# Stored data for newform 690.2.i.f, downloaded from the LMFDB on 27 February 2021.
{"level_primes": [2, 3, 5, 23], "sato_tate_group": "1.2.3.c4", "rm_discs": [], "conrey_indexes": [47, 323], "cm_discs": [], "level_radical": 690, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 5, "is_cm": false, "hecke_orbit": 6, "analytic_conductor": 5.509677739468347, "inner_twist_count": 4, "is_rm": false, "char_order": 4, "level_is_square": false, "weight_parity": 1, "label": "690.2.i.f", "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "690.2.i.f", "dim": 32, "traces": [32, 0, 4, 0, 0, 12, 8, 0, 0, 0, 0, -4, 0, 0, -12, -32, 0, 8, 0, 0, 0, -40, 0, 0, 32, 0, 4, 8, 0, -20, 8, 0, 8, 0, 0, 20, -16, 0, 0, 8, 0, -8, -80, 0, -4, 32, 0, -4, 0, 0, 36, 0, 0, 0, 0, 0, 12, -16, 0, -4, 8, 0, 44, 0, 0, 52, 64, 0, 0, 64, 0, -8, -56, 0, -68, -8, 0, 60, 0, 0, -44, 0, 0, 0, -48, 0, -60, -40, 0, -64, 40, 0, 92, 0, 0, -12, -40, 0, 0, 16, 0, -52, -8, 0, -52, -32, 0, 4, 0, 0, -16, -8, 0, 0, -8, 0, -92, -56, 0, 24, -40, 0, 20, 0, 0, -20, 128, 0, 0, 80, 0, -8, -216, 0, -44, -40, 0, 4, 0, 0, 96, 64, 0, 0, 176, 0, -32, -16, 0, -44, -88, 0, 140, 0, 0, 56, 24, 0, 0, 0, 0, 16, 88, 0, -80, 80, 0, -8, 0, 0, 292, 80, 0, 0, 8, 0, -88, -56, 0, -8, -56, 0, 60, 0, 0, 48, 72, 0, 0, 40, 0, 4, -80, 0, -156, -40, 0, 20, 0, 0, 8, -8, 0, 0, 48, 0, 8, 0, 0, -40, -80, 0, 32, 0, 0, -60, 168, 0, 0, -72, 0, 12, 176, 0, -88, -208, 0, 12, 0, 0, -12, 16, 0, 0, 24, 0, -40, -104, 0, 12, -16, 0, 24, 0, 0, 68, 264, 0, 0, 128, 0, -44, 40, 0, -24, 32, 0, 76, 0, 0, -16, 24, 0, 0, -192, 0, -224, 64, 0, -20, -296, 0, -32, 0, 0, 12, 96, 0, 0, 8, 0, -36, 40, 0, -180, 16, 0, -8, 0, 0, 204, 56, 0, 0, 256, 0, -12, -152, 0, 60, -224, 0, 48, 0, 0, 80, 40, 0, 0, -16, 0, -60, -208, 0, -124, -96, 0, 8, 0, 0, 208, 8, 0, 0, -128, 0, -184, 0, 0, -8, -96, 0, 128, 0, 0, 0, 176, 0, 0, 32, 0, -40, 96, 0, -24, 104, 0, -60, 0, 0, 12, 40, 0, 0, 24, 0, -68, -56, 0, 24, -328, 0, 84, 0, 0, 28, 128, 0, 0, 24, 0, -92, -64, 0, 44, 0, 0, 0, 0, 0, -152, 24, 0, 0, 120, 0, -64, -40, 0, 116, 40, 0, 4, 0, 0, 104, 104, 0, 0, -32, 0, -128, -200, 0, -28, 16, 0, -52, 0, 0, 240, 8, 0, 0, 176, 0, 12, -96, 0, 116, -72, 0, 188, 0, 0, 52, -48, 0, 0, -48, 0, -4, -192, 0, -92, 8, 0, 112, 0, 0, 204, 48, 0, 0, -88, 0, -264, -8, 0, -40, -104, 0, -120, 0, 0, 32, 16, 0, 0, 0, 0, -16, 216, 0, 52, 128, 0, -92, 0, 0, 144, 56, 0, 0, 376, 0, 24, -32, 0, 20, -336, 0, 8, 0, 0, 88, 288, 0, 0, 104, 0, -20, -40, 0, -4, -8, 0, 68, 0, 0, 72, -16, 0, 0, 176, 0, -32, 128, 0, -156, 32, 0, -60, 0, 0, 88, 120, 0, 0, -40, 0, -132, 136, 0, -128, -72, 0, -8, 0, 0, 144, 216, 0, 0, -136, 0, -108, -184, 0, 12, -304, 0, 40, 0, 0, 84, -104, 0, 0, 16, 0, -4, 152, 0, 112, -48, 0, 48, 0, 0, 32, 32, 0, 0, 8, 0, -272, 64, 0, -92, -376, 0, 88, 0, 0, -20, 440, 0, 0, -48, 0, -44, -336, 0, 44, 128, 0, -32, 0, 0, 68, 16, 0, 0, -40, 0, -52, 0, 0, -8, 104, 0, 44, 0, 0, -72, -144, 0, 0, 152, 0, -140, -16, 0, 124, -16, 0, -16, 0, 0, 60, -32, 0, 0, 16, 0, 12, 24, 0, -108, -560, 0, 124, 0, 0, 88, 72, 0, 0, -8, 0, -48, -56, 0, -72, -304, 0, 16, 0, 0, 300, -88, 0, 0, 144, 0, -44, -8, 0, 64, 8, 0, -60, 0, 0, -96, -16, 0, 0, 64, 0, 8, -120, 0, 12, -232, 0, 104, 0, 0, 240, 144, 0, 0, 232, 0, -120, 80, 0, -12, 480, 0, 40, 0, 0, 72, 160, 0, 0, -24, 0, -16, -128, 0, -40, 48, 0, -88, 0, 0, 48, 56, 0, 0, -192, 0, -136, -96, 0, 4, -336, 0, -228, 0, 0, -116, 40, 0, 0, 16, 0, -60, 312, 0, 56, -32, 0, 0, 0, 0, -12, -144, 0, 0, 136, 0, -16, 72, 0, 44, 240, 0, -4, 0, 0, 36, 64, 0, 0, -8, 0, -72, -184, 0, 116, -48, 0, 4, 0, 0, 40, 80, 0, 0, -376, 0, -212, -24, 0, 108, -104, 0, 156, 0, 0, 128, -128, 0, 0, 208, 0, -20, -136, 0, -48, -32, 0, -116, 0, 0, -96, -104, 0, 0, -8, 0, -256, -8, 0, -152, 480, 0, -84, 0, 0, -36, -112, 0, 0, -200, 0, 180, 112, 0, 40, -208, 0, 8, 0, 0, -56, 0, 0, 0, 256, 0, 28, 24, 0, 40, 0, 0, 116, 0, 0, -184, 64, 0, 0, 112, 0, -32, -464, 0, -188, -160, 0, 272, 0, 0, 300, -160, 0, 0, 56, 0, -108, 168, 0, -200, -288, 0, 12, 0, 0, 88, 248, 0, 0, 0, 0, -72, -296, 0, -88, 120, 0, 12, 0, 0, 68, -176, 0, 0, -256, 0, 60, -160, 0, 92, 160, 0, 92, 0, 0, 28, 232, 0, 0, 96, 0, -12, 520, 0, -188, 32, 0, 84, 0, 0, -84, -24, 0, 0, -184, 0, -32, 16, 0, 4, -120, 0, 48, 0, 0, 28, 240, 0, 0, -152, 0, 340, 0, 0, 32, -192, 0, -40, 0, 0, -504, 104, 0, 0, 80, 0, 76, 48, 0, 4, 360, 0, 104, 0, 0, 0, -208, 0, 0, 384, 0, -24, 216, 0, -192, -8, 0, -16, 0, 0, 148, 8, 0, 0, -136, 0, 56, 264, 0, -220, 104, 0, 160, 0, 0, 144, -192, 0, 0, 120], "has_non_self_twist": 1, "char_values": [690, 4, [461, 277, 511], [2, 1, 4]], "Nk2": 2760, "analytic_rank": 0, "char_orbit_label": "i", "weight": 2, "trace_display": [0, 4, 0, 8], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "level_is_prime": false, "char_is_minimal": true, "self_twist_discs": [], "char_is_real": false, "level_is_prime_power": false, "relative_dim": 16, "hecke_cutters": [[7, [19600, -44800, 51200, -22560, 40056, -77072, 84512, -41128, 10817, -1636, 1640, -816, 207, -8, 8, -4, 1]]], "space_label": "690.2.i", "level": 690, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 5, 1, 4, 0]], "char_degree": 2, "char_conductor": 15, "char_orbit_index": 9, "hecke_orbit_code": 22518547926221490, "id": null, "is_polredabs": null, "trace_hash": null, "projective_field": null, "hecke_ring_index_proved": null, "embedded_related_objects": null, "field_disc_factorization": null, "field_poly_is_real_cyclotomic": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "trace_zratio": null, "hecke_ring_index_factorization": null, "artin_image": null, "nf_label": null, "field_poly": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "field_poly_root_of_unity": null, "hecke_ring_index": null, "artin_field": null, "qexp_display": null, "field_disc": null, "hecke_ring_generator_nbound": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "trace_moments": null, "artin_degree": null}