# Stored data for newform 8349.2.a.i, downloaded from the LMFDB on 11 July 2025.
{"Nk2": 33396, "analytic_conductor": 66.667100647567, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [11, -1], [23, -1]], "atkin_lehner_string": "+--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [8349, 1, [5567, 7867, 4720], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 10, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-5, 0, 1]], [5, [-4, 2, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028797052526749, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "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": "8349.2.a.i", "level": 8349, "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": [3, 11, 23], "level_radical": 759, "minimal_twist": "69.2.a.b", "nf_label": "2.2.5.1", "prim_orbit_index": 1, "qexp_display": "q-\\beta q^{2}-q^{3}+3q^{4}+(-1-\\beta )q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "8349.2.a", "trace_display": [0, -2, -2, -2], "trace_hash": 858269475612013574, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.891", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.181", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.966", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.020", "prec": 17}, "traces": [0, 2, 0, -2, 6, -2, 0, -2, 0, 2, 10, 0, -6, 0, -10, 2, -2, 10, 0, -10, -6, 2, 0, 2, 0, 2, 20, -2, -6, 0, -10, -4, 0, 0, -10, -8, 6, 0, -10, 0, 10, 4, 10, -2, 0, -2, 0, -8, 2, -2, -20, -10, 0, -6, 0, 0, -10, 10, -20, 8, 6, 0, -20, -2, -26, 20, 0, 6, 30, -2, 0, -16, 0, 4, 20, -2, -30, 0, -20, -6, 2, 2, 40, -8, 6, -20, 30, 0, 0, 2, 10, -20, 6, 4, 0, 0, 0, 8, 20, 0, 6, -4, 10, -18, 20, 8, -10, -16, -6, 12, 0, 0, 2, 10, 10, -2, 0, 0, -40, 0, -10, 0, -20, -4, -12, -12, -10, -12, 0, 2, -20, -16, 0, 20, -10, 2, -10, 2, 0, 0, -24, 8, 0, 0, -2, -20, -40, 2, 0, 10, 20, 32, -10, 10, 0, -16, 0, -16, -30, 6, -30, -2, 0, -12, 12, 0, 0, -8, 10, 14, 60, -10, -6, 0, 20, 18, 0, -8, -10, 24, -6, 12, -20, 0, 0, 20, 20, 0, -24, 2, -40, 12, 26, -8, 20, -20, -6, -8, 0, 6, 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