# Stored data for newform 1682.2.a.n, downloaded from the LMFDB on 13 September 2025.
{"Nk2": 6728, "analytic_conductor": 13.43083761997936, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [29, 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": [1682, 1, [843], [1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 14, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[3, [1, -1, -2, 1]], [5, [-1, 6, -5, 1]]], "hecke_orbit": 14, "hecke_orbit_code": 58546795189372562, "hecke_ring_generator_nbound": 3, "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": "1682.2.a.n", "level": 1682, "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, 29], "level_radical": 58, "minimal_twist": "58.2.d.a", "nf_label": "3.3.49.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+(1-\\beta _{1})q^{3}+q^{4}+(2+\\beta _{2})q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1682.2.a", "trace_display": [3, 2, 5, 1], "trace_hash": 1024962065807183846, "trace_moments": [{"__RealLiteral__": 0, "data": "0.087", "prec": 17}, {"__RealLiteral__": 0, "data": "2.934", "prec": 17}, {"__RealLiteral__": 0, "data": "0.538", "prec": 17}, {"__RealLiteral__": 0, 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