# Stored data for newform 1600.2.c.c, downloaded from the LMFDB on 13 December 2024. {"Nk2": 6400, "analytic_conductor": 12.776064323404862, "analytic_rank": 1, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [1600, 2, [1151, 901, 577], [2, 2, 1]], "cm_discs": [], "conrey_index": 449, "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": [[3, [4, 0, 1]], [7, [4, 0, 1]], [11, [4, 1]], [19, [8, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007336727250496, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "1600.2.c.c", "level": 1600, "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": [2, 5], "level_radical": 10, "minimal_twist": "160.2.a.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta q^{3}+\\beta q^{7}-q^{9}-4 q^{11}-3\\beta q^{13}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1600.2.c", "trace_display": [0, 0, 0, 0], "trace_hash": 1240228547790976708, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.838", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.983", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "136.524", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.517", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 24, 0, -20, 0, 0, 0, 0, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 0, 0, 0, 0, -16, 0, -22, 0, 0, 0, 0, 0, 0, 0, 12, 0, 24, 0, 0, 0, 0, 0, 0, 0, 8, 0, -28, 0, 0, 0, 0, 0, 0, 0, -28, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 10, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 32, 0, -8, 0, 0, 0, 0, 0, 0, 0, 20, 0, -40, 0, 0, 0, 0, 0, 0, 0, -8, 0, 24, 0, 0, 0, 0, 0, 0, 0, -46, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -32, 0, 24, 0, 0, 0, 0, 0, 0, 0, 64, 0, 8, 0, 0, 0, 0, 0, 0, 0, 40, 0, 24, 0, 0, 0, 0, 0, 0, 0, -20, 0, 32, 0, 0, 0, 0, 0, 0, 0, -16, 0, -36, 0, 0, 0, 0, 0, 0, 0, -40, 0, -40, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 36, 0, -56, 0, 0, 0, 0, 0, 0, 0, 8, 0, -20, 0, 0, 0, 0, 0, 0, 0, 26, 0, -40, 0, 0, 0, 0, 0, 0, 0, -72, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -56, 0, 0, 0, 0, 0, 0, 0, 16, 0, 24, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, -24, 0, 32, 0, 0, 0, 0, 0, 0, 0, -4, 0, 48, 0, 0, 0, 0, 0, 0, 0, 32, 0, 90, 0, 0, 0, 0, 0, 0, 0, 20, 0, -8, 0, 0, 0, 0, 0, 0, 0, -48, 0, 24, 0, 0, 0, 0, 0, 0, 0, 52, 0, 24, 0, 0, 0, 0, 0, 0, 0, 64, 0, 36, 0, 0, 0, 0, 0, 0, 0, -28, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, -96, 0, 40, 0, 0, 0, 0, 0, 0, 0, -32, 0, -6, 0, 0, 0, 0, 0, 0, 0, -44, 0, 80, 0, 0, 0, 0, 0, 0, 0, -16, 0, -12, 0, 0, 0, 0, 0, 0, 0, 24, 0, 40, 0, 0, 0, 0, 0, 0, 0, 48, 0, -24, 0, 0, 0, 0, 0, 0, 0, 24, 0, -40, 0, 0, 0, 0, 0, 0, 0, 80, 0, 56, 0, 0, 0, 0, 0, 0, 0, -36, 0, 40, 0, 0, 0, 0, 0, 0, 0, 24, 0, -12, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 20, 0, 0, 0, 0, 0, 0, 0, 4, 0, 32, 0, 0, 0, 0, 0, 0, 0, 24, 0, 32, 0, 0, 0, 0, 0, 0, 0, 36, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, -40, 0, 0, 0, 0, 0, 0, 0, 64, 0, -88, 0, 0, 0, 0, 0, 0, 0, -48, 0, -52, 0, 0, 0, 0, 0, 0, 0, 16, 0, 24, 0, 0, 0, 0, 0, 0, 0, -16, 0, 48, 0, 0, 0, 0, 0, 0, 0, 8, 0, -72, 0, 0, 0, 0, 0, 0, 0, -24, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 32, 0, -20, 0, 0, 0, 0, 0, 0, 0, -8, 0, 16, 0, 0, 0, 0, 0, 0, 0, -40, 0, -72, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 0, 0, 0, 0, 8, 0, -36, 0, 0, 0, 0, 0, 0, 0, -20, 0, 16, 0, 0, 0, 0, 0, 0, 0, -80, 0, -8, 0, 0, 0, 0, 0, 0, 0, -26, 0, -8, 0, 0, 0, 0, 0, 0, 0, -32, 0, -192, 0, 0, 0, 0, 0, 0, 0, 24, 0, -8, 0, 0, 0, 0, 0, 0, 0, -96, 0, 20, 0, 0, 0, 0, 0, 0, 0, 60, 0, -104, 0, 0, 0, 0, 0, 0, 0, 160, 0, -96, 0, 0, 0, 0, 0, 0, 0, -8, 0, -24, 0, 0, 0, 0, 0, 0, 0, -8, 0, -12, 0, 0, 0, 0, 0, 0, 0, 12, 0, -40, 0, 0, 0, 0, 0, 0, 0, -24, 0, 76, 0, 0, 0, 0, 0, 0, 0, 4, 0, -88, 0, 0, 0, 0, 0, 0, 0, 48, 0, -50, 0, 0, 0, 0, 0, 0, 0, -104, 0, -24, 0, 0, 0, 0, 0, 0, 0, 32, 0, 80, 0, 0, 0, 0, 0, 0, 0, 64, 0, -72, 0, 0, 0, 0, 0, 0, 0, -72, 0, 28, 0, 0, 0, 0, 0, 0, 0, 24, 0, 88, 0, 0, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 28, 0, 56, 0, 0, 0, 0, 0, 0, 0, 112, 0, 88, 0, 0, 0, 0, 0, 0, 0, -12, 0, -48, 0, 0, 0, 0, 0, 0, 0, -24, 0, -76, 0, 0, 0, 0, 0, 0, 0, -120, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -30, 0, 0, 0, 0, 0, 0, 0, 64, 0, 72, 0, 0, 0, 0, 0, 0, 0, -48, 0, 28, 0, 0, 0, 0, 0, 0, 0, 24, 0, 88, 0, 0, 0, 0, 0, 0, 0, 16, 0, -96, 0, 0, 0, 0, 0, 0, 0, -100, 0, 56, 0, 0, 0, 0, 0, 0, 0, -48, 0, 52, 0, 0, 0, 0, 0, 0, 0, -80, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 108, 0, -56, 0, 0, 0, 0, 0, 0, 0, -120, 0, 100, 0, 0, 0, 0, 0, 0, 0, -28, 0, 8, 0, 0, 0, 0, 0, 0, 0, 120, 0, 24, 0, 0, 0, 0, 0, 0, 0, -10, 0, 40, 0, 0, 0, 0, 0, 0, 0, 40, 0, -72, 0, 0, 0, 0, 0, 0, 0, 44, 0, 112, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, -48, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 0, 0, 0, 0, 56, 0, -72, 0, 0, 0, 0, 0, 0, 0, 32, 0, -16, 0, 0, 0, 0, 0, 0, 0, 56, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -132, 0, 0, 0, 0, 0, 0, 0, 40, 0, 104, 0, 0, 0, 0, 0, 0, 0, 112, 0, 28, 0, 0, 0, 0, 0, 0, 0, -96, 0, 24, 0, 0, 0, 0, 0, 0, 0, 24, 0, -32, 0, 0, 0, 0, 0, 0, 0, 60, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 92, 0, -32, 0, 0, 0, 0, 0, 0, 0, -64, 0, 120, 0, 0, 0, 0, 0, 0, 0, -16, 0, 80, 0, 0, 0, 0, 0, 0, 0, 32, 0, 16, 0, 0, 0, 0, 0, 0, 0, 140, 0, -24, 0, 0, 0, 0, 0, 0, 0, -88, 0, 76, 0, 0, 0, 0, 0, 0, 0, 32, 0, -192, 0, 0, 0, 0, 0, 0, 0, -112, 0, 140, 0, 0, 0, 0, 0, 0, 0, -72, 0, 48, 0, 0, 0, 0, 0, 0, 0, 24, 0, -20, 0, 0, 0, 0, 0, 0, 0, -192, 0, 8, 0, 0, 0, 0, 0, 0, 0, 40, 0, 68, 0, 0, 0, 0, 0, 0, 0, 66, 0, 24, 0, 0, 0, 0, 0, 0, 0, -88, 0, -116, 0, 0, 0, 0, 0, 0, 0, 152, 0, -72, 0, 0, 0, 0, 0, 0, 0, 112, 0, 24, 0, 0, 0, 0, 0, 0, 0, -100, 0, -40, 0, 0, 0, 0, 0, 0, 0, 32, 0, -12, 0, 0, 0, 0, 0, 0, 0, -108, 0, -16, 0, 0, 0, 0, 0, 0, 0, 32, 0, -32, 0, 0, 0, 0, 0, 0, 0, -24, 0, 72, 0, 0, 0, 0, 0, 0, 0, 48, 0, 152, 0, 0, 0, 0, 0, 0, 0, 72, 0, 40, 0, 0, 0, 0, 0, 0, 0, 16, 0, -52, 0, 0, 0, 0, 0, 0, 0, -44, 0, -96, 0, 0, 0, 0, 0, 0, 0, 48, 0, 128, 0, 0, 0, 0, 0, 0, 0, 56, 0, -120, 0, 0, 0, 0, 0, 0, 0, -24, 0, 46, 0, 0, 0, 0, 0, 0, 0, -128, 0, -104, 0, 0, 0, 0, 0, 0, 0, 176, 0, -72, 0, 0, 0, 0, 0, 0, 0, -132, 0, 32, 0, 0, 0, 0, 0, 0, 0, -64, 0, -8, 0, 0, 0, 0, 0, 0, 0, 88, 0, 120, 0, 0, 0, 0, 0, 0, 0, -128, 0, 32, 0, 0, 0, 0, 0, 0, 0, -72, 0, 8, 0, 0, 0, 0, 0, 0, 0, -240, 0, 36, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 100, 0, 0, 0, 0, 0, 0, 0, -36, 0, 8, 0, 0, 0, 0, 0, 0, 0, -80, 0, 56, 0, 0, 0, 0, 0, 0, 0, -40, 0, -72, 0, 0, 0, 0, 0, 0, 0, 64, 0, 160, 0, 0, 0, 0, 0, 0, 0, 44, 0, -184, 0, 0, 0, 0, 0, 0, 0, -120, 0, 118, 0, 0, 0, 0, 0, 0, 0, 120, 0, -96, 0, 0, 0, 0, 0, 0, 0, -48, 0, 40, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -76, 0, 0, 0, 0, 0, 0, 0, -192, 0, 152, 0, 0, 0, 0, 0, 0, 0, 8, 0, -44, 0, 0, 0, 0, 0, 0, 0, 32, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 8, 0, -96, 0, 0, 0, 0, 0, 0, 0, 72, 0, 24, 0, 0, 0, 0, 0, 0, 0, 92, 0, 32, 0, 0, 0, 0, 0, 0, 0, -104, 0, 44, 0, 0, 0, 0, 0, 0, 0, 48, 0, -88, 0, 0, 0, 0, 0, 0, 0, 24, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 88, 0, -8, 0, 0, 0, 0, 0, 0, 0, 78, 0, 120, 0, 0, 0, 0, 0, 0, 0, 184, 0, -60, 0, 0, 0, 0, 0, 0, 0, -48, 0, -8, 0, 0, 0, 0, 0, 0, 0, -80, 0, -64, 0, 0, 0, 0, 0, 0, 0, 20, 0, 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, -132, 0, 0, 0, 0, 0, 0, 0, 120, 0, 72, 0, 0, 0, 0, 0, 0, 0, 224, 0, -24, 0, 0, 0, 0, 0, 0, 0, 120, 0, 120, 0, 0, 0, 0, 0, 0, 0, -88, 0, -168, 0, 0, 0, 0, 0, 0, 0, -60, 0, -8, 0, 0, 0, 0, 0, 0, 0, 120, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 48, 0, -104, 0, 0, 0, 0, 0, 0, 0, -24, 0, -144, 0, 0, 0, 0, 0, 0, 0, 16, 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], [0, 0], [0, 0], [0, 1], [0, 0], [-1, 0], [0, 0], [-4, 0], [0, 0], [0, -3], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [-8, 0], [0, 0], [-4, 0], [0, 0], [0, -3], [0, 0], [0, 0], [0, 0], [0, 2], [0, 0], [-2, 0], [0, 0], [-4, 0], [0, 0], [0, -4], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [12, 0], [0, 0], [-10, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [3, 0], [0, 0], [-4, 0], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, -8], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [0, -3], [0, 0], [12, 0], [0, 0], [12, 0], [0, 0], [0, -5], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [-8, 0], [0, 0], [-11, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [6, 0], [0, 0], [12, 0], [0, 0], [0, -4], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [4, 0], [0, 0]]}