# Stored data for newform 363.2.e.g, downloaded from the LMFDB on 26 March 2023.
{"level_primes": [3, 11], "is_polredabs": true, "sato_tate_group": "1.2.3.c5", "rm_discs": [], "conrey_indexes": [124, 130, 148, 202], "cm_discs": [], "trace_hash": 2294629666671212909, "level_radical": 33, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 7, "analytic_conductor": 2.898569593372478, "inner_twist_count": 4, "field_disc_factorization": [[5, 3]], "is_rm": false, "char_order": 5, "level_is_square": false, "weight_parity": 1, "label": "363.2.e.g", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "33.2.a.a", "field_poly_is_cyclotomic": true, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.022", "prec": 17}, "traces": [0, 4, 1, 1, 1, 2, -1, 4, -3, -1, 8, 0, 4, -2, -4, -2, 1, -2, 1, 0, -2, 16, 0, 32, 3, 1, 2, 1, -4, -6, 2, 8, -20, 0, -8, -8, 1, -6, 0, 2, 6, -2, 4, 0, 0, -8, 8, -8, -1, -9, -1, 2, 2, -6, 4, 0, -48, 0, 6, 4, 2, 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-4, 56, 24, -7, -26, 18, 0, -18, -32, 0, -24, -16, -2, -48, 0, -34, 24, 0, -36, 40, 0, -144, 0, -8, 24, -48, -5, 12, 34, -13, -128, 0, -48, 8, -6, -2, 0, 48, -14, 6, 20, -24, 0, 104, 9, 20, 4, 8, 28, 8, 18, 16, -48, 0, -64, 0, -22, 24, 12, 16, 2, 48, -1, 48, 0, 0, 18, 44, 20, -12, -12, 2, 16, -24, 0, 0, 72, 12, 6, 48, -2, -20, 48, -32, 30, 0, 0, -24, 16, -8, 30, 6, -16, 0, -30, -24, 48, 0, 24, 26, 16, -22, -16, -54, -14, -16, -4, -32, 0, 48, -4, -28, 0, 22, 24, 22, 6, 16, 96, 0, 32, 8, -14, -33, 12, -12, -10, 28, 32, -16, 0, 0, -4, 52, -1, 32, -16, -2, -6, 6, 16, 0, 72, -2, -4, -24, 6, 28, 12, -32, 0, 0, 0, 160, -40, -20, 0, 0, 12, 14, -4, 6, 144], "hecke_ring_index_factorization": [], "nf_label": "4.0.125.1", "field_poly": [1, -1, 1, -1, 1], "has_non_self_twist": 1, "char_values": [363, 5, [122, 244], [5, 4]], "Nk2": 1452, "field_poly_root_of_unity": 10, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [1, 1, 2, 4], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+(1-\\zeta_{10}+\\zeta_{10}^{2}-\\zeta_{10}^{3})q^{2}-\\zeta_{10}^{2}q^{3}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 125, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[2, [1, -1, 1, -1, 1]]], "space_label": "363.2.e", "level": 363, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 3, 11, 3, 1, 5, 0]], "char_degree": 4, "char_conductor": 11, "char_orbit_index": 5, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 27021872675684715, "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "3.602", "prec": 17}, {"__RealLiteral__": 0, "data": "1.370", "prec": 17}, {"__RealLiteral__": 0, "data": "84.654", "prec": 20}, {"__RealLiteral__": 0, "data": "78.610", "prec": 20}, {"__RealLiteral__": 0, "data": "3095.099", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [1, -1, 1, -1], [0, 0, -1, 0], [0, 0, 0, 1], [0, 2, 0, 0], [0, -1, 0, 0], [0, 0, 0, 4], [0, 0, 3, 0], [-1, 1, -1, 1], [2, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [-2, 2, -2, 2], [0, 0, 4, 0], [0, 0, 0, -2], [0, 1, 0, 0], [0, -2, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [-2, 2, -2, 2], [4, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [3, -3, 3, -3], [0, 0, -1, 0], [0, 0, 0, 2], [0, 1, 0, 0], [0, -4, 0, 0], [0, 0, 0, -6], [0, 0, -2, 0], [8, -8, 8, -8], [-5, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [-8, 8, -8, 8], [0, 0, -1, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 6], [0, 0, 2, 0], [4, -4, 4, -4], [0, 0, 0, 0], [0, 0, 0, 0], 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