# Stored data for newform 400.3.p.a, downloaded from the LMFDB on 04 October 2023. {"label": "400.3.p.a", "space_label": "400.3.p", "level": 400, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 1030842483088, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 380942692488319804, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [18, 6, 1]], [7, [18, -6, 1]]], "qexp_display": "q+(-3+3i)q^{3}+(3+3i)q^{7}-9iq^{9}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "p", "char_is_real": false, "Nk2": 3600, "analytic_conductor": 10.899210574411876, "hecke_ring_index": 1, "level_radical": 10, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.248", "prec": 17}, 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"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], [1, 0], [0, 0], [-3, 3], [0, 0], [0, 0], [0, 0], [3, 3], [0, 0], [0, -9], [0, 0], [-12, 0], [0, 0], [-12, 12], [0, 0], [0, 0], [0, 0], [12, 12], [0, 0], [0, -20], [0, 0], [-18, 0], [0, 0], [-3, 3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -30], [0, 0], [8, 0], [0, 0], [36, -36], [0, 0], [0, 0], [0, 0], [-48, -48], [0, 0], [0, -72], [0, 0], [-48, 0], [0, 0], [27, -27], [0, 0], [0, 0], [0, 0], [-27, -27], [0, 0], [0, -31], [0, 0], [-72, 0], [0, 0], [-12, 12], [0, 0], [0, 0], [0, 0], [60, 60], [0, 0], [0, 60], [0, 0], [32, 0], [0, 0], [27, -27], [0, 0], [0, 0], [0, 0], [3, 3], [0, 0], [0, -18], [0, 0], [48, 0], [0, 0], [-12, 12], [0, 0], [0, 0], [0, 0], [-36, -36], [0, 0], 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