# Stored data for newform 768.4.a.t, downloaded from the LMFDB on 20 April 2024.
{"label": "768.4.a.t", "space_label": "768.4.a", "level": 768, "weight": 4, "hecke_orbit": 20, "hecke_orbit_code": 85568392987149056, "dim": 3, "is_polredabs": true, "nf_label": "3.3.1436.1", "trace_hash": 195939022022451081, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [104, -164, -10, 1]], [7, [5816, -580, -14, 1]], [11, [49152, -2816, 0, 1]], [19, [-274752, -11088, -28, 1]]], "qexp_display": "q+3q^{3}+(3+\\beta _{2})q^{5}+(5-\\beta _{1})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": 12288, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 45.31346688440879, "hecke_ring_index": 32, "level_radical": 6, "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": [768, 1, [511, 517, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1436, "field_disc_factorization": [[2, 2], [359, 1]], "field_poly": [-12, -11, 0, 1], "hecke_ring_index_factorization": [[2, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "2.793", "prec": 17}, {"__RealLiteral__": 0, "data": "0.357", "prec": 17}, {"__RealLiteral__": 0, "data": "20.019", "prec": 20}, {"__RealLiteral__": 0, "data": "4.254", "prec": 17}, {"__RealLiteral__": 0, "data": "209.736", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "trace_display": [0, 9, 10, 14], "traces": [0, 3, 0, 9, 0, 10, 0, 14, 0, 27, 0, 0, 0, 52, 0, 30, 0, 26, 0, 28, 0, 42, 0, 164, 0, 53, 0, 81, 0, 174, 0, 318, 0, 0, 0, -92, 0, 296, 0, 156, 0, -118, 0, -260, 0, 90, 0, 204, 0, 327, 0, 78, 0, 1086, 0, 512, 0, 84, 0, 196, 0, 1536, 0, 126, 0, -872, 0, -660, 0, 492, 0, -852, 0, -478, 0, 159, 0, 2304, 0, 22, 0, 243, 0, 1136, 0, 2732, 0, 522, 0, 110, 0, -632, 0, 954, 0, -2552, 0, -1222, 0, 0, 0, 2830, 0, -662, 0, -276, 0, 756, 0, 2636, 0, 888, 0, 2574, 0, 824, 0, 468, 0, -3292, 0, 1639, 0, -354, 0, 3108, 0, -254, 0, -780, 0, -2380, 0, 3544, 0, 270, 0, -102, 0, 2180, 0, 612, 0, -3840, 0, 2276, 0, 981, 0, 2946, 0, 2206, 0, 234, 0, -3260, 0, 3352, 0, 3258, 0, -1816, 0, -2908, 0, 1536, 0, -4664, 0, -1679, 0, 252, 0, 3570, 0, 3746, 0, 588, 0, 2972, 0, 2524, 0, 4608, 0, 1328, 0, -1536, 0, 378, 0, -4856, 0, -4370, 0, -2616, 0, 1910, 0, 7226, 0, -1980, 0, 2700, 0, -820, 0, 1476, 0, 1536, 0, 10892, 0, -2556, 0, -6584, 0, -724, 0, -1434, 0, -4072, 0, 9522, 0, 477, 0, -7496, 0, -6764, 0, 6912, 0, 1478, 0, 4584, 0, 66, 0, -5376, 0, 2598, 0, 729, 0, -8382, 0, 5008, 0, 3408, 0, -1536, 0, -4608, 0, 8196, 0, -6090, 0, -12400, 0, 1566, 0, -7568, 0, -2108, 0, 330, 0, -10674, 0, 4082, 0, -1896, 0, 15360, 0, -6068, 0, 2862, 0, -9402, 0, -5444, 0, -7656, 0, -17788, 0, 8185, 0, -3666, 0, -6690, 0, 4920, 0, 0, 0, 4592, 0, -11624, 0, 8490, 0, 2688, 0, 12588, 0, -1986, 0, -17992, 0, 7974, 0, -828, 0, -6082, 0, 7168, 0, 2268, 0, -22456, 0, -15124, 0, 7908, 0, 7032, 0, 916, 0, 2664, 0, -21144, 0, -9958, 0, 7722, 0, -13056, 0, 52, 0, 2472, 0, -6520, 0, -12848, 0, 1404, 0, 9006, 0, -17880, 0, -9876, 0, -19444, 0, 2383, 0, 4917, 0, -13284, 0, 1742, 0, -1062, 0, 19500, 0, -4784, 0, 9324, 0, -3960, 0, -7996, 0, -762, 0, -19224, 0, 2560, 0, -2340, 0, -14422, 0, 8248, 0, -7140, 0, 5780, 0, -11872, 0, 10632, 0, -9750, 0, 20680, 0, 810, 0, -26880, 0, -10862, 0, -306, 0, -10520, 0, -2016, 0, 6540, 0, -11736, 0, -14564, 0, 1836, 0, 18550, 0, 19200, 0, -11520, 0, -10956, 0, -9078, 0, 6828, 0, -5296, 0, 21874, 0, 2943, 0, -16536, 0, -4924, 0, 8838, 0, -6054, 0, -35328, 0, 6618, 0, -14480, 0, -10926, 0, 702, 0, -2310, 0, 11002, 0, -9780, 0, 29752, 0, 3576, 0, 10056, 0, -32256, 0, -17596, 0, 9774, 0, 4460, 0, 17888, 0, -5448, 0, 9580, 0, -3402, 0, -8724, 0, 36076, 0, 7908, 0, 4608, 0, 8760, 0, 18564, 0, -13992, 0, 11964, 0, 28196, 0, -5037, 0, 11502, 0, 21748, 0, 756, 0, -38292, 0, 19968, 0, 10710, 0, 29202, 0, -4188, 0, 11238, 0, -18748, 0, -22373, 0, 1764, 0, 16472, 0, 7640, 0, 8916, 0, -12288, 0, 16828, 0, 7572, 0, 20840, 0, -8828, 0, 13824, 0, -4776, 0, -10596, 0, 3984, 0, 27234, 0, 23056, 0, -4608, 0, 22104, 0, 11652, 0, 1134, 0, -18294, 0, -12244, 0, -14568, 0, -4100, 0, 5890, 0, -13110, 0, 9824, 0, 17408, 0, -7848, 0, -23396, 0, 24472, 0, 5730, 0, 78, 0, 43064, 0, 21678, 0, 24524, 0, -5910, 0, -5940, 0, 14338, 0, -24254, 0, 8100, 0, -14256, 0, 28240, 0, -2460, 0, 33910, 0, 42204, 0, 4428, 0, 7340, 0, 11607, 0, 4608, 0, 32176, 0, -19258, 0, 32676, 0, 5180, 0, 30756, 0, -7668, 0, -45118, 0, -34012, 0, -19752, 0, -16044, 0, -14336, 0, -2172, 0, 33714, 0, 6744, 0, -4302, 0, 14340, 0, -6472, 0, -12216, 0, -44720, 0, 5736, 0, 28566, 0, 19200, 0, 19434, 0, 1431, 0, 39066, 0, -5532, 0, -22488, 0, 21520, 0, 29100, 0, -20292, 0, 21576, 0, 18676, 0, 20736, 0, -13384, 0, 30892, 0, 4434, 0, 7958, 0, -26848, 0, 13752, 0, -30644, 0, 56596, 0, 198, 0, 21800, 0, -32256, 0, -16128, 0, 12244, 0, -6556, 0, 7794, 0, 30978, 0, -16826, 0, 2187, 0, -15736, 0, 25972, 0, -25146, 0, -24576, 0, 19700, 0, 15024, 0, 19312, 0, -18500, 0, 10224, 0, 26568, 0, -40482, 0, -4608, 0, -10620, 0, 40068, 0, -13824, 0, -27806, 0, 16760, 0, 24588, 0, 2032, 0, -30562, 0, -18270, 0, -4010, 0, -55054, 0, -37200, 0, -33016, 0, -4608, 0, 4698, 0, 35152, 0, -84, 0, -22704, 0, 25836, 0, 21888, 0, -6324, 0, 29242, 0, 13032, 0, 990, 0, 24576, 0, 4016, 0, -32022, 0, 35562, 0, 27412, 0, 12246, 0, 31352, 0, 11056, 0, -5688, 0, -12818, 0, -14850, 0, 46080, 0, 2484, 0, -12532, 0, -18204, 0, -60654, 0, -40592, 0, 8586, 0, 83572, 0, -50819, 0, -28206, 0, -9522, 0, -74954, 0, -16332, 0, 43744, 0, -34296, 0, -22968, 0, -65094, 0, -18452, 0, -53364, 0, 61416, 0, -9508, 0, 24555, 0, -9984, 0, 38736, 0, -10998, 0, 61416, 0, 15776, 0, -20070, 0, 78502, 0, -55708, 0, 14760, 0, 8112, 0, 69972, 0, 0, 0, -9360, 0, -504, 0, 13776, 0, -7572, 0, -53820, 0, -34872, 0, 88648, 0, -53092, 0, 25470, 0, 52272, 0, -2560, 0, 8064, 0, -6328, 0, -27314, 0, 37764, 0, 17616, 0, -45800, 0, -5958, 0, -982, 0, 66540, 0, -53976, 0, 86016, 0, -37698, 0, 23922, 0, -101190, 0, 28024, 0, -2484, 0, -81108, 0, 2808, 0, -18246, 0, -63102, 0, 1264, 0, 21504, 0, 86052, 0, 2799, 0, 6804, 0, -53052, 0, -55782, 0, -67368, 0, -62976, 0, -52120, 0, -45372, 0, 55706, 0, 3072, 0, 23724, 0, 109936, 0, 43092, 0, 21096, 0, 6608, 0, -33858, 0, 2748, 0, 113356, 0, -5904, 0, 7992, 0, 78336, 0, 50168, 0, -63432, 0, 73368, 0, 13882, 0, -29874, 0, -39710, 0, 14632, 0, 23166, 0, 25964, 0, -93064, 0, -39168, 0, -76154, 0, -6040, 0, 156, 0, 40480, 0, -59714, 0, 7416, 0, -25344, 0, 21142, 0, -19560, 0, -16044, 0, -76800, 0, -38544, 0, -63690, 0, -10324, 0, 4212, 0, 46376, 0, 7916, 0, 27018, 0, -82318, 0, -31534, 0, -53640, 0, 27648, 0, 18392, 0, -29628, 0, -8688, 0, -114844, 0, -58332, 0, 32576, 0, -1008, 0, 7149, 0, -65816, 0, -9914, 0, 14751, 0, -32256, 0, -55884, 0, -39852, 0, 99766, 0, -90896, 0, 5226, 0, 93288, 0, -21040, 0, -3186, 0, -22014, 0, -50176, 0, 58500, 0, -11300, 0, 7396, 0, -14352, 0, -46640, 0, 147620, 0, 27972, 0, 11220, 0, -29490, 0, -11880, 0, -79104, 0, -150256, 0, -23988, 0, -132696, 0, -119896, 0, -2286, 0, -102440, 0, 68624, 0, -57672, 0, 1584, 0, 55926, 0, 7680, 0, 10952, 0, 52992, 0, -7020, 0, -110940, 0, -94060, 0, -43266, 0, 41680, 0, -14732, 0, 24744, 0, 74772, 0, 56320, 0, -21420, 0, -120662, 0, -56134, 0, 17340, 0, 153940, 0, -43452, 0, -35616, 0, 31926, 0, 9216, 0, 31896, 0, 33024, 0, -45390, 0, -29250, 0, -85804, 0, -123096, 0, 62040, 0, 63924, 0, -28940, 0, 2430, 0, -35026, 0, 30504, 0, -80640, 0, 12120, 0, -94575, 0, -32586, 0, 72666, 0, 111906, 0, -918, 0, 5344, 0, 48460, 0, -31560, 0, -122244, 0, 33792, 0, -6048, 0, -64488, 0, -4070, 0, 19620, 0, -2344, 0, -137728, 0, -35208, 0, 58312, 0, -62312, 0, -43692, 0, 27648, 0, -151784, 0, 5508, 0, 44324, 0, 120816, 0, 55650, 0, 64566, 0, -109302, 0, 57600, 0, -15144, 0, 37044, 0, -34560, 0, 201942, 0, -125332, 0, -32868, 0, 23264, 0, -76786, 0, -27234, 0, -87414, 0, 63522, 0, 20484, 0, 57396, 0, 35328, 0, -15888, 0, 36616, 0, 153376, 0, 65622, 0, 52468, 0, -1198, 0, 8829, 0, 8178, 0, -51978, 0, -49608, 0, -147456, 0, 72280, 0, -14772, 0, -227504, 0, 100248, 0, 26514, 0, 55828, 0, 129956, 0, -18162, 0, 107760, 0, -86356, 0, -105984, 0, -144804, 0, 33584, 0, 19854, 0, 31586, 0, 43512, 0, -43440, 0, -66488, 0, 27817, 0, -32778, 0, 31306, 0, 109568, 0, 2106, 0, 222044, 0, -59876, 0, -6930, 0, 96616, 0, 113640, 0, 33006, 0, -25296, 0, -33660, 0, -29340, 0, 154368, 0, 110578, 0, 89256, 0, 59904, 0, 82836, 0, 10728, 0, -27806, 0, -34016, 0, 30168, 0, -58424, 0, 5072, 0, -96768, 0, -21738, 0, -110726, 0, -52788, 0, -83680, 0, 64360, 0, 29322, 0, -10962, 0, 32120, 0, 13380, 0, 78956, 0, 38912, 0, 53664, 0, -9922, 0, 151922, 0, -16344, 0, 39996, 0, 120764, 0, 28740, 0, -43464, 0, -180556, 0, -10206, 0, 6144, 0, -38780, 0, -26172, 0, 21576, 0, 12394, 0, 108228, 0, 8924, 0, 126776, 0, 23724, 0, 169062, 0, -157316, 0, 13824, 0, -13236, 0, -12022, 0, 26280, 0, 82594, 0, -26848, 0, 55692, 0, -76736, 0, -55432, 0, -41976, 0, -51248, 0, 231936, 0, 35892, 0, 43028, 0, -44444, 0, 84588, 0, 179248, 0, 138342, 0, -15111, 0, -142712, 0, 46080, 0, 34506, 0, -165888, 0, 22228, 0, 65244, 0, -1560, 0, 63212, 0, 2268, 0, -49392, 0, 24454, 0, -114876, 0, -182800, 0, 74952, 0, 59904, 0, 35022, 0, -81520, 0, 32130, 0, -30668, 0, 63284, 0, 87606, 0, 92884, 0, 14166, 0, -12564, 0, 115356, 0, 84388, 0, 33714, 0, 54464, 0, 116228, 0, -56244, 0, -6552, 0, -223292, 0, -67119, 0, 105904, 0, 106016, 0, 5292, 0, 98304, 0, 195804, 0, 49416, 0, -8706, 0, -19640, 0, 22920, 0, -21420, 0, -111474, 0, 26748, 0, 160054, 0, 9968, 0, -36864, 0, 16412, 0, 55788, 0, 50484, 0, -16656, 0, -60964, 0, 22716, 0, -132196, 0, -72048, 0, 62520, 0, 153966, 0, -116224, 0, -26484, 0, 140556, 0, 36240, 0, 41472, 0, 70988, 0, -93640, 0, -14328, 0, -23912, 0, 28338, 0, -31788, 0, -40704, 0, 218650, 0, 11952, 0, -29076, 0, 68940, 0, 81702, 0, 188928, 0, -212364, 0, 69168, 0, -74088, 0, 41761, 0, -13824, 0, 107692, 0, 604, 0, 66312, 0, 46424, 0, 75688, 0, 34956, 0, 56130, 0, 160556, 0, 3402, 0, -90064, 0, -110080, 0, -54882, 0, 29834, 0, 9832, 0, -36732, 0, -117736, 0, 224804, 0, -43704, 0, -307306, 0, 38036, 0, -12300, 0, -165120, 0, 171424, 0, 17670, 0, 190210, 0, 310384, 0, -39330, 0, -58464, 0, -57872, 0, 29472, 0, 83680, 0, 43204, 0, 52224, 0, -215316, 0, 130078, 0, -23544, 0, 131328, 0, -102946, 0, -70188, 0, 190280, 0, -110268, 0, 73416, 0, 100992, 0, 172032, 0, 17190, 0, -144588, 0, 101606, 0, 234, 0, -176616, 0, -246478, 0, 129192, 0, -10360, 0, 173008, 0, 65034, 0, -130560, 0, -208024, 0, 73572, 0, -137988, 0, 45258, 0, -17730, 0, -124494, 0, 162032, 0, -17820, 0, 65932, 0, 24072, 0, 43014, 0, 22600, 0, -8808, 0, -72762, 0, -28116, 0, -52818, 0, 24300, 0, 3880, 0, 39858, 0, -42768, 0, 204324, 0, 76800, 0, 84720, 0, -43424, 0, -92984, 0, -7380, 0, -69892, 0, -8969, 0, 101730, 0, 86248, 0, -142360, 0, 126612, 0, -104448, 0, -254976, 0, 13284, 0, 99808, 0, -198540, 0, 22020, 0, -320120, 0, 12998, 0, 34821, 0, 52402, 0, 185806, 0, 13824, 0, -45876, 0, -99984, 0, 96528, 0, -76178, 0, 155904, 0, -57774, 0, -248776, 0, 8884, 0, 98028, 0, -52414, 0, 51712, 0, 15540, 0, -14756, 0, 53056, 0, 92268, 0, -92450, 0, -62160, 0, -23004, 0, -173864, 0, 13092, 0, -135354, 0, -112896, 0, -116568, 0, -102036, 0, -281452, 0, -50376, 0, -59256, 0, 165816, 0, 18808, 0, -48132, 0, -119688, 0, 132204, 0, -43008, 0, -51094, 0, 263298, 0, -6516, 0, 88720, 0, 203400, 0, 101142, 0, -34416, 0, 94536, 0, 20232, 0, -173412, 0, -53248, 0, -12906, 0, -151746, 0, 26074, 0, 43020, 0, 42648, 0, -329192, 0, -19416, 0, -184000, 0, -84580, 0, -36648, 0, -166656, 0, -266874, 0, -134160, 0, -8294, 0, -125082, 0, 17208, 0, 143332, 0, -202740, 0, 85698, 0, -2622, 0, 3500, 0, 57600, 0, 7408, 0, -203002, 0, 58302, 0, -148752, 0, 299658, 0, 4293, 0, 231904, 0, -89772, 0, 117198, 0, 22416, 0, 7680, 0, -16596, 0, -167964, 0, 92704, 0, -67464, 0, -210628, 0, -7640, 0, 64560, 0, -340884, 0, 14416, 0, 87300, 0, 232658, 0, -99144, 0, -60876, 0, -26520, 0, 76592, 0, 64728, 0, 72558, 0, -38800, 0, 56028, 0, -31472, 0, 137400, 0, 62208, 0, 19474, 0, -73460, 0, -40152, 0, -126776, 0, -1442, 0, 92676, 0, -137632, 0, 305968, 0, 13302, 0, 23940, 0, -374784, 0, 23874, 0, -222776, 0, 108876, 0, -80544, 0, -25356, 0, 137130, 0, 41256, 0, -38220, 0, -67216, 0, -91932, 0, -208896, 0, -19656, 0, 169788, 0, 180598, 0, 315300, 0, 594, 0, -105216, 0, 27286, 0, 65400, 0, -298642, 0, -241170, 0, -96768, 0, 33240, 0, -45192, 0, -48384, 0, -165094, 0, 281112, 0, 36732, 0, -108356, 0, 78234, 0, -19668, 0, -159796, 0, 499712, 0, 23382, 0, -69152, 0, -210396, 0, 92934, 0, -265168, 0, -230388, 0, -50478, 0, 132320, 0, -73888, 0, 6561, 0, 43776, 0, 13916, 0, -47208, 0, 130908, 0, -83272, 0, 77916, 0, 51960, 0, 126060, 0, -75438, 0, -82992, 0, -214269, 0, -73728, 0, -46142, 0, -141136, 0, 59100, 0, 139820, 0, -359796, 0, 45072, 0, -34238, 0, 57880, 0, 57936, 0, -67144, 0, 61952, 0, -55500, 0, 276362, 0, 489394, 0, 30672, 0, -166980, 0, -126420, 0, 79704, 0, 78840, 0, 20292, 0, -121446, 0, -104448, 0, 26496, 0, -13824, 0, -427696, 0, 17684, 0, -31860, 0, -100216, 0, -163512, 0, 120204, 0, 46774, 0, 46520, 0, -41472, 0, -135336, 0, 100546, 0, -83418, 0, -290372, 0, 32978, 0, 50280, 0, 8412, 0, 60824, 0, 73764, 0, -57166, 0, -203156, 0, 6096, 0, -71460, 0, 128972, 0, -91686, 0, -246090, 0, 286962, 0, -54810, 0, -84148, 0, 128008, 0, -12030, 0, 172032, 0, 242408, 0, -165162, 0, 98960, 0, 2700, 0, -111600, 0, -155122, 0, 94736, 0, -99048, 0, -85464, 0, -303388, 0, -13824, 0, -258288, 0, 158788, 0, 14094, 0, 15924, 0, -33392, 0, 105456, 0, 183630, 0, -254940, 0, -252, 0, 19576, 0, -291840, 0, -68112, 0, -29256, 0, -207028, 0, 77508, 0, 75600, 0, -46622, 0, 65664, 0, -430842, 0, 140026, 0, -18972, 0, 374784, 0, 38904, 0, 87726, 0, 280494, 0, -392536, 0, 39096, 0, -364208, 0, -202137, 0, 2970, 0, 45632, 0, 45920, 0, 73728, 0, 331068, 0, 103784, 0, 12048, 0, 134370, 0, 126776, 0, -96066, 0, -19960, 0, 142934, 0, 106686, 0, 24272, 0, -342528, 0, 82236, 0, -390316, 0, 64040, 0, 36738, 0, 391342, 0, -187616, 0, 94056, 0, 207224, 0, -34052, 0, 33168, 0, -48384, 0, 229992, 0, -17064, 0, -98744, 0, -4752, 0, -38454, 0, 282552, 0, -189100, 0, -44550, 0, -221652, 0, -63062, 0, 138240, 0, 244950, 0, -81504, 0, 7452, 0, 68320, 0, -209904, 0, -37596, 0, -100720, 0, 91704, 0, -54612, 0, 176568, 0, 31232, 0, -181962, 0, -214272, 0, -338890, 0, -121776, 0, 135184, 0, 105672, 0, 25758, 0, -72712, 0, 265224, 0, 250716, 0, -135936, 0, -301022, 0, -152457, 0, 99746, 0, 395462, 0, -84618, 0, 70656, 0, -84804, 0, -28566, 0, 20560, 0, 402868, 0, -224862, 0, 95680, 0, 125540, 0, -48996, 0, 304302, 0, 23286, 0, 131232, 0, -196968, 0, 344660, 0, -102888, 0, -290200, 0, -476160, 0, -68904, 0, -83964, 0, -15668, 0, -195282, 0, 176480, 0, -458586, 0, -55356, 0, 188024, 0, -6420, 0, -160092, 0, 199680, 0, -75176, 0, 184248, 0, -264616, 0, 313398, 0, -28524, 0, 255846, 0, 113064, 0, 73665, 0, -4536, 0, -158916, 0, -29952, 0, -344398, 0, 77344, 0, 116208, 0, 205944, 0, -177010, 0, -32994, 0, -413870, 0, -209664, 0, 184248, 0, -179040, 0, 482304, 0, 47328, 0, -144990, 0, 46328, 0, -60210, 0, 4560, 0, 19664, 0, 235506, 0, -76966, 0, -298834, 0, -167124, 0, -211968, 0, 142568, 0, 44280, 0, 223350, 0, 124916, 0, 24336, 0, 75656, 0, 214352, 0, 209916, 0, 386000, 0, 243758, 0, 0, 0, 166956, 0, 103484, 0, -28080, 0, -150000, 0, -14188, 0, -1512, 0, 146228, 0, -57450, 0, 41328, 0, 111090, 0, -271872, 0, -22716, 0, 104796, 0, -275856, 0, -161460, 0, -161144, 0, 245116, 0, -104616, 0, -148448, 0, 22082, 0, 265944, 0, 273408, 0, -446342, 0, -159276, 0, -299548, 0, 209044, 0, 76410, 0, -400606, 0, -70300, 0, 156816, 0, -55112, 0, -107216, 0, -7680, 0, 143010, 0, 82640, 0, 24192, 0, 46440, 0, 330944, 0, -18984, 0, -5982, 0, -241584, 0, -81942, 0, 54668, 0, 11776, 0, 113292, 0, 100616, 0, 65122, 0, 52848, 0, 433720, 0, -4080, 0, -137400, 0, 10938, 0, -376000, 0, -17874, 0, 254804, 0, -301060, 0, -2946, 0, 115446, 0, -154026, 0, 199620, 0, 282592, 0, 454924, 0, -161928, 0, 26538, 0, 118908, 0, 258048, 0, 245316, 0, 153829, 0, -113094, 0, -2268, 0, 389584, 0, 71766, 0, -496344, 0, -73136, 0, -303570, 0, 137634, 0, -104448, 0, 84072, 0, 137832, 0, -276526, 0, -7452, 0, 467506, 0, -317584, 0, -243324, 0, 148928, 0, 7884, 0, 8424, 0, 496128, 0, -283548, 0, -54738, 0, 558056, 0, 227730, 0, -189306, 0, 3654, 0, -590508, 0, 3792, 0, 147456, 0, 123672, 0, 64512, 0, 58494, 0, 76080, 0, 258156, 0, 113368, 0, 331632, 0, 8397, 0, -111012, 0, 574326, 0, 20412, 0, -81036, 0, 340992, 0, -159156, 0, -180070, 0, 275320, 0, -167346, 0, 241524, 0, -125120, 0, -202104, 0, 566370, 0, -54552, 0, -188928, 0, 36864, 0, 560936, 0, -156360, 0, -156200, 0, 102736, 0, -136116, 0, 65736, 0, 170252, 0, 167118, 0, 119568, 0, -312312, 0, 9216, 0, -164288, 0, -192036, 0, 71172, 0, -105008, 0, -365672, 0, 329808, 0, 104992, 0, -1530, 0, 129276, 0, 199430, 0, 338944, 0, 63288, 0, 70952, 0, 535812, 0, 19824, 0, 194030, 0, 183980, 0, -101574, 0, 444796, 0, 110512, 0, 8244, 0, -337152, 0, -325664, 0, 340068, 0, -225756, 0, 225792, 0, -17712, 0, -246756, 0, -17944, 0, 23976, 0, 142516, 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": "24.4.d.a", "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, 0], [1, 0, 0], [0, 0, 0], [3, 0, 0], [0, 0, 0], [3, 0, 1], [0, 0, 0], [5, -1, 0], [0, 0, 0], [9, 0, 0], [0, 0, 0], [0, -2, 2], [0, 0, 0], [18, 1, -3], [0, 0, 0], [9, 0, 3], [0, 0, 0], [6, 2, 6], [0, 0, 0], [12, -2, -6], [0, 0, 0], [15, -3, 0], [0, 0, 0], [54, 2, 0], [0, 0, 0], [15, -4, 12], [0, 0, 0], [27, 0, 0], [0, 0, 0], [57, -2, 5], [0, 0, 0], [109, 3, -12], [0, 0, 0], [0, -6, 6], [0, 0, 0], [-36, 2, 14], [0, 0, 0], [96, 11, -3], [0, 0, 0], [54, 3, -9], [0, 0, 0], [-42, 14, -6], [0, 0, 0], [-84, 10, -18], [0, 0, 0], [27, 0, 9], [0, 0, 0], [66, -6, 12], [0, 0, 0], [117, 0, -24], [0, 0, 0], [18, 6, 18], [0, 0, 0], [369, -10, -11], [0, 0, 0], [160, -4, 36], [0, 0, 0], [36, -6, -18], [0, 0, 0], [60, 8, 8], [0, 0, 0], [516, -9, -3], [0, 0, 0], [45, -9, 0], [0, 0, 0], [-288, 10, -18], [0, 0, 0], [-204, 0, -48], [0, 0, 0], [162, 6, 0], [0, 0, 0], [-270, -6, -36], [0, 0, 0], [-146, -16, -24], [0, 0, 0], [45, -12, 36], [0, 0, 0], [768, 20, -20], [0, 0, 0], [1, 7, 12], [0, 0, 0], [81, 0, 0], [0, 0, 0], [384, -2, -14], [0, 0, 0], [906, -28, 42], [0, 0, 0], [171, -6, 15], [0, 0, 0], [42, -4, -12], [0, 0, 0], [-192, -38, -18], [0, 0, 0], [327, 9, -36], [0, 0, 0], [-852, 28, -24], [0, 0, 0], [-418, -4, 36], [0, 0, 0], [0, -18, 18], [0, 0, 0]]}