# Stored data for newform 78.2.e.b, downloaded from the LMFDB on 23 March 2023.
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20, -46, 14, -10, 30, -17, 16, -20, -8, 16, -16, -6, 35, -6, 22, 5, -30, 12, 24, 4, 8, -32, -44, 4, -52, -23, 25, 48, 1, -4, -14, 1, 26, 40, 66, -14, 98, 22, -2, -18, 90, 10, -100, 10, -10, -2, 92, -1, -22, 42, 8, -8, 8, 18, -14, 4, 2, -12, 18, 26, -37, 10, 2, 2, -17, -3, -16, -35, -16, 20, -24, 11, 48, -2, -2, -32, 4, -3, -6, 4, -12, 60, -36, 4, 5, -20, -20, -3, -10, 6, 44, -14, -10, -10, -64, -2, -12, 3, -22, -10, -16, 10, 16, -6, -14, -6, -28, 8, -44, -14, -10, 18, 23, -4, 12, 6, 6, -22, -20, -2, -2, -4, 6, 2, -44, 7, -30, -16, 2, 20, -8, 8, -65, -16, -33, -10, -54, 2, 4, 6, 36, 32, 34, -1, -30, 22, -36, -7, -17, 12, -100, -7, -10, -4, -20, 1, -24, 52, -28, -22, -21, -20, -4, 6, 2, -30, 120, -5, 6, -45, 8, 14, 120, -2, -18, -4, 56, 28, 10, -12, 23, 0, -11, -18], "hecke_ring_index_factorization": [], "nf_label": "2.0.3.1", "field_poly": [1, -1, 1], "has_non_self_twist": 1, "char_values": [78, 3, [53, 67], [3, 1]], "Nk2": 312, "field_poly_root_of_unity": 6, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [1, 1, -2, 2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": true, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+(1-\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}-\\zeta_{6}q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": -3, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [1, 1]]], "space_label": "78.2.e", "level": 78, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 3, 1, 3, 0]], "char_degree": 2, "char_conductor": 13, "char_orbit_index": 5, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 4503874538831950, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.894", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.629", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.744", "prec": 20}], "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": null, "qexp": [[0, 0], [1, 0], [1, -1], [1, -1], [0, -1], [-1, 0], [0, -1], [0, 2], [-1, 0], [0, -1], [-1, 1], [-2, 2], [-1, 0], [1, 3], [2, 0], [-1, 1], [-1, 1], [0, -5], [-1, 0], [0, 2], [0, 1], [2, 0], [0, 2], [-6, 6], [-1, 1], [-4, 0], [4, -1], [-1, 0], [2, -2], [9, -9], [0, 1], [-4, 0], [0, 1], [0, 2], [-5, 0], [0, -2], [-1, 1], [11, -11], [2, 0], [4, -1], [1, 0], [-5, 5], [2, -2], [0, -10], [2, 0], [0, 1], [0, 6], [2, 0], [0, 1], [3, -3], [-4, 4], [-5, 0], [3, -4], [-1, 0], [-1, 1], [2, -2], [0, -2], [2, 0], [0, -9], [0, 8], [1, 0], [0, 11], [-4, 4], [2, -2], [1, 0], [-1, -3], [2, 0], [-2, 2], [-5, 5], [0, 6], [-2, 0], [0, 14], [0, 1], [-13, 0], [0, -11], [-4, 4], [2, -2], [-4, 0], [3, -4], [-4, 0], [1, -1], [-1, 1], [0, 5], [6, 0], [0, -2], [0, 5], [-10, 0], [0, -9], [2, -2], [-2, 2], [1, 0], [-6, 8], [6, 0], [-4, 4], [2, -2], [0, -2], [1, 0], [0, 2], [0, -3], [2, 0], [0, 4]]}