# Stored data for newform 1344.4.a.bn, downloaded from the LMFDB on 28 March 2024. {"label": "1344.4.a.bn", "space_label": "1344.4.a", "level": 1344, "weight": 4, "hecke_orbit": 40, "hecke_orbit_code": 175640385534559552, "dim": 2, "is_polredabs": true, "nf_label": "2.2.44.1", "trace_hash": 680715810184997514, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-28, 8, 1]], [11, [-1672, 44, 1]]], "qexp_display": "q+3q^{3}+(-4+\\beta )q^{5}+7q^{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": 21504, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 79.29856704771538, "hecke_ring_index": 2, "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": [1344, 1, [127, 1093, 449, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 44, "field_disc_factorization": [[2, 2], [11, 1]], "field_poly": [-11, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "1.926", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.209", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "61.874", "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], [7, -1]], "trace_display": [0, 6, -8, 14], "traces": [0, 2, 0, 6, 0, -8, 0, 14, 0, 18, 0, -44, 0, 60, 0, -24, 0, 48, 0, -80, 0, 42, 0, 140, 0, -130, 0, 54, 0, 60, 0, 232, 0, -132, 0, -56, 0, 180, 0, 180, 0, -344, 0, 224, 0, -72, 0, 312, 0, 98, 0, 144, 0, 20, 0, 792, 0, -240, 0, -64, 0, -204, 0, 126, 0, 464, 0, -872, 0, 420, 0, 164, 0, 1500, 0, -390, 0, -308, 0, 1640, 0, 162, 0, -2200, 0, 952, 0, 180, 0, -264, 0, 420, 0, 696, 0, 496, 0, 2092, 0, -396, 0, 416, 0, 904, 0, -168, 0, 84, 0, -44, 0, 540, 0, 1460, 0, -824, 0, 540, 0, 336, 0, 2618, 0, -1032, 0, 816, 0, 1320, 0, 672, 0, -1912, 0, -560, 0, -216, 0, 1068, 0, -2392, 0, 936, 0, 3608, 0, -416, 0, 294, 0, 4980, 0, -624, 0, 432, 0, -752, 0, -252, 0, 60, 0, 980, 0, 280, 0, 2376, 0, 1352, 0, 3038, 0, -720, 0, 6704, 0, -910, 0, -192, 0, -3172, 0, -1300, 0, -612, 0, -3536, 0, 6952, 0, 378, 0, -6044, 0, 4420, 0, 1392, 0, 260, 0, -656, 0, -2616, 0, 420, 0, -1880, 0, 1260, 0, 2992, 0, 48, 0, 492, 0, -4416, 0, 1624, 0, 4500, 0, 10592, 0, 1712, 0, -1170, 0, 816, 0, -4132, 0, -924, 0, 3388, 0, -5648, 0, 4920, 0, -11284, 0, 11836, 0, 486, 0, -392, 0, -992, 0, -6600, 0, -880, 0, -4928, 0, 2856, 0, -4984, 0, 1260, 0, 540, 0, -6260, 0, 6256, 0, -792, 0, 3736, 0, -2328, 0, 1260, 0, -2068, 0, 8852, 0, 2088, 0, -2948, 0, 5696, 0, 1488, 0, -2408, 0, 6198, 0, 6276, 0, -8736, 0, -5904, 0, -1188, 0, 2088, 0, 1568, 0, 1248, 0, -1472, 0, 1744, 0, 2712, 0, -13112, 0, 2596, 0, -504, 0, 10932, 0, -2552, 0, 252, 0, 368, 0, -9532, 0, -132, 0, 2184, 0, 15456, 0, 1620, 0, 4016, 0, 15060, 0, 4380, 0, -3872, 0, 686, 0, -2472, 0, 2204, 0, -12124, 0, 1620, 0, 16288, 0, 9464, 0, 1008, 0, -2236, 0, -10166, 0, 7854, 0, -4064, 0, 4976, 0, -3096, 0, 140, 0, -4716, 0, 2448, 0, 392, 0, 7392, 0, 3960, 0, 12368, 0, 5544, 0, 2016, 0, 18924, 0, -72, 0, -5736, 0, -48, 0, 4388, 0, -1680, 0, -11732, 0, 8368, 0, -648, 0, -23672, 0, 14828, 0, 3204, 0, -448, 0, 5280, 0, -7176, 0, -3424, 0, -20204, 0, 2808, 0, -12272, 0, -1428, 0, 10824, 0, 724, 0, 13156, 0, -1248, 0, -6128, 0, 800, 0, 882, 0, -980, 0, 11880, 0, 14940, 0, -6028, 0, -15224, 0, -1872, 0, 3248, 0, -24780, 0, 1296, 0, -4128, 0, -5304, 0, -2256, 0, -13104, 0, -6104, 0, -756, 0, -29568, 0, 3792, 0, 180, 0, -9704, 0, -17128, 0, 2940, 0, -3264, 0, 18976, 0, 840, 0, -34948, 0, -848, 0, 7128, 0, 1148, 0, -1664, 0, 4056, 0, 1760, 0, -8792, 0, 9114, 0, 696, 0, 10500, 0, -2160, 0, -9072, 0, -37664, 0, 20112, 0, -7504, 0, 7144, 0, -2730, 0, 7856, 0, -13742, 0, -576, 0, -36368, 0, 16120, 0, -9516, 0, -2156, 0, 14020, 0, -3900, 0, -1232, 0, -23592, 0, -1836, 0, -2752, 0, 11480, 0, -10608, 0, 39156, 0, -21440, 0, 20856, 0, -21440, 0, -23088, 0, 1134, 0, 2348, 0, -22936, 0, -18132, 0, -6988, 0, 1524, 0, 13260, 0, -15400, 0, 43912, 0, 4176, 0, -11280, 0, -8928, 0, 780, 0, -19104, 0, 6664, 0, -1968, 0, -28908, 0, -9852, 0, -7848, 0, -37576, 0, 21248, 0, 1260, 0, -25840, 0, 21748, 0, -5640, 0, -8916, 0, -19288, 0, 3780, 0, -1848, 0, -918, 0, 8976, 0, -32288, 0, 14232, 0, 144, 0, -14608, 0, 2940, 0, 1476, 0, -27124, 0, 24896, 0, -13248, 0, -30248, 0, -41712, 0, 4872, 0, 12028, 0, 9760, 0, 13500, 0, -40908, 0, -19132, 0, 31776, 0, 3472, 0, 4728, 0, 5136, 0, -11528, 0, 2724, 0, -3510, 0, -14432, 0, 14644, 0, 2448, 0, -27300, 0, -1984, 0, -12396, 0, 51288, 0, 28824, 0, -2772, 0, -640, 0, -50584, 0, 10164, 0, 1292, 0, -12832, 0, -16944, 0, 2912, 0, -23292, 0, 14760, 0, 15712, 0, -11440, 0, -33852, 0, 27808, 0, 6328, 0, 35508, 0, -2492, 0, 25672, 0, 1458, 0, -40384, 0, 41804, 0, -1176, 0, 22880, 0, 8248, 0, -2976, 0, -3196, 0, -24848, 0, -19800, 0, 588, 0, 7296, 0, -2640, 0, 9184, 0, -5596, 0, -14784, 0, -56824, 0, -308, 0, 8568, 0, -51200, 0, 35108, 0, -14952, 0, -36976, 0, -16488, 0, 3780, 0, 7248, 0, 67232, 0, 1620, 0, 42368, 0, 7496, 0, -18780, 0, 10220, 0, -24424, 0, 18768, 0, -19568, 0, -49712, 0, -2376, 0, -19448, 0, -5768, 0, 11208, 0, -63308, 0, 45816, 0, -6984, 0, -43888, 0, -16000, 0, 3780, 0, -5084, 0, 12152, 0, -6204, 0, 5508, 0, -5460, 0, 26556, 0, 2352, 0, -14384, 0, 6264, 0, 6152, 0, -46626, 0, -8844, 0, 30088, 0, 18326, 0, 17088, 0, 21048, 0, 3892, 0, 4464, 0, 27080, 0, 78864, 0, -7224, 0, -9636, 0, -28664, 0, 18594, 0, 9504, 0, -21936, 0, 18828, 0, 5712, 0, 71172, 0, -26208, 0, 86768, 0, 5408, 0, -17712, 0, 1640, 0, 9240, 0, -3564, 0, -21280, 0, 25448, 0, 6264, 0, 6608, 0, 82848, 0, 4704, 0, -8176, 0, -21296, 0, 3744, 0, -19084, 0, 23760, 0, -4416, 0, -13384, 0, 30576, 0, 5232, 0, 85880, 0, 10828, 0, 8136, 0, 34984, 0, -3920, 0, -39336, 0, -38192, 0, -40236, 0, 7788, 0, 49864, 0, -14312, 0, -1512, 0, 56148, 0, 60488, 0, 32796, 0, 33524, 0, 12472, 0, -7656, 0, 7476, 0, -32318, 0, 756, 0, -17328, 0, -100344, 0, 1104, 0, 17368, 0, -16744, 0, -28596, 0, -356, 0, 81576, 0, -396, 0, -19088, 0, -19696, 0, 6552, 0, 26240, 0, -11184, 0, 46368, 0, -47008, 0, -11900, 0, 4860, 0, 25256, 0, -81616, 0, 12048, 0, 11872, 0, 16868, 0, 45180, 0, 1936, 0, -2912, 0, 13140, 0, 36740, 0, 22084, 0, -11616, 0, 48408, 0, 101296, 0, 2058, 0, -39628, 0, -51676, 0, -7416, 0, -34640, 0, -60336, 0, 6612, 0, 34860, 0, -40480, 0, -36372, 0, -22256, 0, -27672, 0, 4860, 0, 27264, 0, -4368, 0, 48864, 0, -35204, 0, 56376, 0, 28392, 0, -10296, 0, 35828, 0, 3024, 0, 11032, 0, 13600, 0, -6708, 0, -94160, 0, 35040, 0, -30498, 0, -5264, 0, 34920, 0, 23562, 0, -71640, 0, -17052, 0, -12192, 0, 17568, 0, -1764, 0, 14928, 0, 78076, 0, 8848, 0, -9288, 0, 33056, 0, -59048, 0, 420, 0, 67776, 0, 38948, 0, -14148, 0, -9760, 0, -76120, 0, 7344, 0, 6860, 0, -50204, 0, 1176, 0, -58080, 0, -48496, 0, 22176, 0, -14064, 0, 1960, 0, 11880, 0, -7056, 0, 15248, 0, 37104, 0, -10336, 0, 61004, 0, 16632, 0, 78672, 0, 3584, 0, 6048, 0, -114428, 0, 8800, 0, 56772, 0, 9464, 0, 27072, 0, -216, 0, 14920, 0, 113344, 0, -17208, 0, 56256, 0, 21266, 0, -144, 0, -43916, 0, -3808, 0, 13164, 0, -22352, 0, 58248, 0, -5040, 0, -8888, 0, 109668, 0, -35196, 0, -58080, 0, 135496, 0, 25104, 0, 46928, 0, 13844, 0, -1944, 0, 41688, 0, -17608, 0, -71016, 0, 105816, 0, -6370, 0, 44484, 0, 80580, 0, 38368, 0, 9612, 0, -18912, 0, 18764, 0, -1344, 0, 61168, 0, -152856, 0, 15840, 0, 13760, 0, -24388, 0, -21528, 0, -22204, 0, 9328, 0, -10272, 0, 99160, 0, 103592, 0, -60612, 0, 68640, 0, -9100, 0, 8424, 0, -46416, 0, 35936, 0, -36816, 0, 71328, 0, -37504, 0, -4284, 0, 16084, 0, 70888, 0, 32472, 0, 11076, 0, -124080, 0, 2172, 0, -24752, 0, -26716, 0, 39468, 0, 142280, 0, -133888, 0, -3744, 0, 103656, 0, 48664, 0, -18384, 0, -44544, 0, 31464, 0, 2400, 0, -50600, 0, 58980, 0, 2646, 0, -51988, 0, 90992, 0, -2940, 0, -188760, 0, 18944, 0, 35640, 0, -42308, 0, -16528, 0, 44820, 0, 124016, 0, -84552, 0, -18084, 0, 13680, 0, 30940, 0, -45672, 0, -13392, 0, 14000, 0, -5616, 0, 78368, 0, 18160, 0, 9744, 0, 46988, 0, 5006, 0, -74340, 0, 107644, 0, -115280, 0, 3888, 0, 1820, 0, -36540, 0, -12384, 0, -52656, 0, -56128, 0, -15912, 0, 134168, 0, -4592, 0, -6768, 0, -94336, 0, 23288, 0, -39312, 0, -7416, 0, -10912, 0, -18312, 0, -117820, 0, -98560, 0, -2268, 0, -27184, 0, -12584, 0, -88704, 0, 2940, 0, 68320, 0, 11376, 0, -114792, 0, 55156, 0, 540, 0, 80344, 0, -13160, 0, -29112, 0, 3196, 0, 56848, 0, -51384, 0, 30120, 0, -62808, 0, 8820, 0, 41388, 0, -133900, 0, -9792, 0, 27392, 0, -104992, 0, 56928, 0, 20944, 0, 79912, 0, 2520, 0, -94184, 0, -149008, 0, -104844, 0, 53440, 0, 336, 0, -2544, 0, -62044, 0, -62544, 0, 21384, 0, 126016, 0, 63372, 0, 3444, 0, -43404, 0, 33008, 0, -4992, 0, 83196, 0, -52576, 0, 12168, 0, -30912, 0, -7480, 0, 5280, 0, 82176, 0, 134376, 0, -26376, 0, 73232, 0, 11368, 0, 27342, 0, -6484, 0, 31564, 0, 2088, 0, -18832, 0, 144632, 0, 31500, 0, 118512, 0, -12072, 0, -6480, 0, -62624, 0, 83440, 0, -27216, 0, 74144, 0, -143388, 0, -112992, 0, -74760, 0, 17072, 0, 60336, 0, 65816, 0, 11984, 0, -22512, 0, -104720, 0, 43096, 0, 21432, 0, -38352, 0, -138292, 0, -8190, 0, 80960, 0, -108088, 0, 23568, 0, 52428, 0, -46192, 0, -41226, 0, 5712, 0, 132800, 0, -1728, 0, 32560, 0, 25860, 0, -109104, 0, -14496, 0, -28924, 0, 48360, 0, -62972, 0, -80004, 0, -28548, 0, 39584, 0, -43008, 0, -6468, 0, 150308, 0, -166012, 0, 42060, 0, -86752, 0, -21360, 0, -11700, 0, 23716, 0, -18880, 0, -3696, 0, 127376, 0, -144056, 0, -70776, 0, 14992, 0, -39536, 0, -5508, 0, 116560, 0, -35024, 0, -8256, 0, -65344, 0, 66852, 0, 34440, 0, 60544, 0, 166296, 0, -31824, 0, -98564, 0, -39604, 0, 117468, 0, -78988, 0, 52456, 0, -64320, 0, 99192, 0, 41798, 0, 62568, 0, -69040, 0, 82852, 0, -64320, 0, 32208, 0, -50828, 0, -69264, 0, -117568, 0, 249944, 0, 3402, 0, -40464, 0, 83072, 0, 7044, 0, -35836, 0, 10400, 0, -68808, 0, -2744, 0, -82680, 0, -54396, 0, 6272, 0, -58104, 0, -20964, 0, 295064, 0, -6944, 0, 4572, 0, 20412, 0, -107640, 0, 39780, 0, 168880, 0, -60940, 0, -46200, 0, 39872, 0, 3056, 0, 131736, 0, -49232, 0, -114724, 0, 12528, 0, -6160, 0, -29040, 0, -33840, 0, 91712, 0, -109064, 0, -26784, 0, -1544, 0, -34496, 0, 2340, 0, -91620, 0, 123004, 0, -57312, 0, 50344, 0, 15448, 0, 19992, 0, 149524, 0, -230492, 0, -5904, 0, -305536, 0, -9448, 0, -86724, 0, -34888, 0, 6068, 0, -29556, 0, 26584, 0, -153424, 0, -23544, 0, -56016, 0, 8820, 0, -112728, 0, 95264, 0, 215944, 0, 63744, 0, -41568, 0, -112988, 0, 3780, 0, -19744, 0, -78888, 0, -77520, 0, 85696, 0, -92576, 0, 65244, 0, -43820, 0, -73472, 0, -16920, 0, -25232, 0, 6874, 0, -26748, 0, -19360, 0, 43792, 0, -57864, 0, 228844, 0, 90276, 0, 11340, 0, 79408, 0, 70760, 0, -5544, 0, 25716, 0, 109700, 0, -2754, 0, 52484, 0, -7528, 0, 26928, 0, 26152, 0, 14272, 0, -96864, 0, -235896, 0, -28240, 0, 42696, 0, -128832, 0, -16296, 0, 432, 0, -265372, 0, -160424, 0, -43824, 0, -30808, 0, -143440, 0, 8820, 0, 54732, 0, -146624, 0, 4428, 0, -30896, 0, -189184, 0, -81372, 0, -14476, 0, 109136, 0, 74688, 0, 133040, 0, -12860, 0, -39744, 0, 109976, 0, 61964, 0, -90744, 0, -27216, 0, -120224, 0, -125136, 0, 147440, 0, -234016, 0, 14616, 0, 74032, 0, -47072, 0, 36084, 0, -200952, 0, 34784, 0, 29280, 0, -20636, 0, 159104, 0, 40500, 0, -23368, 0, -158696, 0, -122724, 0, 74048, 0, 39872, 0, -57396, 0, -92352, 0, 90056, 0, 95328, 0, -65032, 0, 6452, 0, 10416, 0, 102860, 0, 4136, 0, 14184, 0, -218908, 0, 69984, 0, 15408, 0, -16856, 0, -179640, 0, -34584, 0, 53472, 0, -119244, 0, 8172, 0, 210944, 0, 43386, 0, -10530, 0, 194172, 0, -118980, 0, -43296, 0, 29552, 0, 212080, 0, 43932, 0, -168540, 0, 323320, 0, 7344, 0, -16544, 0, -50952, 0, -81900, 0, -61152, 0, -41548, 0, -5952, 0, -289520, 0, -15320, 0, -37188, 0, 168096, 0, -41328, 0, 153864, 0, -152164, 0, -1056, 0, 86472, 0, 171160, 0, -100096, 0, -8316, 0, -44948, 0, -119280, 0, -1920, 0, 41228, 0, -39844, 0, -151752, 0, 14616, 0, 105744, 0, 30492, 0, 171576, 0, 51040, 0, 3876, 0, 105104, 0, 10976, 0, -38496, 0, 151324, 0, -185812, 0, -50832, 0, 41128, 0, -333744, 0, 8736, 0, -94776, 0, -161168, 0, -69876, 0, -247764, 0, -180688, 0, 44280, 0, -10304, 0, 19508, 0, 47136, 0, -59312, 0, -166096, 0, -34320, 0, -92896, 0, 12208, 0, -101556, 0, 34292, 0, 102968, 0, 83424, 0, -89584, 0, 165964, 0, 18984, 0, 30800, 0, -136312, 0, 106524, 0, -31248, 0, -237872, 0, -7476, 0, -91784, 0, 18760, 0, 77016, 0, 191360, 0, 47392, 0, 4374, 0, -332992, 0, 18172, 0, -121152, 0, -2144, 0, 297240, 0, 125412, 0, 39264, 0, 80848, 0, -3528, 0, 229876, 0, 61026, 0, 68640, 0, -12436, 0, 62088, 0, 24744, 0, 76524, 0, -94300, 0, -8928, 0, -69432, 0, -18432, 0, -9588, 0, 131128, 0, -17864, 0, -74544, 0, -122148, 0, -148936, 0, -59400, 0, -100448, 0, -7920, 0, 1764, 0, 186336, 0, -219016, 0, 21888, 0, 26576, 0, 54856, 0, -7920, 0, 2576, 0, 177872, 0, 27552, 0, 120464, 0, 30596, 0, -16788, 0, -283864, 0, -66724, 0, -44352, 0, -251200, 0, -9236, 0, -170472, 0, 136432, 0, -196808, 0, -924, 0, 36176, 0, -102124, 0, 25704, 0, 292572, 0, -158928, 0, -153600, 0, 15288, 0, -104664, 0, 105324, 0, 57304, 0, 264224, 0, -44856, 0, -174320, 0, 108192, 0, -110928, 0, 191136, 0, 50504, 0, -49464, 0, 6920, 0, 55376, 0, 11340, 0, -377204, 0, -3376, 0, 21744, 0, 76868, 0, 107580, 0, 201696, 0, 28112, 0, -300896, 0, 4860, 0, 44944, 0, -146008, 0, 127104, 0, -128384, 0, 105420, 0, 22488, 0, -190112, 0, 264704, 0, -56340, 0, 79648, 0, 203856, 0, 30660, 0, -60448, 0, 130740, 0, -73272, 0, -135324, 0, -1536, 0, 56304, 0, -27104, 0, 44852, 0, -58704, 0, -145008, 0, 66800, 0, -149136, 0, 195072, 0, 4802, 0, -7128, 0, 47392, 0, -58960, 0, -58344, 0, 178840, 0, -71456, 0, -17304, 0, 26388, 0, 238928, 0, 33624, 0, 86308, 0, -176812, 0, -189924, 0, 15428, 0, 125488, 0, 137448, 0, 23360, 0, 330420, 0, -20952, 0, 306056, 0, -84868, 0, -131664, 0, 26228, 0, 203264, 0, -48000, 0, 484704, 0, 122280, 0, 11340, 0, 284900, 0, -43488, 0, -15252, 0, 33488, 0, -181960, 0, 36456, 0, 114016, 0, -30924, 0, -18612, 0, -217048, 0, -95376, 0, 16524, 0, -274952, 0, 66248, 0, -16380, 0, 80704, 0, -313680, 0, 79668, 0, 16864, 0, -334576, 0, 7056, 0, 119744, 0, 285016, 0, -43152, 0, 1144, 0, 135416, 0, 18792, 0, -15652, 0, -88000, 0, 18456, 0, -74184, 0, 58612, 0, -139878, 0, 29984, 0, -71162, 0, -26532, 0, 73532, 0, 55456, 0, 90264, 0, 239232, 0, 90336, 0, 54978, 0, 96468, 0, 50808, 0, 51264, 0, -82348, 0, -4728, 0, 63144, 0, -28448, 0, 87716, 0, 11676, 0, -141448, 0, 81928, 0, 13392, 0, 71968, 0, 34832, 0, 81240, 0, -262240, 0, -15112, 0, 236592, 0, -122104, 0, -29568, 0, -21672, 0, 343552, 0, -416736, 0, -28908, 0, -85380, 0, -442060, 0, -85992, 0, 980, 0, 153944, 0, 55782, 0, -38144, 0, -123368, 0, 28512, 0, 252784, 0, -33012, 0, -65808, 0, -117280, 0, -33268, 0, 56484, 0, 296512, 0, 68672, 0, 17136, 0, -309080, 0, 340032, 0, 213516, 0, -396332, 0, 105504, 0, -78624, 0, 2744, 0, 75264, 0, 260304, 0, 18008, 0, 218656, 0, 16224, 0, -335544, 0, 51744, 0, -53136, 0, 213332, 0, -95368, 0, 4920, 0, 122000, 0, -73296, 0, 27720, 0, 531632, 0, 329248, 0, -10692, 0, -137108, 0, 206812, 0, -63840, 0, 86576, 0, -225048, 0, 76344, 0, 53912, 0, -13996, 0, 18792, 0, 86360, 0, 38808, 0, 19824, 0, 80788, 0, 73048, 0, 248544, 0, -78960, 0, 306208, 0, 14112, 0, -103500, 0, -13788, 0, -24528, 0, -138336, 0, -63600, 0, -63888, 0, 132468, 0, 14124, 0, 11232, 0, 87520, 0, -4216, 0, -57252, 0, 237456, 0, -504, 0, 71280, 0, -10692, 0, 221088, 0, -13248, 0, 130448, 0, -72668, 0, -40152, 0, -131852, 0, 23328, 0, 91728, 0, -8976, 0, 60016, 0, 15696, 0, -336, 0, 33112, 0, 257640, 0, -549264, 0, 298016, 0, 32484, 0, 31784, 0, 30716, 0, 24408, 0, 264572, 0, -131632, 0, 104952, 0, 317128, 0, 49376, 0, -11760, 0, 59008, 0, 365156, 0, -118008, 0, 221268, 0, -237432, 0, -114576, 0, -82124, 0, 158638, 0, -120708, 0, 52552, 0, -8048, 0, 23364, 0, 185728, 0, 58576, 0, 149592, 0, 43084, 0, 466312, 0, -42936, 0, -209056, 0, -95692, 0, -4536, 0, 47468, 0, -84240, 0, 168444, 0, 142140, 0, -102144, 0, 181464, 0, -165704, 0, 2448, 0, 98388, 0, 66224, 0, -70716, 0, 100572, 0, -3672, 0, 103796, 0, 37416, 0, 82576, 0, 38336, 0, -22968, 0, 622032, 0, 98832, 0, 22428, 0, -17428, 0, -118784, 0, -96954, 0, -127536, 0, 267960, 0, 2268, 0, -3136, 0, 182688, 0, -51984, 0, 456064, 0, 648352, 0, -301032, 0, -143944, 0, 36960, 0, 3312, 0, -281044, 0, -402648, 0, 52104, 0, -308880, 0, -111660, 0, -50232, 0, 120384, 0, -60784, 0, -85788, 0, 31828, 0, 26736, 0, -1068, 0, -23968, 0, -196176, 0, 244728, 0, -43432, 0, 136872, 0, -1188, 0, 49088, 0, -141428, 0, -57264, 0, -337376, 0, -15628, 0, -59088, 0, 348608, 0, -569448, 0, 19656, 0, -266612, 0, 147960, 0, 78720, 0, -27796, 0, 185752, 0, -33552, 0, -85904, 0, -312632, 0, 139104, 0, -107712, 0, 92800, 0, -141024, 0, 38032, 0, -9996, 0, -35700, 0, -329632, 0, -56936, 0, 14580, 0, -280344, 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.g", "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], [-4, 1], [0, 0], [7, 0], [0, 0], [9, 0], [0, 0], [-22, 7], [0, 0], [30, 8], [0, 0], [-12, 3], [0, 0], [24, 13], [0, 0], [-40, 2], [0, 0], [21, 0], [0, 0], [70, -3], [0, 0], [-65, -8], [0, 0], [27, 0], [0, 0], [30, -2], [0, 0], [116, 2], [0, 0], [-66, 21], [0, 0], [-28, 7], [0, 0], [90, -32], [0, 0], [90, 24], [0, 0], [-172, -37], [0, 0], [112, -40], [0, 0], [-36, 9], [0, 0], [156, -50], [0, 0], [49, 0], [0, 0], [72, 39], [0, 0], [10, 72], [0, 0], [396, -50], [0, 0], [-120, 6], [0, 0], [-32, -70], [0, 0], [-102, -26], [0, 0], [63, 0], [0, 0], [232, -2], [0, 0], [-436, 6], [0, 0], [210, -9], [0, 0], [82, 115], [0, 0], [750, 22], [0, 0], [-195, -24], [0, 0], [-154, 49], [0, 0], [820, 74], [0, 0], [81, 0], [0, 0], [-1100, -40], [0, 0], [476, -28], [0, 0], [90, -6], [0, 0], [-132, 123], [0, 0], [210, 56], [0, 0], [348, 6], [0, 0], [248, -48], [0, 0], [1046, 58], [0, 0], [-198, 63], [0, 0]]}