# Stored data for newform 5292.2.w.b, downloaded from the LMFDB on 25 April 2024.
{"label": "5292.2.w.b", "space_label": "5292.2.w", "level": 5292, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505111489418412, "dim": 16, "is_polredabs": true, "trace_hash": 712744783437948631, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [324, -4698, 62289, -89424, 143289, -45738, 71361, -21573, 23103, -4167, 3600, -423, 405, -24, 24, 0, 1]]], "qexp_display": "q+\\beta _{11}q^{5}+(-\\beta _{2}+\\beta _{3}-\\beta _{4}+\\beta _{6}+\\cdots)q^{11}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "w", "char_is_real": false, "Nk2": 21168, "analytic_conductor": 42.25683274966158, "hecke_ring_index": 729, "level_radical": 42, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.179", "prec": 17}, "analytic_rank_proved": true, "char_values": [5292, 6, [2647, 785, 1081], [6, 1, 1]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [521, 1097], "field_disc": 676080657322439573238336, "field_disc_factorization": [[2, 6], [3, 12], [83, 2], [821, 2], [2069, 2]], "field_poly": [6561, -4374, 3645, -4131, 1782, -837, 558, -156, 52, -52, 62, -31, 22, -17, 5, -2, 1], "hecke_ring_index_factorization": [[3, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "14.347", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "782.225", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "64423.018", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0, 0, 0, 9, 0, 0, 0, 0, 0, -21, 0, -8, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, -2, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 24, 0, 21, 0, 0, 0, 87, 0, -14, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 72, 0, -28, 0, 0, 0, 54, 0, 0, 0, 0, 0, 6, 0, -30, 0, 0, 0, 27, 0, 18, 0, 0, 0, -63, 0, 25, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -30, 0, 7, 0, 0, 0, -90, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, -6, 0, 0, 0, -42, 0, 1, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 60, 0, -21, 0, 0, 0, 96, 0, 24, 0, 0, 0, 84, 0, 39, 0, 0, 0, 0, 0, 3, 0, 0, 0, -36, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 12, 0, 27, 0, 0, 0, 72, 0, -21, 0, 0, 0, -177, 0, -7, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, -45, 0, 3, 0, 0, 0, -210, 0, 0, 0, 0, 0, -15, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 4, 0, 0, 0, -33, 0, -23, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, -21, 0, 0, 0, 102, 0, -54, 0, 0, 0, 147, 0, 34, 0, 0, 0, -12, 0, -99, 0, 0, 0, 0, 0, -19, 0, 0, 0, 186, 0, 34, 0, 0, 0, 117, 0, 0, 0, 0, 0, 69, 0, 72, 0, 0, 0, 84, 0, -3, 0, 0, 0, -183, 0, -51, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 39, 0, -16, 0, 0, 0, -126, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, -198, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 28, 0, 0, 0, -102, 0, 8, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 99, 0, 0, 0, 15, 0, 15, 0, 0, 0, 210, 0, -80, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 60, 0, -54, 0, 0, 0, 105, 0, 0, 0, 0, 0, 69, 0, -117, 0, 0, 0, 84, 0, -33, 0, 0, 0, -126, 0, 59, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, -135, 0, -7, 0, 0, 0, -282, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -126, 0, 0, 0, 0, 0, 0, 0, -118, 0, 0, 0, 0, 0, 93, 0, 0, 0, 0, 0, -90, 0, 0, 0, 9, 0, -6, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, -39, 0, 0, 0, 117, 0, 90, 0, 0, 0, 210, 0, 17, 0, 0, 0, -45, 0, 147, 0, 0, 0, 0, 0, 52, 0, 0, 0, 150, 0, 2, 0, 0, 0, 144, 0, 0, 0, 0, 0, -21, 0, 87, 0, 0, 0, 27, 0, -63, 0, 0, 0, -159, 0, 9, 0, 0, 0, -183, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, -3, 0, -14, 0, 0, 0, -36, 0, 0, 0, 0, 0, -153, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 0, 0, 138, 0, 0, 0, 0, 0, -207, 0, 0, 0, 0, 0, 34, 0, 0, 0, -75, 0, -9, 0, 0, 0, 174, 0, 0, 0, 0, 0, 0, 0, -186, 0, 0, 0, 72, 0, -42, 0, 0, 0, 138, 0, 71, 0, 0, 0, 168, 0, -108, 0, 0, 0, 0, 0, 1, 0, 0, 0, -96, 0, -8, 0, 0, 0, 15, 0, 0, 0, 0, 0, -12, 0, -18, 0, 0, 0, 96, 0, 147, 0, 0, 0, -264, 0, -90, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -156, 0, 60, 0, 0, 0, -312, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 114, 0, 0, 0, 45, 0, 56, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 117, 0, 57, 0, 0, 0, 147, 0, -126, 0, 0, 0, -96, 0, 33, 0, 0, 0, 0, 0, -25, 0, 0, 0, 204, 0, 28, 0, 0, 0, 87, 0, 0, 0, 0, 0, -3, 0, -144, 0, 0, 0, 75, 0, 108, 0, 0, 0, -111, 0, 118, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 69, 0, 19, 0, 0, 0, -120, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, -162, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, -56, 0, 0, 0, -93, 0, -25, 0, 0, 0, 93, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, -18, 0, 0, 0, 0, 0, 129, 0, 67, 0, 0, 0, 120, 0, 141, 0, 0, 0, 0, 0, -15, 0, 0, 0, 120, 0, 62, 0, 0, 0, 18, 0, 0, 0, 0, 0, 273, 0, 162, 0, 0, 0, 120, 0, -102, 0, 0, 0, -108, 0, -19, 0, 0, 0, 147, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, -24, 0, -76, 0, 0, 0, -330, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -222, 0, 0, 0, 0, 0, 0, 0, 166, 0, 0, 0, 0, 0, -243, 0, 0, 0, 0, 0, 20, 0, 0, 0, 93, 0, 29, 0, 0, 0, -66, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 42, 0, -234, 0, 0, 0, 144, 0, 91, 0, 0, 0, -87, 0, -225, 0, 0, 0, 0, 0, -73, 0, 0, 0, 126, 0, 72, 0, 0, 0, 147, 0, 0, 0, 0, 0, -54, 0, -15, 0, 0, 0, -33, 0, -45, 0, 0, 0, 0, 0, -159, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 9, 0, 18, 0, 0, 0, -66, 0, 0, 0, 0, 0, -75, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 117, 0, 0, 0, 0, 0, -16, 0, 0, 0, -174, 0, 18, 0, 0, 0, 141, 0, 0, 0, 0, 0, 0, 0, 165, 0, 0, 0, 75, 0, 159, 0, 0, 0, -30, 0, -171, 0, 0, 0, 87, 0, -57, 0, 0, 0, 0, 0, 33, 0, 0, 0, -294, 0, 18, 0, 0, 0, -45, 0, 0, 0, 0, 0, -36, 0, -126, 0, 0, 0, 87, 0, 21, 0, 0, 0, -222, 0, 189, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, -60, 0, 7, 0, 0, 0, 42, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, 0, 0, -338, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, -180, 0, 0, 0, 57, 0, -60, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, -45, 0, 0, 0, 3, 0, 90, 0, 0, 0, 93, 0, 81, 0, 0, 0, -51, 0, 234, 0, 0, 0, 0, 0, 112, 0, 0, 0, 216, 0, -132, 0, 0, 0, 132, 0, 0, 0, 0, 0, -204, 0, 111, 0, 0, 0, -21, 0, -243, 0, 0, 0, 36, 0, -15, 0, 0, 0, -117, 0, 0, 0, 0, 0, 0, 0, -53, 0, 0, 0, 27, 0, 1, 0, 0, 0, 192, 0, 0, 0, 0, 0, 105, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 358, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, -78, 0, 0, 0, -87, 0, -17, 0, 0, 0, 69, 0, 0, 0, 0, 0, 0, 0, -183, 0, 0, 0, -45, 0, -54, 0, 0, 0, 21, 0, 126, 0, 0, 0, 390, 0, -225, 0, 0, 0, 0, 0, 9, 0, 0, 0, -150, 0, 54, 0, 0, 0, -111, 0, 0, 0, 0, 0, 153, 0, 111, 0, 0, 0, 18, 0, 135, 0, 0, 0, 135, 0, -180, 0, 0, 0, 165, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, -105, 0, 15, 0, 0, 0, -252, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, -150, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 202, 0, 0, 0, 153, 0, 28, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 39, 0, 36, 0, 0, 0, -78, 0, -184, 0, 0, 0, -246, 0, 75, 0, 0, 0, 0, 0, -45, 0, 0, 0, 282, 0, -108, 0, 0, 0, 54, 0, 0, 0, 0, 0, -24, 0, -399, 0, 0, 0, -153, 0, 234, 0, 0, 0, -96, 0, 221, 0, 0, 0, -63, 0, 0, 0, 0, 0, 0, 0, -61, 0, 0, 0, 153, 0, -8, 0, 0, 0, 360, 0, 0, 0, 0, 0, -99, 0, 0, 0, 0, 0, -174, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, 306, 0, 0, 0, 0, 0, 72, 0, 0, 0, -60, 0, -34, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 15, 0, 27, 0, 0, 0, -93, 0, 34, 0, 0, 0, 78, 0, 267, 0, 0, 0, 0, 0, 1, 0, 0, 0, -384, 0, -192, 0, 0, 0, -108, 0, 0, 0, 0, 0, -114, 0, 306, 0, 0, 0, -24, 0, -132, 0, 0, 0, 69, 0, -2, 0, 0, 0, 51, 0, 0, 0, 0, 0, 0, 0, 130, 0, 0, 0, -81, 0, -42, 0, 0, 0, 102, 0, 0, 0, 0, 0, 138, 0, 0, 0, 0, 0, 474, 0, 0, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 192, 0, 0, 0, -66, 0, -66, 0, 0, 0, -99, 0, 0, 0, 0, 0, 0, 0, -345, 0, 0, 0, -36, 0, -273, 0, 0, 0, 84, 0, 115, 0, 0, 0, -420, 0, -435, 0, 0, 0, 0, 0, -72, 0, 0, 0, 6, 0, 18, 0, 0, 0, 51, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, 27, 0, 81, 0, 0, 0, 183, 0, -204, 0, 0, 0, -225, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 219, 0, 38, 0, 0, 0, 390, 0, 0, 0, 0, 0, 87, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 174, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 89, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 159, 0, 0, 0, -156, 0, 48, 0, 0, 0, -255, 0, -223, 0, 0, 0, 153, 0, -36, 0, 0, 0, 0, 0, -7, 0, 0, 0, -102, 0, -38, 0, 0, 0, -189, 0, 0, 0, 0, 0, 90, 0, -234, 0, 0, 0, 24, 0, -90, 0, 0, 0, 114, 0, 186, 0, 0, 0, 489, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, -99, 0, -18, 0, 0, 0, -228, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -422, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -408, 0, 0, 0, 267, 0, -99, 0, 0, 0, -270, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, -21, 0, 84, 0, 0, 0, -183, 0, 147, 0, 0, 0, -15, 0, 540, 0, 0, 0, 0, 0, 127, 0, 0, 0, 210, 0, 88, 0, 0, 0, -147, 0, 0, 0, 0, 0, 102, 0, 342, 0, 0, 0, -261, 0, -147, 0, 0, 0, 234, 0, -63, 0, 0, 0, -111, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 63, 0, -63, 0, 0, 0, 66, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, -531, 0, 0, 0, 0, 0, -242, 0, 0, 0, -87, 0, 81, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -234, 0, 0, 0, -114, 0, -90, 0, 0, 0, -171, 0, 203, 0, 0, 0, 63, 0, -267, 0, 0, 0, 0, 0, -78, 0, 0, 0, -198, 0, 254, 0, 0, 0, -90, 0, 0, 0, 0, 0, -198, 0, 42, 0, 0, 0, -27, 0, -15, 0, 0, 0, 195, 0, -127, 0, 0, 0, 438, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, -6, 0, 79, 0, 0, 0, 234, 0, 0, 0, 0, 0, 309, 0, 0, 0, 0, 0, 420, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 345, 0, 0, 0, 0, 0, 136, 0, 0, 0, 72, 0, 63, 0, 0, 0, -321, 0, 0, 0, 0, 0, 0, 0, 342, 0, 0, 0, -42, 0, 330, 0, 0, 0, -330, 0, -250, 0, 0, 0, -117, 0, 81, 0, 0, 0, 0, 0, -73, 0, 0, 0, -96, 0, 138, 0, 0, 0, 57, 0, 0, 0, 0, 0, -42, 0, -396, 0, 0, 0, -54, 0, 162, 0, 0, 0, 318, 0, 186, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, -126, 0, 0, 0, 216, 0, 53, 0, 0, 0, 288, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 162, 0, 0, 0, 0, 0, 0, 0, -594, 0, 0, 0, 0, 0, 417, 0, 0, 0, 0, 0, 10, 0, 0, 0, -186, 0, 47, 0, 0, 0, -51, 0, 0, 0, 0, 0, 0, 0, -135, 0, 0, 0, -288, 0, -135, 0, 0, 0, -438, 0, 56, 0, 0, 0, -60, 0, 345, 0, 0, 0, 0, 0, -6, 0, 0, 0, -348, 0, 58, 0, 0, 0, -210, 0, 0, 0, 0, 0, 258, 0, 0, 0, 0, 0, 51, 0, -168, 0, 0, 0, 183, 0, -6, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, -75, 0, 54, 0, 0, 0, 66, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 414, 0, 0, 0, 0, 0, -345, 0, 0, 0, 0, 0, 162, 0, 0, 0, 306, 0, -15, 0, 0, 0, -57, 0, 0, 0, 0, 0, 0, 0, -198, 0, 0, 0, -60, 0, -183, 0, 0, 0, -294, 0, 90, 0, 0, 0, -357, 0, -720, 0, 0, 0, 0, 0, -81, 0, 0, 0, 144, 0, 130, 0, 0, 0, -147, 0, 0, 0, 0, 0, -303, 0, 285, 0, 0, 0, -243, 0, 0, 0, 0, 0, 153, 0, -248, 0, 0, 0, -213, 0, 0, 0, 0, 0, 0, 0, 203, 0, 0, 0, -42, 0, -52, 0, 0, 0, 504, 0, 0, 0, 0, 0, -345, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, 123, 0, 0, 0, 0, 0, 136, 0, 0, 0, 171, 0, -52, 0, 0, 0, -57, 0, 0, 0, 0, 0, 0, 0, 492, 0, 0, 0, -60, 0, 27, 0, 0, 0, 60, 0, -360, 0, 0, 0, 117, 0, -18, 0, 0, 0, 0, 0, 65, 0, 0, 0, -480, 0, -258, 0, 0, 0, -345, 0, 0, 0, 0, 0, -48, 0, -531, 0, 0, 0, -276, 0, 168, 0, 0, 0, 357, 0, 206, 0, 0, 0, 237, 0, 0, 0, 0, 0, 0, 0, -118, 0, 0, 0, -9, 0, -126, 0, 0, 0, 84, 0, 0, 0, 0, 0, 207, 0, 0, 0, 0, 0, 474, 0, 0, 0, 0, 0, 0, 0, -516, 0, 0, 0, 0, 0, 279, 0, 0, 0, 0, 0, -194, 0, 0, 0, 54, 0, 92, 0, 0, 0, -138, 0, 0, 0, 0, 0, 0, 0, -99, 0, 0, 0, -51, 0, 306, 0, 0, 0, -273, 0, 122, 0, 0, 0, -498, 0, 459, 0, 0, 0, 0, 0, 270, 0, 0, 0, 336, 0, -348, 0, 0, 0, -27, 0, 0, 0, 0, 0, -333, 0, 216, 0, 0, 0, -36, 0, -96, 0, 0, 0, 354, 0, 35, 0, 0, 0, 246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 330, 0, 0, 0, 0, 0, 606, 0, 0, 0, 0, 0, 225, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 426, 0, 0, 0, 0, 0, -495, 0, 0, 0, 0, 0, -90, 0, 0, 0, 75, 0, -177, 0, 0, 0, -204, 0, 0, 0, 0, 0, 0, 0, -387, 0, 0, 0, -282, 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, 63, 9, 1, 6, 0]], "char_orbit_index": 23, "prim_orbit_index": 9, "minimal_twist": "252.2.w.a", "char_is_minimal": false, "conrey_index": 521, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 0, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 1, 0, 1, 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], [0, 0, 0, -1, 1, 0, -1, 0, 0, 1, -1, 0, -2, 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, 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, 0, -1, 0, -1, -1, 0, 1, -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, 1, 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, 0], [-1, 0, 1, -1, 1, 0, 0, -2, 0, -1, 0, 1, 2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, 0, 1, 1, 0, 1, 1, 2, -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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, -2, 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, 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, -1, -2, 0, -2, 1, 1, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, -2, 2, 0, -2, 0, 0, 0, 0, -3, 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], [-3, 1, 0, 2, -1, 0, 0, 0, 0, 0, -1, 2, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 0, -1, 0, 1, -1, 1, -2, 0, 1, -1, -2, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, -1, 1, 0, -1, 1, 0, 2, -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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, -4, 1, 2, -1, 0, -2, 1, 2, -1, 0, 0, -4, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 1, 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, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, 3, 2, 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], [5, 0, 0, -4, 3, 3, -1, 1, -3, 3, 0, -2, -2, 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, 0, 0, 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, -3, 1, 2, 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], [-2, 0, 1, 2, -1, -1, 1, -2, 2, -2, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, -1, -1, -1, 0, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -1, 4, -2, 0, 1, 1, 3, 2, 1, 1, 1, -1, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, -3, 2, 0, 0, -1, -1, 0, -2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 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, -1, 3, -1, 1, -2, 0, -3, -2, -3, -2, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 1, 0, 0, 1, 0, -1, -2, 1, -1, 1, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}