# Stored data for newform 1305.2.a.n, downloaded from the LMFDB on 27 April 2025.
{"Nk2": 5220, "analytic_conductor": 10.42047746377709, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, 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": [1305, 1, [146, 262, 901], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 8, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [-1, -2, 1]], [7, [-4, 4, 1]]], "hecke_orbit": 14, "hecke_orbit_code": 58546795189372185, "hecke_ring_generator_nbound": 2, "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": "1305.2.a.n", "level": 1305, "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, 5, 29], "level_radical": 435, "minimal_twist": "145.2.a.b", "nf_label": "2.2.8.1", "prim_orbit_index": 1, "qexp_display": "q+(1+\\beta )q^{2}+(1+2\\beta )q^{4}-q^{5}+(-2+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1305.2.a", "trace_display": [2, 0, -2, -4], "trace_hash": 104695641502869168, "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "1.900", "prec": 17}, {"__RealLiteral__": 0, "data": "0.215", "prec": 17}, {"__RealLiteral__": 0, "data": "9.614", "prec": 17}, {"__RealLiteral__": 0, "data": "1.573", "prec": 17}, {"__RealLiteral__": 0, "data": "69.569", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 2, 2, 0, 2, -2, 0, -4, 6, 0, -2, 4, 0, -4, 4, 0, 6, 0, 0, -4, -2, 0, 12, 12, 0, 2, -4, 0, 12, -2, 0, -4, -6, 0, 8, 4, 0, 0, 4, 0, -6, 12, 0, -12, 20, 0, 20, 12, 0, 10, 2, 0, -4, -4, 0, -4, -4, 0, -2, 0, 0, 4, -28, 0, -14, 4, 0, -4, 16, 0, -4, 8, 0, 0, 24, 0, 12, 8, 0, 12, -6, 0, 12, -20, 0, 0, -12, 0, 20, 4, 0, 8, 28, 0, -4, 4, 0, -8, -22, 0, 2, -20, 0, 4, -12, 0, -20, -12, 0, 4, -12, 0, -12, 0, 0, -12, -2, 0, 0, 16, 0, 2, 20, 0, -52, -2, 0, 12, -10, 0, 4, -4, 0, 24, -28, 0, 8, 16, 0, 32, -12, 0, -24, -8, 0, 2, -24, 0, 48, 4, 0, -24, -4, 0, 8, 4, 0, -16, 36, 0, 6, -8, 0, -28, 12, 0, -28, -12, 0, -18, -8, 0, -12, -12, 0, -4, 12, 0, -12, 24, 0, -12, -8, 0, 44, 0, 0, 16, -20, 0, -4, 36, 0, -8, 16, 0, -54, 28, 0, 24, 6, 0, -4, 4, 0, -12, -36, 0, -12, 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