# Stored data for newform 8016.2.a.be, downloaded from the LMFDB on 18 April 2024.
{"label": "8016.2.a.be", "space_label": "8016.2.a", "level": 8016, "weight": 2, "hecke_orbit": 31, "hecke_orbit_code": 135107988854677328, "dim": 11, "is_polredabs": true, "trace_hash": 1027342734704812062, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [512, 5280, -2906, -6948, 2246, 2665, -864, -385, 155, 12, -10, 1]], [7, [256, -704, -2096, 3304, 3572, -4561, -692, 800, 46, -49, -1, 1]], [11, [86400, -69984, -101976, 76492, 26456, -19694, -2359, 1865, 84, -73, -1, 1]], [13, [10688, 16160, -19504, -22496, 16124, 8438, -5699, -408, 484, -27, -10, 1]]], "qexp_display": "q+q^{3}+(1-\\beta _{1})q^{5}-\\beta _{3}q^{7}+q^{9}+\\beta _{10}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32064, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 64.00808226025836, "hecke_ring_index": 4, "level_radical": 1002, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [8016, 1, [3007, 2005, 5345, 673], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [2, 3, 167], "conrey_indexes": [1], "field_disc": 35396938584427419364, "field_disc_factorization": [[2, 2], [563, 1], [15718001147614307, 1]], "field_poly": [242, -5687, 292, 6584, 272, -2470, -151, 417, 22, -33, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.157", "prec": 17}, {"__RealLiteral__": 0, "data": "8.557", "prec": 17}, {"__RealLiteral__": 0, "data": "2.939", "prec": 17}, {"__RealLiteral__": 0, "data": "221.826", "prec": 24}, {"__RealLiteral__": 0, "data": "88.697", "prec": 20}, {"__RealLiteral__": 0, "data": "8913.553", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 11, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [167, 1]], "trace_display": [0, 11, 10, 1], "traces": [0, 11, 0, 11, 0, 10, 0, 1, 0, 11, 0, 1, 0, 10, 0, 10, 0, 17, 0, -2, 0, 1, 0, 3, 0, 21, 0, 11, 0, 17, 0, 15, 0, 1, 0, -11, 0, 4, 0, 10, 0, 16, 0, -10, 0, 10, 0, 16, 0, 22, 0, 17, 0, 42, 0, 5, 0, -2, 0, 2, 0, 12, 0, 1, 0, 10, 0, 1, 0, 3, 0, 9, 0, 24, 0, 21, 0, 22, 0, 30, 0, 11, 0, -16, 0, 25, 0, 17, 0, 37, 0, -1, 0, 15, 0, -5, 0, 4, 0, 1, 0, 37, 0, 3, 0, -11, 0, -14, 0, 4, 0, 4, 0, 35, 0, -17, 0, 10, 0, 4, 0, 26, 0, 16, 0, 75, 0, -2, 0, -10, 0, -30, 0, 17, 0, 10, 0, 33, 0, -9, 0, 16, 0, 2, 0, 32, 0, 22, 0, 40, 0, 18, 0, 17, 0, -7, 0, 49, 0, 42, 0, 42, 0, -8, 0, 5, 0, -11, 0, 11, 0, -2, 0, 71, 0, -7, 0, 2, 0, -7, 0, 35, 0, 12, 0, 29, 0, -21, 0, 1, 0, 3, 0, 12, 0, 10, 0, 84, 0, 8, 0, 1, 0, -23, 0, 3, 0, 3, 0, 27, 0, -22, 0, 9, 0, -54, 0, 21, 0, 24, 0, 78, 0, -8, 0, 21, 0, -53, 0, 47, 0, 22, 0, 24, 0, 3, 0, 30, 0, -6, 0, 22, 0, 11, 0, 129, 0, -2, 0, -16, 0, -25, 0, 17, 0, 25, 0, 87, 0, -17, 0, 17, 0, -14, 0, 15, 0, 37, 0, 56, 0, 20, 0, -1, 0, -31, 0, 13, 0, 15, 0, 6, 0, -13, 0, -5, 0, -76, 0, -6, 0, 4, 0, 58, 0, 13, 0, 1, 0, -29, 0, 5, 0, 37, 0, 105, 0, -42, 0, 3, 0, -10, 0, -1, 0, -11, 0, 107, 0, 12, 0, -14, 0, -48, 0, 25, 0, 4, 0, 18, 0, 53, 0, 4, 0, -19, 0, -30, 0, 35, 0, 80, 0, -4, 0, -17, 0, -64, 0, -30, 0, 10, 0, 49, 0, -47, 0, 4, 0, 1, 0, 5, 0, 26, 0, 47, 0, -27, 0, 16, 0, -62, 0, -42, 0, 75, 0, 47, 0, 16, 0, -2, 0, 26, 0, -95, 0, -10, 0, 94, 0, 35, 0, -30, 0, 38, 0, 18, 0, 17, 0, 9, 0, 19, 0, 10, 0, -72, 0, -66, 0, 33, 0, 46, 0, -35, 0, -9, 0, -14, 0, -63, 0, 16, 0, 78, 0, -59, 0, 2, 0, 43, 0, 7, 0, 32, 0, 125, 0, 90, 0, 22, 0, 25, 0, -36, 0, 40, 0, 40, 0, -11, 0, 18, 0, 57, 0, -21, 0, 17, 0, -8, 0, 50, 0, -7, 0, -34, 0, -64, 0, 49, 0, 50, 0, 9, 0, 42, 0, -12, 0, -93, 0, 42, 0, 93, 0, 12, 0, -8, 0, 4, 0, -49, 0, 5, 0, 25, 0, 25, 0, -11, 0, 41, 0, -21, 0, 11, 0, 55, 0, 38, 0, -2, 0, -49, 0, -56, 0, 71, 0, -27, 0, -56, 0, -7, 0, 72, 0, -62, 0, 2, 0, 22, 0, 35, 0, -7, 0, -5, 0, -117, 0, 35, 0, -22, 0, 44, 0, 12, 0, 85, 0, -151, 0, 29, 0, 102, 0, 29, 0, -21, 0, -31, 0, -67, 0, 1, 0, -17, 0, -54, 0, 3, 0, 21, 0, 25, 0, 12, 0, -43, 0, 114, 0, 10, 0, -23, 0, -170, 0, 84, 0, -6, 0, -12, 0, 8, 0, 3, 0, -107, 0, 1, 0, 8, 0, 32, 0, -23, 0, -82, 0, 27, 0, 3, 0, -103, 0, 14, 0, 3, 0, 8, 0, -37, 0, 27, 0, -53, 0, 112, 0, -22, 0, 55, 0, -163, 0, 9, 0, -24, 0, -2, 0, -54, 0, -76, 0, -122, 0, 21, 0, 26, 0, 17, 0, 24, 0, -83, 0, -36, 0, 78, 0, -114, 0, -60, 0, -8, 0, 119, 0, -89, 0, 21, 0, 142, 0, 123, 0, -53, 0, 95, 0, -46, 0, 47, 0, 28, 0, 62, 0, 22, 0, 118, 0, -18, 0, 24, 0, 19, 0, 16, 0, 3, 0, 4, 0, -126, 0, 30, 0, -50, 0, 67, 0, -6, 0, 56, 0, -38, 0, 22, 0, 30, 0, 50, 0, 11, 0, -80, 0, -93, 0, 129, 0, 26, 0, -45, 0, -2, 0, 134, 0, -115, 0, -16, 0, 74, 0, 166, 0, -25, 0, 2, 0, -39, 0, 17, 0, -52, 0, 21, 0, 25, 0, -104, 0, -60, 0, 87, 0, 35, 0, 74, 0, -17, 0, 4, 0, -99, 0, 17, 0, -48, 0, -30, 0, -14, 0, 191, 0, -37, 0, 15, 0, 48, 0, 51, 0, 37, 0, 13, 0, -146, 0, 56, 0, -15, 0, 39, 0, 20, 0, 60, 0, -62, 0, -1, 0, 37, 0, 41, 0, -31, 0, 60, 0, 8, 0, 13, 0, 37, 0, -10, 0, 15, 0, 129, 0, -140, 0, 6, 0, 95, 0, -34, 0, -13, 0, 31, 0, -166, 0, -5, 0, -106, 0, 30, 0, -76, 0, 91, 0, 88, 0, -6, 0, 50, 0, 144, 0, 4, 0, 29, 0, -137, 0, 58, 0, -51, 0, -105, 0, 13, 0, 105, 0, -206, 0, 1, 0, 70, 0, 18, 0, -29, 0, -90, 0, -65, 0, 5, 0, -29, 0, 2, 0, 37, 0, 109, 0, 58, 0, 105, 0, 40, 0, 3, 0, -42, 0, 156, 0, -100, 0, 3, 0, -4, 0, -15, 0, -10, 0, 71, 0, -23, 0, -1, 0, -82, 0, 60, 0, -11, 0, -125, 0, -107, 0, 107, 0, -26, 0, -158, 0, 12, 0, 117, 0, 12, 0, -14, 0, 22, 0, -21, 0, -48, 0, -47, 0, 31, 0, 25, 0, 20, 0, -93, 0, 4, 0, 83, 0, 120, 0, 18, 0, -97, 0, -25, 0, 53, 0, 79, 0, -135, 0, 4, 0, -191, 0, -29, 0, -19, 0, -1, 0, -29, 0, -30, 0, -12, 0, 10, 0, 35, 0, -17, 0, -148, 0, 80, 0, 48, 0, -237, 0, -4, 0, 100, 0, -64, 0, -17, 0, 116, 0, -158, 0, -64, 0, -55, 0, -101, 0, -30, 0, -98, 0, -68, 0, 10, 0, -2, 0, 100, 0, 49, 0, 121, 0, -51, 0, -47, 0, -46, 0, -43, 0, 4, 0, -7, 0, -279, 0, 1, 0, 109, 0, 56, 0, 5, 0, -14, 0, -38, 0, 26, 0, 27, 0, -53, 0, 47, 0, 25, 0, -59, 0, -27, 0, 88, 0, 130, 0, 16, 0, 41, 0, 136, 0, -62, 0, -45, 0, -44, 0, -42, 0, -25, 0, -125, 0, 75, 0, 24, 0, -66, 0, 47, 0, -39, 0, -71, 0, 16, 0, -16, 0, -116, 0, -2, 0, 63, 0, -242, 0, 26, 0, 59, 0, 149, 0, -95, 0, 106, 0, -6, 0, -10, 0, -10, 0, -139, 0, 94, 0, -1, 0, -58, 0, 35, 0, 129, 0, -143, 0, -30, 0, -22, 0, -186, 0, 38, 0, -172, 0, -24, 0, 18, 0, 6, 0, -20, 0, 17, 0, 36, 0, 51, 0, 9, 0, 103, 0, 33, 0, 19, 0, 119, 0, -120, 0, 10, 0, 111, 0, -84, 0, -72, 0, 62, 0, 261, 0, -66, 0, 96, 0, -16, 0, 33, 0, -255, 0, 33, 0, 46, 0, -152, 0, -195, 0, -35, 0, 15, 0, -49, 0, -9, 0, 13, 0, 81, 0, -14, 0, -14, 0, -132, 0, -63, 0, 0, 0, -225, 0, 16, 0, 43, 0, 18, 0, 78, 0, 69, 0, -89, 0, -59, 0, -20, 0, -176, 0, 2, 0, -65, 0, -113, 0, 43, 0, -11, 0, 104, 0, 7, 0, 3, 0, 32, 0, 32, 0, -227, 0, -266, 0, 125, 0, 55, 0, -244, 0, 90, 0, 43, 0, -56, 0, 22, 0, 56, 0, -335, 0, 25, 0, -54, 0, -69, 0, -36, 0, 24, 0, 47, 0, 40, 0, 88, 0, 136, 0, 40, 0, 11, 0, 146, 0, -11, 0, -22, 0, -4, 0, 18, 0, -14, 0, 46, 0, 57, 0, -117, 0, 57, 0, -21, 0, -24, 0, -109, 0, 17, 0, -159, 0, -32, 0, -8, 0, -112, 0, 43, 0, 50, 0, 113, 0, -30, 0, -7, 0, 102, 0, 16, 0, -34, 0, -43, 0, -47, 0, -64, 0, 63, 0, 47, 0, 49, 0, -12, 0, -45, 0, 50, 0, 5, 0, 38, 0, 9, 0, -140, 0, -153, 0, 42, 0, -52, 0, -269, 0, -12, 0, -5, 0, 173, 0, -93, 0, 103, 0, -40, 0, 42, 0, 43, 0, 62, 0, 93, 0, 13, 0, -117, 0, 12, 0, 200, 0, -307, 0, -8, 0, -16, 0, 148, 0, 4, 0, 26, 0, -133, 0, -49, 0, 22, 0, -129, 0, 5, 0, -172, 0, 117, 0, 25, 0, 71, 0, -87, 0, 25, 0, 29, 0, -256, 0, -11, 0, 56, 0, -247, 0, 41, 0, 152, 0, 160, 0, -21, 0, 75, 0, 35, 0, 11, 0, -11, 0, 75, 0, 55, 0, -59, 0, -32, 0, 38, 0, -31, 0, 167, 0, -2, 0, -103, 0, -38, 0, -49, 0, -103, 0, -98, 0, -56, 0, -10, 0, -11, 0, 71, 0, -64, 0, -111, 0, -27, 0, 25, 0, -64, 0, -56, 0, -55, 0, 71, 0, -7, 0, -165, 0, -117, 0, 72, 0, 203, 0, 234, 0, -62, 0, 30, 0, 232, 0, 2, 0, -91, 0, -66, 0, 22, 0, 44, 0, -198, 0, 35, 0, 0, 0, -100, 0, -7, 0, -75, 0, -295, 0, -5, 0, 20, 0, 7, 0, -117, 0, -26, 0, -179, 0, 35, 0, 13, 0, -14, 0, -22, 0, 19, 0, -90, 0, 44, 0, 183, 0, -129, 0, 12, 0, -19, 0, -145, 0, 85, 0, 50, 0, 68, 0, -151, 0, -122, 0, 113, 0, 29, 0, -155, 0, -116, 0, 102, 0, -198, 0, -105, 0, 29, 0, -80, 0, -91, 0, -21, 0, -140, 0, -54, 0, -31, 0, -164, 0, -29, 0, -67, 0, 28, 0, -121, 0, 1, 0, -26, 0, 192, 0, -17, 0, -8, 0, -17, 0, -54, 0, 4, 0, -86, 0, 3, 0, -130, 0, -83, 0, 21, 0, -208, 0, 172, 0, 25, 0, 40, 0, 72, 0, 12, 0, -4, 0, 42, 0, -43, 0, -214, 0, -177, 0, 114, 0, 151, 0, -21, 0, 10, 0, 32, 0, 47, 0, -23, 0, -17, 0, -12, 0, -170, 0, 61, 0, 108, 0, 84, 0, -40, 0, 22, 0, -6, 0, -73, 0, -23, 0, -12, 0, -4, 0, -242, 0, 8, 0, -163, 0, -129, 0, 3, 0, 35, 0, -185, 0, -107, 0, -116, 0, -35, 0, 1, 0, -171, 0, -26, 0, 8, 0, -29, 0, -96, 0, 32, 0, 68, 0, 59, 0, -23, 0, -95, 0, 23, 0, -82, 0, -37, 0, -1, 0, 27, 0, 75, 0, -11, 0, 3, 0, -124, 0, 15, 0, -103, 0, -160, 0, -274, 0, 14, 0, 98, 0, -141, 0, 3, 0, -296, 0, -79, 0, 8, 0, 210, 0, 213, 0, -37, 0, 23, 0, 72, 0, 27, 0, 66, 0, -148, 0, -53, 0, -61, 0, 2, 0, 112, 0, 191, 0, -111, 0, -22, 0, 8, 0, -134, 0, 55, 0, -239, 0, 3, 0, -163, 0, -97, 0, -37, 0, 9, 0, 1, 0, 159, 0, -24, 0, -332, 0, -130, 0, -2, 0, 9, 0, -201, 0, -54, 0, 28, 0, -139, 0, -76, 0, 123, 0, 227, 0, -122, 0, 71, 0, 236, 0, 21, 0, -213, 0, -15, 0, 26, 0, -215, 0, -93, 0, 17, 0, -54, 0, -212, 0, 24, 0, -2, 0, 59, 0, -83, 0, -40, 0, -253, 0, -36, 0, 67, 0, -284, 0, 78, 0, 75, 0, 206, 0, -114, 0, -45, 0, -168, 0, -60, 0, 39, 0, -32, 0, -8, 0, -208, 0, -10, 0, 119, 0, 206, 0, 187, 0, -89, 0, -50, 0, 39, 0, 21, 0, -249, 0, -21, 0, 142, 0, -104, 0, -187, 0, 123, 0, 19, 0, -14, 0, -53, 0, -99, 0, -173, 0, 95, 0, -5, 0, 53, 0, -46, 0, 78, 0, 43, 0, 47, 0, 48, 0, 280, 0, 28, 0, 134, 0, -15, 0, 62, 0, -211, 0, -58, 0, 22, 0, -140, 0, -155, 0, 118, 0, 45, 0, 100, 0, -18, 0, -26, 0, 39, 0, 24, 0, -69, 0, -91, 0, 19, 0, -256, 0, -328, 0, 16, 0, -32, 0, 82, 0, 3, 0, 171, 0, -70, 0, 4, 0, 128, 0, 154, 0, -126, 0, -57, 0, -186, 0, 30, 0, -93, 0, 49, 0, -50, 0, -160, 0, -35, 0, 67, 0, -2, 0, -9, 0, -6, 0, -45, 0, -117, 0, 56, 0, -111, 0, 337, 0, -38, 0, -19, 0, 58, 0, 22, 0, -10, 0, 49, 0, 30, 0, 17, 0, -78, 0, 50, 0, 155, 0, 79, 0, 11, 0, -13, 0, 59, 0, -80, 0, -197, 0, 98, 0, -93, 0, -47, 0, 77, 0, 129, 0, -173, 0, 159, 0, 26, 0, -102, 0, 1, 0, -45, 0, -200, 0, -274, 0, -2, 0, 43, 0, -346, 0, 134, 0, 61, 0, 136, 0, -115, 0, -65, 0, -213, 0, -16, 0, -38, 0, -45, 0, 74, 0, -88, 0, 69, 0, 166, 0, 250, 0, -1, 0, -25, 0, 33, 0, -41, 0, 2, 0, -20, 0, -156, 0, -39, 0, 142, 0, 175, 0, 17, 0, -30, 0, 63, 0, -52, 0, 40, 0, -187, 0, 21, 0, -167, 0, 66, 0, 25, 0, -1, 0, -335, 0, -104, 0, 192, 0, 84, 0, -60, 0, 80, 0, 358, 0, 87, 0, 47, 0, -126, 0, 35, 0, 188, 0, -147, 0, 74, 0, -365, 0, 170, 0, -17, 0, -289, 0, -183, 0, 4, 0, 152, 0, 73, 0, -99, 0, -106, 0, -128, 0, 17, 0, 19, 0, 83, 0, -48, 0, 80, 0, -43, 0, -30, 0, 38, 0, -167, 0, -14, 0, -55, 0, -115, 0, 191, 0, -31, 0, 289, 0, -37, 0, 26, 0, -68, 0, 15, 0, -343, 0, -179, 0, 48, 0, 9, 0, -178, 0, 51, 0, 228, 0, 75, 0, 37, 0, 2, 0, -200, 0, 13, 0, -105, 0, 46, 0, -146, 0, -3, 0, -47, 0, 56, 0, 50, 0, 49, 0, -15, 0, 210, 0, 180, 0, 39, 0, -72, 0, -143, 0, 20, 0, -69, 0, 116, 0, 60, 0, -179, 0, 319, 0, -62, 0, -22, 0, 34, 0, -1, 0, -98, 0, -152, 0, 37, 0, -32, 0, -293, 0, 41, 0, -77, 0, -71, 0, -31, 0, -8, 0, -142, 0, 60, 0, -139, 0, 182, 0, 8, 0, 255, 0, 75, 0, 13, 0, -145, 0, 276, 0, 37, 0, -99, 0, 17, 0, -10, 0, 107, 0, 60, 0, 15, 0, -295, 0, -25, 0, 129, 0, -197, 0, -4, 0, -140, 0, -90, 0, -88, 0, 6, 0, 21, 0, 67, 0, 95, 0, -100, 0, 50, 0, -34, 0, 286, 0, 11, 0, -13, 0, 100, 0, 198, 0, 31, 0, 191, 0, -192, 0, -166, 0, 282, 0, 208, 0, -5, 0, -122, 0, 174, 0, -106, 0, 66, 0, -145, 0, 30, 0, 113, 0, 83, 0, -76, 0, -632, 0, -227, 0, 91, 0, 17, 0, 218, 0, 88, 0, 156, 0, 180, 0, -6, 0, -55, 0, -108, 0, 50, 0, 16, 0, 152, 0, 144, 0, -308, 0, -23, 0, 4, 0, -309, 0, -165, 0, 29, 0, -211, 0, 104, 0, -137, 0, 6, 0, 344, 0, 58, 0, 196, 0, -155, 0, -51, 0, -335, 0, -19, 0, -105, 0, -51, 0, -262, 0, 13, 0, -1, 0, -127, 0, 105, 0, -147, 0, 22, 0, -206, 0, -127, 0, 81, 0, 1, 0, 204, 0, 59, 0, 70, 0, 148, 0, -39, 0, 18, 0, 136, 0, 50, 0, -29, 0, 169, 0, -123, 0, -90, 0, 51, 0, 121, 0, -65, 0, 9, 0, 128, 0, 5, 0, 204, 0, 56, 0, -29, 0, -45, 0, -196, 0, 2, 0, 394, 0, -40, 0, 37, 0, 7, 0, 279, 0, 109, 0, 143, 0, 48, 0, 58, 0, 47, 0, 99, 0, 105, 0, -136, 0, -148, 0, 40, 0, 1, 0, -15, 0, 3, 0, 223, 0, -129, 0, -42, 0, -592, 0, -55, 0, 156, 0, -115, 0, 5, 0, -100, 0, 0, 0, 0, 0, 3, 0, -185, 0, 388, 0, -4, 0, 65, 0, 284, 0, -15, 0, 307, 0, 5, 0, -10, 0, -273, 0, 94, 0, 71, 0, 46, 0, 1, 0, -23, 0, -64, 0, 219, 0, -1, 0, -19, 0, -303, 0, -82, 0, 159, 0, -240, 0, 60, 0, 345, 0, 199, 0, -11, 0, -113, 0, -17, 0, -125, 0, 293, 0, -189, 0, -107, 0, 392, 0, 278, 0, 107, 0, -71, 0, 98, 0, -26, 0, -214, 0, -144, 0, -158, 0, -110, 0, -63, 0, 12, 0, 57, 0, 40, 0, 117, 0, 37, 0, 139, 0, 12, 0, -163, 0, -162, 0, -14, 0, 152, 0, -141, 0, 22, 0, -79, 0, -138, 0, -21, 0, -13, 0, -120, 0, -48, 0, 77, 0, -117, 0, -47, 0, 87, 0, 37, 0, 31, 0, -2, 0, 88, 0, 25, 0, 181, 0, 222, 0, 20, 0, 92, 0, 238, 0, -93, 0, -137, 0, -43, 0, 4, 0, -234, 0, -16, 0, 83, 0, -226, 0, 190, 0, 120, 0, 14, 0, 25, 0, 18, 0, 208, 0, 186, 0, -97, 0, -190, 0, 139, 0, -25, 0, 63, 0, 83, 0, 53, 0, 150, 0, 157, 0, 79, 0, 46, 0, 274, 0, -135, 0, 6, 0, -230, 0, 4, 0, 102, 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": "4008.2.a.k", "char_is_minimal": false, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -3, 0, 0, 2, 0, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, 0, 0, -1, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -2, 0, -1, 0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 2, -2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 1, 0, 2, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 1, 1, 1, -1, 0, -1, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, -1, 3, 1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, 1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -1, 0, -1, -2, -1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 0, -1, -1, -1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 1, 0, 1, -2, 0, -1, -2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 1, 0, 1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 2, -1, 0, 3, -2, 0, -2, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 2, 1, 1, 0, 2, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 1, 0, -2, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -2, 2, 0, 2, 2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, -1, -1, 2, 3, 1, 2, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 0, -1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 1, 1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 1, 2, -2, 0, -1, 0, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, -1, 0, 0, -3, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}