# Stored data for newform 3240.2.a.e, downloaded from the LMFDB on 10 September 2024.
{"Nk2": 12960, "analytic_conductor": 25.871530254894843, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [5, -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": [3240, 1, [2431, 1621, 3161, 1297], [1, 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, [0, 1]], [11, [1, 1]], [17, [0, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014398543039656, "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": true, "label": "3240.2.a.e", "level": 3240, "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], "level_radical": 30, "minimal_twist": "3240.2.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{5}-q^{11}-7q^{19}-6q^{23}+q^{25}+\\cdots", "related_objects": ["EllipticCurve/Q/3240/e"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "3240.2.a", "trace_display": [0, 0, 1, 0], "trace_hash": 1820567797926714546, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.962", "prec": 17}, {"__RealLiteral__": 0, "data": "0.031", "prec": 17}, {"__RealLiteral__": 0, "data": "4.819", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.032", "prec": 17}, "traces": [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -6, 0, 1, 0, 0, 0, 7, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -9, 0, -6, 0, 0, 0, 2, 0, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, -10, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -7, 0, 2, 0, 0, 0, 9, 0, -6, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -10, 0, 0, 0, 1, 0, -20, 0, 0, 0, -11, 0, 0, 0, 0, 0, 20, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0, -10, 0, -11, 0, 0, 0, 1, 0, -18, 0, 0, 0, 0, 0, -20, 0, 0, 0, -20, 0, -13, 0, 0, 0, 14, 0, 0, 0, 0, 0, -3, 0, 11, 0, 0, 0, -2, 0, 0, 0, 0, 0, -9, 0, -14, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 7, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 20, 0, -10, 0, 0, 0, 14, 0, 2, 0, 0, 0, 0, 0, -11, 0, 0, 0, -7, 0, 0, 0, 0, 0, -20, 0, 6, 0, 0, 0, 22, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 22, 0, 0, 0, -10, 0, 26, 0, 0, 0, 0, 0, -17, 0, 0, 0, -14, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -22, 0, 0, 0, -31, 0, -20, 0, 0, 0, -22, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, -2, 0, 20, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 14, 0, -1, 0, 0, 0, 3, 0, 30, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -10, 0, 0, 0, 0, 0, 6, 0, 0, 0, 24, 0, -31, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 6, 0, 0, 0, 42, 0, 37, 0, 0, 0, -34, 0, 7, 0, 0, 0, 33, 0, 9, 0, 0, 0, 0, 0, 38, 0, 0, 0, -19, 0, 14, 0, 0, 0, 20, 0, 0, 0, 0, 0, 6, 0, -7, 0, 0, 0, -17, 0, 0, 0, 0, 0, 2, 0, -20, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, -40, 0, 9, 0, 0, 0, 10, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, -30, 0, 20, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 39, 0, 0, 0, 3, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -3, 0, 39, 0, 0, 0, -6, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, 0, 17, 0, -19, 0, 0, 0, -10, 0, -38, 0, 0, 0, 0, 0, -20, 0, 0, 0, 20, 0, 20, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 41, 0, 0, 0, -20, 0, 0, 0, 0, 0, -21, 0, -14, 0, 0, 0, 18, 0, 3, 0, 0, 0, 20, 0, -11, 0, 0, 0, -20, 0, 21, 0, 0, 0, 0, 0, -42, 0, 0, 0, 10, 0, 46, 0, 0, 0, 2, 0, 0, 0, 0, 0, 40, 0, 20, 0, 0, 0, 0, 0, -20, 0, 0, 0, 7, 0, 0, 0, 0, 0, -9, 0, 14, 0, 0, 0, 0, 0, -10, 0, 0, 0, -6, 0, 0, 0, 0, 0, -27, 0, 0, 0, 0, 0, 7, 0, 40, 0, 0, 0, 0, 0, 46, 0, 0, 0, 2, 0, 47, 0, 0, 0, 20, 0, -10, 0, 0, 0, 0, 0, -40, 0, 0, 0, -11, 0, -20, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 1, 0, 0, 0, 63, 0, 1, 0, 0, 0, -18, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, 41, 0, 0, 0, -20, 0, 42, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -20, 0, 0, 0, -53, 0, 20, 0, 0, 0, -13, 0, 0, 0, 0, 0, 12, 0, 20, 0, 0, 0, -40, 0, 13, 0, 0, 0, 20, 0, 14, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, -1, 0, -20, 0, 0, 0, 18, 0, 0, 0, 0, 0, -14, 0, -3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 11, 0, -2, 0, 0, 0, -39, 0, -6, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -2, 0, 0, 0, 33, 0, 49, 0, 0, 0, 0, 0, -18, 0, 0, 0, -50, 0, 54, 0, 0, 0, 18, 0, 0, 0, 0, 0, -20, 0, -9, 0, 0, 0, 0, 0, -30, 0, 0, 0, -14, 0, -60, 0, 0, 0, -9, 0, 0, 0, 0, 0, 40, 0, -7, 0, 0, 0, 20, 0, 20, 0, 0, 0, 36, 0, 1, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, -29, 0, 0, 0, -9, 0, 0, 0, 0, 0, -9, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -37, 0, -20, 0, 0, 0, 9, 0, 0, 0, 0, 0, -11, 0, 20, 0, 0, 0, -2, 0, -17, 0, 0, 0, -14, 0, -6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -22, 0, 0, 0, 8, 0, -20, 0, 0, 0, 18, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 3, 0, -9, 0, 0, 0, 20, 0, 22, 0, 0, 0, 21, 0, -40, 0, 0, 0, 42, 0, -13, 0, 0, 0, 6, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, -52, 0, -26, 0, 0, 0, 0, 0, 70, 0, 0, 0, 6, 0, 14, 0, 0, 0, 0, 0, 60, 0, 0, 0, 2, 0, -2, 0, 0, 0, -41, 0, 0, 0, 0, 0, 42, 0, -63, 0, 0, 0, -20, 0, 0, 0, 0, 0, -3, 0, 41, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, -40, 0, 0, 0, 0, 0, -60, 0, -7, 0, 0, 0, -53, 0, -49, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 33, 0, 0, 0, 0, 0, -20, 0, 0, 0, 60, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -9, 0, 14, 0, 0, 0, -40, 0, 37, 0, 0, 0, 60, 0, 22, 0, 0, 0, 30, 0, -20, 0, 0, 0, 0, 0, -62, 0, 0, 0, -9, 0, 20, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 63, 0, -39, 0, 0, 0, 0, 0, -58, 0, 0, 0, 21, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 29, 0, 14, 0, 0, 0, 18, 0, -33, 0, 0, 0, -66, 0, -1, 0, 0, 0, 0, 0, -31, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -53, 0, 0, 0, 60, 0, -10, 0, 0, 0, -17, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -49, 0, 40, 0, 0, 0, -40, 0, 3, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, -17, 0, -38, 0, 0, 0, 60, 0, -40, 0, 0, 0, 2, 0, 23, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -40, 0, 0, 0, -3, 0, 0, 0, 0, 0, -50, 0, -40, 0, 0, 0, 42, 0, 23, 0, 0, 0, 20, 0, 0, 0, 0, 0, 20, 0, -28, 0, 0, 0, 0, 0, -20, 0, 0, 0, 61, 0, 0, 0, 0, 0, 18, 0, -7, 0, 0, 0, -40, 0, -10, 0, 0, 0, -7, 0, -32, 0, 0, 0, -22, 0, 0, 0, 0, 0, 12, 0, -34, 0, 0, 0, 0, 0, -10, 0, 0, 0, -40, 0, -31, 0, 0, 0, 33, 0, 0, 0, 0, 0, -20, 0, -38, 0, 0, 0, -60, 0, 0, 0, 0, 0, -42, 0, 13, 0, 0, 0, -34, 0, -22, 0, 0, 0, 0, 0, 12, 0, 0, 0, -7, 0, 18, 0, 0, 0, 21, 0, 0, 0, 0, 0, -78, 0, -53, 0, 0, 0, 14, 0, 0, 0, 0, 0, -24, 0, -49, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 6, 0, 0, 0, 40, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 40, 0, 0, 0, 11, 0, 46, 0, 0, 0, 78, 0, -23, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 40, 0, 0, 0, 20, 0, 0, 0, 0, 0, -49, 0, -60, 0, 0, 0, 18, 0, -17, 0, 0, 0, 0, 0, -1, 0, 0, 0, -30, 0, -21, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39, 0, 20, 0, 0, 0, 18, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -4, 0, 39, 0, 0, 0, 17, 0, -20, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 7, 0, 0, 0, 54, 0, 14, 0, 0, 0, -70, 0, 0, 0, 0, 0, -1, 0, -38, 0, 0, 0, 0, 0, 14, 0, 0, 0, -18, 0, -67, 0, 0, 0, 20, 0, 3, 0, 0, 0, 0, 0, 10, 0, 0, 0, 30, 0, 0, 0, 0, 0, 60, 0, 14, 0, 0, 0, -24, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, -40, 0, 0, 0, 22, 0, 20, 0, 0, 0, 0, 0, -14, 0, 0, 0, -42, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 38, 0, 0, 0, -20, 0, -20, 0, 0, 0, 79, 0, -54, 0, 0, 0, -18, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, -10, 0, 0, 0, -20, 0, 0, 0, 0, 0, 11, 0, -14, 0, 0, 0, -20, 0, -36, 0, 0, 0, -60, 0, 0, 0, 0, 0, -63, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 51, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 30, 0, 0, 0, -63, 0, -11, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 60, 0, 4, 0, 0, 0, -27, 0, 0, 0, 0, 0, 2, 0, -62, 0, 0, 0, -11, 0, -14, 0, 0, 0, -60, 0, 27, 0, 0, 0, 6, 0, -2, 0, 0, 0, 63, 0, 1, 0, 0, 0, 0, 0, -20, 0, 0, 0, -12, 0, 0, 0, 0, 0, 20, 0, -7, 0, 0, 0, -14, 0, 2, 0, 0, 0, -87, 0, 0, 0, 0, 0, -10, 0, -42, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -7, 0, 0, 0, 54, 0, 0, 0, 0, 0, 67, 0, -21, 0, 0, 0, 6, 0, -2, 0, 0, 0, 61, 0, -26, 0, 0, 0, 20, 0, 33, 0, 0, 0, 0, 0, 24, 0, 0, 0, 3, 0, 9, 0, 0, 0, -31, 0, 42, 0, 0, 0, -1, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -23, 0, 60, 0, 0, 0, 0, 0, 60, 0, 0, 0, 31, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, -19, 0, 0, 0, 0, 0, -71, 0, 0, 0, 6, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -43, 0, 0, 0, 6, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, -1, 0, -14, 0, 0, 0, -40, 0, -43, 0, 0, 0, -6, 0, -34, 0, 0, 0, 0, 0, -19, 0, 0, 0, 7, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 18, 0, 23, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 19, 0, 0, 0, 9, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 47, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, -51, 0, 0, 0, 38, 0, 0, 0, 0, 0, 28, 0, 14, 0, 0, 0, -62, 0, 70, 0, 0, 0, -14, 0, -19, 0, 0, 0, 33, 0, 12, 0, 0, 0, 14, 0, 0, 0, 0, 0, -9, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 20, 0, 0, 0, 20, 0, -31, 0, 0, 0, 0, 0, -18, 0, 0, 0, -39, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 36, 0, 51, 0, 0, 0, -7, 0, 80, 0, 0, 0, 10, 0, 14, 0, 0, 0, 0, 0, -23, 0, 0, 0, -46, 0, -17, 0, 0, 0, 93, 0, 49, 0, 0, 0, 0, 0, 42, 0, 0, 0, -39, 0, 140, 0, 0, 0, 38, 0, 27, 0, 0, 0, 40, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, -20, 0, 0, 0, 21, 0, 0, 0, 0, 0, -60, 0, 4, 0, 0, 0, -20, 0, 9, 0, 0, 0, -83, 0, -12, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, -60, 0, 0, 0, -80, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 37, 0, -20, 0, 0, 0, 90, 0, 46, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 10, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 18, 0, 20, 0, 0, 0, -34, 0, 10, 0, 0, 0, 53, 0, -11, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 3, 0, 49, 0, 0, 0, -2, 0, 0, 0, 0, 0, 51, 0, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, -30, 0, 0, 0, 57, 0, 0, 0, 0, 0, 20, 0, -100, 0, 0, 0, 70, 0, 60, 0, 0, 0, 2, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, 13, 0, 2, 0, 0, 0, 11, 0, 0, 0, 0, 0, 82, 0, 23, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 2, 0, -58, 0, 0, 0, 0, 0, -40, 0, 0, 0, -38, 0, -10, 0, 0, 0, -20, 0, 7, 0, 0, 0, -100, 0, 0, 0, 0, 0, 39, 0, -2, 0, 0, 0, -79, 0, 34, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 3, 0, 0, 0, -90, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 18, 0, 7, 0, 0, 0, 80, 0, -49, 0, 0, 0, 7, 0, 20, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, -6, 0, 0, 0, -60, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -87, 0, -40, 0, 0, 0, 0, 0, -20, 0, 0, 0, -30, 0, -34, 0, 0, 0, 0, 0, -53, 0, 0, 0, 14, 0, 34, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 70, 0, 40, 0, 0, 0, -62, 0, 0, 0, 0, 0, 20, 0, -3, 0, 0, 0, 0, 0, 79, 0, 0, 0, 39, 0, 60, 0, 0, 0, -10, 0, 0, 0, 0, 0, -20, 0, 77, 0, 0, 0, 0, 0, -6, 0, 0, 0, 3, 0, 12, 0, 0, 0, 20, 0, -38, 0, 0, 0, 21, 0, 6, 0, 0, 0, -20, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -50, 0, 9, 0, 0, 0, 0, 0, 78, 0, 0, 0, 120, 0, -8, 0, 0, 0, -80, 0, 63, 0, 0, 0, 0, 0, 38, 0, 0, 0, 63, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 18, 0, 3, 0, 0, 0, -86, 0, 6, 0, 0, 0, -26, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, -42, 0, 70, 0, 0, 0, 0, 0, 17, 0, 0, 0, -40, 0], "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, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, -6, 0, 1, 0, 0, 0, 7, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -9, 0, -6, 0, 0, 0, 2, 0, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, -10, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -7, 0, 2, 0, 0, 0, 9, 0, -6, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -10, 0, 0, 0, 1, 0, -20, 0, 0, 0, -11, 0, 0, 0, 0, 0, 20, 0, 7, 0, 0, 0, 0, 0, 7, 0, 0, 0, -10, 0, -11, 0, 0, 0, 1, 0, -18, 0, 0, 0, 0, 0, -20, 0, 0, 0, -20, 0, -13, 0, 0, 0, 14, 0, 0, 0, 0, 0, -3, 0, 11, 0, 0, 0, -2, 0, 0, 0, 0, 0, -9, 0, -14, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 7, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 20, 0, -10, 0, 0, 0, 14, 0, 2, 0, 0, 0, 0, 0, -11, 0, 0, 0, -7, 0, 0, 0, 0, 0, -20, 0, 6, 0, 0, 0, 22, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 22, 0, 0, 0, -10, 0, 26, 0, 0, 0, 0, 0, -17, 0, 0, 0, -14, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -22, 0, 0, 0, -31, 0, -20, 0, 0, 0, -22, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 0, 0, -2, 0, 20, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 14, 0, -1, 0, 0, 0, 3, 0, 30, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -10, 0, 0, 0, 0, 0, 6, 0, 0, 0, 24, 0, -31, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 0, 6, 0, 0, 0, 42, 0, 37, 0, 0, 0, -34, 0, 7, 0, 0, 0, 33, 0, 9, 0, 0, 0, 0, 0, 38, 0, 0, 0, -19, 0, 14, 0, 0, 0, 20, 0, 0, 0, 0, 0, 6, 0, -7, 0, 0, 0, -17, 0, 0, 0, 0, 0, 2, 0, -20, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, -40, 0, 9, 0, 0, 0, 10, 0, 0, 0, 0, 0, -6, 0, -2, 0, 0, 0, -30, 0, 20, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 2, 0, 0, 0, 7, 0, 39, 0, 0, 0, 3, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -3, 0, 39, 0, 0, 0, -6, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, 0, 17, 0, -19, 0, 0, 0, -10, 0, -38, 0, 0, 0, 0, 0, -20, 0, 0, 0, 20, 0, 20, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 41, 0, 0, 0, -20, 0, 0, 0, 0, 0, -21, 0, -14, 0, 0, 0, 18, 0, 3, 0, 0, 0, 20, 0, -11, 0, 0, 0, -20, 0, 21, 0, 0, 0, 0, 0, -42, 0, 0, 0, 10, 0, 46, 0, 0, 0, 2, 0, 0, 0, 0, 0, 40, 0, 20, 0, 0, 0, 0, 0, -20, 0, 0, 0, 7, 0, 0, 0, 0, 0, -9, 0, 14, 0, 0, 0, 0, 0, -10, 0, 0, 0, -6, 0, 0, 0, 0, 0, -27, 0, 0, 0, 0, 0, 7, 0, 40, 0, 0, 0, 0, 0, 46, 0, 0, 0, 2, 0, 47, 0, 0, 0, 20, 0, -10, 0, 0, 0, 0, 0, -40, 0, 0, 0, -11, 0, -20, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 1, 0, 0, 0, 63, 0, 1, 0, 0, 0, -18, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, 41, 0, 0, 0, -20, 0, 42, 0, 0, 0, -1, 0, -6, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -20, 0, 0, 0, -53, 0, 20, 0, 0, 0, -13, 0, 0, 0, 0, 0, 12, 0, 20, 0, 0, 0, -40, 0, 13, 0, 0, 0, 20, 0, 14, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, -1, 0, -20, 0, 0, 0, 18, 0, 0, 0, 0, 0, -14, 0, -3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 11, 0, -2, 0, 0, 0, -39, 0, -6, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -2, 0, 0, 0, 33, 0, 49, 0, 0, 0, 0, 0, -18, 0, 0, 0, -50, 0, 54, 0, 0, 0, 18, 0, 0, 0, 0, 0, -20, 0, -9, 0, 0, 0, 0, 0, -30, 0, 0, 0, -14, 0, -60, 0, 0, 0, -9, 0, 0, 0, 0, 0, 40, 0, -7, 0, 0, 0, 20, 0, 20, 0, 0, 0, 36, 0, 1, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, -29, 0, 0, 0, -9, 0, 0, 0, 0, 0, -9, 0, -46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -37, 0, -20, 0, 0, 0, 9, 0, 0, 0, 0, 0, -11, 0, 20, 0, 0, 0, -2, 0, -17, 0, 0, 0, -14, 0, -6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -22, 0, 0, 0, 8, 0, -20, 0, 0, 0, 18, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 3, 0, -9, 0, 0, 0, 20, 0, 22, 0, 0, 0, 21, 0, -40, 0, 0, 0, 42, 0, -13, 0, 0, 0, 6, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, -52, 0, -26, 0, 0, 0, 0, 0, 70, 0, 0, 0, 6, 0, 14, 0, 0, 0, 0, 0, 60, 0, 0, 0, 2, 0, -2, 0, 0, 0, -41, 0, 0, 0, 0, 0, 42, 0, -63, 0, 0, 0, -20, 0, 0, 0, 0, 0, -3, 0, 41, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, -40, 0, 0, 0, 0, 0, -60, 0, -7, 0, 0, 0, -53, 0, -49, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -42, 0, 33, 0, 0, 0, 0, 0, -20, 0, 0, 0, 60, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -9, 0, 14, 0, 0, 0, -40, 0, 37, 0, 0, 0, 60, 0, 22, 0, 0, 0, 30, 0, -20, 0, 0, 0, 0, 0, -62, 0, 0, 0, -9, 0, 20, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 63, 0, -39, 0, 0, 0, 0, 0, -58, 0, 0, 0, 21, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 29, 0, 14, 0, 0, 0, 18, 0, -33, 0, 0, 0, -66, 0, -1, 0, 0, 0, 0, 0, -31, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -53, 0, 0, 0, 60, 0, -10, 0, 0, 0, -17, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -49, 0, 40, 0, 0, 0, -40, 0, 3, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, -17, 0, -38, 0, 0, 0, 60, 0, -40, 0, 0, 0, 2, 0, 23, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -40, 0, 0, 0, -3, 0, 0, 0, 0, 0, -50, 0, -40, 0, 0, 0, 42, 0, 23, 0, 0, 0, 20, 0, 0, 0, 0, 0, 20, 0, -28, 0, 0, 0, 0, 0, -20, 0, 0, 0, 61, 0, 0, 0, 0, 0, 18, 0, -7, 0, 0, 0, -40, 0, -10, 0, 0, 0, -7, 0, -32, 0, 0, 0, -22, 0, 0, 0, 0, 0, 12, 0, -34, 0, 0, 0, 0, 0, -10, 0, 0, 0, -40, 0, -31, 0, 0, 0, 33, 0, 0, 0, 0, 0, -20, 0, -38, 0, 0, 0, -60, 0, 0, 0, 0, 0, -42, 0, 13, 0, 0, 0, -34, 0, -22, 0, 0, 0, 0, 0, 12, 0, 0, 0, -7, 0, 18, 0, 0, 0, 21, 0, 0, 0, 0, 0, -78, 0, -53, 0, 0, 0, 14, 0, 0, 0, 0, 0, -24, 0, -49, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 6, 0, 0, 0, 40, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 0, 40, 0, 0, 0, 11, 0, 46, 0, 0, 0, 78, 0, -23, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 40, 0, 0, 0, 20, 0, 0, 0, 0, 0, -49, 0, -60, 0, 0, 0, 18, 0, -17, 0, 0, 0, 0, 0, -1, 0, 0, 0, -30, 0, -21, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39, 0, 20, 0, 0, 0, 18, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -4, 0, 39, 0, 0, 0, 17, 0, -20, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 7, 0, 0, 0, 54, 0, 14, 0, 0, 0, -70, 0, 0, 0, 0, 0, -1, 0, -38, 0, 0, 0, 0, 0, 14, 0, 0, 0, -18, 0, -67, 0, 0, 0, 20, 0, 3, 0, 0, 0, 0, 0, 10, 0, 0, 0, 30, 0, 0, 0, 0, 0, 60, 0, 14, 0, 0, 0, -24, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, -40, 0, 0, 0, 22, 0, 20, 0, 0, 0, 0, 0, -14, 0, 0, 0, -42, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 38, 0, 0, 0, -20, 0, -20, 0, 0, 0, 79, 0, -54, 0, 0, 0, -18, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, -10, 0, 0, 0, -20, 0, 0, 0, 0, 0, 11, 0, -14, 0, 0, 0, -20, 0, -36, 0, 0, 0, -60, 0, 0, 0, 0, 0, -63, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 51, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 30, 0, 0, 0, -63, 0, -11, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 60, 0, 4, 0, 0, 0, -27, 0, 0, 0, 0, 0, 2, 0, -62, 0, 0, 0, -11, 0, -14, 0, 0, 0, -60, 0, 27, 0, 0, 0, 6, 0, -2, 0, 0, 0, 63, 0, 1, 0, 0, 0, 0, 0, -20, 0, 0, 0, -12, 0, 0, 0, 0, 0, 20, 0, -7, 0, 0, 0, -14, 0, 2, 0, 0, 0, -87, 0, 0, 0, 0, 0, -10, 0, -42, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -7, 0, 0, 0, 54, 0, 0, 0, 0, 0, 67, 0, -21, 0, 0, 0, 6, 0, -2, 0, 0, 0, 61, 0, -26, 0, 0, 0, 20, 0, 33, 0, 0, 0, 0, 0, 24, 0, 0, 0, 3, 0, 9, 0, 0, 0, -31, 0, 42, 0, 0, 0, -1, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, -23, 0, 60, 0, 0, 0, 0, 0, 60, 0, 0, 0, 31, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, -19, 0, 0, 0, 0, 0, -71, 0, 0, 0, 6, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -43, 0, 0, 0, 6, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, -1, 0, -14, 0, 0, 0, -40, 0, -43, 0, 0, 0, -6, 0, -34, 0, 0, 0, 0, 0, -19, 0, 0, 0, 7, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 18, 0, 23, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 19, 0, 0, 0, 9, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 47, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, -51, 0, 0, 0, 38, 0, 0, 0, 0, 0, 28, 0, 14, 0, 0, 0, -62, 0, 70, 0, 0, 0, -14, 0, -19, 0, 0, 0, 33, 0, 12, 0, 0, 0, 14, 0, 0, 0, 0, 0, -9, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 20, 0, 0, 0, 20, 0, -31, 0, 0, 0, 0, 0, -18, 0, 0, 0, -39, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 36, 0, 51, 0, 0, 0, -7, 0, 80, 0, 0, 0, 10, 0, 14, 0, 0, 0, 0, 0, -23, 0, 0, 0, -46, 0, -17, 0, 0, 0, 93, 0, 49, 0, 0, 0, 0, 0, 42, 0, 0, 0, -39, 0, 140, 0, 0, 0, 38, 0, 27, 0, 0, 0, 40, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, -20, 0, 0, 0, 21, 0, 0, 0, 0, 0, -60, 0, 4, 0, 0, 0, -20, 0, 9, 0, 0, 0, -83, 0, -12, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, -60, 0, 0, 0, -80, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 37, 0, -20, 0, 0, 0, 90, 0, 46, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 10, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 18, 0, 20, 0, 0, 0, -34, 0, 10, 0, 0, 0, 53, 0, -11, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 3, 0, 49, 0, 0, 0, -2, 0, 0, 0, 0, 0, 51, 0, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, -30, 0, 0, 0, 57, 0, 0, 0, 0, 0, 20, 0, -100, 0, 0, 0, 70, 0, 60, 0, 0, 0, 2, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, -49, 0, 0, 0, 13, 0, 2, 0, 0, 0, 11, 0, 0, 0, 0, 0, 82, 0, 23, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 2, 0, -58, 0, 0, 0, 0, 0, -40, 0, 0, 0, -38, 0, -10, 0, 0, 0, -20, 0, 7, 0, 0, 0, -100, 0, 0, 0, 0, 0, 39, 0, -2, 0, 0, 0, -79, 0, 34, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 3, 0, 0, 0, -90, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 18, 0, 7, 0, 0, 0, 80, 0, -49, 0, 0, 0, 7, 0, 20, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, -6, 0, 0, 0, -60, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -87, 0, -40, 0, 0, 0, 0, 0, -20, 0, 0, 0, -30, 0, -34, 0, 0, 0, 0, 0, -53, 0, 0, 0, 14, 0, 34, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 70, 0, 40, 0, 0, 0, -62, 0, 0, 0, 0, 0, 20, 0, -3, 0, 0, 0, 0, 0, 79, 0, 0, 0, 39, 0, 60, 0, 0, 0, -10, 0, 0, 0, 0, 0, -20, 0, 77, 0, 0, 0, 0, 0, -6, 0, 0, 0, 3, 0, 12, 0, 0, 0, 20, 0, -38, 0, 0, 0, 21, 0, 6, 0, 0, 0, -20, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -50, 0, 9, 0, 0, 0, 0, 0, 78, 0, 0, 0, 120, 0, -8, 0, 0, 0, -80, 0, 63, 0, 0, 0, 0, 0, 38, 0, 0, 0, 63, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 18, 0, 3, 0, 0, 0, -86, 0, 6, 0, 0, 0, -26, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, -42, 0, 70, 0, 0, 0, 0, 0, 17, 0, 0, 0, -40, 0]}