# Stored data for newform 650.6.b.a, downloaded from the LMFDB on 12 September 2024.
{"Nk2": 23400, "analytic_conductor": 104.2494828784374, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": 1, "char_values": [650, 2, [27, 301], [1, 2]], "cm_discs": [], "conrey_index": 599, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 68820140682, "hecke_ring_generator_nbound": 13, "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, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "650.6.b.a", "level": 650, "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": false, "level_primes": [2, 5, 13], "level_radical": 130, "minimal_twist": "26.6.a.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+4iq^{2}-2^{4}q^{4}+170iq^{7}-2^{6}iq^{8}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "650.6.b", "trace_display": [0, 0, 0, 0], "trace_hash": 1019818517001140665, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.918", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.571", "prec": 20}, {"__RealLiteral__": 0, "data": "0.705", "prec": 17}, {"__RealLiteral__": 0, "data": "139.923", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 0, -32, 0, 0, 0, 0, 486, 0, -500, 0, 0, -1360, 0, 512, 0, 0, 156, 0, 0, 0, 0, 0, 0, 1352, 0, 0, -5156, 0, -17308, 0, 0, 8496, 0, -7776, 0, 0, 0, 0, 2100, 0, 0, 8000, 0, -12608, 0, 0, -24186, 0, 0, 0, 0, 0, 0, 21760, 0, 0, 27844, 0, -65764, 0, 0, -8192, 0, 0, 0, 0, 0, 0, -101084, 0, 0, 87888, 0, -2496, 0, 0, 38696, 0, 118098, 0, 0, 0, 0, 47200, 0, 0, -188340, 0, 57460, 0, 0, -47696, 0, 0, 0, 0, -121500, 0, -37028, 0, 0, -21632, 0, -232368, 0, 0, 357244, 0, 0, 0, 0, 0, 0, 82496, 0, 0, 361080, 0, -197102, 0, 0, 276928, 0, -330480, 0, 0, 0, 0, -525472, 0, 0, -556528, 0, -135936, 0, 0, 115552, 0, 0, 0, 0, 124416, 0, 374000, 0, 0, -57732, 0, 79740, 0, 0, 340000, 0, 0, 0, 0, 0, 0, -535840, 0, 0, -33600, 0, 699504, 0, 0, -57122, 0, 37908, 0, 0, 0, 0, -128000, 0, 0, 1349832, 0, 372564, 0, 0, 201728, 0, 0, 0, 0, 0, 0, 1624360, 0, 0, 1462288, 0, 386976, 0, 0, 78752, 0, 0, 0, 0, 0, 0, -928448, 0, 0, -39000, 0, -821552, 0, 0, 1228160, 0, 0, 0, 0, 0, 0, -358956, 0, 0, -348160, 0, 1958032, 0, 0, 596220, 0, 0, 0, 0, 328536, 0, -445504, 0, 0, -73140, 0, 761844, 0, 0, 1052224, 0, 0, 0, 0, 0, 0, -2456136, 0, 0, 2052800, 0, 131072, 0, 0, 3735240, 0, -1252908, 0, 0, 0, 0, -106080, 0, 0, -3876804, 0, -1390996, 0, 0, -306288, 0, 0, 0, 0, -4205844, 0, 3462436, 0, 0, 1617344, 0, -338000, 0, 0, 584026, 0, 0, 0, 0, 0, 0, -1406208, 0, 0, 532688, 0, 2006000, 0, 0, 39936, 0, 2064528, 0, 0, 0, 0, 5364480, 0, 0, 1288336, 0, -619136, 0, 0, 1289000, 0, 0, 0, 0, -1889568, 0, -2502640, 0, 0, -2027080, 0, -4114556, 0, 0, 4263408, 0, 0, 0, 0, 0, 0, 4327000, 0, 0, -755200, 0, 5043664, 0, 0, 4876492, 0, 0, 0, 0, 0, 0, 3013440, 0, 0, -3173868, 0, -4940030, 0, 0, -919360, 0, 0, 0, 0, 510300, 0, -9875640, 0, 0, -2124000, 0, 763136, 0, 0, -3351620, 0, 0, 0, 0, 0, 0, 1201136, 0, 0, -2752212, 0, 3347424, 0, 0, 1891152, 0, 1944000, 0, 0, 0, 0, 4453620, 0, 0, 592448, 0, 3506080, 0, 0, -4015652, 0, 0, 0, 0, -3063744, 0, 346112, 0, 0, -11987568, 0, -10654732, 0, 0, 3717888, 0, 0, 0, 0, 0, 0, -10859436, 0, 0, 11769440, 0, -5715904, 0, 0, -13728352, 0, -5877198, 0, 0, 0, 0, -8695056, 0, 0, 2808524, 0, -525000, 0, 0, -2051760, 0, 0, 0, 0, 0, 0, -12509292, 0, 0, -1319936, 0, 4895408, 0, 0, -23652440, 0, 0, 0, 0, 0, 0, -5777280, 0, 0, -4436172, 0, -3713268, 0, 0, 3153632, 0, 0, 0, 0, 0, 0, 12889720, 0, 0, 105456, 0, -4430848, 0, 0, -8516756, 0, 0, 0, 0, 5287680, 0, 3152000, 0, 0, -8478724, 0, 15895000, 0, 0, -3514224, 0, 0, 0, 0, 0, 0, 4773132, 0, 0, 8407552, 0, 13438944, 0, 0, 7905134, 0, 6766092, 0, 0, 0, 0, 8904448, 0, 0, 6046500, 0, 140116, 0, 0, 2174976, 0, 0, 0, 0, -15980652, 0, -402168, 0, 0, -9051024, 0, -1848832, 0, 0, -1994200, 0, 0, 0, 0, 0, 0, 11769952, 0, 0, 23410220, 0, 9637704, 0, 0, -1428000, 0, -1990656, 0, 0, 0, 0, 29728920, 0, 0, -5984000, 0, -23108368, 0, 0, -1350024, 0, 0, 0, 0, 0, 0, 923712, 0, 0, 12932696, 0, -23604148, 0, 0, -1275840, 0, 0, 0, 0, 0, 0, 2015156, 0, 0, 6992944, 0, -5440000, 0, 0, -18863372, 0, 0, 0, 0, 0, 0, 10756688, 0, 0, -23334264, 0, -9749476, 0, 0, 10565904, 0, 0, 0, 0, -24563412, 0, 19485580, 0, 0, 8573440, 0, 662688, 0, 0, -6961000, 0, 0, 0, 0, 0, 0, 537600, 0, 0, 12049152, 0, -40140956, 0, 0, -11192064, 0, 21356784, 0, 0, 0, 0, 16441000, 0, 0, 3627184, 0, 913952, 0, 0, 62147240, 0, 0, 0, 0, -606528, 0, -6411040, 0, 0, 9817548, 0, 31523444, 0, 0, -9845184, 0, 0, 0, 0, 0, 0, -28407228, 0, 0, 2048000, 0, 21465200, 0, 0, -32143540, 0, 9403128, 0, 0, 0, 0, -21597312, 0, 0, 41415568, 0, -39459040, 0, 0, -5961024, 0, 0, 0, 0, 28697814, 0, -12531600, 0, 0, -480416, 0, -3227648, 0, 0, -27798300, 0, 0, 0, 0, 0, 0, 32148272, 0, 0, 52196800, 0, -3252480, 0, 0, -3485456, 0, 0, 0, 0, 0, 0, 44342628, 0, 0, -25989760, 0, -5498064, 0, 0, -2179092, 0, 0, 0, 0, 11469600, 0, -23396608, 0, 0, 163800, 0, 25271000, 0, 0, -6191616, 0, 0, 0, 0, 0, 0, 83216360, 0, 0, -5769584, 0, -1260032, 0, 0, 12663288, 0, -45766620, 0, 0, 0, 0, -11700208, 0, 0, -23193612, 0, -49506812, 0, 0, -21972000, 0, 0, 0, 0, 13962780, 0, -4949404, 0, 0, 14855168, 0, -18933920, 0, 0, 34782388, 0, 0, 0, 0, 0, 0, 624000, 0, 0, 68765092, 0, -27730130, 0, 0, 13144832, 0, -11590128, 0, 0, 0, 0, 34627872, 0, 0, 44719520, 0, -19650560, 0, 0, -17642704, 0, 0, 0, 0, 0, 0, -59518352, 0, 0, -9674000, 0, 23513308, 0, 0, -983424, 0, 0, 0, 0, 0, 0, -26105436, 0, 0, 5743296, 0, 27730368, 0, 0, 87244000, 0, -29524500, 0, 0, 0, 0, 5570560, 0, 0, 44620024, 0, 61693704, 0, 0, -31328512, 0, 0, 0, 0, -8997804, 0, -65466984, 0, 0, -47605744, 0, -9539520, 0, 0, 25543416, 0, 0, 0, 0, 0, 0, 12404368, 0, 0, -69659412, 0, -1886508, 0, 0, -14438368, 0, -5256576, 0, 0, 0, 0, -90129740, 0, 0, 7128064, 0, -11800000, 0, 0, -15801500, 0, 0, 0, 0, -56465424, 0, 1170240, 0, 0, -13017240, 0, 92525130, 0, 0, -12189504, 0, 0, 0, 0, 0, 0, -80172768, 0, 0, -49141424, 0, -16835584, 0, 0, 47085000, 0, 86810292, 0, 0, 0, 0, -21902688, 0, 0, 18596800, 0, -64820616, 0, 0, 68737120, 0, 0, 0, 0, 0, 0], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 4], [0, 0], [-16, 0], [0, 0], [0, 0], [0, 170], [0, -64], [243, 0], [0, 0], [-250, 0], [0, 0], [0, -169], [-680, 0], [0, 0], [256, 0], [0, -1062], [0, 972], [78, 0], [0, 0], [0, 0], [0, -1000], [0, 1576], [0, 0], [0, 0], [676, 0], [0, 0], [0, -2720], [-2578, 0], [0, 0], [-8654, 0], [0, 1024], [0, 0], [4248, 0], [0, 0], [-3888, 0], [0, -10986], [0, 312], [0, 0], [0, 0], [1050, 0], [0, 0], [0, -5900], [4000, 0], [0, 0], [-6304, 0], [0, 5962], [0, 0], [-12093, 0], [0, 0], [0, 0], [0, 2704], [0, 29046], [0, 0], [0, 0], [10880, 0], [0, 0], [0, -10312], [13922, 0], [0, 0], [-32882, 0], [0, -34616], [0, 41310], [-4096, 0], [0, 0], [0, 0], [0, 69566], [0, 16992], [0, 0], [0, 0], [-50542, 0], [0, -15552], [0, -46750], [43944, 0], [0, 0], [-1248, 0], [0, -42500], [0, 0], [19348, 0], [0, 0], [59049, 0], [0, 4200], [0, -87438], [0, 0], [0, 0], [23600, 0], [0, 0], [0, 16000], [-94170, 0], [0, 0], [28730, 0], [0, -25216], [0, 0], [-23848, 0], [0, 0], [0, 0], [0, -182786], [0, -48372], [-60750, 0], [0, 0]]}