# Stored data for newform 91.3.b.b, downloaded from the LMFDB on 04 June 2024.
{"Nk2": 819, "analytic_conductor": 2.479570405678702, "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, [-3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503668397178971, "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_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": true, "label": "91.3.b.b", "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": "91.3.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 2, "qexp_display": "q+4q^{4}+3q^{5}-7q^{7}+9q^{9}+13q^{13}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "2.2.1.d2", "self_twist_discs": [-91], "self_twist_type": 1, "space_label": "91.3.b", "trace_display": [0, 0, 3, -7], "trace_hash": 1579202812451510955, "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.964", "prec": 17}, {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "2.859", "prec": 17}, {"__RealLiteral__": 0, "data": "0.080", "prec": 17}, {"__RealLiteral__": 0, "data": "9.476", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 1, 0, 0, 4, 3, 0, -7, 0, 9, 0, 0, 0, 13, 0, 0, 16, 0, 0, -25, 12, 0, 0, -45, 0, -16, 0, 0, -28, -33, 0, 55, 0, 0, 0, -21, 36, 0, 0, 0, 0, -30, 0, -5, 0, 27, 0, -81, 0, 49, 0, 0, 52, 15, 0, 0, 0, 0, 0, 90, 0, 0, 0, -63, 64, 39, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, -100, 0, 0, 67, 48, 81, 0, 159, 0, 0, 0, 0, 0, -165, 0, -91, -180, 0, 0, -75, 0, 131, 0, 0, -64, 0, 0, 0, 0, 0, 0, -150, 0, 0, 0, 0, -112, 135, 0, -135, -132, 117, 0, 0, 0, 121, 0, 0, 220, -123, 0, -110, 0, 0, 0, 0, 0, 175, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 144, -99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 165, 0, 0, 0, 0, 0, 315, 0, 0, -120, 0, 0, -9, 0, 169, 0, -225, -20, 0, 0, 112, 0, 0, 0, 267, 108, 0, 0, 0, 0, 0, 0, 0, -324, 0, 0, 18, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, 0, 231, 0, -90, 0, -405, 208, 0, 0, -397, 60, 0, 0, -15, 0, -385, 0, 0, 0, 0, 0, -121, 0, -144, 0, -246, 0, 10, 0, 0, 0, 375, 0, -243, 360, 0, 0, 0, 0, -365, 0, 0, 0, 147, 0, -325, 0, 0, 0, 0, -252, 0, 0, 0, 256, 0, 0, 0, 156, -297, 0, 435, 0, 45, 0, 0, 0, 0, 0, 290, 0, 0, 0, 0, 0, -265, 0, 495, 0, 0, 0, 0, 0, 0, 0, 210, 0, 289, 0, 0, -116, -261, 0, 270, 0, 0, 0, -585, 0, 35, 0, 0, -400, 0, 0, 439, 0, 0, 0, 0, 0, 0, 0, -189, 268, 0, 0, 0, 192, 0, 0, 0, 324, -208, 0, 0, 0, 567, 0, 0, 636, 0, 0, 0, 0, -145, 0, 0, 0, 0, 0, -343, 0, 0, 0, 330, 0, 355, 0, 0, 0, 594, 0, 0, -660, 0, 0, 0, 0, 264, 0, 0, -364, -87, 0, 0, -720, -270, 0, -105, 0, -710, 0, 0, 0, -429, 0, 0, -300, 0, 0, 66, 0, 0, 0, -45, 524, -678, 0, 0, 0, 0, 0, 201, 0, -781, 0, 0, -256, 0, 0, 715, 0, 243, 0, 0, 0, 755, 0, 0, 0, -630, 0, 477, 0, 0, 0, 0, 0, 0, 0, -729, 0, 0, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 1125, 0, 0, 0, 441, 0, 795, 0, -495, 0, 0, -448, 0, 0, 0, 540, 0, 0, -273, 0, 0, 0, 0, -540, -870, 0, 0, -528, 0, 0, 0, 468, 0, 0, 0, 0, 0, 0, 400, 0, 135, 0, 615, 0, 0, 0, 0, 484, 393, 0, 0, 0, 0, 0, 618, 0, 0, 0, 0, 880, 0, 0, 0, -492, 0, 0, 0, 0, 0, 0, 0, -440, -1005, 0, 203, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1496, 0, 810, 700, -390, 0, -450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 275, 0, 0, 0, 825, 0, -469, 0, 0, 0, 0, 0, -65, -336, 0, 0, 0, 0, 405, 0, -567, 0, -1137, 0, -1133, 0, 0, 0, 720, 576, 146, 0, 0, -396, -1113, 0, 0, 0, 351, 0, -849, 0, -1375, 0, 0, 0, 1011, 0, 0, 0, 0, 0, -1077, 0, 0, 0, 0, 0, 363, 0, 0, 0, 0, 0, -1053, 0, 0, 0, 0, 0, 0, 0, -1030, 660, 0, 0, 1155, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, -330, 0, 637, 0, 0, 0, -993, 0, 586, 1260, 0, 0, 0, 0, 0, 0, 0, 0, -150, 0, 0, -480, -261, 0, -957, 0, -1205, 0, 0, 0, 525, 0, 1485, -36, 0, 0, 0, 0, 1255, 0, 0, 676, 0, 0, -917, 0, 0, 0, 0, -900, 0, 0, 0, -80, 195, 0, 815, 0, 0, 0, 0, 0, 0, 0, 0, 448, -873, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603, 0, -2475, 0, 0, 1068, 0, 0, 0, 432, 0, 0, 0, 0, 528, 0, 0, 0, 729, 0, 0, 0, 1459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1431, 0, 1050, 0, -773, -1296, 0, 0, 0, 0, 695, 0, 0, 0, 675, 0, 0, 72, 0, 0, 1170, 0, -485, 0, 0, 0, -246, 0, -880, 0, 0, 0, 750, 0, 0, 0, 0, 784, 0, 0, -1, 0, 0, 0, -945, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1485, 0, 0, 0, 945, 0, 0, 0, -657, 0, 250, 924, 0, 0, 0, 0, 125, 0, -819, -360, 0, 0, -1630, 0, 0, 0, 0, -1620, 0, 0, 0, 832, 0, 0, -27, 0, 0, 0, 1650, 0, 248, 0, 0, -1588, 507, 0, -847, 240, 0, 0, 0, 0, -1381, 0, -675, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -1540, 0, 0, 0, 0, 1179, 0, 861, 0, 0, 0, 0, 0, 0, 0, -1510, 0, 0, 0, 0, 0, 770, 0, 0, -484, 2025, 0, 801, 0, 0, 0, -1815, -576, 0, 0, 0, 0, 0, 0, 995, -984, 0, 0, -453, 0, 0, 0, 0, 40, 0, 0, -1438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1845, 0, -1225, 1500, 0, 0, 0, 0, 0, 0, 0, -972, 1875, 0, 1350, 1440, 0, 0, 0, 0, -377, 0, 0, 0, 1815, 0, 54, 0, 0, 0, 0, 0, 2064, 0, -1350, -1460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 588, 0, 0, 1791, 0, 0, 0, 0, -1300, 225, 0, 1618, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 3, "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], 1, 0, 0, 4, 3, 0, -7, 0, 9, 0, 0, 0, 13, 0, 0, 16, 0, 0, -25, 12, 0, 0, -45, 0, -16, 0, 0, -28, -33, 0, 55, 0, 0, 0, -21, 36, 0, 0, 0, 0, -30, 0, -5, 0, 27, 0, -81, 0, 49, 0, 0, 52, 15, 0, 0, 0, 0, 0, 90, 0, 0, 0, -63, 64, 39, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, -100, 0, 0, 67, 48, 81, 0, 159, 0, 0, 0, 0, 0, -165, 0, -91, -180, 0, 0, -75, 0, 131, 0, 0, -64, 0, 0, 0, 0, 0, 0, -150, 0, 0, 0, 0, -112, 135, 0, -135, -132, 117, 0, 0, 0, 121, 0, 0, 220, -123, 0, -110, 0, 0, 0, 0, 0, 175, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 144, -99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 165, 0, 0, 0, 0, 0, 315, 0, 0, -120, 0, 0, -9, 0, 169, 0, -225, -20, 0, 0, 112, 0, 0, 0, 267, 108, 0, 0, 0, 0, 0, 0, 0, -324, 0, 0, 18, 0, 0, 0, 0, 196, 0, 0, 0, 0, 0, 0, 231, 0, -90, 0, -405, 208, 0, 0, -397, 60, 0, 0, -15, 0, -385, 0, 0, 0, 0, 0, -121, 0, -144, 0, -246, 0, 10, 0, 0, 0, 375, 0, -243, 360, 0, 0, 0, 0, -365, 0, 0, 0, 147, 0, -325, 0, 0, 0, 0, -252, 0, 0, 0, 256, 0, 0, 0, 156, -297, 0, 435, 0, 45, 0, 0, 0, 0, 0, 290, 0, 0, 0, 0, 0, -265, 0, 495, 0, 0, 0, 0, 0, 0, 0, 210, 0, 289, 0, 0, -116, -261, 0, 270, 0, 0, 0, -585, 0, 35, 0, 0, -400, 0, 0, 439, 0, 0, 0, 0, 0, 0, 0, -189, 268, 0, 0, 0, 192, 0, 0, 0, 324, -208, 0, 0, 0, 567, 0, 0, 636, 0, 0, 0, 0, -145, 0, 0, 0, 0, 0, -343, 0, 0, 0, 330, 0, 355, 0, 0, 0, 594, 0, 0, -660, 0, 0, 0, 0, 264, 0, 0, -364, -87, 0, 0, -720, -270, 0, -105, 0, -710, 0, 0, 0, -429, 0, 0, -300, 0, 0, 66, 0, 0, 0, -45, 524, -678, 0, 0, 0, 0, 0, 201, 0, -781, 0, 0, -256, 0, 0, 715, 0, 243, 0, 0, 0, 755, 0, 0, 0, -630, 0, 477, 0, 0, 0, 0, 0, 0, 0, -729, 0, 0, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 1125, 0, 0, 0, 441, 0, 795, 0, -495, 0, 0, -448, 0, 0, 0, 540, 0, 0, -273, 0, 0, 0, 0, -540, -870, 0, 0, -528, 0, 0, 0, 468, 0, 0, 0, 0, 0, 0, 400, 0, 135, 0, 615, 0, 0, 0, 0, 484, 393, 0, 0, 0, 0, 0, 618, 0, 0, 0, 0, 880, 0, 0, 0, -492, 0, 0, 0, 0, 0, 0, 0, -440, -1005, 0, 203, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1496, 0, 810, 700, -390, 0, -450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 275, 0, 0, 0, 825, 0, -469, 0, 0, 0, 0, 0, -65, -336, 0, 0, 0, 0, 405, 0, -567, 0, -1137, 0, -1133, 0, 0, 0, 720, 576, 146, 0, 0, -396, -1113, 0, 0, 0, 351, 0, -849, 0, -1375, 0, 0, 0, 1011, 0, 0, 0, 0, 0, -1077, 0, 0, 0, 0, 0, 363, 0, 0, 0, 0, 0, -1053, 0, 0, 0, 0, 0, 0, 0, -1030, 660, 0, 0, 1155, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, -330, 0, 637, 0, 0, 0, -993, 0, 586, 1260, 0, 0, 0, 0, 0, 0, 0, 0, -150, 0, 0, -480, -261, 0, -957, 0, -1205, 0, 0, 0, 525, 0, 1485, -36, 0, 0, 0, 0, 1255, 0, 0, 676, 0, 0, -917, 0, 0, 0, 0, -900, 0, 0, 0, -80, 195, 0, 815, 0, 0, 0, 0, 0, 0, 0, 0, 448, -873, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603, 0, -2475, 0, 0, 1068, 0, 0, 0, 432, 0, 0, 0, 0, 528, 0, 0, 0, 729, 0, 0, 0, 1459, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1431, 0, 1050, 0, -773, -1296, 0, 0, 0, 0, 695, 0, 0, 0, 675, 0, 0, 72, 0, 0, 1170, 0, -485, 0, 0, 0, -246, 0, -880, 0, 0, 0, 750, 0, 0, 0, 0, 784, 0, 0, -1, 0, 0, 0, -945, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1485, 0, 0, 0, 945, 0, 0, 0, -657, 0, 250, 924, 0, 0, 0, 0, 125, 0, -819, -360, 0, 0, -1630, 0, 0, 0, 0, -1620, 0, 0, 0, 832, 0, 0, -27, 0, 0, 0, 1650, 0, 248, 0, 0, -1588, 507, 0, -847, 240, 0, 0, 0, 0, -1381, 0, -675, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -1540, 0, 0, 0, 0, 1179, 0, 861, 0, 0, 0, 0, 0, 0, 0, -1510, 0, 0, 0, 0, 0, 770, 0, 0, -484, 2025, 0, 801, 0, 0, 0, -1815, -576, 0, 0, 0, 0, 0, 0, 995, -984, 0, 0, -453, 0, 0, 0, 0, 40, 0, 0, -1438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1845, 0, -1225, 1500, 0, 0, 0, 0, 0, 0, 0, -972, 1875, 0, 1350, 1440, 0, 0, 0, 0, -377, 0, 0, 0, 1815, 0, 54, 0, 0, 0, 0, 0, 2064, 0, -1350, -1460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 588, 0, 0, 1791, 0, 0, 0, 0, -1300, 225, 0, 1618, 0, 0, 0, 0, 0, 0, 0, 0, 0]}