# Stored data for newform 2312.4.a.k, downloaded from the LMFDB on 24 May 2022.
{"level_primes": [2, 17], "is_polredabs": true, "sato_tate_group": "3.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 2258732197130063641, "level_radical": 34, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 11, "analytic_conductor": 136.4124159332723, "inner_twist_count": 2, "field_disc_factorization": [[2, 11], [125826577, 2]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "2312.4.a.k", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "136.4.b.b", "field_poly_is_cyclotomic": false, "dim": 8, "trace_zratio": {"__RealLiteral__": 0, "data": "0.515", "prec": 17}, "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 44, 0, -24, 0, 0, 0, -48, 0, 308, 0, 0, 0, 520, 0, 0, 0, 0, 0, 0, 0, 812, 0, -1064, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 312, 0, 1124, 0, 0, 0, -472, 0, 1416, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -624, 0, -180, 0, 0, 0, 0, 0, 0, 0, -1660, 0, 0, 0, 3156, 0, -2472, 0, 0, 0, 6664, 0, 68, 0, 0, 0, 4036, 0, 0, 0, 0, 0, 0, 0, 1276, 0, 1216, 0, 0, 0, 0, 0, 0, 0, -9976, 0, 0, 0, 2344, 0, 412, 0, 0, 0, 4164, 0, -896, 0, 0, 0, -1392, 0, 0, 0, 0, 0, 0, 0, -2304, 0, -4172, 0, 0, 0, 0, 0, 0, 0, -8144, 0, 0, 0, 7504, 0, 5536, 0, 0, 0, 8312, 0, 12312, 0, 0, 0, 11268, 0, 0, 0, 0, 0, 0, 0, 6736, 0, -2720, 0, 0, 0, 0, 0, 0, 0, -18560, 0, 0, 0, 23768, 0, 1072, 0, 0, 0, 20384, 0, 6360, 0, 0, 0, 26880, 0, 0, 0, 0, 0, 0, 0, 8440, 0, -25856, 0, 0, 0, 0, 0, 0, 0, -11156, 0, 0, 0, 16172, 0, -4832, 0, 0, 0, 19176, 0, 39388, 0, 0, 0, 20132, 0, 0, 0, 0, 0, 0, 0, 20796, 0, 1352, 0, 0, 0, 0, 0, 0, 0, -21392, 0, 0, 0, 13024, 0, 6492, 0, 0, 0, 21468, 0, 2424, 0, 0, 0, 2736, 0, 0, 0, 0, 0, 0, 0, 3288, 0, -50016, 0, 0, 0, 0, 0, 0, 0, -16672, 0, 0, 0, 42976, 0, 13696, 0, 0, 0, 47488, 0, 33584, 0, 0, 0, 40160, 0, 0, 0, 0, 0, 0, 0, 13840, 0, 15048, 0, 0, 0, 0, 0, 0, 0, -101176, 0, 0, 0, 31080, 0, 6764, 0, 0, 0, 25988, 0, 3224, 0, 0, 0, 32120, 0, 0, 0, 0, 0, 0, 0, -29264, 0, -23564, 0, 0, 0, 0, 0, 0, 0, -24088, 0, 0, 0, 41984, 0, -26712, 0, 0, 0, 59656, 0, 30504, 0, 0, 0, 49600, 0, 0, 0, 0, 0, 0, 0, 35196, 0, 20784, 0, 0, 0, 0, 0, 0, 0, -50416, 0, 0, 0, 38808, 0, 13636, 0, 0, 0, 31420, 0, -22840, 0, 0, 0, -27408, 0, 0, 0, 0, 0, 0, 0, -28376, 0, -18888, 0, 0, 0, 0, 0, 0, 0, -9548, 0, 0, 0, 12508, 0, 3848, 0, 0, 0, 64680, 0, 78048, 0, 0, 0, 63404, 0, 0, 0, 0, 0, 0, 0, 90072, 0, -3728, 0, 0, 0, 0, 0, 0, 0, -90688, 0, 0, 0, 44800, 0, 40188, 0, 0, 0, -15992, 0, -5600, 0, 0, 0, -16800, 0, 0, 0, 0, 0, 0, 0, -30032, 0, -105744, 0, 0, 0, 0, 0, 0, 0, 19456, 0, 0, 0, 55900, 0, -61680, 0, 0, 0, 97432, 0, 84292, 0, 0, 0, 114540, 0, 0, 0, 0, 0, 0, 0, 39920, 0, 27680, 0, 0, 0, 0, 0, 0, 0, -73416, 0, 0, 0, -26064, 0, 39164, 0, 0, 0, -23868, 0, -37752, 0, 0, 0, -8568, 0, 0, 0, 0, 0, 0, 0, -15576, 0, -103920, 0, 0, 0, 0, 0, 0, 0, 62548, 0, 0, 0, 52140, 0, 25712, 0, 0, 0, -11992, 0, 99872, 0, 0, 0, 48312, 0, 0, 0, 0, 0, 0, 0, 21380, 0, 70224, 0, 0, 0, 0, 0, 0, 0, -12832, 0, 0, 0, 26632, 0, 8120, 0, 0, 0, -43916, 0, -89152, 0, 0, 0, -42240, 0, 0, 0, 0, 0, 0, 0, -67552, 0, -34960, 0, 0, 0, 0, 0, 0, 0, 85824, 0, 0, 0, -40648, 0, -13936, 0, 0, 0, 65464, 0, 69380, 0, 0, 0, -31540, 0, 0, 0, 0, 0, 0, 0, 86656, 0, 107688, 0, 0, 0, 0, 0, 0, 0, -96024, 0, 0, 0, -56856, 0, -14640, 0, 0, 0, -20448, 0, -5944, 0, 0, 0, -20360, 0, 0, 0, 0, 0, 0, 0, -20800, 0, -101220, 0, 0, 0, 0, 0, 0, 0, 63928, 0, 0, 0, -38228, 0, -32712, 0, 0, 0, -84304, 0, -30804, 0, 0, 0, -12128, 0, 0, 0, 0, 0, 0, 0, 62292, 0, 182592, 0, 0, 0, 0, 0, 0, 0, -42048, 0, 0, 0, -21144, 0, -49080, 0, 0, 0, -1296, 0, -325096, 0, 0, 0, -99184, 0, 0, 0, 0, 0, 0, 0, -201704, 0, -72092, 0, 0, 0, 0, 0, 0, 0, 132356, 0, 0, 0, -61196, 0, 60968, 0, 0, 0, -25360, 0, 65156, 0, 0, 0, -48220, 0, 0, 0, 0, 0, 0, 0, -23396, 0, 190528, 0, 0, 0, 0, 0, 0, 0, -27312, 0, 0, 0, -101520, 0, 38992, 0, 0, 0, -194892, 0, -59808, 0, 0, 0, -177848, 0, 0, 0, 0, 0, 0, 0, -39320, 0, 35168, 0, 0, 0, 0, 0, 0, 0, 272420, 0, 0, 0, -90408, 0, -153000, 0, 0, 0, -94104, 0, 54592, 0, 0, 0, 17352, 0, 0, 0, 0, 0, 0, 0, -75316, 0, 57864, 0, 0, 0, 0, 0, 0, 0, 53496, 0, 0, 0, -39248, 0, 118096, 0, 0, 0, -105460, 0, -227632, 0, 0, 0, -136368, 0, 0, 0, 0, 0, 0, 0, -105728, 0, -86848, 0, 0, 0, 0, 0, 0, 0, 125472, 0, 0, 0, -75712, 0, -48808, 0, 0, 0, -34816, 0, 5744, 0, 0, 0, -29396, 0, 0, 0, 0, 0, 0, 0, 123220, 0, 88504, 0, 0, 0, 0, 0, 0, 0, 191072, 0, 0, 0, -253024, 0, -23668, 0, 0, 0, -117944, 0, 35408, 0, 0, 0, -119360, 0, 0, 0, 0, 0, 0, 0, 81784, 0, -69628, 0, 0, 0, 0, 0, 0, 0, 73508, 0, 0, 0, -122656, 0, 71432, 0, 0, 0, -163176, 0, 15260, 0, 0, 0, -56104, 0, 0, 0, 0, 0, 0, 0, 171952, 0, 89872, 0, 0, 0, 0, 0, 0, 0, 186200, 0, 0, 0, -140416, 0, -92480, 0, 0, 0, -440544, 0, -233152, 0, 0, 0, -145264, 0, 0, 0, 0, 0, 0, 0, -239848, 0, 97292, 0, 0, 0, 0, 0, 0, 0, 440128, 0, 0, 0, -200060, 0, -164232, 0, 0, 0, 37136, 0, -178260, 0, 0, 0, 20064, 0, 0, 0, 0, 0, 0, 0, -65876, 0, 56088, 0, 0, 0, 0, 0, 0, 0, 35448, 0, 0, 0, -18176, 0, 110452, 0, 0, 0, -203920, 0, 142056, 0, 0, 0, -228144, 0, 0, 0, 0, 0, 0, 0, -18512, 0, 35496, 0, 0, 0, 0, 0, 0, 0, 266960, 0, 0, 0, -49724, 0, 71824, 0, 0, 0, -196160, 0, -8836, 0, 0, 0, -177672, 0, 0, 0, 0, 0, 0, 0, -35552, 0, 172056, 0, 0, 0, 0, 0, 0, 0, -9664, 0, 0, 0, -183448, 0, 122732, 0, 0, 0, -10604, 0, -439184, 0, 0, 0, -39528, 0, 0, 0, 0, 0, 0, 0, -350320, 0, 41864, 0, 0, 0, 0, 0, 0, 0, -38624, 0, 0, 0, 137540, 0, -46864, 0, 0, 0, -52888, 0, 25980, 0, 0, 0, 23604, 0, 0, 0, 0, 0, 0, 0, -12928, 0, 15752, 0, 0, 0, 0, 0, 0, 0, 108344, 0, 0, 0, -164736, 0, -201088, 0, 0, 0, -137664, 0, -121016, 0, 0, 0, -255720, 0, 0, 0, 0, 0, 0, 0, 214704, 0, 249916, 0, 0, 0, 0, 0, 0, 0, 100612, 0, 0, 0, -382576, 0, 37280, 0, 0, 0, -69712, 0, -264640, 0, 0, 0, -9508, 0, 0, 0, 0, 0, 0, 0, -27804, 0, -33176, 0, 0, 0, 0, 0, 0, 0, -58600, 0, 0, 0, 16832, 0, 9728, 0, 0, 0, -52940, 0, 49552, 0, 0, 0, -114336, 0, 0, 0, 0, 0, 0, 0, -138152, 0, 101244, 0, 0, 0, 0, 0, 0, 0, -47580, 0, 0, 0, -237680, 0, -292992, 0, 0, 0, 49040, 0, -219496, 0, 0, 0, -418836, 0, 0, 0, 0, 0, 0, 0, -258024, 0, 198832, 0, 0, 0, 0, 0, 0, 0, 352192, 0, 0, 0, -383456, 0, -16424, 0, 0, 0, 86960, 0, 187504, 0, 0, 0, 115568, 0, 0, 0, 0, 0, 0, 0, 364800, 0, -79184, 0, 0, 0, 0, 0, 0, 0, -73080, 0, 0, 0, 298092, 0, 312048, 0, 0, 0, -530120, 0, 31576, 0, 0, 0, -87408, 0, 0, 0, 0, 0, 0, 0, -168772, 0, -171800, 0, 0, 0, 0, 0, 0, 0, 192024, 0, 0, 0, 578704, 0, -49144, 0, 0, 0, 188272, 0, -128568, 0, 0, 0, 332032, 0, 0, 0, 0, 0, 0, 0, -187856, 0, 222236, 0, 0, 0, 0, 0, 0, 0, -144892, 0, 0, 0, -140788, 0, -170624, 0, 0, 0, 396960, 0, 32908, 0, 0, 0, 35824, 0, 0, 0, 0, 0, 0, 0, 154708, 0, -178640, 0, 0, 0, 0, 0, 0, 0, 51064, 0, 0, 0, -137896, 0, 228204, 0, 0, 0, 200764, 0, 529088, 0, 0, 0, 46136, 0, 0, 0, 0, 0, 0, 0, 344384, 0, -186012, 0, 0, 0, 0, 0, 0, 0, -258944, 0, 0, 0, 123796, 0, 220776, 0, 0, 0, -510976, 0, 5888, 0, 0, 0, 14116, 0, 0, 0, 0, 0, 0, 0, -152572, 0, 65736, 0, 0, 0, 0, 0, 0, 0, -160928, 0, 0, 0, 345112, 0, -476736, 0, 0, 0, 49748, 0, -124560, 0, 0, 0, 649512, 0, 0, 0, 0, 0, 0, 0, 32928, 0, -301088, 0, 0, 0, 0, 0, 0, 0, -14852, 0, 0, 0, 171872, 0, 251640, 0, 0, 0, 150904, 0, 195024, 0, 0, 0, 91220, 0, 0, 0, 0, 0, 0, 0, 37592, 0, -622144, 0, 0, 0, 0, 0, 0, 0, 242320, 0, 0, 0, -158032, 0, -87276, 0, 0, 0, 74548, 0, 341296, 0, 0, 0, -51800, 0, 0, 0, 0, 0, 0, 0, 534928, 0, 369308, 0, 0, 0, 0, 0, 0, 0, -297220, 0, 0, 0, -169632, 0, 493376, 0, 0, 0, 101184, 0, -384928, 0, 0, 0, -157140, 0, 0, 0, 0, 0, 0, 0, -142576, 0, -308968, 0, 0, 0, 0, 0, 0, 0, -360592, 0, 0, 0, 310816, 0, 287416, 0, 0, 0, 484960, 0, 359424, 0, 0, 0, 269008, 0, 0, 0, 0, 0, 0, 0, 100720, 0, 123404, 0, 0, 0, 0, 0, 0, 0, -378256, 0, 0, 0, 545748, 0, -432192, 0, 0, 0, 468648, 0, -88712, 0, 0, 0, 165380, 0, 0, 0, 0, 0, 0, 0, 5816, 0, 86984, 0, 0, 0, 0, 0, 0, 0, 69600, 0, 0, 0, -292088, 0, -507576, 0, 0, 0, 547288, 0, 1004736, 0, 0, 0, 20392, 0, 0, 0, 0, 0, 0, 0, 360240, 0, 195152, 0, 0, 0, 0, 0, 0, 0, -543992, 0, 0, 0, 501256, 0, 516088, 0, 0, 0, -293896, 0, 245132, 0, 0, 0, 212044, 0, 0, 0, 0, 0, 0, 0, -150236, 0, -948880, 0, 0, 0, 0, 0, 0, 0, 79576, 0, 0, 0, 1273784, 0, -29652, 0, 0, 0, 357860, 0, -385400, 0, 0, 0, 1033576, 0, 0, 0, 0, 0, 0, 0, -132104, 0, 628252, 0, 0, 0, 0, 0, 0, 0, -1003648, 0, 0, 0, -393656, 0, -611056, 0, 0, 0, 979472, 0, -543156, 0, 0, 0, -165624, 0, 0, 0, 0, 0, 0, 0, -783296, 0, -315552, 0, 0, 0, 0, 0, 0, 0, -295632, 0, 0, 0, -15944, 0, 521088, 0, 0, 0, 246572, 0, 907080, 0, 0, 0, -113976, 0, 0, 0, 0, 0, 0, 0, 578456, 0, 214464, 0, 0, 0, 0, 0, 0, 0, -777428, 0, 0, 0, 357472, 0, -61776, 0, 0, 0, 13952, 0, -223764, 0, 0, 0, 108252, 0, 0, 0, 0, 0, 0, 0, 139624, 0, -277016, 0, 0, 0, 0, 0, 0, 0, -325536, 0, 0, 0, 198464, 0, 7812, 0, 0, 0, 299904, 0, 146216, 0, 0, 0, 511264, 0, 0, 0, 0, 0, 0, 0, -47168, 0, -139620, 0, 0, 0, 0, 0, 0, 0, -617372, 0, 0, 0, 702000, 0, -92216, 0, 0, 0, 226440, 0, -45724, 0, 0, 0, 133940, 0, 0, 0, 0, 0, 0, 0, 6144, 0, -504680, 0, 0, 0, 0, 0, 0, 0, 457280, 0, 0, 0, 258864, 0, -16704, 0, 0, 0, 362764, 0, 441256, 0, 0, 0, 8296, 0, 0, 0, 0, 0, 0, 0, 320160, 0, 462824, 0, 0, 0, 0, 0, 0, 0, -313268, 0, 0, 0, -290344, 0, 563328, 0, 0, 0, -15992, 0, -99148, 0, 0, 0, 250432, 0, 0, 0, 0, 0, 0, 0, 337372, 0, -857976, 0, 0, 0, 0, 0, 0, 0, -679040, 0, 0, 0, 564624, 0, 300936, 0, 0, 0, 354592, 0, 626200, 0, 0, 0, 343040, 0, 0, 0, 0, 0, 0, 0, -36744, 0, 147808, 0, 0, 0, 0, 0, 0, 0, -534464, 0, 0, 0, 681888, 0, -175792, 0, 0, 0, 716680, 0, 110008, 0, 0, 0, 204480, 0, 0, 0, 0, 0, 0, 0, 40624, 0, 147472, 0, 0, 0, 0, 0, 0, 0, 290168, 0, 0, 0, -560568, 0, -537124, 0, 0, 0, 836920, 0, 1252064, 0, 0, 0, 501992, 0, 0, 0, 0, 0, 0, 0, 1168344, 0, -513116, 0, 0, 0, 0, 0, 0, 0, -527136, 0, 0, 0, 543204, 0, 1117488, 0, 0, 0, -710872, 0, 174232, 0, 0, 0, 3764, 0, 0, 0, 0, 0, 0, 0, -552536, 0, -1113872, 0, 0, 0, 0, 0, 0, 0, -10872, 0, 0, 0, 1125552, 0, -542132, 0, 0, 0, 205236, 0, -376768, 0, 0, 0, 1174576, 0, 0, 0, 0, 0, 0, 0, -261032, 0, 722592, 0, 0, 0, 0, 0, 0, 0, 123452, 0, 0, 0, -460336, 0, -591216, 0, 0, 0, 840544, 0, -461504, 0, 0, 0, 490472, 0, 0, 0, 0, 0, 0, 0, -24812, 0, -494288, 0, 0, 0, 0, 0, 0, 0, 47416, 0, 0, 0, 240104, 0, 349648, 0, 0, 0, 174000, 0, 1336800, 0, 0, 0, -127000, 0, 0, 0, 0, 0, 0, 0, 1157104, 0, 196876, 0, 0, 0, 0, 0, 0, 0, -116684, 0, 0, 0, 393388, 0, -66000, 0, 0, 0, -680536, 0, -264532, 0, 0, 0, -464640, 0, 0, 0, 0, 0, 0, 0, -109856, 0, 280960, 0, 0, 0, 0, 0, 0, 0, 78160, 0, 0, 0, -554512, 0, 85956, 0, 0, 0, 673024, 0, -388048, 0, 0, 0, 662888, 0, 0, 0, 0, 0, 0, 0, -430784, 0, -432488, 0, 0, 0, 0, 0, 0, 0, -873148, 0, 0, 0, 418868, 0, 480952, 0, 0, 0, -429688, 0, 434084, 0, 0, 0, -586496, 0, 0, 0, 0, 0, 0, 0, 960, 0, -796976, 0, 0, 0, 0, 0, 0, 0, 933920, 0, 0, 0, 127984, 0, -677884, 0, 0, 0, 45076, 0, 601944, 0, 0, 0, 258664, 0, 0, 0, 0, 0, 0, 0, 522552, 0, 666980, 0, 0, 0, 0, 0, 0, 0, -726240, 0, 0, 0, -416100, 0, 450888, 0, 0, 0, -153088, 0, -423188, 0, 0, 0, -106592, 0, 0, 0, 0, 0, 0, 0, -976140, 0, 66016, 0, 0, 0, 0, 0, 0, 0, -387440, 0, 0, 0, 929240, 0, -65140, 0, 0, 0, 2432, 0, -293960, 0, 0, 0, -25064, 0, 0, 0, 0, 0, 0, 0, -702760, 0, -639852, 0, 0, 0, 0, 0, 0, 0, -294924, 0, 0, 0, -142424, 0, -12200, 0, 0, 0, 592568, 0, -242464, 0, 0, 0, -1154628, 0, 0, 0, 0, 0, 0, 0, -191140, 0, 508216, 0, 0, 0, 0, 0, 0, 0, -162264, 0, 0, 0, -905104, 0, 238336, 0, 0, 0, -133044, 0, 436464, 0, 0, 0, 201920, 0, 0, 0, 0, 0, 0, 0, 1506240, 0, -265824, 0, 0, 0, 0, 0, 0, 0, -153412, 0, 0, 0, -42736, 0, 398064, 0, 0, 0, -472560, 0, 70848, 0, 0, 0, 461632, 0, 0, 0, 0, 0, 0, 0, 270704, 0, 153088, 0, 0, 0, 0, 0, 0, 0, 614024, 0, 0, 0, 1078456, 0, -4600, 0, 0, 0, 190776, 0, -1198784, 0, 0, 0, -367280, 0, 0, 0, 0, 0, 0, 0, -808000, 0, 1347172, 0, 0, 0, 0, 0, 0, 0, 774292, 0, 0, 0, -1339264, 0, -1205152, 0, 0, 0, 837568, 0, -837484, 0, 0, 0, 188932, 0, 0, 0, 0, 0, 0, 0, -662240, 0, 21984, 0, 0, 0, 0, 0, 0, 0, -344904, 0, 0, 0, -1114712, 0, 414144, 0, 0, 0, 180336, 0, 628440, 0, 0, 0, -656688, 0, 0, 0, 0, 0, 0, 0, 208216, 0, 567628, 0, 0, 0, 0, 0, 0, 0, -204920, 0, 0, 0, 265284, 0, -573848, 0, 0, 0, -1756640, 0, -261764, 0, 0, 0, -901072, 0, 0, 0, 0, 0, 0, 0, -58748, 0, 894016, 0, 0, 0, 0, 0, 0, 0, 784584, 0, 0, 0, -107008, 0, -1204896, 0, 0, 0, 19200, 0, -1499688, 0, 0, 0, 217208, 0, 0, 0, 0, 0, 0, 0, -769792, 0, 53040, 0, 0, 0, 0, 0, 0, 0, 480308, 0, 0, 0, 920548, 0, 805144, 0, 0, 0, -570944, 0, 524344, 0, 0, 0, 492288, 0, 0, 0, 0, 0, 0, 0, -17440, 0, -818488, 0, 0, 0, 0, 0, 0, 0, 955360, 0, 0, 0, -1228504, 0, -5116, 0, 0, 0, -1222844, 0, 122056, 0, 0, 0, -93248, 0, 0, 0, 0, 0, 0, 0, 293816, 0, 425848, 0, 0, 0, 0, 0, 0, 0, 1458080, 0, 0, 0, -1439744, 0, 609528, 0, 0, 0, -417872, 0, -896736, 0, 0, 0, -569568, 0, 0, 0, 0, 0, 0, 0, -307264, 0, 45736, 0, 0, 0, 0, 0, 0, 0, -377824, 0, 0, 0, 358216, 0, 1187008, 0, 0, 0, -260792, 0, 20992, 0, 0, 0, -909904, 0, 0, 0, 0, 0, 0, 0, -483800, 0, 240212, 0, 0, 0, 0, 0, 0, 0, -264180, 0, 0, 0, -537792, 0, -570176, 0, 0, 0, 713408, 0, 49824, 0, 0, 0, -467348, 0, 0, 0, 0, 0, 0, 0, 265528, 0, 411432, 0, 0, 0, 0, 0, 0, 0, 234432, 0, 0, 0, -303136, 0, -651972, 0, 0, 0, 26472, 0, 1144344, 0, 0, 0, -748992, 0, 0, 0, 0, 0, 0, 0, 664584, 0, -513920, 0, 0, 0, 0, 0, 0, 0], "hecke_ring_index_factorization": [[2, 13]], "field_poly": [1152, 0, -1780, 0, 756, 0, -95, 0, 1], "atkin_lehner_string": "++", "has_non_self_twist": 1, "atkin_lehner_eigenvals": [[2, 1], [17, 1]], "char_values": [2312, 1, [1735, 1157, 1737], [1, 1, 1]], "Nk2": 36992, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 4, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 8192, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-\\beta _{2}q^{3}+\\beta _{4}q^{5}+(-\\beta _{1}-\\beta _{2}-\\beta _{4}+\\cdots)q^{7}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 32424606678091630592, "level_is_prime_power": false, "relative_dim": 8, "hecke_cutters": [[3, [373248, 0, -106624, 0, 8760, 0, -174, 0, 1]]], "space_label": "2312.4.a", "level": 2312, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 2, 1, 2, 0]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 7, "hecke_orbit_code": 45035996340816136, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.145", "prec": 17}, {"__RealLiteral__": 0, "data": "6.894", "prec": 17}, {"__RealLiteral__": 0, "data": "3.941", "prec": 17}, {"__RealLiteral__": 0, "data": "279.485", "prec": 24}, {"__RealLiteral__": 0, "data": "127.231", "prec": 24}, {"__RealLiteral__": 0, "data": "17603.904", "prec": 30}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "nf_label": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [38, 0, 0, -1, 0, -2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [63, 0, 0, 0, 0, -3, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -6, -19, 0, -3, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -18, 0, -5, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -14, 0, 4, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [98, 0, 0, 1, 0, -5, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-130, 0, 0, 0, 0, 8, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 28, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 10, -3, 0, 21, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 2, 0, -16, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 1, 0, -4, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 20, 10, 0, 43, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [41, 0, 0, 1, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [136, 0, 0, -4, 0, -6, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-57, 0, 0, -3, 0, 10, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [171, 0, 0, 3, 0, -8, 7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 0, 28, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, -1, 0, 4, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -16, -74, 0, 5, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, -15, -80, 0, -70, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -20, -78, 0, 16, 0, 0, 10], [0, 0, 0, 0, 0, 0, 0, 0], [-73, 0, 0, -3, 0, 4, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, -8, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -29, 31, 0, -27, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, -20, 6, 0, 26, 0, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, -151, 0, 12, 0, 0, 12], [0, 0, 0, 0, 0, 0, 0, 0], [-207, 0, 0, -4, 0, 2, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, -64, 0, -16, 0, 0, -11], [0, 0, 0, 0, 0, 0, 0, 0], [391, 0, 0, -3, 0, -7, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-297, 0, 0, -1, 0, 16, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [819, 0, 0, -5, 0, -24, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [19, 0, 0, 4, 0, 18, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -20, 139, 0, 21, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [505, 0, 0, 4, 0, -10, -7, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 32, -120, 0, -12, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [0, 24, -140, 0, 22, 0, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0], [0, 10, -183, 0, 70, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0]]}