# Stored data for newform 1323.4.a.o, downloaded from the LMFDB on 10 September 2024.
{"Nk2": 21168, "analytic_conductor": 78.05952693759484, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [7, -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": [1323, 1, [785, 1081], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 12, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [6, 6, 1]], [5, [-39, -6, 1]], [13, [-1052, 52, 1]]], "hecke_orbit": 15, "hecke_orbit_code": 63050394850297131, "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": "1323.4.a.o", "level": 1323, "level_is_powerful": true, "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, 7], "level_radical": 21, "minimal_twist": "189.4.a.e", "nf_label": "2.2.12.1", "prim_orbit_index": 1, "qexp_display": "q+(-3+\\beta )q^{2}+(4-6\\beta )q^{4}+(3-4\\beta )q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1323.4.a", "trace_display": [-6, 0, 6, 0], "trace_hash": 629138695452500765, "trace_moments": [{"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "1.911", "prec": 17}, {"__RealLiteral__": 0, "data": "0.431", "prec": 17}, {"__RealLiteral__": 0, "data": "9.511", "prec": 17}, {"__RealLiteral__": 0, "data": "3.543", "prec": 17}, {"__RealLiteral__": 0, "data": "66.989", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, -6, 0, 8, 6, 0, 0, -12, 0, -42, -48, 0, -52, 0, 0, 56, 30, 0, -64, 168, 0, 48, -60, 0, -136, 12, 0, 0, -360, 0, 140, -72, 0, 78, 0, 0, -230, 552, 0, -372, 234, 0, -938, 384, 0, -228, 618, 0, 0, 264, 0, 656, 420, 0, 240, 0, 0, 1296, 282, 0, 32, -852, 0, -736, 420, 0, 544, -888, 0, 0, 504, 0, 764, 1122, 0, -2416, 0, 0, 238, 168, 0, -1926, -522, 0, -582, 2742, 0, -1056, 708, 0, 0, 2208, 0, -798, -1632, 0, -664, 0, 0, 320, 1092, 0, -2092, -1704, 0, -3084, 1092, 0, -1346, -432, 0, 0, -1476, 0, 1452, -2736, 0, -1326, 0, 0, 26, -1824, 0, 3152, -582, 0, -2126, 4080, 0, -1068, 3912, 0, 0, -336, 0, 2172, -660, 0, -952, 0, 0, -792, 3552, 0, -1944, -4092, 0, -3512, 2496, 0, 3658, 5424, 0, 0, 2148, 0, 656, -3954, 0, 1800, 0, 0, 2362, 8280, 0, -1026, 3834, 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