# Stored data for newform 6026.2.a.f, downloaded from the LMFDB on 23 April 2024.
{"label": "6026.2.a.f", "space_label": "6026.2.a", "level": 6026, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22517998170412938, "dim": 20, "is_polredabs": true, "trace_hash": 2119921865674164796, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [-18, 78, 1159, -576, -9137, -2042, 25315, 14682, -28084, -21886, 14837, 14776, -3723, -5359, 248, 1083, 78, -115, -17, 5, 1]], [5, [-27, -279, 1366, 4899, -12300, -30034, 30717, 69769, -33296, -76849, 17176, 44069, -3579, -13685, -193, 2285, 190, -189, -25, 6, 1]]], "qexp_display": "q+q^{2}-\\beta _{1}q^{3}+q^{4}+\\beta _{3}q^{5}-\\beta _{1}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 24104, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 48.11785225802356, "hecke_ring_index": 1, "level_radical": 6026, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [6026, 1, [787, 4325], [1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 1, "level_primes": [2, 23, 131], "conrey_indexes": [1], "field_disc": 71943644777887303165102556102296224300, "field_disc_factorization": [[2, 2], [3, 1], [5, 2], [13, 1], [44089, 1], [39352335281201, 1], [10632296294691133, 1]], "field_poly": [-18, -78, 1159, 576, -9137, 2042, 25315, -14682, -28084, 21886, 14837, -14776, -3723, 5359, 248, -1083, 78, 115, -17, -5, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.148", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "620.873", "prec": 24}, {"__RealLiteral__": 0, "data": "406.885", "prec": 24}, {"__RealLiteral__": 0, "data": "46685.923", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 20, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [23, -1], [131, 1]], "trace_display": [20, -5, -6, -12], "traces": [0, 20, 20, -5, 20, -6, -5, -12, 20, -1, -6, -3, -5, -13, -12, -10, 20, -14, -1, -21, -6, -8, -3, 20, -5, -14, -13, -5, -12, -27, -10, -27, 20, -12, -14, -23, -1, -19, -21, -35, -6, -17, -8, -27, -3, 4, 20, -28, -5, -10, -14, 6, -13, -47, -5, -4, -12, -16, -27, -16, -10, -9, -27, -9, 20, 9, -12, -8, -14, -5, -23, -30, -1, -26, -19, -18, -21, -50, -35, -35, -6, -60, -17, 2, -8, -62, -27, 1, -3, -25, 4, 22, 20, -21, -28, -14, -5, 2, -10, -5, -14, -9, 6, -32, -13, -1, -47, 5, -5, -70, -4, 37, -12, -33, -16, -6, -27, -17, -16, -53, -10, -33, -9, -25, -27, -39, -9, -60, 20, -12, 9, -20, -12, -11, -8, 0, -14, -25, -5, -25, -23, -10, -30, -32, -1, 7, -26, 27, -19, -56, -18, -61, -21, -6, -50, -35, -35, -4, -35, 11, -6, -12, -60, -15, -17, -1, 2, -42, -8, -71, -62, -20, -27, -65, 1, -3, -3, -40, -25, 0, 4, 12, 22, -35, 20, -30, -21, -5, -28, 8, -14, -16, -5, -70, 2, 13, -10, -56, -5, 2, -14, -44, -9, 62, 6, -32, -32, -1, -13, -34, -1, -42, -47, -34, 5, -12, -5, -7, -70, 4, -4, 30, 37, 13, -12, -11, -33, 32, -16, 11, -6, 14, -27, -48, -17, 50, -16, 93, -53, -69, -10, -34, -33, -5, -9, 74, -25, -1, -27, 36, -39, 6, -9, -3, -60, 16, 20, -16, -12, -22, 9, 15, -20, 2, -12, -6, -11, 23, -8, -51, 0, -34, -14, -19, -25, 33, -5, -30, -25, -22, -23, -41, -10, 42, -30, 42, -32, -28, -1, 22, 7, 106, -26, -90, 27, 2, -19, -2, -56, -13, -18, -41, -61, -47, -21, -66, -6, 28, -50, -72, -35, 25, -35, 81, -4, -2, -35, -20, 11, -108, -6, 17, -12, -34, -60, 8, -15, 137, -17, 54, -1, -47, 2, 10, -42, 64, -8, -25, -71, -38, -62, 69, -20, -30, -27, -10, -65, -28, 1, -47, -3, 32, -3, -8, -40, 19, -25, 72, 0, 61, 4, -81, 12, 87, 22, -79, -35, 14, 20, 3, -30, 12, -21, 36, -5, 122, -28, -29, 8, -46, -14, 23, -16, 85, -5, -50, -70, 95, 2, -9, 13, -14, -10, 5, -56, 72, -5, -9, 2, 115, -14, 0, -44, -66, -9, 37, 62, -56, 6, -20, -32, 2, -32, -1, -1, -15, -13, 8, -34, 37, -1, -6, -42, 27, -47, 16, -34, 47, 5, 32, -12, -83, -5, 31, -7, 12, -70, -21, 4, -45, -4, -13, 30, -21, 37, -91, 13, 109, -12, -91, -11, 21, -33, -60, 32, 40, -16, -127, 11, 35, -6, -38, 14, -76, -27, 68, -48, 146, -17, -56, 50, 71, -16, -54, 93, 94, -53, -154, -69, 97, -10, -25, -34, -8, -33, 17, -5, -32, -9, 19, 74, 60, -25, -31, -1, 75, -27, 30, 36, -34, -39, 46, 6, 37, -9, -27, -3, 99, -60, 29, 16, 126, 20, 93, -16, 102, -12, -25, -22, 10, 9, 67, 15, 25, -20, 120, 2, 110, -12, 20, -6, 98, -11, -12, 23, -27, -8, 22, -51, 155, 0, -101, -34, 36, -14, -19, -19, 54, -25, 43, 33, 145, -5, 7, -30, 30, -25, -11, -22, 107, -23, 57, -41, 85, -10, 61, 42, 138, -30, -41, 42, 34, -32, 91, -28, -14, -1, -61, 22, 28, 7, -41, 106, 5, -26, 6, -90, 95, 27, 66, 2, 30, -19, 38, -2, 127, -56, 87, -13, 13, -18, -82, -41, 78, -61, 137, -47, -15, -21, -116, -66, 22, -6, 9, 28, 167, -50, 12, -72, -23, -35, -5, 25, 70, -35, 60, 81, -12, -4, 54, -2, -73, -35, -113, -20, 188, 11, -27, -108, 11, -6, 20, 17, 8, -12, 71, -34, 44, -60, 69, 8, 164, -15, -8, 137, 6, -17, 81, 54, 137, -1, -50, -47, 140, 2, 67, 10, -27, -42, -76, 64, 148, -8, -115, -25, 121, -71, 13, -38, -7, -62, -4, 69, -145, -20, 25, -30, 40, -27, 19, -10, 52, -65, -46, -28, -4, 1, 140, -47, 88, -3, -31, 32, 43, -3, 52, -8, 30, -40, 99, 19, -100, -25, -27, 72, -21, 0, 63, 61, -55, 4, 61, -81, 86, 12, -39, 87, -14, 22, -22, -79, 184, -35, 18, 14, 36, 20, -56, 3, -50, -30, 195, 12, 66, -21, 57, 36, 88, -5, -4, 122, 66, -28, 88, -29, 154, 8, -27, -46, -12, -14, 58, 23, 54, -16, -78, 85, 38, -5, 8, -50, 10, -70, 137, 95, -104, 2, 54, -9, 42, 13, 12, -14, 70, -10, 51, 5, 133, -56, 111, 72, 108, -5, 30, -9, 89, 2, 63, 115, -210, -14, 195, 0, 30, -44, -23, -66, 55, -9, -69, 37, -38, 62, 64, -56, 111, 6, 9, -20, 171, -32, -195, 2, 67, -32, -136, -1, 71, -1, 34, -15, 77, -13, 16, 8, 266, -34, 108, 37, 5, -1, -33, -6, 150, -42, 23, 27, 25, -47, 105, 16, -19, -34, 16, 47, 84, 5, -10, 32, 22, -12, 15, -83, -147, -5, -27, 31, 33, -7, -8, 12, -107, -70, -36, -21, 64, 4, 41, -45, 47, -4, 99, -13, 93, 30, -22, -21, 111, 37, -120, -91, 37, 13, 5, 109, -67, -12, -35, -91, 112, -11, 44, 21, 5, -33, -16, -60, 60, 32, -64, 40, 70, -16, -88, -127, 212, 11, 12, 35, -150, -6, 169, -38, 166, 14, 63, -76, 144, -27, -23, 68, -112, -48, 11, 146, 55, -17, -152, -56, 2, 50, -25, 71, -17, -16, 94, -54, 70, 93, -148, 94, 67, -53, -30, -154, -90, -69, 131, 97, -133, -10, -77, -25, 45, -34, 63, -8, -11, -33, -113, 17, 163, -5, 149, -32, 166, -9, -163, 19, -46, 74, -66, 60, 85, -25, -2, -31, -48, -1, -27, 75, -102, -27, 29, 30, 86, 36, -59, -34, -36, -39, -24, 46, 115, 6, -61, 37, 191, -9, -21, -27, 94, -3, 61, 99, 84, -60, 86, 29, 148, 16, -104, 126, 115, 20, 33, 93, 27, -16, -188, 102, 122, -12, 40, -25, 4, -22, -106, 10, -138, 9, 17, 67, 41, 15, -48, 25, 26, -20, 187, 120, -363, 2, 143, 110, 84, -12, -59, 20, 116, -6, 47, 98, 236, -11, 113, -12, 94, 23, -80, -27, 35, -8, 14, 22, -18, -51, 82, 155, -114, 0, -28, -101, 121, -34, 91, 36, -209, -14, -70, -19, 87, -19, -18, 54, 21, -25, -53, 43, 127, 33, -88, 145, 22, -5, 37, 7, 123, -30, 31, 30, 177, -25, 271, -11, -71, -22, -33, 107, 102, -23, 18, 57, 73, -41, -9, 85, -10, -10, -144, 61, 135, 42, -131, 138, -70, -30, -17, -41, 188, 42, -38, 34, -38, -32, 122, 91, 99, -28, -64, -14, 28, -1, 73, -61, 213, 22, 48, 28, -116, 7, -133, -41, 24, 106, -148, 5, -104, -26, 115, 6, 39, -90, 6, 95, 115, 27, 170, 66, 1, 2, 7, 30, 105, -19, -29, 38, 194, -2, -188, 127, 154, -56, 71, 87, -48, -13, -21, 13, -173, -18, 65, -82, 179, -41, -133, 78, -99, -61, 122, 137, 177, -47, -148, -15, 141, -21, -111, -116, -47, -66, 14, 22, 55, -6, -151, 9, -10, 28, 26, 167, -274, -50, 197, 12, -17, -72, 149, -23, -44, -35, -57, -5, -49, 25, -23, 70, -35, -35, -21, 60, 73, 81, 37, -12, -136, -4, 18, 54, 6, -2, -147, -73, 161, -35, -4, -113, 52, -20, 41, 188, 88, 11, -35, -27, 98, -108, -14, 11, -57, -6, -85, 20, 185, 17, 156, 8, 131, -12, -113, 71, -75, -34, 9, 44, 144, -60, 21, 69, -51, 8, 96, 164, 61, -15, -54, -8, 170, 137, -88, 6, -16, -17, 105, 81, -59, 54, 74, 137, -52, -1, -61, -50, -53, -47, 224, 140, -238, 2, 30, 67, 156, 10, -27, -27, 42, -42, 160, -76, 125, 64, 175, 148, 26, -8, -113, -115, 47, -25, 55, 121, -210, -71, 83, 13, 144, -38, -16, -7, -69, -62, 200, -4, 13, 69, 21, -145, 96, -20, -193, 25, 40, -30, -96, 40, 269, -27, -6, 19, 61, -10, -128, 52, 219, -65, 139, -46, 99, -28, 24, -4, 213, 1, 3, 140, 120, -47, -124, 88, -149, -3, 62, -31, -9, 32, 140, 43, 278, -3, -267, 52, -50, -8, -98, 30, -22, -40, -11, 99, -167, 19, 66, -100, 119, -25, -102, -27, 65, 72, -178, -21, 222, 0, 115, 63, 117, 61, -88, -55, 48, 4, 3, 61, -51, -81, 180, 86, -67, 12, -9, -39, 138, 87, 70, -14, -81, 22, 8, -22, -89, -79, 16, 184, 294, -35, -128, 18, 119, 14, -153, 36, -224, 20, 137, -56, 119, 3, 274, -50, 96, -30, -100, 195, 68, 12, 28, 66, 197, -21, -211, 57, 209, 36, -197, 88, 9, -5, -57, -4, 177, 122, -53, 66, -89, -28, -51, 88, 53, -29, -55, 154, -181, 8, -98, -27, 131, -46, 26, -12, 30, -14, 87, 58, 257, 23, 160, 54, 70, -16, -80, -78, 1, 85, 161, 38, 2, -5, 86, 8, 88, -50, -8, 10, 49, -70, 91, 137, 104, 95, -67, -104, 46, 2, -83, 54, -83, -9, -151, 42, 318, 13, -55, 12, -43, -14, -69, 70, -1, -10, -15, 51, 350, 5, -28, 133, 46, -56, 51, 111, -118, 72, -267, 108, 63, -5, -206, 30, -5, -9, -2, 89, 68, 2, -128, 63, -80, 115, -202, -210, -54, -14, 126, 195, 29, 0, -5, 30, -64, -44, 54, -23, -112, -66, 12, 55, 179, -9, 252, -69, -317, 37, 97, -38, 112, 62, 57, 64, 34, -56, 99, 111, 7, 6, -30, 9, 230, -20, 181, 171, -197, -32, -63, -195, 299, 2, -76, 67, -38, -32, -189, -136, 194, -1, 49, 71, 129, -1, -35, 34, -251, -15, 33, 77, 248, -13, -74, 16, 217, 8, -169, 266, 131, -34, -6, 108, -83, 37, 46, 5, -26, -1, -119, -33, 232, -6, -122, 150, -145, -42, -244, 23, -86, 27, 7, 25, -307, -47, 56, 105, 82, 16, 98, -19, 13, -34, -136, 16, 310, 47, -22, 84, -135, 5, 61, -10, 194, 32, -86, 22, -176, -12, 40, 15, -243, -83, -18, -147, 141, -5, -134, -27, -101, 31, 34, 33, -106, -7, -144, -8, 133, 12, -231, -107, 170, -70, -185, -36, -131, -21, -147, 64, 16, 4, 145, 41, 3, -45, -58, 47, -311, -4, 2, 99, 196, -13, -243, 93, -170, 30, -83, -22, -50, -21, -296, 111, -1, 37, -407, -120, -170, -91, 111, 37, -156, 13, 19, 5, -18, 109, -190, -67, -33, -12, 50, -35, 155, -91, 24, 112, 47, -11, 178, 44, -73, 21, -84, 5, 34, -33, 220, -16, 21, -60, -203, 60, -298, 32, -35, -64, -78, 40, 426, 70, -34, -16, -22, -88, 44, -127, -358, 212, -124, 11, -30, 12, 312, 35, -71, -150, -161, -6, 176, 169, 11, -38, 50, 166, 147, 14, -107, 63, 31, -76, -168, 144, -158, -27, -201, -23, 85, 68, -87, -112, -60, -48, -126, 11, 2, 146, -271, 55, -103, -17, -44, -152, -135, -56, -157, 2, -393, 50, -142, -25, 146, 71, -90, -17, -74, -16, 6, 94, 14, -54, 129, 70, -62, 93, -77, -148, 260, 94, -57, 67, -138, -53, 34, -30, 90, -154, 2, -90, -20, -69, 7, 131, 117, 97, -102, -133, -71, -10, -253, -77, 28, -25, 17, 45, -54, -34, -181, 63, 192, -8, -137, -11, -11, -33, -139, -113, 110, 17, -157, 163, -78, -5, 78, 149, -16, -32, -210, 166, 1, -9, -91, -163, -62, 19, -49, -46, -177, 74, -55, -66, 89, 60, 10, 85, 38, -25, -50, -2, -125, -31, -138, -48, -214, -1, -198, -27, 58, 75, -231, -102, 163, -27, 153, 29, -20, 30, -132, 86, -120, 36, -368, -59, -167, -34, -134, -36, -325, -39, 1, -24, -81, 46, 202, 115, -17, 6, -12, -61, 65, 37, -82, 191, -45, -9, -456, -21, 280, -27, -96, 94, -75, -3, -212, 61, 79, 99, -107, 84, 288, -60, -333, 86, -125, 29, -247, 148, 142, 16, -343, -104, 129, 126, -26, 115, -25, 20, 4, 33, 242, 93, -249, 27, 37, -16, 62, -188, -376, 102, -33, 122, -193, -12, -58, 40, 338, -25, -144, 4, 300, -22, 47, -106, 204, 10, 230, -138, -123, 9, -256, 17, 97, 67, 13, 41, -164, 15, -188, -48, -202, 25, 22, 26, 138, -20, 85, 187, -81, 120, -444, -363, -102, 2, -318, 143, -106, 110, -373, 84, 293, -12, -29, -59, 38, 20, -75, 116, -315, -6, 135, 47, 135, 98, -31, 236, -156, -11, -104, 113, -107, -12, -23, 94, -64, 23, -182, -80, -21, -27, -11, 35, 42, -8, 58, 14, 409, 22, -178, -18, -232, -51, 64, 82, -185, 155, -272, -114, 6, 0, 234, -28, -144, -101, -16, 121, 282, -34, -15, 91, -44, 36, -128, -209, 207, -14, -15, -70, -330, -19, 224, 87, -74, -19, -14, -18, 246, 54, -59, 21, -259, -25, -81, -53, 133, 43, -161, 127, -104, 33, 9, -88, 257, 145, -31, 22, 17, -5, -262, 37, -167, 7, -33, 123, 59, -30, -97, 31, -15, 30, 20, 177, -23, -25, 149, 271, 14, -11, -384, -71, 2, -22, 139, -33, 61, 107, -239, 102, -197, -23, 23, 18, -63, 57, -162, 73, -310, -41, -150, -9, 139, 85, -391, -10, -211, -10, -26, -144, -37, 61, 141, 135, 45, 42, 40, -131, 30, 138, -183, -70, -201, -30, 73, -17, -21, -41, -5, 188, -138, 42, 153, -38, -22, 34, 54, -38, 112, -32, -45, 122, -50, 91, -60, 99, 43, -28, -119, -64, -348, -14, 193, 28, -195, -1, 61, 73, 197, -61, -257, 213, -61, 22, 52, 48, 153, 28, -257, -116, 59, 7, -138, -133, -9, -41, 155, 24, 214, 106, -105, -148, 157, 5, -40, -104, -21, -26, -93, 115, -420, 6, 313, 39, -111, -90, 89, 6, -149, 95, -67, 115, 163, 27, 169, 170, 65, 66, 26, 1, -130, 2, -241, 7, 2, 30, 43, 105, -115, -19, -32, -29, -23, 38, 297, 194, -267, -2, -56, -188, -131, 127, -315, 154, -62, -56, 28, 71, 257, 87, -129, -48, -94, -13, -285, -21, 79, 13, -72, -173, 72, -18, -192, 65, -24, -82, -58, 179, -124, -41, -14, -133, 191, 78, -74, -99, -1, -61, -28, 122, 10, 137, -47, 177, 71, -47, -194, -148, -242, -15, 69, 141, -170, -21, -31, -111, 94, -116, -66, -47, -105, -66, 194, 14, 153, 22, 32, 55, -143, -6, 11, -151, 178, 9, 290, -10, -115, 28, -97, 26, -145, 167, 5, -274, 83, -50, 50, 197, -10, 12, -143, -17, 66, -72, 11, 149, -14, -23, -245, -44, -123, -35, -145, -57, 67, -5, 157, -49, 144, 25, 21, -23, 256, 70, -127, -35, 88, -35, 60, -21, 51, 60, -135, 73, -84, 81, -484, 37, -70, -12, 13, -136, 273, -4, 173, 18, -428, 54, -334, 6, -125, -2, -433, -147, -287, -73, 149, 161, -19, -35, -161, -4, -18, -113, -232, 52, 97, -20, 223, 41, -21, 188, -111, 88, 43, 11, -103, -35, -274, -27, 22, 98, -470, -108, 37, -14, 315, 11, 58, -57, -306, -6, -102, -85, 123, 20, -198, 185, 270, 17, -538, 156, -2, 8, -75, 131, -2, -12, -59, -113, 19, 71, 386, -75, 21, -34, -103, 9, -202, 44, -19, 144, 250, -60, -148, 21, 421, 69, -205, -51, -33, 8, 5, 96, 134, 164, -225, 61, 429, -15, -124, -54, -107, -8, -49, 170, -247, 137, 75, -88, -115, 6, 302, -16, 24, -17, -120, 105, -50, 81, 73, -59, -302, 54, -86, 74, 294, 137, -72, -52, 22, -1, -51, -61, -78, -50, -6, -53, 68, -47, -127, 224, -72, 140, -187, -238, -110, 2, -223, 30, 22, 67, -404, 156, 17, 10, 87, -27, -102, -27, -32, 42, -17, -42, 144, 160, -55, -76, -133, 125, -38, 64, -5, 175, 7, 148, -257, 26, -95, -8, -196, -113, -17, -115, 335, 47, -85, -25, -220, 55, 295, 121, 67, -210, -438, -71, 161, 83, 77, 13, 131, 144, 158, -38, -309, -16, 48, -7, 229, -69, 57, -62, 479, 200, -154, -4, 278, 13, 32, 69, -204, 21, 30, -145, -135, 96, -234, -20, -53, -193, -182, 25, 162, 40, 66, -30, -31, -96, 375, 40, -71, 269, 8, -27, -409, -6, 329, 19, -71, 61, -193, -10, -47, -128, -133, 52, 89, 219, -5, -65, -49, 139, 26, -46, 117, 99, 161, -28, -253, 24, -150, -4, -278, 213, -33, 1, -185, 3, 373, 140, -342, 120, -120, -47, 11, -124, -75, 88, -113, -149, -95, -3, -70, 62, -209, -31, 136, -9, -250, 32, -93, 140, 321, 43, 115, 278, -227, -3, 186, -267, -146, 52, -301, -50, -387, -8, 238, -98, -241, 30, -25, -22, 26, -40, 245, -11, 53, 99, -86, -167, -298, 19, -38, 66, 127, -100, -205, 119, 193, -25, 104, -102, -86, -27, 229, 65, -287, 72, -33, -178, 219, -21, 32, 222, 179, 0, 75, 115, 158, 63, 47, 117, -70, 61, -166, -88, -39, -55, -144, 48, -130, 4, 128, 3, -161, 61, 164, -51, 71, -81, -150, 180, -81, 86, -182, -67, -114, 12, 121, -9, -194, -39, 100, 138, 75, 87, 192, 70, -57, -14, 19, -81, 5, 22, 298, 8, 178, -22, -86, -89, -488, -79, -60, 16, 28, 184, 137, 294, -41, -35, -245, -128, 162, 18, -27, 119, -87, 14, -128, -153, 131, 36, 262, -224, -112, 20, 257, 137, 97, -56, -140, 119, -85, 3, 42, 274, 175, -50, -180, 96, -244, -30, -25, -100, 302, 195, -248, 68, -12, 12, -164, 28, 295, 66, 288, 197, 483, -21, 128, -211, -155, 57, -76, 209, -433, 36, -311, -197, 220, 88, -102, 9, -50, -5, 96, -57, 169, -4, 134, 177, -217, 122], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "6026.2.a.f", "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, 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, 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, 1, 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, -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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, -1, 1, 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, 1, 0, 0, 0, 0, 0, -1, 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, -1, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 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, 0, 1, 0, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1], [0, 1, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0], [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 1, 0, 0, 1, -1, 1, 0, -1, 0, 0, -2, 0, 0, 0, 1, 0], [-1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, 2, -1, 0, 0, 0, -1, 1, 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, -1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, -1, -1], [-1, 0, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0], [0, 0, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 0, 1, 2, 0, 0, 0, 0, -2], [1, 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, 1, -2, 1, -1, 0, 2, 1, 0, 2, -1, 0, 1, -1, 0], [0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, -1, 0], [-2, -1, 1, -1, 1, 1, 0, -2, 1, -1, 0, 1, 1, -1, 1, -1, 0, 1, -1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 1, 0, 1, 1, 1, -2, 0, -1, 1, 1, 2, 0, 1, -1, 0, 0, 0, -1], [-2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0, 0, 0], [-3, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, -1, 1, 0, -1, 1, 0, 2, -1, -1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 1, -1, -1, 2, -1, 2, 0, 1, 0, -1, -1, 0, -2, 0, -2, -1, 1, 1], [-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1], [-1, 1, 1, 0, -2, 1, 0, 1, -2, 1, 0, -1, 0, 1, -1, 1, 0, 1, 0, 1], [0, 1, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0], [-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 1, -1, -1, 0, -1, 1, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 1, -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], [0, -1, -1, 0, 0, -1, -1, -1, 1, 0, -1, 2, -1, 1, 1, -1, 0, 0, 0, 0], [-2, 1, 0, 0, 1, 0, 0, 1, -1, 1, 0, -1, 0, 0, -2, 0, 0, 0, 1, 0], [1, 1, -1, 1, -1, -1, 1, 0, -1, 0, 1, 1, 0, 0, 1, 0, 0, 0, -2, 1], [-1, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-2, 2, -2, 0, 1, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 1, 0, 1, -1], [-1, 2, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, 0, -1, -1, -1, 2, -1, 1, 0, -1, -1, 1, -1, 1, 1, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-2, 4, -1, -1, -2, -2, -2, 1, 0, 1, -2, -1, -2, 0, -1, 1, 0, -2, 1, 2], [0, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, -1, -1], [-2, 2, 2, 0, -1, 0, 1, 1, -1, 1, -1, -1, 1, 0, -2, 1, 1, 1, -1, 2], [-1, 0, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0], [1, 2, -2, -3, 1, -3, 1, -2, -1, -1, -2, 0, -1, 1, 2, -2, 2, -2, 1, 0], [0, 0, -1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 0, 1, 2, 0, 0, 0, 0, -2], [1, 1, -1, -1, 0, -1, -1, -2, 0, 0, -1, 1, 0, 1, 1, -1, 0, -2, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 0], [0, -1, 0, 0, 1, 0, 1, -2, 1, -1, 0, 2, 1, 0, 2, -1, 0, 1, -1, 0], [-1, 0, 0, 0, 0, 2, -2, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, -1, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -1, 1, 1, 0, -2, 1, -1, 0, 1, 1, -1, 1, -1, 0, 1, -1, 0], [-3, -1, 0, -3, 4, 0, 0, -6, 2, -2, -2, 0, -2, -1, 0, -2, 0, -3, 2, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -2, 3, -1, 0, 2, 1, 1, 1, 0, 1, -2, 0, -3, -2, 0, -1, 1, -1, -1], [1, -2, 1, 0, 1, 1, 1, -2, 0, -1, 1, 1, 2, 0, 1, -1, 0, 0, 0, -1], [2, -1, 1, 2, -1, 1, 1, -2, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, -1, -1], [-2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0, 0, 0], [-2, 0, -1, -1, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, -1, 1, -1, -1, 2, -1], [-3, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, -1, 1, 0, -1, 1, 0, 2, -1, -1], [-1, -3, 0, 0, 2, 0, -1, -3, 3, -1, -1, 3, 0, 0, 1, -1, -1, -2, 1, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, -1, -1, 0, 1, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0], [-3, 0, 1, -1, -1, 2, -1, 2, 0, 1, 0, -1, -1, 0, -2, 0, -2, -1, 1, 1], [-3, -3, 2, 0, 3, 2, -1, -1, 1, 0, 0, -1, -1, -2, -2, -1, -1, 0, 1, -1], [-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, -1], [-4, 2, -1, -3, -2, -1, 0, 1, 1, -1, -1, -1, -1, 0, 1, 1, 0, -1, -1, 1], [-1, 1, 1, 0, -2, 1, 0, 1, -2, 1, 0, -1, 0, 1, -1, 1, 0, 1, 0, 1], [0, 4, -1, -2, -1, -1, -1, 0, -2, 0, -2, -1, -2, 2, -2, 1, 1, -2, 1, 2], [0, 1, -1, -1, -1, -1, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0], [-1, 0, 1, -1, 0, -2, 0, -1, 0, 0, 0, 0, 1, -1, 2, -2, 1, 0, -1, 0], [-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 1, -1, -1, 0, -1, 1, -1, 0, 0, 0], [1, -1, 3, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, -1, 0, 1, -1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, -1, -1, 0, -2, -1, -1, -1, -1, -2, 1, -1, -1, 0, -2, 1, -3, 1, 2], [-2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 1, -1, 1, -1, -1, 0, 0, 1, 1, 0], [5, -1, -2, 0, -2, -1, 1, -1, -1, -1, 1, 3, 1, 2, 5, 0, 1, 0, -2, -1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 2, 1, 1, -1, 1, 0, 2, -1, 0, 0, 1, -2, 0, 0, 1, 3, -2, 0], [0, -1, -1, 0, 0, -1, -1, -1, 1, 0, -1, 2, -1, 1, 1, -1, 0, 0, 0, 0], [0, 0, 1, 1, 2, 1, 1, -3, 0, 0, -1, 1, 2, 0, 1, -1, 2, 2, -1, 1], [-2, 1, 0, 0, 1, 0, 0, 1, -1, 1, 0, -1, 0, 0, -2, 0, 0, 0, 1, 0]]}