# Stored data for newform 8550.2.a.cs, downloaded from the LMFDB on 18 May 2022.
{"level_primes": [2, 3, 5, 19], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 2245943043146762138, "level_radical": 570, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 71, "analytic_conductor": 68.27209372819473, "inner_twist_count": 1, "field_disc_factorization": [[2, 2], [3, 1], [47, 1]], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "8550.2.a.cs", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "8550.2.a.cd", "field_poly_is_cyclotomic": false, "dim": 3, "trace_zratio": {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, "traces": [0, 3, 3, 0, 3, 0, 0, 2, 3, 0, 0, 5, 0, 0, 2, 0, 3, -6, 0, 3, 0, 0, 5, 1, 0, 0, 0, 0, 2, 15, 0, -1, 3, 0, -6, 0, 0, -4, 3, 0, 0, 6, 0, 10, 5, 0, 1, 0, 0, 3, 0, 0, 0, 5, 0, 0, 2, 0, 15, 12, 0, 1, -1, 0, 3, 0, 0, 1, -6, 0, 0, 24, 0, 9, -4, 0, 3, -4, 0, 5, 0, 0, 6, 11, 0, 0, 10, 0, 5, 23, 0, -38, 1, 0, 0, 0, 0, 14, 3, 0, 0, 16, 0, 23, 0, 0, 5, -16, 0, 14, 0, 0, 2, 3, 0, 0, 15, 0, 12, -12, 0, -14, 1, 0, -1, 0, 0, 1, 3, 0, 0, 1, 0, 2, 1, 0, -6, -6, 0, 26, 0, 0, 24, 4, 0, 0, 9, 0, -4, 26, 0, -12, 3, 0, -4, 0, 0, 4, 5, 0, 0, 16, 0, 2, 6, 0, 11, -14, 0, 33, 0, 0, 10, 25, 0, 0, 5, 0, 23, 22, 0, -54, -38, 0, 1, 0, 0, -24, 0, 0, 0, 45, 0, 2, 14, 0, 3, -10, 0, -2, 0, 0, 16, 18, 0, 0, 23, 0, 0, 5, 0, -19, 5, 0, -16, 0, 0, -30, 14, 0, 0, 30, 0, -1, 2, 0, 3, 2, 0, 7, 0, 0, 15, 4, 0, 0, 12, 0, -12, 4, 0, 10, -14, 0, 1, 0, 0, 0, -1, 0, 0, 42, 0, 5, 1, 0, 3, -11, 0, 12, 0, 0, 1, 29, 0, 0, 2, 0, 1, 26, 0, -38, -6, 0, -6, 0, 0, 5, 26, 0, 0, 33, 0, 20, 24, 0, 4, -42, 0, -3, 0, 0, 9, 3, 0, 0, -4, 0, 26, -34, 0, 14, -12, 0, 3, 0, 0, -31, -4, 0, 0, 28, 0, -15, 4, 0, 5, -51, 0, 39, 0, 0, 16, -6, 0, 0, 2, 0, 6, -30, 0, -3, 11, 0, -14, 0, 0, -26, 33, 0, 0, 41, 0, 34, 10, 0, 25, -12, 0, -15, 0, 0, 5, 34, 0, 0, 23, 0, 22, 4, 0, 3, -54, 0, -38, 0, 0, -36, 1, 0, 0, 56, 0, -28, -24, 0, 0, -30, 0, 76, 0, 0, 45, 2, 0, 0, 2, 0, 14, 8, 0, -24, 3, 0, -10, 0, 0, -69, -2, 0, 0, 39, 0, 16, 16, 0, 18, -28, 0, 32, 0, 0, 23, 90, 0, 0, 0, 0, 5, -28, 0, 14, -19, 0, 5, 0, 0, 68, -16, 0, 0, -18, 0, -36, -30, 0, 14, 1, 0, 21, 0, 0, 30, 39, 0, 0, -1, 0, 2, 5, 0, 0, 3, 0, 2, 0, 0, 14, 7, 0, 0, -12, 0, 32, 15, 0, 4, -41, 0, 38, 0, 0, 12, 6, 0, 0, -12, 0, 4, 21, 0, -8, 10, 0, -14, 0, 0, -52, 1, 0, 0, 24, 0, -66, 0, 0, -1, 24, 0, -38, 0, 0, 42, -24, 0, 0, 5, 0, 1, -1, 0, -8, 3, 0, -11, 0, 0, 18, 12, 0, 0, 39, 0, 16, 1, 0, 29, -54, 0, -50, 0, 0, 2, 102, 0, 0, 1, 0, 26, 15, 0, -7, -38, 0, -6, 0, 0, -39, -6, 0, 0, 15, 0, 18, 5, 0, 26, 36, 0, -4, 0, 0, 33, 44, 0, 0, 20, 0, 24, 6, 0, -2, 4, 0, -42, 0, 0, -51, -3, 0, 0, 14, 0, -17, 9, 0, 3, -69, 0, -1, 0, 0, -4, -6, 0, 0, 26, 0, -34, 52, 0, 16, 14, 0, -12, 0, 0, -43, 3, 0, 0, 42, 0, -10, -31, 0, -4, 14, 0, 4, 0, 0, 28, 32, 0, 0, -15, 0, 4, 36, 0, 30, 5, 0, -51, 0, 0, -102, 39, 0, 0, -10, 0, -36, 16, 0, -6, 15, 0, -48, 0, 0, 2, 26, 0, 0, 6, 0, -30, 12, 0, -14, -3, 0, 11, 0, 0, 27, -14, 0, 0, -45, 0, -58, -26, 0, 33, -51, 0, -12, 0, 0, 41, -32, 0, 0, 34, 0, 10, -80, 0, -56, 25, 0, -12, 0, 0, 54, -15, 0, 0, -6, 0, -4, 5, 0, 34, 34, 0, 15, 0, 0, 23, 13, 0, 0, 22, 0, 4, 69, 0, 0, 3, 0, -54, 0, 0, -36, -38, 0, 0, -6, 0, -59, -36, 0, 1, -27, 0, 12, 0, 0, 56, 12, 0, 0, -28, 0, -24, 26, 0, -28, 0, 0, -30, 0, 0, -107, 76, 0, 0, 2, 0, -36, 45, 0, 2, -96, 0, -7, 0, 0, 2, -66, 0, 0, 14, 0, 8, 6, 0, 54, -24, 0, 3, 0, 0, 7, -10, 0, 0, 48, 0, -88, -69, 0, -2, 4, 0, -6, 0, 0, 39, 61, 0, 0, 16, 0, 16, 22, 0, -37, 18, 0, -28, 0, 0, 10, 32, 0, 0, 50, 0, -12, 23, 0, 90, 90, 0, 48, 0, 0, 0, -72, 0, 0, 5, 0, -28, -22, 0, 24, 14, 0, -19, 0, 0, -54, 5, 0, 0, -8, 0, -110, 68, 0, -16, -70, 0, -30, 0, 0, -18, -70, 0, 0, -36, 0, -30, -13, 0, -46, 14, 0, 1, 0, 0, -20, 21, 0, 0, 10, 0, 40, 30, 0, 39, 68, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 5, 51, 0, -12, 0, 0, 3, 0, 0, 6, 2, 0, 0, -18, 0, -17, 14, 0, 7, -38, 0, 68, 0, 0, -12, -30, 0, 0, 32, 0, 15, -102, 0, 3, 4, 0, -41, 0, 0, -66, 38, 0, 0, -9, 0, -54, 12, 0, 6, 12, 0, -18, 0, 0, -12, -51, 0, 0, 4, 0, 21, 12, 0, 78, -8, 0, 10, 0, 0, 20, -14, 0, 0, 28, 0, -66, -52, 0, 1, 94, 0, 91, 0, 0, 24, 30, 0, 0, -66, 0, 0, 0, 0, -23, -1, 0, 24, 0, 0, -49, -38, 0, 0, -80, 0, 30, 42, 0, -24, 5, 0, 18, 0, 0, 5, -64, 0, 0, 1, 0, -1, -54, 0, 34, -8, 0, 3, 0, 0, -8, -11, 0, 0, -88, 0, -9, 18, 0, 12, 24, 0, 19, 0, 0, 39, -28, 0, 0, 16, 0, 1, 30, 0, -42, 29, 0, -54, 0, 0, -98, -50, 0, 0, 24, 0, -96, 2, 0, 102, 80, 0, -39, 0, 0, 1, -48, 0, 0, 26, 0, 15, 22, 0, -12, -7, 0, -38, 0, 0, 86, -6, 0, 0, 6, 0, -6, -39, 0, -6, 5, 0, -58, 0, 0, 15, 31, 0, 0, 18, 0, 5, -12, 0, 44, 26, 0, 36, 0, 0, -64, -4, 0, 0, 12, 0, 89, 33, 0, 44, 57, 0, -58, 0, 0, 20, 35, 0, 0, 24, 0, 6, 18, 0, -60, -2, 0, 4, 0, 0, -84, -42, 0, 0, 3, 0, -54, -51, 0, -3, -86, 0, 1, 0, 0, 14, 19, 0, 0, -17, 0, 9, 112, 0, -79, 3, 0, -69, 0, 0, -80, -1, 0, 0, -77, 0, 144, -4, 0, -6, 114, 0, -36, 0, 0, 26, -22, 0, 0, -34, 0, 52, 38, 0, 91, 16, 0, 14, 0, 0, -84, -12, 0, 0, -50, 0, -109, -43, 0, 3, -114, 0, 29, 0, 0, 42, -109, 0, 0, -10, 0, -31, -49, 0, 16, -4, 0, 14, 0, 0, -16, 4, 0, 0, -96, 0, 15, 28, 0, 32, 36, 0, -88, 0, 0, -15, -32, 0, 0, 4, 0, 36, -119, 0, -14, 30, 0, 5, 0, 0, -14, -51, 0, 0, -42, 0, 1, -102, 0, 39, 86, 0, 98, 0, 0, -10, -44, 0, 0, -36, 0, 16, -8, 0, -94, -6, 0, 15, 0, 0, 29, -48, 0, 0, -84, 0, 46, 2, 0, 26, 14, 0, 6, 0, 0, 6, -64, 0, 0, -30, 0, 12, 90, 0, -16, -14, 0, -3, 0, 0, 30, 11, 0, 0, -39, 0, -46, 27, 0, -14, 90, 0, 34, 0, 0, -45, 18, 0, 0, -58, 0, -26, 24, 0, 24, 33, 0, -51, 0, 0, 18, -12, 0, 0, -17, 0, 6, 41, 0, -32, 32, 0, -63, 0, 0, 34, -68, 0, 0, 10, 0, -80, -58, 0, 98, -56, 0, 25, 0, 0, 9, -12, 0, 0, -20, 0, -124, 54, 0, -15, 51, 0, 47, 0, 0, -6, 21, 0, 0, -4, 0, 5, 70, 0, 42, 34, 0, 34, 0, 0, 76, 15, 0, 0, 81, 0, -18, 23, 0, 13, 6, 0, -44, 0, 0, 22, 13, 0, 0, 4, 0, 69, -72, 0, -19, 0, 0, 3, 0, 0, 20, -54, 0, 0, 31, 0, 38, -36, 0, -38, 72, 0, 65, 0, 0, -6, -4, 0, 0, -59, 0, -36, -102, 0, -45, 1, 0, -27, 0, 0, 24, 12, 0, 0, -5, 0, -14, 56, 0, 12, -36, 0, 14, 0, 0, -28, -38, 0, 0, -24, 0, 26, -72, 0, 5, -28, 0, 0, 0, 0, 18, -30, 0, 0, 8, 0, -168, -107, 0, 76, 12, 0, 39, 0, 0, 2, -76, 0, 0, -36, 0, 45, 62, 0, -28, 2, 0, -96, 0, 0, 27, -7, 0, 0, 9, 0, 94, 2, 0, -66, 186, 0, 52, 0, 0, 14, 114, 0, 0, 8, 0, 6, -177, 0, 60, 54, 0, -24, 0, 0, 14, 3, 0, 0, -118, 0, 50, 7, 0, -10, 11, 0, -13, 0, 0, 48, -21, 0, 0, -88, 0, -69, -88, 0, 8, -2, 0, 4, 0, 0, -1, -6, 0, 0, -100, 0, -34, 39, 0, 61, -3, 0, -58, 0, 0, 16, -24, 0, 0, 16, 0, 22, 115, 0, -70, -37, 0, 18, 0, 0, -85, -28, 0, 0, -128, 0, 30, 10, 0, 32, 54, 0, 58, 0, 0, 50, -103, 0, 0, -12, 0, 23, -120, 0, -52, 90, 0, 90, 0, 0, 78, 48, 0, 0, 34, 0, 117, 0, 0, -72, -154, 0, -43, 0, 0, 5, -26, 0, 0, -28, 0, -22, 35, 0, 57, 24, 0, 14, 0, 0, 92, -19, 0, 0, 23, 0, -22, -54, 0, 5, 96, 0, -91, 0, 0, -8, 98, 0, 0, -110, 0, 68, 90, 0, 6, -16, 0, -70, 0, 0, -90, -30, 0, 0, -104, 0, 65, -18, 0, -70, 18, 0, -38, 0, 0, -36, -148, 0, 0, -30, 0, -13, -36, 0, -114, -46, 0, 14, 0, 0, -41, 1, 0, 0, -24, 0, 37, -20, 0, 21, -18, 0, -6, 0, 0, 10, 30, 0, 0, 40, 0, 30, -21, 0, 26, 39, 0, 68, 0, 0, -10, 2, 0, 0, -60, 0, -28, -1, 0, 0, -89, 0, 10, 0, 0, 2, -10, 0, 0, 5, 0, 51, -68, 0, 16, -12, 0, 0, 0, 0, 148, 3, 0, 0, -121, 0, -24, 6, 0, 2, -5, 0, 102, 0, 0, -18, -152, 0, 0, -17, 0, 14, -276, 0, -104, 7, 0, -38, 0, 0, -46, 68, 0, 0, -148, 0, 14, -12, 0, -30, 8, 0, -85, 0, 0, 32, -12, 0, 0, 15, 0, -102, 57, 0, -2, 3, 0, 4, 0, 0, 138, -41, 0, 0, -88, 0, 119, -66, 0, 38, 11, 0, 30, 0, 0, -9, 152, 0, 0, -54, 0, 12, 149, 0, -187, 6, 0, 12, 0, 0, -4, -18, 0, 0, -72, 0, 113, -12, 0, -51, 85, 0, -25, 0, 0, 4, 114, 0, 0, 21, 0, 12, 16, 0, -72, 78, 0, -8, 0, 0, 36, 10, 0, 0, -14, 0, 34, 20, 0, -14, 76, 0, 72, 0, 0, 28, -15, 0, 0, -66, 0, -52, 16, 0, -12, 1, 0, 94, 0, 0, 23, 91, 0, 0, 44, 0, 126, 24, 0, 30, -54, 0, 2, 0, 0, -66, -32, 0, 0, 0, 0, 0, -28, 0, 12, -23, 0, -1, 0, 0, 90, 24, 0, 0, -122, 0, 79, -49, 0, -38, 93, 0, -32, 0, 0, -80, -196, 0, 0, 30, 0, 42, -162, 0, 36, -24, 0, 5, 0, 0, -36, 18, 0, 0, -18, 0, 44, 5, 0, -64, 36, 0, 100, 0, 0, 1, -16, 0, 0, -1, 0, -54, 15, 0, 110, 34, 0, -8, 0, 0, 77, 3, 0, 0, -96, 0, -109, -8, 0, -11, -6, 0, 156, 0, 0, -88, 43, 0, 0, -9, 0, 18, -84, 0, 14, 12, 0, 24, 0, 0, -115, 19, 0, 0, -69, 0, 71, 39, 0, -28, 104, 0, 78, 0, 0, 16, -106, 0, 0, 1, 0, 30, -35, 0, 39, -42, 0, 29, 0, 0, 0, -54, 0, 0, 0, 0, 18, -98, 0, -50, 123, 0, 136, 0, 0, 24, -4, 0, 0, -96, 0, 2, -90, 0, -16, 102, 0, 80, 0, 0, 158, -39, 0, 0, -42, 0, 92, 1, 0, -48, 3, 0, -90, 0, 0, 26, -88, 0, 0, 15, 0, 22, -102, 0, 126, -12, 0, -7, 0, 0, 58, -38, 0, 0, -220, 0, -72, 86, 0, -6, -26, 0, 58, 0, 0, 6, 120, 0, 0, -6, 0, -39, -30, 0, -56, -6, 0, 5, 0, 0, -246, -58, 0, 0, 48, 0, 82, 15, 0, 31, -88, 0, -93, 0, 0, 18, -102, 0, 0, 5, 0, -12, -42, 0, 39, 44, 0, 26, 0, 0, 78, 36, 0, 0, 40, 0, -18, -64, 0, -4, 19, 0, 98, 0, 0, 12, 123, 0, 0, 89, 0, 33, 62, 0, -72, 44, 0, 57, 0, 0, 92, -58, 0, 0, -12, 0, 181, 20, 0, 35, 33, 0, 78, 0, 0, 24, -17, 0, 0, 6, 0, 18, 42, 0, 131, -60, 0, -2, 0, 0, -126, 4, 0, 0, -3, 0, -72, -84, 0, -42, -4, 0, -14, 0, 0, 3, -36, 0, 0, -54, 0, -51, 147, 0, -87, -3, 0, -86, 0, 0, -146, 1, 0, 0, -85, 0, 46, 14, 0, 19, 128, 0, -60, 0, 0, -17, 15, 0, 0, 9, 0, 112, 162, 0, 65, -79, 0, 3, 0, 0, -7, -69, 0, 0, -8, 0, -12, -80, 0, -1, -156, 0, -4, 0, 0, -77, -6, 0, 0, 144, 0, -4, -11, 0, -77, -6, 0, 114, 0, 0, 98, -36, 0, 0, -18, 0, 87, 26, 0, -22, -100, 0, -108, 0, 0, -34, -97, 0, 0, 52, 0, 38, -195, 0, 3, 91, 0, 16, 0, 0, -9, 14, 0, 0, -45, 0, 1, -84, 0, -12, -32, 0, -18, 0, 0, -50, -140, 0, 0, -109, 0, -43, 36, 0, -12, 3, 0, -114, 0, 0, 123, 29, 0, 0, -32, 0, 70, 42, 0, -109, 32, 0, -87, 0, 0, -10, -13, 0, 0, -31, 0, -49, 6, 0, -22, 16, 0, -4, 0, 0, -2, 14, 0, 0, -92, 0, -88, -16, 0, 4, -24, 0, 56, 0, 0, -96, -84, 0, 0, 15, 0, 28, 1, 0, -78, 32, 0, 36, 0, 0, 82, -88, 0, 0, -60, 0, 84, -15, 0, -32, -26, 0, -38, 0, 0, 4, 214, 0, 0, 36, 0, -119, -9, 0, -60, -14, 0, 30, 0, 0, 2, 5, 0, 0, 33, 0, -36, -14, 0, -51, 108, 0, 63, 0, 0, -42, -32, 0, 0, 1, 0, -102, -7, 0, -4, 39, 0, 86, 0, 0, -86, 98, 0, 0, 28, 0, -34, -10, 0, -44, 6, 0, -152, 0, 0, -36, -145, 0, 0, 16, 0, -8, -6, 0, 237, -94, 0, -6, 0, 0, 272, 15, 0, 0, -3, 0, 101, 29, 0, -48, 87, 0, 57, 0, 0, -84, -6, 0, 0, 46, 0, 2, 128, 0, 186, 26, 0, 14, 0, 0, 80, 6, 0, 0, 2, 0, 50, 6, 0, -64, -60, 0, 74, 0, 0, -30, 12, 0, 0, 12, 0, 90, -300, 0, 26, -16, 0, -14, 0, 0, -26, -3, 0, 0, 72, 0, 68, 30, 0, 11, -84, 0, -7, 0, 0, -39, -136, 0, 0, -46, 0, 27, 30, 0, -32, -14, 0, 90, 0, 0, -74, 34, 0, 0, 176, 0, 4, -45, 0, 18, 78, 0, 0, 0, 0, -58, 143, 0, 0, -26, 0, 24, -69, 0, -104, 24, 0, 33, 0, 0, 56, -51, 0, 0, 38, 0, -4, 18, 0, -12, 4, 0, -24, 0, 0, -17, -40, 0, 0, 6, 0, 41, -139, 0, -27, -32, 0, 32, 0, 0, -84, -63, 0, 0, -48, 0, -20, 34, 0, -68, -24, 0, -96, 0, 0, 10, 150, 0, 0, -80, 0, -58, 203, 0, 60, 98, 0, -56, 0, 0, -72, 25, 0, 0, 84, 0, -150, 9, 0, -12, 125, 0, -56, 0, 0, -20, -10, 0, 0, -124, 0, 54, 47, 0, 32, -15, 0, 51, 0, 0, 223, 47, 0, 0, 69, 0, 27, -6, 0, 21, -66, 0, -20, 0, 0, -4, 162, 0, 0, 5, 0, 70, -85, 0, -54, 42, 0, 34, 0, 0, -7, 34, 0, 0, 26, 0, 54, 76, 0, 15, 68, 0, -48, 0, 0, 81, 18, 0, 0, -18, 0, 23, 56, 0, 102, 13, 0, 6, 0, 0, 81, -44, 0, 0, -110, 0, 156, 22, 0, 13, -114, 0, -12, 0, 0, 4, -192, 0, 0, 69, 0, -72, 226, 0, 32, -19, 0, 0, 0, 0, -117, 3, 0, 0, 54, 0, 61, 20, 0, -54, 94, 0, -110, 0, 0, 31, 84, 0, 0, 38, 0, -36, -10, 0, -18, -38, 0, 72, 0, 0, 4, 65, 0, 0, 51, 0, 36, -6, 0, -4, -95, 0, 138, 0, 0, -59, -64, 0, 0, -36, 0, -102, -42, 0, -126, -45, 0, 1, 0, 0, 192, -27, 0, 0, 100, 0, -124, 24, 0, 12, -110, 0, -50, 0, 0, -5, -58, 0, 0, -14, 0, 56, -72, 0, -24, 12, 0, -36, 0, 0, 98, 14, 0, 0, -120, 0, 4, -28, 0, -38, 93, 0, 63, 0, 0, -24, -78, 0, 0, 26, 0, -72, 63, 0, 32, 5, 0, -28, 0, 0, 222, 0, 0, 0, 68, 0, -59, 18, 0, -30, -180, 0, 50, 0, 0, 8, -84, 0, 0, -168, 0, -107, 302, 0, -152, 76, 0, 12, 0, 0, -51, 39, 0, 0, 32, 0, 72, 2, 0, -76, 11, 0, -231, 0, 0, -36, 66, 0, 0, 45, 0, 62, 16, 0, 36, -28, 0, 2, 0, 0, 63, -96, 0, 0, 56, 0, 46, 27, 0, -7, 150, 0, -58, 0, 0, 9, 60, 0, 0, 94, 0, 2, -16, 0, 63, -66, 0, 186, 0, 0, 2, 52, 0, 0, 6, 0, -150, 14, 0, 114, -10, 0, 98, 0, 0, 8, -16, 0, 0, 6, 0, -177, 162, 0, 111, 60, 0, 54, 0, 0, 252, -24, 0, 0, 64, 0, -226, 14, 0, 3, 93, 0, -16, 0, 0, -118, -208, 0, 0, 50, 0, 7, -66, 0, 42, -10, 0, 11, 0, 0, -90, -13, 0, 0, 54, 0, 182, 48, 0, -21, -54, 0, -134, 0, 0, -88, -14, 0, 0, -69, 0, -88, 5, 0, 50, 8, 0, -2, 0, 0, 123, 4, 0, 0, 42, 0, -21, -1, 0, -6, -56, 0, 102, 0, 0, -100, 63, 0, 0, -34, 0, 39, -130, 0, 33, 61, 0, -3, 0, 0, 23, -58, 0, 0, 143, 0, 45, 16, 0, -24, 204, 0, -102, 0, 0, 16, 183, 0, 0, 22, 0, 115, 30, 0, 36, -70, 0, -37, 0, 0, -78, 18, 0, 0, 36, 0, 54, -85, 0, -28, 21, 0, 83, 0, 0, -128, 102, 0, 0, 30, 0, 10, -200, 0, 27, 32, 0, 54, 0, 0, 81, 58, 0, 0, -12, 0, 27, 50, 0, -103, 25, 0, -38, 0, 0, -12, -136, 0, 0, 23, 0, -120, -28, 0, 82, -52, 0, 90, 0, 0, 92, 90, 0, 0, 12, 0, -115, 78, 0, 48, -208, 0, -83, 0, 0, 34, 5, 0, 0, 117, 0, 0, 238, 0, 74, -72, 0, -154, 0, 0, 6, -43, 0, 0, 110, 0, 123, 5, 0, -26, 174, 0, -78, 0, 0, -28, 60, 0, 0, -22, 0, 35, -190, 0, 114, 57, 0, 24, 0, 0, 84, 14, 0, 0, 120, 0, -148, 92, 0, -19, -79, 0, 54, 0, 0, 23, 180, 0, 0, -22, 0, -54, 218, 0, -116, 5, 0, 96, 0, 0, 38, -91, 0, 0, 22, 0, 108, -8, 0, 98, -73, 0, -168, 0, 0, -110, 161, 0, 0, 68, 0, 90, 322, 0, 86, 6, 0, -16, 0, 0, -22, -70, 0, 0, 60, 0, -58, -90, 0, -30, -12, 0, -54, 0, 0, -104, -35, 0, 0, 65, 0, -18, -51, 0, -114, -70, 0, 18, 0, 0, -122, -38, 0, 0, 64, 0, -10, -36, 0, -148, -90, 0, -23, 0, 0, -30, -40, 0, 0, -13, 0, -36, 90, 0, 375, -114, 0, -46, 0, 0, -99, 14, 0, 0, -30, 0, -154, -41, 0, 1, -176, 0, 0, 0, 0, -24, 39, 0, 0, 37, 0, -20, -36, 0, 12, 21, 0, -18, 0, 0, 6, -6, 0, 0, -168, 0, 14, 10, 0, 30, -10, 0, -104, 0, 0, 40, 51, 0, 0, 30, 0, -21, -221, 0, -118, 26, 0, 39, 0, 0, 92, 68, 0, 0, 105, 0, -24, -10, 0, 2, 0, 0, -46, 0, 0, -60, 56, 0, 0, -28, 0, -1, 72, 0, -69, 0, 0, -89, 0, 0, 105, 10, 0, 0, 42, 0, 92, 2, 0, -10, 108, 0, -132, 0, 0, 5, -37, 0, 0, 51, 0, -68, 372, 0, -140], "hecke_ring_index_factorization": [], "nf_label": "3.3.564.1", "field_poly": [3, -5, -1, 1], "atkin_lehner_string": "-+--", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [5, -1], [19, -1]], "char_values": [8550, 1, [1901, 1027, 1351], [1, 1, 1]], "Nk2": 34200, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [3, 0, 0, 2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+q^{2}+q^{4}+(\\beta _{1}-\\beta _{2})q^{7}+q^{8}+(2+\\cdots)q^{11}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 564, "level_is_prime_power": false, "relative_dim": 3, "hecke_cutters": [[7, [2, -10, -2, 1]], [11, [3, 3, -5, 1]], [13, [82, -36, 0, 1]], [17, [-54, -6, 6, 1]], [23, [-3, -9, -1, 1]], [53, [183, -57, -5, 1]]], "space_label": "8550.2.a", "level": 8550, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 11, "hecke_orbit_code": 315251973949497702, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.999", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.851", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "244.473", "prec": 24}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0, 0, 0], [1, 0, 0], [1, 0, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, -1], [1, 0, 0], [0, 0, 0], [0, 0, 0], [2, -1, 0], [0, 0, 0], [1, -1, 2], [0, 1, -1], [0, 0, 0], [1, 0, 0], [-2, 1, 1], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [2, -1, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [1, -1, 2], [0, 0, 0], [0, 1, -1], [5, -1, -1], [0, 0, 0], [1, -4, 0], [1, 0, 0], [0, 0, 0], [-2, 1, 1], [0, 0, 0], [0, 0, 0], [-2, 2, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [3, 0, 3], [0, 0, 0], [3, 1, 0], [2, -1, 0], [0, 0, 0], [0, 0, -1], [1, -2, 1], [0, 0, 0], [0, 0, -3], [0, 0, 0], [0, 0, 0], [1, -1, 2], [0, 3, -2], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [5, -1, -1], [1, 7, -2], [0, 0, 0], [-2, 5, -2], [1, -4, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [-1, 3, -1], [-2, 1, 1], [0, 0, 0], [0, 0, 0], [8, -1, -1], [0, 0, 0], [4, -4, -1], [-2, 2, 0], [0, 0, 0], [1, 0, 0], [-3, 3, -2], [0, 0, 0], [1, 2, 0], [0, 0, 0], [0, 0, 0], [3, 0, 3], [3, 3, 1], [0, 0, 0], [0, 0, 0], [3, 1, 0], [0, 0, 0], [2, -1, 0], [8, -4, -3], [0, 0, 0], [-11, 0, 5], [0, 0, -1], [0, 0, 0], [1, -2, 1], [0, 0, 0], [0, 0, 0], [6, -5, -1], [0, 0, -3], [0, 0, 0], [0, 0, 0]]}