# Stored data for newform 3600.3.l.n, downloaded from the LMFDB on 19 April 2024.
{"label": "3600.3.l.n", "space_label": "3600.3.l", "level": 3600, "weight": 3, "hecke_orbit": 14, "hecke_orbit_code": 58547551120395792, "dim": 4, "is_polredabs": true, "nf_label": "4.0.6400.1", "trace_hash": 858582782981941518, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [-74, 8, 1]], [11, [26244, 0, 396, 0, 1]], [13, [-86, 4, 1]]], "qexp_display": "q+(-4+\\beta _{2})q^{7}+(-\\beta _{1}+\\beta _{3})q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "l", "char_is_real": true, "Nk2": 32400, "analytic_conductor": 98.09289516970688, "hecke_ring_index": 108, "level_radical": 30, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [3600, 2, [3151, 901, 2801, 577], [2, 2, 1, 2]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [1601], "field_disc": 6400, "field_disc_factorization": [[2, 8], [5, 2]], "field_poly": [9, 0, -4, 0, 1], "hecke_ring_index_factorization": [[2, 2], [3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.767", "prec": 17}, {"__RealLiteral__": 0, "data": "0.669", "prec": 17}, {"__RealLiteral__": 0, "data": "72.540", "prec": 20}, {"__RealLiteral__": 0, "data": "49.725", "prec": 20}, {"__RealLiteral__": 0, "data": "2007.204", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, -16], "traces": [0, 4, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -328, 0, 0, 0, 0, 0, 424, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, -392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, -784, 0, 0, 0, 0, 0, -300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, -440, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, -688, 0, 0, 0, 0, 0, -256, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, 784, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1448, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1040, 0, 0, 0, 0, 0, 1376, 0, 0, 0, 0, 0, -1208, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 880, 0, 0, 0, 0, 0, -824, 0, 0, 0, 0, 0, -3008, 0, 0, 0, 0, 0, -376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, -1640, 0, 0, 0, 0, 0, -728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 736, 0, 0, 0, 0, 0, -1192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -808, 0, 0, 0, 0, 0, -2000, 0, 0, 0, 0, 0, 1912, 0, 0, 0, 0, 0, -200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3096, 0, 0, 0, 0, 0, 1960, 0, 0, 0, 0, 0, 896, 0, 0, 0, 0, 0, 1216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1352, 0, 0, 0, 0, 0, 1712, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -1328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2768, 0, 0, 0, 0, 0, 432, 0, 0, 0, 0, 0, -2320, 0, 0, 0, 0, 0, 1108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1880, 0, 0, 0, 0, 0, -2464, 0, 0, 0, 0, 0, -1360, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 2160, 0, 0, 0, 0, 0, 1504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -1264, 0, 0, 0, 0, 0, 2152, 0, 0, 0, 0, 0, -1688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1304, 0, 0, 0, 0, 0, 2424, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 0, 0, 936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2344, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, -2792, 0, 0, 0, 0, 0, -2416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1312, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, -3248, 0, 0, 0, 0, 0, -1720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5848, 0, 0, 0, 0, 0, 848, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -2096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, -1208, 0, 0, 0, 0, 0, 3184, 0, 0, 0, 0, 0, -1216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2304, 0, 0, 0, 0, 0, -3520, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, 4032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -632, 0, 0, 0, 0, 0, 800, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 2024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1964, 0, 0, 0, 0, 0, 5552, 0, 0, 0, 0, 0, -440, 0, 0, 0, 0, 0, -824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 608, 0, 0, 0, 0, 0, -4280, 0, 0, 0, 0, 0, -400, 0, 0, 0, 0, 0, 2920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, -448, 0, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 0, 6184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3936, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 3312, 0, 0, 0, 0, 0, -1856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2388, 0, 0, 0, 0, 0, -544, 0, 0, 0, 0, 0, 5888, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2936, 0, 0, 0, 0, 0, -1208, 0, 0, 0, 0, 0, 4896, 0, 0, 0, 0, 0, -3616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6008, 0, 0, 0, 0, 0, 2560, 0, 0, 0, 0, 0, 1528, 0, 0, 0, 0, 0, 856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2056, 0, 0, 0, 0, 0, -4480, 0, 0, 0, 0, 0, -4912, 0, 0, 0, 0, 0, -3448, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 2720, 0, 0, 0, 0, 0, 616, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6336, 0, 0, 0, 0, 0, -2120, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 0, -1888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, -2432, 0, 0, 0, 0, 0, 1624, 0, 0, 0, 0, 0, 4640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, 2640, 0, 0, 0, 0, 0, 4608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3704, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, -920, 0, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2968, 0, 0, 0, 0, 0, -392, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, 1568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, -4208, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0, 0, -536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1760, 0, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 1520, 0, 0, 0, 0, 0, -9792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 1280, 0, 0, 0, 0, 0, -5176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1760, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 6624, 0, 0, 0, 0, 0, 2388, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3112, 0, 0, 0, 0, 0, -3104, 0, 0, 0, 0, 0, 1376, 0, 0, 0, 0, 0, -1688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, -3808, 0, 0, 0, 0, 0, 800, 0, 0, 0, 0, 0, 7160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4248, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 2344, 0, 0, 0, 0, 0, 2728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3080, 0, 0, 0, 0, 0, 12128, 0, 0, 0, 0, 0, -3184, 0, 0, 0, 0, 0, 2696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5920, 0, 0, 0, 0, 0, -12528, 0, 0, 0, 0, 0, -6048, 0, 0, 0, 0, 0, 5304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4432, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 1664, 0, 0, 0, 0, 0, 7304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3656, 0, 0, 0, 0, 0, 6080, 0, 0, 0, 0, 0, -3704, 0, 0, 0, 0, 0, -9008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 560, 0, 0, 0, 0, 0, -248, 0, 0, 0, 0, 0, 5728, 0, 0, 0, 0, 0, -712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2216, 0, 0, 0, 0, 0, -2320, 0, 0, 0, 0, 0, 3168, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3400, 0, 0, 0, 0, 0, 4312, 0, 0, 0, 0, 0, -4672, 0, 0, 0, 0, 0, -3064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5444, 0, 0, 0, 0, 0, 2080, 0, 0, 0, 0, 0, 1432, 0, 0, 0, 0, 0, -2576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7632, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 4352, 0, 0, 0, 0, 0, 1184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1544, 0, 0, 0, 0, 0, -3808, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -2360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9936, 0, 0, 0, 0, 0, -2888, 0, 0, 0, 0, 0, 4880, 0, 0, 0, 0, 0, 6008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2968, 0, 0, 0, 0, 0, -3536, 0, 0, 0, 0, 0, -888, 0, 0, 0, 0, 0, 6336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2984, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 0, 0, -4356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1736, 0, 0, 0, 0, 0, -7936, 0, 0, 0, 0, 0, -3800, 0, 0, 0, 0, 0, 2248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4400, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, -12528, 0, 0, 0, 0, 0, -3168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7488, 0, 0, 0, 0, 0, 2736, 0, 0, 0, 0, 0, 1528, 0, 0, 0, 0, 0, -12760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4760, 0, 0, 0, 0, 0, -9904, 0, 0, 0, 0, 0, 4240, 0, 0, 0, 0, 0, 3240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9824, 0, 0, 0, 0, 0, 12944, 0, 0, 0, 0, 0, -680, 0, 0, 0, 0, 0, 12712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8320, 0, 0, 0, 0, 0, 7240, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 1592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 184, 0, 0, 0, 0, 0, -1584, 0, 0, 0, 0, 0, -12536, 0, 0, 0, 0, 0, 8352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8032, 0, 0, 0, 0, 0, 608, 0, 0, 0, 0, 0, -7360, 0, 0, 0, 0, 0, 752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4752, 0, 0, 0, 0, 0, 10320, 0, 0, 0, 0, 0, 13144, 0, 0, 0, 0, 0, 5168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4304, 0, 0, 0, 0, 0, -2456, 0, 0, 0, 0, 0, 3152, 0, 0, 0, 0, 0, -9824, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9280], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 12, "prim_orbit_index": 2, "minimal_twist": "180.3.g.a", "char_is_minimal": false, "conrey_index": 1601, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[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], [-4, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 1], [0, 0, 0, 0], [-2, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [-8, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 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, -1], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [34, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 4], [0, 0, 0, 0], [20, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -14, 0, -2], [0, 0, 0, 0], [57, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -10, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -17, 0, -3], [0, 0, 0, 0], [-10, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-76, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -12, 0, 2], [0, 0, 0, 0], [-38, 0, 6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 34, 0, -7], [0, 0, 0, 0], [-50, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 21, 0, 2], [0, 0, 0, 0], [-82, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [106, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}