# Stored data for newform 775.4.a.d, downloaded from the LMFDB on 14 September 2025.
{"Nk2": 12400, "analytic_conductor": 45.72648025444897, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, 1], [31, -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": [775, 1, [652, 251], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 17, "field_disc_factorization": [[17, 1]], "field_poly": [-4, -1, 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, [2, -5, 1]], [3, [-16, -2, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949221127, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "775.4.a.d", "level": 775, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 31], "level_radical": 155, "minimal_twist": "31.4.a.a", "nf_label": "2.2.17.1", "prim_orbit_index": 1, "qexp_display": "q+(3-\\beta )q^{2}+2\\beta q^{3}+(5-5\\beta )q^{4}+(-8+\\cdots)q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "775.4.a", "trace_display": [5, 2, 0, 19], "trace_hash": 411209439981229241, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, 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