# Stored data for newform 528.8.a.a, downloaded from the LMFDB on 28 May 2024.
{"Nk2": 33792, "analytic_conductor": 164.93929345561628, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [11, -1]], "atkin_lehner_string": "-+-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [528, 1, [463, 133, 353, 145], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[5, [410, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 134218256, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "528.8.a.a", "level": 528, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 11], "level_radical": 66, "minimal_twist": "33.8.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-3^{3}q^{3}-410q^{5}+1028q^{7}+3^{6}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "528.8.a", "trace_display": [0, -27, -410, 1028], "trace_hash": 708248688230956139, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.997", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.017", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.104", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 1, 0, -27, 0, -410, 0, 1028, 0, 729, 0, 1331, 0, 12958, 0, 11070, 0, 17062, 0, 54168, 0, -27756, 0, 11488, 0, 89975, 0, -19683, 0, -186654, 0, 188672, 0, -35937, 0, -421480, 0, 395886, 0, -349866, 0, -47546, 0, -602088, 0, -298890, 0, 647200, 0, 233241, 0, -460674, 0, -1312722, 0, -545710, 0, -1462536, 0, 2681140, 0, 551190, 0, 749412, 0, -5312780, 0, -459260, 0, -310176, 0, 18072, 0, -426062, 0, -2429325, 0, 1368268, 0, -297764, 0, 531441, 0, -5684028, 0, -6995420, 0, 5039658, 0, -6342966, 0, 13320824, 0, -5094144, 0, -22208880, 0, 16651586, 0, 970299, 0, -2083270, 0, 2390464, 0, 11379960, 0, 14061468, 0, -11132066, 0, -10688922, 0, 5669034, 0, -4710080, 0, 9446382, 0, 17539736, 0, 1771561, 0, 1283742, 0, -4858500, 0, 20917036, 0, 16256376, 0, 11264892, 0, 55684704, 0, 8070030, 0, 444290, 0, 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