# Stored data for newform 784.4.a.bf, downloaded from the LMFDB on 20 April 2024.
{"label": "784.4.a.bf", "space_label": "784.4.a", "level": 784, "weight": 4, "hecke_orbit": 32, "hecke_orbit_code": 139611588515595024, "dim": 4, "is_polredabs": true, "nf_label": "4.4.270400.4", "trace_hash": 527705687172375421, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[3, [784, 0, -74, 0, 1]], [5, [784, 0, -186, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{3}+\\beta _{3}q^{5}+(10-3\\beta _{1})q^{9}+(-5^{2}+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12544, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 46.25749744450064, "hecke_ring_index": 14, "level_radical": 14, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 1, [687, 197, 689], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 270400, "field_disc_factorization": [[2, 6], [5, 2], [13, 2]], "field_poly": [194, 36, -35, -2, 1], "hecke_ring_index_factorization": [[2, 1], [7, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.725", "prec": 17}, {"__RealLiteral__": 0, "data": "0.319", "prec": 17}, {"__RealLiteral__": 0, "data": "68.899", "prec": 20}, {"__RealLiteral__": 0, "data": "12.686", "prec": 20}, {"__RealLiteral__": 0, "data": "1821.021", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [7, 1]], "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 40, 0, -100, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -352, 0, -128, 0, 0, 0, 260, 0, 0, 0, 0, 0, 0, 0, 212, 0, -952, 0, 0, 0, -540, 0, 0, 0, 0, 0, 0, 0, -428, 0, 16, 0, 0, 0, -1884, 0, 0, 0, 0, 0, 0, 0, -756, 0, 1944, 0, 0, 0, -2248, 0, 0, 0, 0, 0, 0, 0, 1048, 0, -1256, 0, 0, 0, -3284, 0, 0, 0, 0, 0, 0, 0, -5368, 0, -2192, 0, 0, 0, -3340, 0, 0, 0, 0, 0, 0, 0, -3768, 0, -516, 0, 0, 0, -2316, 0, 0, 0, 0, 0, 0, 0, -484, 0, 4396, 0, 0, 0, -1576, 0, 0, 0, 0, 0, 0, 0, -4208, 0, 1752, 0, 0, 0, -1800, 0, 0, 0, 0, 0, 0, 0, -2616, 0, -6120, 0, 0, 0, -944, 0, 0, 0, 0, 0, 0, 0, -2172, 0, 1520, 0, 0, 0, -2320, 0, 0, 0, 0, 0, 0, 0, 5972, 0, -4552, 0, 0, 0, -8336, 0, 0, 0, 0, 0, 0, 0, -7128, 0, -6228, 0, 0, 0, 2864, 0, 0, 0, 0, 0, 0, 0, 868, 0, -400, 0, 0, 0, 4024, 0, 0, 0, 0, 0, 0, 0, 7076, 0, 5852, 0, 0, 0, -9860, 0, 0, 0, 0, 0, 0, 0, -4912, 0, 10240, 0, 0, 0, -4544, 0, 0, 0, 0, 0, 0, 0, 13496, 0, -364, 0, 0, 0, 5680, 0, 0, 0, 0, 0, 0, 0, 8060, 0, -10152, 0, 0, 0, 28036, 0, 0, 0, 0, 0, 0, 0, 11780, 0, -12472, 0, 0, 0, 22240, 0, 0, 0, 0, 0, 0, 0, 9476, 0, 22148, 0, 0, 0, -4304, 0, 0, 0, 0, 0, 0, 0, -736, 0, 5692, 0, 0, 0, 10520, 0, 0, 0, 0, 0, 0, 0, -13424, 0, -11960, 0, 0, 0, 17844, 0, 0, 0, 0, 0, 0, 0, 15412, 0, 4460, 0, 0, 0, 5076, 0, 0, 0, 0, 0, 0, 0, -9792, 0, 404, 0, 0, 0, 5264, 0, 0, 0, 0, 0, 0, 0, -27624, 0, 2056, 0, 0, 0, 11668, 0, 0, 0, 0, 0, 0, 0, 27848, 0, 1392, 0, 0, 0, 31324, 0, 0, 0, 0, 0, 0, 0, 21900, 0, 2900, 0, 0, 0, 20012, 0, 0, 0, 0, 0, 0, 0, 27596, 0, 33152, 0, 0, 0, -7640, 0, 0, 0, 0, 0, 0, 0, -2912, 0, 26964, 0, 0, 0, -9624, 0, 0, 0, 0, 0, 0, 0, 34720, 0, -53216, 0, 0, 0, -3120, 0, 0, 0, 0, 0, 0, 0, -18888, 0, 37948, 0, 0, 0, 14232, 0, 0, 0, 0, 0, 0, 0, -23028, 0, 37696, 0, 0, 0, -12272, 0, 0, 0, 0, 0, 0, 0, 40088, 0, -13800, 0, 0, 0, -13880, 0, 0, 0, 0, 0, 0, 0, -21756, 0, -13456, 0, 0, 0, -232, 0, 0, 0, 0, 0, 0, 0, -16648, 0, -43848, 0, 0, 0, 2092, 0, 0, 0, 0, 0, 0, 0, 18768, 0, 50000, 0, 0, 0, -38072, 0, 0, 0, 0, 0, 0, 0, 3128, 0, -13532, 0, 0, 0, -27244, 0, 0, 0, 0, 0, 0, 0, 1752, 0, -79016, 0, 0, 0, 53948, 0, 0, 0, 0, 0, 0, 0, 272, 0, -56320, 0, 0, 0, -19720, 0, 0, 0, 0, 0, 0, 0, -75836, 0, 4268, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, 13640, 0, 19740, 0, 0, 0, 62824, 0, 0, 0, 0, 0, 0, 0, -19256, 0, -45712, 0, 0, 0, -10200, 0, 0, 0, 0, 0, 0, 0, 560, 0, 27652, 0, 0, 0, -79204, 0, 0, 0, 0, 0, 0, 0, -10944, 0, 60360, 0, 0, 0, -46488, 0, 0, 0, 0, 0, 0, 0, -33400, 0, -51644, 0, 0, 0, -45040, 0, 0, 0, 0, 0, 0, 0, -5444, 0, 27936, 0, 0, 0, -50548, 0, 0, 0, 0, 0, 0, 0, -15600, 0, 32480, 0, 0, 0, 38088, 0, 0, 0, 0, 0, 0, 0, 2668, 0, 11576, 0, 0, 0, -12760, 0, 0, 0, 0, 0, 0, 0, -86128, 0, -3416, 0, 0, 0, -61508, 0, 0, 0, 0, 0, 0, 0, -15020, 0, -62840, 0, 0, 0, -8400, 0, 0, 0, 0, 0, 0, 0, 17436, 0, -28340, 0, 0, 0, -24188, 0, 0, 0, 0, 0, 0, 0, -18960, 0, -36556, 0, 0, 0, -52424, 0, 0, 0, 0, 0, 0, 0, -51200, 0, 86324, 0, 0, 0, -70972, 0, 0, 0, 0, 0, 0, 0, 41260, 0, -31528, 0, 0, 0, -99476, 0, 0, 0, 0, 0, 0, 0, -51828, 0, 67120, 0, 0, 0, -45676, 0, 0, 0, 0, 0, 0, 0, 44324, 0, 18976, 0, 0, 0, -93960, 0, 0, 0, 0, 0, 0, 0, -14680, 0, -57020, 0, 0, 0, 43168, 0, 0, 0, 0, 0, 0, 0, -130744, 0, 105152, 0, 0, 0, 89256, 0, 0, 0, 0, 0, 0, 0, 33376, 0, -10144, 0, 0, 0, -67916, 0, 0, 0, 0, 0, 0, 0, 99828, 0, -15536, 0, 0, 0, 46720, 0, 0, 0, 0, 0, 0, 0, -6792, 0, 63764, 0, 0, 0, 47120, 0, 0, 0, 0, 0, 0, 0, -4380, 0, 54096, 0, 0, 0, 52072, 0, 0, 0, 0, 0, 0, 0, 47780, 0, -21160, 0, 0, 0, 69216, 0, 0, 0, 0, 0, 0, 0, -62748, 0, -84296, 0, 0, 0, 29784, 0, 0, 0, 0, 0, 0, 0, 135280, 0, -131348, 0, 0, 0, -15364, 0, 0, 0, 0, 0, 0, 0, -69152, 0, 8000, 0, 0, 0, 71660, 0, 0, 0, 0, 0, 0, 0, -45684, 0, -54124, 0, 0, 0, 99296, 0, 0, 0, 0, 0, 0, 0, 81044, 0, -45480, 0, 0, 0, -7792, 0, 0, 0, 0, 0, 0, 0, 70504, 0, -35880, 0, 0, 0, 139140, 0, 0, 0, 0, 0, 0, 0, 83920, 0, 25520, 0, 0, 0, -17968, 0, 0, 0, 0, 0, 0, 0, 44708, 0, 70624, 0, 0, 0, 21428, 0, 0, 0, 0, 0, 0, 0, -115980, 0, -22808, 0, 0, 0, 235600, 0, 0, 0, 0, 0, 0, 0, -78584, 0, 15696, 0, 0, 0, -59564, 0, 0, 0, 0, 0, 0, 0, -13840, 0, 75768, 0, 0, 0, -28008, 0, 0, 0, 0, 0, 0, 0, 26564, 0, -49852, 0, 0, 0, -21408, 0, 0, 0, 0, 0, 0, 0, 19240, 0, -82820, 0, 0, 0, 5096, 0, 0, 0, 0, 0, 0, 0, 100784, 0, 112160, 0, 0, 0, 126428, 0, 0, 0, 0, 0, 0, 0, 296528, 0, 118312, 0, 0, 0, 7168, 0, 0, 0, 0, 0, 0, 0, 67760, 0, 16368, 0, 0, 0, -48476, 0, 0, 0, 0, 0, 0, 0, 191032, 0, -87360, 0, 0, 0, 118224, 0, 0, 0, 0, 0, 0, 0, 38840, 0, -113980, 0, 0, 0, 112104, 0, 0, 0, 0, 0, 0, 0, -206164, 0, 68928, 0, 0, 0, -92968, 0, 0, 0, 0, 0, 0, 0, 58168, 0, 78224, 0, 0, 0, 102000, 0, 0, 0, 0, 0, 0, 0, 114528, 0, -83400, 0, 0, 0, 53768, 0, 0, 0, 0, 0, 0, 0, -131400, 0, 160596, 0, 0, 0, 41628, 0, 0, 0, 0, 0, 0, 0, 157460, 0, 115360, 0, 0, 0, -20128, 0, 0, 0, 0, 0, 0, 0, -96076, 0, 195120, 0, 0, 0, 25320, 0, 0, 0, 0, 0, 0, 0, -97936, 0, 150720, 0, 0, 0, 28600, 0, 0, 0, 0, 0, 0, 0, 86912, 0, 69132, 0, 0, 0, -111132, 0, 0, 0, 0, 0, 0, 0, -130080, 0, -163576, 0, 0, 0, -97844, 0, 0, 0, 0, 0, 0, 0, -173308, 0, -106028, 0, 0, 0, -65260, 0, 0, 0, 0, 0, 0, 0, 91044, 0, -41468, 0, 0, 0, 196216, 0, 0, 0, 0, 0, 0, 0, 148112, 0, 2324, 0, 0, 0, -66480, 0, 0, 0, 0, 0, 0, 0, 50968, 0, 27200, 0, 0, 0, 28200, 0, 0, 0, 0, 0, 0, 0, -113120, 0, -225840, 0, 0, 0, 180620, 0, 0, 0, 0, 0, 0, 0, -191800, 0, -112176, 0, 0, 0, 18360, 0, 0, 0, 0, 0, 0, 0, -9424, 0, -189036, 0, 0, 0, 48028, 0, 0, 0, 0, 0, 0, 0, 5420, 0, 246120, 0, 0, 0, -124508, 0, 0, 0, 0, 0, 0, 0, 74800, 0, -15200, 0, 0, 0, 41012, 0, 0, 0, 0, 0, 0, 0, -204160, 0, 25844, 0, 0, 0, 76224, 0, 0, 0, 0, 0, 0, 0, 145920, 0, 108908, 0, 0, 0, -182132, 0, 0, 0, 0, 0, 0, 0, 118840, 0, -70128, 0, 0, 0, -61376, 0, 0, 0, 0, 0, 0, 0, 37420, 0, 235020, 0, 0, 0, 109360, 0, 0, 0, 0, 0, 0, 0, -109172, 0, -144180, 0, 0, 0, -118896, 0, 0, 0, 0, 0, 0, 0, 43160, 0, -107056, 0, 0, 0, 14720, 0, 0, 0, 0, 0, 0, 0, -121672, 0, 102928, 0, 0, 0, -52872, 0, 0, 0, 0, 0, 0, 0, -51600, 0, -212688, 0, 0, 0, -313496, 0, 0, 0, 0, 0, 0, 0, 15020, 0, -167092, 0, 0, 0, 123208, 0, 0, 0, 0, 0, 0, 0, -227584, 0, -31720, 0, 0, 0, -210592, 0, 0, 0, 0, 0, 0, 0, -112544, 0, 205680, 0, 0, 0, -217216, 0, 0, 0, 0, 0, 0, 0, -22268, 0, -105020, 0, 0, 0, -91316, 0, 0, 0, 0, 0, 0, 0, 15652, 0, -82812, 0, 0, 0, -273232, 0, 0, 0, 0, 0, 0, 0, -1320, 0, 75536, 0, 0, 0, -36504, 0, 0, 0, 0, 0, 0, 0, -49888, 0, 125704, 0, 0, 0, -206200, 0, 0, 0, 0, 0, 0, 0, -55400, 0, -143428, 0, 0, 0, 18592, 0, 0, 0, 0, 0, 0, 0, 183264, 0, -200656, 0, 0, 0, 265080, 0, 0, 0, 0, 0, 0, 0, -101648, 0, 217952, 0, 0, 0, -153400, 0, 0, 0, 0, 0, 0, 0, 73440, 0, 42880, 0, 0, 0, -154876, 0, 0, 0, 0, 0, 0, 0, 46472, 0, 1120, 0, 0, 0, -142012, 0, 0, 0, 0, 0, 0, 0, -266188, 0, -460188, 0, 0, 0, 86704, 0, 0, 0, 0, 0, 0, 0, -148008, 0, -60640, 0, 0, 0, 121752, 0, 0, 0, 0, 0, 0, 0, -19564, 0, 8280, 0, 0, 0, -197576, 0, 0, 0, 0, 0, 0, 0, -229188, 0, 161212, 0, 0, 0, -278340, 0, 0, 0, 0, 0, 0, 0, 270004, 0, -52852, 0, 0, 0, -439480, 0, 0, 0, 0, 0, 0, 0, 88072, 0, -65660, 0, 0, 0, 93092, 0, 0, 0, 0, 0, 0, 0, 454520, 0, 111976, 0, 0, 0, -70300, 0, 0, 0, 0, 0, 0, 0, -54924, 0, 281136, 0, 0, 0, 176760, 0, 0, 0, 0, 0, 0, 0, -550156, 0, 177212, 0, 0, 0, -75656, 0, 0, 0, 0, 0, 0, 0, -163744, 0, -189984, 0, 0, 0, -189456, 0, 0, 0, 0, 0, 0, 0, -244152, 0, 121168, 0, 0, 0, 242544, 0, 0, 0, 0, 0, 0, 0, -156604, 0, -62300, 0, 0, 0, 73372, 0, 0, 0, 0, 0, 0, 0, 246492, 0, 19780, 0, 0, 0, 88688, 0, 0, 0, 0, 0, 0, 0, -30536, 0, -50496, 0, 0, 0, 5776, 0, 0, 0, 0, 0, 0, 0, 14560, 0, 7736, 0, 0, 0, 339536, 0, 0, 0, 0, 0, 0, 0, 73000, 0, -320, 0, 0, 0, -98016, 0, 0, 0, 0, 0, 0, 0, -384228, 0, -254528, 0, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, -86520, 0, -40684, 0, 0, 0, 315064, 0, 0, 0, 0, 0, 0, 0, -433656, 0, 57200, 0, 0, 0, -326360, 0, 0, 0, 0, 0, 0, 0, 387792, 0, -315720, 0, 0, 0, -13192, 0, 0, 0, 0, 0, 0, 0, 274480, 0, -111712, 0, 0, 0, 235304, 0, 0, 0, 0, 0, 0, 0, 435728, 0, 279084, 0, 0, 0, -198100, 0, 0, 0, 0, 0, 0, 0, 127164, 0, 159360, 0, 0, 0, 588020, 0, 0, 0, 0, 0, 0, 0, -244540, 0, 451760, 0, 0, 0, 67432, 0, 0, 0, 0, 0, 0, 0, 100252, 0, 383556, 0, 0, 0, -152088, 0, 0, 0, 0, 0, 0, 0, -21296, 0, -194852, 0, 0, 0, -68748, 0, 0, 0, 0, 0, 0, 0, -309608, 0, 17632, 0, 0, 0, -171600, 0, 0, 0, 0, 0, 0, 0, 61712, 0, -433788, 0, 0, 0, 281196, 0, 0, 0, 0, 0, 0, 0, 520088, 0, 348276, 0, 0, 0, -225016, 0, 0, 0, 0, 0, 0, 0, -215264, 0, 209840, 0, 0, 0, 98640, 0, 0, 0, 0, 0, 0, 0, -113112, 0, -223456, 0, 0, 0, -91040, 0, 0, 0, 0, 0, 0, 0, 371760, 0, 243888, 0, 0, 0, -271760, 0, 0, 0, 0, 0, 0, 0, -203320, 0, 337184, 0, 0, 0, 425816, 0, 0, 0, 0, 0, 0, 0, 369520, 0, 31124, 0, 0, 0, 556856, 0, 0, 0, 0, 0, 0, 0, 169036, 0, -497480, 0, 0, 0, 229712, 0, 0, 0, 0, 0, 0, 0, 331756, 0, -203336, 0, 0, 0, 284416, 0, 0, 0, 0, 0, 0, 0, 412680, 0, 69040, 0, 0, 0, 64912, 0, 0, 0, 0, 0, 0, 0, 101736, 0, -40812, 0, 0, 0, -191988, 0, 0, 0, 0, 0, 0, 0, 203072, 0, 145880, 0, 0, 0, -231412, 0, 0, 0, 0, 0, 0, 0, 224384, 0, 262684, 0, 0, 0, 33488, 0, 0, 0, 0, 0, 0, 0, 164668, 0, -112296, 0, 0, 0, 49280, 0, 0, 0, 0, 0, 0, 0, -222216, 0, -204000, 0, 0, 0, -332772, 0, 0, 0, 0, 0, 0, 0, 184720, 0, -165960, 0, 0, 0, 552868, 0, 0, 0, 0, 0, 0, 0, -102960, 0, 187168, 0, 0, 0, 170668, 0, 0, 0, 0, 0, 0, 0, 205940, 0, -416724, 0, 0, 0, 62600, 0, 0, 0, 0, 0, 0, 0, -316800, 0, -133360, 0, 0, 0, 543576, 0, 0, 0, 0, 0, 0, 0, 42828, 0, -74544, 0, 0, 0, 457596, 0, 0, 0, 0, 0, 0, 0, -223876, 0, -119860, 0, 0, 0, 536844, 0, 0, 0, 0, 0, 0, 0, -115884, 0, 802116, 0, 0, 0, -262200, 0, 0, 0, 0, 0, 0, 0, 92464, 0, 156984, 0, 0, 0, 400240, 0, 0, 0, 0, 0, 0, 0, 310256, 0, -800632, 0, 0, 0, 36240, 0, 0, 0, 0, 0, 0, 0, -343232, 0, -12768, 0, 0, 0, -185480, 0, 0, 0, 0, 0, 0, 0, 200160, 0, 198044, 0, 0, 0, 340528, 0, 0, 0, 0, 0, 0, 0, 110320, 0, 460740, 0, 0, 0, 10088, 0, 0, 0, 0, 0, 0, 0, 128528, 0, -290712, 0, 0, 0, 99640, 0, 0, 0, 0, 0, 0, 0, 423624, 0, 321184, 0, 0, 0, -40560, 0, 0, 0, 0, 0, 0, 0, -292668, 0, 407180, 0, 0, 0, 73392, 0, 0, 0, 0, 0, 0, 0, 355536, 0, -331876, 0, 0, 0, 46880, 0, 0, 0, 0, 0, 0, 0, -275492, 0, -185824, 0, 0, 0, 237808, 0, 0, 0, 0, 0, 0, 0, -137424, 0, -61656, 0, 0, 0, -275988, 0, 0, 0, 0, 0, 0, 0, 91360, 0, 418808, 0, 0, 0, -88080, 0, 0, 0, 0, 0, 0, 0, 433088, 0, -145396, 0, 0, 0, 448904, 0, 0, 0, 0, 0, 0, 0, 36808, 0, -664104, 0, 0, 0, -136160, 0, 0, 0, 0, 0, 0, 0, -538196, 0, 2184, 0, 0, 0, -171844, 0, 0, 0, 0, 0, 0, 0, -62560, 0, 133504, 0, 0, 0, -547072, 0, 0, 0, 0, 0, 0, 0, 80048, 0, -541720, 0, 0, 0, 458996, 0, 0, 0, 0, 0, 0, 0, -324352, 0, 317232, 0, 0, 0, 349664, 0, 0, 0, 0, 0, 0, 0, -130064, 0, -301360, 0, 0, 0, 2500, 0, 0, 0, 0, 0, 0, 0, 47908, 0, 558796, 0, 0, 0, 12144, 0, 0, 0, 0, 0, 0, 0, -24320, 0, -212560, 0, 0, 0, -920088, 0, 0, 0, 0, 0, 0, 0, 451172, 0, -108376, 0, 0, 0, 149176, 0, 0, 0, 0, 0, 0, 0, 426872, 0, 141408, 0, 0, 0, -377068, 0, 0, 0, 0, 0, 0, 0, -585520, 0, 117304, 0, 0, 0, -184232, 0, 0, 0, 0, 0, 0, 0, -488728, 0, 878488, 0, 0, 0, -348320, 0, 0, 0, 0, 0, 0, 0, -512588, 0, -28048, 0, 0, 0, -557096, 0, 0, 0, 0, 0, 0, 0, -18200, 0, 222196, 0, 0, 0, 37420, 0, 0, 0, 0, 0, 0, 0, 55064, 0, 17680, 0, 0, 0, -913576, 0, 0, 0, 0, 0, 0, 0, -118848, 0, 585984, 0, 0, 0, -293000, 0, 0, 0, 0, 0, 0, 0, -557920, 0, 198592, 0, 0, 0, -303372, 0, 0, 0, 0, 0, 0, 0, 420560, 0, -671592, 0, 0, 0, 45004, 0, 0, 0, 0, 0, 0, 0, -511204, 0, -127484, 0, 0, 0, 76336, 0, 0, 0, 0, 0, 0, 0, -324080, 0, 414452, 0, 0, 0, -277648, 0, 0, 0, 0, 0, 0, 0, 375804, 0, -344232, 0, 0, 0, 1026444, 0, 0, 0, 0, 0, 0, 0, 261672, 0, -82760, 0, 0, 0, -192576, 0, 0, 0, 0, 0, 0, 0, -220128, 0, 398880, 0, 0, 0, -408200, 0, 0, 0, 0, 0, 0, 0, -161128, 0, -608240, 0, 0, 0, -582884, 0, 0, 0, 0, 0, 0, 0, 414480, 0, 188432, 0, 0, 0, -262640, 0, 0, 0, 0, 0, 0, 0, -452580, 0, -180, 0, 0, 0, 758708, 0, 0, 0, 0, 0, 0, 0, 211488, 0, -17776, 0, 0, 0, -730640, 0, 0, 0, 0, 0, 0, 0, -442960, 0, -834280, 0, 0, 0, -611948, 0, 0, 0, 0, 0, 0, 0, -294440, 0, -134232, 0, 0, 0, -522016, 0, 0, 0, 0, 0, 0, 0, 933084, 0, 109740, 0, 0, 0, -213072, 0, 0, 0, 0, 0, 0, 0, 190540, 0, 53500, 0, 0, 0, -258264, 0, 0, 0, 0, 0, 0, 0, -874784, 0, 184352, 0, 0, 0, -82948, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "49.4.a.e", "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, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, -3, 0, 0], [0, 0, 0, 0], [-25, 3, 0, 0], [0, 0, 0, 0], [0, 0, 6, -1], [0, 0, 0, 0], [16, 4, 0, 0], [0, 0, 0, 0], [0, 0, -1, -9], [0, 0, 0, 0], [0, 0, 11, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-88, -4, 0, 0], [0, 0, 0, 0], [-32, 11, 0, 0], [0, 0, 0, 0], [0, 0, -4, -12], [0, 0, 0, 0], [65, -7, 0, 0], [0, 0, 0, 0], [0, 0, 38, 4], [0, 0, 0, 0], [0, 0, 46, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [53, -3, 0, 0], [0, 0, 0, 0], [-238, 14, 0, 0], [0, 0, 0, 0], [0, 0, -31, -3], [0, 0, 0, 0], [-135, -35, 0, 0], [0, 0, 0, 0], [0, 0, 12, -11], [0, 0, 0, 0], [0, 0, 26, 32], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-107, -39, 0, 0], [0, 0, 0, 0], [4, 18, 0, 0], [0, 0, 0, 0], [0, 0, -12, -4], [0, 0, 0, 0], [-471, 17, 0, 0], [0, 0, 0, 0], [0, 0, -49, -20], [0, 0, 0, 0], [0, 0, 68, 27], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-189, -35, 0, 0], [0, 0, 0, 0], [486, 38, 0, 0], [0, 0, 0, 0], [0, 0, 60, -16], [0, 0, 0, 0], [-562, 14, 0, 0], [0, 0, 0, 0], [0, 0, -37, 25], [0, 0, 0, 0], [0, 0, 109, 44], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [262, 94, 0, 0], [0, 0, 0, 0], [-314, 21, 0, 0], [0, 0, 0, 0], [0, 0, -1, -8], [0, 0, 0, 0], [-821, -95, 0, 0], [0, 0, 0, 0], [0, 0, -114, -28], [0, 0, 0, 0], [0, 0, -157, 75], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1342, 130, 0, 0], [0, 0, 0, 0], [-548, -88, 0, 0], [0, 0, 0, 0], [0, 0, -189, -91], [0, 0, 0, 0], [-835, 105, 0, 0], [0, 0, 0, 0]]}