# Stored data for newform 4225.2.a.t, downloaded from the LMFDB on 16 June 2025.
{"Nk2": 16900, "analytic_conductor": 33.736794853990965, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[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": [4225, 1, [677, 3551], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 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": [[2, [-3, 1, 1]], [3, [1, 1]], [7, [1, 1]], [11, [-9, -4, 1]]], "hecke_orbit": 20, "hecke_orbit_code": 85568392953598081, "hecke_ring_generator_nbound": 2, "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": "4225.2.a.t", "level": 4225, "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": [5, 13], "level_radical": 65, "minimal_twist": "65.2.e.b", "nf_label": "2.2.13.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta q^{2}-q^{3}+(1+\\beta )q^{4}+\\beta q^{6}-q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "4225.2.a", "trace_display": [-1, -2, 0, -2], "trace_hash": 1906174346800000204, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.954", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.309", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.497", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 2, -1, -2, 3, 0, 1, -2, -6, -4, 0, 4, -3, 0, 1, 0, -3, -8, 2, 4, 0, 2, 11, 6, 6, 0, 0, 10, -3, 2, 0, 8, 7, -4, 17, 0, -6, 0, -15, 0, 0, -6, -1, 6, -7, 0, -3, 4, 3, -12, 0, 8, 0, -8, -5, 0, 6, -4, 25, 0, 0, -2, -4, 4, -4, 0, -11, -14, -25, -6, 0, 12, 12, -16, -13, 0, 19, -4, 0, -4, 0, 2, 3, -4, 3, 0, -29, -2, -12, -2, 0, 0, 9, -8, -28, 0, -7, -24, 6, -8, 0, -18, -17, 8, 0, 0, -22, 2, 15, 24, 0, 0, 3, -4, 15, 0, -23, 0, -39, 8, 0, 12, 1, 6, 12, 0, -2, -6, 27, -6, 0, -28, 7, -4, 7, 0, 24, 4, 3, 20, 0, -4, 33, 0, 6, 0, -18, 12, 13, -6, 0, -12, -12, 16, -11, 0, 0, -8, -24, 8, 0, -6, -1, -22, -9, 0, 28, 18, -6, 0, 0, -8, 35, 12, -25, 0, -19, 0, -25, 24, 0, -8, 0, 2, -18, 0, 4, 10, 32, -10, 0, 12, 4, 24, -1, 0, -18, 24, -22, 4, 0, 14, 9, -2, 25, 0, -4, -12, 0, -18, 0, -40, 14, -12, 25, 0, -30, -8, -38, 16, 0, 0, 13, 6, -7, 0, -11, -26, -19, -28, 0, 4, -6, -16, 0, 0, 39, 4, -17, 0, 0, -18, 46, -32, -3, 0, -3, 0, -24, 4, 0, -36, 6, 12, -23, 0, -25, 40, 29, 0, 0, -4, 40, -38, 12, 0, 15, 2, -21, -18, 0, 20, -1, 0, 11, 0, -9, -48, 3, -16, 0, 12, 28, -10, -21, 0, 0, 6, -14, 24, 0, 24, 2, 28, -6, 0, 0, 20, 3, 0, 0, -6, -20, 18, 7, 0, -34, -32, 7, -8, 0, -4, 0, -28, 30, 0, 20, 12, 22, 56, 0, -2, 3, -42, 3, 0, -15, -24, 18, -4, 0, 16, -32, 0, -9, 0, -3, 8, 0, 4, 0, 16, 30, 26, -18, 0, 33, -26, 23, 22, 0, 0, 1, 12, 39, 0, 23, -8, -51, -8, 0, -4, -74, -12, 0, 0, -1, 6, -9, 12, 0, 8, -12, 48, -31, 0, -12, 0, 5, -12, 0, 6, -45, -6, -27, 0, -25, -12, -23, -16, 0, -24, 36, 28, 27, 0, 14, 8, -41, 4, 0, -10, -7, 0, -27, 0, -25, -26, -24, -2, 0, -4, 12, 0, 6, 0, 0, -20, 9, -16, 0, -36, 33, -8, 24, 0, -33, 2, -23, 0, 0, -8, -15, 0, 4, 0, 62, 12, 18, -4, 0, 24, 0, 16, -13, 0, 23, 6, 4, -18, 0, -12, 7, 12, 65, 0, 12, -32, 14, -40, 0, -58, 11, -40, -29, 0, 34, -20, 0, 14, 0, 8, 0, -40, 24, 0, 25, 16, 0, 36, 0, 0, -17, 6, -34, 0, 16, -2, 6, 22, 0, -12, 9, 44, 0, 0, -12, -12, -28, 24, 0, -18, -21, -6, -12, 0, 33, 0, 17, -6, 0, 16, -22, 20, -7, 0, -35, -44, 13, -12, 0, 36, -50, -26, -68, 0, -7, -32, 19, -28, 0, 0, -19, 0, 25, 0, 42, -24, 9, -24, 0, 8, -49, 8, -41, 0, 0, -8, -7, 4, 0, -48, 18, 4, 37, 0, 17, 4, 8, 0, 0, -10, -6, 10, -32, 0, 5, -2, -36, -26, 0, -16, 0, -12, -3, 0, 8, 16, -116, -24, 0, 4, 1, -68, 48, 0, -1, -38, 18, 16, 0, -24, 13, 56, 55, 0, -9, -4, 0, -28, 0, 42, 29, 28, 8, 0, -9, 54, 27, 2, 0, 0, 50, -4, 16, 0, 12, -12, 4, 0, 0, 30, 28, 2, 0, 0, 14, 18, -38, -26, 0, 36, 12, 40, -6, 0, -14, 0, 37, -24, 0, -10, -25, -38, -9, 0, 99, -50, -6, -78, 0, 8, -7, 36, 38, 0, 9, 32, 28, -48, 0, -34, 57, 0, 12, 0, 26, 6, 27, -6, 0, -4, 7, 28, -82, 0, 0, -24, 11, 24, 0, 26, 44, 58, -38, 0, -13, 28, 17, 0, 0, 24, -21, 8, -13, 0, 6, 24, 15, 16, 0, -44, 0, 26, 70, 0, -45, 18, -39, -30, 0, 8, 6, 24, 17, 0, 75, 0, 56, -44, 0, -8, -50, 18, 66, 0, -46, -56, 0, 26, 0, -76, 3, -36, 49, 0, 21, -28, -6, 64, 0, 0, 22, 30, 24, 0, -11, 8, 41, -2, 0, 28, 20, 36, 0, 0, -15, 20, 19, -12, 0, 6, 23, -24, 57, 0, 81, 0, 25, -22, 0, -40, 49, 52, 58, 0, 72, 0, 34, -12, 0, 102, 51, 10, 18, 0, -40, -14, -3, 38, 0, 4, 24, 0, -69, 0, 45, -36, -15, -68, 0, 4, 31, -84, 21, 0, 0, 18, 54, -38, 0, 64, 23, -20, -13, 0, 1, 64, 27, 0, 0, -14, -11, -10, -24, 0, 39, -56, -18, 30, 0, 48, 0, 48, -3, 0, -27, 40, -83, 4, 0, 48, 70, -12, -73, 0, 56, -12, 38, 10, 0, 0, 21, 80, -1, 0, -6, -12, 0, 36, 0, -6, 95, 72, 35, 0, 13, -24, -12, -60, 0, 0, -72, 48, -45, 0, -2, -40, 93, -28, 0, 14, -12, 20, 0, 0, 44, 2, 0, 6, 0, 4, -17, 60, -3, 0, -27, 0, 87, 8, 0, -20, -33, 6, 12, 0, 20, -10, -91, 36, 0, -72, -7, 44, 55, 0, -42, 28, 85, -56, 0, 32, 55, 0, -7, 0, 72, -16, -19, 2, 0, -24, -50, 4, -16, 0, 0, -8, -7, 28, 0, -24, -30, -18, 39, 0, 7, 6, -20, 0, 0, -12, -24, -36, 44, 0, 0, -56, -57, -4, 0, -30, 0, -4, -1, 0, -3, 12, -36, 42, 0, -52, -48, -20, 1, 0, 3, 36, 15, -56, 0, -48, 45, 8, -18, 0, -113, 4, 0, 18, 0, 44, 28, -16, -33, 0, 32, -28, 40, 0, 0, 0, 9, -78, -15, 0, 3, 36, -6, -76, 0, -8, -21, 8, 0, 0, 18, 8, 3, 44, 0, -46, 18, -16, 9, 0, -75, 0, 47, -26, 0, 44, 18, -24, -4, 0, -13, 8, -33, 0, 0, 26, -18, 6, 46, 0, -39, -22, 84, -14, 0, 0, -31, 0, 68, 0, -1, 12, 14, -12, 0, 16, 78, 46, 12, 0, 0, -74, -23, 10, 0, -16, 21, -52, 51, 0, -27, 8, -66, 0, 0, 12, -82, 4, 69, 0, 74, -36, 94, -24, 0, 64, 0, 20, 108, 0, -12, 16, -2, 8, 0, -6, 63, 6, 9, 0, 24, -30, -85, -30, 0, -36, -60, -8, 11, 0, -24, 28, 0, -48, 0, 78, 31, -68, 18, 0, 47, -36, 12, 30, 0, 0, -15, 16, 1, 0, -57, 12, 65, 56, 0, 22, -96, 12, 0, 0, 45, 0, 9, 6, 0, 28, -54, -24, 70, 0, 140, 0, 25, -4, 0, 30, -28, -6, 23, 0, -70, 16, 50, -18, 0, -20, 29, 24, 71, 0, -36, 56, -60, 56, 0, 6, -27, 0, 13, 0, -2, 18, -35, -6, 0, -8, 18, 8, 41, 0, 0, 8, 40, -4, 0, -40, 5, 10, -35, 0, -14, 30, 36, 0, 0, -12, 27, 20, -53, 0, -86, 24, 25, -24, 0, 26, 0, 24, -48, 0, 15, 2, -48, -50, 0, -96, 19, -8, 123, 0, -12, -36, 52, 0, 0, 12, -15, -34, -32, 0, 25, -98, 0, -8, 0, -40, -42, -24, -9, 0, 24, 16, 65, 36, 0, 0, -83, 36, 32, 0, -33, 8, 18, 20, 0, -24, -24, -28, 0, 0, 19, 52, -66, -52, 0, -2, -47, -22, 23, 0, -59, 0, 18, -30, 0, 4, -141, 8, 77, 0, -3, 4, -39, 0, 0, 40, -4, -66, 66, 0, 21, -78, -62, -10, 0, -12, -21, 0, 36, 0, -32, 4, 63, -24, 0, 60, -61, -60, -41, 0, 0, 20, -20, -16, 0, 84, -26, 24, 75, 0, -54, -12, -23, 0, 0, 12, -11, -36, -4, 0, -27, 18, 90, -54, 0, -24, 0, 12, -66, 0, -7, 0, 1, 24, 0, 50, -65, -100, -28, 0, -55, 110, 24, -48, 0, 32, 39, 40, -14, 0, 47, -8, 0, -24, 0, 90, -77, 58, -36, 0, 22, 20, -13, 40, 0, 0, 29, -4, -51, 0, 7, -64, -34, 48, 0, 20, 74, -6, 0, 0, -39, -14, 15, 88, 0, 68, 57, 16, -9, 0, 0, 0, -89, 40, 0, -12, 48, -14, 29, 0, -12, 10, -25, 4, 0, -40, -72, 8, 0, 0, -64, -36, 35, 12, 0, -4, 4, 0, 46, 0, 17, -98, 24, 12, 0, 44, 34, 44, -24, 0, 0, 16, -13, 12, 0, 2, 181, 18, -6, 0, 122, 44, -43, 0, 0, 68, -12, 12, -77, 0, 18, 40, -45, -44, 0, 0, 0, -72, -14, 0, -93, -48, 12, -42, 0, 12, 59, 52, -56, 0, -30, -24, -25, -36, 0, 44, -131, -36, 40, 0, 21, 34, 0, 6, 0, -84, 30, -44, 29, 0, -31, 0, -33, -48, 0, 0, 75, -98, -17, 0, 38, 6, -36, 66, 0, -20, -87, -16, 0, 0, 22, -112, 11, 4, 0, -42, 7, -2, -72, 0, -13, 0, -70, -18, 0, 44, 49, 12, -13, 0, -50, -24, 45, -32, 0, -6, 105, -36, -75, 0, 125, -6, -42, 26, 0, -16, 68, 0, -71, 0, -72, -60, 7, 124, 0, 32, 11, -18, 38, 0, 0, 28, 77, 26, 0, 52, -12, 0, -99, 0, 19, -24, 164, 0, 0, 118, 50, 28, -41, 0, -114, 120, -42, -6, 0, -48, 0, 72, -9, 0, 27, 24, 149, -36, 0, 74, -84, -8, 6, 0, 49, -70, -13, 16, 0, 16, 41, 36, -123, 0, -29, -16, 0, -12, 0, 8, 59, -32, 7, 0, -73, -10, -12, 70, 0, 0, -39, 48, 80, 0, 36, -88, -67, -4, 0, -76, -37, 40, 0, 0, -102, 18, -17, -92, 0, -4, 54, 0, -20, 0, 67, 0, -67, -48, 0, -64, 28, -20, -106, 0, 6, 18, 120, -10, 0, 48, -64, 8, -46, 0, -2, 72, -5, 28, 0, 32, -39, 0, 36, 0, -66, 26, 3, 46, 0, -156, -29, 16, 6, 0, 0, 72, 8, -24, 0, -84, 3, 62, -103, 0, -36, 36, -20, 0, 0, -16, -13, 36, 116, 0, 24, -48, -48, 52, 0, -68, 0, -4, -10, 0, 2, -24, 57, 68, 0, -32, -48, 108, -45, 0, -97, 36, 1, 100, 0, 38, 97, -18, 36, 0, 68, -16, 0, -2, 0, -12, -28, -48, -131, 0, -13, -36, 23, -56, 0, 0, 11, 62, -18, 0, -108, 22, 9, -36, 0, -8, 25, -96, 0, 0, -105, 28, 100, -40, 0, 70, 62, -42, 21, 0, -29, 0, 19, -70, 0, -84, -8, 0, -151, 0, 78, -12, -18, 44, 0, -54, 36, -38, -27, 0, 4, 4, -87, 0, 0, -44, 84, 0, -40, 0, -125, 36, 67, 4, 0, 38, -16, -22, -113, 0, 0, -12, -12, 36, 0, 12, -112, -148, 8, 0, 152, 0, -53, 0, 0, -2, 90, 6, 48, 0, -28, 0, -4, -2, 0, -40, 0, -32, 186, 0, 21, 8, -14, 16, 0, 36, -66, 18, 38, 0, 9, 26, 39, -82, 0, -8, -47, -36, 75, 0, -12, -20, 0, 80, 0, 54, 6, 102, 1, 0, -99, -118, -28, -12, 0, 0, 0, -128, -37, 0, 93, 60, -11, -36, 0, -10, 15, 10, 0, 0, -50, -12, 54, 38, 0, -96, 9, -16, 176, 0, -70, 0, -99, 48, 0, 50, 91, -14, 96, 0, -3, 78, -3, 4, 0, -76, -7, 16, -57, 0, 7, 16, -37, -36, 0, 52, 76, 0, -57, 0, -56, -12, -9, -30, 0, -80, 157, 40, -28, 0, 0, 48, -87, -84, 0, 10, -87, 34, -16, 0, -57, 10, 21, 0, 0, -172, -12, -48, -103, 0, -16, -140, -65, -108, 0, -6, 0, -72, -27, 0, 195, -12, 108, 36, 0, -20, -9, 4, -18, 0, 14, -64, 38, -28, 0, 116, 82, -24, -36, 0, 22, 60, 0, -60, 0, 24, 35, -48, 22, 0, -9, -24, -152, -88, 0, 0, 23, 52, -2, 0, -44, -6, -45, -58, 0, -28, 95, -72, 0, 0, -120, 56, 13, 168, 0, 56, 43, -90, -17, 0, -1, 0, -40, 126, 0, 100, 0, -24, -17, 0, 21, -56, 104, -20, 0, -60, 13, -114, 54, 0, -3, 54, 12, 54, 0, -24, 13, 0, -15, 0, 16, 32, -19, 44, 0, -54, -65, 44, 114, 0, 0, -36, -100, -26, 0, 12, -70, -40, 20, 0, -42, -120, 45, 0, 0, -18, 122, 22, -78, 0, 81, 30, -7, 78, 0, 24, 0, -20, -145, 0, -6, -4, 73, -24, 0, -6, 34, -38, -49, 0, 13, 18, -75, 32, 0, 0, 54, -52, -56, 0, 42, 44, 0, -28, 0, -22, -84, 8, 90, 0, 50, 126, -60, 36, 0, 0, -66, 24, 44, 0, -147, 4, -92, 40, 0, 56, 20, 78, 0, 0, 146, 70, -116, -70, 0, 28, -19, 76, -190, 0, 6, 0, -30, 36, 0, 48, -49, 34, -111, 0, -81, 66, -21, 18, 0, 28, -20, -8, 15, 0, 144, -64, -63, -12, 0, 114, -99, 0, -43, 0, -22, 164, -7, -30, 0, -72, 48, -56, 90, 0, 0, -24, 11, 56, 0, -20, -117, 30, -41, 0, -44, 2, -36, 0, 0, 88, -37, -28, 18, 0, -20, 0, 115, 72, 0, 42, 0, -64, 30, 0, 44, -96, -3, 6, 0, -20, 3, 88, -19, 0, -91, -24, -119, 80, 0, 54, 15, -6, 80, 0, 46, 0, 0, 24, 0, -108, -57, -96, -52, 0, -18, 48, -81, -80, 0, 0, 77, -24, 50, 0, 181, 22, -54, 84, 0, -116, -72, -80, 0, 0, -49, -16, 15, -52, 0, -54, -145, -54, 32, 0, -75, 0, -72, 10, 0, 0, 2, 144, -34, 0, -30, 12, 9, 112, 0, 20, -68, -102, -84, 0, -51, -26, -109, 2, 0, -72, -18, 0, 37, 0, 76, 104, -80, -8, 0, 14, 75, -54, 3, 0, 0, 76, -78, 24, 0, 92, 58, -4, -9, 0, -60, -68, -75, 0, 0, -62, 69, 26, 9, 0, 61, -16, -45, 66, 0, 36, 0, 48, -30, 0, -68, 68, 106, 52, 0, 58, 98, -10, 37, 0, -31, 100, 18, 84, 0, 60, 42, 40, -93, 0, 44, -60, 0, 0, 0, 36, -33, 144, -54, 0, -127, 38, 107, 26, 0, 0, 93, -64, 66, 0, -23, -4, -66, -40, 0, 102, 13, -22, 0, 0, -12, -70, 2, -16, 0, -64, -19, 64, -27, 0, 96, 0, -1, -12, 0, 6, 35, 14, -1, 0, -22, 70, -135, 10, 0, -12, 24, 152, -73, 0, -52, -92, -39, 0, 0, 56, -6, 0, 45, 0, -35, -30, 12, -108, 0, 88, -23, 96, 101, 0, 0, 52, 82, -48, 0, 6, -6, 86, 84, 0, 51, 72, 27, 0, 0, 8, -14, 8, 83, 0, -91, -4, 99, -56, 0, 12, 0, -48, 119, 0, -70, 4, 12, -24, 0, -16, 73, 24, 74, 0, -36, 156, -140, 84, 0, 12, 12, -36, -38, 0, 105, 20, 0, -80, 0, -108, -168, 0, 65, 0, 42, -8, 104, -80, 0, 0, 1, 20, 37, 0, 115, -4, 6, -6, 0, 12, 21, -16, 0, 0, 9, -36, 15, 48, 0, -106, 115, -12, 126, 0, -95, 0, -127, -72, 0, -56, 7, 0, 141, 0, -39, 48, -13, -12, 0, -48, -46, -18, 12, 0, 85, 60, 59, -30, 0, -48, 15, 0, -39, 0, 72, -52, 31, -120, 0, 84, 45, -6, 12, 0, 0, -78, -4, 0, 0, 40, 12, -92, -93, 0, -111, -56, -27, 0, 0, 14, -134, -14, 27, 0, 30, -8, -48, -20, 0, -88, 0, 12, -88, 0, -40, 24, -44, -100, 0, -2, -3, 50, 0, 0, -116, -6, -69, 84, 0, -72, -27, -64, 45, 0, 17, 16, 0, -60, 0, 6, -6, 60, 7, 0, 96, 90, 27, 86, 0, 0, 55, -56, -87, 0, -24, -8, 27, -60, 0, 52, 25, 20, 0, 0, 33, 146, 42, 12, 0, 96, -12, 56, -117, 0, 23, 0, 40, 12, 0, 10, 1, 16, 91, 0, 76, -90, -48, 72, 0, 124, 113, 72, -29, 0, -14, 24, 24, -44, 0, 78, -55, 0, -78, 0, -46, 42, 42, 102, 0, -28, -168, 16, 17, 0, 0, 56, -27, -8, 0, -150, -19, 64, 101, 0, -55, -166, -57, 0, 0, 36, -14, 156, 42, 0, 78, 48, -72, -8, 0, 40, 0, 36, 19, 0, 41, -2, 75, 6, 0, -168, -66, 24, -59, 0, 50, -60, -128, 8, 0, -42, 16, -136, -118, 0, 3, 10, 0, 30, 0, 8, 65, -76, 7, 0, -11, 56, -70, -36, 0, 0, -164, 24, -36, 0, -60, 106, 27, 18, 0, -12, -39, 40, 0, 0, 59, -108, -7, -72, 0, -6, -150, -30, -40, 0, 85, 0, 19, 26, 0, -20, 36, -24, 125, 0, 24, -64, 154, 36, 0, 0, -110, 2, 3, 0, 61, -4, 0, 28, 0, -112, 24, 0, 57, 0, -79, 4, -201, 72, 0, -42, -128, 30, -12, 0, 0, -48, 12, 10, 0, 0, 1, -128, 75, 0, 90, -92, -6, 0, 0, -12, 4, -194, 36, 0, -139, 84, -32, 114, 0, -36, 0, 52, -112, 0, 39, -56, -19, 20, 0, -18, -1, 52, -257, 0, -9, 70, -3, -18, 0, -36, -158, 16, 30, 0, -18, 56, 0, 176, 0, 30, -73, 120, 81, 0, -45, 36, 49, -8, 0, 0, -36, 36, -33, 0, 109, 60, 113, -36, 0, 8, 78, 56, 0, 0, 88, -18, -24, -116, 0, 8, 123, -44, -132, 0, -28, 0, 151, -32, 0, -38, 33, -68, -144, 0, -13, 8, 64, 12, 0, 28, 11, 48, -40, 0, 23, 0, 135, 68, 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, 0], [1, 0], [0, -1], [-1, 0], [1, 1], [0, 0], [0, 1], [-1, 0], [-3, 0], [-2, 0], [0, 0], [3, -2], [-1, -1], [0, 0], [0, 1], [0, 0], [-2, 1], [-3, -2], [0, 2], [1, 2], [0, 0], [1, 0], [6, -1], [3, 0], [3, 0], [0, 0], [0, 0], [5, 0], [-1, -1], [3, -4], [0, 0], [4, 0], [3, 1], [-3, 2], [6, 5], [0, 0], [-2, -2], [-1, 2], [-6, -3], [0, 0], [0, 0], [-3, 0], [0, -1], [1, 4], [-3, -1], [0, 0], [0, -3], [0, 4], [2, -1], [-6, 0], [0, 0], [3, 2], [0, 0], [-6, 4], [0, -5], [0, 0], [3, 0], [-1, -2], [12, 1], [-3, 6], [0, 0], [-1, 0], [0, -4], [2, 0], [1, -6], [0, 0], [-6, 1], [-7, 0], [-9, -7], [-3, 0], [0, 0], [9, -6], [6, 0], [-10, 4], [-6, -1], [0, 0], [7, 5], [-3, 2], [0, 0], [-4, 4], [0, 0], [1, 0], [0, 3], [0, -4], [1, 1], [0, 0], [-12, -5], [-3, 4], [-9, 6], [-3, 4], [0, 0], [0, 0], [3, 3], [-4, 0], [-12, -4], [0, 0], [-3, -1], [-13, 2], [0, 6], [-6, 4], [0, 0]]}