# Stored data for newform 8001.2.a.w, downloaded from the LMFDB on 28 March 2024. {"label": "8001.2.a.w", "space_label": "8001.2.a", "level": 8001, "weight": 2, "hecke_orbit": 23, "hecke_orbit_code": 99079191835713345, "dim": 20, "is_polredabs": true, "trace_hash": 1275957716558146007, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [31, 425, 609, -6812, -8607, 25504, 32493, -35701, -52271, 17664, 39579, 56, -15474, -2977, 3125, 1061, -274, -152, 0, 8, 1]], [5, [-203968, -1241664, -467616, 5947520, 2267944, -8263246, -2710324, 5458748, 1651483, -2020391, -595740, 445364, 132200, -58925, -17889, 4519, 1412, -183, -59, 3, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{4}+\\beta _{16}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": 2, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [8001, 1, [3557, 1144, 7750], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [3, 7, 127], "conrey_indexes": [1], "field_disc": 411102131650701070875492242301442027696372, "field_disc_factorization": [[2, 2], [7, 1], [151, 1], [370181731769737, 1], [262663524380673860066677, 1]], "field_poly": [31, -425, 609, 6812, -8607, -25504, 32493, 35701, -52271, -17664, 39579, -56, -15474, 2977, 3125, -1061, -274, 152, 0, -8, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.953", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "834.820", "prec": 24}, {"__RealLiteral__": 0, "data": "1069.044", "prec": 27}, {"__RealLiteral__": 0, "data": "78855.758", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 20, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [7, -1], [127, 1]], "trace_display": [-8, 0, -3, 20], "traces": [0, 20, -8, 0, 24, -3, 0, 20, -24, 0, -8, -26, 0, -4, -8, 0, 24, -4, 0, 1, 2, 0, 1, -31, 0, 27, -4, 0, 24, -16, 0, 6, -41, 0, -10, -3, 0, 2, -3, 0, -38, -25, 0, 13, -66, 0, 20, -19, 0, 20, 4, 0, 20, -24, 0, -3, -24, 0, 12, -23, 0, -27, -7, 0, 2, -26, 0, 9, 25, 0, -8, -63, 0, -21, -21, 0, -10, -26, 0, 18, 23, 0, -42, 1, 0, -41, 12, 0, 57, 16, 0, -4, -17, 0, 7, -75, 0, -32, -8, 0, 8, -41, 0, -43, 7, 0, -44, -33, 0, -14, 59, 0, 24, -40, 0, -5, -32, 0, -16, -4, 0, -6, 2, 0, -64, 21, 0, -20, -69, 0, -53, -59, 0, 1, 28, 0, -27, -43, 0, -18, 2, 0, -28, -38, 0, -43, -15, 0, -60, -55, 0, 43, 30, 0, 1, -12, 0, 0, -17, 0, -79, -31, 0, 29, -40, 0, -109, -24, 0, -18, -9, 0, -67, 18, 0, 27, -26, 0, 3, -3, 0, 3, -4, 0, -15, 19, 0, -37, 8, 0, -141, -125, 0, -34, 54, 0, 24, -12, 0, 42, 6, 0, -126, -16, 0, 3, 0, 0, -83, 47, 0, -2, 32, 0, 10, -89, 0, 6, 26, 0, -107, -18, 0, -77, -41, 0, 3, -64, 0, -37, 138, 0, -60, -75, 0, -78, 89, 0, -10, -137, 0, -5, -61, 0, -86, -3, 0, 52, 42, 0, -114, 2, 0, -34, 8, 0, 132, 92, 0, 2, 28, 0, 32, -100, 0, -77, -3, 0, 65, -77, 0, 91, 50, 0, -9, -116, 0, 20, 127, 0, -38, 18, 0, 8, -54, 0, 112, -25, 0, -10, -44, 0, -82, 41, 0, -12, -24, 0, 137, -79, 0, 13, -31, 0, 1, -13, 0, -37, -66, 0, 135, -129, 0, -80, 9, 0, -7, -30, 0, -42, 57, 0, 20, -18, 0, -58, -149, 0, 49, -19, 0, 6, 39, 0, -5, 23, 0, 8, 31, 0, 73, 50, 0, 20, 2, 0, 141, 20, 0, -45, 4, 0, 151, 46, 0, 23, 56, 0, -87, -221, 0, 45, 48, 0, 20, 27, 0, 50, -94, 0, 103, -24, 0, -30, 41, 0, -17, 82, 0, -9, -49, 0, 195, -108, 0, -3, -104, 0, -11, -55, 0, -51, -24, 0, -36, -101, 0, 19, -71, 0, 34, -89, 0, -53, -55, 0, 12, -3, 0, -25, 51, 0, 69, -23, 0, 155, -12, 0, -113, 40, 0, -120, 0, 0, 10, -9, 0, -27, -29, 0, 190, -94, 0, -134, -7, 0, -9, 4, 0, 20, 95, 0, -27, -37, 0, -15, -23, 0, 2, -72, 0, 114, -234, 0, -1, -26, 0, -2, 138, 0, -62, -78, 0, 44, -52, 0, 152, 70, 0, 9, 5, 0, 173, -32, 0, -54, 25, 0, 17, -236, 0, -64, -61, 0, -67, 9, 0, -35, 83, 0, -8, -126, 0, -57, 130, 0, 99, -63, 0, -30, 22, 0, -108, 8, 0, -65, -34, 0, -24, 1, 0, -21, -110, 0, 111, 24, 0, 11, -21, 0, -178, 127, 0, -21, -284, 0, -62, -172, 0, 37, -14, 0, -10, -65, 0, 34, -55, 0, 281, -26, 0, -44, 4, 0, -12, 28, 0, -35, 162, 0, 108, -182, 0, 18, -72, 0, 137, -37, 0, -132, 23, 0, 215, 115, 0, 4, -122, 0, -125, 43, 0, -30, -120, 0, -42, -161, 0, 54, -32, 0, 234, 1, 0, -50, 180, 0, -126, -65, 0, -63, 74, 0, -2, 73, 0, -41, -181, 0, 127, -43, 0, -109, 12, 0, 32, 58, 0, 35, 101, 0, -233, 27, 0, -41, -28, 0, 57, -89, 0, -56, -133, 0, 115, 16, 0, -82, 136, 0, -87, -15, 0, 29, 92, 0, -57, 3, 0, -4, 76, 0, -5, -30, 0, -31, -17, 0, 0, 122, 0, -31, -304, 0, 73, 24, 0, -67, -179, 0, 7, -112, 0, -51, -73, 0, -218, -75, 0, 37, 26, 0, -29, -140, 0, -110, 106, 0, -62, 75, 0, -32, -65, 0, 94, 67, 0, -117, -8, 0, -138, 13, 0, 21, -199, 0, -38, -82, 0, -88, 251, 0, 8, -72, 0, -43, -100, 0, 293, -41, 0, -151, 269, 0, -239, 194, 0, -132, 24, 0, 216, -310, 0, -43, -108, 0, -115, 120, 0, -89, 7, 0, -230, 126, 0, 104, -85, 0, -135, 10, 0, -165, -154, 0, -44, -88, 0, -107, -146, 0, -149, -33, 0, -28, 172, 0, -124, 33, 0, -30, 75, 0, 231, -40, 0, -14, -295, 0, 94, -32, 0, -40, 59, 0, -121, 163, 0, -117, -294, 0, -141, 113, 0, 28, -204, 0, 24, -72, 0, -75, 125, 0, 23, -40, 0, -129, 259, 0, 198, 121, 0, -9, 294, 0, 39, 5, 0, -5, -111, 0, -81, -80, 0, 24, -32, 0, -1, -53, 0, -181, 143, 0, -155, -21, 0, -47, -137, 0, -16, -87, 0, -142, -35, 0, 119, -4, 0, -145, 307, 0, -86, -31, 0, 124, 55, 0, -72, 152, 0, -6, 162, 0, 106, -25, 0, -45, 2, 0, 24, 193, 0, 61, -309, 0, -78, -76, 0, -305, -32, 0, -64, 15, 0, -34, 38, 0, -89, 21, 0, -7, 234, 0, -176, 83, 0, -150, 176, 0, 1, -101, 0, -20, -33, 0, -47, 76, 0, -19, -69, 0, -79, 78, 0, -20, -63, 0, 107, 13, 0, -132, -129, 0, -53, -19, 0, -95, -91, 0, 134, -59, 0, 59, 307, 0, 199, 148, 0, -99, 292, 0, -74, 84, 0, 1, -235, 0, 3, 230, 0, -171, 28, 0, -126, 128, 0, 9, -6, 0, -59, 38, 0, -153, 284, 0, -27, -110, 0, 52, -151, 0, 277, -43, 0, 20, 343, 0, -128, 93, 0, 56, 87, 0, -34, -106, 0, -18, -241, 0, 17, -83, 0, -184, 2, 0, -186, -2, 0, 102, -78, 0, -190, -32, 0, -25, -220, 0, -28, -50, 0, -139, 241, 0, -118, -38, 0, -82, 72, 0, -91, 132, 0, -83, 216, 0, 223, 78, 0, -43, 24, 0, 172, 131, 0, -34, -15, 0, 123, 120, 0, 196, 213, 0, 449, -160, 0, -36, -121, 0, -60, -27, 0, 67, 327, 0, 169, -55, 0, 132, -92, 0, 24, 102, 0, 48, -104, 0, -264, -176, 0, 43, -72, 0, 183, -139, 0, -138, 30, 0, 41, 188, 0, 84, -170, 0, 1, -11, 0, 0, -206, 0, 1, -108, 0, -115, 4, 0, 65, -12, 0, 37, 102, 0, 41, 45, 0, 67, 126, 0, 169, -7, 0, 0, -175, 0, 448, 164, 0, 204, -17, 0, 114, 261, 0, 93, 165, 0, -32, 104, 0, -21, 298, 0, -79, -271, 0, 33, 7, 0, 279, -31, 0, 43, 272, 0, 67, 104, 0, 83, 272, 0, 77, -163, 0, 29, -311, 0, 210, -106, 0, -155, -40, 0, 284, -378, 0, -40, 117, 0, -84, -92, 0, -54, -137, 0, -109, -215, 0, 37, 90, 0, 47, -24, 0, -85, 400, 0, 333, -138, 0, 253, 212, 0, -282, 148, 0, -18, 17, 0, 157, 7, 0, -77, -9, 0, 642, 169, 0, -159, -347, 0, -379, -289, 0, -5, -87, 0, -67, -75, 0, 121, 13, 0, -8, 18, 0, -58, -8, 0, -11, -37, 0, 55, 468, 0, 181, -123, 0, 27, -81, 0, 323, -52, 0, 90, -26, 0, -118, 174, 0, 106, 94, 0, 60, -118, 0, 19, -358, 0, 3, -9, 0, -32, 24, 0, -97, -3, 0, 41, 148, 0, 205, 32, 0, -32, 13, 0, -274, 49, 0, 3, -8, 0, 8, -186, 0, 12, -4, 0, -96, 70, 0, 289, 75, 0, 31, 70, 0, 6, -82, 0, -15, -276, 0, 39, -45, 0, -118, 19, 0, -15, 161, 0, 585, 44, 0, -103, -92, 0, 165, 129, 0, -37, 158, 0, 423, -6, 0, -49, 8, 0, 36, -374, 0, -214, -165, 0, 194, 184, 0, 28, 276, 0, -141, 81, 0, -47, 310, 0, 365, -125, 0, 92, 409, 0, 154, 1, 0, -179, 210, 0, 51, -217, 0, -34, -102, 0, 270, -2, 0, -59, 54, 0, 84, 122, 0, 19, -110, 0, -139, -39, 0, -128, 14, 0, 24, -70, 0, 150, 311, 0, -334, -12, 0, -123, 90, 0, 405, 69, 0, -138, 274, 0, 2, -127, 0, 42, -56, 0, 53, 26, 0, 182, 6, 0, 236, -75, 0, 259, -330, 0, 227, 146, 0, 119, -268, 0, -126, -42, 0, -57, 205, 0, 126, -16, 0, 231, 419, 0, -41, -25, 0, 131, 289, 0, -378, 47, 0, 3, -198, 0, 337, -41, 0, 103, 0, 0, 203, 94, 0, 9, 78, 0, -373, -97, 0, 35, -398, 0, -83, -200, 0, 252, 46, 0, 255, 47, 0, -91, 226, 0, -75, -122, 0, 90, 195, 0, -227, -68, 0, -2, 61, 0, 417, -226, 0, -39, 32, 0, 16, -10, 0, 215, 197, 0, -259, -37, 0, -44, 434, 0, 10, 128, 0, 66, 60, 0, -301, -89, 0, 96, 404, 0, -236, -220, 0, 185, 516, 0, 320, 76, 0, 6, -478, 0, 330, 43, 0, 444, 26, 0, 130, 98, 0, -37, -270, 0, -135, -15, 0, -59, 109, 0, -107, -116, 0, 14, -136, 0, -81, -18, 0, -44, 174, 0, 405, 195, 0, -64, 335, 0, -51, -205, 0, -77, 409, 0, -54, 106, 0, -142, -41, 0, 104, 34, 0, 194, 60, 0, -216, -142, 0, -166, -75, 0, 3, -142, 0, -106, -127, 0, 97, -64, 0, 213, 91, 0, -166, -45, 0, 185, 350, 0, -278, 23, 0, -37, -52, 0, 127, 20, 0, 79, 138, 0, -116, 218, 0, -4, 177, 0, -116, -68, 0, 51, 110, 0, -60, -105, 0, 12, 352, 0, 63, -75, 0, 27, 333, 0, -297, 84, 0, 75, 374, 0, -143, -50, 0, -78, 139, 0, -238, 42, 0, 4, 89, 0, 150, -182, 0, 73, -40, 0, 500, 95, 0, -100, 127, 0, -10, -7, 0, -30, 141, 0, -212, -137, 0, -16, 106, 0, -37, -100, 0, 53, 245, 0, -514, -153, 0, -5, 332, 0, 312, -99, 0, -40, -61, 0, -82, 212, 0, 58, -14, 0, -245, -44, 0, 33, 292, 0, -86, -76, 0, 58, 112, 0, -240, -3, 0, 5, 449, 0, 497, 17, 0, -2, 278, 0, 228, -193, 0, 52, 359, 0, 298, -65, 0, 73, 42, 0, 22, 270, 0, 352, -169, 0, -277, 226, 0, -286, 261, 0, -114, -274, 0, 215, 234, 0, -128, 2, 0, 141, 627, 0, -32, 16, 0, 311, 80, 0, -189, 192, 0, -34, -137, 0, -154, -217, 0, -122, 8, 0, 179, 258, 0, -38, -286, 0, -45, -50, 0, 102, 135, 0, 132, -48, 0, -92, -282, 0, 71, 92, 0, -126, 489, 0, 393, 228, 0, -181, -161, 0, -38, 228, 0, 2, -30, 0, 260, -53, 0, -237, 28, 0, 364, 9, 0, 240, 308, 0, -57, 244, 0, 18, 91, 0, 32, 51, 0, 8, -55, 0, 65, -100, 0, 131, 102, 0, -216, -41, 0, 87, 77, 0, 102, 309, 0, -77, 119, 0, 195, 38, 0, 303, -3, 0, 337, 202, 0, 191, 504, 0, -178, -133, 0, -228, -141, 0, 65, -18, 0, 326, 324, 0, -127, -77, 0, -33, 604, 0, 124, 68, 0, -339, 336, 0, 86, 494, 0, 91, 163, 0, -151, -111, 0, -10, 50, 0, -412, -70, 0, 276, 129, 0, 419, -144, 0, -258, -286, 0, -9, -61, 0, -115, 253, 0, -244, -116, 0, 198, 640, 0, 355, -223, 0, 152, 627, 0, -16, 187, 0, 20, -8, 0, 69, -52, 0, -264, 127, 0, 351, 270, 0, -36, 375, 0, -56, 305, 0, -138, 250, 0, -38, -202, 0, -298, 439, 0, 165, 18, 0, -73, 407, 0, -259, -123, 0, -144, 467, 0, -328, 41, 0, 8, 44, 0, 262, -280, 0, 0, -54, 0, -173, -158, 0, 105, 151, 0, -321, 151, 0, -122, 220, 0, 112, 56, 0, 202, 129, 0, -597, -25, 0, -156, 542, 0, -104, -216, 0, 67, 193, 0, 122, 146, 0, -10, -340, 0, -229, 5, 0, -66, -44, 0, -24, 104, 0, 100, -192, 0, 16, -288, 0, 303, 215, 0, -82, -228, 0, 139, -63, 0, -83, 41, 0, -115, 281, 0, -134, 229, 0, -148, 263, 0, 24, -93, 0, -12, 67, 0, 340, 28, 0, 110, -24, 0, 395, 85, 0, 56, 53, 0, -399, -13, 0, -44, 232, 0, 137, 210, 0, 39, 319, 0, -78, -79, 0, -174, -72, 0, -308, 10, 0, 459, 348, 0, -33, 213, 0, 13, -66, 0, 566, -251, 0, -58, -31, 0, 292, 139, 0, -71, -27, 0, 216, 450, 0, -459, 454, 0, 1, -119, 0, 111, -35, 0, -292, -13, 0, 141, -20, 0, -322, -31, 0, 32, -76, 0, 605, 107, 0, -37, 161, 0, 170, -358, 0, -148, -66, 0, -186, 4, 0, -26, -102, 0, 101, -63, 0, 262, -177, 0, 135, 174, 0, -144, -194, 0, -8, -129, 0, 110, 184, 0, 214, -78, 0, 121, 174, 0, -286, -171, 0, -80, 59, 0, -283, -334, 0, -188, 9, 0, 321, 78, 0, -138, -571, 0, 144, -5, 0, -247, 299, 0, -7, -93, 0, 242, -450, 0, 237, -30, 0, 82, 404, 0, 109, 22, 0, -21, 256, 0, 301, -4, 0, -42, 85, 0, -182, 22, 0, 304, 57, 0, 354, -201, 0, 183, -359, 0, 119, 57, 0, -143, 189, 0, 20, 80, 0, 90, 192, 0, -280, -18, 0, -43, -166, 0, -350, 143, 0, 128, 327, 0, -162, 1, 0, -58, 566, 0, 187, -214, 0, 212, -149, 0, 301, 114, 0, -218, -403, 0, 148, -98, 0, 657, -234, 0, 49, -386, 0, -82, -747, 0, -93, -19, 0, 95, -183, 0, -54, -97, 0, -37, -28, 0, -127, 354, 0, 6, 373, 0, 838, -40, 0, -118, 39, 0, 155, 26, 0, -169, -412, 0, 22, -52, 0, 221, 529, 0, -5, -208, 0, -212, -174, 0, -219, 23, 0, 64, -368, 0, 175, -577, 0, 40, 133, 0, -87, 224, 0, 8, -145, 0, -136, -124, 0, 646, 31, 0, -91, 190, 0, 163, -193, 0, -79, -424, 0, -133, 472, 0, 73, 88, 0, -48, -723, 0, -426, 50, 0, 7, 340, 0, 287, 73, 0, -100, 437, 0, 172, -174, 0, 20, -234, 0, -209, -205, 0, -65, 2, 0, 128, -176, 0, -1, -239, 0, 552, -3, 0, -140, 287, 0, 141, 222, 0, -79, -276, 0, 194, 20, 0, -70, 60, 0, -25, 300, 0, 2, -253, 0, -133, 245, 0, -45, -259, 0, 207, -202, 0, -73, 4, 0, 206, 331, 0, 10, -116, 0, -160, -22, 0, -29, 95, 0, 151, 221, 0, 16, -225, 0, 545, 46, 0, 433, 585, 0, -782, -136, 0, -439, 374, 0, 587, 231, 0, 23, -109, 0, 297, -166, 0, 145, 56, 0, 153, -324, 0, 206, -244, 0, -336, 229, 0, -218, 190, 0, -87, 348, 0, 170, -120, 0, -415, -221, 0, 164, -15, 0, 99, -275, 0, -132, 302, 0, 43, -4, 0, 45, 94, 0, -460, 132, 0, 356, 48, 0, 31, 248, 0, -153, -2, 0, 746, -206, 0, -80, 201, 0, 20, -354, 0, 176, 538, 0, 512, 27, 0, -122, 22, 0, 238, -58, 0, -43, 178, 0, -79, 382, 0, 50, -411, 0, -367, 107, 0, -408, -94, 0, 447, -247, 0, 389, -76, 0, -125, -109, 0, -38, 308, 0, 103, -302, 0, 136, -749, 0, -127, -24, 0, 79, -147, 0, 80, 3, 0, 281, 187, 0, 524, 116, 0, -30, -173, 0, -277, -398, 0, -88, 41, 0, 128, 137, 0, -77, -669, 0, -43, 30, 0, 433, -38, 0, -17, -9, 0, 98, -121, 0, 63, 82, 0, -337, 199, 0, 252, -218, 0, -152, 19, 0, -2, 389, 0, -9, -664, 0, -256, -65, 0, -100, -49, 0, 349, -272, 0, -370, -432, 0, -134, 127, 0, -43, -336, 0, 195, 3, 0, 22, -68, 0, 18, -108, 0, -161, 211, 0, 32, 50, 0, 272, 579, 0, 24, 35, 0, -3, 289, 0, 76, -344, 0, 144, -104, 0, -36, 241, 0, -426, 40, 0, 199, 93, 0, -145, -261, 0, -11, 237, 0, 99, -747, 0, 14, -55, 0, -89, 225, 0, -88, -221, 0, -96, 23, 0, -63, 13, 0, -51, 170, 0, 16, -408, 0, -22, -24, 0, -26, -88, 0, 178, 225, 0, -64, -217, 0, -484, 88, 0, -36, 146, 0, -161, 109, 0, -544, -101, 0, -25, -321, 0, 5, 77, 0, 85, 412, 0, -32, 394, 0, 19, -269, 0, 368, -111, 0, 28, -71, 0, -296, -96, 0, -155, 187, 0, -1, 214, 0, -167, -244, 0, 34, -106, 0, -60, 26, 0, 312, -89, 0, 132, -179, 0, 510, -241, 0, -493, -373, 0, -449, -81, 0, -53, 15, 0, 689, -10, 0, -578, -55, 0, 548, 83, 0, 246, 99, 0, -142, 83, 0, 284, -210, 0, 12, 215, 0, -127, -187, 0, -330, -3, 0, -65, 765, 0, -188, -24, 0, -223, 20, 0, -27, 331, 0, -25, 195, 0, 611, 113, 0, 230, 51, 0, 654, -95, 0, 26, -739, 0, 119, -590, 0, -154, 23, 0, 69, 194, 0, -111, -300, 0, -484, -23, 0, 34, 196, 0, -856, 451, 0, -136, 161, 0, 47, 122, 0, 155, -162, 0, 270, -136, 0, -245, -12, 0, -224, -203, 0, -273, -162, 0, -366, 31, 0, 171, -417, 0, -113, -28, 0, -119, -413, 0, -209, 40, 0, -62, -410, 0, 159, -61, 0, 108, 30, 0, -246, -12, 0, -120, -70, 0, -52, -392, 0, -7, 0, 0, -64, -14, 0, -301, -594, 0, 157, -142, 0, 265, -113, 0, 10, 46, 0, -244, -295, 0, -58, -9, 0, 363, -860, 0, -360, -363, 0, -24, 335, 0, 602, 341, 0, -27, -199, 0, -263, -252, 0, 16, -29, 0, -179, -420, 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": "889.2.a.d", "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], [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, 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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [-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, 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, -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, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 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], [-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1], [-1, 1, 1, 1, 0, 0, 0, -1, 1, -1, 1, 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, 0, 0, 0], [-1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-2, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 0, -1, 1, -1, -1, 0, -1, 0, 1, 0, 0, 0, 0, -1, -1, -1, -1], [0, -1, 1, 0, 0, -1, 1, 0, -1, 2, 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, 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], [1, -1, 1, 1, 0, -1, 0, -1, 0, 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, 0, 0, 1, -1, 0, 1, 1, -1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0], [-1, 1, -3, -1, -2, 1, -1, -1, -1, 1, -1, 1, 0, 0, 0, -1, -2, -1, -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, -1, -1, -1, 0, 1, 0, -1, -1, 0, -1, 0, -1, 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], [1, -1, 0, 0, 0, 0, 1, 0, -2, 2, -1, 0, 0, 1, 1, -1, 1, 0, 0, 1], [0, 1, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0, 2, -2, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, 0, 0, 0, 1, 1, -1, 0, -1, 0, 0, 0, 1, -2, -1, 0, 0, 0], [-1, 2, -2, -1, -1, 0, 1, 0, 0, 0, -1, 2, 0, 0, 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, -2, 0, 0, 1, 0, 0, -1, 1, -1, 0, 1, -1, 1, -1, -1, 0, 0, 0], [-3, 1, -2, 0, -1, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, -2, -1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -1, 0, -1, -1, 1, -1, 1, -3, -1, 2, -1, 0, -1, 0, 0, -1, -1, -1], [-1, 0, 0, 0, 0, 0, 1, 0, -1, 1, 0, 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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 0, 0, 0, 0, 1, 0, 1, 1, -1, 1, 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], [2, 1, -2, 0, 0, 1, -1, -1, 1, -2, 0, 1, 1, 0, -2, 1, 0, 0, -1, 0], [-3, 3, -1, 0, 1, 1, -2, 0, 1, -2, 2, 0, -1, -1, -1, 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], [0, 0, -1, 0, -1, 1, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, -3, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, -1, 2, 1, -2, 2, -2, 0, 1, 2, 1, -2, 0, 1, 0, 0], [-1, -1, 1, -1, 0, 0, 0, 0, -1, 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, 0, 0, 0], [-2, 1, 0, 0, -1, 1, 0, -2, 0, 0, 1, 1, -2, 0, 1, 1, -1, -1, -1, -1], [0, 1, 1, 0, -3, -1, 1, -1, 0, 0, -1, 2, -1, 1, 1, 0, -1, -1, -1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 3, 2, 2, 2, 0, -1, 1, 1, -1, 2, -2, 1, -1, -1, 1, 1, 1, 2, 0], [-5, 3, 1, 1, 0, 1, 0, -1, 1, 0, 3, -1, -1, -2, 0, 2, -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, 0, 2, 1, -1, -1, 0, -1, 1, -2, 1, 0, -2, -1, 0, 1, -1, -1, 0, -1], [0, -1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2], [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, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [-4, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 2], [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, -1, -2, -1, 2, 1, -1, -1, 0, 1, 1, 0, -1, 0, -1], [0, 1, -1, 1, 1, 0, -1, -1, 1, 0, 0, 0, 1, 0, -3, 0, 2, 1, 0, 1], [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, -1, 0, 1, -2, 2, 0, -1, 1, 2, 1, -1, 0, 0, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 1, -1, 1, 0, 0, -1, 0, -1, -1, 0, -1, 1, 0, 0, -1, 1], [2, 3, -1, 1, 1, 0, -1, 0, 3, -2, -1, 0, 2, 0, -3, 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], [-4, 2, 1, 1, 3, -1, -1, 1, 3, -3, 2, -3, 0, 0, -2, 3, 1, 1, 1, 0], [-2, 3, 0, 1, 1, 1, -2, 0, 2, -1, 2, -2, 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, 0, 0], [-2, -3, 3, 0, 2, -3, 2, 1, 2, 1, 0, -1, 0, 1, -1, 1, 2, 1, 1, 2], [0, 1, 1, 2, -1, 1, -2, -1, 0, 0, 2, 0, 1, 1, -3, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, 1, 0, -1, -1, 2, -4, 1, 0, 1, 0, -3, 2, 1, 2, 0, 1], [1, -2, 3, 2, -1, 1, 0, 0, -1, 3, -1, 0, 1, 2, 1, 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, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-2, -1, 0, 1, 3, -2, 1, 3, 1, -1, 0, -3, 0, 1, 0, 0, 1, 2, 1, 2], [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, -1, 0, 1, 0, -1, 1, 1, -2, 1, 1, 2, -1, 1], [-6, 1, 0, -2, 0, 0, 2, 1, -2, 3, -1, -1, -1, 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], [-2, 2, 0, 2, 0, 0, -1, 0, 1, -1, 2, 0, 0, -2, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, -2, -1, 0, 0, -2, 1, -2, 1, 1, -1, -1, -2, 3, 0, 0, 0, -1]]}