# Stored data for newform 441.2.a.d, downloaded from the LMFDB on 06 October 2024. {"Nk2": 1764, "analytic_conductor": 3.521402729138465, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [7, 1]], "atkin_lehner_string": "++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [441, 1, [344, 199], [1, 1]], "cm_discs": [-3], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [0, 1]], [5, [0, 1]], [13, [7, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798915666361, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], "is_cm": true, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "441.2.a.d", "level": 441, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3, 7], "level_radical": 21, "minimal_twist": "63.2.e.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-2q^{4}-7q^{13}+4q^{16}-7q^{19}-5q^{25}+\\cdots", "related_objects": ["EllipticCurve/Q/441/d"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.1.d1", "self_twist_discs": [-3], "self_twist_type": 1, "space_label": "441.2.a", "trace_display": [0, 0, 0, 0], "trace_hash": 1050498587621707302, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.835", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.320", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "traces": [0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 4, 0, 0, -7, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -8, 0, 0, 11, 0, 0, 0, 0, 0, -7, 0, 0, 14, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 10, 0, 0, -7, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 14, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 36, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -28, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, -28, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -17, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 35, 0, 0, 0, 0, 0, 35, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -37, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, -20, 0, 0, 49, 0, 0, 0, 0, 0, -7, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, -34, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 7, 0, 0, 22, 0, 0, -25, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -43, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 8, 0, 0, -49, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 25, 0, 0, -28, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -37, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -49, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 50, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -98, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -7, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -28, 0, 0, -61, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 17, 0, 0, 0, 0, 0, -49, 0, 0, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 4, 0, 0, -7, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -8, 0, 0, 11, 0, 0, 0, 0, 0, -7, 0, 0, 14, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 10, 0, 0, -7, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 14, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 36, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -28, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, -28, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -17, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 35, 0, 0, 0, 0, 0, 35, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -37, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, -20, 0, 0, 49, 0, 0, 0, 0, 0, -7, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, -34, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 7, 0, 0, 22, 0, 0, -25, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -43, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 8, 0, 0, -49, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 25, 0, 0, -28, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -37, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -49, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 50, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -98, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -7, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, -29, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -28, 0, 0, -61, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 17, 0, 0, 0, 0, 0, -49, 0, 0, 0]}