# Stored data for newform 570.2.f.b, downloaded from the LMFDB on 26 March 2023.
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-32, 216, -20, 0, 0, 36, 0, 96, 40, 0, 0, -16, -24, 0, -24, 0, 0, 24, 16, 0, 4, 80, 48, -16, 0, 184, 24, 0, 0, 32, 0, 24, 48, 0, 8, 48, -48, 0, 4, 0, 0, 72, 40, 32, -48, 0, -32, -64, 40, 48, 0, 176, 8, -48, 0, 0, -16, 48, -24, 80, 0, 0, 16, 0, -8, 64, -8, 0, -16, -96, 0, -40, 0, 0, 48, -88, 0, -56, 24, 24, -16, 0, -40, -8, 0, 0, 64, 0, 0, -24, 0, 72, 24, 24, 0, -144, 0, 0, 0, 28, -88, 8, 0, 16, -48, 184, -28, 0, -32, 120, 4, -48, 0, -24, 16, -72, 0, 0, 0, -64, 0, 0, -16, 16, 0, 80, 8, 0, -16, 0, 0, -96, 16, 0, 16, -32, -80, 24, 0], "hecke_ring_index_factorization": [[2, 1]], "nf_label": "4.0.256.1", "field_poly": [1, 0, 0, 0, 1], "has_non_self_twist": 1, "char_values": [570, 2, [191, 457, 211], [1, 2, 1]], "Nk2": 2280, "field_poly_root_of_unity": 8, "analytic_rank": 0, "char_orbit_label": "f", "weight": 2, "trace_display": [4, 4, 0, 8], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 2, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+q^{2}+(1+\\zeta_{8}^{2})q^{3}+q^{4}+\\zeta_{8}q^{5}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 256, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[7, [2, -4, 1]], [29, [-46, 4, 1]]], "space_label": "570.2.f", "level": 570, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 57, 4, 1, 2, 0]], "char_degree": 1, "char_conductor": 57, "char_orbit_index": 6, "hecke_ring_generator_nbound": 5, "hecke_orbit_code": 4503943258309178, "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "3.715", "prec": 17}, {"__RealLiteral__": 0, "data": "1.164", "prec": 17}, {"__RealLiteral__": 0, "data": "74.072", "prec": 20}, {"__RealLiteral__": 0, "data": "57.945", "prec": 20}, {"__RealLiteral__": 0, "data": "2158.222", "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, 0, 0, 0], [1, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, 0, 1, 0], [2, 0, 0, 1], [1, 0, 0, 0], [-1, 0, 2, 0], [0, 1, 0, 0], [0, -4, 1, 0], [1, 0, 1, 0], [0, -2, -3, 0], [2, 0, 0, 1], [0, 1, 0, -1], [1, 0, 0, 0], [0, 0, 2, 0], [-1, 0, 2, 0], [0, 1, 0, -3], [0, 1, 0, 0], [2, 2, 2, 1], [0, -4, 1, 0], [0, 6, 0, 0], [1, 0, 1, 0], [-1, 0, 0, 0], [0, -2, -3, 0], [-5, 0, 1, 0], [2, 0, 0, 1], [-2, 0, 0, -5], [0, 1, 0, -1], [0, 4, -2, 0], [1, 0, 0, 0], [-2, -4, 1, 4], [0, 0, 2, 0], [0, 2, 1, 0], [-1, 0, 2, 0], [0, -2, -3, 0], [0, 1, 0, -3], [6, -2, -3, 2], [0, 1, 0, 0], [-4, 0, 0, 5], [2, 2, 2, 1], [8, 0, 0, 1], [0, -4, 1, 0], [0, -1, 0, -2], [0, 6, 0, 0], [0, -6, -2, 0], [1, 0, 1, 0], [-1, 0, 0, 4], [-1, 0, 0, 0], [-4, 0, 2, 0], [0, -2, -3, 0], 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