# Stored data for newform 678.2.a.d, downloaded from the LMFDB on 01 June 2024.
{"Nk2": 2712, "analytic_conductor": 5.41385725704281, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [113, -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": [678, 1, [227, 229], [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, [4, 1]], [7, [-4, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798915666598, "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": true, "label": "678.2.a.d", "level": 678, "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": true, "level_primes": [2, 3, 113], "level_radical": 678, "minimal_twist": "678.2.a.d", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+4q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/678/d"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "678.2.a", "trace_display": [1, 1, -4, 4], "trace_hash": 2114740974880215864, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.961", "prec": 17}, {"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": 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