# Stored data for newform 1150.2.b.a, downloaded from the LMFDB on 18 April 2025.
{"Nk2": 4600, "analytic_conductor": 9.182796232447243, "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": [1150, 2, [277, 51], [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, [9, 0, 1]], [7, [16, 0, 1]], [11, [-3, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 68753032318, "hecke_ring_generator_nbound": 2, "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": true, "label": "1150.2.b.a", "level": 1150, "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, 23], "level_radical": 230, "minimal_twist": "1150.2.a.d", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}-4 i q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1150.2.b", "trace_display": [0, 0, 0, 0], "trace_hash": 1130129306486409668, "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "1.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.079", "prec": 17}, {"__RealLiteral__": 0, "data": "15.464", "prec": 20}, {"__RealLiteral__": 0, "data": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "155.618", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.517", "prec": 17}, "traces": [0, 2, 0, 0, -2, 0, -6, 0, 0, -12, 0, 6, 0, 0, 8, 0, 2, 0, 0, 2, 0, 24, 0, 0, 6, 0, 12, 0, 0, 16, 0, -16, 0, 0, 10, 0, 12, 0, 0, 36, 0, -14, 0, 0, -6, 0, -2, 0, 0, -18, 0, 30, 0, 0, 18, 0, -8, 0, 0, -8, 0, -16, 0, 0, -2, 0, -18, 0, 0, -6, 0, 8, 0, 0, 4, 0, -2, 0, 0, 12, 0, 18, 0, 0, -24, 0, -8, 0, 0, 6, 0, -48, 0, 0, 20, 0, -6, 0, 0, -36, 0, 8, 0, 0, -12, 0, 24, 0, 0, 20, 0, 12, 0, 0, -6, 0, -16, 0, 0, -40, 0, -4, 0, 0, 16, 0, -48, 0, 0, -24, 0, 24, 0, 0, 6, 0, -10, 0, 0, 38, 0, 60, 0, 0, -12, 0, 14, 0, 0, -12, 0, 40, 0, 0, 24, 0, -36, 0, 0, 72, 0, 8, 0, 0, 14, 0, -22, 0, 0, -46, 0, -12, 0, 0, -48, 0, 6, 0, 0, 6, 0, -44, 0, 0, 2, 0, 48, 0, 0, -72, 0, 24, 0, 0, -28, 0, 18, 0, 0, -36, 0, 18, 0, 0, -30, 0, -20, 0, 0, 6, 0, -2, 0, 0, 10, 0, -18, 0, 0, 42, 0, -60, 0, 0, 8, 0, -30, 0, 0, 60, 0, 72, 0, 0, -72, 0, 8, 0, 0, 12, 0, 46, 0, 0, 16, 0, 42, 0, 0, -66, 0, -14, 0, 0, -16, 0, 2, 0, 0, -16, 0, -96, 0, 0, 18, 0, 8, 0, 0, 12, 0, 20, 0, 0, -6, 0, 6, 0, 0, 96, 0, -60, 0, 0, -8, 0, 36, 0, 0, -16, 0, -84, 0, 0, 54, 0, -4, 0, 0, 12, 0, 32, 0, 0, 2, 0, -60, 0, 0, -60, 0, 4, 0, 0, 28, 0, -12, 0, 0, 48, 0, 30, 0, 0, -18, 0, -10, 0, 0, -80, 0, 50, 0, 0, 44, 0, 24, 0, 0, -90, 0, -48, 0, 0, 8, 0, -8, 0, 0, -52, 0, -108, 0, 0, 24, 0, -6, 0, 0, 40, 0, -36, 0, 0, 48, 0, 48, 0, 0, 84, 0, -96, 0, 0, 30, 0, -20, 0, 0, -10, 0, -48, 0, 0, 6, 0, 18, 0, 0, 72, 0, 10, 0, 0, -16, 0, 36, 0, 0, 24, 0, -10, 0, 0, -8, 0, 64, 0, 0, -42, 0, -18, 0, 0, 12, 0, 12, 0, 0, -6, 0, -28, 0, 0, -24, 0, -24, 0, 0, 108, 0, -8, 0, 0, -64, 0, -20, 0, 0, 12, 0, 108, 0, 0, -12, 0, 0, 0, 0, -10, 0, -42, 0, 0, -16, 0, 6, 0, 0, -90, 0, -48, 0, 0, 16, 0, 28, 0, 0, -24, 0, 84, 0, 0, -36, 0, 40, 0, 0, 8, 0, -24, 0, 0, 4, 0, 0, 0, 0, -30, 0, 0, 0, 0, 12, 0, -16, 0, 0, 24, 0, 132, 0, 0, 48, 0, -6, 0, 0, -72, 0, -56, 0, 0, 4, 0, 24, 0, 0, -24, 0, 62, 0, 0, -24, 0, 8, 0, 0, -2, 0, 48, 0, 0, -18, 0, -6, 0, 0, -54, 0, 32, 0, 0, 10, 0, 144, 0, 0, 96, 0, 16, 0, 0, -56, 0, -38, 0, 0, 48, 0, 90, 0, 0, -60, 0, 66, 0, 0, 18, 0, 8, 0, 0, -56, 0, 12, 0, 0, 54, 0, 88, 0, 0, -14, 0, -48, 0, 0, -16, 0, -48, 0, 0, 54, 0, 12, 0, 0, 40, 0, 62, 0, 0, -40, 0, -24, 0, 0, 192, 0, -120, 0, 0, -18, 0, -24, 0, 0, -56, 0, 18, 0, 0, 36, 0, 20, 0, 0, -20, 0, 60, 0, 0, 24, 0, -72, 0, 0, -48, 0, 60, 0, 0, -8, 0, 10, 0, 0, -24, 0, -192, 0, 0, -60, 0, -14, 0, 0, -10, 0, 0, 0, 0, 22, 0, -24, 0, 0, 0, 0, -48, 0, 0, 6, 0, 46, 0, 0, 112, 0, -48, 0, 0, 12, 0, -16, 0, 0, -144, 0, 58, 0, 0, 14, 0, 48, 0, 0, 84, 0, -16, 0, 0, -6, 0, -36, 0, 0, -32, 0, -72, 0, 0, 120, 0, -6, 0, 0, -16, 0, 80, 0, 0, 44, 0, 12, 0, 0, 54, 0, 40, 0, 0, 4, 0, -2, 0, 0, 8, 0, 36, 0, 0, -48, 0, 24, 0, 0, -40, 0, 48, 0, 0, 96, 0, 72, 0, 0, -18, 0, -30, 0, 0, -24, 0, 12, 0, 0, 42, 0, 12, 0, 0, 48, 0, 28, 0, 0, -14, 0, 24, 0, 0, -18, 0, -72, 0, 0, 24, 0, 120, 0, 0, -24, 0, 36, 0, 0, -100, 0, -36, 0, 0, -18, 0, -96, 0, 0, -20, 0, 8, 0, 0, 12, 0, 30, 0, 0, 288, 0, 32, 0, 0, 20, 0, -32, 0, 0, -48, 0, -168, 0, 0, -114, 0, -6, 0, 0, -52, 0, 70, 0, 0, 2, 0, -120, 0, 0, 198, 0, 4, 0, 0, -64, 0, -10, 0, 0, 22, 0, -168, 0, 0, 18, 0, -58, 0, 0, 36, 0, -36, 0, 0, -2, 0, -42, 0, 0, -144, 0, -60, 0, 0, 60, 0, 78, 0, 0, 64, 0, 54, 0, 0, 36, 0, -8, 0, 0, -128, 0, -120, 0, 0, 30, 0, -120, 0, 0, -48, 0, -20, 0, 0, -14, 0, -60, 0, 0, -104, 0, -54, 0, 0, -72, 0, -52, 0, 0, 44, 0, -18, 0, 0, 56, 0, 72, 0, 0, 60, 0, 8, 0, 0, -8, 0, -24, 0, 0, -84, 0, 72, 0, 0, -144, 0, -12, 0, 0, 24, 0, 66, 0, 0, -46, 0, -24, 0, 0, 30, 0, 30, 0, 0, -60, 0, -16, 0, 0, 18, 0, -120, 0, 0, -42, 0, 80, 0, 0, -8, 0, 4, 0, 0, 32, 0, 66, 0, 0, -36, 0, -144, 0, 0, 14, 0, 48, 0, 0, -14, 0, 18, 0, 0, 138, 0, 16, 0, 0, -18, 0, -24, 0, 0, -2, 0, 18, 0, 0, -48, 0, -28, 0, 0, 60, 0, 16, 0, 0, -20, 0, 42, 0, 0, 96, 0, -74, 0, 0, 46, 0, -50, 0, 0, -80, 0, -18, 0, 0, -108, 0, 64, 0, 0, -8, 0, -84, 0, 0, -16, 0, 240, 0, 0, -18, 0, -12, 0, 0, 132, 0, 20, 0, 0, -20, 0, 132, 0, 0, 24, 0, 14, 0, 0, -34, 0, 6, 0, 0, -112, 0, 12, 0, 0, -6, 0, 48, 0, 0, 100, 0, 24, 0, 0, -60, 0, -96, 0, 0, 72, 0, -8, 0, 0, 60, 0, 8, 0, 0, -90, 0, 288, 0, 0, 72, 0, 8, 0, 0, -30, 0, 40, 0, 0, -36, 0, -72, 0, 0, 36, 0, 60, 0, 0, 34, 0, 16, 0, 0, -16, 0, 72, 0, 0, 84, 0, 72, 0, 0, -176, 0, -102, 0, 0, 34, 0, -54, 0, 0, -144, 0, -20, 0, 0, 4, 0, 70, 0, 0, -112, 0, -72, 0, 0, 108, 0, -12, 0, 0, 60, 0, 34, 0, 0, -32, 0, -36, 0, 0, -288, 0, 32, 0, 0, 20, 0, -2, 0, 0, 24, 0, 36, 0, 0, 60, 0, 16, 0, 0, 100, 0, 60, 0, 0, 60, 0, 60, 0, 0, -96, 0, -70, 0, 0, -4, 0, 24, 0, 0, -34, 0, -228, 0, 0, -18, 0, -28, 0, 0, 72, 0, 168, 0, 0, 12, 0, 6, 0, 0, -180, 0, 112, 0, 0, -108, 0, -48, 0, 0, -40, 0, -192, 0, 0, -30, 0, -64, 0, 0, -12, 0, 96, 0, 0, 56, 0, 18, 0, 0, -174, 0, -108, 0, 0, 10, 0, -28, 0, 0, -120, 0, -6, 0, 0, -84, 0, 80, 0, 0, 104, 0, -90, 0, 0, -50, 0, 180, 0, 0, 234, 0, -78, 0, 0, -16, 0, -44, 0, 0, 120, 0, 72, 0, 0, -24, 0, -68, 0, 0, 8, 0, -72, 0, 0, 84, 0, 90, 0, 0, -240, 0, 90, 0, 0, 48, 0, -70, 0, 0, 66, 0, -42, 0, 0, -180, 0, -8, 0, 0, 64, 0, -80, 0, 0, 8, 0, -144, 0, 0, -156, 0, -60, 0, 0, -70, 0, 52, 0, 0, 40, 0, 168, 0, 0, 108, 0, 4, 0, 0, 70, 0, 110, 0, 0, 32, 0, -24, 0, 0, -72, 0, -144, 0, 0, 6, 0, 16, 0, 0, 16, 0, -216, 0, 0, -36, 0, -40, 0, 0, 40, 0, 72, 0, 0, 36, 0, -138, 0, 0, -48, 0, 46, 0, 0, -56, 0, -48, 0, 0, 110, 0, -180, 0, 0, -48, 0, -76, 0, 0, 180, 0, -28, 0, 0, 18, 0, -84, 0, 0, 240, 0, -18, 0, 0, 96, 0, -52, 0, 0, -94, 0, 96, 0, 0, 132, 0, -30, 0, 0, 66, 0, 12, 0, 0, 20, 0, 42, 0, 0, 144, 0, 48, 0, 0, 32, 0, 10, 0, 0, 144, 0, 276, 0, 0, 48, 0, 80, 0, 0, 114, 0, -10, 0, 0, -48, 0, -6, 0, 0, 18, 0, 6, 0, 0, -18, 0, -8, 0, 0, 120, 0, 180, 0, 0, 48, 0, -72, 0, 0, 136, 0, 0, 0, 0, -10, 0, 144, 0, 0, -222, 0, 112, 0, 0, -104, 0, 16, 0, 0, 6, 0, -240, 0, 0, -36, 0, -96, 0, 0, 64, 0, 16, 0, 0, -36, 0, -24, 0, 0, -252, 0, 50, 0, 0, 10, 0, 42, 0, 0, -2, 0, -36, 0, 0, -36, 0, 8, 0, 0, -110, 0, -120, 0, 0, -64, 0, -60, 0, 0, 264, 0, -112, 0, 0, -8, 0, 42, 0, 0, -36, 0, -102, 0, 0, 18, 0, 52, 0, 0, 140, 0, 96, 0, 0, -34, 0, -12, 0, 0, 144, 0, 120, 0, 0, -12, 0, -90, 0, 0, 32, 0, -180, 0, 0, -144, 0, 6, 0, 0, 14, 0, 16, 0, 0, 28, 0, 180, 0, 0, 24, 0, 6, 0, 0, -16, 0, 24, 0, 0, -6, 0, 0, 0, 0, 24, 0, -24, 0, 0, -60, 0, -64, 0, 0, -42, 0, -108, 0, 0, -144, 0, 108, 0, 0, 8, 0, -48, 0, 0, -48, 0, 102, 0, 0, 48, 0, 64, 0, 0, -40, 0, 96, 0, 0, 20, 0, 168, 0, 0, 216, 0, 100, 0, 0, 76, 0, -12, 0, 0, 28, 0, 102, 0, 0, -108, 0, 74, 0, 0, -128, 0, 24, 0, 0, 24, 0, 12, 0, 0, 210, 0, 36, 0, 0, 0, 0, 20, 0, 0, 108, 0, 216, 0, 0, -36, 0, 10, 0, 0, -16, 0, 4, 0, 0, 42, 0, -96, 0, 0, -54, 0, 30, 0, 0, -56, 0, 16, 0, 0, -50, 0, 60, 0, 0, -6, 0, -66, 0, 0, 64, 0, -76, 0, 0, 96, 0, 90, 0, 0, 48, 0, -32, 0, 0, 48, 0, 48, 0, 0, 54, 0, 180, 0, 0, 120, 0, -16, 0, 0, -138, 0, -24, 0, 0, -28, 0, -12, 0, 0, 72, 0, 24, 0, 0, -18, 0, 24, 0, 0, -124, 0, -36, 0, 0, -84, 0, 14, 0, 0, -132, 0, 128, 0, 0, 24, 0, 36, 0, 0, 12, 0, -16, 0, 0, -40, 0, 54, 0, 0, -22, 0, -324, 0, 0, -144, 0, -8, 0, 0, 8, 0, 150, 0, 0, 24, 0, -60, 0, 0, -192, 0, 154, 0, 0, -56, 0, -4, 0, 0, 224, 0, 168, 0, 0, 0, 0, 152, 0, 0, -12, 0, -140, 0, 0, 34, 0, 30, 0, 0, -84, 0, -48, 0, 0, 0, 0, -84, 0, 0, 18, 0, -126, 0, 0, 240, 0, -12, 0, 0, 136, 0, -264, 0, 0, 16, 0, -150, 0, 0, 360, 0, -132, 0, 0, 44, 0, -24, 0, 0, -88, 0], "weight": 2, "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, 1], [0, 3], [-1, 0], [0, 0], [-3, 0], [0, -4], [0, -1], [-6, 0], [0, 0], [3, 0], [0, -3], [0, -6], [4, 0], [0, 0], [1, 0], [0, -5], [0, -6], [1, 0], [0, 0], [12, 0], [0, 3], [0, 1], [3, 0], [0, 0], [6, 0], [0, -9], [0, 4], [8, 0], [0, 0], [-8, 0], [0, 1], [0, 9], [5, 0], [0, 0], [6, 0], [0, -2], [0, 1], [18, 0], [0, 0], [-7, 0], [0, 12], [0, 4], [-3, 0], [0, 0], [-1, 0], [0, -10], [0, 3], [-9, 0], [0, 0], [15, 0], [0, 6], [0, -12], [9, 0], [0, 0], [-4, 0], [0, 3], [0, 8], [-4, 0], [0, 0], [-8, 0], [0, -8], [0, 24], [-1, 0], [0, 0], [-9, 0], [0, -3], [0, 5], [-3, 0], [0, 0], [4, 0], [0, 6], [0, -7], [2, 0], [0, 0], [-1, 0], [0, -12], [0, 18], [6, 0], [0, 0], [9, 0], [0, -7], [0, 11], [-12, 0], [0, 0], [-4, 0], [0, 24], [0, -3], [3, 0], [0, 0], [-24, 0], [0, -1], [0, -24], [10, 0], [0, 0], [-3, 0], [0, 14], [0, -9], [-18, 0], [0, 0]]}