# Stored data for newform 294.4.a.k, downloaded from the LMFDB on 18 April 2024.
{"label": "294.4.a.k", "space_label": "294.4.a", "level": 294, "weight": 4, "hecke_orbit": 11, "hecke_orbit_code": 45035996340814118, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 1063611609885682579, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-62, 12, 1]], [11, [-3524, 4, 1]]], "qexp_display": "q-2q^{2}+3q^{3}+4q^{4}+(-6+\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 4704, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 17.34656154168774, "hecke_ring_index": 7, "level_radical": 42, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "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": [294, 1, [197, 199], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [[7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.420", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.392", "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": [-4, 6, -12, 0], "traces": [0, 2, -4, 6, 8, -12, -12, 0, -16, 18, 24, -4, 24, -48, 0, -36, 32, -84, -36, 72, -48, 0, 8, -308, -48, 18, 96, 54, 0, -80, 72, -384, -64, -12, 168, 0, 72, 536, -144, -144, 96, -756, 0, 400, -16, -108, 616, -312, 96, 0, -36, -252, -192, -52, -108, -1152, 0, 216, 160, -864, -144, -1416, 768, 0, 128, -300, 24, 144, -336, -924, 0, -1524, -144, -744, -1072, 54, 288, 0, 288, 976, -192, 162, 1512, 312, 0, 700, -800, -240, 32, -108, 216, 0, -1232, -1152, 624, -40, -192, 744, 0, -36, 72, 1236, 504, 192, 384, 0, 104, -908, 216, 1568, 2304, 1608, 0, 1932, -432, 3024, -320, -432, 1728, 0, 288, 4402, 2832, -2268, -1536, -960, 0, -1432, -256, 1200, 600, 120, -48, 0, -288, -324, 672, 648, 1848, 24, 0, -936, 3048, 3624, 288, 4008, 1488, 0, 2144, -2308, -108, 2008, -576, -756, 0, 3480, -576, -24, -1952, -156, 384, 0, -324, -2416, -3024, -3456, -624, 2760, 0, -1478, -1400, 648, 1600, -2004, 480, 0, -64, -2592, 216, 1188, -432, 432, 0, -4248, 2464, -5568, 2304, -1008, -1248, 0, 80, 2380, 384, -1916, -1488, -900, 0, 628, 72, 2304, -144, 432, -2472, 0, -1008, 3556, -384, -2772, -768, -2496, 0, 1512, -208, -4572, 1816, 2304, -432, 0, -3136, -2232, -4608, 1428, -3216, 3216, 0, 162, -3864, 4080, 864, -6144, -6048, 0, 640, 72, 864, 3832, -3456, 2928, 0, 2556, -576, -10968, -8804, 486, -5664, 0, 4536, -2904, 3072, 936, 1920, 2256, 0, -6440, 2864, 2100, 512, 3420, -2400, 0, -1200, -720, -240, 6084, 96, -4392, 0, -324, 576, -13860, 648, -912, -1344, 0, -1296, 14076, -3696, -6460, -48, -3456, 0, 8552, 1872, -1176, -6096, -120, -7248, 0, -576, -6102, -8016, 2232, -2976, 3588, 0, 4792, -4288, -108, 4616, 3864, 216, 0, -4016, 3708, 1152, 11044, 1512, 7320, 0, 576, -6960, 6024, 1152, 16896, 48, 0, 3904, -7132, 312, -21008, -768, -2724, 0, -2632, 648, 6624, 4832, 4704, 6048, 0, 6912, -88, 1248, 4824, -5520, 3840, 0, -1568, 2956, 5796, 2800, -6288, -1296, 0, -3200, 9072, 4008, 6060, -960, -10104, 0, -1296, 128, 10980, 5184, 3264, -432, 0, -2376, -2428, 864, -10342, -864, 13206, 0, -11804, 8496, 6816, -4928, -6804, 11136, 0, -4608, -4924, 2016, -2880, 2496, -8664, 0, -9448, -160, -4296, -4760, 5808, -768, 0, 3832, 3600, 2976, 2416, 1800, 14112, 0, 360, -1256, 10608, -144, -16392, -4608, 0, 288, -7128, -864, 5688, 4944, -972, 0, 13040, 2016, -5736, -7112, 1944, 768, 0, 5544, -28528, 1536, 72, 4992, 4032, 0, 2868, -3024, -2808, 416, -3108, 9144, 0, -3632, 10872, -4608, 9756, 864, 3120, 0, 12024, 6272, -8736, 4464, -8400, 9216, 0, -2856, 5188, 6432, 6332, -6432, -6924, 0, -13332, -324, 7392, 7728, 6024, -8160, 0, -1728, 9180, 12288, -2268, 12096, 2124, 0, 5336, -1280, 10440, -144, -11232, -1728, 0, -7664, -72, 6912, -29024, -5856, -4056, 0, -468, -5112, -6744, 1152, -5808, 21936, 0, 17608, 20036, -972, -18264, 11328, -7248, 0, -276, -9072, 6888, 5808, -10368, -6144, 0, -1872, -6656, -3840, 8280, -4512, 8592, 0, 9636, 12880, -4434, -5728, -6708, -4200, 0, -1024, 1944, -6840, 19624, 4800, -11136, 0, -6012, 2400, -108, 1440, 23928, 480, 0, -12168, 17304, -192, 30154, 8784, -7776, 0, 21084, 648, 23088, -1152, 3564, 27720, 0, -1296, -27028, 1824, 1296, 2688, -28224, 0, -13144, 2592, -12744, -28152, 4176, 7392, 0, 12920, -16704, 96, -8796, 6912, -23712, 0, -3024, -17104, 10944, -3744, -21000, 2352, 0, 12192, -1768, 240, 10088, 14496, 7140, 0, -16884, 1152, -45264, 12204, -5748, 16032, 0, -4464, 28328, 5952, -2700, -7176, -11424, 0, -11472, -9584, 1884, 8576, 30396, 216, 0, -9232, 6912, -7728, -25652, -432, 4080, 0, 1296, 8032, -21708, -7416, 19152, -2304, 0, -22088, 1608, -3024, -15696, -14640, 10668, 0, -8440, -1152, -17256, 13920, -8316, -12048, 0, -2304, -5114, -33792, -7488, -96, -24864, 0, -13832, -7808, 4536, 14264, -29040, -624, 0, 42016, -13716, 1536, 5416, 5448, -24936, 0, 6912, 5264, -27912, -1296, 4080, -13248, 0, -9664, -51984, -9408, -5424, -12096, -6696, 0, 38172, -13824, -34776, 176, 4284, -2496, 0, -9648, 33488, 11040, 9648, -7680, -12456, 0, 17544, 3136, 486, -5912, -25236, -11592, 0, -5600, 12240, 12576, 15300, 2592, -9768, 0, -18432, 6400, 15360, -18144, -37944, -8016, 0, -12120, 17888, 1920, 30772, 20208, 216, 0, 14208, 2592, 14592, -256, 11496, -21960, 0, -10368, 56912, -6528, 8784, 864, 66192, 0, 7656, 4752, 7668, 4856, -24960, -1728, 0, 20684, -32904, 1728, -43056, -26412, 32016, 0, 1458, 23608, -12096, -16992, 15216, -13632, 0, 9856, -28512, 13608, -6768, -22272, -8712, 0, -51604, 9216, 51480, 9848, 2808, -4032, 0, 5760, -5936, -4992, 6768, 17328, 9120, 0, 37792, 18896, -19320, 320, 10452, 8592, 0, 9520, 6300, -11616, 21912, 1536, 40176, 0, 10260, -7664, -1812, -7200, -17568, -5952, 0, -4832, -29176, -3600, 38328, -28224, -2160, 0, -30628, -720, -14232, 2512, 18252, -21216, 0, 288, 26340, 32784, -13176, 9216, 8676, 0, 15064, -576, -972, 14256, 99096, 1728, 0, -11376, -41580, -9888, -58268, 1944, 45384, 0, -2736, -26080, 40368, -4032, 23808, 11472, 0, 14224, -15804, -3888, 40784, -1536, 42228, 0, 18804, -11088, 20304, 57056, -19380, -3072, 0, -144, 296, -9984, -10368, -8064, -37080, 0, 17926, -5736, 25656, 6048, 37092, 5616, 0, -832, -3528, 6216, -96656, -18288, -1464, 0, -360, 7264, 53844, -21744, -6024, 9216, 0, -19512, 34492, -1728, -9732, -6240, -18306, 0, -100736, -24048, -17568, -12544, 6696, 17472, 0, -8928, 59824, 16800, 10764, -18432, 57132, 0, -33200, 5712, 14376, -10376, -5448, -12864, 0, -12664, -324, 12864, -7312, 13848, 15216, 0, 11592, 26664, 36528, 648, -2520, -14784, 0, -15456, -39636, -12048, 35120, 16320, 11124, 0, -6260, 3456, 159312, -18360, 33132, -24576, 0, 4536, -42136, -24192, 21960, -4248, 54216, 0, 33048, -10672, 1728, 2560, -30636, -20880, 0, 288, 18072, 22464, 55048, 3456, -34272, 0, 50688, 15328, 7212, 144, 110544, -13824, 0, 58048, 8148, 11712, 66660, 8112, -21396, 0, 9956, 936, -57792, 10224, -63024, 13488, 0, -2304, 21202, 11616, -8172, -43872, 30312, 0, 57720, -35216, -7896, -40072, -37896, 1944, 0, 36528, 19872, -22656, -35112, 14496, -33888, 0, 14112, 552, -52368, 18144, 43272, -13776, 0, -11616, -33376, 20736, -42104, 12288, -264, 0, -53808, 3744, -69048, 13312, 14472, 7680, 0, -16560, 35896, 9024, 11520, -17184, -11280, 0, -54292, -19272, -4704, -25760, -16668, 8868, 0, 11456, 17388, 13416, 51780, 8400, 29208, 0, -18864, 2048, 4956, -3888, -72816, 13680, 0, -39248, 58476, -9600, 2840, 22272, 27216, 0, 62020, 12024, -89088, -4800, 18180, 216, 0, -2880, -28144, -47856, -30312, -960, -24204, 0, -8088, 24336, -3888, -34608, -20832, 384, 0, -60308, 32940, -17568, -18528, 15552, 27360, 0, 9792, -42168, -148488, -1296, -24408, -46176, 0, 2304, -63776, -7128, -52848, -55440, -7284, 0, 72480, 2592, 59808, 54056, -31026, -3648, 0, -2592, -71344, -5376, 39618, 56448, -108744, 0, 12168, 26288, -35412, -5184, 26532, 25488, 0, 56304, 20448, -8352, -53716, -14784, 11424, 0, -20412, -25840, 37692, 33408, -104784, -192, 0, 17592, 39504, -13824, 3396, 47424, -14772, 0, -31888, 6048, -17352, 34208, -8640, -21888, 0, 7488, -22424, 42000, -25992, -4704, -125040, 0, -20952, -24384, -28344, 3536, -1344, -480, 0, -20176, -12888, -28992, 82140, -14280, -117024, 0, 17424, 33768, -38400, -2304, -1080, 90528, 0, -24408, -14460, 11496, -45880, -32064, 10800, 0, -8292, 8928, -107448, -56656, 7248, -11904, 0, 5400, -75464, 14352, 42336, 22848, -26328, 0, -104024, 22944, 1080, 19168, -132444, -3768, 0, -17152, 31824, -60792, 115908, -432, 12600, 0, -49176, 18464, 40668, -13824, 32880, 15456, 0, 51304, 109760, 864, -115608, -8160, -21384, 0, 35820, -2592, 58128, -16064, 17064, 43416, 0, 14832, -41752, -38304, -2916, 4608, 276, 0, -20216, 44176, 39120, -3216, -2520, 6048, 0, 31392, -17208, 29280, -112644, -21336, -122544, 0, 5832, 16880, -13152, 2304, -50400, 34512, 0, -27840, 14980, 16632, 52584, 24096, -85584, 0, 68672, 4608, 44760, 10228, 216, 67584, 0, 14976, -109576, 192, 12096, 49728, 90792, 0, -91356, 27664, 8604, 15616, 217392, -9072, 0, -28528, -8424, 58080, 139272, 1248, 14592, 0, -9324, -84032, -27396, 27432, 40944, -3072, 0, -10832, 33660, -10896, -78732, 49872, 32616, 0, 41740, -13824, 16200, -10528, 29268, 55824, 0, 2592, 992, -8160, 9360, 26496, 98172, 0, 146648, 19328, 36072, 103968, -40344, 18816, 0, 10848, -26208, 24192, -80820, 13392, -49440, 0, -25200, -76344, -19368, 27648, -18432, 69552, 0, -352, 55980, -8568, -72200, 4992, 15564, 0, -31704, 19296, -48576, -66976, 18996, -22080, 0, -19296, -66936, 15360, -20772, 24912, -24528, 0, 87668, -35088, -39996, -6272, -66624, -972, 0, 11824, 22176, 50472, -83512, 23184, 130704, 0, 18072, 11200, 42084, -24480, 47760, -25152, 0, -30600, 95916, -5184, 70566, 19536, 27540, 0, -59664, 36864, 53664, -12800, -6804, -30720, 0, 36288, 99520, 75888, 6372, 16032, 29352, 0, -59320, 24240, 16008, -35776, -31128, -3840, 0, -61544, 31320, -40416, 228656, -432, 26880, 0, -33696, -28416, 233352, -5184, 48648, -29184, 0, 512, -15324, -22992, -39760, 43920, -216, 0, 128968, 20736, 18816, -113824, -87072, 13056, 0, -17568, -30560, -1728, -12168, -132384, -88968, 0, -20680, -15312, -1404, -9504, 98532, -15336, 0, -9712, -20232, 49920, 113588, 3456, 27984, 0, -17424, -41368, 20148, 65808, -183264, -3456, 0, 86112, 81924, 52824, -49136, -64032, 60108, 0, 71664, -2916, -6312, -47216, -54792, 24192, 0, 33984, -24076, -30432, -21744, 27264, -18144, 0, -39928, -19712, -828, 57024, -3072, -27216, 0, 13536, 20664, 44544, 88668, 17424, 61464, 0, -31104, 103208, 22368, -18432, 87192, -102960, 0, -19696, -150356, -5616, 39144, 8064, -19968, 0, -34964, -11520, 68064, 11872, 24840, 9984, 0, -13536, 33984, -34656, 25776, -18240, 67344, 0, 10220, -75584, 28908, -37792, -190848, 38640, 0, -640, -13302, -20904, 31260, -17184, -43320, 0, -20124, -19040, -108240, -12600, 122472, 23232, 0, -43824, -11384, -3072, -82592, -80352, 5832, 0, 6048, -20520, -24288, 15328, 58872, 3624, 0, 14400, -47124, 35136, -33408, 11904, 8460, 0, -118072, 9664, -18036, 58352, 98520, 7200, 0, -76656, -324, 56448, -104316, 4320, -57840, 0, 71784, 61256, -59616, 1440, -119760, 28464, 0, -5024, -42080, -36504, -109448, 42432, 51912, 0, -45452, -576, 28680, -52680, 90462, -65568, 0, 26352, 50752, -18432, -23328, -17352, 166032, 0, 63844, -30128, 63252, 1152, -12300, 1944, 0, -28512, 69264, -198192, -59876, -3456, 13128, 0, 10692, 22752, -56412, 83160, 6384, 19776, 0, 116536, -75340, -3888, 36056, -90768, -81084, 0, 48912, 5472, -26856, 52160, 3888, -80736, 0, 8064, 199416, -47616, -84672, -22944, -41868, 0, -221176, -28448, -39432, 31608, -18240, 7776, 0, -81568, -38232, 3072, -6748, -84456, 147264, 0, 12528, -37608, -32400, 22176, 164832, -40608, 0, -114112, -131024, 38760, 52736, 6144, -50112, 0, -37300, 288, -3072, -592, -26388, 19968, 0, 20736, -55152, 16128, -71136, 74160, 16968, 0, 152826, -35852, -9072, 11472, 58800, -51312, 0, -12096, 32832, -74184, 7480, -11232, 1704, 0, -63000, 1664, 98412, 7056, -11928, -12432, 0, 193312, 11232, 36576, 261168, 2928, -5304, 0, 33564, 720, 27504, -14528, 30264, -107688, 0, 43488, -34860, 12048, 21420, -18432, -144708, 0, 240568, 39024, -50652, -68984, 184680, 3456, 0, 19464, -135792, 12480, 22880, 36612, 80064, 0, -17244, 201472, -107136, 48096, -180648, 35136, 0, 25088, 54156, -13392, -22504, -34944, 84984, 0, 12712, 17856, -99672, -119648, -8100, -33600, 0, -21528, 97088, 36864, -34272, -114264, -174720, 0, -90380, 66400, -34416, -11424, 102504, -28752, 0, 20752, 5652, 10896, 56844, 25728, -119304, 0, 91188, 25328, 2088, 648, 30192, -25728, 0, 14624, -48396, -27696, -31964, -30432, 20736, 0, -150400, -23184, 135696, -53328, -76956, -73056, 0, -1296, 86644, 5040, 12240, 29568, 90276, 0, -54672, 30912, 3888, 79272, -76800, 24096, 0, -70240, -65124, -32640, -51520, -22248, 55776, 0, 57456, 12520, 67296, -6912, 188520, -318624, 0, 36720, 163536, -66264, 157736, 49152, 4824, 0, -28352, -9072, -106656, 84272, -47088, 48384, 0, -43920, 75784, 8496, 32004, -108432, 133872, 0, 33882, -66096, -25320, 21344, -84672, -3456, 0, -5120, -51768, 61272, -166388, 41760, -254280, 0, -24948, -576, -69240, -36144, 82680, -44928, 0, -110096, -189012, -6912, 7892, 68544, -15342, 0, -100412, -101376, -112560, -30656, -22464, -14424, 0, -288, -9168, -221088, -74592, 27648, 152148, 0, 287160, -116096, -41496, -16296, -98544, -23424, 0, -133320, 13608, -16224, -77860, 42792, 134544, 0, -87120, -19912, -51096, -1872, -207984, 115584, 0, -20448, 95896, 126048, -7408, -26976, -41148, 0, 78600, 4608, -90552, -42404, 16248, -23232, 0, 16344, 108136, 87744, -74808, -60624, 41952, 0, -77876, -115440, 20736, 70432, -57504, 15792, 0, 80144, -83736, 75792, 78912, -3888, 73704, 0, 12240, -73056, -210684, -39744, 264336, 45312, 0, 70224, -164248, -28992, 48464, 67776, -155952, 0, 42512, -28224, -111696, -1104, -16272, 104736, 0, -36288, -136440, -86544, -20088, 27552, -51324, 0, -188784, 23232, 114516, 66752, 125184, -41472, 0, 84208, -104328, -24576, -27676, 528, 25320, 0, 12852, 107616, 221400, -7488, 64464, 138096, 0, -26624, 140688, -28944, 34104, -15360, 100464, 0, -68628, 33120, 39240, -71792, 28944, -18048, 0, -23040, 148072, 34368, -37368, 22560, 50544, 0, -116688, 108584, 52632, 38544, -15360, 9408, 0, 51520, 1458, 33336, 73980, -17736, -172896, 0, -75708, -22912, 2592, -34776, -388704, -26832, 0, -103560, 70500, -16800, 92892, -58416, 36720, 0, 160836, 37728, 50736, -4096, 45900, -9912, 0, 7776, 185108, 145632, -29304, -27360, -180180, 0, -44880, 78496, -55296, -116952, -139968, 19200, 0, -5680, 46080, -44544, 73152, -54432, 18816, 0, -113832, -124040, 322680, -24048, 576, 178176, 0, 9600, -185624, -36360, 67904, -432, 53664, 0, 73260, 5760, 174360, 56288, 92316, 95712, 0, 60624, 85960, 1920, 648, 48408, -53592, 0, 256312, 16176, 42624, -48672, -144216, 7776, 0, 69216, 43776, 41664, 11612, -768, -157704, 0, 34488, 120616, -263064, -65880, -19632, 35136, 0, 37056, -109064, -31104, 31696, -54720, 170736, 0, 92184, -19584, 310248, 84336, 26352, 296976, 0, 2592, -107032, 48816, 198576, 92352, 54828, 0, -26520, -4608, 22968, 127552, 50736, 14256, 0, 105696, 23004, 110880, -107052, 14568, 126096, 0, -74880, -144960, 22512, -5184, -119160, -119616, 0, -108112, -126324, 62052, -283496, 7296, -98712, 0, -116808, 5184, 43176, 142688, -129168, 10752, 0, -79236, 119920, -112896, 96048, 217488, -226848, 0, 34384, -24336, 4374, -52576, 235296, 70824, 0, 10368, -36288, -53064, -20160, -50976, 56256, 0, 45648, -112608, 257328, -40896, -7752, 16704, 0, 107432, 169276, 29568, -139374, -22848, -85536, 0, -52448, 40824, 108816, 51680, -20304, -75384, 0, -66816, -102948, 209568, -26136, 384, -69180, 0, -9744, -35184, -154812, -79008, 32424, 27648, 0, -6792, 154440, -94848, 49808, 29544, 189888, 0, 8424, 63776, -77760, -12096, -4680, 34704, 0, -68416, 113364, 17280, -169424, 43776, -17808, 0, 402136, -14976, -410064, 44848, 20304, -84000, 0, 51984, 45240, 9408, 27360, 250080, -70368, 0, -119856, 41904, 113376, 48768, 91764, 56688, 0, -7072, -57960, 2688, -123296, 960, 184536, 0, 31356, 40352, 123672, 25776, 110256, 57984, 0, -164280, 257312, 28560, -20228, 234048, 18900, 0, -56408, -34848, 167880, -67536, 65736, 76800, 0, 4608, -270484, 2160, 120528, -181056, -16668, 0, -31584, 48816, 30780, 28920, -72000, -22992, 0, 91760, -5436, 64128, 67536, -21600, -88032, 0, -52704, 16584, -95544, -17856, -33096, 214896, 0, 113312, -136352, -14496, 123448, 23808, -87528, 0, -276524, -10800, -68352, 150928, 114984, -28704, 0, -84672, -242944, -45696, -6480, 52656, 308208, 0, 100764, 208048, -91884, -45888, -118884, -2160, 0, -38336, -42696, 264888, 17024, 7536, -70464, 0, 54756, 34304, 95088, -63648, 167064, 121584, 0, -231816, -51808, 864, -198908, -25200, 79020, 0, -239092, 98352, 161328, -36928, -39528, -81336, 0, 27648, -285668, -65760, 26028, -30912, 221172, 0, -112808, -102608, 45192, -219520, -195264, -1728, 0, 231216, -2916, 16320, -66288, 42768, -492288, 0, 297288, -71640, -52392, 5184, -126816, -116256, 0, 32128, 62796, -34128, 328552, -86832, -124740, 0, 176636, -29664, -287304, 83504, -174804, 76608, 0, 5832, -122808, -9216, 136152, -552, 215424, 0, -23836, 40432, -8208, -88352, 221244, -78240, 0, 6432, 121104, 5040, -134052, -12096, -88608, 0, 71424, -62784, -359232, 34416, -185328, -58560, 0, 225288, -101172, 42672, 245672, 245088, -47412, 0, -197344, -11664, 21000, -33760, 122352, 26304, 0, -4608, 95144, 100800, 126684, -69024, -230748, 0, -17856, 55680, 56412, -29960, 73416, -33264, 0, -105168, 60912, -48192, -5088, 171168, -38928, 0, -58140, -137344, 216336, -9216, -29328, -89520, 0, -20456, 522508, -432, -93184, -135168, 888, 0, -354368, -29952, -10464, 219152, -31104, -384, 0, -24192, 142880, -99456, -111240, -181584, -259368, 0, -326732, 182712, 53778, -55328, -193500, -17208, 0, -31232, 76968, -434784, -149508, 18144, 134568, 0, 111276, 57056, -182208, 16848, 305400, -116160, 0, -278544, -125116, -2496, -225724, -29184, -10584, 0, 123372, 18648, -95280, 168064, -289968, 54792, 0, -54864, -169380, -81888, -4392, 6144, -156192, 0, 641952, 21664, -1080, -67320, -63168, 21792, 0, 157464, 161532, -99744, -219840, -65232, -247584, 0, -18072, -83480, -87048, 27648, 106632, -32400, 0, 21056, 246352, -58536, 64656, -111648, 103476, 0, 38916, -5184, -142608, -1984, -29196, 16320, 0, -18720, -353976, -52992, -54918, -196344, 11568, 0, 112564, -293296, -302208, -38656, -341220, -72144, 0, -207936, -52704, 80688, -117696, -37632, 267192, 0, 20088, -21696, -61188, 52416, -222048, -48384, 0, 161640, -337872, -26784, -294408, 98880, 179472, 0, -73804, 50400, -190848, 152688, 32292, 38736, 0, -55296, 36928, 36864, 171396, -139104, -543132, 0, -36768, 704, -99600, -111960, 201864, 17136, 0, 144400, 43128, -9984, 208684, -31128, -127080, 0, -16344, 63408, -197904, -38592, 119280, 97152, 0, 133952, -29764, -37992, 191832, 44160, -972, 0, -219852, 38592, 124464, 133872, -21936, -30720, 0, 41544, -72760, -49824, 45648, 49056, 210024, 0, -146984, -175336, 34776, 70176, 50172, 79992, 0, 12544, 109584, 133248, 27340, 1944, -4176, 0, -7560, -23648, -25992, -44352, -208200, -100944, 0, 167024, -106564, -46368, 122880, -261408, -118908, 0, 189264, -36144, -460752, -22400, 105360, -84168, 0, 48960, 239904, -95520, 33372, 50304, 58548, 0, 191064, 61200, -18780, -191832, 297600, 10368, 0, -141132, 477936, -39072, 299840, -55080, -1008, 0, 99396, 119328, -77952, -73728, 233880, -107328, 0, 25600, -123204, 13608, 86272, 61440, -126408, 0, 54840, -72576, 571728, -199040, 65880, -151776, 0, -12744, 93784, -32064, 162648, -58704, 127344, 0, 130864, 118640, 99144, -48480, 29004, -32016, 0, 71552, 5184, 62256, -649684, 7680, 170376, 0, -91908, 123088, 297780, -62640, 148368, 80832, 0, -457312, -88224, 864, 138116, -53760, 54216, 0, -61924, 67392, -147768, 56832, 165144, -466704, 0, 10368, -183506, -97296, -102816, 58368, 411240, 0, -432968, -1024, 152064, 30648, -511488, 45984, 0, 79520, 21636, -87840, 130284, 432, 342432, 0, 331632, -257936, -7824, -41472, -242448, -37632, 0, 227648, -53424, 174144, -99064, -26112, 24444, 0, -224052, 35136, 254040, 61120, 199980, 3456, 0, 24336, 255968, 264768, -64188, 177936, -114624, 0, 164696, 41360, 29868, 30624, 292620, 2808, 0, 19008, -173376, -197064, 246376, 30672, 114624, 0, -189072, 19424, 90300, 40464, 96096, -99840, 0, -227176, 277116, -6912, 141696, -55968, 63606, 0, 222780, 34848, 74592, 82736, -24516, -40296, 0, -131616, 65448, 366528, 90936, 6912, 255468, 0, -253584, -172224, 173160, -163848, 133416, -105648, 0, 98272, -23688, 128064, -33360, -120216, 605472, 0, -113688, -143328, -129984, 5832, 136728, 12624, 0, 94432, -5264, 109584, 64000, -48384, 59616, 0, -123132, -67968, 257496, 48152, -105336, 60864, 0, 43488, -210168, -54528, -101664, 36288, -127656, 0, 62412, 79856, 42336, 39424, 35904, 1656, 0, -114048, -157104, 6144, -108504, 54432, -214032, 0, 129816, -27072, 339828, -41328, 672, -89088, 0, -177336, -393396, -34848, -428356, -122928, -100128, 0, 238600, 62208, 365880, -206416, -126312, -44736, 0, 36864, 11628, -174384, -792, 205920, 535728, 0, -62408, 39392, -161424, 300712, 366288, 11232, 0, -78288, -207144, -16128, 362572, 39936, -110688, 0, 43416, 69928, 264024, 23040], "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": "294.4.a.j", "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], [-2, 0], [3, 0], [4, 0], [-6, 1], [-6, 0], [0, 0], [-8, 0], [9, 0], [12, -2], [-2, -6], [12, 0], [-24, -3], [0, 0], [-18, 3], [16, 0], [-42, 1], [-18, 0], [36, 2], [-24, 4], [0, 0], [4, 12], [-154, 6], [-24, 0], [9, -12], [48, 6], [27, 0], [0, 0], [-40, 18], [36, -6], [-192, 6], [-32, 0], [-6, -18], [84, -2], [0, 0], [36, 0], [268, -12], [-72, -4], [-72, -9], [48, -8], [-378, -5], [0, 0], [200, 24], [-8, -24], [-54, 9], [308, -12], [-156, 10], [48, 0], [0, 0], [-18, 24], [-126, 3], [-96, -12], [-26, -24], [-54, 0], [-576, 34], [0, 0], [108, 6], [80, -36], [-432, -2], [-72, 12], [-708, 13], [384, -12], [0, 0], [64, 0], [-150, -6], [12, 36], [72, 24], [-168, 4], [-462, 18], [0, 0], [-762, -30], [-72, 0], [-372, -83], [-536, 24], [27, -36], [144, 8], [0, 0], [144, 18], [488, 84], [-96, 16], [81, 0], [756, 10], [156, -136], [0, 0], [350, -48], [-400, -48], [-120, 54], [16, 48], [-54, 29], [108, -18], [0, 0], [-616, 24], [-576, 18], [312, -20], [-20, 24], [-96, 0], [372, 125], [0, 0], [-18, -54], [36, -48]]}