# Stored data for newform 5070.2.a.b, downloaded from the LMFDB on 07 September 2026.
{"Nk2": 20280, "analytic_conductor": 40.48415382478915, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, 1], [5, 1], [13, 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": [5070, 1, [1691, 4057, 1861], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 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": [[7, [-3, 1]], [11, [3, 1]], [17, [0, 1]], [31, [-6, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599660929998, "hecke_ring_generator_nbound": 1, "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": "5070.2.a.b", "level": 5070, "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, 13], "level_radical": 390, "minimal_twist": "390.2.i.e", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/5070/b"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "5070.2.a", "trace_display": [-1, -1, -1, 3], "trace_hash": 1833326658783826434, "trace_moments": [0, {"__RealLiteral__": 0, "data": "0.970", "prec": 10}, 0, {"__RealLiteral__": 0, "data": "1.918", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "4.775", "prec": 14}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.012", "prec": 7}, "traces": [0, 1, -1, -1, 1, -1, 1, 3, -1, 1, 1, -3, -1, 0, -3, 1, 1, 0, -1, 3, -1, -3, 3, -4, 1, 1, 0, -1, 3, -4, -1, 6, -1, 3, 0, -3, 1, 9, -3, 0, 1, -10, 3, -10, -3, -1, 4, -3, -1, 2, -1, 0, 0, 9, 1, 3, -3, -3, 4, 12, 1, -6, -6, 3, 1, 0, -3, -8, 0, 4, 3, -14, -1, -8, -9, -1, 3, -9, 0, 6, -1, 1, 10, 16, -3, 0, 10, 4, 3, -3, 1, 0, -4, -6, 3, -3, 1, 8, -2, -3, 1, 0, 0, -15, 0, 3, -9, 2, -1, -2, -3, -9, 3, -8, 3, 4, -4, 0, -12, 0, -1, -2, 6, 10, 6, -1, -3, 3, -1, 10, 0, -3, 3, 9, 8, 1, 0, 12, -4, -17, -3, 3, 14, 0, 1, 4, 8, -2, 9, -2, 1, 14, -3, 0, 9, -6, 0, -17, -6, -9, 1, -12, -1, 20, -10, -3, -16, 9, 3, 0, 0, 3, -10, 13, -4, 3, -3, -12, 3, 4, -1, -10, 0, 6, 4, -9, 6, 0, -3, -3, 3, -6, -1, 8, -8, 0, 2, 11, 3, -10, -1, 8, 0, -12, 0, 10, 15, -4, 0, -9, -3, 9, 9, 14, -2, 10, 1, 18, 2, 8, 3, 0, 9, -11, -3, 1, 8, -16, -3, -10, -4, 9, 4, -6, 0, 3, 12, -6, 0, -26, 1, 7, 2, -1, -6, -2, -10, 0, -6, -16, 1, -1, 3, 12, -3, 0, 1, 12, -10, 27, 0, -4, 3, -31, -3, -9, -9, 3, -8, -4, -1, -12, 0, 0, -12, -3, 4, -31, 17, 6, 3, -30, -3, 6, -14, 3, 0, -30, -1, -17, -4, -8, -8, -1, 2, -12, -9, 3, 2, 0, -1, -30, -14, 0, 3, 6, 0, 26, -9, 15, 6, -4, 0, 26, 17, -3, 6, 17, 9, 12, -1, -2, 12, 0, 1, 0, -20, 2, 10, -9, 3, -28, 16, 9, -9, 8, -3, 6, 0, 8, 0, -18, -3, -15, 10, -4, -13, -24, 4, 16, -3, 0, 3, -8, 12, 14, -3, 0, -4, 30, 1, -10, 10, 2, 0, 8, -6, 8, -4, -10, 9, 27, -6, -26, 0, 1, 3, 0, 3, -33, -3, -3, 6, 4, 1, 9, -8, -10, 8, 24, 0, 0, -2, 3, -11, -6, -3, -23, 10, -9, 1, -27, -8, 0, 0, -1, 12, -27, 0, -7, -10, -12, -15, 36, 4, -16, 0, 17, 9, -12, 3, -28, -9, -3, -9, 0, -14, -18, 2, 0, -10, -12, -1, -16, -18, -4, -2, -12, -8, -30, -3, 2, 0, -10, -9, 3, 11, 2, 3, -35, -1, 30, -8, -14, 16, 0, 3, -42, 10, 0, 4, -32, -9, -24, -4, 6, 6, 8, 0, -24, -3, 17, -12, 30, 6, 3, 0, 9, 26, 12, -1, 0, -7, 12, -2, -8, 1, 29, 6, -20, 2, 5, 10, 0, 0, 3, 6, -42, 16, 20, -1, -9, 1, 21, -3, 0, -12, 0, 3, 10, 0, -24, -1, -3, -12, 15, 10, 9, -27, -13, 0, -35, 4, 22, -3, -3, 31, 0, 3, -7, 9, 12, 9, 0, -3, -2, 8, -4, 4, -6, 1, -22, 12, 10, 0, 2, 0, 22, 12, -6, 3, -12, -4, 18, 31, 9, -17, -9, -6, 0, -3, 0, 30, 20, 3, 8, -6, 3, 14, -39, -3, 23, 0, 6, 30, -4, 1, -38, 17, -8, 4, 48, 8, -27, 8, 0, 1, 18, -2, 18, 12, -11, 9, 36, -3, 0, -2, 10, 0, -30, 1, 21, 30, -8, 14, 2, 0, 27, -3, 12, -6, 0, 0, -7, -26, -10, 9, -30, -15, -23, -6, 4, 4, -9, 0, 1, -26, 9, -17, 0, 3, 12, -6, -9, -17, -3, -9, 0, -12, -14, 1, 35, 2, 28, -12, -10, 0, -45, -1, -36, 0, -18, 20, 3, -2, 3, -10, -8, 9, 4, -3, 30, 28, 0, -16, -9, -9, 16, 9, 11, -8, 18, 3, 48, -6, -1, 0, -6, -8, 24, 0, 16, 18, 30, 3, -12, 15, 10, -10, 0, 4, -7, 13, -9, 24, 17, -4, 0, -16, 6, 3, 24, 0, 27, -3, -3, 8, 0, -12, -40, -14, 6, 3, -24, 0, 0, 4, 26, -30, -36, -1, -45, 10, -7, -10, -4, -2, -3, 0, 1, -8, 0, 6, 53, -8, 2, 4, 24, 10, 11, -9, 0, -27, 48, 6, 2, 26, 16, 0, 6, -1, -24, -3, 1, 0, -14, -3, 17, 33, -12, 3, -31, 3, -6, -6, 0, -4, 0, -1, 46, -9, -12, 8, -7, 10, 6, -8, -27, -24, -30, 0, 42, 0, 4, 2, 17, -3, -36, 11, 31, 6, -24, 3, 0, 23, 9, -10, -42, 9, 0, -1, -3, 27, 24, 8, 12, 0, 4, 0, -10, 1, -31, -12, 12, 27, -20, 0, -30, 7, 0, 10, 50, 12, -11, 15, 3, -36, -18, -4, 0, 16, 31, 0, 0, -17, -9, -9, -6, 12, -6, -3, -13, 28, 30, 9, 0, 3, -6, 9, -6, 0, -36, 14, -26, 18, -3, -2, -50, 0, -5, 10, 30, 12, -24, 1, -13, 16, 17, 18, -18, 4, 0, 2, 8, 12, -3, 8, -38, 30, 1, 3, -23, -2, 22, 0, 12, 10, 9, 9, 9, -3, -3, -11, -9, -2, -4, -3, 0, 35, -24, 1, 0, -30, 30, 8, 10, 14, -14, -16, 0, 0, 28, -3, -48, 42, -6, -10, -9, 0, 14, -4, -26, 32, 0, 9, 9, 24, -15, 4, 2, -6, 6, -6, 4, -8, 0, 0, 14, 24, -26, 3, -32, -17, 40, 12, 3, -30, 18, -6, 0, -3, -17, 0, 34, -9, 6, -26, -12, -12, 36, 1, 5, 0, 2, 7, -8, -12, 25, 2, 0, 8, 15, -1, -51, -29, 0, -6, -44, 20, 9, -2, -2, -5, 55, -10, -11, 0, 9, 0, 40, -3, 58, -6, 28, 42, 10, -16, 47, -20, -9, 1, 0, 9, 0, -1, -8, -21, 27, 3, 23, 0, -6, 12, -54, 0, 12, -3, -8, -10, -52, 0, 22, 24, 18, 1, -10, 3, 0, 12, 15, -15, 6, -10, -46, -9, 4, 27, 0, 13, -34, 0, 24, 35, -6, -4, 9, -22, -16, 3, 45, 3, 48, -31, 0, 0, -9, -3, 42, 7, 8, -9, 20, -12, -16, -9, -14, 0, -24, 3, -26, 2, 0, -8, -36, 4, -10, -4, -30, 6, 0, -1, 12, 22, 10, -12, -18, -10, -20, 0, -2, -2, 47, 0, 41, -22, -8, -12, -56, 6, -51, -3, -8, 12, -23, 4, 0, -18, 10, -31, 38, -9, 0, 17, -27, 9, 11, 6, -17, 0, 26, 3, 36, 0, 4, -30, -1, -20, -8, -3, 29, -8, 0, 6, 45, -3, 16, -14, 33, 39, 0, 3, 60, -23, 3, 0, 10, -6, 54, -30, -4, 4, 18, -1, 26, 38, -9, -17, 0, 8, -18, -4, 10, -48, 44, -8, 6, 27, -24, -8, 27, 0, 45, -1, 0, -18, -3, 2, -6, -18, -3, -12, -6, 11, 0, -9, 6, -36, 38, 3, 40, 0, 23, 2, 46, -10, 26, 0, 9, 30, 6, -1, -62, -21, 27, -30, -7, 8, 0, -14, 0, -2, 39, 0, 11, -27, 1, 3, 12, -12, -36, 6, 27, 0, 56, 0, 2, 7, 7, 26, 26, 10, 10, -9, 12, 30, 0, 15, 2, 23, -36, 6, 0, -4, 24, -4, 16, 9, 40, 0, -11, -1, -17, 26, 12, -9, 1, 17, 12, 0, 47, -3, 0, -12, 28, 6, -12, 9, -30, 17, 3, 3, -60, 9, -24, 0, 0, 12, -14, 14, 16, -1, 18, -35, 0, -2, -12, -28, 0, 12, 29, 10, 17, 0, 12, 45, -27, 1, -40, 36, 16, 0, -46, 18, -5, -20, 4, -3, 22, 2, 0, -3, 12, 10, 0, 8, 31, -9, 30, -4, -18, 3, 23, -30, -2, -28, 9, 0, -16, 16, 10, 9, 39, 9, -60, -16, -3, -9, -18, -11, 0, 8, -2, -18, 0, -3, 4, -48, 35, 6, -42, 1, 24, 0, -30, 6, 12, 8, -48, -24, 14, 0, -15, -16, 12, -18, 0, -30, -23, -3, 44, 12, 42, -15, -49, -10, 3, 10, 0, 0, 33, -4, -28, 7, 32, -13, 31, 9, -24, -24, 24, -17, 0, 4, -30, 0, -6, 16, -9, -6, -14, -3, -8, -24, 24, 0, 30, -27, 24, 3, -1, 3, 0, -8, -17, 0, -6, 12, 0, 40, -30, 14, -8, -6, 20, -3, -3, 24, -50, 0, -8, 0, -9, -4, 18, -26, 30, 30, -12, 36, 22, 1, 9, 45, 0, -10, 17, 7, -8, 10, -12, 4, 47, 2, 19, 3, 8, 0, -18, -1, 61, 8, -29, 0, -27, -6, 1, -53, 20, 8, 0, -2, 0, -4, -5, -24, 12, -10, 27, -11, 0, 9, 41, 0, 40, 27, -3, -48, 45, -6, -50, -2, 42, -26, -18, -16, 0, 0, -20, -6, -3, 1, 18, 24, 9, 3, 30, -1, -36, 0, -21, 14, 18, 3, 0, -17, 0, -33, -90, 12, 12, -3, 0, 31, -6, -3, -6, 6, -10, 6, 51, 0, -12, 4, 24, 0, -26, 1, -36, -46, 3, 9, 32, 12, -29, -8, -15, 7, 0, -10, 70, -6, -9, 8, 42, 27, 4, 24, 13, 30, 24, 0, -33, -42, 35, 0, -26, -4, -40, -2, -22, -17, 13, 3, 0, 36, 3, -11, 48, -31, -71, -6, 0, 24, 47, -3, -17, 0, 7, -23, -48, -9, -90, 10, -12, 42, -12, -9, 62, 0, 0, 1, 27, 3, -30, -27, 2, -24, 33, -8, 22, -12, 4, 0, -55, -4, 0, 0, 6, 10, 39, -1, 58, 31, 22, 12, 0, -12, 50, -27, -10, 20, -18, 0, 56, 30, -2, -7, -51, 0, 6, -10, -22, -50, 54, -12, 9, 11, 6, -15, 0, -3, 0, 36, 12, 18, 28, 4, 14, 0, -18, -16, -42, -31, -55, 0, -9, 0, 20, 17, 52, 9, 9, 9, -78, 6, -8, -12, 0, 6, 32, 3, 59, 13, 0, -28, -6, -30, 21, -9, -20, 0, -9, -3, -78, 6, -8, -9, -50, 6, -48, 0, -3, 36, 0, -14, 18, 26, 39, -18, -6, 3, -48, 2, -23, 50, 15, 0, 0, 5, -6, -10, -21, -30, -4, -12, 4, 24, 51, -1, 0, 13, 38, -16, 18, -17, 24, -18, 8, 18, -27, -4, -54, 0, -48, -2, -16, -8, 44, -12, 27, 3, 0, -8, 4, 38, 0, -30, -3, -1, 60, -3, -18, 23, 100, 2, 8, -22, -18, 0, 24, -12, 36, -10, 11, -9, -14, -9, -48, -9, -36, 3, 0, 3, -64, 11, 0, 9, 22, 2, 46, 4, -10, 3, -60, 0, -30, -35, 30, 24, 36, -1, -38, 0, -21, 30, 10, -30, 0, -8, 8, -10, -12, -14, 18, 14, -2, 16, -24, 0, 0, 0, -27, -28, -27, 3, -8, 48, -12, -42, 72, 6, -56, 10, 0, 9, -8, 0, -27, -14, 7, 4, -93, 26, 24, -32, 10, 0, 36, -9, 57, -9, 30, -24, 0, 15, -27, -4, 23, -2, 0, 6, -28, -6, -4, 6, 26, -4, -18, 8, 9, 0, -6, 0, 66, -14, -1, -24, 63, 26, 62, -3, -9, 32, -12, 17, 0, -40, 0, -12, -9, -3, -36, 30, -12, -18, 33, 6, -36, 0, 9, 3, -56, 17, -39, 0, 3, -34, 72, 9, -64, -6, 0, 26, 24, 12, -4, 12, 14, -36, 0, -1, 0, -5, -35, 0, -9, -2, 30, -7, -28, 8, 5, 12, 14, -25, 10, -2, 0, 0, -93, -8, 45, -15, 32, 1, -24, 51, 36, 29, 18, 0, -42, 6, 18, 44, 0, -20, -45, -9, -3, 2, 81, 2, 0, 5, -3, -55, -90, 10, -12, 11, 8, 0, -61, -9, 6, 0, -4, -40, 36, 3, 18, -58, -30, 6, 23, -28, -60, -42, 0, -10, 30, 16, -44, -47, 9, 20, -78, 9, 52, -1, -16, 0, -54, -9, 27, 0, -11, 1, -20, 8, -4, 21, -18, -27, 0, -3, 22, -23, -48, 0, 30, 6, -51, -12, 1, 54, 24, 0, -70, -12, 6, 3, 6, 8, 27, 10, -24, 52, -32, 0, 0, -22, -16, -24, 7, -18, 12, -1, -30, 10, -3, -3, -41, 0, 12, -12, 0, -15, 56, 15, -10, -6, -1, 10, -36, 46, 0, 9, -30, -4, -6, -27, 7, 0, 16, -13, -48, 34, 9, 0, 9, -24, -32, -35, -17, 6, 29, 4, -67, -9, 0, 22, 0, 16, 12, -3, -6, -45, 8, -3, 18, -48, -24, 31, 28, 0, -20, 0, -27, 9, -38, 3, 62, -42, 3, -7, 32, -8, 0, 9, 0, -20, -24, 12, 0, 16, 40, 9, 18, 14, 12, 0, -6, 24, 18, -3, 12, 26, 24, -2, -48, 0, 0, 8, 0, 36, -24, -4, 78, 10, -26, 4, -62, 30, 12, -6, 36, 0, 0, 1, -82, -12, 45, -22, 16, -10, -33, 12, 7, 18, 0, 10, -90, 20, 4, 0, -12, 2, 52, 2, 3, -47, 108, 0, 12, -41, -1, 22, 30, 8, 78, 12, 0, 56, 30, -6, 0, 51, -53, 3, -84, 8, 50, -12, -2, 23, -23, -4, -38, 0, -24, 18, -6, -10, 10, 31, -11, -38, 51, 9, 12, 0, 0, -17, -3, 27, 0, -9, -48, -11, -32, -6, 36, 17, -2, 0, -53, -26, -32, -3, -16, -36, -92, 0, 35, -4, -6, 30, 0, 1, 60, 20, 24, 8, -30, 3, -54, -29, -1, 8, 0, 0, -48, -6, 14, -45, 20, 3, 0, -16, -17, 14, 36, -33, 0, -39, 12, 0, -90, -3, -59, -60, 31, 23, 42, -3, -49, 0, 6, -10, -24, 6, 39, -54, 0, 30, -40, 4, -6, -4, 0, -18, -6, 1, 32, -26, -46, -38, -78, 9, 16, 17, 12, 0, 24, -8, -84, 18, 7, 4, -27, -10, 0, 48, -6, -44, 0, 8, 0, -6, 27, -27, 81, 24, -8, 8, 30, -27, 3, 0, 36, -45, -42, 1, 24, 0, 6, 18, -4, 3, -2, -2, 0, 6, -17, 18, -5, 3, 18, 12, 36, 6, 0, -11, -30, 0, -31, 9, 60, -6, 49, 36, 24, -38, -3, -3, -28, -40, 0, 0, 58, -23, -43, -2, -9, -46, -54, 10, -24, -26, 42, 0, 14, -9, -12, -30, 0, -6, 52, 1, -59, 62, 3, 21, 0, -27, -64, 30, -24, 7, -25, -8, 9, 0, -12, 14, -12, 0, -120, 2, -4, -39, 51, 0, 8, -11, 10, 27, -72, -1, 0, -3, 31, -12, -29, 12, -57, 36, -12, -6, 75, -27, 48, 0, 20, -56, 72, 0, 36, -2, 30, -7, 33, -7, -5, -26, 0, -26, 27, -10, -8, -10, -50, 9, 0, -12, -90, -30, 11, 0, -24, -15, 36, -2, -3, -23, -2, 36, -72, -6, 18, 0, 0, 4, 42, -24, 0, 4, -9, -16, -27, -9, -31, -40, -20, 0, 48, 11, 0, 1, 60, 17, -83, -26, 9, -12, 8, 9, 0, -1, 6, -17, 90, -12, -21, 0, 6, -47, 30, 3, 58, 0, 13, 12, 0, -28, -30, -6, -30, 12, -44, -9, 0, 30, 0, -17, -120, -3, 47, -3, 6, 60, 24, -9, -10, 24, 6, 0, 92, 0, 4, -12, 36, 14, 24, -14, 78, -16, 26, 1, 0, -18, 18, 35, 3, 0, 0, 2, 24, 12, 50, 28, 96, 0, -15, -12, 5, -29, 55, -10, 12, -17, -30, 0, -9, -12, 0, -45, 24, 27, 6, -1, -74, 40, 13, -36, 18, -16, 32, 0, -17, 46, 36, -18, 35, 5, 18, 20, -87, -4, -78, 3, 0, -22, -22, -2, -28, 0, -8, 3, -30, -12, 60, -10, 3, 0, -126, -8, 78, -31, 38, 9, 0, -30, 0, 4, -1, 18, 0, -3, -51, -23, 23, 30, 7, 2, 45, 28, -22, -9, -21, 0, -99, 16, -12, -16, -36, -10, 5, -9, -9, -39, 3, -9, 0, 60, -9, 16, 0, 3, 58, 9, 3, 18, 2, 11, -10, 0, 9, -8, 12, 2, -86, 18, 4, 0, 68, 3, -49, -4, 0, 48, 27, -35, 6, -6, 24, 42, -89, -1, -72, -24, 0, 0, 22, 30, 16, -6, -30, -12, 44, -8, -66, 48, -10, 24, 0, -14, 46, 0, 14, 15, 72, 16, -2, -12, 0, 18, -82, 0, -36, 30, -28, 23, -22, 3, 0, -44, 48, -12, 6, -42, 0, 15, 6, 49, 80, 10, 78, -3, 9, -10, 60, 0, 12, 0, -14, -33, -18, 4, 3, 28, 26, -7, -18, -32, 40, 13, 0, -31, 0, -9, -36, 24, -9, 24, 12, -24, -69, 17, 15, 0, 8, -4, 9, 30, -2, 0, -102, 6, -30, -16, -6, 9, 0, 6, -2, 14, -4, 3, -15, 8, -34, 24, 0, -24, -81, 0, 28, -30, -14, 27, -32, -24, -20, -3, 26, 1, 65, -3, 0, 0, 32, 8, -8, 17, -36, 0, -40, 6, -6, -12, -74, 0, -3, -40, 29, 30, 0, -14, -18, 8, -4, 6, 39, -20, 0, 3, -81, 3, 53, -24, 17, 50, -23, 0, 26, 8, -34, 0, 18, 9, -21, 4, -6, -18, 18, 26, 42, -30, 12, -30, 0, 12, 4, -36, -36, -22, 26, -1, 80, -9, -5, -45, 38, 0, -49, 10, -2, -17, 24, -7, 93, 8, 8, -10, 30, 12, 0, -4, -25, -47, 72, -2, -48, -19, 0, -3, -30, -8, 140, 0, -15, 18, 27, 1, 31, -61, 51, -8, -12, 29, 54, 0, 0, 27, 3, 6, 0, -1, 44, 53, -36, -20, -18, -8, -9, 0, -75, 2, 0, 0, 2, 4, -18, 5, -84, 24, -55, -12, 0, 10, 0, -27, 11, 11, 51, 0, 12, -9, -9, -41, -40, 0, -36, -40, -40, -27, -13, 3, -5, 48, -58, -45, 0, 6, 0, 50, -28, 2, 36, -42, -51, 26, -10, 18, 60, 16, -12, 0, -47, 0, 80, 20, 30, 6, 9, 3, 26, -1], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, -1, -1, 1, -1, 1, 3, -1, 1, 1, -3, -1, 0, -3, 1, 1, 0, -1, 3, -1, -3, 3, -4, 1, 1, 0, -1, 3, -4, -1, 6, -1, 3, 0, -3, 1, 9, -3, 0, 1, -10, 3, -10, -3, -1, 4, -3, -1, 2, -1, 0, 0, 9, 1, 3, -3, -3, 4, 12, 1, -6, -6, 3, 1, 0, -3, -8, 0, 4, 3, -14, -1, -8, -9, -1, 3, -9, 0, 6, -1, 1, 10, 16, -3, 0, 10, 4, 3, -3, 1, 0, -4, -6, 3, -3, 1, 8, -2, -3, 1, 0, 0, -15, 0, 3, -9, 2, -1, -2, -3, -9, 3, -8, 3, 4, -4, 0, -12, 0, -1, -2, 6, 10, 6, -1, -3, 3, -1, 10, 0, -3, 3, 9, 8, 1, 0, 12, -4, -17, -3, 3, 14, 0, 1, 4, 8, -2, 9, -2, 1, 14, -3, 0, 9, -6, 0, -17, -6, -9, 1, -12, -1, 20, -10, -3, -16, 9, 3, 0, 0, 3, -10, 13, -4, 3, -3, -12, 3, 4, -1, -10, 0, 6, 4, -9, 6, 0, -3, -3, 3, -6, -1, 8, -8, 0, 2, 11, 3, -10, -1, 8, 0, -12, 0, 10, 15, -4, 0, -9, -3, 9, 9, 14, -2, 10, 1, 18, 2, 8, 3, 0, 9, -11, -3, 1, 8, -16, -3, -10, -4, 9, 4, -6, 0, 3, 12, -6, 0, -26, 1, 7, 2, -1, -6, -2, -10, 0, -6, -16, 1, -1, 3, 12, -3, 0, 1, 12, -10, 27, 0, -4, 3, -31, -3, -9, -9, 3, -8, -4, -1, -12, 0, 0, -12, -3, 4, -31, 17, 6, 3, -30, -3, 6, -14, 3, 0, -30, -1, -17, -4, -8, -8, -1, 2, -12, -9, 3, 2, 0, -1, -30, -14, 0, 3, 6, 0, 26, -9, 15, 6, -4, 0, 26, 17, -3, 6, 17, 9, 12, -1, -2, 12, 0, 1, 0, -20, 2, 10, -9, 3, -28, 16, 9, -9, 8, -3, 6, 0, 8, 0, -18, -3, -15, 10, -4, -13, -24, 4, 16, -3, 0, 3, -8, 12, 14, -3, 0, -4, 30, 1, -10, 10, 2, 0, 8, -6, 8, -4, -10, 9, 27, -6, -26, 0, 1, 3, 0, 3, -33, -3, -3, 6, 4, 1, 9, -8, -10, 8, 24, 0, 0, -2, 3, -11, -6, -3, -23, 10, -9, 1, -27, -8, 0, 0, -1, 12, -27, 0, -7, -10, -12, -15, 36, 4, -16, 0, 17, 9, -12, 3, -28, -9, -3, -9, 0, -14, -18, 2, 0, -10, -12, -1, -16, -18, -4, -2, -12, -8, -30, -3, 2, 0, -10, -9, 3, 11, 2, 3, -35, -1, 30, -8, -14, 16, 0, 3, -42, 10, 0, 4, -32, -9, -24, -4, 6, 6, 8, 0, -24, -3, 17, -12, 30, 6, 3, 0, 9, 26, 12, -1, 0, -7, 12, -2, -8, 1, 29, 6, -20, 2, 5, 10, 0, 0, 3, 6, -42, 16, 20, -1, -9, 1, 21, -3, 0, -12, 0, 3, 10, 0, -24, -1, -3, -12, 15, 10, 9, -27, -13, 0, -35, 4, 22, -3, -3, 31, 0, 3, -7, 9, 12, 9, 0, -3, -2, 8, -4, 4, -6, 1, -22, 12, 10, 0, 2, 0, 22, 12, -6, 3, -12, -4, 18, 31, 9, -17, -9, -6, 0, -3, 0, 30, 20, 3, 8, -6, 3, 14, -39, -3, 23, 0, 6, 30, -4, 1, -38, 17, -8, 4, 48, 8, -27, 8, 0, 1, 18, -2, 18, 12, -11, 9, 36, -3, 0, -2, 10, 0, -30, 1, 21, 30, -8, 14, 2, 0, 27, -3, 12, -6, 0, 0, -7, -26, -10, 9, -30, -15, -23, -6, 4, 4, -9, 0, 1, -26, 9, -17, 0, 3, 12, -6, -9, -17, -3, -9, 0, -12, -14, 1, 35, 2, 28, -12, -10, 0, -45, -1, -36, 0, -18, 20, 3, -2, 3, -10, -8, 9, 4, -3, 30, 28, 0, -16, -9, -9, 16, 9, 11, -8, 18, 3, 48, -6, -1, 0, -6, -8, 24, 0, 16, 18, 30, 3, -12, 15, 10, -10, 0, 4, -7, 13, -9, 24, 17, -4, 0, -16, 6, 3, 24, 0, 27, -3, -3, 8, 0, -12, -40, -14, 6, 3, -24, 0, 0, 4, 26, -30, -36, -1, -45, 10, -7, -10, -4, -2, -3, 0, 1, -8, 0, 6, 53, -8, 2, 4, 24, 10, 11, -9, 0, -27, 48, 6, 2, 26, 16, 0, 6, -1, -24, -3, 1, 0, -14, -3, 17, 33, -12, 3, -31, 3, -6, -6, 0, -4, 0, -1, 46, -9, -12, 8, -7, 10, 6, -8, -27, -24, -30, 0, 42, 0, 4, 2, 17, -3, -36, 11, 31, 6, -24, 3, 0, 23, 9, -10, -42, 9, 0, -1, -3, 27, 24, 8, 12, 0, 4, 0, -10, 1, -31, -12, 12, 27, -20, 0, -30, 7, 0, 10, 50, 12, -11, 15, 3, -36, -18, -4, 0, 16, 31, 0, 0, -17, -9, -9, -6, 12, -6, -3, -13, 28, 30, 9, 0, 3, -6, 9, -6, 0, -36, 14, -26, 18, -3, -2, -50, 0, -5, 10, 30, 12, -24, 1, -13, 16, 17, 18, -18, 4, 0, 2, 8, 12, -3, 8, -38, 30, 1, 3, -23, -2, 22, 0, 12, 10, 9, 9, 9, -3, -3, -11, -9, -2, -4, -3, 0, 35, -24, 1, 0, -30, 30, 8, 10, 14, -14, -16, 0, 0, 28, -3, -48, 42, -6, -10, -9, 0, 14, -4, -26, 32, 0, 9, 9, 24, -15, 4, 2, -6, 6, -6, 4, -8, 0, 0, 14, 24, -26, 3, -32, -17, 40, 12, 3, -30, 18, -6, 0, -3, -17, 0, 34, -9, 6, -26, -12, -12, 36, 1, 5, 0, 2, 7, -8, -12, 25, 2, 0, 8, 15, -1, -51, -29, 0, -6, -44, 20, 9, -2, -2, -5, 55, -10, -11, 0, 9, 0, 40, -3, 58, -6, 28, 42, 10, -16, 47, -20, -9, 1, 0, 9, 0, -1, -8, -21, 27, 3, 23, 0, -6, 12, -54, 0, 12, -3, -8, -10, -52, 0, 22, 24, 18, 1, -10, 3, 0, 12, 15, -15, 6, -10, -46, -9, 4, 27, 0, 13, -34, 0, 24, 35, -6, -4, 9, -22, -16, 3, 45, 3, 48, -31, 0, 0, -9, -3, 42, 7, 8, -9, 20, -12, -16, -9, -14, 0, -24, 3, -26, 2, 0, -8, -36, 4, -10, -4, -30, 6, 0, -1, 12, 22, 10, -12, -18, -10, -20, 0, -2, -2, 47, 0, 41, -22, -8, -12, -56, 6, -51, -3, -8, 12, -23, 4, 0, -18, 10, -31, 38, -9, 0, 17, -27, 9, 11, 6, -17, 0, 26, 3, 36, 0, 4, -30, -1, -20, -8, -3, 29, -8, 0, 6, 45, -3, 16, -14, 33, 39, 0, 3, 60, -23, 3, 0, 10, -6, 54, -30, -4, 4, 18, -1, 26, 38, -9, -17, 0, 8, -18, -4, 10, -48, 44, -8, 6, 27, -24, -8, 27, 0, 45, -1, 0, -18, -3, 2, -6, -18, -3, -12, -6, 11, 0, -9, 6, -36, 38, 3, 40, 0, 23, 2, 46, -10, 26, 0, 9, 30, 6, -1, -62, -21, 27, -30, -7, 8, 0, -14, 0, -2, 39, 0, 11, -27, 1, 3, 12, -12, -36, 6, 27, 0, 56, 0, 2, 7, 7, 26, 26, 10, 10, -9, 12, 30, 0, 15, 2, 23, -36, 6, 0, -4, 24, -4, 16, 9, 40, 0, -11, -1, -17, 26, 12, -9, 1, 17, 12, 0, 47, -3, 0, -12, 28, 6, -12, 9, -30, 17, 3, 3, -60, 9, -24, 0, 0, 12, -14, 14, 16, -1, 18, -35, 0, -2, -12, -28, 0, 12, 29, 10, 17, 0, 12, 45, -27, 1, -40, 36, 16, 0, -46, 18, -5, -20, 4, -3, 22, 2, 0, -3, 12, 10, 0, 8, 31, -9, 30, -4, -18, 3, 23, -30, -2, -28, 9, 0, -16, 16, 10, 9, 39, 9, -60, -16, -3, -9, -18, -11, 0, 8, -2, -18, 0, -3, 4, -48, 35, 6, -42, 1, 24, 0, -30, 6, 12, 8, -48, -24, 14, 0, -15, -16, 12, -18, 0, -30, -23, -3, 44, 12, 42, -15, -49, -10, 3, 10, 0, 0, 33, -4, -28, 7, 32, -13, 31, 9, -24, -24, 24, -17, 0, 4, -30, 0, -6, 16, -9, -6, -14, -3, -8, -24, 24, 0, 30, -27, 24, 3, -1, 3, 0, -8, -17, 0, -6, 12, 0, 40, -30, 14, -8, -6, 20, -3, -3, 24, -50, 0, -8, 0, -9, -4, 18, -26, 30, 30, -12, 36, 22, 1, 9, 45, 0, -10, 17, 7, -8, 10, -12, 4, 47, 2, 19, 3, 8, 0, -18, -1, 61, 8, -29, 0, -27, -6, 1, -53, 20, 8, 0, -2, 0, -4, -5, -24, 12, -10, 27, -11, 0, 9, 41, 0, 40, 27, -3, -48, 45, -6, -50, -2, 42, -26, -18, -16, 0, 0, -20, -6, -3, 1, 18, 24, 9, 3, 30, -1, -36, 0, -21, 14, 18, 3, 0, -17, 0, -33, -90, 12, 12, -3, 0, 31, -6, -3, -6, 6, -10, 6, 51, 0, -12, 4, 24, 0, -26, 1, -36, -46, 3, 9, 32, 12, -29, -8, -15, 7, 0, -10, 70, -6, -9, 8, 42, 27, 4, 24, 13, 30, 24, 0, -33, -42, 35, 0, -26, -4, -40, -2, -22, -17, 13, 3, 0, 36, 3, -11, 48, -31, -71, -6, 0, 24, 47, -3, -17, 0, 7, -23, -48, -9, -90, 10, -12, 42, -12, -9, 62, 0, 0, 1, 27, 3, -30, -27, 2, -24, 33, -8, 22, -12, 4, 0, -55, -4, 0, 0, 6, 10, 39, -1, 58, 31, 22, 12, 0, -12, 50, -27, -10, 20, -18, 0, 56, 30, -2, -7, -51, 0, 6, -10, -22, -50, 54, -12, 9, 11, 6, -15, 0, -3, 0, 36, 12, 18, 28, 4, 14, 0, -18, -16, -42, -31, -55, 0, -9, 0, 20, 17, 52, 9, 9, 9, -78, 6, -8, -12, 0, 6, 32, 3, 59, 13, 0, -28, -6, -30, 21, -9, -20, 0, -9, -3, -78, 6, -8, -9, -50, 6, -48, 0, -3, 36, 0, -14, 18, 26, 39, -18, -6, 3, -48, 2, -23, 50, 15, 0, 0, 5, -6, -10, -21, -30, -4, -12, 4, 24, 51, -1, 0, 13, 38, -16, 18, -17, 24, -18, 8, 18, -27, -4, -54, 0, -48, -2, -16, -8, 44, -12, 27, 3, 0, -8, 4, 38, 0, -30, -3, -1, 60, -3, -18, 23, 100, 2, 8, -22, -18, 0, 24, -12, 36, -10, 11, -9, -14, -9, -48, -9, -36, 3, 0, 3, -64, 11, 0, 9, 22, 2, 46, 4, -10, 3, -60, 0, -30, -35, 30, 24, 36, -1, -38, 0, -21, 30, 10, -30, 0, -8, 8, -10, -12, -14, 18, 14, -2, 16, -24, 0, 0, 0, -27, -28, -27, 3, -8, 48, -12, -42, 72, 6, -56, 10, 0, 9, -8, 0, -27, -14, 7, 4, -93, 26, 24, -32, 10, 0, 36, -9, 57, -9, 30, -24, 0, 15, -27, -4, 23, -2, 0, 6, -28, -6, -4, 6, 26, -4, -18, 8, 9, 0, -6, 0, 66, -14, -1, -24, 63, 26, 62, -3, -9, 32, -12, 17, 0, -40, 0, -12, -9, -3, -36, 30, -12, -18, 33, 6, -36, 0, 9, 3, -56, 17, -39, 0, 3, -34, 72, 9, -64, -6, 0, 26, 24, 12, -4, 12, 14, -36, 0, -1, 0, -5, -35, 0, -9, -2, 30, -7, -28, 8, 5, 12, 14, -25, 10, -2, 0, 0, -93, -8, 45, -15, 32, 1, -24, 51, 36, 29, 18, 0, -42, 6, 18, 44, 0, -20, -45, -9, -3, 2, 81, 2, 0, 5, -3, -55, -90, 10, -12, 11, 8, 0, -61, -9, 6, 0, -4, -40, 36, 3, 18, -58, -30, 6, 23, -28, -60, -42, 0, -10, 30, 16, -44, -47, 9, 20, -78, 9, 52, -1, -16, 0, -54, -9, 27, 0, -11, 1, -20, 8, -4, 21, -18, -27, 0, -3, 22, -23, -48, 0, 30, 6, -51, -12, 1, 54, 24, 0, -70, -12, 6, 3, 6, 8, 27, 10, -24, 52, -32, 0, 0, -22, -16, -24, 7, -18, 12, -1, -30, 10, -3, -3, -41, 0, 12, -12, 0, -15, 56, 15, -10, -6, -1, 10, -36, 46, 0, 9, -30, -4, -6, -27, 7, 0, 16, -13, -48, 34, 9, 0, 9, -24, -32, -35, -17, 6, 29, 4, -67, -9, 0, 22, 0, 16, 12, -3, -6, -45, 8, -3, 18, -48, -24, 31, 28, 0, -20, 0, -27, 9, -38, 3, 62, -42, 3, -7, 32, -8, 0, 9, 0, -20, -24, 12, 0, 16, 40, 9, 18, 14, 12, 0, -6, 24, 18, -3, 12, 26, 24, -2, -48, 0, 0, 8, 0, 36, -24, -4, 78, 10, -26, 4, -62, 30, 12, -6, 36, 0, 0, 1, -82, -12, 45, -22, 16, -10, -33, 12, 7, 18, 0, 10, -90, 20, 4, 0, -12, 2, 52, 2, 3, -47, 108, 0, 12, -41, -1, 22, 30, 8, 78, 12, 0, 56, 30, -6, 0, 51, -53, 3, -84, 8, 50, -12, -2, 23, -23, -4, -38, 0, -24, 18, -6, -10, 10, 31, -11, -38, 51, 9, 12, 0, 0, -17, -3, 27, 0, -9, -48, -11, -32, -6, 36, 17, -2, 0, -53, -26, -32, -3, -16, -36, -92, 0, 35, -4, -6, 30, 0, 1, 60, 20, 24, 8, -30, 3, -54, -29, -1, 8, 0, 0, -48, -6, 14, -45, 20, 3, 0, -16, -17, 14, 36, -33, 0, -39, 12, 0, -90, -3, -59, -60, 31, 23, 42, -3, -49, 0, 6, -10, -24, 6, 39, -54, 0, 30, -40, 4, -6, -4, 0, -18, -6, 1, 32, -26, -46, -38, -78, 9, 16, 17, 12, 0, 24, -8, -84, 18, 7, 4, -27, -10, 0, 48, -6, -44, 0, 8, 0, -6, 27, -27, 81, 24, -8, 8, 30, -27, 3, 0, 36, -45, -42, 1, 24, 0, 6, 18, -4, 3, -2, -2, 0, 6, -17, 18, -5, 3, 18, 12, 36, 6, 0, -11, -30, 0, -31, 9, 60, -6, 49, 36, 24, -38, -3, -3, -28, -40, 0, 0, 58, -23, -43, -2, -9, -46, -54, 10, -24, -26, 42, 0, 14, -9, -12, -30, 0, -6, 52, 1, -59, 62, 3, 21, 0, -27, -64, 30, -24, 7, -25, -8, 9, 0, -12, 14, -12, 0, -120, 2, -4, -39, 51, 0, 8, -11, 10, 27, -72, -1, 0, -3, 31, -12, -29, 12, -57, 36, -12, -6, 75, -27, 48, 0, 20, -56, 72, 0, 36, -2, 30, -7, 33, -7, -5, -26, 0, -26, 27, -10, -8, -10, -50, 9, 0, -12, -90, -30, 11, 0, -24, -15, 36, -2, -3, -23, -2, 36, -72, -6, 18, 0, 0, 4, 42, -24, 0, 4, -9, -16, -27, -9, -31, -40, -20, 0, 48, 11, 0, 1, 60, 17, -83, -26, 9, -12, 8, 9, 0, -1, 6, -17, 90, -12, -21, 0, 6, -47, 30, 3, 58, 0, 13, 12, 0, -28, -30, -6, -30, 12, -44, -9, 0, 30, 0, -17, -120, -3, 47, -3, 6, 60, 24, -9, -10, 24, 6, 0, 92, 0, 4, -12, 36, 14, 24, -14, 78, -16, 26, 1, 0, -18, 18, 35, 3, 0, 0, 2, 24, 12, 50, 28, 96, 0, -15, -12, 5, -29, 55, -10, 12, -17, -30, 0, -9, -12, 0, -45, 24, 27, 6, -1, -74, 40, 13, -36, 18, -16, 32, 0, -17, 46, 36, -18, 35, 5, 18, 20, -87, -4, -78, 3, 0, -22, -22, -2, -28, 0, -8, 3, -30, -12, 60, -10, 3, 0, -126, -8, 78, -31, 38, 9, 0, -30, 0, 4, -1, 18, 0, -3, -51, -23, 23, 30, 7, 2, 45, 28, -22, -9, -21, 0, -99, 16, -12, -16, -36, -10, 5, -9, -9, -39, 3, -9, 0, 60, -9, 16, 0, 3, 58, 9, 3, 18, 2, 11, -10, 0, 9, -8, 12, 2, -86, 18, 4, 0, 68, 3, -49, -4, 0, 48, 27, -35, 6, -6, 24, 42, -89, -1, -72, -24, 0, 0, 22, 30, 16, -6, -30, -12, 44, -8, -66, 48, -10, 24, 0, -14, 46, 0, 14, 15, 72, 16, -2, -12, 0, 18, -82, 0, -36, 30, -28, 23, -22, 3, 0, -44, 48, -12, 6, -42, 0, 15, 6, 49, 80, 10, 78, -3, 9, -10, 60, 0, 12, 0, -14, -33, -18, 4, 3, 28, 26, -7, -18, -32, 40, 13, 0, -31, 0, -9, -36, 24, -9, 24, 12, -24, -69, 17, 15, 0, 8, -4, 9, 30, -2, 0, -102, 6, -30, -16, -6, 9, 0, 6, -2, 14, -4, 3, -15, 8, -34, 24, 0, -24, -81, 0, 28, -30, -14, 27, -32, -24, -20, -3, 26, 1, 65, -3, 0, 0, 32, 8, -8, 17, -36, 0, -40, 6, -6, -12, -74, 0, -3, -40, 29, 30, 0, -14, -18, 8, -4, 6, 39, -20, 0, 3, -81, 3, 53, -24, 17, 50, -23, 0, 26, 8, -34, 0, 18, 9, -21, 4, -6, -18, 18, 26, 42, -30, 12, -30, 0, 12, 4, -36, -36, -22, 26, -1, 80, -9, -5, -45, 38, 0, -49, 10, -2, -17, 24, -7, 93, 8, 8, -10, 30, 12, 0, -4, -25, -47, 72, -2, -48, -19, 0, -3, -30, -8, 140, 0, -15, 18, 27, 1, 31, -61, 51, -8, -12, 29, 54, 0, 0, 27, 3, 6, 0, -1, 44, 53, -36, -20, -18, -8, -9, 0, -75, 2, 0, 0, 2, 4, -18, 5, -84, 24, -55, -12, 0, 10, 0, -27, 11, 11, 51, 0, 12, -9, -9, -41, -40, 0, -36, -40, -40, -27, -13, 3, -5, 48, -58, -45, 0, 6, 0, 50, -28, 2, 36, -42, -51, 26, -10, 18, 60, 16, -12, 0, -47, 0, 80, 20, 30, 6, 9, 3, 26, -1]}