# Stored data for newform 672.4.a.c, downloaded from the LMFDB on 19 April 2024.
{"label": "672.4.a.c", "space_label": "672.4.a", "level": 672, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321850528, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 706838634898912855, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [18, 1]], [11, [-44, 1]]], "qexp_display": "q+3q^{3}-18q^{5}-7q^{7}+9q^{9}+44q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10752, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 39.64928352385769, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [672, 1, [127, 421, 449, 577], [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": "1.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.939", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.718", "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, -18, -7], "traces": [0, 1, 0, 3, 0, -18, 0, -7, 0, 9, 0, 44, 0, 58, 0, -54, 0, -130, 0, 92, 0, -21, 0, 84, 0, 199, 0, 27, 0, -250, 0, -72, 0, 132, 0, 126, 0, -354, 0, 174, 0, 334, 0, -416, 0, -162, 0, -464, 0, 49, 0, -390, 0, -450, 0, -792, 0, 276, 0, -516, 0, 58, 0, -63, 0, -1044, 0, -656, 0, 252, 0, -940, 0, 178, 0, 597, 0, -308, 0, 1072, 0, 81, 0, 660, 0, 2340, 0, -750, 0, 1254, 0, -406, 0, -216, 0, -1656, 0, 210, 0, 396, 0, -186, 0, 472, 0, 378, 0, -1212, 0, -1386, 0, -1062, 0, 114, 0, -1512, 0, 522, 0, 910, 0, 605, 0, 1002, 0, -1332, 0, 792, 0, -1248, 0, -428, 0, -644, 0, -486, 0, -2238, 0, 300, 0, -1392, 0, 2552, 0, 4500, 0, 147, 0, 1646, 0, -1184, 0, -1170, 0, 1296, 0, -1150, 0, -1350, 0, -588, 0, -344, 0, -2376, 0, -2304, 0, 1167, 0, 828, 0, 2742, 0, -1393, 0, -1548, 0, -3940, 0, 1970, 0, 174, 0, 6372, 0, -5720, 0, -189, 0, -476, 0, -782, 0, -3132, 0, -2066, 0, 768, 0, -1968, 0, 1750, 0, -6012, 0, 756, 0, 4048, 0, 4248, 0, -2820, 0, 7488, 0, 504, 0, 534, 0, -7540, 0, -3496, 0, 1791, 0, -5620, 0, -1982, 0, -924, 0, -1342, 0, 8352, 0, 3216, 0, -2828, 0, 2002, 0, 243, 0, -882, 0, 5336, 0, 1980, 0, 1188, 0, 3696, 0, 7020, 0, -5506, 0, 2478, 0, -2250, 0, 4076, 0, 8100, 0, 3762, 0, -5938, 0, 592, 0, -1218, 0, 8756, 0, 5254, 0, -648, 0, 3410, 0, -2212, 0, -4968, 0, -2338, 0, 11987, 0, 630, 0, -2122, 0, 9288, 0, 1188, 0, 4872, 0, 2912, 0, -558, 0, -1044, 0, 2588, 0, 1416, 0, 2728, 0, -6446, 0, 1134, 0, -4234, 0, -11000, 0, -3636, 0, -11960, 0, 11542, 0, -4158, 0, 3248, 0, -4592, 0, -3186, 0, 11808, 0, -1006, 0, 342, 0, -3168, 0, -343, 0, -4536, 0, 4644, 0, 4786, 0, 1566, 0, 1302, 0, 16920, 0, 2730, 0, 11260, 0, 1605, 0, 1815, 0, -3204, 0, 2792, 0, 3006, 0, 3150, 0, 4118, 0, -3996, 0, -14500, 0, 8624, 0, 2376, 0, 6488, 0, 5544, 0, -3744, 0, 1406, 0, -10920, 0, -1284, 0, -19296, 0, 9378, 0, -1932, 0, 2890, 0, -4176, 0, -1458, 0, -15576, 0, -10582, 0, -6714, 0, 3612, 0, -11880, 0, 900, 0, -9500, 0, 598, 0, -4176, 0, -25870, 0, -406, 0, 7656, 0, 3708, 0, 13706, 0, 13500, 0, 7728, 0, -8232, 0, 441, 0, 2524, 0, -22572, 0, 4938, 0, -3630, 0, 14696, 0, -3552, 0, 7308, 0, 5386, 0, -3510, 0, 11766, 0, -10240, 0, 3888, 0, 6076, 0, 4592, 0, -3450, 0, -18304, 0, 18308, 0, -4050, 0, 6480, 0, -20532, 0, -1764, 0, -3780, 0, 4240, 0, -1032, 0, -17892, 0, 32500, 0, -7128, 0, 6580, 0, -4616, 0, -6912, 0, 3696, 0, 3348, 0, 3501, 0, -16738, 0, -1246, 0, 2484, 0, -8496, 0, -20416, 0, 8226, 0, 19062, 0, -12268, 0, -4179, 0, 9360, 0, -5111, 0, -4644, 0, 19372, 0, 21816, 0, -11820, 0, 2156, 0, -17042, 0, 5910, 0, 24948, 0, -3656, 0, 522, 0, -23000, 0, -7504, 0, 19116, 0, 14038, 0, -24128, 0, -17160, 0, -18332, 0, -2052, 0, -567, 0, -10046, 0, -5704, 0, -1428, 0, 16716, 0, 24610, 0, -2346, 0, -4620, 0, -19800, 0, -9396, 0, 18516, 0, -6624, 0, -6198, 0, 20038, 0, -16380, 0, 2304, 0, 2596, 0, -5190, 0, -5904, 0, -10890, 0, 6536, 0, 5250, 0, -26912, 0, 4702, 0, -18036, 0, -8638, 0, -19676, 0, 2268, 0, -8778, 0, -899, 0, 12144, 0, 46020, 0, 26720, 0, 12744, 0, -14256, 0, 2842, 0, -8460, 0, -1990, 0, -6956, 0, 22464, 0, -15984, 0, -22704, 0, 1512, 0, 6614, 0, 7704, 0, 1602, 0, -29364, 0, -3150, 0, -22620, 0, 11592, 0, -21000, 0, -10488, 0, 2552, 0, 8402, 0, 5373, 0, 7854, 0, -1470, 0, -16860, 0, -14244, 0, 40284, 0, -5946, 0, -26100, 0, 22420, 0, -2772, 0, -5400, 0, -43420, 0, -4026, 0, 19814, 0, -32568, 0, 25056, 0, 1302, 0, -15986, 0, 9648, 0, -6048, 0, -45936, 0, -8484, 0, 22440, 0, -3304, 0, 6006, 0, -49750, 0, 10264, 0, 729, 0, 54080, 0, 9282, 0, -2646, 0, -28864, 0, 12792, 0, 16008, 0, 25644, 0, -29628, 0, 5940, 0, 8484, 0, -4528, 0, 3564, 0, 21312, 0, 31310, 0, 11088, 0, 16622, 0, 9702, 0, 21060, 0, -29928, 0, -9814, 0, -16518, 0, 7686, 0, -14328, 0, 7434, 0, 30728, 0, -41360, 0, -6750, 0, 20700, 0, 5860, 0, 12228, 0, -798, 0, 3364, 0, 24300, 0, -15450, 0, 60320, 0, 11286, 0, 7832, 0, 10584, 0, -17814, 0, -26726, 0, -3052, 0, 1776, 0, 6192, 0, -38272, 0, -3654, 0, 23838, 0, 19136, 0, 26268, 0, -32556, 0, -33086, 0, 15762, 0, -6370, 0, 41472, 0, -1944, 0, 35248, 0, 38111, 0, 10230, 0, -21006, 0, -4235, 0, -6636, 0, -29736, 0, 8922, 0, -14904, 0, 28126, 0, 28916, 0, -7014, 0, -22308, 0, -49356, 0, 35961, 0, 47168, 0, -38048, 0, 1890, 0, 9324, 0, -34970, 0, -6366, 0, -858, 0, 24088, 0, 27864, 0, -30960, 0, -5544, 0, 3564, 0, -42688, 0, 70920, 0, 14616, 0, 18000, 0, 58500, 0, 8736, 0, -35460, 0, -37048, 0, -1674, 0, 25228, 0, 29040, 0, -3132, 0, 2996, 0, -19336, 0, 7764, 0, -54520, 0, -70446, 0, 4248, 0, 11926, 0, 4508, 0, 8184, 0, 102960, 0, 4698, 0, -19338, 0, -12986, 0, 28056, 0, 3402, 0, -17972, 0, 10324, 0, -12702, 0, -5414, 0, 8568, 0, -33000, 0, 15666, 0, -24607, 0, -10908, 0, 14076, 0, -57496, 0, -35880, 0, -36812, 0, -2100, 0, 34626, 0, 26442, 0, 55176, 0, -12474, 0, 35240, 0, 37188, 0, 9744, 0, -34944, 0, -36472, 0, -13776, 0, -13824, 0, 25090, 0, -9558, 0, -17864, 0, 67080, 0, 35424, 0, -41400, 0, 21986, 0, -3018, 0, -15202, 0, -31500, 0, 1026, 0, 38324, 0, -27102, 0, -9504, 0, 66466, 0, 62176, 0, -1029, 0, 14292, 0, -13078, 0, -13608, 0, -7540, 0, -24832, 0, 13932, 0, -11522, 0, -72864, 0, 14358, 0, 16350, 0, -9744, 0, 4698, 0, -76464, 0, 8288, 0, 3906, 0, -57506, 0, -27264, 0, 50760, 0, 9240, 0, -60022, 0, 8190, 0, 88500, 0, -82784, 0, 33780, 0, 38280, 0, -38976, 0, 4815, 0, -9072, 0, -31144, 0, 5445, 0, 32732, 0, -49202, 0, -9612, 0, 35646, 0, 8050, 0, 8376, 0, 56948, 0, 135720, 0, 9018, 0, 64894, 0, -8184, 0, 9450, 0, 62928, 0, -28450, 0, 12354, 0, -47472, 0, -45628, 0, -11988, 0, 4116, 0, 52778, 0, -43500, 0, 20768, 0, 101160, 0, 25872, 0, 85280, 0, 2408, 0, 7128, 0, 35676, 0, 25488, 0, 19464, 0, 20216, 0, -62998, 0, 16632, 0, 72732, 0, 5336, 0, -11232, 0, 45284, 0, 24156, 0, 4218, 0, 16128, 0, -42872, 0, -32760, 0, -92336, 0, -53328, 0, -3852, 0, 37190, 0, -8169, 0, -57888, 0, 53172, 0, -83500, 0, 28134, 0, 30030, 0, 50904, 0, -5796, 0, -60984, 0, -39854, 0, 8670, 0, -36036, 0, 122200, 0, -12528, 0, -19194, 0, 25814, 0, -4374, 0, 24078, 0, -37800, 0, -46728, 0, -13528, 0, 9751, 0, -31746, 0, 67862, 0, 3520, 0, -20142, 0, -96048, 0, -48630, 0, 10836, 0, -23140, 0, 5016, 0, -35640, 0, 104000, 0, -64598, 0, 2700, 0, 27580, 0, -21384, 0, -28500, 0, -77404, 0, 12180, 0, 1794, 0, -66528, 0, -13790, 0, -12528, 0, -24048, 0, -60352, 0, -77610, 0, 34494, 0, 21216, 0, -1218, 0, -31844, 0, 99108, 0, 22968, 0, 12490, 0, -43868, 0, 11124, 0, -44604, 0, 48066, 0, 41118, 0, -30770, 0, -81248, 0, 40500, 0, -83868, 0, 40040, 0, 23184, 0, -10788, 0, -73368, 0, -24696, 0, 41976, 0, 1330, 0, 1323, 0, -89550, 0, -47080, 0, 7572, 0, -31944, 0, 29952, 0, -67716, 0, 3332, 0, 27376, 0, 14814, 0, -139360, 0, 106884, 0, -10890, 0, -86480, 0, 5474, 0, 44088, 0, -10656, 0, -43344, 0, -10656, 0, 16238, 0, 116000, 0, 21924, 0, 74604, 0, 74663, 0, 16158, 0, 5798, 0, -58608, 0, -10530, 0, 14462, 0, 32878, 0, 35298, 0, -94572, 0, 16376, 0, -30720, 0, -70296, 0, -5376, 0, 11664, 0, 34848, 0, -2272, 0, 18228, 0, 4872, 0, -61380, 0, 13776, 0, 12546, 0, -85800, 0, -10350, 0, 39816, 0, -80388, 0, -54912, 0, -12250, 0, -94352, 0, 54924, 0, 59908, 0, 73710, 0, -12150, 0, 14630, 0, 42084, 0, 19440, 0, -45708, 0, -18832, 0, -61596, 0, -215766, 0, -5600, 0, -5292, 0, 1092, 0, 43718, 0, -11340, 0, 33408, 0, -27020, 0, 12720, 0, -28336, 0, 38196, 0, -3096, 0, 6612, 0, 96680, 0, -53676, 0, -102684, 0, -29736, 0, 97500, 0, -86022, 0, -11604, 0, -21384, 0, 22880, 0, 91570, 0, 19740, 0, 65262, 0, -87696, 0, -13848, 0, -6164, 0, 98624, 0, -20736, 0, -52416, 0, -98472, 0, 11088, 0, -29472, 0, -163020, 0, 10044, 0, -118236, 0, -3528, 0, 10503, 0, -28652, 0, 11542, 0, -50214, 0, 13200, 0, 7284, 0, -3738, 0, -46584, 0, 112500, 0, 7452, 0, -55104, 0, -75512, 0, -25488, 0, 52780, 0, 2350, 0, -61248, 0, -24290, 0, -49104, 0, 24678, 0, -18960, 0, 24472, 0, 57186, 0, 116028, 0, -11648, 0, -36804, 0, -28372, 0, 35090, 0, -12537, 0, 60720, 0, 30392, 0, 28080, 0, -54132, 0, 76212, 0, -15333, 0, 39340, 0, 147264, 0, -13932, 0, 198000, 0, 45502, 0, 58116, 0, 84470, 0, 13874, 0, 65448, 0, -22172, 0, 103922, 0, -35460, 0, 10062, 0, 215280, 0, 6468, 0, 61140, 0, -89650, 0, -51126, 0, -77256, 0, -101628, 0, 17730, 0, 9394, 0, -78960, 0, 74844, 0, 29526, 0, 72424, 0, -10968, 0, 32400, 0, -58464, 0, 1566, 0, -27300, 0, 45936, 0, -69000, 0, 82656, 0, 26386, 0, -22512, 0, -52096, 0, 37192, 0, 57348, 0, 90660, 0, 65738, 0, 42114, 0, 19796, 0, -130544, 0, -72384, 0, 14952, 0, 42635, 0, -51480, 0, 18108, 0, -14014, 0, -54996, 0, 115368, 0, 90138, 0, -6156, 0, -39666, 0, 32748, 0, -1701, 0, -24824, 0, 57024, 0, -30138, 0, -69290, 0, 129000, 0, -17112, 0, 6174, 0, 24180, 0, -4284, 0, 21022, 0, -84800, 0, 50148, 0, -50600, 0, -37352, 0, 73830, 0, 56894, 0, -83592, 0, -7038, 0, 164256, 0, 116402, 0, -13860, 0, -86148, 0, 56000, 0, -59400, 0, -61360, 0, 37458, 0, -28188, 0, -8316, 0, -71984, 0, 55548, 0, -138944, 0, -23436, 0, -19872, 0, -14500, 0, -25872, 0, -18594, 0, -187060, 0, -114982, 0, 60114, 0, -129804, 0, 64832, 0, -49140, 0, 65500, 0, 31470, 0, 6912, 0, -15136, 0, -202680, 0, 7788, 0, 38542, 0, 8138, 0, -15570, 0, -28890, 0, 17400, 0, -17712, 0, 21756, 0, -17346, 0, -32670, 0, 90048, 0, 157560, 0, 19608, 0, -688, 0, 35422, 0, 15750, 0, 37152, 0, -3984, 0, -80736, 0, -50256, 0, -101376, 0, 14106, 0, -28532, 0, 19320, 0, -54108, 0, -71160, 0, 93549, 0, -25914, 0, 180180, 0, -56700, 0, -59028, 0, 51348, 0, -53630, 0, 6804, 0, -74124, 0, 98564, 0, -26334, 0, -39060, 0, 33026, 0, -2697, 0, 13358, 0, 72008, 0, 36432, 0, 41566, 0, 261000, 0, 138060, 0, -153874, 0, -4176, 0, 80160, 0, -155232, 0, -4144, 0, 38232, 0, 112182, 0, 120648, 0, -42768, 0, -129276, 0, 55440, 0, 8526, 0, -153870, 0, -116784, 0, -25380, 0, -17112, 0, -14820, 0, -5970, 0, -61292, 0, -154976, 0, -20868, 0, 109772, 0, 10478, 0, 67392, 0, 95468, 0, -36778, 0, -47952, 0, 164000, 0, -25308, 0, -68112, 0, -22394, 0, 15896, 0, 4536, 0, 196560, 0, 43424, 0, 19842, 0, 159300, 0, -68672, 0, 23112, 0, -23870, 0, -173360, 0, 4806, 0, -9018, 0, 213328, 0, -88092, 0, 55284, 0, 15484, 0, -9450, 0, -168804, 0, 109004, 0, -67860, 0, 86680, 0, 109266, 0, 34776, 0, 75510, 0, 96976, 0, -63000, 0, -59140, 0, -52020, 0, -31464, 0, 16366, 0, -162552, 0, 7656, 0, 75168, 0, -84526, 0, 25206, 0, 193024, 0, -83909, 0, 16119, 0, -71676, 0, 34674, 0, 23562, 0, -111504, 0, 280368, 0, -4410, 0, 49884, 0, -66700, 0, -50580, 0, 190476, 0, 105336, 0, -42732, 0, 14854, 0, 55622, 0, 120852, 0, -78650, 0, 235000, 0, -17838, 0, -114144, 0, -65016, 0, -78300, 0, 84398, 0, -127512, 0, 67260, 0, 131340, 0, 47232, 0, -8316, 0, 130250, 0, -40192, 0, -16200, 0, 116028, 0, -67310, 0, -130260, 0, -34104, 0, 171000, 0, -12078, 0, -92324, 0, -20944, 0, 59442, 0, -10764, 0, -20384, 0, -97704, 0, 107004, 0, -152614, 0, 75168, 0, -44500, 0, -19952, 0, 3906, 0, -34408, 0, 173160, 0, -47958, 0, -102454, 0, 180564, 0, 28944, 0, 7308, 0, 67306, 0, -18144, 0, -2354, 0, -88552, 0, -137808, 0, 10488, 0, -18116, 0, -25452, 0, 71706, 0, -66744, 0, 67320, 0, -102960, 0, 48354, 0, -9912, 0, -246708, 0, -90904, 0, 18018, 0, -133632, 0, -150300, 0, -149250, 0, -19096, 0, 171080, 0, 30792, 0, 182664, 0, -139104, 0, 2187, 0, 33792, 0, 45122, 0, 162240, 0, 148176, 0, -59740, 0, 27846, 0, 67680, 0, -193172, 0, -7938, 0, 161580, 0, 111473, 0, -86592, 0, 160350, 0, -45432, 0, 38376, 0, 29638, 0, -102626, 0, 48024, 0, 249546, 0, 55640, 0, 76932, 0, 17640, 0, 77000, 0, -88884, 0, -89626, 0, 108920, 0, 17820, 0, -32316, 0, 65340, 0, 25452, 0, 159036, 0, -134720, 0, -13584, 0, -264528, 0, -20532, 0, 10692, 0, 83720, 0, -12816, 0, 63936, 0, 178636, 0, -182938, 0, 93930, 0, -193522, 0, -80794, 0, 33264, 0, 187200, 0, 13202, 0, 49866, 0, -96948, 0, -169688, 0, 29106, 0, -268000, 0, -59290, 0, 63180, 0, -59150, 0, 55660, 0, -89784, 0, -22736, 0, -211788, 0, -29442, 0, -207050, 0, 81464, 0, -49554, 0, 184320, 0, 32144, 0, 23058, 0, 186912, 0, -15624, 0, -42984, 0, -228520, 0, 290940, 0, 22302, 0, -203834, 0, -109368, 0, 92184, 0, -133540, 0, -10318, 0, -124080, 0, -82656, 0, 51776, 0, -20250, 0, 60512, 0, 114260, 0, 62100, 0, -132730, 0, 7042, 0, 17580, 0, -39000, 0, 329472, 0, 36684, 0, 39648, 0, -153580, 0, -2394, 0, -122544, 0, 140874, 0, 10092, 0, -89242, 0, -197760, 0, 72900, 0, 22176, 0, 222214, 0, -46350, 0, 54942, 0, -116640, 0, 180960, 0, 65000, 0, 2401, 0, 33858, 0, 369576, 0, -165000, 0, 23496, 0, -145980, 0, 72864, 0, 31752, 0, 60098, 0, -172344, 0, -53442, 0, -118020, 0, 41790, 0, -80178, 0, -32508, 0, -331760, 0, -9156, 0, -76320, 0, 97382, 0, 5328, 0, 6662, 0, -33502, 0, 18576, 0, -191204, 0, -77184, 0, -114816, 0, -153824, 0, 322056, 0, -10962, 0, -79596, 0, -101808, 0, 71514, 0, -585000, 0, 156916, 0, 57408, 0, -9114, 0, 79402, 0, 78804, 0, -116162, 0, 232224, 0, -97668, 0, -27608, 0, -118440, 0, -99258, 0, -39376, 0, 208800, 0, 47286, 0, 83088, 0, -247280, 0, -19110, 0, 19372, 0, -141496, 0, 124416, 0, -116424, 0, -45356, 0, -5832, 0, -78820, 0, -66528, 0, 105744, 0, -87208, 0, 237162, 0, 114333, 0, -37014, 0, -11235, 0, 30690, 0, -113604, 0, -213980, 0, -63018, 0, 214656, 0, 208980, 0, -12705, 0, -50412, 0, 301284, 0, -19908, 0, -106050, 0, -237392, 0, -89208, 0, 22428, 0, 74414, 0, 26766, 0, -119828, 0, -59048, 0, -44712, 0, 153920, 0, -19544, 0, 84378, 0, -47520, 0, 93928, 0, 86748, 0, 129556, 0, -313500, 0, -21042, 0, 367488, 0, 44544, 0, -66924, 0, -209276, 0, -148430, 0, -148068, 0, -22050, 0, 9576, 0, 107883, 0, -205896, 0, -343116, 0, 141504, 0, 26446, 0, -28826, 0, -114144, 0, 220824, 0, -141462, 0, 5670, 0, 197078, 0, -24128, 0, 27972, 0, 332760, 0, -124432, 0, -104910, 0, 18138, 0, -168480, 0, -19098, 0, 101500, 0, 27600, 0, -2574, 0, 91998, 0, 21704, 0, 72264, 0, 88088, 0, -60368, 0, 83592, 0, -125742, 0, 102796, 0, -92880, 0, -194144, 0, -348696, 0, -16632, 0, 149500, 0, -244792, 0, 10692, 0, -241188, 0, -106486, 0, -128064, 0, -45416, 0, -248528, 0, 212760, 0, -117024, 0, -141550, 0, 43848, 0, 130862, 0, -38808, 0, 54000, 0, 21188, 0, -63012, 0, 175500, 0, 306756, 0, -81900, 0, 26208, 0, 131852, 0, -13846, 0, -106380, 0, 234784, 0, -161536, 0, -111144, 0, -9842, 0, -275814, 0, -5022, 0, -222682, 0, 92448, 0, 75684, 0, 65808, 0, 76440, 0, 87120, 0, 14894, 0, 246384, 0, -9396, 0, -219104, 0, -7798, 0, 8988, 0, 139026, 0, 414000, 0, -58008, 0, -90288, 0, 52272, 0, 23292, 0, 135072, 0, -55408, 0, -163560, 0, 44720, 0, 239424, 0, -211338, 0, 180606, 0, -65646, 0, 12744, 0, 50820, 0, -252684, 0, 35778, 0, -42954, 0, 229456, 0, 13524, 0, 434304, 0, 62062, 0, 24552, 0, 84146, 0, 33436, 0, 308880, 0, -20230, 0, 53623, 0, 14094, 0, -52500, 0, 329976, 0, -58014, 0, -187900, 0, 29232, 0, -38958, 0, 22686, 0, -242264, 0, 84168, 0, 151432, 0, -161278, 0, 10206, 0, -82386, 0, 299520, 0, -53916, 0, -66540, 0, 180828, 0, 30972, 0, 109032, 0, 77432, 0, -38106, 0, 102672, 0, -121686, 0, -16242, 0, -108626, 0, 74074, 0, 25704, 0, -26912, 0, -108928, 0, -99000, 0, -151710, 0, -111888, 0, 46998, 0, -140292, 0, 272896, 0, -73821, 0, -442980, 0, -225016, 0, -32724, 0, -25284, 0, 179344, 0, 42228, 0, 168478, 0, -202768, 0, -172488, 0, -189080, 0, 83160, 0, -107640, 0, 24230, 0, -313960, 0, -110436, 0, 356400, 0, -145294, 0, -6300, 0, 66528, 0, -379488, 0, 103878, 0, 123764, 0, 46500, 0, 79326, 0, 66500, 0, -333288, 0, 165528, 0, 302124, 0, -356460, 0, -37422, 0, 119232, 0, -4186, 0, 105720, 0, -325960, 0, 161938, 0, 111564, 0, -48354, 0, -261272, 0, 29232, 0, -91660, 0, -360684, 0, -104832, 0, 170946, 0, 182284, 0, -109416, 0, 181090, 0, -114956, 0, -41328, 0, 26048, 0, -105800, 0, -41472, 0, -118000, 0, 2842, 0, 75270, 0, 59452, 0, -46728, 0, -28674, 0, -133552, 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": "672.4.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], [-7], [0], [9], [0], [44], [0], [58], [0], [-54], [0], [-130], [0], [92], [0], [-21], [0], [84], [0], [199], [0], [27], [0], [-250], [0], [-72], [0], [132], [0], [126], [0], [-354], [0], [174], [0], [334], [0], [-416], [0], [-162], [0], [-464], [0], [49], [0], [-390], [0], [-450], [0], [-792], [0], [276], [0], [-516], [0], [58], [0], [-63], [0], [-1044], [0], [-656], [0], [252], [0], [-940], [0], [178], [0], [597], [0], [-308], [0], [1072], [0], [81], [0], [660], [0], [2340], [0], [-750], [0], [1254], [0], [-406], [0], [-216], [0], [-1656], [0], [210], [0], [396], [0]]}