# Stored data for newform 729.2.e.n, downloaded from the LMFDB on 31 March 2023. {"level_primes": [3], "is_polredabs": true, "sato_tate_group": "1.2.3.c9", "rm_discs": [], "conrey_indexes": [82, 163, 325, 406, 568, 649], "cm_discs": [], "trace_hash": 730595707232694039, "level_radical": 3, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 5, "is_cm": false, "hecke_orbit": 14, "analytic_conductor": 5.82109430735134, "inner_twist_count": 12, "field_disc_factorization": [[2, 12], [3, 18]], "is_rm": false, "char_order": 9, "level_is_square": true, "weight_parity": 1, "label": "729.2.e.n", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "243.2.a.c", "field_poly_is_cyclotomic": true, "dim": 12, "trace_zratio": {"__RealLiteral__": 0, "data": "0.838", "prec": 17}, "traces": [0, 12, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 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"is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 2, 9, 3, 1, 3, 0], [1, 2, 9, 4, -1, 6, 0], [1, 3, 27, 5, 1, 9, 0], [1, 3, 27, 6, -1, 18, 0]], "char_degree": 6, "char_conductor": 27, "char_orbit_index": 5, "hecke_ring_generator_nbound": 4, "hecke_orbit_code": 58547070067278553, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.522", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3185.222", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1199450.773", "prec": 37}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": 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