# Stored data for newform 441.3.n.f, downloaded from the LMFDB on 29 December 2025.
{"Nk2": 3969, "analytic_conductor": 12.016379658289093, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 63, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 14, "char_orbit_label": "n", "char_order": 6, "char_parity": -1, "char_values": [441, 6, [344, 199], [1, 2]], "cm_discs": [], "conrey_index": 128, "dim": 22, "has_non_self_twist": 1, "hecke_cutters": [[2, [2187, -40095, 175041, 1283040, 2181978, 59535, -2151333, -559467, 1590579, 804789, -485559, -336231, 112326, 93906, -12503, -15735, 887, 1884, 63, -132, -10, 6, 1]], [13, [7596761218181286529, 26143745105921885295, 83724438910104141433, 24684542823396957004, 10966334171611871347, 1137745737161247568, 486934829931132680, 22315556559703339, 17170887052899920, -131275944070445, 332311298052074, -5560171261793, 4368441957341, -115087193417, 34159786319, -678688883, 170265317, -3524738, 547897, -8096, 1051, -18, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518891540382137, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 14, -1, 6, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "441.3.n.f", "level": 441, "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": [3, 7], "level_radical": 21, "minimal_twist": "63.3.j.b", "prim_orbit_index": 14, "related_objects": [], "relative_dim": 11, "rm_discs": [], "sato_tate_group": "2.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "441.3.n", "trace_display": [-6, -8, 0, 0], "traces": [22, -6, -8, 12, 0, 8, 0, 0, 20, -25, 0, 20, 18, 0, 53, 12, -6, -56, -3, 39, 0, -59, 0, -15, -114, 3, 97, 0, -63, -20, 29, 246, -77, 99, 0, 76, -20, 0, 200, -210, 51, 0, 65, 54, -71, 75, -261, 113, 0, 63, -78, -92, -63, 485, 100, 0, 224, -80, 102, 103, -78, 0, 0, 106, -225, 401, -132, 0, 297, 0, 0, -66, -1, 0, 245, -233, 0, -440, 140, -96, 104, 157, -255, 0, 102, 0, 136, -816, 720, -418, 0, -1239, 210, -261, 642, -539, -178, 0, -103, -125, 0, 147, -26, -429, 0, 294, 864, -985, -467, -1620, -270, 0, 522, -263, -252, -99, 928, 540, 0, 1488, 162, 978, -158, -583, 0, 0, 196, -597, 620, 40, 0, -142, 0, 0, 113, -126, 0, 636, -187, 0, -690, -363, -363, -686, -110, -435, 0, -248, 0, 286, -574, 1896, 627, 0, -1380, 109, 21, 621, -1587, 85, 0, -1199, 141, 0, 1205, 180, -177, 0, 81, -168, -695, 369, -1194, 326, 0, 1272, -726, 266, -1287, 2315, -408, 0, 1433, 900, 960, 465, -417, 0, 0, -20, 753, 1222, -145, 0, -350, 0, 0, 874, -514, 0, 1231, 91, 0, -561, 325, -2433, -513, -224, 828, 0, -678, 0, 447, -1136, 1026, 3, 0, -1152, -378, -256, 1557, -2238, 174, 0, -371, 97, 0, 715, -158, -2190, 0, -483, 957, -2011, 102, -3066, -712, 0, 1755, -1787, 790, -363, 847, 844, 0, 3170, -572, 1890, -129, 228, 0, 0, 384, -3135, 1029, 16, 0, 583, 0, 0, 1130, 1268, 0, 39, -459, 0, -1927, -265, -2205, -2237, 150, 1413, 0, 333, 0, 1629, 1266, 3882, 1335, 0, -2175, 465, 813, 1110, -4124, -484, 0, -715, -1193, 0, 765, 1820, 990, 0, 45, 1548, -2279, 543, -2433, -152, 0, 2088, -1676, -2768, -3135, 1716, 720, 0, 1444, 1056, 2691, 1557, 1051, 0, 0, -42, 234, 333, 851, 0, 604, 0, 0, 2152, -719, 0, 1122, 585, 0, -3047, -163, -1836, -312, -157, 1293, 0, 870, 0, 2029, 2886, 3312, -1825, 0, -1974, 546, 544, 1941, -4999, -948, 0, -334, 1391, 0, -384, -1032, 3, 0, -289, -480, -3450, 162, -3714, -1360, 0, 3780, -689, 1274, -930, 2195, 960, 0, 2997, -370, 2256, 432, 384, 0, 0, 1066, -954, 1107, -338, 0, 846, 0, 0, -761, 845, 0, 608, 234, 0, -1873, -557, -3312, -3131, -784, 3168, 0, 391, 0, -445, -100, 3969, 1099, 0, -1128, 1140, -2000, -2424, -4278, 1263, 0, -960, -606, 0, 474, -832, 1200, 0, -1417, 1734, -624, 471, -198, 321, 0, 4686, -1072, 3676, -2229, 2846, -2820, 0, 2300, -4016, 273, 120, 1415, 0, 0, -2706, -30, 312, 632, 0, -1047, 0, 0, 3731, 125, 0, 2372, 81, 0, -4008, 1179, -495, 327, 258, -1473, 0, -1005, 0, 510, 3618, -231, -385, 0, -882, 938, 2259, 504, -1874, -1208, 0, -2283, 477, 0, 770, 1180, -3438, 0, -551, 1332, -2290, -1497, -2193, -2414, 0, 3531, 1127, -2598, 2157, -14, -2932, 0, 3195, 324, 2277, -2005, -589, 0, 0, -398, -3021, 714, 1564, 0, -1575, 0, 0, -1060, -2297, 0, -1487, -207, 0, -1169, -822, 21, -6083, -96, -633, 0, 1510, 0, -538, -1640, 4170, 3462, 0, -4032, -1304, 127, -1419, -4468, -771, 0, -4193, 632, 0, 1613, 1428, 1677, 0, 1422, 765, -2276, 965, 1494, -1983, 0, -951, -2598, 3332, -3861, 417, -3492, 0, -573, 4172, 414, 1995, -215, 0, 0, -1050, 1104, 3617, -802, 0, 619, 0, 0, -1453, 798, 0, 2417, 3008, 0, 3531, 957, -3033, -43, 868, -1404, 0, 155, 0, 319, 676, 1863, -4915, 0, -147, 1815, -2421, 3288, 759, 2492, 0, 3974, -399, 0, -1693, 1348, -1236, 0, 328, -1215, 2046, -90, -7497, -2263, 0, 828, 2027, 2526, 2682, -216, 2904, 0, 1888, -6618, -384, -955, 1549, 0, 0, -1546, -3777, 409, -267, 0, 4521, 0, 0, -303, 2379, 0, -1891, -2426, 0, -1370, -423, 822, -2838, 111, 5094, 0, -229, 0, -1713, 1130, -870, 1941, 0, -2490, 586, 1239, -1371, -630, 663, 0, 24, -669, 0, 4358, -604, 1647, 0, -807, 873, -97, -2235, 5457, 2621, 0, -963, 657, -6120, -1764, -202, 2070, 0, -335, 7176, -3327, 6342, -1439, 0, 0, -1732, 3621, 3846, -1692, 0, 1683, 0, 0, -866, -2552, 0, 2580, -802, 0, 393, -1838, 2325, 5806, -129, -5367, 0, 1157, 0, -429, 1286, -3021, -2269, 0, 3630, 856, 199, 1266, 5251, -3281, 0, -979, 3507, 0, -1331, -2416, -2334, 0, 4143, 3600, -1370, 1096, -3246, -3380, 0, -3297, -1572, -1128, 1206, -1797, -1836, 0, -627, -546, 549, -4822, 194, 0, 0, 2360, -5421, -1890, -4074, 0, 5163, 0, 0, -3270, 981, 0, -2924, 2905, 0, 3262, 3168, 2589, 731, 944, 2016, 0, -849, 0, -3055, 396, -711, 5155, 0, -1110, -1898, -636, -1272, 4054, 5677, 0, 2166, -2243, 0, 1152, -8386, 9987, 0, 273, 1818, 1777, 1263, 2946, 2060, 0, -915, -3339, -1974, -3795, 1295, 3604, 0, -4090, -4404, -1239, 4632, 15, 0, 0, 5264, 2994, -441, 1066, 0, -1471, 0, 0, -1953, 1795, 0, 2449, 96, 0, 327, 2015, 2007, 2058, 882, -5046, 0, -126, 0, 5579, -10660, -7281, -3237, 0, 4944, 1424, 3390, 7356, 2298, -920, 0, 5795, -4254, 0, -3233, 898, -8838, 0, -2541, -6342, -1532, -4304, 2331, -554, 0, 3060, 7156, -5776, 10341, -2865, 4164, 0, -6288, 2730, -2343, -6395, -1216, 0, 0, -1648, 1551, -2301, 1401, 0, -3078, 0, 0, 986, -2306, 0, -2076, -2746, 0, 3540, -3597, 150, -58, -1857, 846, 0, -1386, 0, -2951, -1924, 3309, 3719, 0, -645, 541, -3216, -3411, 1939, 381, 0, -3588, 5783, 0, -1102, 2584, 573, 0, 814, 777, 7739, 1883, 2151, 9297, 0, -13242, -477, 7950, -924, 1800, -3634, 0, -3824, -738, -2622, 8296, -3876, 0, 0, 6320, 6165, -7472, -1237, 0, -5421, 0, 0, -3204, -236, 0, 4048, 2785, 0, 8330, 2380, 5796, 4667, 4143, -8907, 0, -2838, 0, -5007, -456, -8052, -9727, 0, 2253, -1445, -4106, 5367, 11405, 4750, 0, 672, -2053, 0, -1905, -2780, -6018, 0, -1386, -1647, 10853, 1448, 3828, -3022, 0, -7248, 3702, 4158, 8508, -7032, 1266], "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}