# Stored data for newform 475.2.a.f, downloaded from the LMFDB on 22 September 2023.
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"analytic_rank_proved": true, "char_values": [475, 1, [77, 401], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 19], "conrey_indexes": [1], "field_disc": 148, "field_disc_factorization": [[2, 2], [37, 1]], "field_poly": [1, -3, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.855", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.513", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "261.230", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [19, 1]], "trace_display": [-1, -2, 0, 0], "traces": [0, 3, -1, -2, 1, 0, -4, 0, -3, 3, 0, -8, 10, -8, -4, 0, -3, -2, -5, -3, 0, -12, 16, 4, -4, 0, -6, -8, -12, -10, 0, 4, 3, -4, 18, 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"level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "95.2.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, -1, 0], [-1, 1, 1], [0, 1, 1], [0, 0, 0], [-1, -1, -1], [0, 0, -2], [-1, 0, -1], [1, 0, -2], [0, 0, 0], [-2, -2, 0], [3, 1, -1], [-3, 1, -1], [-2, 2, 0], [0, 0, 0], [-1, 0, -2], [0, -2, 2], [-2, 1, 0], [-1, 0, 0], [0, 0, 0], [-4, 0, 4], [4, 4, 2], [2, -2, 0], [-1, -1, 1], [0, 0, 0], [-3, 3, -1], [-2, -2, 2], [-4, 0, 2], [-4, 2, 2], [0, 0, 0], [0, 4, 0], [0, 3, 2], [0, -4, -4], [6, 0, 2], [0, 0, 0], [-4, 1, 3], [-7, 1, -1], [0, 1, 0], [2, -2, 0], [0, 0, 0], [0, -2, 2], [4, 0, 0], [0, 4, 6], 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