# Stored data for newform 91.9.b.a, downloaded from the LMFDB on 23 May 2024.
{"Nk2": 7371, "analytic_conductor": 37.071453515562574, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 91, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": -1, "char_values": [91, 2, [66, 15], [1, 1]], "cm_discs": [-91], "conrey_index": 90, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 0, "hecke_cutters": [[2, [0, 1]], [5, [431, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 68870471771, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 91, 2, -1, 2, -91]], "is_cm": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "91.9.b.a", "level": 91, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [7, 13], "level_radical": 91, "minimal_twist": "91.9.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 2, "qexp_display": "q+2^{8}q^{4}-431q^{5}-7^{4}q^{7}+3^{8}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "8.2.1.d2", "self_twist_discs": [-91], "self_twist_type": 1, "space_label": "91.9.b", "trace_display": [0, 0, -431, -2401], "trace_hash": 460588017699542437, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.815", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.214", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 1, 0, 0, 256, -431, 0, -2401, 0, 6561, 0, 0, 0, -28561, 0, 0, 65536, 0, 0, 251233, -110336, 0, 0, 375407, 0, -204864, 0, 0, -614656, -1062913, 0, 630433, 0, 0, 0, 1034831, 1679616, 0, 0, 0, 0, -409922, 0, 6653327, 0, -2827791, 0, 5166913, 0, 5764801, 0, 0, -7311616, 13303487, 0, 0, 0, 0, 0, 22939678, 0, 0, 0, -15752961, 16777216, 12309791, 0, 0, 0, 0, 0, 0, 0, -39577007, 0, 0, 64315648, 0, 0, -14012113, -28246016, 43046721, 0, -37402367, 0, 0, 0, 0, 0, -4088207, 0, 68574961, 96104192, 0, 0, -108281423, 0, 174312913, 0, 0, -52445184, 0, 0, 0, 0, 0, 0, -262000798, 0, 0, 0, 0, -157351936, -272614753, 0, -161800417, -272105728, -187388721, 0, 0, 0, 214358881, 0, 0, 161390848, 256655759, 0, -113944318, 0, 0, 0, 0, 0, -603210433, 0, 0, 0, 0, 0, 0, 264916736, 0, 0, 0, 429981696, 458115503, 0, 0, 0, 0, 0, 0, 0, 0, 0, -271716623, 0, 0, 0, 0, 0, -901352207, 0, 0, -104940032, 0, 0, -1546563167, 0, 815730721, 0, 1648339713, 1703251712, 0, 0, 491878464, 0, 0, 0, -2001310513, -723914496, 0, 0, 0, 0, 0, 0, 0, 1322729728, 0, 0, 2614552322, 0, 0, 0, 0, 1475789056, 0, 0, 0, 0, 0, 0, 2552054113, 0, 176676382, 0, 2463045327, -1871773696, 0, 0, 737194607, 3405692672, 0, 0, -2867583937, 0, -1513669633, 0, 0, 0, 0, 0, -2247976607, 0, -1344112704, 0, 3500653918, 0, -5479150562, 0, 0, 0, -4867580833, 0, -2226939503, 5872557568, 0, 0, 0, 0, 6455659153, 0, 0, 0, -2484629231, 0, -7175465713, 0, 0, 0, 0, -4032758016, 0, 0, 0, 4294967296, 0, 0, 0, 3151306496, -6973772193, 0, -6979214353, 0, -5733802897, 0, 0, 0, 0, 0, 6845581438, 0, 0, 0, 0, 0, -4846946593, 0, 4136270913, 0, 0, 0, 0, 0, 0, 0, 984222722, 0, 6975757441, 0, 0, -10131713792, 4011906673, 0, -9887001218, 0, 0, 0, -10721999327, 0, -15974638127, 0, 0, 16464805888, 0, 0, 17747914273, 0, 0, 0, 0, 0, 0, 0, 6789526191, -3587100928, 0, 0, 0, -7230980096, 0, 0, 0, 11019960576, 5851120704, 0, 0, 0, -12405758113, 0, 0, -9575005952, 0, 0, 0, 0, 16686733247, 0, 0, 0, 0, 0, -13841287201, 0, 0, 0, -11594295838, 0, 15846616273, 0, 0, 0, 20318115838, 0, 0, -1046580992, 0, 0, 0, 0, 46134457248, 0, 0, 17555190016, 17057690017, 0, 0, 24602673152, -2689498242, 0, -31941672287, 0, 12290851682, 0, 0, 0, 30357858193, 0, 0, -27720044288, 0, 0, -40498391042, 0, 0, 0, 43652478447, 44624105728, -21133900318, 0, 0, 0, 0, 0, 6039220703, 0, -37192242287, 0, 0, -13425967104, 0, 0, -18005796913, 0, -18553136751, 0, 0, 0, 523041553, 0, 0, 0, -55078166878, 0, 16120420177, 0, 0, 0, 0, 0, 0, 0, 33900116193, 0, 0, 0, 0, -67072204288, 0, 0, 0, 0, 0, 0, 0, 0, 94314626831, 0, 0, 0, 37822859361, 0, -19654156273, 0, 1762017217, 0, 0, -40282095616, 0, 0, 0, -69789376768, 0, 0, -29555808191, 0, 0, 0, 0, -41420906752, -19799381282, 0, 0, -69659066368, 0, 0, 0, -47971512576, 0, 0, 0, 0, 0, 0, -51468597312, 0, 87284178207, 0, 98780793313, 0, 0, 0, 0, 54875873536, -75128865503, 0, 0, 0, 0, 0, -106192440478, 0, 0, 0, 0, 41316057088, 0, 0, 0, 65703874304, 0, 0, 0, 0, 0, 0, 0, -29169745408, -107683281647, 0, 95024393807, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62619430368, 0, 150507227358, -154421870848, 11707782242, 0, 112922343938, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94260469487, 0, 0, 0, -267038821729, 0, 33643083313, 0, 0, 0, 0, 0, -190025672447, 67818684416, 0, 0, 0, 0, 117496958543, 0, -103355177121, 0, 206701320767, 0, 186321935087, 0, 0, 0, -76907379648, 110075314176, -193750951682, 0, 0, 117277568768, 89803083167, 0, 0, 0, 80764538751, 0, 236453045953, 0, 158385573889, 0, 0, 0, 145665933073, 0, 0, 0, 0, 0, -61823140273, 0, 0, 0, 0, 0, -92388677711, 0, 0, 0, 0, 0, -147572202193, 0, 0, 0, 0, 0, 0, 0, 206848505758, -69559455488, 0, 0, 9815785007, 0, -30593632129, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49110001058, 0, -164648481361, 0, 0, 0, -310656173953, 0, 108105967198, -230746164992, 0, 0, 0, 0, 0, 0, 0, 0, 325778710562, 0, 0, -26864648192, -259664742927, 0, -374963913553, 0, 47504338993, 0, 0, 0, 259983696623, 0, -399024980591, -395920170752, 0, 0, 0, 0, 37495115807, 0, 0, 208827064576, 0, 0, -418525304113, 0, 0, 0, 0, 421974966528, 0, 0, 0, 436032438272, -379960892207, 0, 371448207553, 0, 0, 0, 0, 0, 0, 0, 0, 125920886784, -434253312673, 0, 0, 0, 0, 0, 0, 0, 0, 0, -91933473393, 0, 236668961231, 0, 0, -512335491328, 0, 0, 0, -185322110976, 0, 0, 0, 0, 217752608832, 0, 0, 0, 282429536481, 0, 0, 0, -533774195567, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -245396929887, 0, 629063915998, 0, -354792652273, 338618810368, 0, 0, 0, 0, -217104509473, 0, 0, 0, 177091616593, 0, 0, 669325394432, 0, 0, -655180143358, 0, -198334900367, 0, 0, 0, -573103738082, 0, -129153026112, 0, 0, 0, -102985933826, 0, 0, 0, 0, 377801998336, 0, 0, -767233438847, 0, 0, 0, 654548021953, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26822726127, 0, 0, 0, 388482801217, 0, 0, 0, -87012658753, 0, -704669827682, 653325852928, 0, 0, 0, 0, 1671535302191, 0, 449920319121, 45229153792, 0, 0, 778285078082, 0, 0, 0, 0, 630539603712, 0, 0, 0, -479174066176, 0, 0, 666568724977, 0, 0, 0, -737316108482, 0, 629537632608, 0, 0, 188721819392, -351579940751, 0, -514675673281, 871857324032, 0, 0, 0, 0, 854577238513, 0, -710434416303, 0, 0, 0, 0, -734101487872, 0, 0, 0, 0, 0, 0, 0, -387499426048, 0, 0, 0, 0, 1143667022193, 0, -616230477359, 0, 0, 0, 0, 0, 0, 0, -696389672158, 0, 0, 0, 0, 0, 273580307518, 0, 0, -575482011392, 1298099053729, 0, 862564831103, 0, 0, 0, -670095431329, -344092852224, 0, 0, 0, 0, 0, 0, -924120049873, 896167403008, 0, 0, 738419432207, 0, 0, 0, 0, -1402662543872, 0, 0, -1283136212158, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1325813175887, 0, 1448308249633, -1246100693248, 0, 0, 0, 0, 0, 0, 0, -570096512768, -1475695780847, 0, -153887588254, 1503374737408, 0, 0, 0, 0, 1130358896927, 0, 0, 0, 534226353887, 0, -1126872050782, 0, 0, 0, 0, 0, -455445269952, 0, -1718987235678, 1652648743168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -636065083136, 0, 0, 241541202433, 0, 0, 0, 0, -1836919222528, 2497705529089, 0, -1501561428478, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 9, "weight_parity": -1, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [0], [0], [256], [-431], [0], [-2401], [0], [6561], [0], [0], [0], [-28561], [0], [0], [65536], [0], [0], [251233], [-110336], [0], [0], [375407], [0], [-204864], [0], [0], [-614656], [-1062913], [0], [630433], [0], [0], [0], [1034831], [1679616], [0], [0], [0], [0], [-409922], [0], [6653327], [0], [-2827791], [0], [5166913], [0], [5764801], [0], [0], [-7311616], [13303487], [0], [0], [0], [0], [0], [22939678], [0], [0], [0], [-15752961], [16777216], [12309791], [0], [0], [0], [0], [0], [0], [0], [-39577007], [0], [0], [64315648], [0], [0], [-14012113], [-28246016], [43046721], [0], [-37402367], [0], [0], [0], [0], [0], [-4088207], [0], [68574961], [96104192], [0], [0], [-108281423], [0], [174312913], [0], [0], [-52445184]]}