# Stored data for newform 7168.2.a.bi, downloaded from the LMFDB on 23 April 2024.
{"label": "7168.2.a.bi", "space_label": "7168.2.a", "level": 7168, "weight": 2, "hecke_orbit": 35, "hecke_orbit_code": 153122387364158464, "dim": 12, "is_polredabs": true, "trace_hash": 666901885478106900, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [64, 0, -384, 0, 772, 0, -632, 0, 196, 0, -24, 0, 1]], [5, [2304, 0, -10176, 0, 9892, 0, -3688, 0, 580, 0, -40, 0, 1]], [11, [541696, 0, -569344, 0, 190080, 0, -28736, 0, 2148, 0, -76, 0, 1]], [13, [3211264, 0, -2563072, 0, 694020, 0, -82856, 0, 4548, 0, -112, 0, 1]], [17, [-96, -288, 40, 200, -44, -4, 1]], [23, [-3184, 2656, 340, -320, -36, 8, 1]], [31, [64, -96, -24, 72, -16, -4, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(-\\beta _{1}-\\beta _{2}-\\beta _{4})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": 28672, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 57.23676816885378, "hecke_ring_index": 128, "level_radical": 14, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [7168, 1, [1023, 5125, 1025], [1, 1, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 20621403497592520704, "field_disc_factorization": [[2, 26], [3, 2], [184777, 2]], "field_poly": [196, 0, -1640, 0, 2008, 0, -968, 0, 221, 0, -24, 0, 1], "hecke_ring_index_factorization": [[2, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.137", "prec": 17}, {"__RealLiteral__": 0, "data": "9.885", "prec": 17}, {"__RealLiteral__": 0, "data": "5.618", "prec": 17}, {"__RealLiteral__": 0, "data": "579.424", "prec": 24}, {"__RealLiteral__": 0, "data": "733.795", "prec": 24}, {"__RealLiteral__": 0, "data": "58765.818", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [7, 1]], "trace_display": [0, 0, 0, -12], "traces": [0, 12, 0, 0, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, -24, 0, 8, 0, 0, 0, 0, 0, -16, 0, 20, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 32, 0, 0, 0, 0, 0, 16, 0, 12, 0, 0, 0, 0, 0, -24, 0, 64, 0, 0, 0, 0, 0, -12, 0, 32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 44, 0, 0, 0, 0, 0, 32, 0, 24, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 32, 0, 24, 0, 0, 0, 0, 0, 24, 0, 32, 0, 0, 0, 0, 0, -8, 0, 20, 0, 0, 0, 0, 0, 48, 0, 8, 0, 0, 0, 0, 0, -40, 0, 112, 0, 0, 0, 0, 0, 40, 0, 32, 0, 0, 0, 0, 0, -16, 0, 16, 0, 0, 0, 0, 0, 8, 0, 16, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -20, 0, 64, 0, 0, 0, 0, 0, -40, 0, 88, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 56, 0, 8, 0, 0, 0, 0, 0, -56, 0, 128, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, 8, 0, 52, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, 0, 40, 0, 64, 0, 0, 0, 0, 0, 40, 0, 160, 0, 0, 0, 0, 0, -72, 0, 40, 0, 0, 0, 0, 0, 24, 0, 16, 0, 0, 0, 0, 0, 16, 0, 64, 0, 0, 0, 0, 0, -32, 0, 4, 0, 0, 0, 0, 0, -32, 0, 64, 0, 0, 0, 0, 0, 64, 0, 80, 0, 0, 0, 0, 0, 56, 0, 64, 0, 0, 0, 0, 0, -112, 0, 80, 0, 0, 0, 0, 0, 120, 0, -16, 0, 0, 0, 0, 0, -80, 0, 80, 0, 0, 0, 0, 0, -12, 0, 48, 0, 0, 0, 0, 0, -72, 0, 96, 0, 0, 0, 0, 0, 32, 0, 28, 0, 0, 0, 0, 0, 144, 0, 104, 0, 0, 0, 0, 0, -56, 0, 168, 0, 0, 0, 0, 0, 104, 0, 24, 0, 0, 0, 0, 0, -120, 0, 176, 0, 0, 0, 0, 0, -64, 0, 96, 0, 0, 0, 0, 0, -48, 0, 24, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 232, 0, 96, 0, 0, 0, 0, 0, -176, 0, 64, 0, 0, 0, 0, 0, 80, 0, 12, 0, 0, 0, 0, 0, -32, 0, 8, 0, 0, 0, 0, 0, -32, 0, -40, 0, 0, 0, 0, 0, -64, 0, 104, 0, 0, 0, 0, 0, 32, 0, 24, 0, 0, 0, 0, 0, 64, 0, 32, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 24, 0, 8, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -128, 0, 144, 0, 0, 0, 0, 0, 32, 0, -4, 0, 0, 0, 0, 0, 200, 0, 56, 0, 0, 0, 0, 0, -136, 0, 56, 0, 0, 0, 0, 0, -24, 0, -24, 0, 0, 0, 0, 0, -112, 0, -112, 0, 0, 0, 0, 0, -44, 0, 120, 0, 0, 0, 0, 0, -280, 0, 32, 0, 0, 0, 0, 0, 192, 0, -64, 0, 0, 0, 0, 0, 72, 0, 112, 0, 0, 0, 0, 0, -128, 0, -88, 0, 0, 0, 0, 0, 8, 0, -32, 0, 0, 0, 0, 0, -88, 0, 104, 0, 0, 0, 0, 0, -24, 0, -20, 0, 0, 0, 0, 0, -48, 0, 104, 0, 0, 0, 0, 0, 184, 0, -64, 0, 0, 0, 0, 0, 40, 0, -64, 0, 0, 0, 0, 0, 24, 0, -112, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, -88, 0, -136, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -192, 0, 16, 0, 0, 0, 0, 0, -80, 0, 32, 0, 0, 0, 0, 0, 128, 0, -72, 0, 0, 0, 0, 0, 88, 0, -8, 0, 0, 0, 0, 0, 56, 0, -32, 0, 0, 0, 0, 0, -192, 0, -36, 0, 0, 0, 0, 0, -24, 0, 88, 0, 0, 0, 0, 0, -80, 0, -64, 0, 0, 0, 0, 0, 144, 0, -160, 0, 0, 0, 0, 0, 240, 0, -40, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 0, 0, -80, 0, -24, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -32, 0, -64, 0, 0, 0, 0, 0, -48, 0, -136, 0, 0, 0, 0, 0, 32, 0, 72, 0, 0, 0, 0, 0, 168, 0, 24, 0, 0, 0, 0, 0, -40, 0, -304, 0, 0, 0, 0, 0, -160, 0, 8, 0, 0, 0, 0, 0, 88, 0, -36, 0, 0, 0, 0, 0, -20, 0, -96, 0, 0, 0, 0, 0, -168, 0, 144, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 176, 0, 24, 0, 0, 0, 0, 0, -112, 0, 96, 0, 0, 0, 0, 0, 112, 0, -48, 0, 0, 0, 0, 0, -32, 0, -80, 0, 0, 0, 0, 0, -8, 0, 48, 0, 0, 0, 0, 0, -144, 0, -64, 0, 0, 0, 0, 0, 168, 0, -96, 0, 0, 0, 0, 0, 296, 0, 48, 0, 0, 0, 0, 0, -176, 0, -24, 0, 0, 0, 0, 0, -72, 0, 40, 0, 0, 0, 0, 0, -8, 0, 176, 0, 0, 0, 0, 0, -112, 0, -276, 0, 0, 0, 0, 0, -192, 0, -24, 0, 0, 0, 0, 0, 200, 0, 56, 0, 0, 0, 0, 0, 152, 0, -328, 0, 0, 0, 0, 0, -24, 0, -280, 0, 0, 0, 0, 0, 104, 0, -40, 0, 0, 0, 0, 0, 256, 0, -240, 0, 0, 0, 0, 0, -32, 0, -112, 0, 0, 0, 0, 0, 64, 0, 136, 0, 0, 0, 0, 0, -8, 0, -112, 0, 0, 0, 0, 0, 240, 0, -168, 0, 0, 0, 0, 0, -152, 0, 112, 0, 0, 0, 0, 0, 80, 0, 16, 0, 0, 0, 0, 0, 24, 0, -416, 0, 0, 0, 0, 0, -16, 0, 104, 0, 0, 0, 0, 0, -304, 0, -200, 0, 0, 0, 0, 0, -48, 0, -172, 0, 0, 0, 0, 0, 528, 0, 24, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -200, 0, -8, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, -16, 0, -144, 0, 0, 0, 0, 0, -32, 0, -88, 0, 0, 0, 0, 0, 440, 0, 80, 0, 0, 0, 0, 0, 528, 0, -72, 0, 0, 0, 0, 0, -128, 0, -272, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 0, 136, 0, -8, 0, 0, 0, 0, 0, -68, 0, -96, 0, 0, 0, 0, 0, -296, 0, 80, 0, 0, 0, 0, 0, -112, 0, -144, 0, 0, 0, 0, 0, 112, 0, -136, 0, 0, 0, 0, 0, -200, 0, 160, 0, 0, 0, 0, 0, 104, 0, 20, 0, 0, 0, 0, 0, -176, 0, -48, 0, 0, 0, 0, 0, -64, 0, -80, 0, 0, 0, 0, 0, -128, 0, -160, 0, 0, 0, 0, 0, 136, 0, -112, 0, 0, 0, 0, 0, 400, 0, -96, 0, 0, 0, 0, 0, -32, 0, -24, 0, 0, 0, 0, 0, 112, 0, 40, 0, 0, 0, 0, 0, -472, 0, 24, 0, 0, 0, 0, 0, -88, 0, 16, 0, 0, 0, 0, 0, -80, 0, -200, 0, 0, 0, 0, 0, 88, 0, 208, 0, 0, 0, 0, 0, 224, 0, -232, 0, 0, 0, 0, 0, -352, 0, -88, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, -96, 0, -240, 0, 0, 0, 0, 0, -96, 0, -112, 0, 0, 0, 0, 0, -280, 0, -120, 0, 0, 0, 0, 0, -32, 0, -100, 0, 0, 0, 0, 0, 304, 0, -112, 0, 0, 0, 0, 0, -360, 0, 128, 0, 0, 0, 0, 0, 8, 0, -56, 0, 0, 0, 0, 0, -272, 0, -224, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, -184, 0, -96, 0, 0, 0, 0, 0, 272, 0, -176, 0, 0, 0, 0, 0, 472, 0, 112, 0, 0, 0, 0, 0, -208, 0, -48, 0, 0, 0, 0, 0, -104, 0, 56, 0, 0, 0, 0, 0, -488, 0, 80, 0, 0, 0, 0, 0, -128, 0, -304, 0, 0, 0, 0, 0, -288, 0, -424, 0, 0, 0, 0, 0, 320, 0, -128, 0, 0, 0, 0, 0, 120, 0, -224, 0, 0, 0, 0, 0, -280, 0, -160, 0, 0, 0, 0, 0, 200, 0, -16, 0, 0, 0, 0, 0, -48, 0, -144, 0, 0, 0, 0, 0, 8, 0, -252, 0, 0, 0, 0, 0, -88, 0, -128, 0, 0, 0, 0, 0, 312, 0, -168, 0, 0, 0, 0, 0, -88, 0, -360, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -16, 0, -8, 0, 0, 0, 0, 0, -72, 0, 32, 0, 0, 0, 0, 0, -52, 0, 112, 0, 0, 0, 0, 0, -232, 0, -248, 0, 0, 0, 0, 0, -48, 0, -288, 0, 0, 0, 0, 0, 104, 0, -88, 0, 0, 0, 0, 0, 208, 0, -240, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -304, 0, 16, 0, 0, 0, 0, 0, -64, 0, -128, 0, 0, 0, 0, 0, 128, 0, -432, 0, 0, 0, 0, 0, 200, 0, 208, 0, 0, 0, 0, 0, 544, 0, -72, 0, 0, 0, 0, 0, -144, 0, -240, 0, 0, 0, 0, 0, 24, 0, -16, 0, 0, 0, 0, 0, 112, 0, -252, 0, 0, 0, 0, 0, 8, 0, -192, 0, 0, 0, 0, 0, -504, 0, 184, 0, 0, 0, 0, 0, -16, 0, -112, 0, 0, 0, 0, 0, 152, 0, -40, 0, 0, 0, 0, 0, -112, 0, -32, 0, 0, 0, 0, 0, -104, 0, -40, 0, 0, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -64, 0, -160, 0, 0, 0, 0, 0, -288, 0, -216, 0, 0, 0, 0, 0, 192, 0, -464, 0, 0, 0, 0, 0, 152, 0, -16, 0, 0, 0, 0, 0, 248, 0, -48, 0, 0, 0, 0, 0, 400, 0, -40, 0, 0, 0, 0, 0, -240, 0, -56, 0, 0, 0, 0, 0, -160, 0, -296, 0, 0, 0, 0, 0, -72, 0, -96, 0, 0, 0, 0, 0, 296, 0, 208, 0, 0, 0, 0, 0, 208, 0, -272, 0, 0, 0, 0, 0, -104, 0, -328, 0, 0, 0, 0, 0, -80, 0, 72, 0, 0, 0, 0, 0, -72, 0, -76, 0, 0, 0, 0, 0, -40, 0, -16, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, -48, 0, -168, 0, 0, 0, 0, 0, 24, 0, 48, 0, 0, 0, 0, 0, 64, 0, 96, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 88, 0, -256, 0, 0, 0, 0, 0, -16, 0, 40, 0, 0, 0, 0, 0, 40, 0, -376, 0, 0, 0, 0, 0, 80, 0, 160, 0, 0, 0, 0, 0, 512, 0, 152, 0, 0, 0, 0, 0, 96, 0, 56, 0, 0, 0, 0, 0, 24, 0, -16, 0, 0, 0, 0, 0, 16, 0, 120, 0, 0, 0, 0, 0, -64, 0, -136, 0, 0, 0, 0, 0, -264, 0, -224, 0, 0, 0, 0, 0, -64, 0, 256, 0, 0, 0, 0, 0, 344, 0, -48, 0, 0, 0, 0, 0, -240, 0, -424, 0, 0, 0, 0, 0, -56, 0, 32, 0, 0, 0, 0, 0, 136, 0, 184, 0, 0, 0, 0, 0, -4, 0, -188, 0, 0, 0, 0, 0, 136, 0, 256, 0, 0, 0, 0, 0, 272, 0, -320, 0, 0, 0, 0, 0, 224, 0, 112, 0, 0, 0, 0, 0, -512, 0, 328, 0, 0, 0, 0, 0, 80, 0, 32, 0, 0, 0, 0, 0, 128, 0, -112, 0, 0, 0, 0, 0, -64, 0, -104, 0, 0, 0, 0, 0, -224, 0, 32, 0, 0, 0, 0, 0, -24, 0, -64, 0, 0, 0, 0, 0, -64, 0, -16, 0, 0, 0, 0, 0, -352, 0, -160, 0, 0, 0, 0, 0, 536, 0, -64, 0, 0, 0, 0, 0, -680, 0, 264, 0, 0, 0, 0, 0, -80, 0, 224, 0, 0, 0, 0, 0, -24, 0, -192, 0, 0, 0, 0, 0, 424, 0, 56, 0, 0, 0, 0, 0, 408, 0, 40, 0, 0, 0, 0, 0, 32, 0, 64, 0, 0, 0, 0, 0, 616, 0, -56, 0, 0, 0, 0, 0, -32, 0, -320, 0, 0, 0, 0, 0, -64, 0, -96, 0, 0, 0, 0, 0, 184, 0, -128, 0, 0, 0, 0, 0, -112, 0, -20, 0, 0, 0, 0, 0, 480, 0, 144, 0, 0, 0, 0, 0, -640, 0, 24, 0, 0, 0, 0, 0, -24, 0, 112, 0, 0, 0, 0, 0, -184, 0, -112, 0, 0, 0, 0, 0, -80, 0, 224, 0, 0, 0, 0, 0, -176, 0, -40, 0, 0, 0, 0, 0, 160, 0, -64, 0, 0, 0, 0, 0, 320, 0, 336, 0, 0, 0, 0, 0, -240, 0, 152, 0, 0, 0, 0, 0, 240, 0, -120, 0, 0, 0, 0, 0, -240, 0, 56, 0, 0, 0, 0, 0, 16, 0, -128, 0, 0, 0, 0, 0, -560, 0, 128, 0, 0, 0, 0, 0, 24, 0, 104, 0, 0, 0, 0, 0, 512, 0, 96, 0, 0, 0, 0, 0, -208, 0, 232, 0, 0, 0, 0, 0, 48, 0, 80, 0, 0, 0, 0, 0, -56, 0, 240, 0, 0, 0, 0, 0, -80, 0, -160, 0, 0, 0, 0, 0, -472, 0, 216, 0, 0, 0, 0, 0, 216, 0, 144, 0, 0, 0, 0, 0, 16, 0, -288, 0, 0, 0, 0, 0, -656, 0, 88, 0, 0, 0, 0, 0, -8, 0, 12, 0, 0, 0, 0, 0, -176, 0, -96, 0, 0, 0, 0, 0, -48, 0, 184, 0, 0, 0, 0, 0, 48, 0, 232, 0, 0, 0, 0, 0, 368, 0, 32, 0, 0, 0, 0, 0, -56, 0, 56, 0, 0, 0, 0, 0, 384, 0, 80, 0, 0, 0, 0, 0, 416, 0, 72, 0, 0, 0, 0, 0, -528, 0, 96, 0, 0, 0, 0, 0, -96, 0, 136, 0, 0, 0, 0, 0, -288, 0, -480, 0, 0, 0, 0, 0, -24, 0, 320, 0, 0, 0, 0, 0, 248, 0, -112, 0, 0, 0, 0, 0, 80, 0, -280, 0, 0, 0, 0, 0, 64, 0, -32, 0, 0, 0, 0, 0, 152, 0, -184, 0, 0, 0, 0, 0, -28, 0, 80, 0, 0, 0, 0, 0, -32, 0, 296, 0, 0, 0, 0, 0, 120, 0, -112, 0, 0, 0, 0, 0, 136, 0, -88, 0, 0, 0, 0, 0, -96, 0, -224, 0, 0, 0, 0, 0, -168, 0, -144, 0, 0, 0, 0, 0, 8, 0, 304, 0, 0, 0, 0, 0, -104, 0, 208, 0, 0, 0, 0, 0, -112, 0, 312, 0, 0, 0, 0, 0, -24, 0, -476, 0, 0, 0, 0, 0, 416, 0, 144, 0, 0, 0, 0, 0, -256, 0, -64, 0, 0, 0, 0, 0, -224, 0, 56, 0, 0, 0, 0, 0, 184, 0, 200, 0, 0, 0, 0, 0, -168, 0, -128, 0, 0, 0, 0, 0, -328, 0, 336, 0, 0, 0, 0, 0, 200, 0, 216, 0, 0, 0, 0, 0, 624, 0, -56, 0, 0, 0, 0, 0, -376, 0, 336, 0, 0, 0, 0, 0, 408, 0, -104, 0, 0, 0, 0, 0, 408, 0, 0, 0, 0, 0, 0, 0, -24, 0, -160, 0, 0, 0, 0, 0, -176, 0, 416, 0, 0, 0, 0, 0, 176, 0, -32, 0, 0, 0, 0, 0, 136, 0, -408, 0, 0, 0, 0, 0, -248, 0, 136, 0, 0, 0, 0, 0, -40, 0, 120, 0, 0, 0, 0, 0, -192, 0, 16, 0, 0, 0, 0, 0, -176, 0, 216, 0, 0, 0, 0, 0, -224, 0, -320, 0, 0, 0, 0, 0, 128, 0, 64, 0, 0, 0, 0, 0, 112, 0, 400, 0, 0, 0, 0, 0, 48, 0, -104, 0, 0, 0, 0, 0, 48, 0, 64, 0, 0, 0, 0, 0, 472, 0, -96, 0, 0, 0, 0, 0, -96, 0, 60, 0, 0, 0, 0, 0, 144, 0, 392, 0, 0, 0, 0, 0, -48, 0, 256, 0, 0, 0, 0, 0, 104, 0, -200, 0, 0, 0, 0, 0, -112, 0, -96, 0, 0, 0, 0, 0, -32, 0, 48, 0, 0, 0, 0, 0, 128, 0, -16, 0, 0, 0, 0, 0, -24, 0, 560, 0, 0, 0, 0, 0, -368, 0, 272, 0, 0, 0, 0, 0, -648, 0, -56, 0, 0, 0, 0, 0, 352, 0, 464, 0, 0, 0, 0, 0, -408, 0, 448, 0, 0, 0, 0, 0, -176, 0, -88, 0, 0, 0, 0, 0, -16, 0, 80, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -184, 0, 472, 0, 0, 0, 0, 0, 544, 0, -64, 0, 0, 0, 0, 0, 488, 0, 104, 0, 0, 0, 0, 0, 56, 0, 392, 0, 0, 0, 0, 0, 440, 0, -232, 0, 0, 0, 0, 0, 160, 0, 176, 0, 0, 0, 0, 0, -96, 0, -144, 0, 0, 0, 0, 0, -168, 0, -72, 0, 0, 0, 0, 0, -104, 0, 96, 0, 0, 0, 0, 0, 72, 0], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 8, 2, 1, 2, 0]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "112.2.m.d", "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, 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, 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, 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, 1, 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, 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, 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, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 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, -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, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [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, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 2, 0, 0, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, -2, 1, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -1, 0, -5, 1, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0, 0, 1, 1, 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, 0, 0], [0, 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, -1, 0, 0, 1, 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, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, -1, 0, 0, 0, -1, 2, 2, -1, 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], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -2, -1, 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, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -2, 0, 0, 0, 2, -1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 0, -1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, -1, 0, -1, 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, 0, 0, 2, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0, 0, 0, -2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 3, 0, 6, -3, -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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0, 0, -1, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -1, 0, 0, 0, -1, 2, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -3, 0, -3, 1, 2, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -3, 0, -2, 0, 1, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 3, 0, 0, 0, 1, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3, 0, 0, 0, -1, -1, 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, -1, -2, 0, -5, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -2, 0, 0, 0, 2, -1, -2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 2, 0, 0, 0, -1, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, -3, 0, 2, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}