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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 15952, 'field_bad_primes': [2, 997], 'field_label': '4.4.15952.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.15952.1-11.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [11], 'level_ideal': '[11, 11, -w + 2]', 'level_label': '11.2', 'level_norm': 11, 'parallel_weight': 2, 'short_label': '11.2-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[11, 11, -w + 2]', -1]], 'hecke_eigenvalues': [1, -2, 2, 1, 1, 4, -8, 3, -1, -8, -3, 4, -7, 9, 6, -16, -11, -2, -10, 20, -18, 4, -13, 15, 10, 6, -8, -11, -15, 4, 14, -13, 6, -14, 6, -4, -24, 21, 25, -4, -25, -1, -22, 20, 24, 13, -1, -11, 10, -14, -23, -14, -8, 32, -18, -11, 20, -10, -2, 14, -19, 2, -24, 6, -16, 8, -18, -20, -6, -8, 33, -6, -30, -12, 16, -5, 16, -30, 0, 26, 24, 19, -26, -14, -24, -10, -32, -34, 12, 38, 23, 8, -20, 2, 21, 42, 17, -25, 17, 15, 46, -13, 32, -33, -23, -17, 26, 41, 14, 2, 20, -37, 18, 32, 10, -12, -34, -27, -44, 10, -8, 8, 18, -12, 1, 25, -17, 5, 30, 28, -14, 6, -6, 51, 34, -3, -32, 3, -13, -36, 2, -28, 2, 20, -14, -19, 27, -8, -2, -24, -56, -12, 25, 40, -17, -19, -12, -42, 26, 22, 17, 52, 45, -23, 9, -11, -55, 58], 'hecke_polynomial': 'x', 'label': '4.4.15952.1-11.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 15952, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[3, 3, -w^3 + w^2 + 5*w - 2]', '[4, 2, -w^2 + 2*w + 1]', '[6, 6, w - 1]', '[8, 2, w^3 - w^2 - 5*w + 3]', '[9, 9, w^3 - w^2 - 6*w + 3]', '[11, 11, -w^3 + 5*w + 1]', '[11, 11, -w + 2]', '[12, 6, w^3 - 5*w - 2]', '[13, 13, -w^3 + w^2 + 4*w + 1]', '[16, 2, 2]', '[17, 17, -w^3 + w^2 + 6*w - 1]', '[17, 17, -w^2 - w + 3]', '[18, 18, -w^2 - w + 2]', '[22, 22, -w^2 + w + 2]', '[22, 22, -w + 3]', '[23, 23, w^3 - 6*w]', '[24, 6, w^3 - w^2 - 7*w + 1]', '[26, 26, w^3 - w^2 - 6*w + 4]', '[27, 3, w^3 + w^2 - 5*w - 4]', '[27, 27, w^2 - w - 3]', '[32, 4, 2*w + 2]', '[33, 33, 2*w^3 - w^2 - 12*w + 2]', '[33, 33, w^2 - 4]', '[34, 34, w + 3]', '[34, 34, w^3 - w^2 - 4*w + 2]', '[36, 18, -w^3 + 7*w]', '[39, 39, w^3 - 7*w - 3]', '[41, 41, -w^3 + w^2 + 5*w]', '[41, 41, 2*w^3 - 11*w - 4]', '[44, 22, -w^2 + 2*w + 3]', '[44, 22, -2*w^3 + w^2 + 12*w - 1]', '[46, 46, w^3 - 4*w - 1]', '[48, 6, -2*w^3 + 2*w^2 + 10*w - 4]', '[51, 51, w^3 - 5*w - 5]', '[51, 51, w^3 + w^2 - 6*w - 5]', '[52, 26, -w^2 + 3]', '[53, 53, 2*w^3 - 2*w^2 - 11*w + 6]', '[54, 6, w^3 + w^2 - 8*w - 4]', '[54, 54, w^3 - 4*w - 3]', '[59, 59, 2*w^3 - 11*w - 2]', '[64, 4, -2*w^2 + 4*w + 2]', '[66, 66, w^3 - w^2 - 6*w]', '[66, 66, w^3 + w^2 - 4*w - 4]', '[67, 67, w^3 - 7*w - 1]', '[68, 34, -2*w^3 + w^2 + 10*w + 1]', '[68, 34, -w^3 + 7*w + 2]', '[69, 69, -2*w^3 + 10*w + 1]', '[71, 71, 3*w^3 - 2*w^2 - 15*w + 1]', '[72, 18, -w^3 + w^2 + 5*w + 1]', '[78, 78, 2*w^3 - 9*w + 1]', '[79, 79, -3*w^3 + w^2 + 16*w + 3]', '[81, 3, 3]', '[81, 81, -w^3 - w^2 + 5*w + 6]', '[82, 82, 3*w + 1]', '[82, 82, 2*w^3 + w^2 - 11*w - 6]', '[88, 22, w^3 - w^2 - 7*w + 3]', '[88, 22, -w^3 + w^2 + 7*w + 1]', '[89, 89, -4*w^3 + 2*w^2 + 22*w - 3]', '[92, 46, 2*w^3 + w^2 - 10*w - 7]', '[96, 12, 2*w - 2]', '[99, 99, -2*w^3 + 2*w^2 + 8*w + 1]', '[99, 99, -2*w^3 + 10*w + 7]', '[101, 101, -2*w^3 + 13*w + 6]', '[101, 101, w^3 + w^2 - 6*w - 3]', '[101, 101, -3*w^3 + 2*w^2 + 17*w - 3]', '[101, 101, w^3 - w^2 - 8*w - 3]', '[102, 102, -w^3 + 4*w - 3]', '[102, 102, -2*w^3 + 2*w^2 + 11*w - 5]', '[104, 26, -w^3 - w^2 + 3*w + 3]', '[106, 106, w^2 + w - 4]', '[107, 107, 2*w^3 - 3*w^2 - 6*w]', '[108, 6, 2*w^3 - w^2 - 10*w + 1]', '[108, 54, 2*w^3 - w^2 - 12*w - 1]', '[109, 109, -w^3 + w^2 + 4*w - 3]', '[113, 113, w^3 - 8*w - 4]', '[113, 113, 7*w^3 - 4*w^2 - 39*w + 7]', '[117, 117, -2*w^3 + w^2 + 10*w]', '[118, 118, 2*w^3 + w^2 - 9*w - 4]', '[121, 11, w^3 - w^2 - 6*w - 1]', '[121, 11, -2*w^3 + w^2 + 11*w + 1]', '[121, 121, 2*w + 5]', '[121, 121, -w^3 - w^2 + 5*w + 2]', '[123, 123, 2*w^3 - 14*w + 3]', '[123, 123, -3*w^3 + w^2 + 18*w - 1]', '[127, 127, -2*w^3 + w^2 + 9*w + 3]', '[127, 127, 2*w^3 - 13*w]', '[128, 4, 2*w^3 - 2*w^2 - 10*w + 6]', '[131, 131, 6*w^3 - 3*w^2 - 34*w + 6]', '[132, 66, w^3 - 7*w - 6]', '[132, 66, 2*w^3 - w^2 - 10*w - 3]', '[134, 134, w^3 - w^2 - 6*w - 2]', '[136, 34, -w^3 - w^2 + 7*w + 3]', '[136, 34, -w^3 + w^2 + 7*w + 3]', '[138, 138, -w^3 + 8*w - 1]', '[139, 139, w^2 - 2*w - 4]', '[142, 142, w^3 + w^2 - 8*w - 2]', '[143, 143, -w^3 + 4*w + 4]', '[143, 143, -3*w^3 + w^2 + 16*w - 1]', '[144, 18, 2*w^3 - 2*w^2 - 12*w + 6]', '[149, 149, 3*w^3 - w^2 - 18*w - 3]', '[151, 151, -2*w^3 + 2*w^2 + 9*w - 4]', '[153, 153, -w^3 + w^2 + 7*w + 2]', '[153, 153, -w + 4]', '[156, 78, -2*w^3 + w^2 + 12*w - 5]', '[158, 158, -2*w^3 - w^2 + 13*w + 6]', '[159, 159, -3*w^3 + 14*w - 2]', '[162, 6, 3*w + 3]', '[162, 162, w^3 - 2*w^2 - 2*w + 3]', '[163, 163, 3*w^3 - 2*w^2 - 16*w + 2]', '[163, 163, 2*w^3 - 10*w + 1]', '[164, 82, 2*w^3 - 5*w^2 - 2*w + 3]', '[164, 82, w^3 + 2*w^2 - 9*w - 8]', '[167, 167, 3*w^3 - 18*w - 4]', '[169, 169, w + 4]', '[173, 173, -3*w^3 + w^2 + 18*w - 3]', '[176, 22, -2*w^3 + 10*w + 2]', '[176, 22, -2*w + 4]', '[177, 177, -5*w^3 + 3*w^2 + 28*w - 5]', '[178, 178, -2*w^3 + 11*w + 1]', '[184, 46, 5*w^3 - 3*w^2 - 27*w + 5]', '[187, 187, -3*w^3 + 2*w^2 + 15*w - 3]', '[187, 187, -2*w^3 + w^2 + 10*w + 4]', '[187, 187, w^3 - w^2 - 5*w + 6]', '[187, 187, w^3 - 2*w^2 - 8*w + 4]', '[192, 12, 2*w^3 - 10*w - 4]', '[193, 193, 4*w^3 - 3*w^2 - 23*w + 9]', '[197, 197, 3*w^3 - w^2 - 17*w + 2]', '[197, 197, -3*w^3 - 2*w^2 + 15*w + 9]', '[198, 198, -3*w^3 + w^2 + 18*w - 4]', '[198, 198, w^3 - w^2 - 4*w + 4]', '[199, 199, 2*w^3 - w^2 - 8*w - 6]', '[201, 201, -4*w^3 + 3*w^2 + 20*w - 4]', '[202, 202, -2*w^3 + w^2 + 15*w + 8]', '[202, 202, 2*w^3 + w^2 - 7*w - 4]', '[202, 202, -w^3 + w^2 + 8*w]', '[202, 202, w^3 - 4*w - 5]', '[204, 102, w^2 + 2*w - 3]', '[204, 102, 3*w^3 - 2*w^2 - 15*w + 2]', '[207, 207, 2*w^3 + w^2 - 12*w - 6]', '[208, 26, -2*w^3 + 2*w^2 + 8*w + 2]', '[212, 106, w^3 + 2*w^2 - 3*w - 4]', '[213, 213, w^3 - w^2 - 7*w + 4]', '[214, 214, -3*w^3 + 2*w^2 + 18*w - 7]', '[216, 6, w^3 + w^2 - 5*w - 7]', '[216, 54, w^3 - w^2 - 9*w - 3]', '[218, 218, -w^2 - w - 2]', '[221, 221, -2*w^3 + 10*w + 3]', '[221, 221, -2*w^3 + 13*w + 2]', '[223, 223, -6*w^3 + 3*w^2 + 35*w - 7]', '[226, 226, 3*w^3 - w^2 - 18*w]', '[226, 226, w^3 - 2*w^2 - 10*w - 5]', '[227, 227, 2*w^3 - 12*w - 1]', '[227, 227, -w^3 + w^2 + 7*w - 8]', '[227, 227, 3*w^3 - w^2 - 18*w - 1]', '[227, 227, -4*w^3 - 2*w^2 + 21*w + 14]', '[229, 229, -w^3 + 2*w^2 + 3*w - 5]', '[233, 233, w^3 - 3*w - 3]', '[233, 233, -3*w^3 + 3*w^2 + 15*w - 8]', '[234, 234, -w^3 - w^2 + 6*w + 2]', '[236, 118, w^3 - 5*w - 6]', '[237, 237, 6*w^3 - 2*w^2 - 37*w + 6]', '[241, 241, 4*w^2 - 7*w - 8]', '[241, 241, w^3 + w^2 - 4*w - 5]', '[242, 22, -w^2 - 5*w - 2]', '[242, 22, -w^3 + 8*w + 3]', '[242, 242, w^3 - 2*w^2 - 4*w + 3]', '[242, 242, w^3 - 3*w^2 + 4]', '[243, 9, -3*w^3 + 3*w^2 + 15*w - 6]', '[243, 243, -2*w^3 + 2*w^2 + 10*w - 7]', '[246, 246, -2*w^3 + w^2 + 11*w + 2]', '[246, 246, 2*w^3 - 2*w^2 - 7*w + 1]', '[251, 251, 2*w^3 - w^2 - 13*w - 1]', '[251, 251, 2*w^3 - 9*w - 6]', '[253, 253, -w^3 + w^2 + 4*w - 5]', '[253, 253, 2*w^3 - 14*w + 1]', '[254, 254, 2*w^3 - w^2 - 9*w - 2]', '[254, 254, 2*w^3 - 2*w^2 - 11*w + 9]', '[256, 4, 4]', '[257, 257, w^3 - 8*w]', '[262, 262, 3*w^3 - w^2 - 16*w]', '[263, 263, -w^3 + 2*w^2 + 5*w - 7]', '[264, 66, -w^3 + 3*w^2 + w - 3]', '[264, 66, 3*w^3 - w^2 - 17*w + 3]', '[267, 267, -2*w^3 + 3*w^2 + 14*w - 6]', '[268, 134, 2*w^3 - 3*w^2 - 4*w - 3]', '[269, 269, 3*w^3 - 3*w^2 - 12*w - 1]', '[271, 271, 2*w^3 - w^2 - 12*w - 2]', '[271, 271, 9*w^3 - 5*w^2 - 50*w + 9]', '[272, 34, -2*w^3 + 2*w^2 + 12*w - 2]', '[272, 34, -2*w^2 - 2*w + 6]', '[276, 138, -w^2 + 2*w + 5]', '[277, 277, w^3 - 2*w^2 - 6*w + 6]', '[277, 277, w^3 + w^2 - 7*w - 2]', '[278, 278, w^3 - w^2 - 6*w - 4]', '[281, 281, 4*w^3 - 2*w^2 - 24*w + 5]', '[281, 281, -7*w^3 + 4*w^2 + 40*w - 12]', '[284, 142, 2*w^3 - w^2 - 8*w - 3]', '[286, 286, 2*w^3 - w^2 - 9*w + 4]', '[286, 286, -2*w^3 - w^2 + 9*w + 2]', '[288, 36, -2*w^2 - 2*w + 4]', '[289, 17, -2*w^2 + 2*w + 7]', '[289, 17, -5*w^3 + 5*w^2 + 26*w - 15]', '[289, 289, -2*w^3 - w^2 + 11*w + 5]', '[289, 289, -w^3 + 6*w + 6]', '[293, 293, -w^3 + 2*w^2 + 4*w - 4]', '[293, 293, -9*w^3 + 5*w^2 + 51*w - 12]', '[297, 33, w^3 + w^2 - 8*w - 1]', '[297, 33, w^3 + w^2 - 8*w - 7]', '[297, 297, 2*w^3 + w^2 - 8*w - 4]', '[297, 297, 2*w^3 - 13*w - 4]', '[298, 298, 2*w^3 - w^2 - 15*w - 6]', '[299, 299, -w^3 + 3*w^2 + w - 4]', '[302, 302, -w^2 + w - 2]', '[303, 303, 3*w^3 - w^2 - 16*w - 1]', '[303, 303, -3*w^3 - w^2 + 11*w - 4]', '[303, 303, -2*w^3 + 2*w^2 + 9*w]', '[303, 303, -2*w^3 + 11*w]', '[306, 306, -w^2 + 3*w + 4]', '[306, 306, -w^3 + w^2 + 2*w + 4]', '[307, 307, -2*w^3 + 2*w^2 + 12*w - 7]', '[311, 311, -4*w^3 + 24*w + 11]', '[312, 78, -w^3 + w^2 + 3*w - 3]', '[313, 313, 2*w^3 - 9*w - 4]', '[316, 158, w^3 - 6*w^2 + 5*w + 10]', '[317, 317, 2*w^3 - 4*w^2 - 2*w - 3]', '[317, 317, 2*w^3 - 14*w - 7]', '[318, 318, 4*w^3 - 3*w^2 - 21*w + 8]', '[321, 321, -w^3 + 8*w + 2]', '[324, 6, -3*w^2 + 6*w + 3]', '[324, 162, -2*w^3 - w^2 + 14*w + 7]', '[326, 326, w^3 - 8*w - 1]', '[326, 326, 2*w^3 + 2*w^2 - 5*w - 1]', '[327, 327, 4*w^3 - 2*w^2 - 25*w + 8]', '[328, 82, -3*w^3 + w^2 + 19*w - 3]', '[328, 82, 5*w^3 - w^2 - 29*w - 3]', '[331, 331, -3*w^3 + 19*w + 3]', '[334, 334, 3*w^3 - 16*w - 7]', '[338, 338, -3*w^3 + 2*w^2 + 14*w + 1]', '[339, 339, -2*w^3 + w^2 + 9*w + 1]', '[339, 339, 5*w^3 - 3*w^2 - 27*w + 10]', '[346, 346, -2*w^3 + w^2 + 9*w]', '[349, 349, -w^3 - 2*w^2 + 8*w + 8]', '[349, 349, w^3 + w^2 - 5*w - 8]', '[351, 39, 2*w^3 - w^2 - 13*w + 1]', '[351, 351, 3*w^3 - 16*w - 2]', '[352, 44, -2*w^2 + 2*w + 4]', '[352, 44, -2*w + 6]', '[354, 354, -2*w^3 + w^2 + 13*w]', '[356, 178, -2*w^3 - w^2 + 8*w + 3]', '[361, 19, -w^3 + w^2 + 7*w - 6]', '[361, 19, w^3 + w^2 - 3*w - 4]', '[363, 33, -w^3 - w^2 + 2*w - 3]', '[363, 33, -2*w^3 + 13*w - 2]', '[363, 363, 2*w^3 - 2*w^2 - 10*w + 1]', '[363, 363, -3*w^3 + 3*w^2 + 17*w - 8]', '[368, 46, 2*w^3 - 12*w]', '[369, 369, -4*w^3 + 2*w^2 + 21*w - 4]', '[369, 369, 5*w^3 - 2*w^2 - 29*w - 1]', '[373, 373, 2*w^3 - w^2 - 11*w - 3]', '[374, 374, -4*w^3 + 3*w^2 + 21*w - 4]', '[374, 374, -w^2 - w + 6]', '[374, 374, -2*w^3 + 11*w - 1]', '[374, 374, 3*w + 5]', '[379, 379, -4*w^3 + 25*w + 14]', '[381, 381, 3*w^3 + w^2 - 17*w - 8]', '[381, 381, -9*w^3 + 7*w^2 + 46*w - 11]', '[383, 383, -3*w^3 + w^2 + 15*w - 2]', '[383, 383, 3*w^3 - 4*w^2 - 10*w]', '[384, 12, 2*w^3 - 2*w^2 - 14*w + 2]', '[386, 386, w^3 - 2*w^2 - 6*w + 5]', '[391, 391, 3*w^3 - 2*w^2 - 19*w + 1]', '[391, 391, w^2 - 4*w - 4]', '[393, 393, 4*w^3 - 4*w^2 - 24*w + 9]', '[394, 394, -2*w^3 - 2*w^2 + 15*w + 11]', '[394, 394, 2*w^3 - 9*w - 1]', '[396, 198, w^3 - 2*w^2 - 5*w + 6]', '[396, 198, w^2 + 2*w + 3]', '[398, 398, 5*w^3 - 2*w^2 - 28*w - 1]', '[401, 401, 4*w^3 - w^2 - 24*w - 4]', '[402, 402, -w^3 - w^2 + 8*w]', '[404, 202, -3*w^3 + 15*w + 10]', '[404, 202, 3*w^3 - 4*w^2 - 9*w - 4]', '[404, 202, 3*w^2 + 6*w + 1]', '[404, 202, -3*w^3 + 2*w^2 + 15*w - 6]', '[408, 102, 3*w^3 + w^2 - 15*w - 7]', '[408, 102, w^3 + w^2 - 7*w - 1]', '[409, 409, w^2 + 5*w + 5]', '[414, 414, 2*w^3 - 2*w^2 - 13*w + 1]', '[416, 52, 2*w^3 - 2*w^2 - 12*w + 8]', '[417, 417, w^3 - 9*w + 5]', '[419, 419, w^2 - 2*w - 6]', '[419, 419, -6*w^3 + 3*w^2 + 34*w - 8]', '[424, 106, w^3 + w^2 - 9*w - 3]', '[426, 426, -5*w^3 + 5*w^2 + 22*w - 4]', '[428, 214, -w^3 + 2*w^2 + 5*w - 4]', '[429, 429, -2*w^3 + 3*w^2 + 7*w - 5]', '[429, 429, 2*w^3 + w^2 - 13*w - 5]', '[432, 6, 2*w^3 + 2*w^2 - 10*w - 8]', '[432, 54, 2*w^2 - 2*w - 6]', '[433, 433, 3*w^3 - 16*w - 6]', '[433, 433, 3*w^3 - w^2 - 16*w - 5]', '[436, 218, 3*w^3 - 4*w^2 - 9*w]', '[442, 442, -2*w^3 + w^2 + 11*w + 4]', '[442, 442, -2*w^3 - 2*w^2 + 9*w + 5]', '[443, 443, -w^3 + 2*w^2 + w + 3]', '[446, 446, -3*w^3 + 2*w^2 + 16*w - 1]', '[447, 447, -8*w^3 + 4*w^2 + 45*w - 8]', '[449, 449, 2*w^2 - 2*w - 5]', '[451, 451, -w^2 - 2*w + 4]', '[451, 451, 4*w^3 - w^2 - 22*w - 6]', '[451, 451, -3*w^3 + 3*w^2 + 12*w - 1]', '[451, 451, 2*w^3 + w^2 - 13*w - 13]', '[452, 226, 3*w^3 - 2*w^2 - 11*w - 6]', '[452, 226, 2*w^3 - w^2 - 12*w - 3]', '[453, 453, 7*w^3 - 3*w^2 - 44*w + 13]', '[454, 454, 2*w^3 - 9*w - 3]', '[454, 454, 2*w^2 - 3*w - 7]', '[454, 454, 2*w^3 - w^2 - 13*w - 4]', '[454, 454, -5*w^3 + 28*w + 15]', '[457, 457, -4*w^3 + 4*w^2 + 20*w - 9]', '[457, 457, w^2 + w - 7]', '[458, 458, w^3 - w^2 - 4*w - 4]', '[459, 51, -2*w^3 + w^2 + 13*w - 7]', '[459, 51, -w^3 + 2*w^2 + 5*w - 5]', '[459, 459, 2*w^3 - 12*w + 1]', '[459, 459, w^2 - 2*w - 8]', '[463, 463, w^3 - 7*w - 7]', '[463, 463, w^3 + 2*w^2 - 5*w - 9]', '[466, 466, w^3 + 3*w^2 - 4*w - 4]', '[466, 466, w - 5]', '[468, 234, 3*w^3 - 2*w^2 - 15*w + 8]', '[472, 118, 7*w^3 - 3*w^2 - 39*w + 3]', '[474, 474, 4*w^3 - 3*w^2 - 19*w]', '[477, 477, 2*w^3 - 9*w - 2]', '[482, 482, 5*w^3 - w^2 - 30*w - 2]', '[482, 482, 2*w^3 + 3*w^2 - 7*w - 6]', '[484, 22, -w^3 + 4*w^2 - w - 4]', '[484, 22, -3*w^3 + 13*w - 2]', '[484, 242, -2*w^3 - w^2 + 12*w + 5]', '[484, 242, 2*w^3 - w^2 - 14*w + 5]', '[486, 18, 3*w - 3]', '[486, 486, -w - 5]', '[487, 487, w^3 + 2*w^2 - 5*w - 5]', '[487, 487, -w^3 + w^2 + 6*w - 7]', '[489, 489, 2*w^3 - 9*w + 4]', '[489, 489, -7*w^3 + 5*w^2 + 39*w - 10]', '[492, 246, w^3 - 3*w - 4]', '[492, 246, -4*w^3 - w^2 + 24*w + 17]', '[501, 501, -8*w^3 + 5*w^2 + 43*w - 7]', '[502, 502, w^3 - 2*w^2 - 10*w - 3]', '[502, 502, 3*w^3 - w^2 - 18*w - 4]', '[506, 506, -w^2 - 3*w - 4]', '[506, 506, 2*w^3 - 2*w^2 - 9*w - 1]', '[507, 507, -3*w^3 + 3*w^2 + 16*w - 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6*w - 4]', '[1741, 1741, -w^3 + 2*w^2 + 7*w - 9]', '[1742, 1742, 6*w^3 - 2*w^2 - 35*w + 3]', '[1744, 218, -2*w^3 + 2*w^2 + 8*w - 6]', '[1747, 1747, -w^3 - 2*w^2 + 4]', '[1749, 1749, -6*w^3 + 4*w^2 + 36*w - 7]', '[1749, 1749, w^3 - 2*w^2 - w + 5]', '[1754, 1754, -7*w^3 + w^2 + 36*w + 22]', '[1758, 1758, 14*w^3 - 8*w^2 - 81*w + 21]', '[1758, 1758, 3*w^3 - 4*w^2 - 10*w + 5]', '[1759, 1759, 2*w^3 + w^2 - 12*w - 2]', '[1768, 442, w^3 - w^2 - 9*w + 5]', '[1768, 442, -w^3 - 3*w^2 + 3*w + 9]', '[1772, 886, -3*w^3 + 17*w]', '[1773, 1773, w^3 + w^2 - w - 4]', '[1773, 1773, -3*w^3 + 19*w - 1]', '[1774, 1774, 3*w^2 - 3*w - 10]', '[1774, 1774, 4*w^3 + 5*w^2 - 15*w - 10]', '[1777, 1777, -7*w^3 + 4*w^2 + 42*w - 16]', '[1777, 1777, 4*w^3 - 21*w - 8]', '[1779, 1779, 6*w^3 - 2*w^2 - 36*w + 5]', '[1782, 66, -3*w^2 + 3*w + 6]', '[1782, 66, -3*w + 9]', '[1782, 1782, -2*w^3 - w^2 + 15*w + 12]', '[1782, 1782, -2*w^3 - w^2 + 13*w + 2]', '[1783, 1783, -7*w^3 + 4*w^2 + 41*w - 7]', '[1783, 1783, 4*w^3 - 23*w - 4]', '[1784, 446, 3*w^3 - 7*w^2 - 5*w + 7]', '[1787, 1787, -w^3 + 4*w^2 + w - 11]', '[1788, 894, -4*w^3 - 3*w^2 + 22*w + 21]', '[1789, 1789, 2*w^3 - 15*w - 6]', '[1791, 1791, w^2 + w - 11]', '[1793, 1793, -3*w^3 + 11*w - 7]', '[1793, 1793, -w^3 + w - 5]', '[1793, 1793, 4*w^3 - 2*w^2 - 25*w + 4]', '[1793, 1793, 3*w^3 - 17*w + 3]', '[1794, 1794, -2*w^3 - 3*w^2 + 9*w + 8]', '[1796, 898, 6*w^3 - 9*w^2 - 16*w - 3]', '[1801, 1801, -4*w^2 + 6*w + 9]', '[1802, 1802, -2*w^3 + 5*w - 11]', '[1802, 1802, 5*w^3 - w^2 - 24*w + 4]', '[1804, 902, -3*w^2 + 8*w + 3]', '[1804, 902, -w^3 + 4*w^2 + 5*w - 18]', '[1804, 902, 4*w^3 - 3*w^2 - 20*w + 9]', '[1804, 902, 5*w^3 + 2*w^2 - 31*w - 16]', '[1807, 1807, 5*w^2 - 11*w - 7]', '[1808, 226, 2*w^3 - 16*w - 8]', '[1808, 226, 14*w^3 - 8*w^2 - 78*w + 14]', '[1809, 201, -4*w^3 - w^2 + 20*w + 10]', '[1809, 1809, -4*w^3 + 2*w^2 + 19*w + 4]', '[1812, 906, -2*w^3 - w^2 + 14*w + 1]', '[1816, 454, -w^3 + 5*w^2 - 5*w - 7]', '[1816, 454, -13*w^3 + 11*w^2 + 69*w - 29]', '[1816, 454, 13*w^3 - 7*w^2 - 73*w + 11]', '[1816, 454, -5*w^3 - 3*w^2 + 29*w + 23]', '[1817, 1817, -3*w^3 + 5*w^2 + 13*w - 16]', '[1818, 1818, w^3 - 3*w^2 - 12*w - 4]', '[1818, 1818, -5*w^3 - 3*w^2 + 22*w + 10]', '[1818, 1818, -7*w^3 + 2*w^2 + 36*w - 7]', '[1818, 1818, 2*w^3 - w^2 - 15*w + 2]', '[1819, 1819, 3*w^3 - 21*w + 1]', '[1819, 1819, 3*w^3 - w^2 - 14*w - 1]', '[1821, 1821, -2*w^3 + 10*w - 5]', '[1822, 1822, 3*w^3 - 14*w - 5]', '[1823, 1823, -3*w^3 + w^2 + 24*w + 13]', '[1828, 914, 3*w^2 - 2*w - 5]', '[1828, 914, w^3 + 4*w^2 - 15*w - 6]', '[1831, 1831, -w^3 + 7*w^2 - 7*w - 10]', '[1831, 1831, -3*w^3 - 3*w^2 + 15*w + 14]', '[1832, 458, -5*w^3 + 3*w^2 + 31*w - 15]', '[1836, 102, 4*w^3 + w^2 - 26*w - 13]', '[1836, 102, 4*w^3 - 5*w^2 - 14*w - 1]', '[1836, 918, 3*w^3 + 2*w^2 - 13*w - 10]', '[1836, 918, 4*w^3 - w^2 - 20*w - 7]', '[1837, 1837, 6*w^3 - 38*w - 5]', '[1837, 1837, w^3 + 3*w^2 - 8*w - 19]', '[1838, 1838, 5*w^3 - 6*w^2 - 16*w - 3]', '[1838, 1838, -3*w^3 + w^2 + 14*w + 2]', '[1839, 1839, -6*w^3 + w^2 + 41*w - 9]', '[1839, 1839, w^3 - 10*w + 6]', '[1842, 1842, 4*w^3 - 2*w^2 - 23*w + 9]', '[1846, 1846, -3*w^3 + 10*w^2 - 2*w - 9]', '[1847, 1847, 4*w^3 + 2*w^2 - 20*w - 9]', '[1852, 926, 6*w^3 - 3*w^2 - 36*w + 7]', '[1852, 926, 4*w^3 - w^2 - 22*w - 9]', '[1853, 1853, -2*w^3 + 4*w^2 + 14*w - 9]', '[1853, 1853, 4*w^3 - 3*w^2 - 26*w + 6]', '[1857, 1857, 10*w^3 - 7*w^2 - 57*w + 21]', '[1859, 1859, -4*w^3 - w^2 + 19*w + 5]', '[1859, 1859, -w^2 - 2*w + 8]', '[1863, 69, 3*w^3 - 18*w]', '[1863, 1863, 4*w^3 - w^2 - 25*w - 5]', '[1864, 466, -w^3 + 3*w^2 + 3*w - 7]', '[1864, 466, -w^3 + 7*w^2 - 9*w - 5]', '[1866, 1866, 4*w^3 - 21*w - 7]', '[1867, 1867, -w^3 + 3*w^2 + 3*w - 6]', '[1867, 1867, -3*w^3 + 5*w^2 + 5*w + 6]', '[1872, 234, -4*w^3 + 2*w^2 + 20*w]', '[1873, 1873, -3*w^3 - 2*w^2 + 15*w + 7]', '[1875, 15, 5*w^3 - 5*w^2 - 25*w + 10]', '[1877, 1877, -2*w^3 - 3*w^2 + 10*w + 14]', '[1878, 1878, -2*w^3 + 3*w^2 + 9*w + 2]', '[1882, 1882, 2*w^2 - 7*w - 3]', '[1886, 1886, w^3 - 3]', '[1886, 1886, -2*w^3 + 13*w + 11]', '[1888, 236, 4*w^3 + 2*w^2 - 18*w - 8]', '[1894, 1894, -7*w - 3]', '[1894, 1894, -2*w^2 - w + 11]', '[1896, 474, -5*w^3 + 5*w^2 + 27*w - 15]', '[1901, 1901, w^3 + 2*w^2 - 9*w - 11]', '[1902, 1902, 5*w^3 - 4*w^2 - 30*w + 11]', '[1902, 1902, -2*w^3 - 2*w^2 + 11*w + 5]', '[1903, 1903, -2*w^2 - 4*w + 5]', '[1903, 1903, -4*w^3 + 4*w^2 + 22*w - 5]', '[1906, 1906, 3*w^3 - 14*w - 3]', '[1906, 1906, -w^3 + 10*w + 1]', '[1908, 954, -2*w^3 - w^2 + 4*w - 7]', '[1913, 1913, -4*w^3 + 2*w^2 + 20*w - 1]', '[1917, 213, -4*w^3 - w^2 + 26*w + 10]', '[1917, 1917, -2*w^3 - w^2 + 9*w + 9]', '[1921, 1921, 5*w^3 + 4*w^2 - 21*w - 11]', '[1921, 1921, w^3 + w^2 - 4*w - 11]', '[1921, 1921, w^3 + w^2 - 9*w - 10]', '[1921, 1921, -w^3 - w^2 - w - 4]', '[1922, 62, w^3 + 3*w^2 - 6]', '[1922, 62, 3*w^3 - w^2 - 10*w - 6]', '[1923, 1923, 2*w^3 - 2*w^2 - 13*w - 2]', '[1926, 1926, w^3 + 2*w^2 - 8*w - 1]', '[1928, 482, 3*w^3 + w^2 - 21*w - 11]', '[1928, 482, -w^3 + 3*w^2 + 5*w - 11]', '[1929, 1929, w^3 - w^2 - 9*w + 12]', '[1929, 1929, -6*w^3 + 3*w^2 + 32*w - 2]', '[1933, 1933, -4*w^3 + w^2 + 26*w + 8]', '[1933, 1933, -w^3 - 2*w^2 + 12*w + 2]', '[1934, 1934, -5*w^3 + w^2 + 26*w + 16]', '[1936, 22, 2*w^3 - 2*w^2 - 12*w - 2]', '[1936, 22, -4*w^3 + 2*w^2 + 22*w + 2]', '[1936, 242, 4*w + 10]', '[1936, 242, -2*w^3 - 2*w^2 + 10*w + 4]', '[1937, 1937, 2*w^3 + w^2 - 12*w - 14]', '[1941, 1941, 4*w^3 - 5*w^2 - 18*w + 10]', '[1942, 1942, 4*w^3 + 2*w^2 - 25*w - 13]', '[1942, 1942, -3*w^3 + 2*w^2 + 20*w - 3]', '[1944, 18, 3*w^3 - 3*w^2 - 21*w + 3]', '[1944, 486, w^3 + 3*w^2 - 11*w - 5]', '[1947, 1947, 7*w^3 - 6*w^2 - 40*w + 18]', '[1947, 1947, -7*w^3 + 2*w^2 + 42*w + 8]', '[1948, 974, 4*w^3 - 3*w^2 - 18*w + 3]', '[1948, 974, w^3 - 2*w^2 - 9*w - 6]', '[1949, 1949, 2*w^3 - 10*w - 11]', '[1949, 1949, 2*w^3 + 3*w^2 - 14*w - 16]', '[1956, 978, -w^3 - 2*w^2 + 9*w]', '[1956, 978, w^3 - w + 6]', '[1958, 1958, w^3 - w^2 - 2*w + 10]', '[1958, 1958, -4*w^3 + w^2 + 25*w]', '[1959, 1959, 8*w^3 - 3*w^2 - 51*w + 13]', '[1962, 1962, -w^3 + 3*w^2 + 10*w - 6]', '[1963, 1963, -w^3 + 6*w^2 - 9*w - 1]', '[1966, 1966, w^3 - 4*w^2 + 7]', '[1968, 246, 4*w^3 - 28*w + 6]', '[1968, 246, -6*w^3 + 2*w^2 + 36*w - 2]', '[1977, 1977, -2*w^3 + 5*w^2 + 16*w - 10]', '[1977, 1977, 3*w^3 - 14*w - 4]', '[1979, 1979, -5*w - 6]', '[1979, 1979, 3*w^2 - 6*w - 8]', '[1986, 1986, 3*w^3 + w^2 - 22*w]', '[1987, 1987, -11*w^3 + 6*w^2 + 63*w - 11]', '[1987, 1987, -9*w^3 + 5*w^2 + 49*w - 10]', '[1989, 1989, -5*w^3 + 3*w^2 + 30*w - 1]', '[1989, 1989, 4*w^3 - 3*w^2 - 25*w + 9]', '[1994, 1994, 3*w^3 + 2*w^2 - 10*w - 5]', '[1994, 1994, 3*w^3 + 2*w^2 - 12*w - 9]', '[1994, 1994, -w^3 + 3*w^2 + 4*w - 10]', '[1997, 1997, -2*w^3 + 3*w^2 + 9*w - 15]', '[1997, 1997, -5*w^3 - 2*w^2 + 24*w + 14]', '[1997, 1997, -w^3 + 2*w^2 + 3*w - 9]', '[1997, 1997, w^3 + w^2 - 9*w - 12]', '[2003, 2003, 3*w^3 - 2*w^2 - 16*w - 2]', '[2004, 1002, -4*w^3 - 3*w^2 + 26*w + 23]', '[2006, 2006, 5*w^3 - 2*w^2 - 26*w + 3]', '[2006, 2006, 6*w^3 + w^2 - 31*w - 8]', '[2007, 2007, w^2 - 3*w + 5]', '[2008, 502, 9*w^3 - 5*w^2 - 51*w + 7]', '[2008, 502, w^3 + 3*w^2 - 9*w - 11]', '[2011, 2011, 3*w^3 + 3*w^2 - 18*w - 13]', '[2011, 2011, 2*w^3 - 2*w^2 - 14*w - 3]', '[2017, 2017, -4*w^3 - w^2 + 27*w + 19]', '[2018, 2018, -2*w^3 + 3*w^2 + 9*w - 12]', '[2024, 506, w^3 + 3*w^2 - 9*w - 5]', '[2024, 506, -w^3 + 3*w^2 + 7*w - 7]', '[2028, 1014, 4*w^3 + w^2 - 20*w - 9]', '[2032, 254, -4*w^3 + 2*w^2 + 18*w + 6]', '[2032, 254, 4*w^3 - 26*w]', '[2034, 2034, 4*w^3 + 4*w^2 - 13*w - 7]', '[2034, 2034, 15*w^3 - 8*w^2 - 84*w + 17]', '[2036, 1018, -7*w^3 + 6*w^2 + 27*w + 12]', '[2036, 1018, 2*w^3 - w^2 - 8*w - 9]', '[2036, 1018, w^3 - w - 4]', '[2036, 1018, -7*w^3 + 4*w^2 + 37*w - 8]', '[2038, 2038, w^3 - 2*w^2 - 12*w - 3]', '[2042, 2042, 4*w^3 - w^2 - 27*w - 14]', '[2042, 2042, 4*w^3 + 3*w^2 - 23*w - 16]', '[2043, 2043, 2*w^3 - 6*w - 5]', '[2043, 2043, 2*w^3 - 2*w^2 - 13*w + 10]', '[2043, 2043, 14*w^3 - 7*w^2 - 78*w + 14]', '[2043, 2043, -14*w^3 + 10*w^2 + 79*w - 30]', '[2047, 2047, -11*w^3 + 8*w^2 + 60*w - 22]', '[2048, 8, 4*w^3 - 4*w^2 - 20*w + 12]', '[2049, 2049, w^2 - 4*w + 6]', '[2054, 2054, -13*w^3 + 6*w^2 + 72*w - 3]', '[2056, 514, 7*w^3 - 5*w^2 - 37*w + 7]', '[2057, 187, -2*w^3 - w^2 + 8*w - 4]', '[2057, 187, 4*w^3 - 2*w^2 - 22*w + 9]', '[2057, 187, w^3 - 4*w^2 - 10*w + 6]', '[2057, 187, 4*w^3 + 2*w^2 - 16*w - 3]', '[2057, 2057, -3*w^3 + 4*w^2 + 11*w + 1]', '[2057, 2057, -4*w^3 + 20*w + 3]', '[2057, 2057, -3*w^3 - w^2 + 15*w + 12]', '[2057, 2057, -3*w^3 + 19*w - 3]', '[2061, 2061, -7*w^3 + 6*w^2 + 38*w - 16]', '[2062, 2062, -4*w^3 + w^2 + 23*w + 14]', '[2063, 2063, 5*w^3 + 2*w^2 - 25*w - 13]', '[2066, 2066, -5*w^3 + 2*w^2 + 28*w + 3]', '[2067, 2067, w^3 - 3*w^2 - 7*w + 6]', '[2069, 2069, 3*w^3 - 17*w + 1]', '[2073, 2073, -2*w^3 - w^2 + 16*w + 2]', '[2076, 1038, 3*w^3 - 4*w^2 - 13*w + 2]', '[2083, 2083, 2*w^3 - w^2 - 15*w - 3]', '[2084, 1042, -3*w^3 + 19*w - 2]', '[2087, 2087, -5*w^3 + 5*w^2 + 26*w - 13]', '[2089, 2089, -5*w^3 + 3*w^2 + 29*w - 2]', '[2089, 2089, -6*w^3 + 3*w^2 + 32*w - 4]', '[2091, 2091, 2*w^3 + 2*w^2 - 13*w - 6]', '[2091, 2091, -9*w^3 - 2*w^2 + 55*w + 31]', '[2091, 2091, 4*w^3 - 3*w^2 - 18*w - 4]', '[2091, 2091, -10*w^3 - w^2 + 57*w + 29]', '[2094, 2094, -w^3 + 4*w^2 - 2*w - 7]', '[2094, 2094, -w + 7]', '[2096, 262, 12*w^3 - 6*w^2 - 68*w + 12]', '[2097, 2097, -w^3 + 4*w - 6]', '[2097, 2097, 3*w^3 - 3*w^2 - 13*w - 2]', '[2098, 2098, -2*w^3 + 3*w^2 + 11*w - 16]', '[2099, 2099, 3*w^3 - w^2 - 14*w - 11]', '[2103, 2103, -4*w^3 + 2*w^2 + 19*w - 8]', '[2103, 2103, 4*w^3 - 3*w^2 - 23*w + 13]', '[2103, 2103, 14*w^3 - 10*w^2 - 77*w + 28]', '[2103, 2103, w^3 - 4*w^2 - 12*w + 6]', '[2104, 526, w^3 + 3*w^2 - 13*w - 7]', '[2106, 78, 3*w^3 - 3*w^2 - 18*w + 12]', '[2106, 2106, -3*w^3 + 2*w^2 + 20*w - 1]', '[2111, 2111, -w^3 + 2*w^2 + 13*w + 5]', '[2112, 132, 2*w^3 - 14*w - 12]', '[2112, 132, 4*w^3 - 2*w^2 - 20*w - 6]', '[2113, 2113, -4*w^3 - 4*w^2 + 18*w + 15]', '[2116, 1058, -3*w^3 + 21*w + 10]', '[2119, 2119, 2*w^3 + 3*w^2 - 8*w - 4]', '[2119, 2119, -w^3 + 3*w^2 + 4*w - 5]', '[2122, 2122, -w - 7]', '[2123, 2123, 6*w^3 - 3*w^2 - 30*w + 10]', '[2123, 2123, -4*w^3 - 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6]', '[2167, 2167, 3*w^3 - 4*w^2 - 20*w + 4]', '[2168, 542, 7*w^3 - 3*w^2 - 41*w + 3]', '[2168, 542, w^3 - w^2 - w - 9]', '[2169, 2169, -w^3 + 4*w^2 + w - 13]', '[2169, 2169, -2*w^3 + w^2 + 8*w - 10]', '[2171, 2171, w^3 + 5*w^2 - 13*w - 16]', '[2173, 2173, -3*w^3 - 2*w^2 + 22*w + 12]', '[2173, 2173, 2*w^3 - 2*w^2 - 16*w + 3]', '[2174, 2174, 3*w^3 - 14*w - 11]', '[2176, 68, -2*w^3 - 2*w^2 + 14*w + 6]', '[2176, 68, -2*w^3 + 2*w^2 + 14*w + 6]', '[2178, 198, 3*w^3 + 3*w^2 - 10*w - 2]', '[2178, 198, -4*w^3 + 21*w + 1]', '[2178, 2178, 3*w^3 - 4*w^2 - 14*w + 9]', '[2178, 2178, -w^3 - 3*w^2 + 8*w + 8]', '[2179, 2179, -5*w^3 + 5*w^2 + 28*w - 21]', '[2181, 2181, w^3 - 2*w^2 - 4*w - 4]', '[2182, 2182, 3*w^3 + 3*w^2 - 16*w - 12]', '[2186, 2186, -6*w^3 + 31*w + 21]', '[2186, 2186, -w^2 - 7*w - 6]', '[2187, 9, 3*w^3 + 3*w^2 - 15*w - 12]', '[2187, 81, 3*w^2 - 3*w - 9]', '[2187, 2187, 2*w^3 - 2*w^2 - 12*w - 3]', '[2188, 1094, -6*w^3 + 3*w^2 + 32*w - 3]', '[2188, 1094, -w^3 + 2*w^2 + 7*w - 10]', '[2189, 2189, -2*w^3 + 3*w^2 + 10*w - 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32*w - 16]', '[4457, 4457, 4*w^3 - 3*w^2 - 27*w + 9]', '[4458, 4458, 3*w^2 - 7*w + 4]', '[4461, 4461, -7*w^3 + 2*w^2 + 38*w + 6]', '[4463, 4463, 5*w^3 - w^2 - 26*w - 7]', '[4468, 2234, -5*w^3 + 4*w^2 + 25*w - 2]', '[4469, 4469, 5*w^3 - 29*w - 5]', '[4469, 4469, -2*w^3 + 2*w^2 + 12*w - 13]', '[4471, 4471, 5*w^3 + 3*w^2 - 21*w - 12]', '[4471, 4471, 3*w^3 + w^2 - 22*w - 11]', '[4474, 4474, -3*w^3 - 5*w^2 + 26*w + 20]', '[4476, 2238, -4*w^3 - w^2 + 20*w + 15]', '[4479, 4479, -w^3 - w^2 + 4*w - 5]', '[4481, 4481, 5*w^3 - 27*w - 3]', '[4486, 4486, 3*w^3 - 2*w^2 - 24*w - 9]', '[4488, 1122, 5*w^3 - w^2 - 29*w - 11]', '[4488, 1122, -w^3 + w^2 + 9*w - 9]', '[4488, 1122, w^3 + 3*w^2 - 15*w - 1]', '[4488, 1122, -w^3 + w^2 + w - 7]', '[4489, 4489, 2*w - 9]', '[4492, 2246, -2*w^3 + w^2 + 12*w - 9]', '[4493, 4493, 7*w^3 - 3*w^2 - 39*w - 2]', '[4493, 4493, 3*w^3 - 2*w^2 - 16*w - 10]', '[4496, 562, 8*w^3 - 4*w^2 - 48*w + 10]', '[4496, 562, -14*w^3 + 8*w^2 + 80*w - 24]', '[4497, 4497, -3*w^3 - w^2 + 15*w + 16]', '[4498, 4498, -3*w^3 + 5*w^2 + 4*w + 4]', '[4499, 4499, -3*w^3 + w^2 + 21*w - 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w^2 - 29*w + 6]', '[4981, 4981, -w^3 - 2*w^2 + w + 7]', '[4983, 4983, 5*w^3 - 4*w^2 - 30*w + 14]', '[4983, 4983, -17*w^3 + 12*w^2 + 92*w - 24]', '[4986, 4986, 4*w^3 - 15*w + 11]', '[4986, 4986, 2*w^3 - 3*w^2 - 15*w - 2]', '[4987, 4987, -5*w^2 + 7*w + 9]', '[4987, 4987, w^3 + 2*w^2 - 10*w - 12]', '[4989, 4989, -3*w^3 + 13*w + 11]', '[4992, 156, -2*w^3 + 2*w^2 + 6*w - 6]', '[4993, 4993, 3*w^3 - 22*w - 10]', '[4993, 4993, -w^3 + 3*w^2 + 8*w - 11]', '[4994, 4994, 4*w^3 - 3*w^2 - 19*w - 4]', '[4994, 4994, 10*w^3 - 3*w^2 - 59*w]', '[4994, 4994, -4*w^3 + 2*w^2 + 31*w - 25]', '[4994, 4994, 5*w^3 - w^2 - 26*w - 6]', '[4994, 4994, -2*w^3 + 7*w^2 + w - 14]', '[4994, 4994, -10*w^3 - 3*w^2 + 57*w + 38]', '[4994, 4994, w^3 - w^2 - 10*w - 10]', '[4994, 4994, -4*w^2 - 3*w + 11]', '[4996, 2498, -5*w^3 + 2*w^2 + 31*w - 2]', '[4996, 2498, -3*w^3 + 6*w^2 + 9*w - 10]', '[4999, 4999, 4*w^3 - 2*w^2 - 22*w - 5]', '[5000, 10, -5*w^3 + 5*w^2 + 25*w - 15]', '[5001, 5001, -4*w^3 + 2*w^2 + 26*w - 3]', '[5001, 5001, -4*w^3 - 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11*w^2 - 109*w + 32]', '[5091, 5091, 5*w^3 - 6*w^2 - 23*w + 9]', '[5093, 5093, 6*w^3 - 2*w^2 - 40*w - 13]', '[5093, 5093, 3*w^2 - 3*w - 17]', '[5093, 5093, 6*w^3 - 5*w^2 - 29*w + 3]', '[5093, 5093, 2*w^3 + w^2 - 9*w - 13]', '[5098, 5098, -8*w^3 - 4*w^2 + 51*w + 35]', '[5102, 5102, 10*w^3 - 4*w^2 - 55*w - 1]', '[5102, 5102, w^3 + w^2 - 12*w - 4]', '[5107, 5107, 3*w^3 - 19*w - 15]', '[5108, 2554, -w^3 - 8*w^2 + 19*w + 16]', '[5108, 2554, -w^3 - 2*w^2 + 15*w - 2]', '[5109, 5109, -5*w^3 + w^2 + 28*w - 3]', '[5112, 1278, w^3 - 3*w^2 + 5*w - 9]', '[5114, 5114, -2*w^3 - 2*w^2 + 19*w + 1]', '[5116, 2558, 5*w^3 + 2*w^2 - 21*w - 12]', '[5119, 5119, -2*w^3 - 5*w^2 + 20*w + 12]', '[5119, 5119, -3*w^3 + 6*w^2 + 15*w - 25]', '[5121, 5121, -7*w^3 + 6*w^2 + 37*w - 21]', '[5122, 5122, 2*w^3 - w^2 - 5*w - 6]', '[5122, 5122, -6*w^3 + 39*w + 19]', '[5126, 5126, 5*w^3 - w^2 - 26*w - 4]', '[5126, 5126, 3*w^3 - 3*w^2 - 8*w - 8]', '[5126, 5126, -w^2 + 7*w - 10]', '[5126, 5126, -w^3 + 4*w^2 - 6*w - 7]', '[5128, 1282, -5*w^3 - 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7]', '[5261, 5261, w^3 + 2*w^2 - 11*w - 11]', '[5262, 5262, 4*w^3 - 2*w^2 - 25*w - 13]', '[5266, 5266, -3*w^2 - 9*w - 8]', '[5267, 5267, -7*w^3 + 5*w^2 + 34*w - 3]', '[5272, 1318, -w^3 - 3*w^2 + 11*w + 13]', '[5272, 1318, -5*w^3 + w^2 + 31*w + 13]', '[5273, 5273, -15*w^3 + 8*w^2 + 85*w - 19]', '[5273, 5273, -7*w^3 + 4*w^2 + 36*w - 2]', '[5274, 5274, -20*w^3 + 13*w^2 + 113*w - 28]', '[5274, 5274, -2*w^3 + 9*w - 7]', '[5276, 2638, 7*w^3 - 10*w^2 - 17*w - 8]', '[5276, 2638, w^3 - 4*w^2 + w + 10]', '[5276, 2638, 2*w^3 + 3*w^2 - 2*w - 5]', '[5276, 2638, 3*w^3 - 4*w^2 - 13*w + 12]', '[5277, 5277, -7*w^3 + 6*w^2 + 35*w - 7]', '[5279, 5279, -7*w^3 + 5*w^2 + 40*w - 19]', '[5279, 5279, -4*w^3 + 30*w + 21]', '[5281, 5281, w^3 - 12*w]', '[5284, 2642, 5*w^3 - 6*w^2 - 13*w - 6]', '[5287, 5287, w^3 - w^2 - 2*w + 13]', '[5287, 5287, -10*w^3 + 5*w^2 + 56*w - 4]', '[5293, 5293, 5*w^3 - w^2 - 32*w - 15]', '[5296, 662, -6*w^3 + 38*w + 6]', '[5302, 5302, 2*w^3 + w^2 - 13*w - 16]', '[5302, 5302, 2*w^3 + w^2 - 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7]', '[5324, 2662, -3*w^2 - 4*w + 9]', '[5324, 2662, -2*w^3 - w^2 + 16*w + 15]', '[5326, 5326, 2*w^3 - 3*w^2 - 13*w - 2]', '[5329, 73, -w^3 + 3*w^2 + w - 10]', '[5329, 73, -w^3 + w^2 + w - 8]', '[5331, 5331, -5*w^3 + w^2 + 32*w - 1]', '[5331, 5331, -8*w^3 + 6*w^2 + 45*w - 10]', '[5333, 5333, 9*w^3 - 6*w^2 - 49*w + 9]', '[5333, 5333, 2*w^3 - 16*w - 3]', '[5337, 5337, -10*w^3 + 4*w^2 + 55*w - 4]', '[5344, 668, 6*w^3 - 32*w - 14]', '[5346, 198, 3*w^3 - 3*w^2 - 18*w]', '[5346, 198, 3*w^3 + 3*w^2 - 12*w - 12]', '[5346, 5346, w^2 + 3*w - 10]', '[5346, 5346, 5*w^3 + w^2 - 24*w - 6]', '[5349, 5349, -11*w^3 + 7*w^2 + 60*w - 11]', '[5349, 5349, -7*w^3 - w^2 + 27*w - 10]', '[5352, 1338, w^3 + w^2 - 3*w - 11]', '[5353, 5353, 5*w^3 - 2*w^2 - 29*w - 5]', '[5353, 5353, -w^2 - 6]', '[5353, 5353, -4*w^3 + 12*w^2 - 9]', '[5353, 5353, 2*w^3 + 5*w^2 - 21*w - 11]', '[5354, 5354, 5*w^3 + 4*w^2 - 26*w - 21]', '[5357, 5357, -2*w^3 + 4*w^2 + 12*w - 7]', '[5357, 5357, 5*w^2 - 11*w - 1]', '[5357, 5357, 2*w^3 - 2*w^2 - 18*w - 5]', '[5357, 5357, 3*w^2 - 7*w - 9]', '[5359, 5359, -14*w^3 + 9*w^2 + 75*w - 15]', '[5359, 5359, -w^3 - w^2 + 12*w + 3]', '[5361, 5361, 6*w^3 - w^2 - 44*w + 18]', '[5364, 2682, -4*w^3 + 5*w^2 + 20*w - 21]', '[5366, 5366, -7*w^3 - 2*w^2 + 36*w + 23]', '[5367, 5367, -5*w^3 + 3*w^2 + 24*w - 1]', '[5371, 5371, 6*w^3 - 4*w^2 - 29*w + 10]', '[5371, 5371, 2*w^3 + 4*w^2 - 18*w - 17]', '[5372, 2686, -w^3 - 2*w^2 + w + 28]', '[5372, 2686, -2*w^3 - 5*w^2 + 16*w + 25]', '[5373, 597, 2*w^3 - 4*w^2 - 10*w + 13]', '[5373, 5373, -w^3 - 3*w^2 + 9*w + 22]', '[5374, 5374, 2*w^3 + 4*w^2 - 7*w - 9]', '[5378, 5378, -w^3 - 2*w - 5]', '[5378, 5378, 2*w^3 + 2*w^2 - 5*w + 5]', '[5379, 5379, 12*w^3 - 9*w^2 - 70*w + 22]', '[5379, 5379, 4*w^3 - 3*w^2 - 26*w + 10]', '[5379, 5379, -5*w^3 + 7*w^2 + 13*w]', '[5379, 5379, -6*w^3 + 5*w^2 + 38*w - 4]', '[5382, 5382, -w^2 + w - 6]', '[5386, 5386, -3*w^3 + 24*w + 13]', '[5386, 5386, 2*w^3 - 5*w^2 - 9*w + 20]', '[5388, 2694, -3*w^3 - 2*w^2 + 23*w + 12]', '[5389, 5389, -w^3 - w^2 - 2*w - 7]', '[5389, 5389, 8*w^3 + 5*w^2 - 37*w - 19]', '[5389, 5389, -5*w^3 + 7*w^2 + 21*w - 16]', '[5389, 5389, w^2 + 3*w - 11]', '[5393, 5393, -5*w^3 - 2*w^2 + 27*w + 21]', '[5398, 5398, 3*w^3 - 2*w^2 - 20*w - 7]', '[5403, 5403, -4*w^3 - 2*w^2 + 21*w + 18]', '[5406, 5406, -3*w^3 - w^2 + 22*w + 18]', '[5406, 5406, -3*w^3 - 2*w^2 + 16*w + 19]', '[5407, 5407, -3*w^3 + 5*w^2 + 20*w - 9]', '[5408, 676, -6*w^3 + 4*w^2 + 28*w + 2]', '[5412, 2706, 2*w^3 - 3*w^2 - 4*w - 7]', '[5412, 2706, -7*w^3 - 2*w^2 + 39*w + 30]', '[5412, 2706, 3*w^3 - 2*w^2 - 19*w - 6]', '[5412, 2706, -12*w^3 - 3*w^2 + 68*w + 37]', '[5413, 5413, -4*w^3 + 3*w^2 + 22*w - 14]', '[5414, 5414, -4*w^3 + 25*w - 5]', '[5417, 5417, -w^2 - 4*w - 8]', '[5419, 5419, w^3 - w^2 - 3*w - 8]', '[5421, 5421, -5*w^3 + w^2 + 29*w + 14]', '[5422, 5422, 4*w^3 + 3*w^2 - 25*w - 14]', '[5422, 5422, 2*w^3 + w^2 - 5*w - 6]', '[5424, 678, -4*w^3 + 2*w^2 + 18*w + 2]', '[5424, 678, 10*w^3 - 6*w^2 - 54*w + 20]', '[5426, 5426, 4*w^3 - w^2 - 19*w - 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45*w - 27]', '[5454, 5454, -3*w^3 + 5*w^2 + 24*w - 2]', '[5457, 5457, -6*w^3 + 2*w^2 + 39*w - 8]', '[5457, 5457, 3*w^3 - w^2 - 11*w + 6]', '[5463, 5463, -6*w^3 + 2*w^2 + 31*w + 12]', '[5464, 1366, w^3 + w^2 - 3*w - 13]', '[5466, 5466, -3*w^3 + 22*w - 1]', '[5469, 5469, 4*w^3 - 19*w - 6]', '[5471, 5471, -5*w^3 + 6*w^2 + 23*w - 11]', '[5471, 5471, -7*w^3 + 3*w^2 + 37*w + 2]', '[5482, 5482, -5*w^3 + 3*w^2 + 28*w]', '[5483, 5483, -2*w^3 - 2*w^2 + 15*w + 18]', '[5483, 5483, 6*w^3 - 34*w - 7]', '[5484, 2742, -6*w^3 + w^2 + 34*w + 13]', '[5484, 2742, 3*w^2 - 8*w + 5]', '[5492, 2746, -2*w^3 + 3*w^2 + 14*w + 5]', '[5493, 5493, -5*w^3 - w^2 + 26*w + 19]', '[5493, 5493, -2*w^3 + 2*w^2 + 10*w - 13]', '[5494, 5494, 2*w^3 + 4*w^2 - 9*w - 5]', '[5494, 5494, -4*w^3 - w^2 + 27*w + 12]', '[5496, 1374, -7*w^3 + 5*w^2 + 39*w - 7]', '[5498, 5498, -6*w^2 - 13*w - 3]', '[5498, 5498, -w^3 - 3*w^2 + 14*w + 6]', '[5501, 5501, -w^3 + 3*w^2 + 7*w - 14]', '[5501, 5501, 4*w^3 - 3*w^2 - 14*w - 4]', '[5506, 5506, -4*w^2 - w + 19]', '[5506, 5506, 5*w^3 + w^2 - 26*w - 6]', '[5507, 5507, w^3 + w^2 - 7*w - 14]', '[5508, 102, -6*w^3 + 3*w^2 + 30*w + 3]', '[5508, 102, -3*w^3 + 21*w + 6]', '[5508, 2754, w^3 - 2*w^2 - w + 8]', '[5508, 2754, -2*w^3 - 3*w^2 + 4*w + 7]', '[5511, 5511, -12*w^3 + 2*w^2 + 69*w + 16]', '[5511, 5511, 10*w^3 - 8*w^2 - 57*w + 28]', '[5512, 1378, -w^3 + w^2 + w - 11]', '[5514, 5514, 5*w^3 - w^2 - 34*w + 6]', '[5514, 5514, -4*w^3 - 2*w^2 + 25*w + 11]', '[5517, 5517, 11*w^3 - 7*w^2 - 61*w + 12]', '[5517, 5517, -2*w^3 + 4*w^2 + 12*w - 11]', '[5522, 5522, -2*w^3 + 4*w^2 + 9*w - 7]', '[5522, 5522, 4*w^3 - 19*w - 5]', '[5522, 5522, 4*w^3 + 3*w^2 - 15*w - 2]', '[5522, 5522, 7*w^3 - 2*w^2 - 42*w - 1]', '[5524, 2762, 5*w^3 - 2*w^2 - 31*w]', '[5524, 2762, -w^3 - 2*w^2 + 3*w - 4]', '[5526, 5526, -6*w^3 + 3*w^2 + 29*w - 14]', '[5527, 5527, 3*w^3 - 3*w^2 - 9*w - 10]', '[5528, 1382, 5*w^3 + w^2 - 31*w - 9]', '[5531, 5531, 2*w^3 - 5*w^2 - 5*w + 7]', '[5534, 5534, 7*w^2 + 11*w - 2]', '[5536, 692, -4*w^3 + 2*w^2 + 18*w]', '[5538, 5538, -4*w^3 + 19*w + 15]', '[5541, 5541, -5*w^3 + 3*w^2 + 29*w]', '[5542, 5542, 7*w^3 - 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22*w + 1]', '[5599, 5599, -2*w^2 + 4*w + 11]', '[5599, 5599, -6*w^3 - w^2 + 39*w + 21]', '[5601, 5601, w^3 + 3*w^2 - 10*w - 15]', '[5601, 5601, 4*w^3 - 30*w + 11]', '[5602, 5602, 3*w^3 - 4*w^2 - 28*w - 9]', '[5608, 1402, -3*w^3 + 5*w^2 + 17*w - 23]', '[5608, 1402, -15*w^3 + 13*w^2 + 83*w - 41]', '[5608, 1402, 3*w^3 - 9*w^2 - w + 9]', '[5608, 1402, 3*w^3 - 5*w^2 - 7*w - 5]', '[5609, 5609, w^3 - w - 7]', '[5616, 78, 4*w^3 - 2*w^2 - 26*w + 2]', '[5616, 702, 6*w^3 - 32*w - 4]', '[5618, 5618, 4*w^3 + w^2 - 17*w - 8]', '[5619, 5619, 4*w^3 - 3*w^2 - 22*w]', '[5623, 5623, 4*w^3 - 2*w^2 - 28*w - 11]', '[5623, 5623, -4*w^3 + 5*w^2 + 21*w - 15]', '[5625, 45, -5*w^3 + 5*w^2 + 30*w - 15]', '[5627, 5627, -5*w^3 + w^2 + 29*w + 18]', '[5627, 5627, -3*w^3 - 5*w^2 + 24*w + 19]', '[5629, 5629, 5*w^3 - w^2 - 23*w - 16]', '[5629, 5629, 5*w^3 + 5*w^2 - 25*w - 16]', '[5631, 5631, 5*w^3 - 4*w^2 - 27*w + 17]', '[5632, 88, -4*w^2 + 4*w + 8]', '[5632, 88, -4*w + 12]', '[5634, 5634, w^3 - 3*w^2 - 16*w - 6]', '[5639, 5639, 5*w^3 - 30*w - 4]', '[5639, 5639, 8*w^3 - 3*w^2 - 48*w - 6]', '[5641, 5641, 3*w^3 - 2*w^2 - 19*w - 7]', '[5641, 5641, -3*w^3 - 2*w^2 + 21*w + 19]', '[5646, 5646, -6*w^3 + 8*w^2 + 19*w - 3]', '[5651, 5651, 3*w^2 - 6*w - 10]', '[5653, 5653, 11*w^3 - 6*w^2 - 61*w + 7]', '[5654, 5654, 3*w^3 + 2*w^2 - 26*w + 1]', '[5654, 5654, 4*w^3 - 4*w^2 - 13*w - 1]', '[5657, 5657, w^3 + w^2 - 3*w - 12]', '[5657, 5657, 4*w^3 - 2*w^2 - 18*w - 1]', '[5657, 5657, -3*w^3 + 3*w^2 + 19*w - 12]', '[5657, 5657, 4*w^3 + 2*w^2 - 16*w - 7]', '[5658, 5658, -2*w^3 + 4*w^2 + 9*w - 11]', '[5658, 5658, 5*w^3 - 6*w^2 - 18*w + 7]', '[5664, 708, -4*w^3 + 2*w^2 + 26*w]', '[5666, 5666, -8*w^3 - w^2 + 43*w + 28]', '[5666, 5666, 4*w^3 + 3*w^2 - 27*w - 14]', '[5668, 2834, -w^3 + 2*w^2 + 9*w - 8]', '[5669, 5669, 8*w^3 - 9*w^2 - 27*w - 9]', '[5671, 5671, 5*w^3 - w^2 - 33*w - 12]', '[5674, 5674, -4*w^3 - 4*w^2 + 27*w + 21]', '[5674, 5674, 7*w^3 - w^2 - 38*w - 12]', '[5678, 5678, 9*w^3 - 52*w - 15]', '[5678, 5678, 8*w^3 - 5*w^2 - 41*w + 4]', '[5682, 5682, 3*w^3 + 5*w^2 - 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2*w^2 + 21*w + 14]', '[229, 229, -w^3 + 2*w^2 + 3*w - 5]', '[233, 233, w^3 - 3*w - 3]', '[233, 233, -3*w^3 + 3*w^2 + 15*w - 8]', '[241, 241, 4*w^2 - 7*w - 8]', '[241, 241, w^3 + w^2 - 4*w - 5]', '[251, 251, 2*w^3 - w^2 - 13*w - 1]', '[251, 251, 2*w^3 - 9*w - 6]', '[257, 257, w^3 - 8*w]', '[263, 263, -w^3 + 2*w^2 + 5*w - 7]', '[269, 269, 3*w^3 - 3*w^2 - 12*w - 1]', '[271, 271, 2*w^3 - w^2 - 12*w - 2]', '[271, 271, 9*w^3 - 5*w^2 - 50*w + 9]', '[277, 277, w^3 - 2*w^2 - 6*w + 6]', '[277, 277, w^3 + w^2 - 7*w - 2]', '[281, 281, 4*w^3 - 2*w^2 - 24*w + 5]', '[281, 281, -7*w^3 + 4*w^2 + 40*w - 12]', '[289, 17, -5*w^3 + 5*w^2 + 26*w - 15]', '[293, 293, -w^3 + 2*w^2 + 4*w - 4]', '[293, 293, -9*w^3 + 5*w^2 + 51*w - 12]', '[307, 307, -2*w^3 + 2*w^2 + 12*w - 7]', '[311, 311, -4*w^3 + 24*w + 11]', '[313, 313, 2*w^3 - 9*w - 4]', '[317, 317, 2*w^3 - 4*w^2 - 2*w - 3]', '[317, 317, 2*w^3 - 14*w - 7]', '[331, 331, -3*w^3 + 19*w + 3]', '[349, 349, -w^3 - 2*w^2 + 8*w + 8]', '[349, 349, w^3 + w^2 - 5*w - 8]', '[361, 19, -w^3 + w^2 + 7*w - 6]', '[361, 19, w^3 + w^2 - 3*w - 4]', '[373, 373, 2*w^3 - w^2 - 11*w - 3]', '[379, 379, -4*w^3 + 25*w + 14]', '[383, 383, -3*w^3 + w^2 + 15*w - 2]', '[383, 383, 3*w^3 - 4*w^2 - 10*w]', '[401, 401, 4*w^3 - w^2 - 24*w - 4]', '[409, 409, w^2 + 5*w + 5]', '[419, 419, w^2 - 2*w - 6]', '[419, 419, -6*w^3 + 3*w^2 + 34*w - 8]', '[433, 433, 3*w^3 - 16*w - 6]', '[433, 433, 3*w^3 - w^2 - 16*w - 5]', '[443, 443, -w^3 + 2*w^2 + w + 3]', '[449, 449, 2*w^2 - 2*w - 5]', '[457, 457, -4*w^3 + 4*w^2 + 20*w - 9]', '[457, 457, w^2 + w - 7]', '[463, 463, w^3 - 7*w - 7]', '[463, 463, w^3 + 2*w^2 - 5*w - 9]', '[487, 487, w^3 + 2*w^2 - 5*w - 5]', '[487, 487, -w^3 + w^2 + 6*w - 7]', '[509, 509, -2*w^3 - 2*w^2 + 13*w + 10]', '[509, 509, 3*w^3 - 17*w - 3]', '[509, 509, -5*w^3 + 3*w^2 + 30*w - 11]', '[509, 509, -w^3 - 2*w^2 + 4*w + 6]', '[521, 521, -2*w^3 - w^2 + 9*w + 7]', '[541, 541, -2*w^3 - 2*w^2 + 12*w + 9]', '[541, 541, -2*w^3 + 12*w + 9]', '[547, 547, 2*w^3 + w^2 - 7*w - 3]', '[547, 547, 5*w^3 - 3*w^2 - 30*w + 3]', '[557, 557, w^3 + 2*w^2 - 5*w - 11]', '[557, 557, -w^3 + w^2 + 3*w - 4]', '[563, 563, 3*w^3 - w^2 - 15*w - 4]', '[569, 569, 2*w^2 - w - 8]', '[577, 577, 4*w^3 - 22*w - 7]', '[593, 593, -3*w^3 + w^2 + 17*w + 4]', '[607, 607, -w^3 - 3*w^2 + w + 4]', '[613, 613, 3*w^3 - 2*w^2 - 14*w]', '[613, 613, w^2 - 3*w - 5]', '[619, 619, -w^3 + 2*w^2 + 4*w - 10]', '[625, 5, -5]', '[641, 641, -3*w^3 - 3*w^2 + 12*w + 7]', '[643, 643, 2*w^3 + 2*w^2 - 14*w - 13]', '[643, 643, 3*w^3 - 19*w - 7]', '[647, 647, w^3 - 5*w - 7]', '[653, 653, -3*w^3 + 2*w^2 + 14*w - 2]', '[659, 659, -6*w^3 + 2*w^2 + 34*w - 1]', '[659, 659, -2*w^3 + w^2 + 17*w + 9]', '[683, 683, w^3 + 2*w^2 - 7*w - 7]', '[691, 691, 3*w^3 - 15*w - 7]', '[701, 701, w^3 + 2*w^2 - 6*w - 10]', '[701, 701, -w^3 + 3*w^2 + 6*w - 13]', '[701, 701, 5*w^3 - 2*w^2 - 30*w + 4]', '[701, 701, 4*w^3 - 2*w^2 - 21*w + 2]', '[727, 727, -2*w^3 - 3*w^2 + 9*w + 7]', '[743, 743, 3*w - 4]', '[751, 751, w^3 - 9*w - 3]', '[757, 757, w^3 - 5*w^2 + 4*w + 7]', '[757, 757, 4*w^3 - 5*w^2 - 11*w - 5]', '[761, 761, 4*w^3 - 5*w^2 - 20*w + 16]', '[769, 769, -3*w^3 + 16*w + 12]', '[773, 773, 2*w^3 + 2*w^2 - 11*w - 10]', '[773, 773, w^3 - 3*w - 5]', '[773, 773, -w^3 + 2*w^2 + 9*w + 3]', '[773, 773, 5*w^3 - w^2 - 27*w]', '[787, 787, -4*w^3 + 3*w^2 + 22*w - 4]', '[787, 787, -2*w^3 + w^2 + 14*w - 6]', '[797, 797, 2*w^3 - w^2 - 14*w + 2]', '[797, 797, -3*w^3 + 2*w^2 + 19*w - 7]', '[811, 811, 2*w^3 + w^2 - 14*w - 12]', '[811, 811, 2*w^3 + 2*w^2 - 8*w - 3]', '[829, 829, -2*w^3 + 14*w + 11]', '[857, 857, -3*w^3 + 3*w^2 + 14*w - 7]', '[859, 859, 3*w^3 - w^2 - 15*w]', '[859, 859, -11*w^3 + 7*w^2 + 60*w - 15]', '[863, 863, 2*w^2 - 2*w - 13]', '[863, 863, 2*w^3 + w^2 - 12*w - 4]', '[877, 877, -6*w^3 - 2*w^2 + 32*w + 19]', '[887, 887, 3*w^3 + w^2 - 14*w - 7]', '[887, 887, 2*w^3 - w^2 - 15*w - 5]', '[911, 911, 3*w^3 - 18*w - 2]', '[919, 919, w^3 - w^2 - 6*w - 5]', '[919, 919, -4*w^3 + w^2 + 24*w - 2]', '[941, 941, 3*w^3 - 3*w^2 - 13*w]', '[947, 947, 2*w^3 - 2*w^2 - 10*w - 1]', '[947, 947, -3*w^3 + 2*w^2 + 14*w + 6]', '[953, 953, -4*w^3 + 3*w^2 + 21*w - 3]', '[953, 953, 4*w^3 - w^2 - 23*w + 1]', '[961, 31, -2*w^3 + 3*w^2 + 12*w - 8]', '[961, 31, 3*w^2 - 4*w - 6]', '[967, 967, -5*w^3 - 3*w^2 + 23*w + 14]', '[971, 971, 5*w^3 - w^2 - 27*w - 8]', '[971, 971, -9*w^3 + 6*w^2 + 50*w - 12]', '[983, 983, -w^3 + w^2 + 10*w + 3]', '[997, 997, 2*w^3 + w^2 - 11*w - 3]', '[997, 997, w^3 + 2*w^2 - 6*w - 8]', '[997, 997, -5*w^3 + 4*w^2 + 29*w - 15]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 15952, 'disc_rad': 1994, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 1], [1, 1]]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[2, 1], [1, 2]]], [13, [[3, 1], [1, 1]]], [17, [[2, 1], [1, 2]]], [19, [[2, 2]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[4, 1]]], [53, [[3, 1], [1, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 12], 'galois_label': '4T5', 'galt': 5, 'grd': 70.88416711072195, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.15952.1', 'local_algs': ['2.4.4.5', 'm997.1.1.0', 'm997.1.1.0', 'm997.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 997], 'rd': 11.2383818778, 'regulator': {'__RealLiteral__': 0, 'data': '11.0135361031', 'prec': 44}, 'res': {'gal': ['1,0,-94,0,2725,0,-32422,0,167834,0,-389290,0,462669,0,-302046,0,110098,0,-21730,0,2109,0,-82,0,1'], 'sib': ['-190,-162,336,116,-50,-2,1', '-4,0,32,0,-12,0,1', '2403,-1442,-2070,616,587,-28,-44,0,1', '27,-126,-42,1040,-1771,562,1016,-888,99,114,-32,-2,1', '625,0,-7125,0,9418,0,-4113,0,738,0,-53,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{3} - 5 a - 3 \\)', '\\( a^{3} + a^{2} - 4 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}