# Stored data for newform 1680.2.t.c, downloaded from the LMFDB on 15 November 2024.
{"Nk2": 6720, "analytic_conductor": 13.414867539575104, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 20, "char_orbit_label": "t", "char_order": 2, "char_parity": 1, "char_values": [1680, 2, [1471, 421, 1121, 337, 241], [2, 2, 2, 1, 2]], "cm_discs": [], "conrey_index": 1009, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[11, [2, 1]], [13, [4, 0, 1]], [19, [-2, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008504958355088, "hecke_ring_generator_nbound": 3, "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, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1680.2.t.c", "level": 1680, "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": [2, 3, 5, 7], "level_radical": 210, "minimal_twist": "840.2.t.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+i q^{3}+(-2 i-1)q^{5}+i q^{7}-q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1680.2.t", "trace_display": [0, 0, -2, 0], "trace_hash": 21673108958908829, "trace_moments": [{"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "1.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.564", "prec": 17}, {"__RealLiteral__": 0, "data": "16.014", "prec": 20}, {"__RealLiteral__": 0, "data": "6.791", "prec": 17}, {"__RealLiteral__": 0, "data": "162.148", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.511", "prec": 17}, "traces": [0, 2, 0, 0, 0, -2, 0, 0, 0, -2, 0, -4, 0, 0, 0, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, -6, 0, 0, 0, -4, 0, 12, 0, 0, 0, 4, 0, 0, 0, 4, 0, -20, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, -16, 0, -28, 0, 0, 0, -8, 0, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 12, 0, 4, 0, 0, 0, -4, 0, 0, 0, 4, 0, 12, 0, 0, 0, 2, 0, 0, 0, 12, 0, -16, 0, 0, 0, 32, 0, 0, 0, 0, 0, -14, 0, 0, 0, 22, 0, 0, 0, 0, 0, -24, 0, 0, 0, -4, 0, 0, 0, -28, 0, -24, 0, 0, 0, 4, 0, 0, 0, -12, 0, -32, 0, 0, 0, -12, 0, 0, 0, -4, 0, -16, 0, 0, 0, -8, 0, 0, 0, 18, 0, -4, 0, 0, 0, -8, 0, 0, 0, 4, 0, -4, 0, 0, 0, 32, 0, 0, 0, 2, 0, -36, 0, 0, 0, -4, 0, 0, 0, 20, 0, 8, 0, 0, 0, 20, 0, 0, 0, -8, 0, 16, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 60, 0, 4, 0, 0, 0, 48, 0, 0, 0, -20, 0, -20, 0, 0, 0, 2, 0, 0, 0, -32, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 4, 0, 0, 0, 8, 0, 0, 0, 36, 0, -28, 0, 0, 0, 12, 0, 0, 0, -12, 0, 12, 0, 0, 0, 8, 0, 0, 0, 34, 0, -4, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -4, 0, 0, 0, -32, 0, 48, 0, 0, 0, -4, 0, 0, 0, 8, 0, 8, 0, 0, 0, 16, 0, 0, 0, -24, 0, 64, 0, 0, 0, -16, 0, 0, 0, 28, 0, -24, 0, 0, 0, 16, 0, 0, 0, 44, 0, -4, 0, 0, 0, 28, 0, 0, 0, 68, 0, -30, 0, 0, 0, 8, 0, 0, 0, 20, 0, -4, 0, 0, 0, -4, 0, 0, 0, -8, 0, -24, 0, 0, 0, -8, 0, 0, 0, -60, 0, 0, 0, 0, 0, -8, 0, 0, 0, -4, 0, -28, 0, 0, 0, -2, 0, 0, 0, 44, 0, -20, 0, 0, 0, 64, 0, 0, 0, 24, 0, -76, 0, 0, 0, 0, 0, 0, 0, -8, 0, -44, 0, 0, 0, -8, 0, 0, 0, -12, 0, 2, 0, 0, 0, -12, 0, 0, 0, 60, 0, 40, 0, 0, 0, -4, 0, 0, 0, 0, 0, -60, 0, 0, 0, 24, 0, 0, 0, 8, 0, -44, 0, 0, 0, -12, 0, 0, 0, 16, 0, 32, 0, 0, 0, 8, 0, 0, 0, 16, 0, -52, 0, 0, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, -12, 0, 0, 0, -68, 0, -4, 0, 0, 0, 64, 0, 0, 0, 48, 0, 20, 0, 0, 0, 6, 0, 0, 0, -82, 0, 0, 0, 0, 0, -16, 0, 0, 0, 4, 0, 92, 0, 0, 0, -12, 0, 0, 0, -4, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, -36, 0, -56, 0, 0, 0, -64, 0, 0, 0, 32, 0, -32, 0, 0, 0, 8, 0, 0, 0, 24, 0, 12, 0, 0, 0, 0, 0, 0, 0, -28, 0, -84, 0, 0, 0, 14, 0, 0, 0, 4, 0, 48, 0, 0, 0, -40, 0, 0, 0, -28, 0, 16, 0, 0, 0, -14, 0, 0, 0, 0, 0, 8, 0, 0, 0, 48, 0, 0, 0, 28, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, -84, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -4, 0, 16, 0, 0, 0, 40, 0, 0, 0, 8, 0, -60, 0, 0, 0, 28, 0, 0, 0, -36, 0, -76, 0, 0, 0, 24, 0, 0, 0, 76, 0, -8, 0, 0, 0, 16, 0, 0, 0, 104, 0, -32, 0, 0, 0, 12, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -72, 0, 8, 0, 0, 0, 12, 0, 0, 0, 8, 0, -40, 0, 0, 0, 32, 0, 0, 0, 32, 0, 44, 0, 0, 0, 0, 0, 0, 0, 52, 0, 24, 0, 0, 0, -36, 0, 0, 0, -40, 0, 56, 0, 0, 0, 88, 0, 0, 0, 0, 0, 28, 0, 0, 0, 4, 0, 0, 0, 0, 0, -12, 0, 0, 0, 16, 0, 0, 0, -12, 0, -36, 0, 0, 0, -32, 0, 0, 0, -4, 0, 36, 0, 0, 0, 16, 0, 0, 0, 52, 0, -48, 0, 0, 0, 0, 0, 0, 0, 72, 0, -50, 0, 0, 0, -18, 0, 0, 0, -24, 0, -128, 0, 0, 0, 4, 0, 0, 0, -52, 0, 20, 0, 0, 0, -96, 0, 0, 0, -16, 0, -16, 0, 0, 0, -4, 0, 0, 0, 16, 0, 20, 0, 0, 0, 0, 0, 0, 0, -24, 0, -4, 0, 0, 0, -4, 0, 0, 0, -24, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -84, 0, 0, 0, 8, 0, 0, 0, -72, 0, 40, 0, 0, 0, -64, 0, 0, 0, 68, 0, -4, 0, 0, 0, 0, 0, 0, 0, -28, 0, 52, 0, 0, 0, -2, 0, 0, 0, 8, 0, 36, 0, 0, 0, 36, 0, 0, 0, -20, 0, 10, 0, 0, 0, -64, 0, 0, 0, 0, 0, 96, 0, 0, 0, -12, 0, 0, 0, -24, 0, -12, 0, 0, 0, -24, 0, 0, 0, 0, 0, -8, 0, 0, 0, -20, 0, 0, 0, 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, -100, 0, 64, 0, 0, 0, -8, 0, 0, 0, 52, 0, -84, 0, 0, 0, 60, 0, 0, 0, 2, 0, 36, 0, 0, 0, -32, 0, 0, 0, -20, 0, 40, 0, 0, 0, 8, 0, 0, 0, -44, 0, 96, 0, 0, 0, -16, 0, 0, 0, -48, 0, 124, 0, 0, 0, -56, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, -192, 0, 0, 0, 24, 0, 0, 0, 14, 0, 48, 0, 0, 0, 4, 0, 0, 0, -44, 0, -32, 0, 0, 0, 0, 0, 0, 0, -20, 0, -24, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -22, 0, 0, 0, -92, 0, -8, 0, 0, 0, -32, 0, 0, 0, 0, 0, 16, 0, 0, 0, -60, 0, 0, 0, -48, 0, 120, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, -56, 0, 0, 0, -96, 0, 0, 0, 24, 0, -36, 0, 0, 0, 16, 0, 0, 0, 40, 0, 60, 0, 0, 0, 20, 0, 0, 0, -24, 0, 68, 0, 0, 0, 20, 0, 0, 0, 24, 0, 48, 0, 0, 0, 4, 0, 0, 0, -32, 0, 32, 0, 0, 0, 6, 0, 0, 0, 60, 0, 124, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, -44, 0, 28, 0, 0, 0, -16, 0, 0, 0, -112, 0, 8, 0, 0, 0, -64, 0, 0, 0, 24, 0, -120, 0, 0, 0, 0, 0, 0, 0, 140, 0, -4, 0, 0, 0, -48, 0, 0, 0, 68, 0, 4, 0, 0, 0, 16, 0, 0, 0, 36, 0, -108, 0, 0, 0, -4, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, -16, 0, 0, 0, 24, 0, 72, 0, 0, 0, 24, 0, 0, 0, 64, 0, 12, 0, 0, 0, -36, 0, 0, 0, -56, 0, 32, 0, 0, 0, 28, 0, 0, 0, 32, 0, 76, 0, 0, 0, 8, 0, 0, 0, -54, 0, 24, 0, 0, 0, -44, 0, 0, 0, 12, 0, 52, 0, 0, 0, 96, 0, 0, 0, 8, 0, -16, 0, 0, 0, 12, 0, 0, 0, -28, 0, 0, 0, 0, 0, -12, 0, 0, 0, -60, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 4, 0, 0, 0, -16, 0, 0, 0, -52, 0, 4, 0, 0, 0, -40, 0, 0, 0, 52, 0, 48, 0, 0, 0, -34, 0, 0, 0, 16, 0, -36, 0, 0, 0, 4, 0, 0, 0, -60, 0, -40, 0, 0, 0, -32, 0, 0, 0, -56, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 8, 0, 0, 0, 140, 0, 28, 0, 0, 0, -32, 0, 0, 0, -44, 0, 16, 0, 0, 0, 0, 0, 0, 0, -32, 0, 120, 0, 0, 0, 24, 0, 0, 0, -12, 0, -18, 0, 0, 0, -12, 0, 0, 0, 56, 0, 44, 0, 0, 0, -80, 0, 0, 0, 4, 0, 64, 0, 0, 0, 32, 0, 0, 0, 20, 0, 48, 0, 0, 0, -48, 0, 0, 0, 104, 0, 0, 0, 0, 0, 56, 0, 0, 0, 8, 0, 24, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, -40, 0, 108, 0, 0, 0, -8, 0, 0, 0, -20, 0, -4, 0, 0, 0, 0, 0, 0, 0, -60, 0, 100, 0, 0, 0, 8, 0, 0, 0, 4, 0, -36, 0, 0, 0, 24, 0, 0, 0, 24, 0, 8, 0, 0, 0, 24, 0, 0, 0, 0, 0, 48, 0, 0, 0, -64, 0, 0, 0, -8, 0, 64, 0, 0, 0, -32, 0, 0, 0, -68, 0, -12, 0, 0, 0, 32, 0, 0, 0, -32, 0, 118, 0, 0, 0, -128, 0, 0, 0, 24, 0, 24, 0, 0, 0, -28, 0, 0, 0, -84, 0, -2, 0, 0, 0, 24, 0, 0, 0, 140, 0, 0, 0, 0, 0, -4, 0, 0, 0, 36, 0, -44, 0, 0, 0, 48, 0, 0, 0, 8, 0, -20, 0, 0, 0, -80, 0, 0, 0, -192, 0, -52, 0, 0, 0, -44, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 152, 0, 56, 0, 0, 0, 96, 0, 0, 0, -8, 0, 32, 0, 0, 0, 84, 0, 0, 0, -16, 0, 40, 0, 0, 0, 0, 0, 0, 0, 60, 0, -20, 0, 0, 0, -68, 0, 0, 0, 24, 0, 12, 0, 0, 0, 30, 0, 0, 0, -8, 0, -16, 0, 0, 0, -28, 0, 0, 0, 0, 0, -32, 0, 0, 0, -16, 0, 0, 0, 0, 0, -152, 0, 0, 0, 64, 0, 0, 0, -32, 0, 0, 0, 0, 0, -20, 0, 0, 0, 86, 0, -76, 0, 0, 0, 4, 0, 0, 0, -36, 0, 140, 0, 0, 0, -80, 0, 0, 0, -12, 0, 60, 0, 0, 0, 48, 0, 0, 0, 20, 0, 8, 0, 0, 0, 16, 0, 0, 0, 100, 0, 24, 0, 0, 0, 8, 0, 0, 0, -16, 0, 116, 0, 0, 0, 24, 0, 0, 0, -256, 0, -4, 0, 0, 0, 96, 0, 0, 0, 24, 0, 0, 0, 0, 0, 16, 0, 0, 0, 24, 0, -24, 0, 0, 0, 0, 0, 0, 0, -48, 0, -16, 0, 0, 0, 60, 0, 0, 0, 60, 0, -28, 0, 0, 0, 0, 0, 0, 0, -60, 0, -32, 0, 0, 0, -48, 0, 0, 0, -8, 0, 4, 0, 0, 0, -24, 0, 0, 0, -80, 0, -24, 0, 0, 0, -120, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 112, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 1], [0, 0], [-1, -2], [0, 0], [0, 1], [0, 0], [-1, 0], [0, 0], [-2, 0], [0, 0], [0, -2], [0, 0], [2, -1], [0, 0], [0, 0], [0, 0], [2, 0], [0, 0], [-1, 0], [0, 0], [0, 8], [0, 0], [-3, 4], [0, 0], [0, -1], [0, 0], [-2, 0], [0, 0], [6, 0], [0, 0], [0, -2], [0, 0], [2, -1], [0, 0], [0, 8], [0, 0], [2, 0], [0, 0], [-10, 0], [0, 0], [0, 0], [0, 0], [1, 2], [0, 0], [0, 12], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 2], [0, 0], [2, 4], [0, 0], [0, 2], [0, 0], [0, 0], [0, 0], [2, 0], [0, 0], [0, -1], [0, 0], [-4, 2], [0, 0], [0, -4], [0, 0], [-8, 0], [0, 0], [-14, 0], [0, 0], [0, 2], [0, 0], [-4, -3], [0, 0], [0, -2], [0, 0], [4, 0], [0, 0], [1, 0], [0, 0], [0, 16], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [6, 0], [0, 0], [2, 0], [0, 0], [0, 6], [0, 0], [-2, -4], [0, 0], [0, 2], [0, 0], [2, 0], [0, 0]]}