# Stored data for newform 405.2.a.g, downloaded from the LMFDB on 27 March 2023.
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46, 0, 116, 6, 0, -96, 56, 0, -4, 12, 0, 66, 0, 0, 168, -8, 0, -22, -56, 0, 90, -22, 0, 24, 52, 0, 0, -108, 0, 24, 204, 0, 12, -6, 0, 60, 46, 0, -40, -56, 0, -50, -16, 0, 48, 78, 0, 48, 18, 0, -160, -26, 0, -8, 96, 0, 50, 12, 0, -16, 50, 0, 0, 46, 0, -60, 136, 0, -24, 16, 0, 6, 4, 0, -48, -54, 0, -10, -24, 0, -30, -4, 0, -2, -36, 0, 176, -16, 0, 82, 96, 0, 124, 14, 0, -36, -24, 0, -16, 8, 0, 36, -184, 0, -64, -60, 0, -64, 10, 0, -24, 52, 0, 8, -40, 0, 90, -24, 0, -44, 8, 0, 124, -14, 0, -62, 0, 0, -28, -24, 0, -30, 8, 0, 64, 4, 0, -18, -52, 0, 94, 66, 0, 0, 8, 0, 64, -36, 0, 34, 48, 0, 12, -4, 0, 6, 46, 0, -12], "hecke_ring_index_factorization": [], "nf_label": "2.2.12.1", "field_poly": [-3, 0, 1], "atkin_lehner_string": "--", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[3, -1], [5, -1]], "char_values": [405, 1, [326, 82], [1, 1]], "Nk2": 1620, "field_poly_root_of_unity": 12, "analytic_rank": 1, "char_orbit_label": "a", "weight": 2, "trace_display": [-2, 0, 2, -6], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+(-1+\\beta )q^{2}+(2-2\\beta )q^{4}+q^{5}+(-3+\\cdots)q^{7}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 12, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [-2, 2, 1]], [11, [13, 8, 1]]], "space_label": "405.2.a", "level": 405, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 27021597797777813, "fricke_eigenval": 1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.119", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "60.853", "prec": 20}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [-1, 1], [0, 0], [2, -2], [1, 0], [0, 0], [-3, -1], [-6, 2], [0, 0], [-1, 1], [-4, -1], [0, 0], [-2, 2], [0, -2], [0, 0], [8, -4], [-1, -1], [0, 0], [1, 2], [2, -2], [0, 0], [1, -3], [0, -2], [0, 0], [1, 0], [8, -4], [0, 0], [0, 4], [-2, 3], [0, 0], [-3, 0], [-8, 8], [0, 0], [-2, 0], [-3, -1], [0, 0], [-1, -1], [5, -1], [0, 0], [-6, 2], [-2, -3], [0, 0], [-5, 3], [-2, 6], [0, 0], [-6, 2], [-7, -1], [0, 0], [5, 6], [-1, 1], [0, 0], [-16, 8], [5, 1], [0, 0], [-4, -1], [12, 0], [0, 0], [11, -5], [-10, 1], [0, 0], [4, 0], [3, -3], [0, 0], [16, -8], [-2, 2], [0, 0], [0, 2], [4, 0], [0, 0], [0, -2], [-2, -1], [0, 0], [1, -5], [-2, 0], [0, 0], [-10, 2], [15, 7], [0, 0], [12, 2], [8, -4], [0, 0], [-7, 1], [-3, 3], [0, 0], [-1, -1], [14, -8], [0, 0], [18, -2], [0, 3], [0, 0], [0, -4], [12, -4], [0, 0], [4, -6], [1, 2], [0, 0], [-1, -5], [13, -1], [0, 0], [2, -2]]}