# Stored data for newform 775.2.f.c, downloaded from the LMFDB on 25 April 2024.
{"label": "775.2.f.c", "space_label": "775.2.f", "level": 775, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007542885679879, "dim": 8, "is_polredabs": true, "nf_label": "8.0.3317760000.2", "trace_hash": 1532533939192752196, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [36, 0, 0, 0, 1]], [3, [25, 0, 0, 0, 1]]], "qexp_display": "q-\\beta _{6}q^{2}-\\beta _{3}q^{3}-4\\beta _{2}q^{4}-\\beta _{7}q^{6}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 155, "char_orbit_label": "f", "char_is_real": false, "Nk2": 3100, "analytic_conductor": 6.18840615664923, "hecke_ring_index": 64, "level_radical": 155, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "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": "0.876", "prec": 17}, "analytic_rank_proved": true, "char_values": [775, 4, [652, 251], [1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 8, "level_primes": [5, 31], "conrey_indexes": [557, 743], "field_disc": 3317760000, "field_disc_factorization": [[2, 16], [3, 4], [5, 4]], "field_poly": [625, 0, 0, 0, -25, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "7.330", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "872.505", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "131464.528", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -64, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, -72, 0, 0, 0, 0, 224, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 96, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, -48, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 240, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, 0, 0, -320, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -216, 0, 0, 0, 0, 224, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, -40, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, -216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 480, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, -160, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, -288, 0, 0, 0, 0, 328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 152, 0, 0, 0, 0, 480, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 200, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -232, 0, 0, 0, 0, 480, 0, 0, 0, 0, -264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 2, 5, 3, -1, 4, 0], [1, 1, 31, 2, -1, 2, 0], [1, 1, 155, 3, -1, 2, 0], [1, 2, 155, 6, 1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "775.2.f.c", "char_is_minimal": true, "conrey_index": 557, "id": null, "fricke_eigenval": null, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 2, 0, 0, 0], [0, 0, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [12, 0, 0, 0, 0, 0, 0, 0], [0, -7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2], [0, -6, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, -2, 0, 0, 0], [0, 0, -8, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-30, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, -4, 0, 0, 0, 0], [0, 0, -10, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 4, 0], [0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [28, 0, 0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -9, 0], [0, 0, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -3], [0, 0, 0, 0, 0, 0, 5, 0], [0, 0, 0, 12, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -6, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}