# Stored data for newform 4005.2.a.k, downloaded from the LMFDB on 28 March 2024. {"label": "4005.2.a.k", "space_label": "4005.2.a", "level": 4005, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307263397, "dim": 4, "is_polredabs": true, "nf_label": "4.4.8069.1", "trace_hash": 1630578242413801333, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -5, -5, 1, 1]], [7, [-3, 1]], [11, [13, -19, -14, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}-q^{5}+3q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16020, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 31.980086009522793, "hecke_ring_index": 1, "level_radical": 1335, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [4005, 1, [3116, 802, 181], [1, 1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5, 89], "conrey_indexes": [1], "field_disc": 8069, "field_disc_factorization": [[8069, 1]], "field_poly": [1, 5, -5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.727", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "36.964", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "549.745", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1], [89, -1]], "trace_display": [-1, 0, -4, 12], "traces": [0, 4, -1, 0, 3, -4, 0, 12, 3, 0, 1, -2, 0, -7, -3, 0, -3, -1, 0, -1, -3, 0, -14, -13, 0, 4, -7, 0, 9, -14, 0, -11, 0, 0, -16, -12, 0, -5, -12, 0, -3, -9, 0, -9, -3, 0, 12, -6, 0, 8, -1, 0, -24, -5, 0, 2, 9, 0, 43, 18, 0, -3, -12, 0, -23, 7, 0, 13, -19, 0, 3, 28, 0, -1, -15, 0, 12, -6, 0, -7, 3, 0, -17, -20, 0, 1, 29, 0, -18, 4, 0, -21, 9, 0, 17, 1, 0, -13, -2, 0, 3, -15, 0, -4, 4, 0, -25, -34, 0, -33, 14, 0, -9, 34, 0, 13, 28, 0, 21, -3, 0, -12, 37, 0, -41, -4, 0, 15, -15, 0, 7, -37, 0, -3, 33, 0, -17, -1, 0, -3, -9, 0, 7, 3, 0, 14, 29, 0, 43, -17, 0, -11, 17, 0, -42, 11, 0, 22, -13, 0, 0, -39, 0, -18, -61, 0, 46, 18, 0, -3, 16, 0, -18, -20, 0, 12, 5, 0, -1, 6, 0, -2, -21, 0, -19, 5, 0, 33, -15, 0, 12, 14, 0, -54, -2, 0, 6, -29, 0, 12, 3, 0, 31, -42, 0, 9, -49, 0, 6, -5, 0, -24, -60, 0, -6, 9, 0, -33, -17, 0, 3, 20, 0, 4, 0, 0, 0, -50, 0, -14, -12, 0, 13, 35, 0, 6, -17, 0, -48, 59, 0, -32, 19, 0, -31, -8, 0, 19, -46, 0, 1, -70, 0, 7, -23, 0, 1, -13, 0, -15, 24, 0, -27, -5, 0, 5, -36, 0, 46, -11, 0, 2, 19, 0, 15, -2, 0, 20, -30, 0, -9, -29, 0, 44, 25, 0, 80, -27, 0, -17, -43, 0, -29, -47, 0, -18, -12, 0, 25, -14, 0, -27, 32, 0, -42, 3, 0, 25, -9, 0, 12, -16, 0, 11, -39, 0, 27, 16, 0, -56, 23, 0, 36, -18, 0, -7, -47, 0, 12, -18, 0, -15, 9, 0, 9, -13, 0, -15, 33, 0, 19, 58, 0, -60, -8, 0, -3, -39, 0, -3, -3, 0, 62, -1, 0, -28, 3, 0, -41, -7, 0, -3, 71, 0, -72, 1, 0, 55, 9, 0, 15, -15, 0, -51, 40, 0, -44, -30, 0, 25, -12, 0, 30, -9, 0, 6, -9, 0, -60, -13, 0, -15, 6, 0, -19, 7, 0, -40, 23, 0, -3, -18, 0, 29, -25, 0, 129, 27, 0, -43, 17, 0, 53, 54, 0, 20, -1, 0, 8, 29, 0, -66, -16, 0, 24, -1, 0, -9, 38, 0, -29, 46, 0, -35, -36, 0, 37, -14, 0, 44, 18, 0, 83, 28, 0, -4, -36, 0, -69, -5, 0, 5, 78, 0, 21, 21, 0, -60, 32, 0, -9, -15, 0, 37, -12, 0, -80, 21, 0, 39, -17, 0, 47, -21, 0, -1, -57, 0, -86, -55, 0, -30, 47, 0, 43, 13, 0, 40, 35, 0, 2, -63, 0, -98, 3, 0, 64, 84, 0, 12, -3, 0, 23, -4, 0, 15, -10, 0, 87, 42, 0, -3, 29, 0, 28, 4, 0, 27, -45, 0, -4, -40, 0, 45, 1, 0, -49, 88, 0, -13, 25, 0, 36, 108, 0, 34, 55, 0, -30, -4, 0, -12, 9, 0, 65, 33, 0, 7, 97, 0, -14, 10, 0, -21, -31, 0, -22, 11, 0, -1, 9, 0, -2, -32, 0, -34, 38, 0, 3, 65, 0, -16, 31, 0, -51, -13, 0, 37, 90, 0, -28, -60, 0, 1, 11, 0, -26, 51, 0, -76, -21, 0, -51, 27, 0, 3, -31, 0, 15, -26, 0, 80, 87, 0, -39, 12, 0, 13, -11, 0, -37, -34, 0, -4, -52, 0, -54, -39, 0, 63, 41, 0, 112, 12, 0, 4, 90, 0, -8, -21, 0, -95, -35, 0, 122, -15, 0, -14, -44, 0, 15, -79, 0, -30, 27, 0, 3, 52, 0, -68, -7, 0, 50, 0, 0, 37, 23, 0, 51, -72, 0, -26, -11, 0, -13, 3, 0, 100, -38, 0, -33, -72, 0, 13, -84, 0, 68, -7, 0, -39, 17, 0, 81, -11, 0, 1, 15, 0, 46, 119, 0, -92, -12, 0, -89, 3, 0, 57, -36, 0, 9, -22, 0, 64, -8, 0, 95, -45, 0, -47, -7, 0, 3, 26, 0, -3, 31, 0, 97, -17, 0, -12, -8, 0, -42, -14, 0, 94, 12, 0, -29, -12, 0, -55, -39, 0, 1, -88, 0, -64, -43, 0, -75, -132, 0, 17, 28, 0, 82, -102, 0, -40, 70, 0, -141, 11, 0, 38, 114, 0, -17, 24, 0, -99, 100, 0, -31, 7, 0, -49, 42, 0, -104, -3, 0, -11, -9, 0, -103, 24, 0, -10, -3, 0, -6, -22, 0, 92, -13, 0, 13, 102, 0, 35, -77, 0, -31, 40, 0, 36, 0, 0, 73, -40, 0, 39, 139, 0, 22, 70, 0, 10, 84, 0, -68, 18, 0, -65, -38, 0, 61, 20, 0, 44, -1, 0, 63, 44, 0, 116, -46, 0, 141, -2, 0, -18, 32, 0, 8, -75, 0, 152, 3, 0, -84, 3, 0, -36, 6, 0, -16, 55, 0, 6, 111, 0, -34, 66, 0, 14, 18, 0, -31, -49, 0, 20, 158, 0, -123, 48, 0, -50, -37, 0, 57, -12, 0, 114, 89, 0, -5, 20, 0, 62, 77, 0, -57, 25, 0, 45, 1, 0, 51, -119, 0, -6, -45, 0, -82, -109, 0, 56, 178, 0, 3, 2, 0, -33, -43, 0, 21, 103, 0, -33, 67, 0, -135, -111, 0, -49, 19, 0, -37, -85, 0, -5, 75, 0, -126, -7, 0, -2, 45, 0, 40, -33, 0, 79, 99, 0, 15, 42, 0, -63, 9, 0, 26, -63, 0, 13, -12, 0, -51, 31, 0, -14, -2, 0, -43, -3, 0, 85, 74, 0, 82, 54, 0, -63, -6, 0, 2, -70, 0, -9, 74, 0, 30, -33, 0, -2, -6, 0, 43, 72, 0, 29, -100, 0, -20, 46, 0, -15, 105, 0, 21, -12, 0, -37, 88, 0, -3, 9, 0, -33, -36, 0, -130, 53, 0, -83, -31, 0, -16, 55, 0, 42, 46, 0, 106, 34, 0, 6, 87, 0, 62, -9, 0, -35, -62, 0, 49, -41, 0, 56, -13, 0, 129, -44, 0, -19, -6, 0, -2, -51, 0, 5, 8, 0, -65, 32, 0, 21, 14, 0, 139, 24, 0, -33, -52, 0, 60, -20, 0, 88, 51, 0, 36, 11, 0, 18, 6, 0, -55, 54, 0, -9, -11, 0, -28, -28, 0, 64, 134, 0, -16, 33, 0, 79, 26, 0, 17, -69, 0, -15, 111, 0, 45, -96, 0, 66, -3, 0, 58, -5, 0, -20, -39, 0, 55, -74, 0, -53, -35, 0, -160, -4, 0, 2, -62, 0, 0, -19, 0, 136, -38, 0, 130, -26, 0, 36, 0, 0, -11, 50, 0, 50, 7, 0, 128, -121, 0, -54, 84, 0, 41, 14, 0, -55, -183, 0, 12, 10, 0, 35, -19, 0, 35, -7, 0, -26, -13, 0, 138, -36, 0, -35, 184, 0, 46, 54, 0, 29, -57, 0, -23, -6, 0, 40, 56, 0, 17, 20, 0, -9, 49, 0, 0, -89, 0, -116, 48, 0, 64, -95, 0, -59, 13, 0, 3, 54, 0, -31, 5, 0, -54, 32, 0, -7, 38, 0, -19, -60, 0, 39, -24, 0, 88, -23, 0, -94, 31, 0, 43, 41, 0, 8, -166, 0, -65, 8, 0, -107, 15, 0, 109, -19, 0, -23, -106, 0, 46, -12, 0, -3, -69, 0, -3, 88, 0, -13, -1, 0, 123, 18, 0, 70, 40, 0, -41, -94, 0, 79, 84, 0, -12, -7, 0, -6, 55, 0, 23, 77, 0, 51, -14, 0, -171, 98, 0, -72, -1, 0, 170, -116, 0, 13, 132, 0, -57, 139, 0, -8, 66, 0, -150, 15, 0, -34, 6, 0, -24, 88, 0, -140, -115, 0, -6, -33, 0, 99, 27, 0, 1, 46, 0, 5, -45, 0, -55, 18, 0, 56, -53, 0, 151, -5, 0, 85, 30, 0, 36, 9, 0, 51, -74, 0, 78, 42, 0, 3, -46, 0, 69, 14, 0, 11, 70, 0, -49, -67, 0, -162, 17, 0, -49, -2, 0, -97, -6, 0, -19, 103, 0, 7, 105, 0, 138, 43, 0, 31, -15, 0, -45, -67, 0, 2, -51, 0, 32, -87, 0, 100, -22, 0, -75, -20, 0, -62, -28, 0, 30, 2, 0, 36, 183, 0, 36, -23, 0, -22, 9, 0, 17, -20, 0, 29, 7, 0, 97, -21, 0, -62, 39, 0, 93, -44, 0, 9, -18, 0, -25, -28, 0, 44, -3, 0, -79, 42, 0, -59, -80, 0, -11, 59, 0, 27, 32, 0, -17, 58, 0, 92, -147, 0, -151, 17, 0, -17, 60, 0, 43, 51, 0, 111, -149, 0, 18, 156, 0, 56, 29, 0, 5, -15, 0, 47, -40, 0, -27, -143, 0, -49, -26, 0, -109, 18, 0, -72, -85, 0, 12, -56, 0, -103, -180, 0, 56, -51, 0, 154, -25, 0, -138, 20, 0, 14, 39, 0, -18, -153, 0, 4, -139, 0, 48, 27, 0, -60, -71, 0, -32, 44, 0, -1, 91, 0, 14, -113, 0, -22, 42, 0, -40, 27, 0, -3, -51, 0, -5, 65, 0, -129, 65, 0, -175, -25, 0, -146, 103, 0, 9, -15, 0, -79, -125, 0, -146, 60, 0, -33, -12, 0, 54, -66, 0, 16, -8, 0, -11, 19, 0, 12, -138, 0, 18, -11, 0, -81, 0, 0, 39, -14, 0, -44, -94, 0, 14, -49, 0, 31, -27, 0, 0, -13, 0, -16, -178, 0, -97, -150, 0, -76, -48, 0, -91, 56, 0, 34, 14, 0, -23, -108, 0, -42, -102, 0, 43, -41, 0, 10, -36, 0, 179, -38, 0, 18, 19, 0, -112, -99, 0, 6, -52, 0, 39, 7, 0, 20, 77, 0, 47, 105, 0, -55, 55, 0, -80, -84, 0, -89, -12, 0, -81, 43, 0, 18, -69, 0, -105, 58, 0, -48, -51, 0, 206, 15, 0, 125, -86, 0, -9, -70, 0, 46, 24, 0, -32, -25, 0, 77, -9, 0, -26, 177, 0, 13, 240, 0, -57, -8, 0, 95, 56, 0, -128, 15, 0, -96, -68, 0, -33, -1, 0, 23, 57, 0, -3, 47, 0, -26, -19, 0, 1, 35, 0, -58, 20, 0, -93, 61, 0, -14, -44, 0, -55, 60, 0, -43, -93, 0, 8, 136, 0, -25, 274, 0, 60, -1, 0, 57, 3, 0, 44, 103, 0, 39, -138, 0, -55, -55, 0, -11, -222, 0, -50, 3, 0, 12, -40, 0, 3, -7, 0, -227, -24, 0, 51, -210, 0, -153, -62, 0, 44, -2, 0, 1, 178, 0, 66, 99, 0, 21, -118, 0, -14, 28, 0, -38, -69, 0, -3, -65, 0, -6, -69, 0, 73, 63, 0, -58, 41, 0, 3, 162, 0, 7, -20, 0, -287, -39, 0, -59, 185, 0, 65, 3, 0, 23, -47, 0, -71, -96, 0, -10, -69, 0, 57, 70, 0, -32, 72, 0, -147, 36, 0, -1, -17, 0, -118, -89, 0, -66, -28, 0, -81, -55, 0, -87, -169, 0, -9, -15, 0, -35, -76, 0, -55, 5, 0, -59, -15, 0, 83, -16, 0, 15, -21, 0, -52, -50, 0, -18, -24, 0, 34, 51, 0, -67, -93, 0, -40, -117, 0, 142, -105, 0, 138, 160, 0, 115, 44, 0, 10, -33, 0, 30, 49, 0, -118, 149, 0, -46, -99, 0, -120, -25, 0, 6, -108, 0, 12, 59, 0, 78, 57, 0, 2, -153, 0, 128, -30, 0, 44, 7, 0, 9, -144, 0, 45, 2, 0, -47, 213, 0, -94, -6, 0, -65, -27, 0, 9, -178, 0, -73, 124, 0, -30, 104, 0, 60, 60, 0, -71, 181, 0, 13, -90, 0, -4, -165, 0, -78, -147, 0, 58, 15, 0, 161, -14, 0, -6, -110, 0, 67, 4, 0, -43, -87, 0, 52, 19, 0, -131, -1, 0, -7, 53, 0, -83, -6, 0, 132, -28, 0, 22, 40, 0, 137, 75, 0, -23, -131, 0, 114, -116, 0, 49, 91, 0, -17, 3, 0, 240, -111, 0, 18, -62, 0, -40, -18, 0, -74, 58, 0, -39, -29, 0, 157, 45, 0, 25, 110, 0, -51, 49, 0, 9, 60, 0, 139, -129, 0, -141, 84, 0, -27, 27, 0, -30, 170, 0, 43, -198, 0, -87, 43, 0, -13, -53, 0, -17, -141, 0, -13, 116, 0, 93, -68, 0, -66, -53, 0, 91, -145, 0, -54, 80, 0, -18, 105, 0, 96, -36, 0, -3, -20, 0, -244, 166, 0, 1, 170, 0, 93, -181, 0, 75, -96, 0, 55, -8, 0, 23, -42, 0, -29, 0, 0, 64, -23, 0, -25, -159, 0, -148, 66, 0, -18, 126, 0, 16, 48, 0, -18, 96, 0, -127, 45, 0, -82, -24, 0, -82, 134, 0, 1, -233, 0, -126, -1, 0, 19, 236, 0, 152, 9, 0, 9, 56, 0, -38, 74, 0, 192, -163, 0, 125, -18, 0, 75, 29, 0, -54, 40, 0, -46, -6, 0, -92, -95, 0, 29, -128, 0, -5, 35, 0, 5, 40, 0, 36, 71, 0, 288, 2, 0, 83, -48, 0, -68, -37, 0, -112, -165, 0, 14, 97, 0, 196, 25, 0, 33, -128, 0, -115, -44, 0, 13, -117, 0, -18, -31, 0, 116, -150, 0, 95, 89, 0, 36, -83, 0, 81, 147, 0, -28, 72, 0, 67, 48, 0, 105, 86, 0, 24, 4, 0, 54, 13, 0, 36, -14, 0, -168, 14, 0, 61, -9, 0, -78, 69, 0, -62, -232, 0, 5, -93, 0, -47, -20, 0, -92, -5, 0, 24, -5, 0, -155, -98, 0, -78, -54, 0, 24, 87, 0, -46, -66, 0, -90, -21, 0, 8, 98, 0, -21, -30, 0, -197, -39, 0, 89, -141, 0, -5, 60, 0, -70, 11, 0, -32, 15, 0, 26, -36, 0, 36, 11, 0, 29, 9, 0, 8, -12, 0, 15, 10, 0, 144, 39, 0, 21, 4, 0, -7, -37, 0, -45, 8, 0, 12, 84, 0, 29, 27, 0, -31, -13, 0, -158, 80, 0, 81, 83, 0, -21, -81, 0, 27, -124, 0, -132, 41, 0, -59, -39, 0, 30, 106, 0, 17, -50, 0, 35, -2, 0, 131, -103, 0, -45, -47, 0, 1, 84, 0, 21, 99, 0, -49, 17, 0, -94, -9, 0, 118, 1, 0, 34, -295, 0, 57, 58, 0, 51, -25, 0, 113, 174, 0, 44, 86, 0, -76, 142, 0, 55, -125, 0, 5, 91, 0, -236, -157, 0, 97, 30, 0, 243, -24, 0, -47, -200, 0, 180, -148, 0, 22, 128, 0, 67, -43, 0, -9, 132, 0, -13, 126, 0, 35, -117, 0, -149, 30, 0, 144, -40, 0, -41, 93, 0, -35, 93, 0, -9, 52, 0, -82, -23, 0, 44, -2, 0, 60, 105, 0, 63, -73, 0, -125, 19, 0, 168, 159, 0, 186, 98, 0, -38, 25, 0, -3, -3, 0, 60, 116, 0, -22, -31, 0, 20, -64, 0, 3, -163, 0, -84, -255, 0, -73, 36, 0, -126, 9, 0, -143, -12, 0, -78, 154, 0, 3, 95, 0, 84, 24, 0, -123, 156, 0, 96, -23, 0, -49, -21, 0, 4, 105, 0, -122, -4, 0, 60, 37, 0, 7, -15, 0, -9, 89, 0, 10, 69, 0, -75, 213, 0, -25, 33, 0, -64, -87, 0, 324, -131, 0, -42, -48, 0, -48, 32, 0, 39, 1, 0, 116, 3, 0, 56, 148, 0, -29, 104, 0, 46, -66, 0, -35, -42, 0, 165, -28, 0, -95, 1, 0, -4, 27, 0, -24, -92, 0, -14, -151, 0, 16, -27, 0, -64, -102, 0, 45, -106, 0, -73, 34, 0, -149, -10, 0, -27, 4, 0, -10, 160, 0, 40, -118, 0, 0, -95, 0, -153, 51, 0, -137, -45, 0, 62, 120, 0, -1, -55, 0, 107, 293, 0, -122, -51, 0, 42, 49, 0, -132, -21, 0, -88, -189, 0, -13, -90, 0, -23, -102, 0, -69, 13, 0, 7, -25, 0, -25, -20, 0, 75, -85, 0, -86, 37, 0, 55, -36, 0, 79, 210, 0, -108, -101, 0, -69, 29, 0, 60, -13, 0, 90, -34, 0, 150, 153, 0, -55, -27, 0, 137, -180, 0, -7, 95, 0, -168, 30, 0, -149, -76, 0, 4, -166, 0, -52, 163, 0, -141, -27, 0, -55, 12, 0, -106, 36, 0, -9, -131, 0, 138, 70, 0, -180, -56, 0, -208, -65, 0, -139, -39, 0, -33, -146, 0, 120, -63, 0, 21, -79, 0, -163, -7, 0, -45, -95, 0, -97, 34, 0, 80, -45, 0, -45, -120, 0, 19, 14, 0, -11, -137, 0, -10, 225, 0, -57, -11, 0, 17, -119, 0, 6, 21, 0, 208, 64, 0, 31, 94, 0, -54, 20, 0, -76, 13, 0, -120, 22, 0, 120, 104, 0, -11, 69, 0, 139, 37, 0, 5, 51, 0, -150, 1, 0, -195, -22, 0, -9, 135, 0, 191, -123, 0, -7, -54, 0, 125, 2, 0, -100, -70, 0, 32, 56, 0, -44, 60, 0, 87, -50, 0, 145, 34, 0, -121, -75, 0, -38, 98, 0, 101, 158, 0, 63, -214, 0, -31, -3, 0, 86, -30, 0, -65, 26, 0, 0, 81, 0, -48, 26, 0, 42, 16, 0, 72, -64, 0, -31, -49, 0, -129, -55, 0, -94, -7, 0, 6, 51, 0, 175, -121, 0, 13, 15, 0, -102, 49, 0, -2, 71, 0, 159, -37, 0, -51, -9, 0, -90, 36, 0, 197, -87, 0, 51, 83, 0, -92, 28, 0, -285, -69, 0, 60, -85, 0, -112, 44, 0, -139, -3, 0, -83, -1, 0, -37, -169, 0, -11, -27, 0, 135, -91, 0, 24, 81, 0, 140, 26, 0, 203, 87, 0, -51, 13, 0, -40, 13, 0, 70, 155, 0, 51, 76, 0, -198, -200, 0, 21, 179, 0, 25, -48, 0, -68, 4, 0, 84, 51, 0, -65, -167, 0, -27, 153, 0, 72, -60, 0, -135, -45, 0, 163, -3, 0, 103, -124, 0, 31, -49, 0, 84, 18, 0, 322, -22, 0, -6, -15, 0, -48, 53, 0, 26, 114, 0, 117, 32, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "445.2.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [1, 0, 1, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [1, 0, 0, -1], [0, 0, 0, 0], [0, 1, 0, 0], [-1, 1, 0, 1], [0, 0, 0, 0], [-2, 1, -1, -1], [0, -3, 0, 0], [0, 0, 0, 0], [-1, -1, -1, 1], [-1, 1, -1, 1], [0, 0, 0, 0], [0, 2, 1, -2], [-1, 0, -1, 0], [0, 0, 0, 0], [-4, 1, -2, -1], [-3, -1, 1, 1], [0, 0, 0, 0], [1, 0, 0, 0], [-3, 3, 0, 2], [0, 0, 0, 0], [3, 0, 3, 0], [-2, -3, 2, -1], [0, 0, 0, 0], [-4, 0, -2, 3], [-1, 2, 0, 2], [0, 0, 0, 0], [-5, 2, -2, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [-1, 2, 3, 0], [-3, -1, 0, 1], [0, 0, 0, 0], [-1, 0, 0, 1], [-3, 2, -3, -2], [0, 0, 0, 0], [-2, -3, -1, 1], [-2, 4, 0, 1], [0, 0, 0, 0], [3, 2, 0, -2], [-2, -3, -1, 4], [0, 0, 0, 0], [2, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-7, 1, -3, 0], [-2, 3, -3, -3], [0, 0, 0, 0], [1, -1, 0, -1], [3, 0, 0, -3], [0, 0, 0, 0], [12, 0, 4, -1], [5, -2, -2, -2], [0, 0, 0, 0], [0, -3, -2, -2], [-5, 6, -3, -1], [0, 0, 0, 0], [-6, 3, -2, -4], [2, -1, 1, 1], [0, 0, 0, 0], [5, -2, 2, -3], [-6, 5, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [7, -2, 0, 2], [0, 0, 0, 0], [0, -3, -2, 0], [-3, -2, -2, -3], [0, 0, 0, 0], [2, -1, -2, 3], [-3, 3, 0, 3], [0, 0, 0, 0], [-2, 1, 2, 2], [1, 1, 1, -1], [0, 0, 0, 0], [-7, 6, 0, 5], [-4, -4, 1, 1], [0, 0, 0, 0], [1, -1, 1, -1], [7, 3, 2, 0], [0, 0, 0, 0], [-5, 0, -1, 1], [1, 0, 0, 0], [0, 0, 0, 0], [-6, 3, -3, -3], [2, -1, -2, 0], [0, 0, 0, 0], [4, 3, -1, -3], [0, -2, -1, 2], [0, 0, 0, 0], [-4, 0, -3, 0], [0, -2, 0, 0], [0, 0, 0, 0], [1, 0, 1, 0]]}