# Stored data for newform 8001.2.a.r, downloaded from the LMFDB on 19 April 2024.
{"label": "8001.2.a.r", "space_label": "8001.2.a", "level": 8001, "weight": 2, "hecke_orbit": 18, "hecke_orbit_code": 76561193698860865, "dim": 16, "is_polredabs": true, "trace_hash": 1309034681367187629, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 148, 416, -1002, -3341, 158, 5821, 2747, -3082, -2282, 565, 712, 9, -98, -13, 5, 1]], [5, [-27136, 208768, -344128, -359328, 542544, 232104, -316420, -73336, 91364, 12600, -14371, -1185, 1249, 56, -56, -1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}-\\beta _{13}q^{5}-q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 32004, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 63.88830665722644, "hecke_ring_index": 8, "level_radical": 2667, "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": [8001, 1, [3557, 1144, 7750], [1, 1, 1]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 1, "level_primes": [3, 7, 127], "conrey_indexes": [1], "field_disc": 3925253247562629319229522462576, "field_disc_factorization": [[2, 4], [331, 1], [1049, 1], [479041, 1], [1474930415904160909, 1]], "field_poly": [4, -148, 416, 1002, -3341, -158, 5821, -2747, -3082, 2282, 565, -712, 9, 98, -13, -5, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.951", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "528.790", "prec": 24}, {"__RealLiteral__": 0, "data": "62.045", "prec": 20}, {"__RealLiteral__": 0, "data": "36287.289", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, 1], [127, -1]], "trace_display": [-5, 0, 1, -16], "traces": [0, 16, -5, 0, 19, 1, 0, -16, -6, 0, -12, -11, 0, 18, 5, 0, 25, 5, 0, -11, 1, 0, 1, -13, 0, 33, -8, 0, -19, -24, 0, -42, -42, 0, 9, -1, 0, 40, -38, 0, -61, -9, 0, 7, -3, 0, 24, -31, 0, 16, -6, 0, 52, -66, 0, -36, 6, 0, 19, 7, 0, 6, -52, 0, 10, -51, 0, 16, -14, 0, 12, -46, 0, 39, -72, 0, 24, 11, 0, 4, 2, 0, -18, -15, 0, -4, -14, 0, 58, 1, 0, -18, -26, 0, 5, -44, 0, 41, -5, 0, 65, -26, 0, -32, -56, 0, 42, -6, 0, 20, 26, 0, -25, -9, 0, 3, -88, 0, 48, -5, 0, 43, -38, 0, -88, -9, 0, 16, -103, 0, 24, -12, 0, 11, 28, 0, 18, -2, 0, -74, -1, 0, 0, -88, 0, 30, -43, 0, 104, -76, 0, -49, -81, 0, -1, 10, 0, 24, 9, 0, -79, 13, 0, -10, -101, 0, -21, 8, 0, 94, 22, 0, 31, -12, 0, -33, -16, 0, 10, -34, 0, -54, 8, 0, 41, -20, 0, -57, -88, 0, 83, -75, 0, -21, -16, 0, 19, -105, 0, -60, -26, 0, 10, 24, 0, -18, -54, 0, 11, 34, 0, 10, -154, 0, -86, -53, 0, 42, -11, 0, -62, -54, 0, -65, 42, 0, -93, -112, 0, -68, -69, 0, 73, -39, 0, 12, -21, 0, -9, 5, 0, -1, -110, 0, -112, 1, 0, 53, -59, 0, -165, 47, 0, 12, -5, 0, 47, 17, 0, -40, -135, 0, 49, -76, 0, 70, 38, 0, -90, -7, 0, -74, -19, 0, -23, -38, 0, 53, 142, 0, 61, -18, 0, 55, -74, 0, -145, 9, 0, -19, 23, 0, 73, -92, 0, -2, -73, 0, 13, -4, 0, -7, -72, 0, -56, -66, 0, -53, 3, 0, 35, -83, 0, -4, 146, 0, -70, -61, 0, -36, 244, 0, -24, -70, 0, 123, -28, 0, -7, 31, 0, -22, -35, 0, -127, -23, 0, 70, 93, 0, -171, 41, 0, -16, -1, 0, -42, 9, 0, 4, 6, 0, 43, -107, 0, -1, 144, 0, 109, -97, 0, 63, 85, 0, -52, 12, 0, -63, 51, 0, 80, 66, 0, 105, 15, 0, 10, -88, 0, -19, -26, 0, 98, -50, 0, 36, 45, 0, 100, -31, 0, -157, -6, 0, -154, -104, 0, 15, 54, 0, 110, -27, 0, -43, 116, 0, -19, -11, 0, 32, 20, 0, -91, -7, 0, -26, -66, 0, -45, 49, 0, -23, 112, 0, 10, 72, 0, -6, 78, 0, -195, 22, 0, 41, 52, 0, 7, -142, 0, -86, 199, 0, 25, -19, 0, 86, 143, 0, -10, 27, 0, -110, 162, 0, -109, 51, 0, 6, -77, 0, -127, 54, 0, 17, 7, 0, -135, 16, 0, -16, 84, 0, -4, -53, 0, -187, 14, 0, 3, -34, 0, 21, 78, 0, -4, -10, 0, 24, 171, 0, -12, -105, 0, 83, 118, 0, -86, 46, 0, -80, -99, 0, -96, -5, 0, 29, 16, 0, 19, 22, 0, -39, -49, 0, 31, -55, 0, 28, 72, 0, -237, 26, 0, -3, -49, 0, 27, -53, 0, 121, 249, 0, -24, -151, 0, -76, 155, 0, -17, -11, 0, -97, -38, 0, 129, 72, 0, 2, 235, 0, -176, -31, 0, -4, 53, 0, -246, -72, 0, -64, -2, 0, 13, -135, 0, 16, 168, 0, 64, -64, 0, -36, 131, 0, 18, 96, 0, -6, -48, 0, -28, 15, 0, -105, -102, 0, -81, -19, 0, 141, 239, 0, 85, -64, 0, 4, -64, 0, 26, 48, 0, -99, 14, 0, -240, -199, 0, -2, -53, 0, 41, -18, 0, 80, 37, 0, -58, -16, 0, -128, 265, 0, -8, -1, 0, -18, -8, 0, -176, 40, 0, -72, 266, 0, -33, 1, 0, 18, 213, 0, -178, -48, 0, -129, 26, 0, -239, 49, 0, 10, 151, 0, 50, 36, 0, -60, 40, 0, -5, -35, 0, 1, 72, 0, -221, 44, 0, -80, -94, 0, -245, -19, 0, 124, 256, 0, 37, -181, 0, -41, 293, 0, -79, -138, 0, -59, 5, 0, 108, -133, 0, -127, 112, 0, 127, -33, 0, 117, 135, 0, -65, -114, 0, -66, -107, 0, 184, 26, 0, -57, -255, 0, -166, -89, 0, 41, -30, 0, -27, -26, 0, 32, 138, 0, -38, -301, 0, -135, 56, 0, -264, 118, 0, 247, 148, 0, 128, 100, 0, -10, -8, 0, -42, -88, 0, -99, -58, 0, -10, 6, 0, -17, -61, 0, 36, -8, 0, 56, 55, 0, 281, -78, 0, -20, -114, 0, 52, 46, 0, 82, -26, 0, -398, -208, 0, -177, -218, 0, 248, -46, 0, 148, 293, 0, 25, 13, 0, 40, -185, 0, -50, 9, 0, -57, -22, 0, -122, 17, 0, 118, -111, 0, -161, -141, 0, -3, -94, 0, 39, -108, 0, -43, 88, 0, 80, -72, 0, 134, -184, 0, 68, -54, 0, 64, -130, 0, -48, -3, 0, 63, -1, 0, 20, 5, 0, 21, -286, 0, -136, 64, 0, 96, 153, 0, 1, -379, 0, -43, -321, 0, 316, -6, 0, -85, 38, 0, -301, -33, 0, -32, 19, 0, 209, -109, 0, -2, 47, 0, 88, 1, 0, 19, -21, 0, 2, 9, 0, 97, -158, 0, -101, 33, 0, 58, -7, 0, 280, -43, 0, -16, 110, 0, -27, -86, 0, -88, 103, 0, 153, -40, 0, -45, 156, 0, -68, 35, 0, -52, -2, 0, -24, -27, 0, -2, -117, 0, -167, 12, 0, -72, -426, 0, 204, -135, 0, 168, 64, 0, 39, -2, 0, -11, 108, 0, 287, 2, 0, -172, -28, 0, 70, -123, 0, 76, -68, 0, 119, -7, 0, -22, 144, 0, -18, -38, 0, -213, -118, 0, 206, 2, 0, 54, -342, 0, -13, -25, 0, -7, -250, 0, 125, 81, 0, 74, 63, 0, -14, -49, 0, -95, 1, 0, -196, -44, 0, 37, -273, 0, 303, -104, 0, -184, 200, 0, 0, -70, 0, 29, 31, 0, -230, 88, 0, 25, 22, 0, -38, 95, 0, 13, 216, 0, 85, -121, 0, -30, -6, 0, 106, -98, 0, -116, 43, 0, -24, -2, 0, -28, 13, 0, 83, 63, 0, 94, -106, 0, -104, -233, 0, -86, 148, 0, 104, 76, 0, -30, -41, 0, 75, 238, 0, 83, -206, 0, -16, -300, 0, 49, 0, 0, 132, -23, 0, -36, 81, 0, 80, -116, 0, 221, -156, 0, 35, -283, 0, 62, 307, 0, 1, 44, 0, -261, 437, 0, 144, -10, 0, 73, -392, 0, -112, 126, 0, 181, -71, 0, -278, -79, 0, -24, 60, 0, -145, -50, 0, -226, -9, 0, -217, -45, 0, 23, 285, 0, 291, 5, 0, 178, 317, 0, 79, -27, 0, 53, 57, 0, -51, -13, 0, -59, -267, 0, 220, -26, 0, -65, -16, 0, -190, -108, 0, 10, 94, 0, -187, 121, 0, -152, 101, 0, 84, 6, 0, -18, 125, 0, 184, -68, 0, -111, 314, 0, 21, 16, 0, 288, 88, 0, 364, -8, 0, 1, -338, 0, 140, 2, 0, 207, 336, 0, -116, -55, 0, -94, 57, 0, -103, 40, 0, -13, -22, 0, 123, 51, 0, 205, -67, 0, 286, 1, 0, -38, 78, 0, -31, -187, 0, -60, 138, 0, 475, 12, 0, 91, -202, 0, 15, 135, 0, 110, 349, 0, -86, -136, 0, 33, -40, 0, 85, -82, 0, -315, 16, 0, -122, -40, 0, 68, 100, 0, 326, -81, 0, 134, 34, 0, -10, 104, 0, 7, 371, 0, 16, 34, 0, -242, 278, 0, -80, 51, 0, -143, 259, 0, -297, -67, 0, 54, -270, 0, -12, 91, 0, 2, -8, 0, -244, -121, 0, -110, 487, 0, 77, -105, 0, 212, 69, 0, -41, 118, 0, -172, 347, 0, -133, 20, 0, -230, -304, 0, 607, -83, 0, 84, 112, 0, 210, -76, 0, 57, 112, 0, -74, -132, 0, -52, 88, 0, -35, -273, 0, 19, 226, 0, 195, -247, 0, -5, 236, 0, -83, -42, 0, -72, 253, 0, 72, 75, 0, 23, -75, 0, 411, -37, 0, -86, 101, 0, 92, -126, 0, 21, 281, 0, 231, 25, 0, -43, 16, 0, -602, -10, 0, 92, 193, 0, 276, -177, 0, 6, -32, 0, -19, 42, 0, 72, -270, 0, 191, 105, 0, 33, 321, 0, 14, 324, 0, -178, 59, 0, 414, 29, 0, 60, 289, 0, 236, -11, 0, -40, 26, 0, -4, 63, 0, 286, -368, 0, 249, 172, 0, -41, 176, 0, -10, -133, 0, -104, 114, 0, 336, -24, 0, -39, -42, 0, -111, 92, 0, -11, 281, 0, -54, -86, 0, 18, -222, 0, -135, -117, 0, -262, 54, 0, 203, 170, 0, 35, 262, 0, 233, -34, 0, 157, 113, 0, -11, 150, 0, -195, 416, 0, 193, -34, 0, -101, -354, 0, -20, -18, 0, -133, 313, 0, -237, -91, 0, -10, -134, 0, -72, -101, 0, -12, 154, 0, -220, 19, 0, 14, 268, 0, -165, 132, 0, 140, 1, 0, 86, -54, 0, -2, 140, 0, 139, 53, 0, 84, -603, 0, 325, 86, 0, 25, 66, 0, 189, -159, 0, -42, -152, 0, -269, -16, 0, -205, 11, 0, 459, 109, 0, 44, -5, 0, -125, 82, 0, 31, -19, 0, 62, 57, 0, 161, 404, 0, 297, 54, 0, 61, -461, 0, 279, -147, 0, 104, -56, 0, 129, 157, 0, 65, -38, 0, -430, -46, 0, 54, -42, 0, -48, -92, 0, 322, 167, 0, 78, 161, 0, -3, -159, 0, 93, -94, 0, -364, -182, 0, 86, 112, 0, -145, 273, 0, -269, 225, 0, 100, -297, 0, 61, -69, 0, 68, 136, 0, 493, -8, 0, -13, 69, 0, -125, -42, 0, -198, -274, 0, 228, -86, 0, 368, 117, 0, -73, -79, 0, 24, 221, 0, 252, 39, 0, 98, -222, 0, 76, 338, 0, -59, 67, 0, 159, 84, 0, -12, -26, 0, 117, -132, 0, 18, 21, 0, 173, 54, 0, -42, -129, 0, 517, 225, 0, -102, -61, 0, 9, -73, 0, -70, 272, 0, -39, -5, 0, 40, -402, 0, -140, 98, 0, 213, -600, 0, -122, -173, 0, 1, 259, 0, 35, 130, 0, 124, 110, 0, 220, -83, 0, 35, -266, 0, 309, 167, 0, 112, -119, 0, 112, 141, 0, -150, 621, 0, -83, -1, 0, 51, -447, 0, -206, 85, 0, -16, -328, 0, -311, -290, 0, -53, -143, 0, 192, 69, 0, -33, 59, 0, 350, -8, 0, -229, 373, 0, 133, 173, 0, -24, -503, 0, 165, -90, 0, -147, 112, 0, 277, -47, 0, -51, -132, 0, 65, 178, 0, -120, 0, 0, 75, 188, 0, -12, 473, 0, 233, 184, 0, 90, 5, 0, 55, 102, 0, -38, 348, 0, 319, 112, 0, 257, 240, 0, -47, 251, 0, 47, 26, 0, 380, -17, 0, -140, 17, 0, -343, 329, 0, -156, 270, 0, -304, 121, 0, 40, -240, 0, -406, 124, 0, -66, 135, 0, 53, 58, 0, 96, -286, 0, 210, 34, 0, -40, -36, 0, -49, 80, 0, 14, 246, 0, 679, 76, 0, 123, 212, 0, 14, 46, 0, -7, -305, 0, -163, -165, 0, -70, -59, 0, 139, 201, 0, 166, -38, 0, -469, 193, 0, -41, -30, 0, 171, 89, 0, 253, 242, 0, 90, -34, 0, 77, 461, 0, 116, 7, 0, 86, -461, 0, 282, 297, 0, -58, -642, 0, -42, -54, 0, 74, -133, 0, -99, 24, 0, -165, 19, 0, 335, 44, 0, -222, -104, 0, 210, 63, 0, -112, 206, 0, 23, 149, 0, -39, 507, 0, 151, 38, 0, -40, -305, 0, 352, 27, 0, 406, -288, 0, 372, -104, 0, -53, 619, 0, -201, 121, 0, -138, -142, 0, 250, 79, 0, -65, -6, 0, 322, 77, 0, 292, 386, 0, -61, -109, 0, -234, -6, 0, 114, 18, 0, 14, 282, 0, 391, 206, 0, -84, 6, 0, 67, 53, 0, -55, 623, 0, 52, -61, 0, -8, 74, 0, 278, 104, 0, 88, -111, 0, -64, -202, 0, -322, 268, 0, 145, -16, 0, 295, -167, 0, 157, -9, 0, 20, -18, 0, 219, 208, 0, 108, 233, 0, -193, -284, 0, 19, 145, 0, -191, 138, 0, -11, -23, 0, 25, 170, 0, -379, 151, 0, -104, -176, 0, 224, 368, 0, -73, 159, 0, -59, 84, 0, 204, 92, 0, -34, 22, 0, 55, 292, 0, -14, 139, 0, -249, -214, 0, 2, -230, 0, 364, -119, 0, 18, 73, 0, -134, -5, 0, 128, -33, 0, 18, 179, 0, -90, 192, 0, -13, 47, 0, -217, 442, 0, 258, 4, 0, 121, -243, 0, -2, 266, 0, -108, 16, 0, 90, 52, 0, 7, -117, 0, -23, 97, 0, 247, 72, 0, 133, -30, 0, -315, 300, 0, -50, -125, 0, -228, -171, 0, 56, -45, 0, -229, 59, 0, 414, 66, 0, -6, -290, 0, -82, -133, 0, 10, 20, 0, 565, -137, 0, 53, 806, 0, -2, 188, 0, -148, -3, 0, 69, 5, 0, -18, 106, 0, 91, 223, 0, -19, -105, 0, -35, 39, 0, 226, 184, 0, 385, 83, 0, 9, 301, 0, -146, 275, 0, -183, -146, 0, -159, -167, 0, 4, 501, 0, -414, 93, 0, 84, -146, 0, -365, 272, 0, -167, 214, 0, 273, 3, 0, -169, -249, 0, 70, -28, 0, -6, -239, 0, 276, 61, 0, 1, 349, 0, -612, -302, 0, -61, -450, 0, 97, -5, 0, 36, -161, 0, 182, -176, 0, -128, -244, 0, -363, -264, 0, -97, -168, 0, -23, 235, 0, 4, -19, 0, 24, 607, 0, 152, 465, 0, 257, 70, 0, 25, -1, 0, -18, 168, 0, -215, -209, 0, 28, -271, 0, -123, -44, 0, -15, 7, 0, -304, 28, 0, -183, 125, 0, -225, -159, 0, 112, 193, 0, 410, -160, 0, 7, 13, 0, 38, 291, 0, 328, -31, 0, -153, -1, 0, -110, 116, 0, 173, -395, 0, -274, -140, 0, 22, 326, 0, -342, 227, 0, -123, 35, 0, 115, 6, 0, 60, 120, 0, -286, 85, 0, -223, -205, 0, 127, -66, 0, 21, -128, 0, 174, 23, 0, 64, -667, 0, -392, -157, 0, -97, -36, 0, -88, -57, 0, -70, 191, 0, 72, 109, 0, 208, -93, 0, 93, -9, 0, -32, 22, 0, -226, -354, 0, 138, 8, 0, 171, 4, 0, -116, -209, 0, 386, -41, 0, -317, -116, 0, 74, 39, 0, -502, -181, 0, 47, 147, 0, 16, 170, 0, -142, 51, 0, -137, 1, 0, -17, 109, 0, -11, 470, 0, -185, 322, 0, -383, -335, 0, 42, -21, 0, -347, -30, 0, -162, -9, 0, -109, 401, 0, -297, 110, 0, -31, -570, 0, -76, 77, 0, -4, -84, 0, -103, 0, 0, 13, -6, 0, 139, 485, 0, 200, -401, 0, -138, -212, 0, 232, 58, 0, -43, 321, 0, -352, 721, 0, 314, 107, 0, 29, 247, 0, -445, 47, 0, -341, 56, 0, 1, -2, 0, 1, -95, 0, 12, 270, 0, -38, -144, 0, -582, 109, 0, 58, 74, 0, 444, 73, 0, -103, 340, 0, -109, 138, 0, -77, 82, 0, -573, 97, 0, -18, -103, 0, 10, -81, 0, -534, -335, 0, -116, -325, 0, -63, 606, 0, -494, -48, 0, 271, -85, 0, 239, -186, 0, -314, 1, 0, 513, -23, 0, -22, 338, 0, 52, 72, 0, -29, 768, 0, -286, -12, 0, -107, 135, 0, -225, -29, 0, 162, 90, 0, 163, 142, 0, 63, 111, 0, -606, 312, 0, -178, -51, 0, -287, 41, 0, -107, 243, 0, -392, 131, 0, 50, -177, 0, -80, 59, 0, -136, -71, 0, 998, -66, 0, -36, 150, 0, 456, 213, 0, -303, -381, 0, -126, -68, 0, -105, 191, 0, 20, 381, 0, -315, -15, 0, -560, 35, 0, -248, -13, 0, -258, -248, 0, -20, 907, 0, -10, 160, 0, -147, -161, 0, 320, 88, 0, -1, 237, 0, 48, 155, 0, -386, -426, 0, 121, -312, 0, 19, -294, 0, -520, -144, 0, -300, 26, 0, -21, 226, 0, -346, 135, 0, -175, 252, 0, -34, -18, 0, -98, 168, 0, -84, 194, 0, -89, 50, 0, 86, -119, 0, -240, 120, 0, 215, -467, 0, 399, -255, 0, -36, 543, 0, 431, 177, 0, 159, -45, 0, -215, 171, 0, -64, -159, 0, 111, -171, 0, -125, 207, 0, -100, 504, 0, -691, 819, 0, 390, 31, 0, -176, 52, 0, -651, -146, 0, -66, -468, 0, -316, 122, 0, 157, -215, 0, 52, 108, 0, 1, 6, 0, -141, -47, 0, 308, 200, 0, 120, 88, 0, 205, -491, 0, 154, 213, 0, -321, 255, 0, -290, 104, 0, 326, -81, 0, 13, 62, 0, 69, 129, 0, 186, 52, 0, -15, 379, 0, -76, -254, 0, -279, -54, 0, -4, 68, 0, -270, 174, 0, 1, -397, 0, 435, 411, 0, -110, 31, 0, 107, 9, 0, -239, 27, 0, -38, -222, 0, 161, -210, 0, -81, -366, 0, -362, 90, 0, 43, 440, 0, 269, 291, 0, 20, -116, 0, 237, -159, 0, 363, 45, 0, -532, -195, 0, -193, -275, 0, 19, 44, 0, -15, -583, 0, 265, 11, 0, 230, 33, 0, -390, -181, 0, -322, -391, 0, -282, -188, 0, -32, 37, 0, 454, 182, 0, -227, -20, 0, 66, -50, 0, 196, 323, 0, 220, -285, 0, 68, 116, 0, 91, 309, 0, -96, -188, 0, -86, 7, 0, 299, -43, 0, -78, 24, 0, -242, -974, 0, -123, -85, 0, 26, -154, 0, 167, 96, 0, -22, 66, 0, 77, 112, 0, 41, 125, 0, -663, -13, 0, 20, 474, 0, 45, 242, 0, 20, 377, 0, 107, -49, 0, -37, -99, 0, -290, 156, 0, -455, 68, 0, -687, 220, 0, 23, 300, 0, -209, -213, 0, -238, -112, 0, -140, -328, 0, 262, -5, 0, -366, -192, 0, 310, 314, 0, -10, 85, 0, -116, 48, 0, 376, -72, 0, 15, -599, 0, -493, -3, 0, 25, -161, 0, -8, 121, 0, 6, -213, 0, -343, 94, 0, -75, -78, 0, 93, -22, 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": "2667.2.a.o", "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], [1, 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], [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, 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, -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, 0], [0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0], [-1, 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, 1, 0, -1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 1, 0, 0, 1, 0, 1, 0, -1, 1, 1, 0, 0, 0], [1, 0, 1, 1, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 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, -1, 1, 0, -1, -1, 1, 1, -1], [-1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1, -1, 1, -1], [-1, -1, 0, -1, -1, 0, 2, -1, 2, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 2, 0, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, -2, 1], [0, -1, -1, -1, 0, 0, -1, 0, 0, 1, 1, 0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0], [-3, 0, -2, -1, 1, 1, 0, -1, -1, -1, 0, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, -2, -1, 0, 0, 2, -1, 1, 1, 0, 0, -1, 1], [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, 1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0], [-3, 2, -2, -1, -1, -1, 0, 1, 1, 0, 2, 0, -3, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, -3, 1, 2, 0, -2, 0, -4, 1, -1, -2, 0, 1, 0, -1], [1, 0, 0, 1, -1, -2, 0, 0, 0, 0, 1, 0, 0, 2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 0, -1], [-1, 0, 0, 1, 0, 1, 1, 0, -2, -1, -1, 1, 0, 1, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 3, 2, 0, -1, -1, 0, -2, 1, 2, -2, 0, 1], [-2, 1, 0, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -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], [2, -2, 1, 0, 1, 0, -2, -1, 0, 1, 1, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 3, 2, 1, 0, -1, -1, 0, 0, 0, 1, 0, -2, 3, -2, 0], [-3, -1, -1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, -1, -2, 0, 1, 0, 1, 2, 0, -1, 3, 0, -1], [0, 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, 0], [-1, 3, 1, 0, -2, 0, 2, 0, 0, -2, 0, 1, -1, 1, -1, 1], [0, -1, 0, 1, 0, 2, 0, 0, -2, 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, -3, -2, -1, 0, 3, 1, 2, 0, 0, 0, 0, 1, 1, -1], [-3, 3, -2, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, 1, -1, -2, 0, 2, 0, 3, 0, 0, 1, 0, -2, 1, 0], [-5, -2, -1, 0, 0, 2, 2, 0, 2, -1, -2, 0, 1, -4, 2, -1], [0, 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, -1, 1, -1, 0, 1, 0], [1, 0, 0, 1, 3, 0, -4, -1, -3, 1, 0, -2, 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, 1, 0, 0, 1, 0, -1, 0, 0], [-4, 1, 1, -1, 0, 0, -1, 0, 2, -1, 0, 1, 0, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 2, 0, 2, -1, 0, 1, 0, -1, 1, 0], [-4, -5, -1, -1, 0, 1, 2, 0, 2, 0, -2, 1, 2, -3, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 4, -1, 3, 2, 0, -2, 0, -3, 2, 1, -2, 0, 3, -1, -1], [1, 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, -2, -3, 1, 1, 0, -1, 2, -1, 0, 0, 0, -3, 2, 1], [-1, 2, 3, 0, -4, -2, 4, 0, 5, -1, 1, 2, -1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 5, 2, 2, 2, 0, -5, 0, -2, 0, 0, 0, 0, -1, -1, 2], [-1, 1, 1, 2, -1, 0, -2, 1, -1, 1, 0, 0, 0, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -2, -1, 1, 0, 0, -1, 0, -1, 0, -1, 1, -3, 0, 1], [0, 3, 3, 1, 0, -2, -2, 0, 0, -2, 3, 1, -2, 3, -4, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, -1, 1, 1, 2, -1, 3, 1, -2, 0, 3, -5, 3, -1], [-1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, -1, -1, -2, 2, 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, -1, 0, 1, -1, 0, -1], [-3, -2, 0, -3, -3, 0, 4, 1, 4, -1, 0, 3, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, -1, -2, 0, 1, 0, 1, 1, 0, -1, 0, 0, 2, -2], [-3, -2, -3, -2, -1, 0, 0, 1, -1, 2, 0, -1, -1, 3, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 0, 1, -2, -1, 0, 0, 0, 0, 0, -1, 0, 1, 2, -2], [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], [2, 4, 5, -1, -2, -2, -2, 0, 2, -1, 3, 3, -4, 2, -2, 3]]}