# Stored data for newform 768.3.h.g, downloaded from the LMFDB on 24 February 2021. {"level_primes": [2, 3], "is_polredabs": true, "sato_tate_group": "2.2.3.c2", "rm_discs": [], "conrey_indexes": [641], "cm_discs": [], "trace_hash": 535999108844774516, "level_radical": 6, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 8, "is_cm": false, "hecke_orbit": 7, "analytic_conductor": 20.9264843028708, "inner_twist_count": 4, "field_disc_factorization": [[2, 36], [3, 4], [509, 4]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": -1, "label": "768.3.h.g", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "384.3.e.a", "field_poly_is_cyclotomic": false, "dim": 16, "trace_zratio": {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, "traces": [0, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -112, 0, 16, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, -384, 0, 80, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, -816, 0, 144, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -976, 0, 160, 0, 0, 0, 0, 0, 944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, -752, 0, 176, 0, 0, 0, 0, 0, 1504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, -1616, 0, -64, 0, 0, 0, 0, 0, 1824, 0, 0, 0, 0, 0, 0, 0, 0, 0, -176, 0, 0, 0, 0, 0, -2864, 0, -432, 0, 0, 0, 0, 0, 1488, 0, 0, 0, 0, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, -1104, 0, -336, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, -608, 0, 0, 0, 0, 0, -304, 0, -608, 0, 0, 0, 0, 0, 1856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, -3168, 0, -624, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0, 0, 0, -1840, 0, 512, 0, 0, 0, 0, 0, 1328, 0, 0, 0, 0, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, -192, 0, -112, 0, 0, 0, 0, 0, 608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 704, 0, 0, 0, 0, 0, -2048, 0, 80, 0, 0, 0, 0, 0, 1552, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 544, 0, 1472, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 0, 0, -752, 0, -1216, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -2688, 0, -432, 0, 0, 0, 0, 0, -992, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1184, 0, 0, 0, 0, 0, 3840, 0, 912, 0, 0, 0, 0, 0, -1280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1984, 0, 0, 0, 0, 0, 1584, 0, -2016, 0, 0, 0, 0, 0, -352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2272, 0, 0, 0, 0, 0, -1648, 0, 2400, 0, 0, 0, 0, 0, -944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 960, 0, 0, 0, 0, 0, 4848, 0, 2640, 0, 0, 0, 0, 0, -1856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2784, 0, 0, 0, 0, 0, 2912, 0, -464, 0, 0, 0, 0, 0, -1888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, -1344, 0, 2640, 0, 0, 0, 0, 0, -4368, 0, 0, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 5856, 0, -1984, 0, 0, 0, 0, 0, -3216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640, 0, 0, 0, 0, 0, 5760, 0, -2368, 0, 0, 0, 0, 0, -2720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2656, 0, 0, 0, 0, 0, -2800, 0, -352, 0, 0, 0, 0, 0, -5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3568, 0, 0, 0, 0, 0, 7280, 0, -2512, 0, 0, 0, 0, 0, -4288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1952, 0, 0, 0, 0, 0, 8640, 0, 2304, 0, 0, 0, 0, 0, -4928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, -2592, 0, 976, 0, 0, 0, 0, 0, -2704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3840, 0, 0, 0, 0, 0, 9312, 0, 2176, 0, 0, 0, 0, 0, -2576, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5984, 0, 0, 0, 0, 0, 6576, 0, 3072, 0, 0, 0, 0, 0, -6624, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5280, 0, 0, 0, 0, 0, -2864, 0, -4976, 0, 0, 0, 0, 0, -3392, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1824, 0, 0, 0, 0, 0, 7984, 0, -1664, 0, 0, 0, 0, 0, -4960, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4800, 0, 0, 0, 0, 0, 3840, 0, -2944, 0, 0, 0, 0, 0, -4064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4512, 0, 0, 0, 0, 0, -400, 0, -3984, 0, 0, 0, 0, 0, -1360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1360, 0, 0, 0, 0, 0, 11408, 0, 7952, 0, 0, 0, 0, 0, -4544, 0, 0, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 4896, 0, 3104, 0, 0, 0, 0, 0, -2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3872, 0, 0, 0, 0, 0, -9408, 0, 448, 0, 0, 0, 0, 0, -7328, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6240, 0, 0, 0, 0, 0, 9712, 0, 4848, 0, 0, 0, 0, 0, -3504, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3200, 0, 0, 0, 0, 0, 10496, 0, -8416, 0, 0, 0, 0, 0, 2080, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5616, 0, 0, 0, 0, 0, -13456, 0, -5056, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6816, 0, 0, 0, 0, 0, 2896, 0, -1968, 0, 0, 0, 0, 0, 1552, 0], "hecke_ring_index_factorization": [[2, 34], [3, 2]], "field_poly": [2401, -7056, 11724, -17932, 24840, -25496, 17714, -7060, 555, 640, -66, -104, 50, -28, 14, -4, 1], "has_non_self_twist": 1, "char_values": [768, 2, [511, 517, 257], [2, 1, 1]], "Nk2": 6912, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "h", "weight": 3, "trace_display": [0, 0, 0, -16], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": false, "hecke_ring_index": 154618822656, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+\\beta _{5}q^{3}-\\beta _{9}q^{5}+(-1-\\beta _{2})q^{7}+(\\beta _{1}+\\cdots)q^{9}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 373625055129680348184576, "level_is_prime_power": false, "relative_dim": 16, "hecke_cutters": [[5, [2304, 0, -7040, 0, 3504, 0, -120, 0, 1]], [7, [-176, -368, -108, 4, 1]]], "space_label": "768.3.h", "level": 768, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0], [1, 1, 24, 8, -1, 2, 0], [1, 1, 3, 2, -1, 2, 0]], "char_degree": 1, "char_conductor": 24, "char_orbit_index": 8, "hecke_ring_generator_nbound": 13, "hecke_orbit_code": 27022078850892544, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.171", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1742.298", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "378442.930", "prec": 34}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 3, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 1, -1, 0, 1, 0, -3, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 6, 0, -2, -1, 1, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 2, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 3, 0, -1, 2, 7, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, -3, 1, 0, 0, 0, 3, 0, 0, 0, -2, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, -2, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 1, 0, 0, 6, 0, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -5, 0, 3, 0, -1, 4, 2, 0, 0, 0, 4, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, 0, 0, 0, -1, 0, 0, 0, -3, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -3, 3, 0, 0, 0, -1, 0, 0, 0, -1, -1, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, -2, -3, 0, -1, -10, -5, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -8, 0, 12, 0, 4, 4, 3, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-24, -2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -1, 3, 0, 0, 0, 3, 0, 0, 0, -3, -2, -2, 0, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, -3, 0, 0, -4, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, -10, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [33, 0, 3, 0, 0, 0, -3, 0, 0, 0, 5, 0, -4, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0, 7, 0, 0, 0, 1, -2, -2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 10, 0, 0, 0, 0, -3, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 0, 1, 0, -3, -3, -3, 0, 0, 0, 2, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -1, 0, 0, 0, -3, 0, 0, 0, 7, 1, -3, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [10, 0, -2, 0, 0, 0, -2, 0, 0, 0, -2, -2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -8, -3, 2, 0, -1, -8, -1, 0, 0, 0, -1, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, 12, 0, 4, -4, 2, 0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-51, -2, 0, 0, 0, 0, 3, 0, 0, 0, 3, 3, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 3, 3, 0, 0, 0, -3, 0, 0, 0, 5, -3, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, -6, 0, -1, 2, -9, 0, 0, 0, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -16, 0, 0, 2, 0, 0, 0, 0, 8, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [46, 7, -5, 0, 0, 0, 2, 0, 0, 0, -3, 4, -1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 3, 0, 0, 0, 1, 0, 0, 0, 9, -3, -2, 0, 0, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -7, -4, 0, 0, 6, 0, 0, 0, 0, 2, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -8, -1, -10, 0, 0, -4, -5, 0, 0, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 5, 0, 0, 0, 16, 0, 0, 0, 0, -5, -3, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12, 5, 1, 0, 0, 0, -3, 0, 0, 0, -3, -3, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 10, 5, 1, 0, 0, -16, 4, 0, 0, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}