# Stored data for newform 600.2.bc.a, downloaded from the LMFDB on 05 May 2024.
{"label": "600.2.bc.a", "space_label": "600.2.bc", "level": 600, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1924178903640, "dim": 8, "is_polredabs": true, "nf_label": "8.0.4000000.1", "trace_hash": 1971123592127581954, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [26896, 0, 9056, 0, 1096, 0, 56, 0, 1]]], "qexp_display": "q+\\zeta_{20}q^{3}+(\\zeta_{20}^{2}+\\zeta_{20}^{3}+\\zeta_{20}^{5}+\\cdots)q^{5}+\\cdots", "char_order": 10, "char_parity": 1, "char_degree": 4, "char_conductor": 25, "char_orbit_label": "bc", "char_is_real": false, "Nk2": 2400, "analytic_conductor": 4.791024121276823, "hecke_ring_index": 1, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 20, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.129", "prec": 17}, "analytic_rank_proved": true, "char_values": [600, 10, [151, 301, 401, 577], [10, 10, 10, 9]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [169, 289, 409, 529], "field_disc": 4000000, "field_disc_factorization": [[2, 8], [5, 6]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.043", "prec": 17}, {"__RealLiteral__": 0, "data": "7.701", "prec": 17}, {"__RealLiteral__": 0, "data": "3.025", "prec": 17}, {"__RealLiteral__": 0, "data": "190.291", "prec": 24}, {"__RealLiteral__": 0, "data": "167.313", "prec": 24}, {"__RealLiteral__": 0, "data": "7275.127", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c10", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, -10, 0, -4, 0, 14, 0, 30, 0, -10, 0, 0, 0, -14, 0, -20, 0, -20, 0, -10, 0, 0, 0, 24, 0, -14, 0, 0, 0, 0, 0, 10, 0, -56, 0, 28, 0, 50, 0, -10, 0, 0, 0, -12, 0, -4, 0, 10, 0, 20, 0, -30, 0, 2, 0, 8, 0, -60, 0, 20, 0, 60, 0, 24, 0, -2, 0, 10, 0, 0, 0, -10, 0, -38, 0, 28, 0, 0, 0, -30, 0, -20, 0, 4, 0, 60, 0, 10, 0, 20, 0, 0, 0, -12, 0, -30, 0, -10, 0, -10, 0, 0, 0, -24, 0, -26, 0, 30, 0, -30, 0, -10, 0, -4, 0, 6, 0, 40, 0, 0, 0, 50, 0, -2, 0, 0, 0, 0, 0, -20, 0, -20, 0, -24, 0, 48, 0, -10, 0, -10, 0, 0, 0, 10, 0, 4, 0, -30, 0, -10, 0, 0, 0, 62, 0, 4, 0, 0, 0, -10, 0, 20, 0, -54, 0, 8, 0, 10, 0, -50, 0, 0, 0, 6, 0, -64, 0, 0, 0, -30, 0, 70, 0, -76, 0, -4, 0, 60, 0, -60, 0, 0, 0, -68, 0, -28, 0, 10, 0, -40, 0, -80, 0, 8, 0, 76, 0, 60, 0, 0, 0, 60, 0, 32, 0, 28, 0, 0, 0, -40, 0, 20, 0, 0, 0, 30, 0, 0, 0, 60, 0, 150, 0, -32, 0, -56, 0, 40, 0, 20, 0, 0, 0, -10, 0, -16, 0, -50, 0, 20, 0, -30, 0, 18, 0, 22, 0, -20, 0, 0, 0, -80, 0, 20, 0, -24, 0, 30, 0, -20, 0, -120, 0, 18, 0, 4, 0, 0, 0, -40, 0, -20, 0, 4, 0, 72, 0, -30, 0, 50, 0, 0, 0, -24, 0, 16, 0, -40, 0, -10, 0, 60, 0, -18, 0, 22, 0, 100, 0, 200, 0, -20, 0, 60, 0, -2, 0, 0, 0, -20, 0, 80, 0, 4, 0, -60, 0, 0, 0, -30, 0, 0, 0, 96, 0, -4, 0, -100, 0, 80, 0, 0, 0, 42, 0, 30, 0, -40, 0, -10, 0, -10, 0, -16, 0, -30, 0, 60, 0, -40, 0, 20, 0, -8, 0, 36, 0, 10, 0, -120, 0, -30, 0, -86, 0, -42, 0, 0, 0, -80, 0, 100, 0, 48, 0, -44, 0, 50, 0, 10, 0, 0, 0, -10, 0, -50, 0, -160, 0, 30, 0, -110, 0, 32, 0, -28, 0, -20, 0, 110, 0, -40, 0, -2, 0, 28, 0, -50, 0, -20, 0, 20, 0, 48, 0, 6, 0, 0, 0, 20, 0, -60, 0, -136, 0, 72, 0, -30, 0, 130, 0, 0, 0, 12, 0, -56, 0, -70, 0, 40, 0, -110, 0, 52, 0, 28, 0, -20, 0, 70, 0, 10, 0, 74, 0, -10, 0, 60, 0, -60, 0, -60, 0, 2, 0, -52, 0, 0, 0, 20, 0, 20, 0, 40, 0, -64, 0, -40, 0, 120, 0, 0, 0, 44, 0, -104, 0, -30, 0, -80, 0, -60, 0, 14, 0, -68, 0, 20, 0, 30, 0, 80, 0, 106, 0, -8, 0, 130, 0, -30, 0, -20, 0, -42, 0, -40, 0, 0, 0, -20, 0, -30, 0, 24, 0, -28, 0, -200, 0, 0, 0, 0, 0, 22, 0, 16, 0, 80, 0, 0, 0, 10, 0, 6, 0, 58, 0, -20, 0, -30, 0, 0, 0, 88, 0, 76, 0, 110, 0, 50, 0, 90, 0, -40, 0, 2, 0, 0, 0, 130, 0, 40, 0, -168, 0, -60, 0, -30, 0, -40, 0, 0, 0, 18, 0, 50, 0, -180, 0, 20, 0, 0, 0, 60, 0, -2, 0, 90, 0, 30, 0, 20, 0, -70, 0, 80, 0, -20, 0, 10, 0, -160, 0, 2, 0, 44, 0, 0, 0, 0, 0, 170, 0, 176, 0, -40, 0, 150, 0, 60, 0, 0, 0, 30, 0, 16, 0, -80, 0, 80, 0, -60, 0, 62, 0, 22, 0, 130, 0, -20, 0, -140, 0, 8, 0, 68, 0, -40, 0, -160, 0, -60, 0, -30, 0, -96, 0, 0, 0, -50, 0, -30, 0, -8, 0, -24, 0, -150, 0, 10, 0, 0, 0, -28, 0, 36, 0, -40, 0, -70, 0, -20, 0, 10, 0, -8, 0, -60, 0, -50, 0, -100, 0, 2, 0, -46, 0, 20, 0, 40, 0, -60, 0, -50, 0, -22, 0, 0, 0, -10, 0, 10, 0, -136, 0, 84, 0, 50, 0, -10, 0, 0, 0, -56, 0, -66, 0, -20, 0, 20, 0, 20, 0, 68, 0, -98, 0, 90, 0, 70, 0, 50, 0, 122, 0, -4, 0, -10, 0, -30, 0, 30, 0, -26, 0, 78, 0, 0, 0, 20, 0, 10, 0, 0, 0, 8, 0, 10, 0, 20, 0, 0, 0, 26, 0, -84, 0, -20, 0, 150, 0, 0, 0, 82, 0, -80, 0, -180, 0, 70, 0, 50, 0, -28, 0, -32, 0, 30, 0, -80, 0, -10, 0, 8, 0, -10, 0, 0, 0, -210, 0, 90, 0, 100, 0, 20, 0, 60, 0, 0, 0, 0, 0, -64, 0, 28, 0, -100, 0, 30, 0, -60, 0, 88, 0, -28, 0, -30, 0, 290, 0, 0, 0, 6, 0, -36, 0, -80, 0, -20, 0, 50, 0, 112, 0, 6, 0, 0, 0, -20, 0, 130, 0, 140, 0, -120, 0, 80, 0, 110, 0, 0, 0, 60, 0, -6, 0, -80, 0, -10, 0, -40, 0, -58, 0, 20, 0, -170, 0, -200, 0, -40, 0, 198, 0, -92, 0, 70, 0, 30, 0, -30, 0, 28, 0, -132, 0, 0, 0, -10, 0, 90, 0, 16, 0, 136, 0, 30, 0, -70, 0, 0, 0, -20, 0, -138, 0, 10, 0, -30, 0, 40, 0, -74, 0, -110, 0, 220, 0, 30, 0, 190, 0, -26, 0, -28, 0, 0, 0, 180, 0, 100, 0, 36, 0, -76, 0, 0, 0, 120, 0, -140, 0, -20, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 25, 5, 1, 10, 0]], "char_orbit_index": 29, "prim_orbit_index": 5, "minimal_twist": "600.2.bc.a", "char_is_minimal": true, "conrey_index": 169, "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, 0, 0, 0, 0, 0, 0, 0], [1, 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, 1, 1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, -2, 0, 3, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 2, 0, -3, -1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 0, -5, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 4, 2, -3, -1, 3, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -1, 0, 0, 0, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -2, -2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -1, -1, -1, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 4, -1, -2, 1, 4, 1, 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], [-3, -1, 3, 2, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -5, 0, 0, 0, -5, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 3, 0, -2, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 7, 2, -3, -3, -1, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 5, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 3, 0, -3, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 2, 2, -4, -3, 6, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 6, 1, -3, 0, 3, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 2, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 3, 0, -4, -1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-5, -4, 0, 4, 4, -2, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -2, 0, 2, 1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, -1, 4, 0, 2, 3, -1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [1, -3, -6, 5, 1, 2, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 6, -1, -3, 0, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, -6, -2, 4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -4, -1, 4, 1, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -1, -2, 0, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [7, -3, -3, 6, 10, -8, -5, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -3, 1, -3, -1, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -1, -1, -1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -2, 0, -3, 1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -1, -4, -1, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 4, -1, -2, 1, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -6, -2, -6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 2, -6, -4, 0, 6, -6, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -3, 2, 5, 1, -5, -4, 3], [0, 0, 0, 0, 0, 0, 0, 0], [2, 5, 0, -4, 8, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -3, 1, 3, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -3, -5, 3, 5, -3, 3, 6], [0, 0, 0, 0, 0, 0, 0, 0], [11, -9, -19, -5, 11, -4, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, -5, -1, 0, 1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, -4, 8, 2, -3, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 2, 1, 0, -6, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 0, 3, 1, -2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0]]}