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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 10889, 'field_bad_primes': [10889], 'field_label': '4.4.10889.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.10889.1-1.1-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [], 'hecke_eigenvalues': [1, 0, 3, 4, -4, 2, -2, -2, 2, 2, 6, -4, 8, -2, 10, 4, -6, -18, -10, 4, 12, 2, -10, 8, -12, -4, -6, -10, 8, 18, -20, -24, 8, -18, 20, 18, 8, -18, 10, -14, 14, 18, -8, -16, 8, 8, 6, 18, 8, -2, -18, 12, -4, 18, 30, 14, 18, -30, -14, -8, -28, -12, -20, 4, -28, 0, 26, -22, -2, -24, 2, -32, -16, 22, 10, -20, -24, 34, 30, 2, -10, 22, 4, 4, -8, -40, 12, 20, -22, -40, 20, -28, 0, -8, 16, -16, 4, -30, 20, -12, 10, -6, -36, 28, 30, 34, -42, -42, 2, -22, -4, 50, 4, 20, 34, 36, -34, 30, -20, 36, 4, 30, 10, -34, -40, 4, 20, 24, 32, -42, -50, 18, -20, 4, -14, 42, 38, -44, -20, 42, -8, 20, -44, -14, 34, 42, 38, -6, -32, 0, -14, -10, 4, -8, 16, 18, 18, -30, -38, -6, 6, 6, -18, -56, -16, 60, 30, 32, 32, -22, 42, -58, 34, -46, 10, 30, 42, -32, -60, 36, -18, 22, 6, -44, 28, 6, -54, -32, 10, -4, -36, 4, 30, -30, -12, -12, 54, 54, -34, -66, 2, 66, 58, -58, 10, 62, 28, 12, 24, 36, 68, -22, 30, -22, -8, 66, -24, -22, 38, -56, 64, 64, -8, 44, 72, 32, -14, 14, 52, 16, 44, 14, 2, -66, 0, -12, -16, -64, 34, -56, 0, -16, 32, 32, 24, 12, -68, 30, -2, 32, -26, -38, -22, 18, 36, -44, 44, 12, -40, -60, -26, 50, 62, 30, 74, -66, 58, -54, 66, -70, -28, -36, 70, 26, -60, 24, -8, -22, 26, 0, -46, -34, 16, 42, -54, 6, 54, -4, 60, -76, 58, -10, 10, 54, 78], 'hecke_polynomial': 'x', 'label': '4.4.10889.1-1.1-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 10889, 'ideals': ['[1, 1, 1]', '[2, 2, -w + 1]', '[4, 4, w + 1]', '[7, 7, -w + 2]', '[8, 2, -w^3 + 5*w + 3]', '[8, 8, -w^3 + w^2 + 4*w - 2]', '[11, 11, w^3 - w^2 - 5*w + 4]', '[11, 11, w^3 - w^2 - 4*w + 1]', '[14, 14, -w^3 + 6*w + 3]', '[16, 2, 2]', '[16, 16, -w^2 + 3*w]', '[17, 17, -w^3 + w^2 + 5*w]', '[22, 22, -w^2 + 3]', '[22, 22, w^3 - 2*w^2 - 3*w + 2]', '[25, 5, -w^2 + w + 3]', '[25, 5, -w^2 + 2]', '[28, 28, -w^2 + w + 2]', '[29, 29, w^3 - 2*w^2 - 4*w + 4]', '[29, 29, -w^3 + 4*w + 2]', '[32, 4, -2*w + 2]', '[32, 32, -w^3 + 4*w - 1]', '[34, 34, w^3 - 2*w^2 - 4*w + 5]', '[37, 37, 4*w^3 - 2*w^2 - 21*w - 4]', '[43, 43, 4*w^3 - 2*w^2 - 20*w - 3]', '[44, 44, w^3 - w^2 - 3*w + 3]', '[44, 44, w^3 - 5*w]', '[47, 47, -w^3 + 6*w]', '[49, 49, -w^3 + w^2 + 6*w - 1]', '[50, 10, -w^3 + 7*w]', '[50, 10, w^3 - 2*w^2 - 2*w + 3]', '[53, 53, w^3 - w^2 - 5*w - 2]', '[56, 14, -w^3 + 7*w + 1]', '[56, 56, -2*w^3 + 3*w^2 + 8*w - 5]', '[58, 58, w + 3]', '[58, 58, -w^3 + w^2 + 6*w - 2]', '[64, 4, w^3 - 2*w^2 - 3*w + 5]', '[64, 8, 2*w + 2]', '[64, 64, -w^2 + 2*w + 3]', '[68, 68, -w^3 + 6*w + 5]', '[74, 74, 2*w^3 - w^2 - 9*w]', '[77, 77, -2*w^3 + w^2 + 9*w + 1]', '[77, 77, -2*w - 3]', '[81, 3, -3]', '[83, 83, 2*w^3 - w^2 - 10*w - 4]', '[86, 86, 2*w^3 - 2*w^2 - 9*w + 1]', '[88, 22, -w^3 + 5*w - 1]', '[88, 22, w^3 - 7*w - 3]', '[88, 88, -w^3 + 7*w - 2]', '[88, 88, -w^3 + w^2 + 5*w - 5]', '[89, 89, w^3 - 2*w^2 - 4*w + 2]', '[89, 89, 2*w - 3]', '[94, 94, -w^2 + 4*w - 1]', '[98, 98, -w^3 + 5*w - 2]', '[100, 20, -2*w^3 + w^2 + 9*w - 2]', '[100, 20, -w^3 + 4*w + 3]', '[101, 101, 6*w^3 - 3*w^2 - 31*w - 5]', '[106, 106, w^3 - w^2 - w - 1]', '[107, 107, -w^3 + w^2 + 4*w - 5]', '[107, 107, 3*w^3 - 2*w^2 - 14*w + 2]', '[112, 14, -2*w + 4]', '[112, 112, -2*w^3 + w^2 + 10*w - 1]', '[113, 113, 3*w^3 - 2*w^2 - 16*w - 2]', '[116, 116, -w^3 + 6*w - 3]', '[116, 116, -w^2 - 2*w + 3]', '[119, 119, -2*w^3 + 2*w^2 + 8*w - 1]', '[121, 11, 2*w^3 - 9*w - 4]', '[121, 11, w^3 - w^2 - 7*w + 6]', '[121, 121, -w^3 + 2*w^2 + 6*w - 2]', '[121, 121, -w + 4]', '[127, 127, 2*w^3 + w^2 - 11*w - 11]', '[128, 4, -2*w^3 + 10*w + 6]', '[128, 16, -2*w^3 + 2*w^2 + 8*w - 4]', '[128, 128, w^3 - 3*w^2 - w + 3]', '[131, 131, -2*w^3 + w^2 + 8*w - 2]', '[136, 34, -w^3 + 7*w - 3]', '[136, 136, -w^2 - w + 4]', '[139, 139, w^3 - w^2 - 3*w + 6]', '[148, 148, w^3 - 2*w^2 - 5*w + 2]', '[149, 149, w^3 - 6*w + 2]', '[149, 149, 2*w^3 - 2*w^2 - 11*w + 2]', '[151, 151, w^2 - 2*w - 4]', '[154, 154, w^3 - 2*w^2 - 3*w + 6]', '[154, 154, 3*w^3 - w^2 - 16*w - 2]', '[157, 157, w^3 + w^2 - 7*w - 4]', '[162, 6, 3*w - 3]', '[163, 163, 2*w^2 - 7]', '[166, 166, 2*w^3 - w^2 - 11*w + 2]', '[167, 167, w^2 - 4*w - 2]', '[167, 167, -2*w^3 + 2*w^2 + 10*w - 1]', '[172, 172, 2*w^3 - 3*w^2 - 6*w + 3]', '[173, 173, w^2 - w - 7]', '[175, 35, -2*w^3 + 2*w^2 + 11*w]', '[175, 35, w^3 - 2*w^2 - 2*w + 4]', '[176, 22, 2*w^3 - 2*w^2 - 10*w + 8]', '[176, 22, 2*w^3 - 2*w^2 - 8*w + 2]', '[176, 176, w^3 + w^2 - 5*w - 5]', '[176, 176, -3*w^3 + 2*w^2 + 15*w + 2]', '[178, 178, 2*w^3 - 3*w^2 - 4*w + 3]', '[178, 178, -2*w^2 + 5*w - 3]', '[179, 179, 2*w^3 - 2*w^2 - 8*w + 3]', '[181, 181, w^3 + w^2 - 4*w - 5]', '[187, 187, -2*w^3 + 3*w^2 + 9*w - 5]', '[187, 187, w^3 - 4*w - 4]', '[188, 188, -2*w^3 + w^2 + 8*w + 1]', '[191, 191, -w^3 + w^2 + 2*w - 3]', '[193, 193, -2*w^3 + 2*w^2 + 7*w - 4]', '[193, 193, -w^3 + w^2 + 6*w + 3]', '[193, 193, 2*w^3 - 3*w^2 - 8*w + 4]', '[193, 193, 2*w^3 - 11*w - 2]', '[196, 196, w^3 - 3*w^2 + 4]', '[197, 197, 3*w^3 - 2*w^2 - 14*w]', '[199, 199, -w^3 + 8*w - 2]', '[199, 199, -5*w^3 + 2*w^2 + 26*w + 4]', '[200, 10, -w^3 + 2*w^2 + 7*w - 3]', '[200, 10, -w^3 + 7*w + 5]', '[200, 40, -2*w^3 + 2*w^2 + 9*w + 1]', '[200, 40, -2*w^3 + 2*w^2 + 11*w - 5]', '[202, 202, 3*w^3 - 2*w^2 - 14*w + 1]', '[203, 203, -w^3 + w^2 + 4*w + 3]', '[203, 203, -2*w^3 + w^2 + 12*w + 2]', '[212, 212, w^3 - w^2 - 9*w - 3]', '[214, 214, -w^3 + 2*w^2 + 7*w - 6]', '[214, 214, 2*w^3 - 3*w^2 - 10*w + 5]', '[223, 223, 2*w^3 - w^2 - 9*w + 3]', '[223, 223, 2*w^2 - 3*w - 4]', '[224, 28, -2*w^3 + 12*w + 6]', '[224, 224, -w^3 + w^2 + 7*w - 3]', '[226, 226, 2*w^3 - w^2 - 8*w + 1]', '[229, 229, w^3 - w^2 - 3*w - 4]', '[232, 58, w^3 - 2*w^2 - 3*w + 7]', '[232, 58, w^3 - 2*w^2 - w + 3]', '[232, 232, -2*w^3 + 3*w^2 + 7*w - 2]', '[232, 232, -w^3 + 2*w^2 + 6*w - 1]', '[233, 233, -w - 4]', '[238, 238, -2*w^3 + 4*w^2 + 5*w - 3]', '[239, 239, -w^3 - w^2 + 5*w + 4]', '[241, 241, 2*w^3 - 2*w^2 - 7*w]', '[241, 241, -2*w^3 + w^2 + 10*w - 2]', '[242, 22, 2*w^3 - 2*w^2 - 11*w + 3]', '[242, 22, -w^3 - w^2 + 11*w - 7]', '[242, 242, -3*w^3 + 16*w + 7]', '[242, 242, -w^3 + 4*w + 5]', '[251, 251, 2*w^2 - w - 8]', '[251, 251, -3*w^3 + 3*w^2 + 14*w - 3]', '[254, 254, -w^3 + 2*w^2 + 4*w - 9]', '[256, 4, 4]', '[256, 32, -2*w^2 + 6*w]', '[256, 256, -w^3 + w^2 + 5*w + 3]', '[257, 257, -w^2 - 2]', '[257, 257, -4*w^3 + 5*w^2 + 17*w - 11]', '[257, 257, -3*w^3 + w^2 + 13*w]', '[257, 257, -2*w^3 + 3*w^2 + 7*w - 7]', '[259, 259, 3*w^3 - 16*w - 6]', '[262, 262, -w^3 + 3*w^2 + 6*w - 4]', '[269, 269, -w^3 - w^2 + 6*w + 5]', '[269, 269, w^2 + w - 5]', '[271, 271, 3*w^3 - w^2 - 16*w - 7]', '[272, 34, -2*w^3 + 2*w^2 + 10*w]', '[272, 272, -3*w^3 + 3*w^2 + 13*w - 1]', '[275, 55, -w^3 + w^2 + 2*w + 3]', '[275, 55, -2*w^3 + 3*w^2 + 5*w - 3]', '[275, 55, 2*w^3 - w^2 - 12*w + 2]', '[275, 55, w^3 - w^2 - 7*w + 2]', '[278, 278, -w^3 + 3*w^2 + 7*w - 7]', '[283, 283, 4*w^3 - w^2 - 20*w - 8]', '[283, 283, w^2 - 2*w - 6]', '[283, 283, 2*w^3 - 12*w - 7]', '[283, 283, 3*w^3 - 3*w^2 - 13*w + 6]', '[289, 289, -2*w^3 + w^2 + 11*w + 5]', '[296, 74, 3*w^3 - 2*w^2 - 15*w + 3]', '[296, 296, 3*w^3 - 13*w - 2]', '[298, 298, w^2 - 6*w + 3]', '[298, 298, 2*w^3 - w^2 - 9*w + 4]', '[301, 301, 2*w^3 + w^2 - 14*w - 6]', '[302, 302, -w^3 + 3*w^2 + 2*w - 4]', '[307, 307, w^3 - 6*w - 6]', '[308, 308, 2*w^3 - 4*w^2 - 7*w + 7]', '[308, 308, w^3 - 8*w + 1]', '[311, 311, 2*w^3 - w^2 - 13*w + 5]', '[313, 313, -2*w^3 + 3*w^2 + 7*w + 1]', '[314, 314, -w^3 + 3*w^2 - w - 3]', '[319, 319, 2*w^3 - 2*w^2 - 10*w - 1]', '[319, 319, -2*w^3 + 8*w - 1]', '[319, 319, 2*w^3 - 2*w^2 - 12*w + 7]', '[319, 319, -w^2 - 2*w + 4]', '[324, 12, -3*w - 3]', '[326, 326, -2*w^3 + 2*w^2 + 7*w - 7]', '[329, 329, -w^3 - w^2 + 10*w - 1]', '[332, 332, w^3 - 9*w + 4]', '[334, 334, -w^3 + 5*w^2 - 2*w - 2]', '[334, 334, -2*w^3 + 2*w^2 + 7*w - 3]', '[337, 337, w^3 - 8*w]', '[337, 337, 3*w^3 - 3*w^2 - 13*w + 4]', '[343, 7, -4*w^3 + 3*w^2 + 19*w - 5]', '[343, 343, -2*w^3 + w^2 + 11*w - 3]', '[344, 86, 3*w^3 - 2*w^2 - 17*w + 5]', '[344, 344, 2*w^3 - w^2 - 12*w - 1]', '[346, 346, -w^3 + 2*w^2 + 6*w - 7]', '[349, 349, 2*w^3 - w^2 - 8*w - 4]', '[350, 70, -2*w^3 + 9*w + 5]', '[350, 70, -2*w^3 + w^2 + 7*w - 2]', '[352, 44, -2*w^2 + 6]', '[352, 44, 2*w^3 - 4*w^2 - 6*w + 4]', '[352, 352, -w^3 + w^2 + 2*w - 4]', '[352, 352, -2*w^3 + 2*w^2 + 7*w - 1]', '[356, 356, -w^2 - 4*w + 1]', '[356, 356, 2*w^2 - w - 3]', '[358, 358, 2*w^3 - 4*w^2 - 7*w + 5]', '[359, 359, w^3 + w^2 - 2*w - 3]', '[359, 359, 4*w^3 - 4*w^2 - 20*w + 11]', '[362, 362, -w^3 + 3*w - 4]', '[371, 371, 2*w^3 - 2*w^2 - 6*w - 3]', '[373, 373, -8*w^3 + 2*w^2 + 43*w + 16]', '[373, 373, 2*w^3 - 10*w - 1]', '[374, 374, -3*w^3 + w^2 + 14*w]', '[374, 374, -w^2 + 2*w - 3]', '[376, 94, -5*w^3 + 2*w^2 + 27*w + 5]', '[376, 376, w^3 - 2*w^2 - 2*w + 5]', '[379, 379, w^3 + w^2 - 5*w - 10]', '[382, 382, -w^3 + 4*w^2 + 3*w - 4]', '[383, 383, 2*w^3 - 3*w^2 - 12*w + 8]', '[386, 386, -2*w^3 + 5*w^2 + 7*w - 6]', '[386, 386, 3*w^3 - w^2 - 15*w - 1]', '[386, 386, -w^3 + w + 2]', '[386, 386, w^2 - 5*w]', '[389, 389, -2*w^3 + 2*w^2 + 7*w - 2]', '[389, 389, -3*w^3 + w^2 + 18*w - 1]', '[392, 98, -3*w^3 + 4*w^2 + 11*w - 7]', '[392, 392, w^3 - 3*w^2 - 5*w + 7]', '[394, 394, 2*w^3 - 3*w^2 - 8*w + 3]', '[397, 397, 5*w^3 - 26*w - 14]', '[397, 397, 4*w^3 - 3*w^2 - 19*w - 1]', '[398, 398, -2*w^3 + w^2 + 12*w - 1]', '[398, 398, -3*w^2 + 8*w - 3]', '[400, 10, -2*w^2 + 2*w + 6]', '[400, 10, -2*w^2 + 4]', '[400, 80, w^3 - 3*w^2 - 2*w + 6]', '[400, 80, -4*w^3 + 2*w^2 + 19*w + 1]', '[404, 404, 2*w^3 - 3*w^2 - 9*w + 4]', '[406, 406, -w^2 - w + 6]', '[406, 406, -2*w^3 + w^2 + 12*w - 5]', '[407, 407, -3*w - 4]', '[407, 407, -5*w^3 + w^2 + 25*w + 6]', '[409, 409, -5*w^3 + 6*w^2 + 22*w - 12]', '[419, 419, -2*w^3 + w^2 + 12*w]', '[419, 419, -6*w^3 + 4*w^2 + 31*w]', '[424, 106, 7*w^3 - 2*w^2 - 35*w - 11]', '[424, 424, 2*w^3 - w^2 - 7*w]', '[425, 85, -2*w^3 + 9*w]', '[425, 85, -3*w^3 + w^2 + 16*w + 1]', '[428, 428, w^3 + w^2 - 8*w]', '[428, 428, -w^3 + w - 4]', '[431, 431, 2*w^2 - 5]', '[439, 439, 5*w^3 - 3*w^2 - 24*w + 1]', '[443, 443, -3*w^3 + w^2 + 13*w + 2]', '[443, 443, -w^3 + 3*w^2 + 4*w - 9]', '[446, 446, w^3 - 2*w^2 - 8*w + 5]', '[446, 446, -2*w^3 + 5*w^2 + w - 4]', '[448, 28, -3*w^3 + 2*w^2 + 13*w - 3]', '[448, 56, -2*w^2 + 2*w + 4]', '[448, 448, -3*w^3 + w^2 + 13*w + 1]', '[452, 452, w^3 - 3*w^2 - 5*w + 3]', '[457, 457, -8*w^3 + 3*w^2 + 43*w + 11]', '[458, 458, w^3 - 3*w^2 + 3*w - 3]', '[463, 463, -3*w^3 + 3*w^2 + 12*w - 1]', '[464, 58, 2*w^3 - 4*w^2 - 8*w + 8]', '[464, 58, -2*w^3 + 8*w + 4]', '[464, 464, -4*w^3 + w^2 + 21*w + 4]', '[464, 464, -2*w^3 + w^2 + 8*w + 5]', '[466, 466, w^2 + 3*w - 4]', '[467, 467, -7*w^3 + 3*w^2 + 37*w + 6]', '[467, 467, -4*w^3 + 3*w^2 + 20*w]', '[473, 473, -4*w^3 + w^2 + 23*w + 5]', '[473, 473, 2*w^2 - 2*w - 5]', '[476, 476, -2*w^3 + 11*w + 1]', '[478, 478, w^3 - w^2 - w + 3]', '[479, 479, -2*w^3 + 4*w^2 + 9*w - 10]', '[479, 479, 4*w^3 - 2*w^2 - 19*w - 2]', '[482, 482, 2*w^3 - 5*w^2 - 3*w + 2]', '[482, 482, -w^3 + w^2 + 8*w - 4]', '[484, 44, 2*w^3 - w^2 - 10*w + 5]', '[484, 44, -w^3 + 3*w^2 + 3*w - 5]', '[484, 484, -w^2 + 3*w + 4]', '[484, 484, w^2 - 3*w + 4]', '[487, 487, 2*w^3 - 3*w^2 - 12*w + 4]', '[487, 487, w^2 + w - 7]', '[493, 493, w^3 - w^2 - 8*w + 7]', '[493, 493, -2*w^3 + w^2 + 10*w - 4]', '[499, 499, 2*w^2 - w - 4]', '[502, 502, -2*w^3 + 3*w^2 + 7*w - 8]', '[502, 502, -3*w^3 + 4*w^2 + 11*w - 6]', '[508, 508, -2*w^3 + 3*w^2 + 11*w - 10]', '[512, 8, -3*w^3 + 2*w^2 + 13*w + 1]', '[512, 8, -4*w + 4]', '[512, 64, -2*w^3 + 8*w - 2]', '[512, 512, -2*w^3 + w^2 + 11*w - 4]', '[514, 514, -3*w^3 + 3*w^2 + 16*w - 4]', '[514, 514, 3*w^3 - 4*w^2 - 12*w + 13]', '[514, 514, -3*w^3 + 6*w^2 + 10*w - 9]', '[514, 514, w^3 - w^2 + 2*w - 2]', '[517, 517, -2*w^3 + w^2 + 12*w - 6]', '[517, 517, 2*w^2 - 4*w - 5]', '[518, 518, 3*w^3 - 3*w^2 - 14*w + 2]', '[524, 524, -3*w^3 - w^2 + 10*w]', '[538, 538, w^3 - 2*w^2 - w + 4]', '[538, 538, -w^3 + 6*w - 5]', '[539, 539, 2*w^2 - w - 6]', '[539, 539, -3*w^3 + 3*w^2 + 13*w]', '[541, 541, -w^3 + 3*w^2 + 3*w - 8]', '[542, 542, w^3 - 3*w - 4]', '[544, 68, 2*w^3 - 4*w^2 - 8*w + 10]', '[544, 544, -w^3 - 2*w^2 + 3*w + 4]', '[547, 547, -w^3 + 2*w^2 + 6*w - 8]', '[547, 547, -2*w^3 + 2*w^2 + 12*w - 1]', '[550, 110, -w^2 + w + 8]', '[550, 110, w^3 - 2*w + 5]', '[550, 110, w^3 + 2*w^2 - w - 4]', '[550, 110, -3*w^3 + 4*w^2 + 16*w - 13]', '[556, 556, -w^3 - w^2 - w - 5]', '[566, 566, w^3 - w^2 - 4*w - 4]', '[566, 566, 3*w^3 - 5*w^2 - 13*w + 9]', '[566, 566, -w^3 + 3*w^2 + 4*w - 6]', '[566, 566, 2*w^2 - w - 5]', '[567, 21, 3*w - 6]', '[569, 569, 4*w^3 - 3*w^2 - 21*w - 1]', '[569, 569, -w^3 + 3*w^2 - 5]', '[578, 578, -3*w^3 + 2*w^2 + 15*w - 4]', '[581, 581, -2*w^3 + 4*w^2 + 8*w - 9]', '[583, 583, -3*w^3 + 2*w^2 + 12*w + 2]', '[583, 583, -w^2 + w - 3]', '[587, 587, 7*w^3 - 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2*w^2 - 28*w - 5]', '[1588, 1588, -w^3 + 3*w^2 + 7*w - 9]', '[1591, 1591, -4*w^3 + 3*w^2 + 17*w + 1]', '[1592, 398, -5*w^3 + 2*w^2 + 27*w + 1]', '[1592, 398, -5*w^3 + 6*w^2 + 21*w - 7]', '[1592, 1592, 3*w^3 - 6*w^2 - 10*w + 11]', '[1592, 1592, -3*w^3 + 3*w^2 + 15*w + 1]', '[1594, 1594, w^3 - w^2 - 9*w + 3]', '[1594, 1594, -5*w^3 + 10*w^2 + 12*w - 13]', '[1597, 1597, -2*w^3 + 5*w^2 + 7*w - 5]', '[1597, 1597, 2*w^3 - 4*w^2 - 10*w + 5]', '[1598, 1598, -4*w^3 + 5*w^2 + 17*w - 6]', '[1600, 20, -w^3 - 2*w^2 + 11*w - 1]', '[1600, 20, w^3 - 2*w^2 - 7*w + 9]', '[1600, 40, -4*w^3 + 2*w^2 + 18*w - 4]', '[1600, 40, -2*w^3 + 8*w + 6]', '[1600, 320, -w^3 + 2*w + 5]', '[1600, 320, -2*w^3 + w^2 + 7*w + 8]', '[1603, 1603, 2*w^3 - 4*w^2 - 7]', '[1607, 1607, -8*w^3 + 3*w^2 + 40*w + 6]', '[1609, 1609, 3*w^2 - 4*w - 6]', '[1609, 1609, -2*w^3 - w^2 + 14*w + 8]', '[1613, 1613, -3*w^3 + 3*w^2 + 10*w - 5]', '[1613, 1613, 2*w^3 - 10*w + 3]', '[1616, 202, 12*w^3 - 6*w^2 - 62*w - 10]', '[1616, 1616, -2*w^3 + 3*w^2 + 8*w - 13]', '[1618, 1618, 2*w^2 - 3*w - 11]', '[1622, 1622, -3*w^3 + 13*w]', '[1622, 1622, -2*w^3 + 13*w - 7]', '[1624, 406, w^3 - 4*w^2 - 5*w + 11]', '[1624, 406, -3*w^3 + 4*w^2 + 9*w - 3]', '[1624, 1624, -w^3 - 2*w^2 + 5*w + 6]', '[1624, 1624, -3*w^3 + 3*w^2 + 11*w - 3]', '[1627, 1627, -5*w^3 + 2*w^2 + 28*w + 2]', '[1627, 1627, -3*w^3 + w^2 + 13*w - 4]', '[1627, 1627, 4*w^3 - 5*w^2 - 16*w + 4]', '[1627, 1627, -3*w^3 - w^2 + 17*w + 4]', '[1628, 1628, 4*w^3 - 4*w^2 - 23*w + 1]', '[1628, 1628, -w^2 - 3*w + 6]', '[1631, 1631, w^2 + 2*w - 8]', '[1636, 1636, -4*w^3 + 3*w^2 + 20*w - 7]', '[1639, 1639, 4*w^3 - 3*w^2 - 22*w + 14]', '[1639, 1639, -3*w^3 + w^2 + 11*w]', '[1639, 1639, 2*w^3 - 4*w^2 - 4*w + 7]', '[1639, 1639, -2*w^3 + 7*w - 6]', '[1642, 1642, -4*w^3 + 4*w^2 + 19*w - 3]', '[1646, 1646, -3*w^3 + 4*w^2 + 9*w - 4]', '[1654, 1654, 2*w^3 - 2*w^2 - 13*w + 1]', '[1654, 1654, 5*w^3 - 4*w^2 - 23*w + 4]', '[1658, 1658, -2*w^3 + 5*w^2 - 2*w - 3]', '[1658, 1658, w^3 + w^2 - 11*w - 1]', '[1661, 1661, -3*w^3 + w^2 + 17*w - 2]', '[1661, 1661, -4*w^3 + 6*w^2 + 15*w - 14]', '[1663, 1663, -4*w^3 + w^2 + 22*w + 2]', '[1666, 1666, -3*w^2 + 5]', '[1667, 1667, 2*w^3 - 2*w^2 - 8*w - 5]', '[1669, 1669, 2*w^3 - 2*w^2 - 13*w + 6]', '[1669, 1669, -4*w^3 + 2*w^2 + 21*w - 2]', '[1673, 1673, -2*w^2 + 4*w + 7]', '[1676, 1676, -3*w^3 + 3*w^2 + 16*w + 2]', '[1676, 1676, -3*w^3 + 4*w^2 + 17*w - 10]', '[1682, 58, -2*w^3 - w^2 + 15*w]', '[1682, 58, -3*w^3 + 5*w^2 + 4*w - 2]', '[1682, 1682, -3*w^3 + 14*w + 1]', '[1682, 1682, -3*w^3 + w^2 + 13*w + 7]', '[1687, 1687, 4*w^3 - 7*w^2 - 10*w + 2]', '[1687, 1687, -3*w^3 + 2*w^2 + 18*w - 6]', '[1693, 1693, w^3 - w^2 - 2*w + 9]', '[1693, 1693, -w^3 + w^2 + 9*w - 2]', '[1694, 154, -w^3 + 4*w^2 + w - 10]', '[1694, 154, w^3 - w^2 - 4]', '[1694, 1694, -w^3 + 2*w^2 + 9*w - 4]', '[1694, 1694, -4*w^3 + 3*w^2 + 23*w + 2]', '[1696, 212, 2*w^3 - 2*w^2 - 2*w - 2]', '[1696, 1696, 3*w^3 + 2*w^2 - 11*w - 2]', '[1697, 1697, 6*w^3 - 4*w^2 - 29*w - 4]', '[1697, 1697, -2*w^3 + 11*w - 2]', '[1700, 340, w^3 - 5*w^2 + 3*w + 5]', '[1700, 340, -5*w^3 + 2*w^2 + 23*w + 4]', '[1706, 1706, -3*w^3 + w^2 + 7*w - 3]', '[1706, 1706, -w^2 + 7*w - 2]', '[1712, 214, -2*w^3 + 2*w^2 + 8*w - 10]', '[1712, 214, 2*w^3 + 2*w^2 - 8*w - 6]', '[1712, 1712, w^3 - 10*w + 3]', '[1712, 1712, w^3 + 2*w^2 - 7*w - 8]', '[1717, 1717, -2*w^3 + 4*w^2 + 6*w - 11]', '[1721, 1721, -4*w^3 + 4*w^2 + 14*w - 11]', '[1721, 1721, w^3 - 6*w - 8]', '[1724, 1724, 2*w^3 + 2*w^2 - 5*w - 5]', '[1726, 1726, -w^3 + 2*w^2 + 9*w - 8]', '[1726, 1726, 5*w^3 - 27*w - 12]', '[1727, 1727, -2*w^3 + 5*w^2 + 5*w - 9]', '[1727, 1727, -3*w^3 + 20*w + 2]', '[1733, 1733, 4*w^3 - 2*w^2 - 17*w + 6]', '[1739, 1739, -7*w^3 + 7*w^2 + 35*w - 18]', '[1741, 1741, 5*w^3 - 4*w^2 - 28*w + 14]', '[1747, 1747, -w^3 - 3*w^2 + 6*w + 17]', '[1754, 1754, -w^3 + w^2 + 4*w - 8]', '[1754, 1754, -w^3 - 2*w^2 + 9*w]', '[1756, 1756, 4*w^3 - 4*w^2 - 15*w + 9]', '[1757, 1757, -2*w^3 + 5*w^2 + 6*w - 16]', '[1757, 1757, -6*w^3 + 7*w^2 + 25*w - 9]', '[1766, 1766, -3*w^3 + 6*w^2 + 8*w - 11]', '[1772, 1772, -5*w^3 - w^2 + 21*w + 5]', '[1772, 1772, -4*w^3 + 8*w^2 + 15*w - 13]', '[1778, 1778, -3*w^3 + 5*w^2 + 15*w - 19]', '[1782, 66, 3*w^2 - 9]', '[1782, 66, -3*w^3 + 6*w^2 + 9*w - 6]', '[1784, 446, 5*w^3 - 4*w^2 - 27*w + 1]', '[1784, 446, 5*w^3 - 29*w - 13]', '[1784, 1784, 2*w^3 - w^2 - 14*w + 5]', '[1784, 1784, -4*w^3 + 4*w^2 + 15*w - 13]', '[1787, 1787, 7*w^3 - 5*w^2 - 36*w + 3]', '[1789, 1789, -w^3 - w^2 + 11*w]', '[1789, 1789, w^3 + 2*w^2 - 6*w - 8]', '[1792, 28, -4*w + 8]', '[1792, 224, -4*w^3 + 2*w^2 + 20*w - 2]', '[1792, 1792, -2*w^3 + 2*w^2 + 5*w + 5]', '[1793, 1793, -5*w^3 + 5*w^2 + 26*w - 7]', '[1793, 1793, -7*w^3 + 11*w^2 + 33*w - 28]', '[1799, 1799, w^3 - 2*w^2 + 2*w - 4]', '[1799, 1799, -5*w^3 + 9*w^2 + 17*w - 16]', '[1799, 1799, 4*w^3 - 4*w^2 - 15*w + 14]', '[1799, 1799, -4*w^3 + 4*w^2 + 20*w - 3]', '[1802, 1802, w^3 + 2*w^2 - 7*w - 6]', '[1808, 226, 6*w^3 - 4*w^2 - 32*w - 4]', '[1808, 1808, -2*w^3 + w^2 + 7*w - 8]', '[1811, 1811, 4*w^3 - 2*w^2 - 17*w + 2]', '[1813, 1813, -2*w^3 + 2*w^2 + 9*w - 10]', '[1819, 1819, 2*w^3 - 2*w^2 - 5*w - 6]', '[1819, 1819, 3*w^3 - 4*w^2 - 16*w + 4]', '[1826, 1826, -w^2 + 7*w - 6]', '[1826, 1826, w^3 - 4*w^2 + 11]', '[1828, 1828, -w^2 + 7*w]', '[1832, 458, 7*w^3 - 2*w^2 - 35*w - 15]', '[1832, 1832, 4*w^3 - 5*w^2 - 15*w + 6]', '[1834, 1834, -6*w^3 + 2*w^2 + 29*w + 3]', '[1837, 1837, -2*w^3 + 4*w^2 + w - 4]', '[1837, 1837, -w^3 - 3*w^2 + 11*w + 2]', '[1837, 1837, -5*w^3 + 7*w^2 + 23*w - 14]', '[1837, 1837, w^3 + w^2 - 4*w - 9]', '[1838, 1838, -2*w^3 + 11*w - 5]', '[1838, 1838, 3*w^2 - 2*w - 11]', '[1847, 1847, 6*w^3 - 5*w^2 - 32*w + 2]', '[1847, 1847, -2*w^3 + 3*w^2 + 15*w + 1]', '[1849, 1849, 3*w^3 - w^2 - 19*w - 8]', '[1850, 370, 5*w^3 - 3*w^2 - 27*w - 1]', '[1850, 370, 2*w^3 - 3*w^2 - 14*w + 1]', '[1852, 1852, -3*w^3 + 17*w + 2]', '[1856, 116, -5*w^3 + 2*w^2 + 23*w + 3]', '[1856, 116, -w^3 - 2*w^2 + 7*w + 7]', '[1856, 232, -2*w^3 + 12*w - 6]', '[1856, 232, -2*w^2 - 4*w + 6]', '[1856, 1856, w^3 - w^2 - 9*w + 9]', '[1856, 1856, -3*w^3 - w^2 + 17*w + 7]', '[1861, 1861, 2*w^3 - 3*w^2 - 13*w + 11]', '[1861, 1861, -4*w^3 + 3*w^2 + 17*w - 5]', '[1864, 466, 5*w^3 - 25*w - 13]', '[1864, 1864, 4*w^3 - 3*w^2 - 16*w + 7]', '[1868, 1868, -w^3 - w^2 + 12*w - 4]', '[1868, 1868, -3*w^3 + 6*w^2 + 10*w - 7]', '[1874, 1874, w^3 - 3*w^2 + 6*w - 4]', '[1879, 1879, -8*w^3 + 5*w^2 + 39*w - 1]', '[1882, 1882, 2*w^3 - 4*w^2 - 7*w + 1]', '[1882, 1882, 3*w^3 - 5*w^2 - 14*w + 8]', '[1882, 1882, -w^3 + 5*w - 6]', '[1882, 1882, 5*w^3 - 6*w^2 - 23*w + 10]', '[1883, 1883, -3*w^2 + 5*w + 9]', '[1883, 1883, -w^3 + w^2 + 7*w - 10]', '[1892, 1892, 2*w^2 - 7*w + 7]', '[1892, 1892, 5*w^3 - 3*w^2 - 25*w + 3]', '[1897, 1897, 3*w^3 + w^2 - 19*w - 4]', '[1903, 1903, 2*w^3 - 3*w^2 - 13*w + 7]', '[1903, 1903, -w^3 - 2*w^2 + 6*w + 6]', '[1904, 238, -4*w^3 + 4*w^2 + 16*w - 2]', '[1904, 1904, -3*w^3 - w^2 + 16*w + 10]', '[1906, 1906, 3*w^3 - 8*w^2 - 3*w + 2]', '[1912, 478, -7*w^3 + 2*w^2 + 39*w + 15]', '[1912, 1912, -2*w^3 + 3*w^2 + 13*w - 4]', '[1916, 1916, 3*w^2 + 3*w - 8]', '[1916, 1916, 6*w^3 - w^2 - 29*w - 6]', '[1921, 1921, -2*w^3 + 3*w^2 + 5*w - 7]', '[1922, 62, 9*w^3 - 5*w^2 - 46*w - 6]', '[1922, 62, -2*w^3 + w^2 + 9*w - 8]', '[1925, 385, -5*w^3 + 2*w^2 + 28*w + 4]', '[1925, 385, -2*w^3 + 2*w^2 + 14*w + 1]', '[1925, 385, 2*w^3 + w^2 - 9*w - 9]', '[1925, 385, 2*w^3 - 14*w + 5]', '[1928, 482, 7*w^3 - 4*w^2 - 35*w - 7]', '[1928, 482, -7*w^3 + 4*w^2 + 37*w + 3]', '[1928, 1928, 3*w^3 - 4*w^2 - 11*w + 12]', '[1928, 1928, -w^2 + 2*w - 5]', '[1933, 1933, 5*w^3 - 5*w^2 - 22*w + 7]', '[1934, 1934, -w^3 + w^2 + 9*w - 11]', '[1934, 1934, -2*w^2 + w - 3]', '[1936, 22, 4*w^3 - 18*w - 8]', '[1936, 22, -2*w^3 + 2*w^2 + 14*w - 12]', '[1936, 176, -2*w^3 + 10*w^2 - 13*w + 3]', '[1936, 176, -3*w^3 + 6*w^2 + 14*w - 15]', '[1936, 242, -2*w^3 + 4*w^2 + 12*w - 4]', '[1936, 242, -2*w + 8]', '[1936, 1936, -4*w^3 + 3*w^2 + 22*w - 1]', '[1936, 1936, -4*w^3 + 5*w^2 + 18*w - 7]', '[1942, 1942, -w^3 - w^2 + 8*w - 6]', '[1946, 1946, 3*w^3 - 19*w - 14]', '[1948, 1948, w^3 + 2*w^2 - 6*w - 7]', '[1948, 1948, w^3 - 5*w^2 - 12*w + 2]', '[1949, 1949, 3*w^3 - 3*w^2 - 17*w + 4]', '[1951, 1951, -4*w^3 + 3*w^2 + 23*w - 13]', '[1954, 1954, -w^3 - 2*w^2 + 8*w - 5]', '[1958, 1958, 3*w^3 - w^2 - 13*w + 5]', '[1958, 1958, -2*w^3 + 3*w^2 + 6*w - 9]', '[1958, 1958, 4*w^2 - 9*w + 5]', '[1958, 1958, -5*w^3 + 10*w^2 + 9*w - 8]', '[1961, 1961, w^2 - 10]', '[1966, 1966, 5*w^3 - 7*w^2 - 24*w + 14]', '[1969, 1969, w^3 - w^2 - 6*w + 9]', '[1969, 1969, 7*w^3 - 9*w^2 - 29*w + 20]', '[1972, 1972, w^3 - 4*w^2 - 3*w + 6]', '[1972, 1972, -3*w^3 + w^2 + 10*w - 2]', '[1973, 1973, 9*w^3 - w^2 - 47*w - 22]', '[1973, 1973, -3*w^3 + 12*w - 2]', '[1973, 1973, w^2 - 2*w - 10]', '[1973, 1973, w^3 - w^2 - 10*w + 5]', '[1979, 1979, 5*w^3 - 3*w^2 - 23*w - 2]', '[1979, 1979, 5*w^3 - w^2 - 27*w - 14]', '[1981, 1981, -w^3 + 4*w^2 + 2*w - 12]', '[1981, 1981, 4*w^3 - 3*w^2 - 16*w - 2]', '[1981, 1981, 3*w^3 + w^2 - 22*w - 5]', '[1981, 1981, 6*w^3 - 8*w^2 - 26*w + 15]', '[1982, 1982, -4*w^3 + 5*w^2 + 15*w - 8]', '[1987, 1987, 7*w^3 - w^2 - 35*w - 14]', '[1991, 1991, -4*w^3 + 4*w^2 + 21*w - 2]', '[1991, 1991, -3*w^3 + 6*w^2 + 16*w - 16]', '[1993, 1993, -w^3 + 3*w^2 - 7]', '[1993, 1993, 3*w^2 - w - 5]', '[1993, 1993, -10*w^3 + 5*w^2 + 53*w + 9]', '[1993, 1993, -2*w^3 + 14*w - 7]', '[1996, 1996, 2*w^3 + w^2 - 5*w - 4]', '[1997, 1997, -7*w^3 + 4*w^2 + 36*w + 6]', '[2003, 2003, -3*w^3 + w^2 + 15*w - 2]', '[2008, 502, 7*w^3 - 39*w - 23]', '[2008, 502, -11*w^3 + 6*w^2 + 55*w + 5]', '[2008, 2008, 6*w^3 - 7*w^2 - 30*w + 15]', '[2008, 2008, 3*w^3 - 5*w^2 - 15*w + 17]', '[2011, 2011, -2*w^3 + 4*w^2 + 8*w - 3]', '[2011, 2011, -2*w - 7]', '[2018, 2018, w^3 - 4*w^2 - w + 6]', '[2021, 2021, -2*w^3 + 2*w^2 + 13*w - 2]', '[2023, 2023, -3*w^3 + w^2 + 13*w + 8]', '[2025, 15, 3*w^2 - 3*w - 9]', '[2025, 15, 3*w^2 - 6]', '[2026, 2026, -4*w^3 + 2*w^2 + 23*w + 3]', '[2026, 2026, -w^3 - 2*w^2 + 8*w - 1]', '[2027, 2027, -w^3 + 10*w - 2]', '[2029, 2029, 5*w^3 - 4*w^2 - 28*w + 12]', '[2029, 2029, w^3 + 2*w^2 - 4*w - 10]', '[2032, 254, 4*w^3 + 2*w^2 - 22*w - 22]', '[2032, 2032, 8*w^3 - 9*w^2 - 36*w + 21]', '[2039, 2039, -3*w^3 + w^2 + 14*w - 3]', '[2042, 2042, -2*w^3 + 2*w^2 + 13*w - 5]', '[2048, 8, -4*w^3 + 20*w + 12]', '[2048, 32, -4*w^3 + 4*w^2 + 16*w - 8]', '[2048, 256, 2*w^3 - 6*w^2 - 2*w + 6]', '[2048, 2048, -3*w^3 + 2*w^2 + 11*w - 2]', '[2053, 2053, -6*w^3 + 4*w^2 + 32*w + 1]', '[2053, 2053, 6*w^3 - 4*w^2 - 32*w + 5]', '[2053, 2053, -7*w^3 + 3*w^2 + 38*w + 13]', '[2053, 2053, -4*w^3 + w^2 + 24*w + 4]', '[2056, 514, 3*w^3 - 13*w - 7]', '[2056, 514, w^3 - 2*w^2 - w + 7]', '[2056, 514, -3*w^3 + 4*w^2 + 17*w - 9]', '[2056, 514, -w^3 + 4*w^2 + 3*w - 13]', '[2056, 2056, -2*w^3 + 3*w^2 + 15*w - 10]', '[2056, 2056, 6*w^3 - 6*w^2 - 29*w + 19]', '[2056, 2056, 3*w^3 - 2*w^2 - 9*w + 4]', '[2056, 2056, -7*w^3 + 2*w^2 + 39*w + 14]', '[2057, 187, -2*w^3 + 3*w^2 + 12*w - 12]', '[2057, 187, 4*w^3 - 5*w^2 - 15*w + 7]', '[2057, 2057, -2*w^3 + 16*w - 5]', '[2057, 2057, -4*w^3 + 4*w^2 + 18*w - 1]', '[2066, 2066, -w^3 + 4*w^2 + 5*w - 10]', '[2066, 2066, -w^3 - 2*w^2 + 12*w - 5]', '[2068, 2068, -3*w^3 + 3*w^2 + 10*w - 4]', '[2068, 2068, 2*w^3 - 2*w^2 - 9*w - 5]', '[2069, 2069, 5*w^3 - 5*w^2 - 21*w]', '[2072, 518, w^3 - 9*w - 11]', '[2072, 2072, 3*w^3 - 2*w^2 - 18*w - 1]', '[2075, 415, 7*w^3 - 4*w^2 - 34*w - 2]', '[2075, 415, -w^3 + 3*w^2 + 6*w - 11]', '[2083, 2083, -2*w^3 + 5*w^2 + 6*w - 12]', '[2086, 2086, 3*w^3 - 3*w^2 - 18*w + 10]', '[2086, 2086, 4*w^3 - 3*w^2 - 17*w]', '[2096, 262, -4*w^3 + 2*w^2 + 16*w - 4]', '[2096, 2096, -3*w^2 + 2*w + 5]', '[2098, 2098, 2*w^3 - w^2 - 16*w + 9]', '[2099, 2099, 6*w^3 - 2*w^2 - 32*w - 13]', '[2101, 2101, -2*w^3 + 11*w - 4]', '[2101, 2101, -5*w^3 + 6*w^2 + 18*w - 14]', '[2107, 2107, -2*w^3 + 2*w^2 + 14*w - 13]', '[2111, 2111, w^2 - 4*w - 6]', '[2111, 2111, 2*w^3 - 3*w^2 - 6*w - 4]', '[2113, 2113, 5*w^3 - 3*w^2 - 27*w]', '[2113, 2113, -4*w^3 + 5*w^2 + 22*w - 14]', '[2113, 2113, 3*w^2 - 8]', '[2113, 2113, -w^3 - 3*w^2 + 10*w + 5]', '[2114, 2114, 6*w^3 - 2*w^2 - 31*w - 13]', '[2122, 2122, w^3 - 5*w^2 - w - 1]', '[2123, 2123, w^3 - 4*w + 6]', '[2123, 2123, -2*w^3 - w^2 + 15*w + 7]', '[2123, 2123, w^3 - w^2 - 7*w - 6]', '[2123, 2123, 4*w^3 - 2*w^2 - 17*w - 2]', '[2123, 2123, -8*w^3 + 10*w^2 + 32*w - 23]', '[2123, 2123, -4*w^2 + 8*w - 1]', '[2123, 2123, 2*w^3 - 12*w + 3]', '[2123, 2123, -2*w^3 + w^2 + 11*w - 9]', '[2126, 2126, w^3 + w^2 - 4*w - 10]', '[2143, 2143, -3*w^3 + 3*w^2 + 17*w - 6]', '[2146, 2146, 3*w^3 - 4*w^2 - 17*w + 8]', '[2146, 2146, 5*w^3 - 4*w^2 - 29*w - 6]', '[2149, 2149, 2*w^3 + w^2 - 13*w - 1]', '[2150, 430, 5*w^3 - 2*w^2 - 28*w + 1]', '[2150, 430, 3*w^3 - w^2 - 16*w + 2]', '[2152, 538, -9*w^3 + 2*w^2 + 49*w + 19]', '[2152, 538, 3*w^3 - 17*w - 13]', '[2152, 2152, -3*w^3 + 3*w^2 + 17*w - 5]', '[2152, 2152, 4*w^3 - 6*w^2 - 19*w + 11]', '[2153, 2153, 2*w^3 - 15*w - 6]', '[2156, 2156, 2*w^3 + w^2 - 7*w - 6]', '[2156, 2156, -3*w^3 + w^2 + 19*w + 3]', '[2159, 2159, 6*w^3 - 6*w^2 - 30*w + 17]', '[2161, 2161, -3*w^3 + 3*w^2 + 8*w - 7]', '[2161, 2161, 7*w^3 - 38*w - 24]', '[2164, 2164, w^3 + w^2 - 3*w - 7]', '[2167, 2167, -2*w^3 + 15*w + 2]', '[2167, 2167, -w^3 + 4*w^2 + 2*w - 6]', '[2168, 542, -w^3 + 4*w^2 + w - 9]', '[2168, 2168, 2*w^3 + 2*w^2 - 9*w - 5]', '[2176, 68, -2*w^3 + 14*w - 6]', '[2176, 272, -2*w^2 - 2*w + 8]', '[2176, 2176, -w^3 - 2*w^2 + 10*w - 1]', '[2177, 2177, 2*w^2 + w - 10]', '[2179, 2179, -6*w^3 + 3*w^2 + 28*w]', '[2179, 2179, -3*w^3 + 4*w^2 + 14*w - 4]', '[2182, 2182, 3*w^3 - 4*w^2 - 12*w + 1]', '[2182, 2182, -3*w^3 + w^2 + 18*w - 4]', '[2186, 2186, -6*w^3 + 7*w^2 + 23*w - 16]', '[2186, 2186, -3*w^3 + 14*w + 9]', '[2188, 2188, 3*w^2 - 7]', '[2188, 2188, -2*w^3 + 4*w^2 + 15*w + 1]', '[2189, 2189, -2*w^3 + 6*w^2 + 2*w - 9]', '[2189, 2189, 6*w^3 - 4*w^2 - 29*w - 6]', '[2189, 2189, -4*w^3 + 3*w^2 + 26*w - 16]', '[2189, 2189, -w^3 + 2*w + 6]', '[2191, 2191, -5*w^3 + 9*w^2 + 9*w]', '[2194, 2194, 2*w^3 - 3*w^2 - 13*w + 6]', '[2198, 2198, 11*w^3 - 4*w^2 - 55*w - 18]', '[2200, 110, 3*w^3 - 4*w^2 - 11*w + 13]', '[2200, 110, -3*w^3 + 4*w^2 + 13*w - 3]', '[2200, 110, -w^3 + 4*w^2 + 5*w - 9]', '[2200, 110, 5*w^3 - 2*w^2 - 25*w - 1]', '[2200, 440, -3*w^3 + 5*w^2 + 11*w - 5]', '[2200, 440, -w^3 + 9*w + 8]', '[2200, 440, 3*w^3 - 4*w^2 - 8*w + 3]', '[2200, 440, -2*w^3 + 5*w^2 + 9*w - 10]', '[2209, 2209, 3*w^3 - 3*w^2 - 11*w - 6]', '[2213, 2213, 7*w^3 - 2*w^2 - 38*w - 16]', '[2213, 2213, -11*w^3 + 5*w^2 + 57*w + 14]', '[2222, 2222, -w^3 - w^2 + 6*w + 12]', '[2222, 2222, 7*w^3 - 8*w^2 - 31*w + 18]', '[2224, 278, -2*w^3 + 2*w^2 + 6*w - 12]', '[2224, 2224, 2*w^3 - 2*w^2 - 13*w + 3]', '[2225, 445, 2*w^3 + w^2 - 9*w + 3]', '[2225, 445, 2*w^3 - 13*w + 4]', '[2225, 445, -2*w^3 + 5*w^2 + 3*w - 9]', '[2225, 445, -2*w^3 + 3*w^2 + 4*w - 6]', '[2227, 2227, -2*w^3 - 2*w^2 + 7*w + 8]', '[2233, 2233, -2*w^3 + 2*w^2 + 13*w - 4]', '[2233, 2233, w^3 - 8*w + 8]', '[2233, 2233, 3*w^3 + w^2 - 17*w - 8]', '[2233, 2233, 4*w^3 - 4*w^2 - 15*w]', '[2237, 2237, 3*w^3 - w^2 - 10*w + 1]', '[2239, 2239, w^2 + 4*w - 6]', '[2243, 2243, 4*w^3 - 3*w^2 - 20*w + 8]', '[2246, 2246, -5*w^3 + 7*w^2 + 18*w - 12]', '[2246, 2246, 3*w^3 - 3*w^2 - 10*w + 2]', '[2251, 2251, -12*w^3 + 6*w^2 + 63*w + 10]', '[2258, 2258, -2*w^3 + 5*w^2 + 12*w - 13]', '[2258, 2258, -11*w + 7]', '[2264, 566, -w^3 + 4*w^2 - w - 9]', '[2264, 566, 7*w^3 - 37*w - 19]', '[2264, 566, -w^3 + 2*w^2 + 7*w - 11]', '[2264, 566, 7*w^3 - 6*w^2 - 35*w + 5]', '[2264, 2264, w^3 - 10*w - 5]', '[2264, 2264, -6*w^3 + 7*w^2 + 27*w - 22]', '[2264, 2264, 2*w^3 + w^2 - 6*w - 5]', '[2264, 2264, 5*w^3 - 4*w^2 - 23*w + 10]', '[2268, 84, 3*w^2 - 3*w - 6]', '[2273, 2273, -5*w^3 + 7*w^2 + 18*w - 9]', '[2276, 2276, 2*w^3 - 5*w^2 - 9*w + 6]', '[2276, 2276, w^3 - 2*w^2 - 3*w - 4]', '[2279, 2279, -5*w^3 + 2*w^2 + 24*w]', '[2281, 2281, -6*w^3 + 8*w^2 + 24*w - 15]', '[2281, 2281, -3*w^3 + 3*w^2 + 10*w - 3]', '[2282, 2282, 7*w^3 - 36*w - 19]', '[2287, 2287, 9*w^3 - 6*w^2 - 44*w + 2]', '[2293, 2293, -3*w^3 + 3*w^2 + 18*w - 1]', '[2297, 2297, 9*w^3 - 5*w^2 - 47*w - 4]', '[2297, 2297, -5*w^3 + 6*w^2 + 24*w - 10]', '[2302, 2302, 5*w^3 - 3*w^2 - 23*w - 1]', '[2303, 2303, -2*w^3 + 8*w + 7]', '[2306, 2306, 4*w^3 - 3*w^2 - 17*w + 4]', '[2309, 2309, 2*w^3 - w^2 - 15*w + 7]', '[2309, 2309, 8*w^3 - 3*w^2 - 39*w - 7]', '[2311, 2311, 3*w^3 - 18*w - 14]', '[2312, 578, w^3 - 4*w^2 - w + 7]', '[2312, 2312, -4*w^3 + 2*w^2 + 17*w - 1]', '[2324, 2324, 2*w^2 + 3*w - 7]', '[2326, 2326, 3*w^3 - 3*w^2 - 8*w]', '[2326, 2326, 4*w^3 - 3*w^2 - 16*w + 13]', '[2332, 2332, -w^3 - 2*w - 3]', '[2332, 2332, -4*w^3 - w^2 + 20*w + 5]', '[2333, 2333, 2*w^2 - 5*w - 6]', '[2338, 2338, 6*w^3 - 4*w^2 - 29*w - 9]', '[2338, 2338, -9*w^3 + 4*w^2 + 48*w + 9]', '[2341, 2341, -4*w^3 + 7*w^2 + 17*w - 17]', '[2341, 2341, 3*w^2 - 2*w - 10]', '[2342, 2342, w^3 - 5*w^2 + 7*w - 5]', '[2347, 2347, 4*w^3 - 3*w^2 - 19*w + 9]', '[2347, 2347, 9*w^3 - 3*w^2 - 44*w - 9]', '[2347, 2347, -10*w^3 + 4*w^2 + 54*w + 13]', '[2347, 2347, -2*w^3 + w^2 + 14*w - 4]', '[2348, 2348, 3*w^3 - 5*w^2 - 13*w + 7]', '[2348, 2348, 4*w^3 - 4*w^2 - 21*w - 5]', '[2349, 87, -3*w^3 + 6*w^2 + 12*w - 12]', '[2349, 87, 3*w^3 - 12*w - 6]', '[2350, 470, -4*w^3 + 4*w^2 + 13*w + 7]', '[2350, 470, -4*w^3 + 7*w^2 + 9*w - 4]', '[2354, 2354, 3*w^3 - 2*w^2 - 18*w + 5]', '[2354, 2354, -4*w^3 + 7*w^2 + 17*w - 12]', '[2354, 2354, -2*w^3 + 6*w^2 + 11*w - 15]', '[2354, 2354, 2*w^3 - 4*w^2 - 11*w + 13]', '[2357, 2357, 5*w^3 - 4*w^2 - 26*w + 10]', '[2359, 2359, w^3 + 3*w^2 - 14*w + 1]', '[2359, 2359, 6*w^3 - 8*w^2 - 24*w + 11]', '[2362, 2362, -8*w^3 + 5*w^2 + 39*w]', '[2362, 2362, 5*w^3 - 8*w^2 - 23*w + 16]', '[2363, 2363, 4*w^3 - 5*w^2 - 23*w + 3]', '[2368, 148, 5*w^3 - 2*w^2 - 27*w - 11]', '[2368, 296, 2*w^3 - 4*w^2 - 10*w + 4]', '[2368, 2368, -w^3 - w^2 - 2*w - 6]', '[2371, 2371, w^2 + 3*w - 7]', '[2372, 2372, -5*w^3 - w^2 + 17*w + 1]', '[2374, 2374, w^3 - 7*w^2 + 7*w + 1]', '[2374, 2374, 10*w^3 - 5*w^2 - 51*w - 10]', '[2381, 2381, 5*w^3 - 3*w^2 - 23*w]', '[2383, 2383, -4*w^3 + 4*w^2 + 19*w - 2]', '[2384, 298, 2*w^3 - 12*w + 4]', '[2384, 298, 4*w^3 - 4*w^2 - 22*w + 4]', '[2384, 2384, -5*w^3 + 5*w^2 + 19*w - 15]', '[2384, 2384, 3*w^3 - 8*w^2 + 3*w - 2]', '[2386, 2386, 5*w^3 - 4*w^2 - 24*w - 1]', '[2386, 2386, -w^2 + 3*w - 6]', '[2393, 2393, 2*w^3 + 2*w^2 - 14*w - 7]', '[2393, 2393, -4*w^3 + 3*w^2 + 22*w - 2]', '[2399, 2399, 4*w^3 - 3*w^2 - 21*w + 9]', '[2399, 2399, -3*w^3 + 4*w^2 + 12*w]', '[2401, 7, 7]', '[2401, 2401, 3*w + 8]', '[2402, 2402, 3*w^3 - 2*w^2 - 14*w - 7]', '[2404, 2404, -2*w^3 + 2*w^2 + 5*w - 7]', '[2404, 2404, 3*w^3 - 2*w^2 - 10*w + 3]', '[2407, 2407, 3*w^2 - 3*w - 7]', '[2407, 2407, 4*w^3 - 6*w^2 - 12*w + 5]', '[2408, 602, w^3 + 2*w^2 - 5*w - 13]', '[2408, 2408, 3*w^3 - 19*w]', '[2411, 2411, -w^3 + 5*w^2 - 15]', '[2411, 2411, 5*w^3 - 9*w^2 - 19*w + 24]', '[2416, 302, 2*w^2 - 4*w - 8]', '[2416, 2416, 4*w^3 - 7*w^2 - 10*w + 1]', '[2417, 2417, -2*w^3 + 4*w^2 + 11*w - 4]', '[2422, 2422, -3*w^3 + 3*w^2 + 17*w - 15]', '[2426, 2426, -6*w^3 + 3*w^2 + 31*w]', '[2434, 2434, 3*w^2 - w - 6]', '[2441, 2441, 4*w^3 - 3*w^2 - 17*w + 1]', '[2443, 2443, -4*w^3 + 6*w^2 + 14*w - 13]', '[2447, 2447, 2*w^2 - 3*w + 4]', '[2450, 490, -3*w^3 + 5*w^2 + 12*w - 6]', '[2450, 490, -2*w^3 + w^2 + 9*w + 8]', '[2452, 2452, -w^3 + 4*w^2 + 12*w - 1]', '[2452, 2452, 2*w^3 - 3*w^2 + w - 2]', '[2453, 2453, -2*w^3 - w^2 + 17*w - 1]', '[2453, 2453, 7*w^3 - 7*w^2 - 32*w + 21]', '[2453, 2453, -4*w^3 + 8*w^2 + 12*w - 13]', '[2453, 2453, 2*w^3 - 3*w^2 - 6*w + 10]', '[2456, 614, -3*w^3 + 6*w^2 + 11*w - 13]', '[2456, 2456, w^3 + 3*w^2 - 3*w - 5]', '[2458, 2458, 4*w^3 - 8*w^2 - 9*w + 5]', '[2464, 308, 2*w^3 - 4*w^2 - 6*w + 12]', '[2464, 308, 6*w^3 - 2*w^2 - 32*w - 4]', '[2464, 2464, w^2 + 6*w + 5]', '[2464, 2464, -2*w^3 + 5*w^2 + 6*w - 9]', '[2467, 2467, 4*w^3 - 19*w - 10]', '[2468, 2468, -w^3 + w^2 + 10*w]', '[2474, 2474, 7*w^3 - 4*w^2 - 36*w - 7]', '[2474, 2474, -4*w^3 + 2*w^2 + 17*w + 1]', '[2476, 2476, w^3 + w^2 - w - 5]', '[2477, 2477, 2*w^3 + 2*w^2 - 11*w - 12]', '[2477, 2477, -5*w^3 + 7*w^2 + 17*w - 6]', '[2486, 2486, w + 7]', '[2486, 2486, 5*w^3 - 5*w^2 - 20*w + 12]', '[2488, 622, 3*w^3 - 2*w^2 - 11*w - 7]', '[2488, 2488, 4*w^3 - 7*w^2 - 9*w + 6]', '[2491, 2491, -2*w^3 + 5*w^2 + 9*w - 13]', '[2492, 2492, w^3 + 2*w^2 - 9*w + 2]', '[2492, 2492, -2*w^3 + 5*w^2 + w - 6]', '[2494, 2494, 6*w^3 - 3*w^2 - 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6*w^2 - 28*w + 18]', '[5194, 5194, 2*w^3 + 3*w^2 - 10*w - 1]', '[5197, 5197, -18*w^3 + 9*w^2 + 92*w + 14]', '[5197, 5197, 4*w^3 - 8*w^2 - 19*w + 20]', '[5201, 5201, -6*w^3 + 7*w^2 + 19*w + 3]', '[5201, 5201, -5*w^3 + 9*w^2 + 19*w - 20]', '[5203, 473, -3*w^3 + w^2 + 20*w - 3]', '[5203, 473, -5*w^3 + 5*w^2 + 24*w - 19]', '[5203, 5203, 4*w^3 - 5*w^2 - 10*w - 8]', '[5203, 5203, 6*w^3 + w^2 - 36*w - 14]', '[5204, 5204, -w^3 + 5*w^2 + 3*w - 7]', '[5204, 5204, w^3 - 2*w^2 - 12*w + 7]', '[5209, 5209, -16*w^3 + 9*w^2 + 80*w + 4]', '[5209, 5209, -5*w^3 + 5*w^2 + 23*w - 2]', '[5216, 652, -4*w^3 + 4*w^2 + 14*w - 14]', '[5216, 5216, 3*w^3 - 8*w^2 - 22*w + 9]', '[5218, 5218, -5*w^3 + 6*w^2 + 19*w - 10]', '[5218, 5218, -3*w^3 + 9*w^2 + 3*w - 7]', '[5219, 5219, 2*w^3 - w^2 - 17*w + 9]', '[5222, 5222, -w^3 - 3*w^2 + 10*w + 14]', '[5222, 5222, 11*w^3 - 4*w^2 - 54*w - 13]', '[5224, 1306, 13*w^3 - 4*w^2 - 69*w - 25]', '[5224, 5224, 4*w^3 - 5*w^2 - 20*w + 5]', '[5231, 5231, -10*w^3 + 5*w^2 + 54*w + 10]', '[5231, 5231, -5*w^3 + 5*w^2 + 20*w - 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8]', '[5284, 5284, -w^2 - 7*w - 6]', '[5287, 5287, -w^3 + 5*w^2 - 2*w - 13]', '[5294, 5294, -5*w^3 + 9*w^2 + 12*w - 12]', '[5297, 5297, 4*w^3 - 5*w^2 - 10*w + 6]', '[5297, 5297, 6*w^3 - w^2 - 32*w - 6]', '[5300, 1060, 6*w^3 - 27*w - 5]', '[5300, 1060, 7*w^3 - 2*w^2 - 31*w - 10]', '[5302, 5302, -3*w^3 + 7*w^2 + 9*w - 11]', '[5302, 5302, -5*w^3 + 6*w^2 + 26*w - 7]', '[5302, 5302, -3*w^3 + 8*w^2 - 4*w + 3]', '[5302, 5302, 3*w^3 - 2*w^2 - 19*w]', '[5306, 5306, 15*w^3 - 2*w^2 - 81*w - 34]', '[5308, 5308, 4*w^3 - w^2 - 16*w - 7]', '[5309, 5309, 3*w^3 - w^2 - 12*w - 9]', '[5311, 5311, -8*w^3 + 8*w^2 + 41*w - 24]', '[5312, 332, 3*w^3 + 2*w^2 - 21*w - 13]', '[5312, 664, 2*w^3 - 18*w + 8]', '[5312, 5312, -w^3 + w^2 + 4*w - 10]', '[5318, 5318, 4*w^3 - w^2 - 14*w + 1]', '[5321, 5321, -5*w^3 + 5*w^2 + 22*w + 7]', '[5324, 44, -2*w^3 + w^2 + 16*w - 7]', '[5324, 44, -7*w^3 + 12*w^2 + 28*w - 23]', '[5324, 484, 5*w^3 - 8*w^2 - 14*w + 7]', '[5324, 484, 4*w^3 - 6*w^2 - 13*w + 13]', '[5324, 5324, 3*w^3 - 18*w + 1]', '[5324, 5324, -w^3 - 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19*w + 9]', '[5366, 5366, 7*w^3 - 6*w^2 - 32*w + 15]', '[5378, 5378, 3*w^3 - 7*w^2 - 17*w + 11]', '[5378, 5378, -4*w^3 + 25*w + 11]', '[5381, 5381, 3*w^3 - 7*w^2 - 14*w + 19]', '[5383, 5383, -w^3 + 6*w + 10]', '[5384, 1346, 3*w^3 + 2*w^2 - 17*w - 23]', '[5384, 5384, 9*w^3 - 12*w^2 - 40*w + 25]', '[5387, 5387, 2*w^3 - 11*w - 12]', '[5387, 5387, -4*w^3 + w^2 + 25*w + 3]', '[5392, 674, 2*w^3 - 16*w]', '[5392, 674, 6*w^3 - 6*w^2 - 26*w + 8]', '[5392, 5392, -2*w^3 + 8*w^2 - 3*w - 9]', '[5392, 5392, 5*w^3 - 12*w^2 - 3*w - 2]', '[5398, 5398, -3*w^3 + 4*w^2 + 6*w - 7]', '[5398, 5398, -w^3 - 3*w^2 + 10*w - 2]', '[5404, 5404, -3*w^3 - 2*w^2 + 16*w + 7]', '[5404, 5404, 2*w^3 + w^2 - 16*w + 5]', '[5404, 5404, 5*w^3 - 5*w^2 - 22*w - 4]', '[5404, 5404, -w^3 + w^2 + 12*w - 6]', '[5407, 5407, 17*w^3 - 6*w^2 - 86*w - 22]', '[5407, 5407, 7*w^3 - 5*w^2 - 38*w - 5]', '[5411, 5411, -5*w^3 + 11*w^2 + 6*w - 9]', '[5416, 1354, -7*w^3 + 4*w^2 + 33*w + 1]', '[5416, 5416, 2*w^3 - 4*w^2 - 13*w + 13]', '[5419, 5419, -w^3 - 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7]', '[643, 643, 2*w^3 - 3*w^2 - 11*w + 13]', '[653, 653, 2*w^3 - 9*w - 6]', '[659, 659, -3*w^3 + 3*w^2 + 15*w - 2]', '[673, 673, -w^3 + 2*w^2 + 6*w - 10]', '[677, 677, -2*w^3 + 3*w^2 + 9*w - 3]', '[683, 683, -3*w^3 + 3*w^2 + 16*w - 5]', '[691, 691, -w^3 + w^2 + 8*w - 3]', '[691, 691, w^3 - w^2 - 5*w - 4]', '[701, 701, -2*w^3 - w^2 + 13*w + 9]', '[709, 709, -5*w^3 + 2*w^2 + 24*w + 4]', '[709, 709, -2*w^3 + 4*w^2 + 6*w - 3]', '[719, 719, -w^3 + 2*w^2 + 4*w - 10]', '[739, 739, -3*w^3 + 4*w^2 + 12*w - 4]', '[739, 739, 5*w^3 - w^2 - 25*w - 10]', '[743, 743, -3*w^3 + 18*w + 8]', '[743, 743, -2*w^3 + 3*w^2 + 7*w - 9]', '[761, 761, 2*w^3 - 3*w^2 - 12*w + 10]', '[769, 769, -2*w^3 + 14*w - 3]', '[773, 773, -w^3 + 4*w^2 + 2*w - 4]', '[787, 787, -6*w^3 + 4*w^2 + 29*w - 2]', '[787, 787, -3*w^3 + 2*w^2 + 14*w - 10]', '[797, 797, 3*w^3 - w^2 - 15*w]', '[797, 797, -2*w^3 + 5*w^2 + 5*w - 11]', '[809, 809, 6*w^3 - 32*w - 17]', '[811, 811, 5*w^3 - 28*w - 18]', '[811, 811, -2*w^3 + 2*w^2 + 12*w - 5]', '[821, 821, -4*w^3 + 21*w + 8]', '[823, 823, -3*w^3 + 3*w^2 + 14*w - 1]', '[827, 827, 6*w^3 - 2*w^2 - 30*w - 5]', '[827, 827, -4*w^3 + 4*w^2 + 22*w - 13]', '[829, 829, 5*w^3 - w^2 - 27*w - 6]', '[829, 829, w^3 + 2*w^2 - 8*w - 4]', '[841, 29, -2*w^3 + 3*w^2 + 8*w]', '[853, 853, -w^3 + 3*w^2 + 7*w - 2]', '[853, 853, -2*w^3 + 11*w]', '[863, 863, -w^3 + w^2 + 4*w - 7]', '[863, 863, 2*w - 7]', '[877, 877, 2*w^3 + w^2 - 10*w - 10]', '[877, 877, -3*w^3 + w^2 + 18*w + 3]', '[883, 883, 3*w^2 - 3*w - 11]', '[919, 919, 3*w^3 - 3*w^2 - 17*w + 14]', '[919, 919, -2*w^3 + 2*w^2 + 12*w - 3]', '[937, 937, -w^2 + 2*w - 4]', '[941, 941, 4*w^3 - 3*w^2 - 18*w + 4]', '[941, 941, w^3 + w^2 - 4*w - 7]', '[941, 941, 7*w^3 - 5*w^2 - 34*w + 3]', '[941, 941, 4*w^3 - 2*w^2 - 18*w - 3]', '[953, 953, 3*w^3 - 3*w^2 - 10*w - 1]', '[961, 31, 4*w^3 - 3*w^2 - 21*w + 7]', '[961, 31, 2*w^2 + w - 8]', '[967, 967, w^3 + w^2 - 5*w - 12]', '[967, 967, 2*w^3 - 8*w - 5]', '[971, 971, w^2 + 2*w - 6]', '[977, 977, w^2 + 3*w - 5]', '[983, 983, w^3 + 2*w^2 - 4*w - 6]', '[991, 991, -4*w^3 + 4*w^2 + 19*w - 4]', '[1009, 1009, -w^3 - w^2 + 8*w + 7]', '[1013, 1013, -3*w^3 + 4*w^2 + 10*w - 4]', '[1013, 1013, -2*w^3 + w^2 + 13*w + 1]', '[1021, 1021, -4*w^3 + 2*w^2 + 20*w - 1]', '[1033, 1033, w^3 + w^2 - 8*w - 11]', '[1033, 1033, -2*w^3 + w^2 + 13*w - 3]', '[1049, 1049, 3*w^3 - 2*w^2 - 16*w + 6]', '[1061, 1061, 3*w^3 - w^2 - 11*w - 4]', '[1063, 1063, 6*w^3 - w^2 - 32*w - 16]', '[1091, 1091, 6*w^3 - 3*w^2 - 29*w - 5]', '[1091, 1091, -6*w^3 + 3*w^2 + 32*w + 2]', '[1093, 1093, -10*w^3 + 3*w^2 + 53*w + 19]', '[1093, 1093, -4*w^3 + 6*w^2 + 19*w - 12]', '[1097, 1097, 4*w^3 - 2*w^2 - 19*w + 2]', '[1123, 1123, -4*w^3 + 5*w^2 + 18*w - 8]', '[1123, 1123, 4*w^3 - 3*w^2 - 20*w - 2]', '[1129, 1129, 2*w^3 - 10*w + 5]', '[1129, 1129, -w^3 + 2*w^2 + 2*w - 12]', '[1151, 1151, 11*w^3 - 5*w^2 - 57*w - 12]', '[1153, 1153, 6*w^3 - 4*w^2 - 31*w - 2]', '[1163, 1163, w^3 - 4*w^2 - 6*w + 12]', '[1163, 1163, 4*w^3 - 3*w^2 - 20*w - 4]', '[1171, 1171, w^3 - w^2 - w - 6]', '[1181, 1181, -5*w^3 + 5*w^2 + 26*w - 13]', '[1181, 1181, 5*w^3 - 5*w^2 - 22*w + 11]', '[1187, 1187, -w^3 - w^2 + 11*w + 2]', '[1187, 1187, 3*w^3 - w^2 - 18*w + 3]', '[1193, 1193, 12*w^3 - 5*w^2 - 61*w - 13]', '[1193, 1193, 2*w^3 - 9*w - 8]', '[1201, 1201, 10*w^3 - 3*w^2 - 51*w - 17]', '[1213, 1213, -5*w^3 + 7*w^2 + 20*w - 11]', '[1217, 1217, 2*w^3 - 13*w - 8]', '[1229, 1229, 4*w^3 - 4*w^2 - 16*w + 1]', '[1237, 1237, 2*w^3 - 13*w + 2]', '[1237, 1237, -8*w^3 + 4*w^2 + 42*w + 9]', '[1249, 1249, 4*w^3 - 4*w^2 - 21*w + 6]', '[1249, 1249, 3*w^3 - 2*w^2 - 12*w]', '[1259, 1259, 4*w + 5]', '[1259, 1259, -w^3 - 2*w^2 + 8*w + 12]', '[1279, 1279, -w^3 + w^2 + 9*w - 4]', '[1283, 1283, -10*w^3 + 5*w^2 + 52*w + 6]', '[1291, 1291, 3*w^3 + w^2 - 16*w - 11]', '[1301, 1301, 5*w^3 - 26*w - 12]', '[1301, 1301, 4*w^3 - 3*w^2 - 22*w]', '[1321, 1321, -w - 6]', '[1327, 1327, w^3 + 2*w^2 - 8*w - 6]', '[1361, 1361, 2*w^3 - 3*w^2 - 12*w]', '[1367, 1367, 4*w^3 - 22*w - 15]', '[1381, 1381, -5*w^3 + 2*w^2 + 26*w + 2]', '[1381, 1381, w^3 - w^2 - 6*w - 5]', '[1399, 1399, -w^3 + 6*w - 6]', '[1399, 1399, -2*w^3 + 3*w^2 + 11*w - 1]', '[1423, 1423, 2*w^3 + w^2 - 12*w - 14]', '[1423, 1423, 3*w^3 - 14*w - 8]', '[1427, 1427, -4*w^3 + w^2 + 18*w]', '[1447, 1447, -5*w^3 + w^2 + 29*w + 10]', '[1447, 1447, -4*w^3 + 2*w^2 + 22*w - 3]', '[1453, 1453, 6*w^3 - 3*w^2 - 29*w - 3]', '[1453, 1453, 4*w^3 - 4*w^2 - 22*w + 1]', '[1459, 1459, 6*w^3 - 7*w^2 - 26*w + 12]', '[1471, 1471, -w^3 + w^2 + w - 6]', '[1483, 1483, 6*w^3 - 3*w^2 - 34*w - 8]', '[1489, 1489, -2*w^3 - w^2 + 8*w - 2]', '[1493, 1493, 3*w^3 - w^2 - 10*w + 3]', '[1493, 1493, 3*w^3 - 5*w^2 - 12*w + 7]', '[1511, 1511, 8*w^3 - 3*w^2 - 41*w - 7]', '[1523, 1523, -w^3 + 4*w^2 + 4*w - 6]', '[1543, 1543, -w^3 + w^2 + 5*w - 8]', '[1543, 1543, -3*w^3 + 2*w^2 + 16*w - 8]', '[1553, 1553, w^3 + w^2 - 8*w - 9]', '[1559, 1559, 3*w^3 - 3*w^2 - 15*w - 2]', '[1559, 1559, -3*w^3 + 3*w^2 + 11*w - 4]', '[1567, 1567, w^3 - w^2 - 3*w - 6]', '[1567, 1567, 2*w^3 - 11*w - 10]', '[1567, 1567, -w^3 + 2*w^2 + 8*w - 8]', '[1567, 1567, w^3 + w^2 - 2*w - 5]', '[1579, 1579, w^2 + 2*w - 10]', '[1579, 1579, w^3 + w^2 - 9*w - 6]', '[1597, 1597, -2*w^3 + 5*w^2 + 7*w - 5]', '[1597, 1597, 2*w^3 - 4*w^2 - 10*w + 5]', '[1607, 1607, -8*w^3 + 3*w^2 + 40*w + 6]', '[1609, 1609, 3*w^2 - 4*w - 6]', '[1609, 1609, -2*w^3 - w^2 + 14*w + 8]', '[1613, 1613, -3*w^3 + 3*w^2 + 10*w - 5]', '[1613, 1613, 2*w^3 - 10*w + 3]', '[1627, 1627, -5*w^3 + 2*w^2 + 28*w + 2]', '[1627, 1627, -3*w^3 + w^2 + 13*w - 4]', '[1627, 1627, 4*w^3 - 5*w^2 - 16*w + 4]', '[1627, 1627, -3*w^3 - w^2 + 17*w + 4]', '[1663, 1663, -4*w^3 + w^2 + 22*w + 2]', '[1667, 1667, 2*w^3 - 2*w^2 - 8*w - 5]', '[1669, 1669, 2*w^3 - 2*w^2 - 13*w + 6]', '[1669, 1669, -4*w^3 + 2*w^2 + 21*w - 2]', '[1693, 1693, w^3 - w^2 - 2*w + 9]', '[1693, 1693, -w^3 + w^2 + 9*w - 2]', '[1697, 1697, 6*w^3 - 4*w^2 - 29*w - 4]', '[1697, 1697, -2*w^3 + 11*w - 2]', '[1721, 1721, -4*w^3 + 4*w^2 + 14*w - 11]', '[1721, 1721, w^3 - 6*w - 8]', '[1733, 1733, 4*w^3 - 2*w^2 - 17*w + 6]', '[1741, 1741, 5*w^3 - 4*w^2 - 28*w + 14]', '[1747, 1747, -w^3 - 3*w^2 + 6*w + 17]', '[1787, 1787, 7*w^3 - 5*w^2 - 36*w + 3]', '[1789, 1789, -w^3 - w^2 + 11*w]', '[1789, 1789, w^3 + 2*w^2 - 6*w - 8]', '[1811, 1811, 4*w^3 - 2*w^2 - 17*w + 2]', '[1847, 1847, 6*w^3 - 5*w^2 - 32*w + 2]', '[1847, 1847, -2*w^3 + 3*w^2 + 15*w + 1]', '[1861, 1861, 2*w^3 - 3*w^2 - 13*w + 11]', '[1861, 1861, -4*w^3 + 3*w^2 + 17*w - 5]', '[1879, 1879, -8*w^3 + 5*w^2 + 39*w - 1]', '[1933, 1933, 5*w^3 - 5*w^2 - 22*w + 7]', '[1949, 1949, 3*w^3 - 3*w^2 - 17*w + 4]', '[1951, 1951, -4*w^3 + 3*w^2 + 23*w - 13]', '[1973, 1973, 9*w^3 - w^2 - 47*w - 22]', '[1973, 1973, -3*w^3 + 12*w - 2]', '[1973, 1973, w^2 - 2*w - 10]', '[1973, 1973, w^3 - w^2 - 10*w + 5]', '[1979, 1979, 5*w^3 - 3*w^2 - 23*w - 2]', '[1979, 1979, 5*w^3 - w^2 - 27*w - 14]', '[1987, 1987, 7*w^3 - w^2 - 35*w - 14]', '[1993, 1993, -w^3 + 3*w^2 - 7]', '[1993, 1993, 3*w^2 - w - 5]', '[1993, 1993, -10*w^3 + 5*w^2 + 53*w + 9]', '[1993, 1993, -2*w^3 + 14*w - 7]', '[1997, 1997, -7*w^3 + 4*w^2 + 36*w + 6]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 10889, 'disc_rad': 10889, 'disc_sign': 1, 'frobs': [[2, [[3, 1], [1, 1]]], [3, [[4, 1]]], [5, [[2, 2]]], [7, [[3, 1], [1, 1]]], [11, [[2, 1], [1, 2]]], [13, [[4, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[2, 2]]], [37, [[3, 1], [1, 1]]], [41, [[4, 1]]], [43, [[3, 1], [1, 1]]], [47, [[3, 1], [1, 1]]], [53, [[3, 1], [1, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 104.35037134576953, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.10889.1', 'local_algs': ['m10889.1.1.0', 'm10889.1.1.0', 'm10889.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [10889], 'rd': 10.2152029518, 'regulator': {'__RealLiteral__': 0, 'data': '7.40261033221', 'prec': 44}, 'res': {'gal': ['-188200,1752820,-1211152,-14849471,19042814,38344968,-52594866,-50599956,63161730,40902912,-40044789,-21086828,14649008,6880732,-3243076,-1401828,446088,175075,-38506,-12864,2070,504,-66,-8,1'], 'sib': ['-2680,8952,12898,-35667,-1222,20045,-2140,-3574,502,250,-39,-6,1', '1,14,12,-221,149,411,-300,-267,164,58,-27,-3,1', '342184,127781,-74701,-10858,4845,279,-121,-2,1', '5,-19,9,19,-7,-3,1', '5448,6256,1658,-233,-112,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{3} - a^{2} - 5 a + 2 \\)', '\\( a^{3} - a^{2} - 4 a + 3 \\)', '\\( a^{2} + 2 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}