# Stored data for newform 8004.2.a.k, downloaded from the LMFDB on 25 April 2024.
{"label": "8004.2.a.k", "space_label": "8004.2.a", "level": 8004, "weight": 2, "hecke_orbit": 11, "hecke_orbit_code": 45035996307267396, "dim": 18, "is_polredabs": true, "trace_hash": 1848701870059445286, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-115488, 1509552, -5659296, 5001480, 4260960, -6184176, -855636, 2789438, -114554, -655793, 76571, 88434, -13745, -6888, 1222, 288, -55, -5, 1]], [7, [2162624, -10553984, 2287648, 34280000, -4020656, -31927888, 2685216, 12561120, -1269308, -2471372, 299782, 264892, -36453, -15706, 2356, 483, -77, -6, 1]]], "qexp_display": "q+q^{3}+\\beta _{1}q^{5}+\\beta _{7}q^{7}+q^{9}-\\beta _{9}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32016, "fricke_eigenval": -1, "atkin_lehner_string": "--+-", "analytic_conductor": 63.91226177783282, "hecke_ring_index": 12, "level_radical": 4002, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [8004, 1, [4003, 2669, 3133, 553], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 1, "level_primes": [2, 3, 23, 29], "conrey_indexes": [1], "field_disc": 11061409516040928214855341962673268602580992, "field_disc_factorization": [[2, 12], [3, 6], [479, 1], [2926291, 1], [35998649, 1], [73414824921839144383, 1]], "field_poly": [-115488, 1509552, -5659296, 5001480, 4260960, -6184176, -855636, 2789438, -114554, -655793, 76571, 88434, -13745, -6888, 1222, 288, -55, -5, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.210", "prec": 17}, {"__RealLiteral__": 0, "data": "14.437", "prec": 20}, {"__RealLiteral__": 0, "data": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "648.834", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "49795.115", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 18, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [23, 1], [29, -1]], "trace_display": [0, 18, 5, 6], "traces": [0, 18, 0, 18, 0, 5, 0, 6, 0, 18, 0, 5, 0, 6, 0, 5, 0, 7, 0, 15, 0, 6, 0, -18, 0, 45, 0, 18, 0, 18, 0, 10, 0, 5, 0, -7, 0, 22, 0, 6, 0, 17, 0, 25, 0, 5, 0, -6, 0, 64, 0, 7, 0, 21, 0, 3, 0, 15, 0, 6, 0, 7, 0, 6, 0, 44, 0, 35, 0, -18, 0, 1, 0, 27, 0, 45, 0, 4, 0, 0, 0, 18, 0, 13, 0, 24, 0, 18, 0, 30, 0, 53, 0, 10, 0, 17, 0, 27, 0, 5, 0, 15, 0, 44, 0, -7, 0, 39, 0, 43, 0, 22, 0, 28, 0, -5, 0, 6, 0, -25, 0, 87, 0, 17, 0, 36, 0, -11, 0, 25, 0, 23, 0, 9, 0, 5, 0, 13, 0, 12, 0, -6, 0, 50, 0, 5, 0, 64, 0, 50, 0, 7, 0, 7, 0, 78, 0, 36, 0, 21, 0, -6, 0, 62, 0, 3, 0, -3, 0, 72, 0, 15, 0, -19, 0, -5, 0, 6, 0, 9, 0, 52, 0, 7, 0, -18, 0, 69, 0, 6, 0, -16, 0, 23, 0, 44, 0, -17, 0, 0, 0, 35, 0, 6, 0, 54, 0, -18, 0, 30, 0, 23, 0, 1, 0, 1, 0, -14, 0, 27, 0, 53, 0, 82, 0, 45, 0, 34, 0, 15, 0, 4, 0, 14, 0, 14, 0, 0, 0, 24, 0, 53, 0, 18, 0, 59, 0, 45, 0, 13, 0, 0, 0, -5, 0, 24, 0, -37, 0, 69, 0, 18, 0, 3, 0, 44, 0, 30, 0, 10, 0, -2, 0, 53, 0, -27, 0, -34, 0, 10, 0, 80, 0, 41, 0, 17, 0, -13, 0, 37, 0, 27, 0, -38, 0, 84, 0, 5, 0, -6, 0, 10, 0, 15, 0, 52, 0, 38, 0, 44, 0, -73, 0, 27, 0, -7, 0, 3, 0, 5, 0, 39, 0, -68, 0, 2, 0, 43, 0, -19, 0, 36, 0, 22, 0, -120, 0, 41, 0, 28, 0, 55, 0, 69, 0, -5, 0, -65, 0, -3, 0, 6, 0, 1, 0, 38, 0, -25, 0, -33, 0, 179, 0, 87, 0, 24, 0, 82, 0, 17, 0, -74, 0, 10, 0, 36, 0, 6, 0, 128, 0, -11, 0, 7, 0, 129, 0, 25, 0, 4, 0, -7, 0, 23, 0, -28, 0, 132, 0, 9, 0, 15, 0, -1, 0, 5, 0, -93, 0, -4, 0, 13, 0, 20, 0, -25, 0, 12, 0, 34, 0, 77, 0, -6, 0, -36, 0, -18, 0, 50, 0, -38, 0, 52, 0, 5, 0, -15, 0, 54, 0, 64, 0, 31, 0, -34, 0, 50, 0, 59, 0, -18, 0, 7, 0, 16, 0, 119, 0, 7, 0, -57, 0, -28, 0, 78, 0, -93, 0, 131, 0, 36, 0, -132, 0, 46, 0, 21, 0, -3, 0, -43, 0, -6, 0, 144, 0, -37, 0, 62, 0, -27, 0, 7, 0, 3, 0, 16, 0, 107, 0, -3, 0, 4, 0, 128, 0, 72, 0, -90, 0, 121, 0, 15, 0, -38, 0, 39, 0, -19, 0, 5, 0, 38, 0, -5, 0, -106, 0, 18, 0, 6, 0, -70, 0, 7, 0, 9, 0, -18, 0, -4, 0, 52, 0, -41, 0, -43, 0, 7, 0, 15, 0, 52, 0, -18, 0, 92, 0, -25, 0, 69, 0, -18, 0, -122, 0, 6, 0, -21, 0, 78, 0, -16, 0, -45, 0, 55, 0, 23, 0, 33, 0, -51, 0, 44, 0, -79, 0, 60, 0, -17, 0, -26, 0, 133, 0, 0, 0, -109, 0, 92, 0, 35, 0, -98, 0, -37, 0, 6, 0, -7, 0, -21, 0, 54, 0, 13, 0, 79, 0, -18, 0, -101, 0, -48, 0, 30, 0, -87, 0, 14, 0, 23, 0, -142, 0, 69, 0, 1, 0, -87, 0, 92, 0, 1, 0, -216, 0, 26, 0, -14, 0, -30, 0, 46, 0, 27, 0, 96, 0, -26, 0, 53, 0, -289, 0, -18, 0, 82, 0, -153, 0, 166, 0, 45, 0, 38, 0, -74, 0, 34, 0, -151, 0, 31, 0, 15, 0, 59, 0, 103, 0, 4, 0, -184, 0, -99, 0, 14, 0, 28, 0, 10, 0, 14, 0, -89, 0, 126, 0, 0, 0, -10, 0, 65, 0, 24, 0, -133, 0, -38, 0, 53, 0, 45, 0, 76, 0, 18, 0, 77, 0, -37, 0, 59, 0, 21, 0, -123, 0, 45, 0, -81, 0, 215, 0, 13, 0, -80, 0, -78, 0, 0, 0, -165, 0, 6, 0, -5, 0, 81, 0, -150, 0, 24, 0, -112, 0, 19, 0, -37, 0, 5, 0, -50, 0, 69, 0, -79, 0, 31, 0, 18, 0, 13, 0, -35, 0, 3, 0, -126, 0, 21, 0, 44, 0, 106, 0, 85, 0, 30, 0, -71, 0, 7, 0, 10, 0, -69, 0, 27, 0, -2, 0, -151, 0, 141, 0, 53, 0, -40, 0, -56, 0, -27, 0, 140, 0, -42, 0, -34, 0, 0, 0, -117, 0, 10, 0, -122, 0, 18, 0, 80, 0, 36, 0, 90, 0, 41, 0, -22, 0, 92, 0, 17, 0, 8, 0, 40, 0, -13, 0, -219, 0, -18, 0, 37, 0, 55, 0, 11, 0, 27, 0, -159, 0, -7, 0, -38, 0, -134, 0, 13, 0, 84, 0, -18, 0, 187, 0, 5, 0, -77, 0, -196, 0, -6, 0, 10, 0, -134, 0, 10, 0, 89, 0, 147, 0, 15, 0, -86, 0, 16, 0, 52, 0, -19, 0, 78, 0, 38, 0, -115, 0, 36, 0, 44, 0, -23, 0, 124, 0, -73, 0, -47, 0, 32, 0, 27, 0, -15, 0, -17, 0, -7, 0, -94, 0, 141, 0, 3, 0, 30, 0, -116, 0, 5, 0, -155, 0, 218, 0, 39, 0, 103, 0, -6, 0, -68, 0, -64, 0, -231, 0, 2, 0, 122, 0, 37, 0, 43, 0, -185, 0, 2, 0, -19, 0, -25, 0, 60, 0, 36, 0, -145, 0, -27, 0, 22, 0, -25, 0, -156, 0, -120, 0, -7, 0, -95, 0, 41, 0, -218, 0, -7, 0, 28, 0, -83, 0, 203, 0, 55, 0, -116, 0, 107, 0, 69, 0, -143, 0, -18, 0, -5, 0, 116, 0, -52, 0, -65, 0, -129, 0, -263, 0, -3, 0, 34, 0, 89, 0, 6, 0, -217, 0, 275, 0, 1, 0, -146, 0, -101, 0, 38, 0, -230, 0, -64, 0, -25, 0, 22, 0, 180, 0, -33, 0, -1, 0, 6, 0, 179, 0, -115, 0, -107, 0, 87, 0, -45, 0, 56, 0, 24, 0, -10, 0, -37, 0, 82, 0, -125, 0, 14, 0, 17, 0, 74, 0, -263, 0, -74, 0, -132, 0, -178, 0, 10, 0, 48, 0, 66, 0, 36, 0, -64, 0, -57, 0, 6, 0, -2, 0, -192, 0, 128, 0, 23, 0, -112, 0, -11, 0, 220, 0, 163, 0, 7, 0, -116, 0, -30, 0, 129, 0, -133, 0, 7, 0, 25, 0, -172, 0, 198, 0, 4, 0, -102, 0, -31, 0, -7, 0, -98, 0, -85, 0, 23, 0, 85, 0, -255, 0, -28, 0, -82, 0, 17, 0, 132, 0, -16, 0, 325, 0, 9, 0, -335, 0, 33, 0, 15, 0, -3, 0, 134, 0, -1, 0, -56, 0, 14, 0, 5, 0, 85, 0, -21, 0, -93, 0, -108, 0, 280, 0, -4, 0, 65, 0, -73, 0, 13, 0, -240, 0, 31, 0, 20, 0, 25, 0, -366, 0, -25, 0, 25, 0, -74, 0, 12, 0, 216, 0, 8, 0, 34, 0, -57, 0, -102, 0, 77, 0, -3, 0, 189, 0, -6, 0, -54, 0, -90, 0, -36, 0, -92, 0, -60, 0, -18, 0, 102, 0, 166, 0, 50, 0, -60, 0, -57, 0, -38, 0, -500, 0, 101, 0, 52, 0, -183, 0, 24, 0, 5, 0, 34, 0, 20, 0, -15, 0, 65, 0, -272, 0, 54, 0, -192, 0, 162, 0, 64, 0, 94, 0, 58, 0, 31, 0, -30, 0, 7, 0, -34, 0, -228, 0, -16, 0, 50, 0, -442, 0, 210, 0, 59, 0, 303, 0, 2, 0, -18, 0, -113, 0, -6, 0, 7, 0, -254, 0, -6, 0, 16, 0, -151, 0, 286, 0, 119, 0, -15, 0, 159, 0, 7, 0, 73, 0, -24, 0, -57, 0, -33, 0, -51, 0, -28, 0, -106, 0, -103, 0, 78, 0, -25, 0, 178, 0, -93, 0, -7, 0, 113, 0, 131, 0, 106, 0, -28, 0, 36, 0, -286, 0, -72, 0, -132, 0, 64, 0, -99, 0, 46, 0, -90, 0, 139, 0, 21, 0, -140, 0, -221, 0, -3, 0, -172, 0, 76, 0, -43, 0, -87, 0, 147, 0, -6, 0, -150, 0, -135, 0, 144, 0, 283, 0, 28, 0, -37, 0, -265, 0, 141, 0, 62, 0, -192, 0, -91, 0, -27, 0, -228, 0, -177, 0, 7, 0, 7, 0, 38, 0, 3, 0, 47, 0, 82, 0, 16, 0, -82, 0, -44, 0, 107, 0, -57, 0, 318, 0, -3, 0, -248, 0, 107, 0, 4, 0, -336, 0, 255, 0, 128, 0, 204, 0, -243, 0, 72, 0, -78, 0, -305, 0, -90, 0, 100, 0, -132, 0, 121, 0, -305, 0, 21, 0, 15, 0, -35, 0, 268, 0, -38, 0, -107, 0, -33, 0, 39, 0, -123, 0, 95, 0, -19, 0, -37, 0, 34, 0, 5, 0, -205, 0, -83, 0, 38, 0, -138, 0, -7, 0, -5, 0, -233, 0, 47, 0, -106, 0, -198, 0, -106, 0, 18, 0, 81, 0, -165, 0, 6, 0, 3, 0, -85, 0, -70, 0, 207, 0, -61, 0, 7, 0, -61, 0, 130, 0, 9, 0, -40, 0, -108, 0, -18, 0, -125, 0, 103, 0, -4, 0, 100, 0, 149, 0, 52, 0, -347, 0, -1, 0, -41, 0, 19, 0, -1, 0, -43, 0, -187, 0, 63, 0, 7, 0, -46, 0, -41, 0, 15, 0, -2, 0, -157, 0, 52, 0, 230, 0, -351, 0, -18, 0, 5, 0, -144, 0, 92, 0, -18, 0, -126, 0, -25, 0, -27, 0, 257, 0, 69, 0, 121, 0, 7, 0, -18, 0, -463, 0, -132, 0, -122, 0, 158, 0, 107, 0, 6, 0, -322, 0, -404, 0, -21, 0, -154, 0, 6, 0, 78, 0, -384, 0, 445, 0, -16, 0, -135, 0, 18, 0, -45, 0, -21, 0, -222, 0, 55, 0, 41, 0, -144, 0, 23, 0, -194, 0, -41, 0, 33, 0, 106, 0, 218, 0, -51, 0, -374, 0, 25, 0, 44, 0, -262, 0, -160, 0, -79, 0, -271, 0, -193, 0, 60, 0, 7, 0, -4, 0, -17, 0, -91, 0, 311, 0, -26, 0, -4, 0, -252, 0, 133, 0, -81, 0, 219, 0, 0, 0, 80, 0, -300, 0, -109, 0, -173, 0, -396, 0, 92, 0, 296, 0, -276, 0, 35, 0, -180, 0, 1, 0, -98, 0, 0, 0, -167, 0, -37, 0, -225, 0, 73, 0, 6, 0, -10, 0, -281, 0, -7, 0, 101, 0, -19, 0, -21, 0, 46, 0, -161, 0, 54, 0, -161, 0, 289, 0, 13, 0, -153, 0, -207, 0, 79, 0, -183, 0, -1, 0, -18, 0, -17, 0, -126, 0, -101, 0, -252, 0, -248, 0, -48, 0, 172, 0, -125, 0, 30, 0, -326, 0, 44, 0, -87, 0, -170, 0, 25, 0, 14, 0, -303, 0, 205, 0, 23, 0, 175, 0, 164, 0, -142, 0, -242, 0, -13, 0, 69, 0, -251, 0, -93, 0, 1, 0, 138, 0, 56, 0, -87, 0, 18, 0, -126, 0, 92, 0, 90, 0, -167, 0, 1, 0, -98, 0, -471, 0, -216, 0, 35, 0, -365, 0, 26, 0, 250, 0, 223, 0, -14, 0, -24, 0, 44, 0, -30, 0, 134, 0, -71, 0, 46, 0, -308, 0, 73, 0, 27, 0, -157, 0, -170, 0, 96, 0, 42, 0, -286, 0, -26, 0, 71, 0, 57, 0, 53, 0, -477, 0, 308, 0, -289, 0, 161, 0, -419, 0, -18, 0, 134, 0, -321, 0, 82, 0, 482, 0, -44, 0, -153, 0, -584, 0, 170, 0, 166, 0, 70, 0, 188, 0, 45, 0, -227, 0, -19, 0, 38, 0, -123, 0, 7, 0, -74, 0, -122, 0, 122, 0, 34, 0, 234, 0, -30, 0, -151, 0, 103, 0, -132, 0, 31, 0, -112, 0, 1, 0, 15, 0, -346, 0, 398, 0, 59, 0, 139, 0, -132, 0, 103, 0, 15, 0, -324, 0, 4, 0, 165, 0, -102, 0, -184, 0, 34, 0, -149, 0, -99, 0, -53, 0, 245, 0, 14, 0, 59, 0, 68, 0, 28, 0, -199, 0, -52, 0, 10, 0, -160, 0, -111, 0, 14, 0, 27, 0, -105, 0, -89, 0, -373, 0, -20, 0, 126, 0, -158, 0, 14, 0, 0, 0, 186, 0, 219, 0, -10, 0, 8, 0, -214, 0, 65, 0, -55, 0, 59, 0, 24, 0, 137, 0, -323, 0, -133, 0, -107, 0, 214, 0, -38, 0, -85, 0, -109, 0, 53, 0, -148, 0, -21, 0, 45, 0, 339, 0, 42, 0, 76, 0, -80, 0, -17, 0, 18, 0, 90, 0, -171, 0, 77, 0, 6, 0, 69, 0, -37, 0, 17, 0, 44, 0, 59, 0, 28, 0, -6, 0, 21, 0, 71, 0, -571, 0, -123, 0, 166, 0, -350, 0, 45, 0, 45, 0, -95, 0, -81, 0, -27, 0, 4, 0, 215, 0, -23, 0, -20, 0, 13, 0, -105, 0, 68, 0, -80, 0, 482, 0, 21, 0, -78, 0, -455, 0, -117, 0, 0, 0, -262, 0, -338, 0, -165, 0, -6, 0, 252, 0, 6, 0, -67, 0, 90, 0, -5, 0, -212, 0, -304, 0, 81, 0, -164, 0, 136, 0, -150, 0, 0, 0, -149, 0, 24, 0, 331, 0, 413, 0, -112, 0, -346, 0, -534, 0, 19, 0, 308, 0, 237, 0, -37, 0, 98, 0, -76, 0, 5, 0, 34, 0, -15, 0, -50, 0, 229, 0, 248, 0, 69, 0, -166, 0, 61, 0, -79, 0, -54, 0, 153, 0, 31, 0, 71, 0, -148, 0, 18, 0, -160, 0, -442, 0, 13, 0, 396, 0, -353, 0, -35, 0, -103, 0, -272, 0, 3, 0, -44, 0, 204, 0, -126, 0, -134, 0, 24, 0, 21, 0, -31, 0, 35, 0, 44, 0, 231, 0, -126, 0, 106, 0, 155, 0, -59, 0, 85, 0, -200, 0, 118, 0, 30, 0, -615, 0, 13, 0, -71, 0, -294, 0, 125, 0, 7, 0, 8, 0, 116, 0, 10, 0, -143, 0, -28, 0, -69, 0, 220, 0, -328, 0, 27, 0, 24, 0, -32, 0, -2, 0, -26, 0, 240, 0, -151, 0, -160, 0, 94, 0, 141, 0, -16, 0, 186, 0, 53, 0, -365, 0, -39, 0, -40, 0, 24, 0, 240, 0, -56, 0, 258, 0, 226, 0, -27, 0, -59, 0, -241, 0, 140, 0, 164, 0, -208, 0, -42, 0, 458, 0, -448, 0, -34, 0, -123, 0, -256, 0, 0, 0, 38, 0, -282, 0, -117, 0, -43, 0, 50, 0, 10, 0, -45, 0, -138, 0, -122, 0, -310, 0, 30, 0, 18, 0, 332, 0, -195, 0, 80, 0, 156, 0, -376, 0, 36, 0, -232, 0, 18, 0, 90, 0, -342, 0, 411, 0, 41, 0, 147, 0, 18, 0, -22, 0, -181, 0, -125, 0, 92, 0, 91, 0, 94, 0, 17, 0, -10, 0, -126, 0, 8, 0, -36, 0, -23, 0, 40, 0, -69, 0, 30, 0, -13, 0, -205, 0, 507, 0, -219, 0, -181, 0, -67, 0, -18, 0, 231, 0, -28, 0, 37, 0, -435, 0, 186, 0, 55, 0, 117, 0, -159, 0, 11, 0, -266, 0, 557, 0, 27, 0, 9, 0, -1, 0, -159, 0, -69, 0, -572, 0, -7, 0, -9, 0, -577, 0, -38, 0, 53, 0, -281, 0, -134, 0, 5, 0, 257, 0, 13, 0, -8, 0, -376, 0, 84, 0, 334, 0, 190, 0, -18, 0, 80, 0, -244, 0, 187, 0, -36, 0, -109, 0, 5, 0, 60, 0, 26, 0, -77, 0, 31, 0, -67, 0, -196, 0, 2, 0, 238, 0, -6, 0, -150, 0, -373, 0, 10, 0, 223, 0, -200, 0, -134, 0, 312, 0, 343, 0, 10, 0, -162, 0, -100, 0, 89, 0, 173, 0, -138, 0, 147, 0, -414, 0, 426, 0, 15, 0, 148, 0, 378, 0, -86, 0, -536, 0, 25, 0, 16, 0, 118, 0, 13, 0, 52, 0, 251, 0, 96, 0, -19, 0, -439, 0, 17, 0, 78, 0, 181, 0, 445, 0, 38, 0, 57, 0, -200, 0, -115, 0, 261, 0, -344, 0, 36, 0, 406, 0, 10, 0, 44, 0, -87, 0, -246, 0, -23, 0, 237, 0, 154, 0, 124, 0, -307, 0, -32, 0, -73, 0, 45, 0, 61, 0, -47, 0, -334, 0, -135, 0, 32, 0, 27, 0, 69, 0, 27, 0, -59, 0, 594, 0, -15, 0, 22, 0, -87, 0, -17, 0, 196, 0, -259, 0, -7, 0, 357, 0, -87, 0, -94, 0, 132, 0, -321, 0, 141, 0, 667, 0, 364, 0, 3, 0, -160, 0, 285, 0, 30, 0, 142, 0, 43, 0, -116, 0, 180, 0, -225, 0, 5, 0, -227, 0, -36, 0, -155, 0, 71, 0, -125, 0, 218, 0, 271, 0, 208, 0, 39, 0, 82, 0, 58, 0, 103, 0, 39, 0, -228, 0, -6, 0, -74, 0, -354, 0, -68, 0, 250, 0, -302, 0, -64, 0, 616, 0, -260, 0, -231, 0, 11, 0, 127, 0, 2, 0, 116, 0, 15, 0, 122, 0, -201, 0, 151, 0, 37, 0, 205, 0, 408, 0, 43, 0, 238, 0, 112, 0, -185, 0, -484, 0, 208, 0, 2, 0, -121, 0, 41, 0, -19, 0, 159, 0, 71, 0, -25, 0, 152, 0, 33, 0, 60, 0, -7, 0, 134, 0, 36, 0, 7, 0, -410, 0, -145, 0, 44, 0, -411, 0, -27, 0, 202, 0, 389, 0, 22, 0, 158, 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": "8004.2.a.k", "char_is_minimal": true, "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, 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, 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, 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, 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], [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, 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, 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, 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, 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], [1, 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], [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], [-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, 0, 0, 0, 0], [3, 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, 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, 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, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, -1, 0, -1, 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, -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, 1, 0, 1, 0, 1, -1, 2, 0, 1, 0, 1, -1, -1, 1, -1, -1, -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, 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, 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, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 1, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0, 1, -1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -2, 0, -1, 1, 0, 1, -1, 1, 2, -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, 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], [0, 1, -1, 0, 0, 0, 1, 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, -1, 0, 0, -1, 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, 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], [2, -1, -1, -1, 0, -1, 2, -1, 1, -1, -1, 0, 0, 1, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, -1, 1, 1, -1, 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, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, 0, 0, -1, 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, -1, 0, 1, 0, 1, 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], [3, 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, 0, 0], [-1, 1, 0, 0, -1, 0, 0, 0, 0, -2, 1, 0, -1, 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, 0, 0, 0, 0, 1, 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, 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, 0, 0, 0, 0], [2, 0, 1, -1, -1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 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, 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, 1, -1, 0, -1, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 2, 0, 1, -2, 2, -2, 1, -1, -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], [1, 1, 0, 0, 0, 0, -1, 0, -1, 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, -2, 0, 1, -1, 1, -2, 0, -1, 0, 1, -1, 1, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 2, 1, 0, 0, 1, -2, 1, -1, 2, 2, 2, -1, -1, 2, -1, -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, 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]]}