Database - hmf_fields (Information on base fields for Hilbert modular forms)

Formats: - HTML - YAML - JSON - 2026-03-18T12:36:48.152005

Query: /api/hmf_fields/?_offset=0

Column	Type
degree	smallint
discriminant	bigint
ideals	jsonb
label	text
narrow_class_no	smallint
primes	jsonb

{'degree': 4, 'discriminant': 14272, 'id': 143, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[4, 2, -w^3 + 3*w^2 + w - 2]', '[9, 9, w^2 - 2*w - 3]', '[11, 11, -w^3 + 3*w^2 + 2*w - 5]', '[12, 6, w^3 - 3*w^2 - 3*w + 6]', '[13, 13, w^3 - 2*w^2 - 4*w + 2]', '[13, 13, -w + 2]', '[16, 2, 2]', '[17, 17, w^3 - 3*w^2 - 2*w + 2]', '[19, 19, -w^2 + w + 4]', '[19, 19, w^3 - 2*w^2 - 3*w + 2]', '[23, 23, w^2 - 2*w - 1]', '[27, 3, w^3 - 2*w^2 - 5*w - 1]', '[27, 27, w^3 - 2*w^2 - 3*w]', '[29, 29, -w^3 + 2*w^2 + 5*w - 1]', '[33, 33, w^3 - 3*w^2 - 3*w + 3]', '[36, 18, -w^3 + 2*w^2 + 4*w - 3]', '[37, 37, -w^3 + 2*w^2 + 5*w - 4]', '[39, 39, -w^2 + 2*w]', '[39, 39, w^2 - 3]', '[41, 41, 2*w^3 - 5*w^2 - 6*w + 4]', '[44, 22, w^3 - 2*w^2 - 2*w + 1]', '[48, 6, 2*w]', '[51, 51, -w^3 + 3*w^2 - 3]', '[52, 26, -w^3 + 3*w^2 + w - 4]', '[52, 26, -2*w^3 + 5*w^2 + 7*w - 5]', '[53, 53, w^3 - 2*w^2 - 3*w - 2]', '[57, 57, -2*w^3 + 5*w^2 + 6*w - 6]', '[57, 57, -w^2 + 2*w + 6]', '[59, 59, w - 4]', '[64, 4, -2*w^3 + 6*w^2 + 2*w - 4]', '[67, 67, 2*w^2 - 3*w - 8]', '[68, 34, w^2 - w - 5]', '[69, 69, w^3 - 2*w^2 - w]', '[73, 73, 2*w^3 - 5*w^2 - 6*w + 5]', '[76, 38, -w^3 + 3*w^2 + 3*w - 2]', '[76, 38, w^3 - 4*w^2 + 7]', '[81, 3, 3]', '[81, 81, w^3 - 3*w^2]', '[87, 87, 2*w^3 - 6*w^2 - 4*w + 9]', '[89, 89, -2*w^3 + 6*w^2 + 5*w - 7]', '[92, 46, -3*w^3 + 10*w^2 - 7]', '[97, 97, -2*w^3 + 6*w^2 + 3*w - 7]', '[97, 97, -w^3 + 3*w^2 + 3*w - 1]', '[99, 99, -w^2 + w + 6]', '[103, 103, w^2 - 4*w - 4]', '[108, 6, w^3 - 2*w^2 - 2*w - 1]', '[108, 54, -w^3 + 4*w^2 - 9]', '[111, 111, -2*w + 3]', '[113, 113, 2*w^3 - 5*w^2 - 4*w + 1]', '[113, 113, -w^3 + 3*w^2 + w - 5]', '[116, 58, w^3 - 4*w^2 + 5]', '[117, 117, -w^3 + 4*w^2 - w - 6]', '[117, 117, 2*w^3 - 5*w^2 - 5*w + 6]', '[121, 121, 2*w^2 - 4*w - 5]', '[123, 123, -w^3 + 4*w^2 - 6]', '[132, 66, -w^3 + 2*w^2 + 4*w + 3]', '[139, 139, 2*w^2 - 3*w - 4]', '[139, 139, w^3 - w^2 - 6*w - 1]', '[143, 143, w^2 - 4]', '[143, 143, 2*w^3 - 5*w^2 - 6*w + 2]', '[144, 18, 2*w^2 - 4*w - 6]', '[148, 74, 4*w^3 - 13*w^2 - 3*w + 11]', '[149, 149, 2*w^3 - 5*w^2 - 5*w + 2]', '[149, 149, w^3 - 4*w^2 + 10]', '[151, 151, -3*w - 1]', '[153, 153, 2*w^3 - 5*w^2 - 8*w + 6]', '[156, 78, w^3 - 3*w^2 - w + 6]', '[156, 78, -w^3 + w^2 + 7*w]', '[157, 157, w^2 - w - 8]', '[157, 157, w^3 - 7*w - 8]', '[159, 159, 2*w^2 - 4*w - 3]', '[163, 163, -3*w^3 + 8*w^2 + 8*w - 10]', '[163, 163, w^3 - 3*w^2 - 4*w + 7]', '[163, 163, -w^3 + 4*w^2 + w - 8]', '[163, 163, -2*w^3 + 5*w^2 + 7*w - 4]', '[164, 82, -w^3 + 4*w^2 - 2*w - 5]', '[167, 167, -2*w^3 + 5*w^2 + 8*w - 4]', '[169, 13, 2*w^3 - 5*w^2 - 8*w + 7]', '[169, 13, -2*w^3 + 4*w^2 + 7*w - 5]', '[169, 169, w^3 - 3*w^2 + 4]', '[169, 169, w^3 - w^2 - 5*w - 5]', '[171, 171, w^3 - 4*w^2 - 2*w + 6]', '[171, 171, -w^3 + 2*w^2 + 6*w]', '[173, 173, 2*w^3 - 4*w^2 - 9*w + 4]', '[173, 173, -w^3 + 5*w^2 - 2*w - 5]', '[176, 22, -2*w^3 + 6*w^2 + 4*w - 10]', '[177, 177, w^2 - 4*w]', '[181, 181, 3*w^3 - 7*w^2 - 12*w + 7]', '[187, 187, -w^3 + 2*w^2 + 6*w - 4]', '[191, 191, w^3 - 3*w^2 - 3*w - 1]', '[192, 12, 2*w^3 - 6*w^2 - 6*w + 12]', '[199, 199, 2*w^3 - 3*w^2 - 10*w - 1]', '[199, 199, 2*w^3 - 6*w^2 - 6*w + 13]', '[201, 201, 2*w^3 - 3*w^2 - 8*w]', '[204, 102, w^3 - w^2 - 5*w]', '[207, 207, -2*w^3 + 5*w^2 + 6*w]', '[208, 26, 2*w^3 - 4*w^2 - 8*w + 4]', '[208, 26, -2*w + 4]', '[209, 209, -2*w^2 + 5*w + 7]', '[209, 209, w^2 - 4*w - 1]', '[212, 106, 4*w^3 - 13*w^2 - 3*w + 7]', '[219, 219, -w^3 + 4*w^2 + w - 6]', '[221, 221, w^3 - 4*w^2 - w + 7]', '[221, 221, 2*w^2 - 3*w - 2]', '[223, 223, -2*w^3 + 6*w^2 + 4*w - 11]', '[223, 223, 3*w^3 - 7*w^2 - 12*w + 8]', '[223, 223, -2*w^3 + 5*w^2 + 6*w - 1]', '[228, 114, w^3 - w^2 - 5*w - 6]', '[228, 114, -2*w^3 + 5*w^2 + 5*w - 3]', '[229, 229, -w^3 + 3*w^2 + 2*w + 1]', '[229, 229, 3*w^3 - 4*w^2 - 15*w - 5]', '[233, 233, -3*w^3 + 7*w^2 + 11*w - 5]', '[233, 233, 2*w^3 - 5*w^2 - 4*w + 5]', '[236, 118, 5*w^3 - 16*w^2 - 4*w + 11]', '[241, 241, w^3 - 3*w^2 - 5*w + 7]', '[243, 9, -3*w^3 + 3*w^2 + 18*w + 9]', '[243, 243, 4*w^3 - 10*w^2 - 13*w + 12]', '[247, 247, w^3 - 3*w^2 - 2*w + 8]', '[247, 247, -3*w + 1]', '[247, 247, 2*w^3 - 6*w^2 - 6*w + 7]', '[247, 247, 2*w^2 - 3*w - 5]', '[253, 253, -2*w^3 + 5*w^2 + 5*w - 4]', '[256, 4, 4]', '[257, 257, w^3 - 3*w^2 - 4*w + 8]', '[261, 261, -2*w^3 + 6*w^2 + 5*w - 6]', '[263, 263, w^2 - 4*w - 5]', '[267, 267, -w^3 + 3*w^2 + 4*w - 9]', '[268, 134, w^3 - 2*w^2 - 6*w + 1]', '[271, 271, -2*w^3 + 6*w^2 + 5*w - 13]', '[272, 34, 2*w^3 - 6*w^2 - 4*w + 4]', '[276, 138, w^3 - 2*w^2 - 6*w + 3]', '[277, 277, -2*w^3 + 6*w^2 + 3*w - 8]', '[277, 277, w^3 - 2*w^2 - 2*w - 2]', '[281, 281, 2*w^3 - 5*w^2 - 4*w + 2]', '[283, 283, -3*w^2 + 7*w + 10]', '[283, 283, -w^3 + 4*w^2 - w - 7]', '[289, 289, -2*w^3 + 6*w^2 + 7*w - 11]', '[291, 291, 2*w^3 - 7*w^2 - 3*w + 6]', '[291, 291, w^3 - 2*w^2 + w + 3]', '[292, 146, w^3 - 4*w^2 + 2*w - 1]', '[293, 293, 2*w^3 - 5*w^2 - 3*w + 4]', '[293, 293, w^3 - 8*w - 4]', '[297, 33, -2*w^3 + 4*w^2 + 10*w - 1]', '[297, 297, -w^3 + w^2 + 6*w]', '[299, 299, w + 4]', '[299, 299, -w^3 + 4*w^2 - 3*w - 2]', '[304, 38, -2*w^2 + 2*w + 8]', '[304, 38, 2*w^3 - 4*w^2 - 6*w + 4]', '[307, 307, -w^3 + 2*w^2 + 6*w - 2]', '[309, 309, w^3 - 4*w^2 - 4*w]', '[311, 311, w^2 - 5]', '[317, 317, -w^3 + 5*w^2 - 2*w - 11]', '[319, 319, -w^3 + 3*w^2 - 2*w - 2]', '[323, 323, -w^2 - w + 4]', '[323, 323, 2*w^3 - 4*w^2 - 7*w + 2]', '[324, 6, 3*w^3 - 6*w^2 - 12*w + 3]', '[324, 162, 2*w^3 - 5*w^2 - 7*w + 3]', '[331, 331, -w^3 + 3*w^2 - 5]', '[333, 333, 3*w^3 - 8*w^2 - 8*w + 6]', '[339, 339, w^3 - 4*w^2 - 3*w + 3]', '[339, 339, -w^3 + 6*w^2 - 3*w - 6]', '[348, 174, -2*w^3 + 5*w^2 + 3*w - 3]', '[349, 349, -2*w^2 + 5*w + 2]', '[351, 39, -w^3 - w^2 + 8*w + 10]', '[351, 39, 2*w^3 - 4*w^2 - 7*w + 1]', '[351, 351, 2*w^3 - 6*w^2 - 4*w + 3]', '[351, 351, w^3 - 3*w^2 - 3*w + 9]', '[353, 353, -2*w^3 + 5*w^2 + 4*w - 4]', '[353, 353, 3*w^3 - 7*w^2 - 10*w + 2]', '[353, 353, -2*w^3 + 7*w^2 + 2*w - 10]', '[353, 353, w^3 + w^2 - 9*w - 13]', '[356, 178, w^3 - 3*w^2 - w - 2]', '[361, 19, -w^3 + w^2 + 7*w - 1]', '[361, 19, -w^3 + w^2 + 5*w - 1]', '[361, 361, w^2 + 2]', '[361, 361, -2*w^3 + 7*w^2 + 2*w - 8]', '[363, 363, -w^3 + 5*w^2 - 4*w - 3]', '[368, 46, 2*w^2 - 4*w - 2]', '[369, 369, 2*w^3 - 5*w^2 - 4*w + 3]', '[373, 373, -w^3 + 3*w^2 + 4*w - 11]', '[373, 373, 2*w^3 - 5*w^2 - 5*w - 2]', '[377, 377, -2*w^3 + 4*w^2 + 9*w - 5]', '[377, 377, w^3 - 3*w^2 + w - 1]', '[383, 383, w^3 - 5*w^2 + w + 13]', '[388, 194, -4*w^3 + 15*w^2 - 3*w - 7]', '[388, 194, -3*w^3 + 9*w^2 + w - 4]', '[389, 389, 3*w^3 - 10*w^2 - 4*w + 16]', '[391, 391, 2*w^3 - 8*w^2 + w + 7]', '[396, 198, -3*w^3 + 9*w^2 + 5*w - 6]', '[397, 397, -w^3 + 2*w^2 + 3*w + 5]', '[397, 397, -3*w^3 + 7*w^2 + 10*w - 7]', '[407, 407, 7*w^3 - 19*w^2 - 20*w + 26]', '[412, 206, -2*w^3 + 9*w^2 - 3*w - 7]', '[417, 417, w^3 - w^2 - 3*w - 3]', '[417, 417, 2*w^3 - 3*w^2 - 4*w]', '[419, 419, -w^3 + 2*w^2 + 4*w + 4]', '[419, 419, 3*w^3 - 7*w^2 - 12*w + 5]', '[421, 421, -w^2 + 5*w - 2]', '[421, 421, 3*w^3 - 7*w^2 - 10*w + 5]', '[429, 429, 3*w^3 - 8*w^2 - 7*w + 9]', '[429, 429, -w^3 + 4*w^2 - 2*w - 6]', '[431, 431, w^2 - 10]', '[432, 6, 2*w^3 - 4*w^2 - 10*w - 2]', '[432, 54, 2*w^3 - 4*w^2 - 6*w]', '[437, 437, w^3 - 2*w^2 - 7*w - 1]', '[437, 437, w^3 - 2*w^2 + 4]', '[439, 439, w^3 - w^2 - 7*w - 7]', '[444, 222, -8*w^3 + 21*w^2 + 27*w - 33]', '[447, 447, -2*w^3 + 5*w^2 + 8*w - 3]', '[447, 447, -w^3 + 5*w^2 - 2*w - 6]', '[451, 451, -3*w^3 + 6*w^2 + 12*w - 2]', '[452, 226, 7*w^3 - 24*w^2 - 2*w + 13]', '[452, 226, -w^3 + 5*w^2 - 3*w - 2]', '[453, 453, -3*w^2 - w]', '[459, 51, -w^3 + 2*w^2 + 5*w + 4]', '[459, 459, -w^3 + 2*w^2 + 2*w - 6]', '[461, 461, -2*w^3 + 7*w^2 + 5*w - 10]', '[464, 58, 4*w^3 - 14*w^2 + 2*w + 8]', '[467, 467, -3*w^3 + 6*w^2 + 14*w - 4]', '[468, 234, -2*w^3 + 5*w^2 + 9*w - 9]', '[468, 234, -w^3 + 2*w^2 + 2*w + 3]', '[471, 471, w^3 - w^2 - 8*w]', '[471, 471, 3*w^3 - 7*w^2 - 10*w + 6]', '[477, 477, -w^3 - 2*w^2 + 14*w + 12]', '[479, 479, 3*w^2 - 6*w - 5]', '[479, 479, -4*w^3 + 11*w^2 + 10*w - 10]', '[481, 481, -4*w^3 + 11*w^2 + 12*w - 20]', '[481, 481, -2*w^3 + 4*w^2 + 12*w - 11]', '[484, 242, -w^3 + w^2 + 5*w - 2]', '[489, 489, 2*w^3 - 7*w^2 - 4*w + 9]', '[489, 489, 2*w^3 - 4*w^2 - 6*w + 3]', '[489, 489, w^3 - 3*w^2 + 6]', '[489, 489, w^3 - w^2 - 5*w + 3]', '[491, 491, -w^3 + w^2 + 6*w - 1]', '[492, 246, -3*w^3 + 11*w^2 - 3*w - 6]', '[493, 493, -w^3 + 4*w^2 - w - 8]', '[499, 499, -4*w^3 + 9*w^2 + 15*w - 10]', '[499, 499, 2*w^3 - 5*w^2 - 7*w + 2]', '[501, 501, 3*w^2 - 5*w - 6]', '[503, 503, -2*w^3 + 7*w^2 - 8]', '[507, 39, -w^3 + 2*w^2 + 3*w - 6]', '[507, 39, -3*w^2 - w + 6]', '[507, 507, 3*w^3 - 8*w^2 - 7*w + 6]', '[507, 507, w^3 - 9*w - 3]', '[513, 57, 4*w^3 - 5*w^2 - 20*w - 7]', '[513, 57, -w^3 - w^2 + 5*w + 7]', '[513, 513, 2*w^3 - 4*w^2 - 10*w + 3]', '[513, 513, 2*w^3 - 6*w^2 - 3*w + 9]', '[519, 519, w^2 - 6]', '[519, 519, 2*w^3 - 3*w^2 - 10*w]', '[521, 521, 2*w^2 - w - 7]', '[521, 521, -3*w^3 + 7*w^2 + 11*w - 11]', '[528, 66, 2*w^3 - 6*w^2 - 6*w + 6]', '[529, 529, -w^3 + 5*w^2 - 2*w - 14]', '[531, 531, w^3 - 6*w^2 + 5*w + 12]', '[533, 533, w^3 - w^2 - 8*w - 1]', '[533, 533, -2*w^3 + 7*w^2 + w - 2]', '[543, 543, -6*w^3 + 17*w^2 + 16*w - 27]', '[551, 551, -2*w^2 + 4*w + 1]', '[551, 551, -w^3 + 3*w^2 + 4]', '[556, 278, -3*w^3 + 10*w^2 - 2*w - 7]', '[556, 278, -2*w^3 + 7*w^2 - w - 7]', '[561, 561, w^2 - 2*w + 3]', '[569, 569, 2*w^2 - 5*w - 1]', '[569, 569, -4*w - 1]', '[571, 571, -w^3 + 3*w^2 - 7]', '[572, 286, 2*w^3 - 7*w^2 - 3*w + 5]', '[572, 286, 2*w^3 - 5*w^2 - 7*w + 11]', '[573, 573, -w^3 + 2*w^2 - 3*w - 3]', '[576, 36, -2*w^3 + 4*w^2 + 8*w - 6]', '[577, 577, -w^3 + w^2 + 8*w - 4]', '[583, 583, w^3 - 5*w^2 + 2*w + 10]', '[587, 587, -3*w^3 + 8*w^2 + 7*w - 8]', '[592, 74, -2*w^3 + 4*w^2 + 10*w - 8]', '[593, 593, 3*w^2 - 4*w - 11]', '[593, 593, -3*w^3 + 9*w^2 + 6*w - 14]', '[596, 298, 5*w^3 - 17*w^2 - w + 8]', '[596, 298, -w^3 + w^2 + 7*w - 2]', '[597, 597, -2*w^3 + 7*w^2 + 3*w - 12]', '[597, 597, -2*w^3 + 4*w^2 + 9*w - 6]', '[601, 601, -3*w^3 + 9*w^2 + 4*w - 10]', '[601, 601, 5*w^3 - 9*w^2 - 24*w - 2]', '[603, 603, -3*w^3 + 2*w^2 + 21*w + 18]', '[604, 302, -2*w^3 + 9*w^2 - w - 7]', '[607, 607, 2*w^2 - 7*w - 5]', '[612, 306, -2*w^3 + 7*w^2 + 3*w - 9]', '[613, 613, w^3 - 6*w - 2]', '[613, 613, -w^2 + 3*w + 8]', '[617, 617, -w^2 + 4*w - 5]', '[619, 619, 3*w^3 - 6*w^2 - 13*w + 5]', '[621, 69, w^3 - 2*w^2 - 2*w - 4]', '[621, 621, w^3 - 4*w^2 + 4*w + 6]', '[624, 78, -2*w^2 + 4*w]', '[624, 78, 2*w^2 - 6]', '[625, 5, -5]', '[627, 627, w^3 - 4*w^2 - w]', '[627, 627, -2*w^3 + 5*w^2 + 7*w]', '[628, 314, 3*w^2 - 7*w - 5]', '[628, 314, 2*w^3 - 5*w^2 - 7*w + 1]', '[629, 629, -4*w^3 + 13*w^2 + 5*w - 14]', '[631, 631, -2*w^3 + 4*w^2 + 8*w - 7]', '[636, 318, w^2 - w - 9]', '[647, 647, -2*w^3 + 4*w^2 + 5*w - 1]', '[647, 647, w^3 - 3*w^2 - 2*w - 2]', '[649, 649, 5*w^3 - 15*w^2 - 11*w + 23]', '[652, 326, -w^3 + 5*w^2 - 5*w + 2]', '[652, 326, 4*w^3 - 13*w^2 - 5*w + 11]', '[652, 326, w^2 - 5*w + 1]', '[652, 326, -w^3 + 3*w^2 - w + 2]', '[653, 653, w^3 - 4*w^2 - w + 13]', '[653, 653, w^3 - 2*w^2 - 7*w + 5]', '[656, 82, 4*w^3 - 10*w^2 - 12*w + 8]', '[657, 657, -2*w^3 + 3*w^2 + 12*w]', '[659, 659, -4*w^3 + 10*w^2 + 15*w - 14]', '[659, 659, 5*w^3 - 12*w^2 - 17*w + 14]', '[661, 661, w^2 - 5*w - 2]', '[661, 661, -w^3 + 5*w^2 - 2*w - 7]', '[663, 663, -2*w^3 + 4*w^2 + 5*w - 3]', '[663, 663, -w^3 + 5*w^2 - 12]', '[667, 667, w^3 - w^2 - 4*w - 5]', '[668, 334, 4*w^3 - 13*w^2 - 3*w + 5]', '[669, 669, -w^3 + 3*w^2 + 2*w - 9]', '[669, 669, 2*w^3 - 6*w^2 - 7*w + 6]', '[669, 669, w^3 - 4*w^2 + 3*w + 6]', '[673, 673, -w^3 + w^2 + 6*w - 2]', '[676, 26, -3*w^2 + 7*w + 11]', '[676, 26, 2*w^3 - 5*w^2 - 3*w + 7]', '[676, 338, -2*w^3 + 3*w^2 + 9*w - 1]', '[676, 338, -3*w^3 + 7*w^2 + 9*w - 8]', '[683, 683, 2*w^3 - 8*w^2 + w + 8]', '[683, 683, 5*w^3 - 12*w^2 - 19*w + 14]', '[684, 342, w^3 - 8*w - 3]', '[684, 342, w^3 - 5*w^2 + w + 6]', '[687, 687, w^3 - 3*w^2 + 3*w + 3]', '[687, 687, 2*w^2 - 2*w - 9]', '[689, 689, 2*w^3 - 6*w^2 - 2*w - 1]', '[689, 689, -2*w^3 + 3*w^2 + 12*w + 2]', '[692, 346, -3*w^3 + 10*w^2 + 2*w - 11]', '[692, 346, 3*w^3 - 8*w^2 - 8*w + 5]', '[697, 697, -3*w^2 + 6*w + 8]', '[699, 699, w^3 - 4*w^2 + w + 9]', '[699, 699, -w^3 + 6*w^2 + w - 6]', '[701, 701, -2*w^3 + 6*w^2 + 5*w - 4]', '[703, 703, -4*w^3 + 11*w^2 + 10*w - 17]', '[703, 703, -4*w^3 + 10*w^2 + 15*w - 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w^2 - 9*w + 1]', '[1807, 1807, -2*w^2 + 5*w + 13]', '[1807, 1807, -2*w^3 + 7*w^2 - 2*w - 8]', '[1808, 226, 4*w^3 - 10*w^2 - 8*w + 2]', '[1808, 226, -2*w^3 + 6*w^2 + 2*w - 10]', '[1809, 201, w^3 + w^2 - 8*w - 4]', '[1809, 1809, -4*w^3 + 6*w^2 + 24*w + 9]', '[1811, 1811, -2*w^3 + 7*w^2 + 5*w - 2]', '[1811, 1811, 5*w^3 - 12*w^2 - 16*w + 8]', '[1811, 1811, -2*w^3 + 8*w^2 + w - 16]', '[1811, 1811, w^3 + 2*w^2 - 10*w - 14]', '[1812, 906, 2*w^3 - 3*w^2 - 9*w + 3]', '[1821, 1821, 2*w^3 - 7*w^2 - 5*w]', '[1823, 1823, w^3 - w^2 - 9*w - 1]', '[1823, 1823, -w^3 + 3*w^2 + 3*w - 11]', '[1831, 1831, 4*w^2 - 5*w - 7]', '[1831, 1831, -6*w^3 + 14*w^2 + 22*w - 17]', '[1836, 102, -5*w^3 + 7*w^2 + 25*w + 8]', '[1836, 918, -2*w^3 + 3*w^2 + 13*w - 3]', '[1837, 1837, -2*w^3 + 2*w^2 + 13*w + 2]', '[1839, 1839, 2*w^3 - w^2 - 4*w - 3]', '[1839, 1839, -4*w^3 + 11*w^2 + 12*w - 12]', '[1843, 1843, -3*w^3 + 6*w^2 + 11*w - 11]', '[1843, 1843, -3*w^3 + 4*w^2 + 12*w + 2]', '[1843, 1843, -3*w^3 + 10*w^2 + 7*w - 16]', '[1843, 1843, w^3 + w^2 - 2*w - 5]', '[1844, 922, -w^3 + 3*w^2 - 5*w + 2]', '[1851, 1851, -w^3 + 4*w^2 - 5*w]', '[1856, 116, 2*w^3 - 8*w^2 + 10]', '[1857, 1857, 2*w^2 - w - 9]', '[1859, 143, w^3 + w^2 - 10*w - 5]', '[1859, 143, 8*w^3 - 20*w^2 - 25*w + 28]', '[1859, 1859, w^3 - 6*w^2 + 3*w + 16]', '[1859, 1859, -w^3 + 2*w^2 + 4*w - 8]', '[1863, 69, 3*w^2 - 6*w - 3]', '[1863, 1863, 4*w^3 - 14*w^2 + 3*w + 9]', '[1868, 934, 3*w^3 - 11*w^2 - w + 14]', '[1871, 1871, -4*w^3 + 8*w^2 + 16*w - 7]', '[1872, 234, -2*w^3 + 8*w^2 - 2*w - 12]', '[1872, 234, 4*w^3 - 10*w^2 - 10*w + 12]', '[1875, 15, -5*w]', '[1877, 1877, -6*w^3 + 16*w^2 + 19*w - 20]', '[1877, 1877, 2*w^3 - 2*w^2 - 11*w - 2]', '[1879, 1879, -6*w^3 + 14*w^2 + 22*w - 11]', '[1881, 1881, -2*w^3 + 7*w^2]', '[1881, 1881, 4*w^3 - 10*w^2 - 15*w + 9]', '[1884, 942, -5*w^3 + 18*w^2 - 15]', '[1884, 942, -w^3 + 3*w^2 - 3*w - 6]', '[1887, 1887, 5*w^3 - 15*w^2 - 6*w + 12]', '[1889, 1889, -2*w^3 + 8*w^2 + 2*w - 17]', '[1893, 1893, 2*w^2 + 3*w - 6]', '[1901, 1901, 4*w^3 - 12*w^2 - 7*w + 8]', '[1901, 1901, 4*w^3 - 7*w^2 - 17*w - 4]', '[1903, 1903, -2*w^3 + 5*w^2 + 2*w + 1]', '[1903, 1903, -9*w^3 + 23*w^2 + 29*w - 29]', '[1908, 954, w^3 - w^2 - 9*w]', '[1916, 958, -7*w^3 + 24*w^2 - 2*w - 17]', '[1916, 958, -6*w^3 + 21*w^2 - 3*w - 7]', '[1921, 1921, -6*w^3 + 18*w^2 + 5*w - 7]', '[1921, 1921, -w^2 + 6*w - 1]', '[1924, 962, 6*w^3 - 17*w^2 - 13*w + 19]', '[1924, 962, 9*w^3 - 26*w^2 - 24*w + 41]', '[1931, 1931, -w^3 + 2*w^2 + w - 8]', '[1936, 242, 4*w^2 - 8*w - 10]', '[1937, 1937, 5*w^3 - 15*w^2 - 8*w + 10]', '[1937, 1937, w^3 - 5*w^2 + 3*w + 13]', '[1937, 1937, 4*w^3 - 13*w^2 - 8*w + 23]', '[1937, 1937, 8*w^3 - 18*w^2 - 30*w + 17]', '[1941, 1941, -w^3 + 3*w^2 - 4*w - 3]', '[1941, 1941, -5*w^2 + 3*w + 6]', '[1943, 1943, -3*w^3 + 7*w^2 + 8*w - 4]', '[1947, 1947, -5*w^3 + 14*w^2 + 13*w - 15]', '[1956, 978, -15*w^3 + 41*w^2 + 45*w - 60]', '[1956, 978, -8*w^3 + 23*w^2 + 21*w - 39]', '[1956, 978, -9*w^3 + 23*w^2 + 29*w - 30]', '[1956, 978, -10*w^3 + 27*w^2 + 31*w - 45]', '[1957, 1957, 3*w^3 - w^2 - 18*w - 13]', '[1957, 1957, -2*w^3 + 9*w + 4]', '[1959, 1959, -2*w^2 + 3*w - 3]', '[1959, 1959, -2*w^3 + 4*w^2 + 11*w - 3]', '[1961, 1961, 4*w^3 - 8*w^2 - 14*w + 7]', '[1963, 1963, 3*w^2 - 5*w - 2]', '[1963, 1963, -w^3 - w^2 + 4*w + 7]', '[1964, 982, 4*w^3 - 13*w^2 - w + 11]', '[1968, 246, -2*w^3 + 8*w^2 - 12]', '[1971, 219, w^3 + w^2 - 8*w - 13]', '[1971, 1971, -w^3 + 2*w^2 + 4*w + 6]', '[1972, 986, -2*w^3 + 9*w^2 - 5*w - 5]', '[1977, 1977, -9*w^3 + 25*w^2 + 28*w - 42]', '[1977, 1977, 2*w^3 - 5*w^2 - 6*w + 12]', '[1979, 1979, 2*w^3 - 4*w^2 - 11*w + 4]', '[1983, 1983, 3*w^3 - 7*w^2 - 5*w + 3]', '[1983, 1983, w^3 - 5*w^2 - 2*w]', '[1989, 1989, w^3 - w^2 - 6*w - 9]', '[1989, 1989, 5*w^3 - 12*w^2 - 18*w + 18]', '[1991, 1991, 5*w - 1]', '[1996, 998, 3*w^3 - 9*w^2 - 5*w + 14]', '[1996, 998, 3*w^3 - 9*w^2 - w + 2]', '[1997, 1997, -w^3 + 6*w^2 - w - 7]', '[1999, 1999, -4*w^3 + 11*w^2 + 10*w - 8]', '[2001, 2001, w^3 + w^2 - 7*w - 3]', '[2004, 1002, 4*w^3 - 9*w^2 - 15*w + 3]', '[2007, 2007, w^3 - 3*w^2 - 7*w + 3]', '[2007, 2007, -3*w^2 + 4*w + 15]', '[2007, 2007, 2*w^3 + w^2 - 20*w - 12]', '[2012, 1006, -8*w^3 + 29*w^2 - 3*w - 17]', '[2017, 2017, -2*w^3 + 8*w^2 - 11]', '[2017, 2017, -4*w^3 + 10*w^2 + 13*w - 7]', '[2019, 2019, -w^3 + w^2 + 3]', '[2028, 78, -3*w^3 + 7*w^2 + 11*w]', '[2028, 78, -10*w^3 + 27*w^2 + 33*w - 39]', '[2028, 1014, -w^3 + 5*w^2 - w - 18]', '[2028, 1014, 3*w^3 - 10*w^2 - 6*w + 15]', '[2029, 2029, -w^3 + 4*w^2 - 2*w - 10]', '[2029, 2029, -w^3 + 4*w^2 + 4*w - 10]', '[2041, 2041, 4*w^2 - 8*w - 13]', '[2041, 2041, 2*w^2 - 4*w - 13]', '[2041, 2041, -4*w^3 + 11*w^2 + 6*w - 5]', '[2041, 2041, -w^2 + 6*w + 1]', '[2047, 2047, 3*w^3 - 11*w^2 - 3*w + 11]', '[2049, 2049, -2*w^3 + 6*w^2 + 4*w - 15]', '[2049, 2049, -5*w^3 + 11*w^2 + 20*w - 12]', '[2052, 114, w^3 - 2*w^2 - 8*w - 7]', '[2052, 114, 4*w^3 - 5*w^2 - 23*w - 7]', '[2052, 1026, -3*w^3 + 11*w^2 + w - 12]', '[2052, 1026, w^3 + w^2 - 13*w - 6]', '[2053, 2053, -5*w^3 + 12*w^2 + 18*w - 10]', '[2053, 2053, 5*w^3 - 12*w^2 - 17*w + 8]', '[2057, 2057, 2*w^3 - 5*w^2 - 10*w + 5]', '[2061, 2061, 2*w^3 - 2*w^2 - 9*w]', '[2061, 2061, 5*w^2 - 11*w - 12]', '[2063, 2063, 4*w^3 - 10*w^2 - 11*w + 11]', '[2063, 2063, -4*w^2 + 6*w + 5]', '[2067, 2067, -2*w^3 + 8*w^2 - 5*w - 6]', '[2067, 2067, -w^3 + 2*w^2 + 6*w + 6]', '[2076, 1038, 11*w^3 - 28*w^2 - 38*w + 39]', '[2076, 1038, -2*w^3 + 7*w^2 - w - 9]', '[2084, 1042, 2*w^3 - 7*w^2 - 5*w + 5]', '[2084, 1042, 5*w^3 - 15*w^2 - 7*w + 16]', '[2087, 2087, -4*w^3 + 12*w^2 + 9*w - 25]', '[2091, 2091, w^3 - 6*w^2 + 7*w + 3]', '[2097, 2097, 5*w^3 - 7*w^2 - 28*w - 6]', '[2097, 2097, -w^2 + 6*w]', '[2099, 2099, w^3 - 2*w^2 - w - 5]', '[2099, 2099, w^3 - 6*w^2 + 3*w + 22]', '[2099, 2099, -w^3 + 6*w^2 - 3*w - 8]', '[2099, 2099, w^3 + 2*w^2 - 11*w - 14]', '[2101, 2101, w^3 - 4*w^2 + 3*w + 8]', '[2103, 2103, 2*w^3 - 5*w^2 + 6]', '[2109, 2109, -6*w^3 + 14*w^2 + 23*w - 18]', '[2109, 2109, 10*w^3 - 28*w^2 - 27*w + 42]', '[2111, 2111, -4*w^3 + 9*w^2 + 14*w - 14]', '[2112, 132, -2*w^3 + 4*w^2 + 8*w + 6]', '[2116, 1058, 3*w^3 - 5*w^2 - 11*w - 2]', '[2117, 2117, 3*w^3 - 11*w^2 - 4*w + 23]', '[2119, 2119, -3*w^3 + 7*w^2 + 13*w - 17]', '[2119, 2119, -8*w^3 + 22*w^2 + 22*w - 35]', '[2119, 2119, -8*w^3 + 23*w^2 + 20*w - 29]', '[2119, 2119, -6*w^3 + 15*w^2 + 22*w - 16]', '[2119, 2119, -4*w^3 + 12*w^2 + 8*w - 19]', '[2119, 2119, -3*w^3 + 11*w^2 + 5*w - 23]', '[2119, 2119, -5*w^3 + 13*w^2 + 14*w - 14]', '[2119, 2119, -6*w^3 + 16*w^2 + 21*w - 23]', '[2124, 1062, 4*w^3 - 9*w^2 - 17*w + 15]', '[2127, 2127, -w^3 + 3*w^2 - 4*w]', '[2127, 2127, w^3 - w^2 - 4*w + 6]', '[2129, 2129, -3*w^3 + 5*w^2 + 14*w - 2]', '[2129, 2129, -2*w^2 + 7*w + 13]', '[2131, 2131, -w^3 + 2*w^2 + 6*w - 10]', '[2131, 2131, 5*w^3 - 11*w^2 - 18*w + 13]', '[2132, 1066, -4*w^3 + 15*w^2 - w - 13]', '[2132, 1066, -2*w^3 + 3*w^2 + 13*w - 7]', '[2137, 2137, -3*w^3 + 9*w^2 + 7*w - 7]', '[2141, 2141, -3*w^3 + 8*w^2 + 6*w - 14]', '[2141, 2141, 3*w^3 - 6*w^2 - 9*w - 4]', '[2143, 2143, -4*w^3 + 8*w^2 + 15*w - 5]', '[2143, 2143, -4*w^3 + 9*w^2 + 16*w - 13]', '[2147, 2147, -w^3 + 4*w^2 + 4*w + 2]', '[2147, 2147, 3*w^3 - 6*w^2 - 15*w - 5]', '[2147, 2147, -3*w^3 + 5*w^2 + 10*w - 7]', '[2147, 2147, -w^3 + 6*w^2 - 14]', '[2153, 2153, 2*w^3 - 5*w^2 - 10*w + 8]', '[2157, 2157, w^3 - 7*w]', '[2157, 2157, -w^3 - 2*w^2 + 9*w + 6]', '[2169, 2169, 3*w^3 - 9*w^2 - 4*w + 12]', '[2171, 2171, 4*w^3 - 11*w^2 - 9*w + 4]', '[2171, 2171, -w^3 - w^2 + 12*w + 13]', '[2172, 1086, 3*w^3 - 7*w^2 - 7*w + 6]', '[2173, 2173, 5*w^3 - 8*w^2 - 24*w - 2]', '[2183, 2183, 4*w^3 - 10*w^2 - 11*w + 7]', '[2187, 9, 3*w^3 - 6*w^2 - 6*w + 6]', '[2187, 81, -3*w^3 + 6*w^2 + 9*w]', '[2187, 2187, 3*w^3 - 6*w^2 - 8*w + 6]', '[2189, 2189, -4*w^2 + 5*w + 4]', '[2189, 2189, -2*w^3 + 8*w^2 + 3*w - 20]', '[2197, 13, -4*w^3 + 11*w^2 + 15*w - 16]', '[2197, 13, -5*w^3 + 13*w^2 + 12*w - 25]', '[2197, 169, w^3 - 2*w^2 - 3*w - 7]', '[2197, 169, 3*w^3 - 6*w^2 - 9*w + 5]', '[2197, 2197, 3*w^3 - 6*w^2 - 11*w + 10]', '[2197, 2197, 3*w^3 - 11*w^2 - 2*w + 11]', '[2199, 2199, 3*w^3 - 7*w^2 - 6*w + 6]', '[2204, 1102, w^3 - 4*w^2 + 2*w + 11]', '[2204, 1102, w^3 - 3*w^2 - 7*w + 4]', '[2211, 2211, -5*w^3 + 10*w^2 + 19*w - 9]', '[2217, 2217, -3*w^3 + 7*w^2 + 6*w - 12]', '[2217, 2217, -2*w^3 + 9*w^2 + 2*w - 9]', '[2217, 2217, 5*w^3 - 15*w^2 - 14*w + 30]', '[2217, 2217, -w^3 + 3*w^2 - 3*w + 3]', '[2221, 2221, -3*w^3 + 5*w^2 + 18*w - 7]', '[2221, 2221, w^3 + 2*w^2 - 13*w - 8]', '[2223, 2223, -2*w^3 + 3*w^2 + 10*w - 3]', '[2223, 2223, 2*w^3 - 5*w^2]', '[2223, 2223, 4*w^2 - 7*w - 15]', '[2223, 2223, -3*w^3 + 7*w^2 + 7*w - 3]', '[2224, 278, 4*w^2 - 6*w - 8]', '[2224, 278, 2*w^3 - 2*w^2 - 12*w - 2]', '[2229, 2229, 3*w^3 - 8*w^2 - 10*w + 6]', '[2229, 2229, -w^2 - 5*w]', '[2231, 2231, -4*w^2 + 6*w + 19]', '[2231, 2231, 4*w^3 - 9*w^2 - 14*w - 1]', '[2237, 2237, 3*w^3 - 10*w^2 - 8*w + 20]', '[2239, 2239, -2*w^3 + 8*w^2 - 19]', '[2239, 2239, -2*w^3 + 6*w^2 + 2*w - 11]', '[2243, 2243, -5*w^3 + 10*w^2 + 21*w - 7]', '[2243, 2243, -w^3 + 6*w^2 - 2*w - 16]', '[2243, 2243, 3*w^3 - 6*w^2 - 10*w + 2]', '[2243, 2243, w^2 + w - 8]', '[2244, 1122, -4*w^3 + 9*w^2 + 13*w - 9]', '[2249, 2249, 4*w^3 - 9*w^2 - 18*w + 14]', '[2249, 2249, -2*w^2 + 8*w - 1]', '[2249, 2249, 4*w^3 - 13*w^2 - 8*w + 29]', '[2249, 2249, -5*w^3 + 17*w^2 - w - 13]', '[2251, 2251, 4*w^2 - 5*w - 14]', '[2253, 2253, w^3 - 2*w^2 + 2*w + 6]', '[2253, 2253, 2*w^3 - 10*w^2 + 3*w + 6]', '[2267, 2267, 2*w^3 - 8*w^2 - 3*w + 16]', '[2267, 2267, -w^3 + 4*w^2 - 14]', '[2271, 2271, 8*w^3 - 19*w^2 - 30*w + 24]', '[2271, 2271, 2*w^3 - 7*w^2 - 6*w + 6]', '[2273, 2273, -w^3 + 7*w^2 - 6*w - 22]', '[2276, 1138, -8*w^3 + 27*w^2 + w - 19]', '[2276, 1138, -3*w^3 + 13*w^2 - w - 10]', '[2277, 2277, w^3 - 11*w - 3]', '[2281, 2281, -3*w^3 + 9*w^2 + 5*w - 19]', '[2281, 2281, 3*w^2 - 6*w - 17]', '[2283, 2283, -w^2 - 3*w + 6]', '[2283, 2283, w^3 - 2*w^2 - 5*w - 6]', '[2284, 1142, 3*w^2 - 5*w - 1]', '[2287, 2287, -3*w^3 + 7*w^2 + 12*w - 16]', '[2288, 286, 2*w^2 - 8]', '[2288, 286, 4*w^3 - 10*w^2 - 12*w + 4]', '[2292, 1146, w^3 - w^2 - 3*w - 6]', '[2293, 2293, -5*w^3 + 10*w^2 + 23*w - 5]', '[2297, 2297, 5*w^3 - 15*w^2 - 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8]', '[2348, 1174, -4*w^3 + 15*w^2 - 3*w - 5]', '[2349, 87, -3*w^3 + 6*w^2 + 15*w - 3]', '[2349, 2349, w^3 - 9*w]', '[2353, 2353, w^3 - 3*w^2 - 6*w + 10]', '[2353, 2353, 7*w^3 - 17*w^2 - 25*w + 23]', '[2361, 2361, 2*w^3 - 6*w^2 - 9*w + 3]', '[2363, 2363, w^3 - 7*w^2 + 6*w + 7]', '[2363, 2363, w^3 - 6*w^2 + 4*w + 10]', '[2367, 2367, -4*w^3 + 5*w^2 + 20*w + 12]', '[2368, 148, 8*w^3 - 26*w^2 - 6*w + 22]', '[2369, 2369, -2*w^3 + 5*w^2 + 10*w - 7]', '[2371, 2371, 2*w^3 - 3*w^2 - 9*w + 4]', '[2372, 1186, w^3 - 2*w^2 - 8*w + 1]', '[2372, 1186, 3*w^3 - 7*w^2 - 5*w + 4]', '[2381, 2381, 3*w^3 - 8*w^2 - 9*w + 4]', '[2381, 2381, 3*w^3 - 6*w^2 - 12*w + 8]', '[2384, 298, 4*w^3 - 10*w^2 - 10*w + 4]', '[2384, 298, 2*w^3 - 8*w^2 + 20]', '[2388, 1194, 2*w^3 - 7*w^2 - 5*w + 3]', '[2388, 1194, 5*w^3 - 16*w^2 - 4*w + 15]', '[2391, 2391, 2*w^3 - 8*w^2 - w + 15]', '[2401, 7, -7]', '[2403, 267, -w^3 + 2*w^2 + 2*w - 8]', '[2403, 2403, w^3 - 2*w^2 + w - 3]', '[2404, 1202, -7*w^3 + 26*w^2 - 4*w - 13]', '[2404, 1202, w^3 - 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14]', '[5231, 5231, -4*w^3 + 13*w^2 + 10*w - 29]', '[5231, 5231, 6*w^3 - 14*w^2 - 19*w + 5]', '[5241, 5241, -w^2 - 2*w - 6]', '[5244, 2622, -w^3 - 2*w^2 + 16*w + 9]', '[5244, 2622, -3*w^3 + 11*w^2 - 3*w - 12]', '[5247, 5247, 4*w^3 - 6*w^2 - 19*w - 15]', '[5249, 5249, -w^2 + 4*w - 8]', '[5251, 5251, -w^3 + 2*w^2 + 9*w - 4]', '[5253, 5253, -3*w^3 + 12*w^2 + 5*w - 3]', '[5259, 5259, w^3 - 6*w^2 - 2*w]', '[5259, 5259, -3*w^3 + 6*w^2 + 7*w + 3]', '[5261, 5261, w^3 + 5*w^2 - 16*w - 29]', '[5263, 5263, -2*w^3 + 7*w^2 + 8*w - 4]', '[5263, 5263, -3*w^3 + 11*w^2 + 6*w - 20]', '[5263, 5263, w^3 - w^2 - 9*w - 11]', '[5263, 5263, -4*w^3 + 8*w^2 + 14*w - 13]', '[5267, 5267, -7*w^3 + 20*w^2 + 19*w - 25]', '[5267, 5267, -7*w^3 + 22*w^2 + 13*w - 35]', '[5268, 2634, -w^3 + 7*w^2 - 3*w - 24]', '[5269, 5269, 9*w^3 - 22*w^2 - 35*w + 35]', '[5269, 5269, -4*w^3 + 9*w^2 + 11*w - 2]', '[5273, 5273, -w^3 + 5*w^2 + 3*w - 13]', '[5276, 2638, 3*w^3 - 11*w^2 - 5*w + 8]', '[5277, 5277, -6*w^3 + 17*w^2 + 11*w - 12]', '[5279, 5279, w^3 - 3*w^2 - 3*w - 5]', '[5281, 5281, -2*w^2 + 4*w - 5]', '[5283, 5283, w^3 - 12*w]', '[5287, 5287, -4*w^3 + 10*w^2 + 9*w - 7]', '[5291, 5291, -6*w^3 + 20*w^2 + 7*w - 26]', '[5291, 5291, 4*w^3 - 10*w^2 - 17*w + 16]', '[5296, 662, -2*w^3 + 6*w^2 - 10]', '[5297, 5297, 6*w^3 - 13*w^2 - 26*w + 10]', '[5297, 5297, 4*w^3 - 8*w^2 - 14*w + 1]', '[5303, 5303, -6*w^3 + 17*w^2 + 12*w - 22]', '[5308, 2654, -w^3 + 4*w^2 - 6*w - 1]', '[5308, 2654, -3*w^3 + 10*w^2 - 4*w - 5]', '[5309, 5309, w^3 - 3*w^2 - 7]', '[5309, 5309, 2*w^3 - 8*w^2 + w + 22]', '[5323, 5323, -7*w^3 + 20*w^2 + 17*w - 31]', '[5324, 22, -5*w^3 + 20*w^2 - 4*w - 13]', '[5324, 2662, 6*w^3 - 15*w^2 - 17*w + 19]', '[5328, 666, 6*w^3 - 16*w^2 - 16*w + 12]', '[5329, 5329, -w^3 + 5*w^2 - 4*w - 16]', '[5331, 5331, 3*w^3 - 9*w^2 - 4*w + 15]', '[5331, 5331, 3*w^3 - 9*w^2 - 8*w + 3]', '[5333, 5333, w^3 - 3*w^2 - 4*w - 5]', '[5333, 5333, -6*w^3 + 14*w^2 + 21*w - 20]', '[5337, 5337, -4*w^3 + 3*w^2 + 28*w + 24]', '[5337, 5337, -3*w^3 + 7*w^2 + 3*w - 9]', '[5339, 5339, 2*w^2 + w + 4]', '[5339, 5339, 3*w^3 - 7*w^2 - 14*w - 1]', '[5347, 5347, -4*w^3 + 10*w^2 + 15*w - 22]', '[5347, 5347, -w^3 + 2*w^2 + 9*w - 2]', '[5349, 5349, w^3 - 6*w^2 - 5*w + 12]', '[5351, 5351, -4*w^3 + 12*w^2 + 7*w - 1]', '[5351, 5351, -w^3 - 5*w^2 + 17*w + 29]', '[5351, 5351, 2*w^3 - w^2 - 12*w - 16]', '[5351, 5351, -2*w^3 - w^2 + 20*w + 23]', '[5356, 2678, -2*w^3 + 7*w^2 + 5*w + 1]', '[5356, 2678, 3*w^3 - 4*w^2 - 20*w - 7]', '[5359, 5359, -w^3 - 3*w^2 + 13*w + 13]', '[5359, 5359, -w^3 + 7*w^2 - 6*w - 16]', '[5361, 5361, 2*w^3 - 4*w^2 - w + 9]', '[5361, 5361, -5*w^2 + 2*w + 9]', '[5361, 5361, 10*w^3 - 26*w^2 - 33*w + 33]', '[5361, 5361, 4*w^3 - 6*w^2 - 12*w - 3]', '[5364, 2682, -9*w^3 + 22*w^2 + 30*w - 27]', '[5364, 2682, -3*w^3 + 10*w^2 + 2*w - 15]', '[5367, 5367, -w^3 + 7*w^2 - 6*w - 12]', '[5367, 5367, 4*w^3 - 13*w^2 - 8*w + 12]', '[5373, 597, 5*w^3 - 13*w^2 - 16*w + 25]', '[5373, 597, -7*w^3 + 14*w^2 + 29*w - 5]', '[5373, 5373, -w^3 + 7*w + 15]', '[5373, 5373, 5*w^3 - 12*w^2 - 17*w + 6]', '[5377, 5377, 4*w^3 - 6*w^2 - 21*w - 1]', '[5377, 5377, 5*w^2 - 8*w - 19]', '[5377, 5377, 6*w^3 - 23*w^2 + 4*w + 20]', '[5377, 5377, -3*w^3 + 5*w^2 + 13*w - 5]', '[5379, 5379, -6*w^3 + 17*w^2 + 21*w - 30]', '[5379, 5379, -3*w^3 + 8*w^2 + 8*w - 18]', '[5379, 5379, -7*w^3 + 18*w^2 + 19*w - 24]', '[5379, 5379, -5*w^3 + 11*w^2 + 18*w - 15]', '[5387, 5387, 3*w^3 - 3*w^2 - 18*w - 5]', '[5389, 5389, -5*w^3 + 9*w^2 + 20*w + 5]', '[5393, 5393, -4*w^3 + 10*w^2 + 8*w - 5]', '[5399, 5399, -2*w^3 + 7*w^2 - 14]', '[5399, 5399, 2*w^3 - 10*w^2 + 6*w + 7]', '[5401, 5401, 6*w^3 - 15*w^2 - 18*w + 17]', '[5403, 5403, w^3 - 4*w^2 + 5*w + 9]', '[5409, 5409, -2*w^3 + 6*w^2 - w + 3]', '[5409, 5409, 4*w^3 - 9*w^2 - 18*w + 9]', '[5412, 2706, w^3 - 4*w^2 + 6*w + 3]', '[5421, 5421, w^3 - 4*w^2 - w - 3]', '[5421, 5421, 3*w^3 - 12*w^2 - 4*w + 6]', '[5421, 5421, -2*w^3 + 5*w^2 + 13*w]', '[5421, 5421, w^3 + 5*w + 6]', '[5423, 5423, 3*w^3 - 9*w^2 - 8*w + 22]', '[5424, 678, 2*w^3 - 8*w^2 - 6*w + 6]', '[5424, 678, -2*w^3 + 12*w^2 - 6*w - 12]', '[5427, 201, 3*w^3 - 3*w^2 - 6*w - 3]', '[5427, 5427, w^3 - 5*w^2 + 4*w + 15]', '[5428, 2714, -w^3 + 5]', '[5433, 5433, 3*w^3 - 5*w^2 + 2*w + 6]', '[5433, 5433, -2*w^3 + 9*w^2 - 2*w - 15]', '[5433, 5433, 4*w^3 - 5*w^2 - 16*w - 3]', '[5433, 5433, 4*w^3 - 9*w^2 - 12*w + 6]', '[5436, 2718, w^3 + w^2 - w - 6]', '[5441, 5441, 4*w^3 - 9*w^2 - 12*w + 5]', '[5443, 5443, 5*w^3 - 12*w^2 - 14*w + 4]', '[5447, 5447, 4*w^3 - 16*w^2 - 5*w + 37]', '[5447, 5447, -2*w^3 + 5*w^2 + 2*w + 5]', '[5447, 5447, 4*w^3 - 6*w^2 - 20*w - 1]', '[5447, 5447, 7*w^3 - 17*w^2 - 23*w + 19]', '[5449, 5449, w^2 + 6*w - 1]', '[5449, 5449, -3*w^3 + 9*w^2 + 8*w - 4]', '[5459, 5459, -w^3 + 4*w^2 + w - 16]', '[5463, 5463, -7*w^3 + 13*w^2 + 27*w + 9]', '[5468, 2734, -2*w^3 + 9*w^2 - w - 11]', '[5468, 2734, 7*w^3 - 20*w^2 - 14*w + 19]', '[5469, 5469, w^3 - 4*w^2 - 3*w - 3]', '[5469, 5469, w^3 - 2*w^2 - 9*w + 3]', '[5471, 5471, -6*w^3 + 19*w^2 + 12*w - 37]', '[5471, 5471, 4*w^3 - 10*w^2 - 17*w + 11]', '[5473, 5473, w^3 - 7*w^2 + 12*w - 4]', '[5473, 5473, -2*w^3 + 8*w^2 + 2*w - 1]', '[5473, 5473, 2*w^3 - 3*w^2 - 14*w - 2]', '[5473, 5473, -3*w^3 + 9*w^2 + 11*w - 19]', '[5476, 2738, -3*w^3 + 13*w^2 - 7*w - 4]', '[5477, 5477, 2*w^2 - w - 14]', '[5477, 5477, -3*w^3 + 10*w^2 + 5*w - 25]', '[5489, 5489, -4*w^3 + 9*w^2 + 18*w - 10]', '[5489, 5489, w^3 + w^2 - 7*w + 1]', '[5491, 5491, 4*w^3 - 10*w^2 - 7*w + 8]', '[5491, 5491, -w^3 + w^2 + 2*w + 7]', '[5493, 5493, 4*w^3 - 5*w^2 - 7*w]', '[5493, 5493, 2*w^3 - 8*w^2 - 5*w + 18]', '[5501, 5501, -3*w^3 + 8*w^2 + 12*w - 4]', '[5501, 5501, -3*w^3 + 10*w^2 + 7*w - 8]', '[5503, 5503, 7*w^3 - 11*w^2 - 33*w - 5]', '[5507, 5507, -5*w^3 + 16*w^2 + 13*w - 26]', '[5508, 102, -3*w^3 + 18*w + 15]', '[5508, 2754, -w^3 + 3*w^2 + w + 6]', '[5511, 5511, -2*w^3 + 3*w^2 + 6*w + 6]', '[5513, 5513, -5*w^3 + 9*w^2 + 22*w - 4]', '[5513, 5513, -2*w^3 + 5*w^2 + 6*w + 5]', '[5517, 5517, -4*w^3 + 8*w^2 + 19*w + 6]', '[5517, 5517, 3*w^3 - 8*w^2 - 4*w + 12]', '[5521, 5521, -2*w^3 + 9*w^2 - 2*w - 13]', '[5521, 5521, 2*w^3 - 10*w^2 + 7*w + 7]', '[5521, 5521, -4*w^3 + 14*w^2 + w - 17]', '[5521, 5521, 6*w^3 - 15*w^2 - 18*w + 14]', '[5529, 5529, -2*w^2 - w + 9]', '[5529, 5529, -5*w^3 + 15*w^2 + 10*w - 24]', '[5529, 5529, 7*w^3 - 17*w^2 - 26*w + 30]', '[5529, 5529, -4*w^3 + 8*w^2 + 19*w + 3]', '[5531, 5531, w^2 + 3*w - 8]', '[5531, 5531, 7*w^3 - 22*w^2 - 16*w + 40]', '[5532, 2766, -13*w^3 + 35*w^2 + 37*w - 54]', '[5533, 5533, w^3 - 2*w^2 - 7*w + 13]', '[5539, 5539, -5*w^3 + 13*w^2 + 14*w - 7]', '[5543, 5543, 2*w^3 - w^2 - 14*w - 4]', '[5548, 2774, 6*w^3 - 13*w^2 - 27*w + 17]', '[5548, 2774, -w^3 + 4*w^2 + 4*w - 13]', '[5553, 5553, 4*w^3 - 15*w^2 + 18]', '[5567, 5567, 5*w^3 - 7*w^2 - 31*w - 13]', '[5567, 5567, 2*w^3 - 5*w + 5]', '[5567, 5567, 2*w^3 - 8*w^2 - 8*w + 7]', '[5567, 5567, -w^2 + 8*w + 10]', '[5568, 348, -4*w^3 + 10*w^2 + 6*w - 6]', '[5569, 5569, -5*w^3 + 15*w^2 + 12*w - 16]', '[5571, 5571, -7*w^3 + 13*w^2 + 32*w + 3]', '[5577, 429, -4*w^3 + 15*w^2 + 12*w - 24]', '[5577, 429, -4*w^3 + 15*w^2 - 15]', '[5577, 5577, -6*w^3 + 14*w^2 + 20*w - 9]', '[5577, 5577, -4*w^3 + 8*w^2 + 14*w - 3]', '[5584, 698, -4*w^2 + 10*w + 4]', '[5587, 5587, w^3 - 2*w^2 + w - 5]', '[5589, 207, -6*w^2 + 15*w + 18]', '[5589, 5589, 3*w^3 - 10*w^2 - 3*w + 18]', '[5591, 5591, -5*w^3 + 11*w^2 + 15*w - 13]', '[5591, 5591, -2*w^3 + 6*w^2 + 5*w - 17]', '[5596, 2798, -7*w^3 + 24*w^2 + 2*w - 11]', '[5603, 5603, w^3 - 2*w^2 - 10*w + 20]', '[5603, 5603, 9*w^3 - 20*w^2 - 37*w + 20]', '[5604, 2802, -15*w^3 + 37*w^2 + 53*w - 48]', '[5613, 5613, -4*w^2 + w + 12]', '[5616, 78, -2*w^3 - 2*w^2 + 16*w + 20]', '[5616, 78, 4*w^3 - 8*w^2 - 14*w + 2]', '[5616, 702, 4*w^3 - 12*w^2 - 8*w + 6]', '[5616, 702, 2*w^3 - 6*w^2 - 6*w + 18]', '[5625, 45, -5*w^2 + 10*w + 15]', '[5627, 5627, w^3 - 4*w^2 + 6*w + 2]', '[5631, 5631, 2*w^3 - w^2 - 6*w - 6]', '[5631, 5631, 4*w^3 - 11*w^2 - 8*w + 18]', '[5636, 2818, -11*w^3 + 38*w^2 - 19]', '[5636, 2818, 9*w^3 - 29*w^2 - 9*w + 22]', '[5637, 5637, 2*w^3 - 8*w^2 + w + 18]', '[5641, 5641, 5*w^2 - 10*w - 14]', '[5643, 627, 7*w^3 - 8*w^2 - 44*w - 22]', '[5643, 627, -w^3 - w^2 + 14*w + 13]', '[5643, 5643, -9*w^3 + 23*w^2 + 30*w - 27]', '[5643, 5643, -2*w^3 + 5*w^2 + w - 12]', '[5647, 5647, -3*w^3 + 13*w^2 - 3*w - 23]', '[5647, 5647, -3*w^3 + 11*w^2 + 3*w - 17]', '[5648, 706, -4*w^3 + 10*w^2 + 8*w - 8]', '[5648, 706, 6*w^3 - 14*w^2 - 20*w + 4]', '[5648, 706, -4*w^3 + 14*w^2 + 4*w - 20]', '[5648, 706, 4*w^3 - 12*w^2 - 2*w + 2]', '[5652, 2826, 7*w^3 - 16*w^2 - 28*w + 21]', '[5652, 2826, -3*w^3 + w^2 + 23*w + 12]', '[5657, 5657, -2*w^3 + 9*w^2 - 2*w - 14]', '[5661, 5661, -10*w^3 + 28*w^2 + 31*w - 48]', '[5667, 5667, 4*w^3 - 8*w^2 - 13*w + 6]', '[5679, 5679, -4*w^3 + 11*w^2 + 12*w - 9]', '[5681, 5681, 2*w^3 - 9*w^2 - 2*w + 11]', '[5681, 5681, 2*w^3 - 2*w^2 - 11*w + 1]', '[5681, 5681, -3*w^3 + 9*w^2 + 9*w - 1]', '[5681, 5681, -3*w^3 + 7*w^2 + w - 1]', '[5683, 5683, -5*w^2 + 11*w + 8]', '[5683, 5683, 9*w^3 - 21*w^2 - 34*w + 25]', '[5683, 5683, -w^3 + 8*w^2 - 8*w - 22]', '[5683, 5683, -w^3 + 2*w^2 + 4*w - 10]', '[5689, 5689, -2*w^3 + 3*w^2 + 14*w - 4]', '[5689, 5689, -5*w^3 + 11*w^2 + 22*w - 4]', '[5692, 2846, 5*w^3 - 15*w^2 - 9*w + 10]', '[5696, 356, 2*w^3 - 6*w^2 - 2*w - 4]', '[5699, 5699, -w^3 + 8*w^2 - 9*w - 23]', '[5699, 5699, -w^3 - 2*w^2 + 16*w + 8]', '[5701, 5701, -7*w^3 + 16*w^2 + 26*w - 10]', '[5703, 5703, -4*w^3 + 13*w^2 - 12]', '[5703, 5703, w^3 + 3*w^2 - 12*w - 12]', '[5707, 5707, -6*w^3 + 9*w^2 + 29*w + 4]', '[5707, 5707, w^3 - 5*w - 11]', '[5709, 5709, w^3 - 8*w^2 + 5*w + 6]', '[5709, 5709, 5*w^3 - 16*w^2 - 11*w + 27]', '[5717, 5717, 3*w^3 - 12*w^2 + w + 17]', '[5717, 5717, -6*w^3 + 12*w^2 + 27*w - 10]', '[5723, 5723, w^3 - 4*w^2 + w - 4]', '[5723, 5723, w^3 - 14*w - 8]', '[5724, 318, 7*w^3 - 26*w^2 + 4*w + 23]', '[5724, 2862, -w^3 - 5*w^2 + 19*w + 24]', '[5731, 5731, 4*w^3 - 14*w^2 - 9*w + 26]', '[5731, 5731, 15*w^3 - 40*w^2 - 45*w + 58]', '[5741, 5741, 2*w^3 - w^2 - 19*w + 2]', '[5748, 2874, w^3 - 12*w - 3]', '[5748, 2874, -16*w^3 + 43*w^2 + 47*w - 57]', '[5756, 2878, 5*w^3 - 14*w^2 - 8*w + 11]', '[5756, 2878, -3*w^2 + 11*w + 7]', '[5763, 5763, -w^3 + 6*w^2 - w]', '[5763, 5763, 6*w^3 - 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14*w + 4]', '[821, 821, -w^3 + 5*w^2 - 2*w - 17]', '[827, 827, -3*w^3 + 8*w^2 + 9*w - 7]', '[829, 829, 2*w^3 - 6*w^2 - 5*w + 2]', '[829, 829, -w^3 + 4*w^2 - w - 10]', '[839, 839, w^2 - 8]', '[853, 853, -5*w^3 + 12*w^2 + 18*w - 16]', '[853, 853, w^3 - 6*w - 8]', '[863, 863, 5*w^3 - 11*w^2 - 19*w + 7]', '[881, 881, -3*w^3 + 9*w^2 + 9*w - 11]', '[907, 907, -w^3 + 2*w^2 + 7*w - 4]', '[907, 907, -2*w^3 + 3*w^2 + 7*w + 4]', '[929, 929, -w^3 + 5*w^2 - 3*w - 11]', '[937, 937, 2*w^3 - 5*w^2 - 6*w + 11]', '[937, 937, -2*w^3 + 6*w^2 + 3*w - 11]', '[941, 941, -3*w^3 + 8*w^2 + 11*w - 8]', '[953, 953, -4*w^3 + 10*w^2 + 10*w - 13]', '[953, 953, w^3 - 5*w^2 - w + 13]', '[967, 967, 3*w^3 - 7*w^2 - 9*w + 7]', '[967, 967, -2*w^3 + 5*w^2 + 8*w + 1]', '[967, 967, 4*w^3 - 13*w^2 - 6*w + 20]', '[967, 967, -2*w^2 + 3*w + 13]', '[971, 971, -6*w^3 + 13*w^2 + 25*w - 8]', '[977, 977, w^3 - w^2 - 4*w - 10]', '[977, 977, 2*w^3 - 6*w^2 - 7*w + 13]', '[983, 983, -4*w^3 + 10*w^2 + 11*w - 13]', '[983, 983, -w^3 + 5*w^2 - w - 7]', '[983, 983, 3*w^3 - 9*w^2 - 7*w + 19]', '[983, 983, -2*w^3 + 3*w^2 + 10*w - 1]', '[997, 997, 5*w^3 - 12*w^2 - 17*w + 13]', '[997, 997, -2*w^3 + 3*w^2 + 13*w - 4]', '[997, 997, w^3 - 7*w - 2]', '[997, 997, w^3 - 9*w - 2]']}