# Stored data for newform 3600.3.l.b, downloaded from the LMFDB on 18 July 2025.
{"Nk2": 32400, "analytic_conductor": 98.09289516970688, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 2, "char_parity": -1, "char_values": [3600, 2, [3151, 901, 2801, 577], [2, 2, 1, 2]], "cm_discs": [], "conrey_index": 1601, "dim": 2, "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[7, [9, 1]], [11, [338, 0, 1]], [13, [1, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504355591949840, "hecke_ring_generator_nbound": 17, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "3600.3.l.b", "level": 3600, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "225.3.c.a", "nf_label": "2.0.8.1", "prim_orbit_index": 2, "qexp_display": "q-9q^{7}+13\\beta q^{11}-q^{13}+19\\beta q^{17}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "3600.3.l", "trace_display": [0, 0, 0, -18], "trace_hash": 1572401390343374753, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.908", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.127", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "149.937", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 146, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -434, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 450, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 238, 0, 0, 0, 0, 0, -988, 0, 0, 0, 0, 0, -562, 0, 0, 0, 0, 0, -350, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, -702, 0, 0, 0, 0, 0, -530, 0, 0, 0, 0, 0, -174, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 830, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -156, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 352, 0, 0, 0, 0, 0, -606, 0, 0, 0, 0, 0, -786, 0, 0, 0, 0, 0, -866, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 414, 0, 0, 0, 0, 0, 578, 0, 0, 0, 0, 0, 962, 0, 0, 0, 0, 0, -988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 670, 0, 0, 0, 0, 0, 306, 0, 0, 0, 0, 0, 1136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, -738, 0, 0, 0, 0, 0, -626, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, -78, 0, 0, 0, 0, 0, -206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1120, 0, 0, 0, 0, 0, -1314, 0, 0, 0, 0, 0, 514, 0, 0, 0, 0, 0, 334, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -1134, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 1090, 0, 0, 0, 0, 0, -1444, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2448, 0, 0, 0, 0, 0, -1196, 0, 0, 0, 0, 0, -526, 0, 0, 0, 0, 0, 1022, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 978, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -432, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -754, 0, 0, 0, 0, 0, -1582, 0, 0, 0, 0, 0, 3536, 0, 0, 0, 0, 0, -1950, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466, 0, 0, 0, 0, 0, -1552, 0, 0, 0, 0, 0, -752, 0, 0, 0, 0, 0, -2062, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1490, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -2064, 0, 0, 0, 0, 0, -364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -880, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 528, 0, 0, 0, 0, 0, -126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 364, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 0, 0, 1214, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1980, 0, 0, 0, 0, 0, 142, 0, 0, 0, 0, 0, 1808, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1408, 0, 0, 0, 0, 0, 1954, 0, 0, 0, 0, 0, 450, 0, 0, 0, 0, 0, 2674, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2288, 0, 0, 0, 0, 0, 1406, 0, 0, 0, 0, 0, -146, 0, 0, 0, 0, 0, -1748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2190, 0, 0, 0, 0, 0, 1150, 0, 0, 0, 0, 0, -2030, 0, 0, 0, 0, 0, 300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 238, 0, 0, 0, 0, 0, 3906, 0, 0, 0, 0, 0, 594, 0, 0, 0, 0, 0, 2572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -126, 0, 0, 0, 0, 0, 3198, 0, 0, 0, 0, 0, -386, 0, 0, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5168, 0, 0, 0, 0, 0, -480, 0, 0, 0, 0, 0, -1716, 0, 0, 0, 0, 0, -686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1600, 0, 0, 0, 0, 0, -1218, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1120, 0, 0, 0, 0, 0, 1168, 0, 0, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 3744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1922, 0, 0, 0, 0, 0, 1200, 0, 0, 0, 0, 0, -532, 0, 0, 0, 0, 0, -1874, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2350, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -1086, 0, 0, 0, 0, 0, 1042, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 606, 0, 0, 0, 0, 0, -306, 0, 0, 0, 0, 0, 2770, 0, 0, 0, 0, 0, -3070, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276, 0, 0, 0, 0, 0, 1918, 0, 0, 0, 0, 0, 370, 0, 0, 0, 0, 0, 1170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1872, 0, 0, 0, 0, 0, -1902, 0, 0, 0, 0, 0, -4018, 0, 0, 0, 0, 0, 1342, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -306, 0, 0, 0, 0, 0, -2496, 0, 0, 0, 0, 0, 2866, 0, 0, 0, 0, 0, -3650, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 0, 0, 0, 4368, 0, 0, 0, 0, 0, 3024, 0, 0, 0, 0, 0, -304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4336, 0, 0, 0, 0, 0, -3344, 0, 0, 0, 0, 0, 3984, 0, 0, 0, 0, 0, 816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3708, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 1664, 0, 0, 0, 0, 0, -2416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -2142, 0, 0, 0, 0, 0, -3150, 0, 0, 0, 0, 0, 494, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4270, 0, 0, 0, 0, 0, 2558, 0, 0, 0, 0, 0, -930, 0, 0, 0, 0, 0, 8892, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 592, 0, 0, 0, 0, 0, 2738, 0, 0, 0, 0, 0, -1794, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5058, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -1748, 0, 0, 0, 0, 0, -690, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1954, 0, 0, 0, 0, 0, 6800, 0, 0, 0, 0, 0, 3150, 0, 0, 0, 0, 0, 4286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2508, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 5120, 0, 0, 0, 0, 0, -2126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3120, 0, 0, 0, 0, 0, 3902, 0, 0, 0, 0, 0, -5106, 0, 0, 0, 0, 0, -2384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1346, 0, 0, 0, 0, 0, -882, 0, 0, 0, 0, 0, -3536, 0, 0, 0, 0, 0, 1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 0, 0, 780, 0, 0, 0, 0, 0, 5472, 0, 0, 0, 0, 0, 2496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1842, 0, 0, 0, 0, 0, 5168, 0, 0, 0, 0, 0, 4370, 0, 0, 0, 0, 0, 3858, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4770, 0, 0, 0, 0, 0, 3106, 0, 0, 0, 0, 0, 434, 0, 0, 0, 0, 0, 2558, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, -4016, 0, 0, 0, 0, 0, 1566, 0, 0, 0, 0, 0, -4194, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2798, 0, 0, 0, 0, 0, 2608, 0, 0, 0, 0, 0, -528, 0, 0, 0, 0, 0, -6292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, -2560, 0, 0, 0, 0, 0, 1970, 0, 0, 0, 0, 0, 5392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3298, 0, 0, 0, 0, 0, -7470, 0, 0, 0, 0, 0, -3678, 0, 0, 0, 0, 0, -5036, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -532, 0, 0, 0, 0, 0, -2736, 0, 0, 0, 0, 0, -3584, 0, 0, 0, 0, 0, -450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5762, 0, 0, 0, 0, 0, -6292, 0, 0, 0, 0, 0, -4960, 0, 0, 0, 0, 0, -4110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1404, 0, 0, 0, 0, 0, -2430, 0, 0, 0, 0, 0, -2642, 0, 0, 0, 0, 0, -3234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3282, 0, 0, 0, 0, 0, 208, 0, 0, 0, 0, 0, -2048, 0, 0, 0, 0, 0, 6384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5680, 0, 0, 0, 0, 0, 9360, 0, 0, 0, 0, 0, -350, 0, 0, 0, 0, 0, -2640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -270, 0, 0, 0, 0, 0, -1374, 0, 0, 0, 0, 0, 1282, 0, 0, 0, 0, 0, -1408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5694, 0, 0, 0, 0, 0, -3168, 0, 0, 0, 0, 0, -6396, 0, 0, 0, 0, 0, -396, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2432, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, 4046, 0, 0, 0, 0, 0, 5454, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, -5500, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 4628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7074, 0, 0, 0, 0, 0, -1376, 0, 0, 0, 0, 0, -3264, 0, 0, 0, 0, 0, 2050, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2720, 0, 0, 0, 0, 0, 2414, 0, 0, 0, 0, 0, 7794, 0, 0, 0, 0, 0, -6686, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 3468, 0, 0, 0, 0, 0, -3344, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1250, 0, 0, 0, 0, 0, 4914, 0, 0, 0, 0, 0, -3374, 0, 0, 0, 0, 0, -1438, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -572, 0, 0, 0, 0, 0, -1472, 0, 0, 0, 0, 0, -6738, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2452, 0, 0, 0, 0, 0, -5230, 0, 0, 0, 0, 0, 3938, 0, 0, 0, 0, 0, -5202, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2288], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-9, 0], [0, 0], [0, 0], [0, 0], [0, 13], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 19], [0, 0], [-25, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 19], [0, 0], [39, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-32, 0], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [-23, 0], [0, 0], [0, 0], [0, 0], [0, 23], [0, 0], [32, 0], [0, 0], [0, 0], [0, 0], [0, -68], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [73, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [63, 0], [0, 0], [0, 0], [0, 0], [0, 44], [0, 0], [-136, 0], [0, 0], [0, 0], [0, 0], [0, -117], [0, 0], [24, 0], [0, 0], [0, 0], [0, 0], [0, 33], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -72], [0, 0], [9, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [7, 0], [0, 0], [0, 0], [0, 0]]}