275, 0, 36336, 0, -229726, 0, -25695, 0, 170270, 0, -19263, 0, 165045, 0, -792, 0, -61451, 0, -22860, 0, -63856, 0, -13740, 0, 44118, 0, -31828, 0, 27322, 0, 68985, 0, -21816, 0, -105480, 0, 49173, 0, 82266, 0, 7842, 0, -19305, 0, 222267, 0, 72488, 0, 64362, 0, -62118, 0, -199407, 0, -112518, 0, 45421, 0, 128035, 0, 12006, 0, -10502, 0, 163671, 0, 9405, 0, 167050, 0, -139623, 0, -26496, 0, 21070, 0, 53592, 0, -25668, 0, 30560, 0, 255339, 0, -10179, 0, -114076, 0, -151460, 0, -32466, 0, 37741, 0, -38832, 0, -9477, 0, -34836, 0, -212520, 0, 22458, 0, -47310, 0, 14928, 0, 48618, 0, 102201, 0, -17400, 0, 1998, 0, -57834, 0, -133656, 0, -11262, 0, -77076, 0, 93824, 0, -38421, 0, 89224, 0, 34512, 0, 25839, 0, 248017, 0, 101244, 0, -56364, 0, 209072, 0, -7334, 0, -91749, 0, -13338, 0, 71720, 0, -10125, 0, 207288, 0, -18316, 0, -1791, 0, -76538, 0, 191744, 0, -78024, 0, 58920, 0, 5904, 0, 55791, 0, -102541, 0, 87757, 0, 43392, 0, 120286, 0, -9238, 0, -15618, 0, 200982, 0, -121679, 0, -19143, 0, 32154, 0, 287128, 0, -20142, 0, 14588, 0, -104787, 0, 97992, 0, -274131, 0, 95332, 0, 11340, 0, 21675, 0, 330119, 0, -92376, 0, 117350, 0, -161378, 0, -294, 0, 4446, 0, 72000, 0, -32031, 0, 320940, 0, -29762, 0, -25491, 0, 21626, 0, -285594, 0, 15354, 0, 168086, 0, -18026, 0, 47682, 0, -222100, 0, 114960, 0, 1404, 0, 121869, 0, -118898, 0, 14511, 0, -21152, 0, -7448, 0, -4374, 0, -167425, 0, -113202, 0, 44223, 0, -70830, 0, 48784, 0, -16188, 0, 230688, 0, -3712, 0, 10404, 0, -242132, 0, -167457, 0, -41076, 0, -170135, 0, -53555, 0, -58707, 0, -130896, 0, 143361, 0, -1368, 0, 89856, 0, -118645, 0, -67056, 0, -82148, 0, 14886, 0, -2121, 0, -54086, 0, -18760, 0, -32346, 0, -44823, 0, -3836, 0, -54270, 0, 125284, 0, -206751, 0, -21552, 0, 25656, 0, -19292, 0, 91143, 0, -11229, 0, 197062, 0, -25044, 0, 50135, 0, -198320, 0, -40143, 0, -306690, 0, -97656, 0, 37224, 0, -78542, 0, -232767, 0, -132939, 0, 16471, 0, 44900, 0, -173736, 0, -27288, 0, 295658, 0, -22005, 0, 164225, 0, 26315, 0, 68616, 0, -30632, 0, 7075, 0, -109227, 0, 182782, 0, -55372, 0, -17172, 0, 84287, 0, 185136, 0, -118752, 0, 67736, 0, 66412, 0, 69576, 0, 197508, 0, 56821, 0, -40824, 0, 106540, 0, -63939, 0, -22344, 0, 188302, 0, -9408, 0, -111000, 0, -9060, 0, -90154, 0, -15066, 0, 83650, 0, -298784, 0, 118002, 0, -32015, 0, -118242, 0, 55332, 0, 6879, 0, -13277, 0, 25479, 0, -96856, 0, 96026, 0, 127278, 0, -33345, 0, 108434, 0, 6318, 0, -246101, 0, -43890, 0, 29466, 0, 99618, 0, 59050, 0, -22200, 0, 58758, 0, -15812, 0, 45543, 0, 7354, 0, -117322, 0, -5670, 0, 49416, 0, -189984, 0, -93297, 0, 181286, 0, -8018, 0, 36684, 0, -91015, 0, -219424, 0, -30438, 0, 46062, 0, 48906, 0, 21867, 0, 197361, 0, -60826, 0, -96738, 0, 44140, 0, -105845, 0, -64944, 0, 22648, 0, 110061, 0, -115488, 0, -66216, 0, -131624, 0, 11001, 0, -137036, 0, -94932, 0, -46818, 0, 60296, 0, 223080, 0, -53943, 0, -137778, 0, 288367, 0, -110943, 0, 152646, 0, 87248, 0, -38610, 0, -100400, 0, -118568, 0, -23064, 0, 260158, 0, -62832, 0, 86910, 0, -41249, 0, -45918, 0, -37197, 0, -125589, 0, -149970, 0, -33924, 0, -49096, 0, -315966, 0, 92466, 0, 365228, 0, -44764, 0, 2430, 0, -34605, 0, 167388, 0, 22278, 0, 155031, 0, -97036, 0, 47298, 0, -66014, 0, -1083, 0, -51858, 0, -119434, 0, -61015, 0, 37161, 0, 136428, 0, -287654, 0, -59922, 0, 200643, 0, 33090, 0, 32733, 0, 127892, 0, 108961, 0, 119460, 0, -56103, 0, 85059, 0, -114720, 0, -67736, 0, 63787, 0, -6669, 0, 105300, 0, -132072, 0, -110244, 0, -130440, 0, 115648, 0, -240483, 0, 138614, 0, -160956, 0, 57672, 0, -16977, 0, -174946, 0, -19704, 0, -142170, 0, 116393, 0, 79830, 0, 15784, 0, -265320, 0, -36765, 0, 10925, 0, -42808, 0, 59004, 0, -137933, 0, 196896, 0, -74448, 0, -192326, 0, 87966, 0, -8856, 0, -103170, 0, 27399, 0, 51111, 0, -336584, 0, -24799, 0, 7752, 0, 34175, 0, -104854, 0, -78804, 0, -166500, 0, 3021, 0, 513, 0, 102835, 0, -336413, 0, -63315, 0, 233448, 0, -3090, 0, -59220, 0, 20379, 0, -122830, 0, -95136, 0, -26326, 0, -247440, 0, -128178, 0, -295410, 0, 46948, 0, -9963, 0, -240240, 0, 444352, 0, 15675, 0, -5454, 0, -320093, 0, -93042, 0, -256042, 0, -291490, 0, 96948, 0, 65698, 0, 14386, 0, -80676, 0, 104430, 0, -284292, 0, -53466, 0, -102465, 0, -107041, 0, -45819, 0, -118008, 0, -178012, 0, 142182, 0, -36290, 0, -237956, 0, -10650, 0, -47355, 0, -276042, 0, -15336, 0, -199542, 0, -6658, 0, 46134, 0, 248702, 0, -116940, 0, -34392, 0, 76744, 0, 241304, 0, -13941, 0, 2336, 0, 198490, 0, 30285, 0, 127695, 0, -39558, 0, -193536, 0, -263988, 0, 199019, 0, 18468, 0, 42756, 0, -104606, 0, -240888, 0, 183712, 0, 108988, 0, -112398, 0, -77742, 0, 19749, 0, 38826, 0, 56134, 0, 51439, 0, 111216, 0, -293552, 0, 209179, 0, -13965, 0, 169582, 0, 157619, 0, -63369, 0, -154076, 0, 79346, 0, -19131, 0, -60696, 0, -210438, 0, 183075, 0, -124788, 0, -128740, 0, 1764, 0, -72081, 0, 16116, 0, 226674, 0, 199056, 0, 111624, 0, -61248, 0, -37487, 0, -34076, 0, 13365, 0, -134473, 0, -150130, 0, 15978, 0, 248030, 0, -295478, 0, -205878, 0, -145368, 0, 483835, 0, 31104, 0, -237432, 0, 183520, 0, 77616, 0, -89368, 0, -280350, 0, -41157, 0, 29335, 0, 47652, 0, -10746, 0, -121065, 0, -21492, 0, -84213, 0, 325218, 0, -26964, 0, 9198, 0, 105799, 0, -65116, 0, -67230, 0, -64584, 0, 116963, 0, 38292, 0, -334792, 0, -325688, 0, -16920, 0, 75706, 0, 190500, 0, 17613, 0, 18192, 0, 85952, 0, -110880, 0, 16774, 0, 173176, 0, 3213, 0, 275768, 0, 182864, 0, -72306, 0, 110719, 0, -7428, 0, -70362, 0, 171396, 0, -116767, 0, 57798, 0, 486594, 0, -253334, 0, -10422, 0, -27626, 0, 64290, 0, -58308, 0, -617196, 0, -377766, 0, 15786, 0, -253646, 0, -68458, 0, -12879, 0, 303390, 0, 102742, 0, 65004, 0, -221121, 0, 111581, 0, -226872, 0, 65676, 0, 396186, 0, -52740, 0, -25708, 0, -105336, 0, -86295, 0, 90084, 0, -22440, 0, -178497, 0, 79080, 0, -104700, 0, -22194, 0, 7055, 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": "456.4.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, 0], [1, 0], [0, 0], [-3, 0], [0, 0], [-6, -1], [0, 0], [0, -3], [0, 0], [9, 0], [0, 0], [22, -3], [0, 0], [10, -12], [0, 0], [18, 3], [0, 0], [-50, -3], [0, 0], [-19, 0], [0, 0], [0, 9], [0, 0], [46, -18], [0, 0], [-65, 13], [0, 0], [-27, 0], [0, 0], [-84, -18], [0, 0], [32, -34], [0, 0], [-66, 9], [0, 0], [72, 21], [0, 0], [-154, 34], [0, 0], [-30, 36], [0, 0], [-176, -40], [0, 0], [80, 33], [0, 0], [-54, -9], [0, 0], [134, 7], [0, 0], [-127, 9], [0, 0], [150, 9], [0, 0], [-108, -34], [0, 0], [-60, -1], [0, 0], [57, 0], [0, 0], [320, 44], [0, 0], [98, 5], [0, 0], [0, -27], [0, 0], [228, 74], [0, 0], [212, -40], [0, 0], [-138, 54], [0, 0], [500, -132], [0, 0], [414, -113], [0, 0], [195, -39], [0, 0], [216, -57], [0, 0], [-248, 76], [0, 0], [81, 0], [0, 0], [554, 90], [0, 0], [372, 71], [0, 0], [252, 54], [0, 0], [24, 162], [0, 0], [864, 6], [0, 0], [-96, 102], [0, 0], [114, 19], [0, 0], [110, 108], [0, 0], [198, -27], [0, 0]]}