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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 6224, 'field_bad_primes': [2, 389], 'field_label': '4.4.6224.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.6224.1-29.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [29], 'level_ideal': '[29, 29, w^2 - w - 1]', 'level_label': '29.2', 'level_norm': 29, 'parallel_weight': 2, 'short_label': '29.2-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[29, 29, w^2 - w - 1]', -1]], 'hecke_eigenvalues': [0, 2, 0, -2, -4, -6, 1, 10, -6, -6, -8, -12, 0, 4, -10, 8, -10, 2, -18, 2, 16, 0, -12, 8, 10, 18, 6, -2, -18, 18, -16, 14, -6, -12, -4, -10, -14, -10, -18, -12, 12, 14, -16, 2, 26, 2, -8, 8, 28, 24, 0, -4, -12, 32, -16, 10, 0, -20, -2, -4, -18, -10, -28, -12, -12, -14, -36, 8, 8, 0, -36, -8, 16, 26, -26, 6, 22, -30, 18, 36, 40, 2, 36, 6, 18, -22, -8, -24, 4, 32, -16, 10, 38, -10, 12, -16, 30, 34, 28, -18, 22, -8, -20, 2, 28, -20, -32, 30, 26, -18, -14, -30, -4, 28, -50, -4, -16, 40, 34, -28, -12, -44, 14, 26, -10, -4, -4, -28, -4, 36, -4, -28, 56, 16, 52, -22, 6, 4, 48, -14, -54, 50, -24, -4, 12, 28, 4, -4, 36, 24, -32, 40, -16, -58, -46, 8, -8, -52, -2, -18, 48, -32], 'hecke_polynomial': 'x', 'label': '4.4.6224.1-29.2-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 6224, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - w^2 - 4*w + 2]', '[4, 2, -w^3 + 2*w^2 + 3*w - 4]', '[5, 5, w]', '[7, 7, -w^3 + w^2 + 3*w - 2]', '[8, 2, w^3 - w^2 - 3*w + 1]', '[10, 10, w^3 - w^2 - 4*w]', '[13, 13, -w^3 + 4*w + 2]', '[14, 14, w^2 - w - 2]', '[16, 2, 2]', '[19, 19, w^3 - w^2 - 5*w + 2]', '[20, 10, -w^2 + 5]', '[25, 25, w^3 - w^2 - 5*w]', '[26, 26, -w^3 + 2*w^2 + 4*w - 3]', '[28, 14, w^3 - 2*w^2 - 3*w + 6]', '[29, 29, -w^2 - w + 3]', '[29, 29, w^2 - w - 1]', '[32, 4, 2*w^3 - 2*w^2 - 8*w + 4]', '[35, 35, w^3 - 4*w]', '[37, 37, -w^2 + 2*w + 2]', '[37, 37, -w^3 + 5*w + 1]', '[38, 38, -w - 3]', '[40, 10, -w^3 - w^2 + 5*w + 5]', '[41, 41, -w^3 + 2*w^2 + 3*w - 7]', '[47, 47, w^3 - 2*w^2 - 4*w + 2]', '[47, 47, 2*w^3 - 3*w^2 - 8*w + 6]', '[49, 49, w^3 - 2*w^2 - 5*w + 3]', '[50, 50, -w^3 + 2*w^2 + 2*w - 5]', '[52, 26, w^2 - 2*w - 3]', '[56, 14, -w^3 + w^2 + 5*w + 1]', '[58, 58, 2*w^3 - 3*w^2 - 7*w + 8]', '[58, 58, 2*w^2 - w - 7]', '[59, 59, -2*w^3 + w^2 + 7*w - 3]', '[64, 4, -2*w^3 + 4*w^2 + 6*w - 8]', '[65, 65, -2*w^2 + 5]', '[67, 67, w^3 - 2*w^2 - 3*w + 1]', '[70, 70, w^3 - w^2 - 2*w]', '[73, 73, -2*w - 1]', '[74, 74, -w^3 + 4*w - 1]', '[74, 74, -w^3 - w^2 + 4*w + 6]', '[76, 38, -w^3 + 2*w^2 + w - 4]', '[79, 79, 2*w^2 - 2*w - 9]', '[80, 10, 2*w]', '[81, 3, -3]', '[82, 82, -4*w^3 + 4*w^2 + 17*w - 9]', '[91, 91, 2*w^3 - 2*w^2 - 8*w + 1]', '[94, 94, -w^2 - w + 4]', '[94, 94, 4*w^3 - 6*w^2 - 17*w + 17]', '[95, 95, -w^3 + w^2 + 4*w - 5]', '[97, 97, -3*w + 2]', '[98, 98, -w^3 + 6*w + 3]', '[100, 50, -w^3 + 5*w]', '[101, 101, w^3 - 3*w^2 - w + 4]', '[101, 101, 2*w^3 - w^2 - 9*w + 1]', '[103, 103, -3*w^3 + 2*w^2 + 13*w - 1]', '[103, 103, -2*w^3 + 2*w^2 + 9*w - 2]', '[104, 26, w^3 - 3*w^2 - 3*w + 9]', '[107, 107, w^3 - 3*w^2 - 3*w + 6]', '[107, 107, -2*w^2 + w + 4]', '[109, 109, w^2 + 2*w + 2]', '[109, 109, -2*w^3 + 2*w^2 + 7*w - 4]', '[112, 14, -2*w^3 + 2*w^2 + 6*w - 4]', '[113, 113, -2*w^3 + 2*w^2 + 7*w - 2]', '[116, 58, -2*w^3 + 3*w^2 + 6*w - 7]', '[116, 58, -w^3 + 2*w^2 + 5*w - 2]', '[118, 118, -4*w^3 + 5*w^2 + 15*w - 16]', '[121, 11, w^3 - 3*w - 3]', '[121, 11, -2*w^2 + 3*w + 6]', '[125, 5, w^3 - 6*w - 2]', '[125, 125, -w^3 + w^2 + 2*w - 5]', '[127, 127, -w^3 + 2*w^2 + 2*w - 6]', '[128, 4, 2*w^3 - 2*w^2 - 6*w + 2]', '[130, 130, w^3 - w^2 - 6*w]', '[133, 133, 2*w^3 - 3*w^2 - 7*w + 3]', '[134, 134, 2*w^3 - 2*w^2 - 7*w + 3]', '[140, 70, -2*w^3 + 3*w^2 + 8*w - 5]', '[145, 145, -2*w^3 + 4*w^2 + 7*w - 10]', '[145, 145, -2*w^3 + w^2 + 8*w]', '[146, 146, w^3 - 3*w^2 - 4*w + 8]', '[148, 74, 2*w^3 - w^2 - 8*w - 1]', '[148, 74, w^2 + 1]', '[149, 149, -w^3 - 2*w^2 + 3*w + 7]', '[149, 149, w^3 + w^2 - 5*w - 4]', '[151, 151, -2*w^3 + 4*w^2 + 7*w - 6]', '[151, 151, -w^3 + 3*w^2 + 3*w - 8]', '[152, 38, w^3 - 3*w^2 - 3*w + 7]', '[157, 157, -w^3 + 2*w^2 + 5*w - 1]', '[157, 157, -3*w^3 + 4*w^2 + 10*w - 8]', '[157, 157, w^3 - w^2 - 2*w - 3]', '[157, 157, -w^2 + 2*w + 8]', '[158, 158, 2*w^3 - 4*w^2 - 7*w + 9]', '[160, 20, 2*w^3 - 2*w^2 - 8*w]', '[162, 6, -3*w^3 + 3*w^2 + 12*w - 6]', '[163, 163, -w^3 + 3*w^2 + 4*w - 7]', '[163, 163, 2*w^3 - 2*w^2 - 6*w - 1]', '[164, 82, w^3 - 2*w^2 - 5*w + 8]', '[169, 169, -w^3 + 5*w - 1]', '[173, 173, w + 4]', '[175, 175, -3*w^3 + 3*w^2 + 12*w - 5]', '[179, 179, 2*w^3 - 4*w^2 - 8*w + 7]', '[181, 181, 3*w^3 - 4*w^2 - 10*w + 6]', '[182, 182, 2*w^3 - w^2 - 7*w + 2]', '[185, 185, -w^3 + 2*w^2 + 2*w]', '[185, 185, -w^2 - w + 5]', '[188, 94, 2*w^3 - 5*w^2 - 4*w + 7]', '[188, 94, -w^3 + 7*w - 4]', '[190, 190, w^3 - 3*w^2 - 2*w + 10]', '[194, 194, -2*w^2 + w + 11]', '[196, 98, -w^3 + 5*w - 2]', '[197, 197, -2*w^3 + 3*w^2 + 10*w - 6]', '[197, 197, 3*w^3 - 3*w^2 - 13*w + 4]', '[200, 50, -w^3 - w^2 + 3*w + 5]', '[202, 202, -3*w^3 + 5*w^2 + 10*w - 12]', '[202, 202, w^3 + 2*w^2 - 4*w - 9]', '[203, 203, -w^3 + w^2 + 5*w - 6]', '[203, 203, -w^3 + w^2 + 6*w - 1]', '[205, 205, 2*w^3 - 3*w^2 - 9*w + 5]', '[206, 206, -4*w^3 + 8*w^2 + 15*w - 27]', '[206, 206, -3*w^3 + 6*w^2 + 12*w - 19]', '[208, 26, -2*w^3 + 8*w + 4]', '[211, 211, 3*w^3 - 3*w^2 - 11*w + 2]', '[214, 214, w^3 - w^2 - 6*w + 2]', '[214, 214, -w^3 + 2*w^2 + 2*w - 7]', '[218, 218, 2*w^3 - 3*w^2 - 3*w + 6]', '[218, 218, -3*w^3 + 4*w^2 + 12*w - 13]', '[223, 223, -w^3 + w^2 + 3*w - 6]', '[224, 28, 2*w^2 - 2*w - 4]', '[226, 226, -w^3 + 2*w^2 + 4*w - 9]', '[227, 227, -w^3 + 6*w - 2]', '[227, 227, 2*w^3 - w^2 - 7*w - 1]', '[232, 58, -w^3 + w^2 + 3*w + 3]', '[232, 58, w^3 + w^2 - 7*w - 7]', '[235, 235, -2*w^3 + 2*w^2 + 4*w - 5]', '[235, 235, -3*w^3 + 4*w^2 + 10*w - 10]', '[236, 118, 2*w^3 - 3*w^2 - 10*w + 7]', '[239, 239, 3*w^3 - 4*w^2 - 9*w + 7]', '[242, 22, -2*w^3 + 2*w^2 + 9*w - 1]', '[242, 22, -w^3 + 4*w^2 + 2*w - 13]', '[245, 245, -2*w^3 + 2*w^2 + 10*w - 5]', '[247, 247, -2*w^2 + w + 2]', '[250, 10, -2*w^3 + 5*w^2 + 7*w - 16]', '[250, 250, 2*w^3 - 4*w^2 - 7*w + 5]', '[251, 251, w^3 - 3*w^2 + 7]', '[251, 251, 2*w^3 - w^2 - 6*w - 2]', '[254, 254, -2*w^3 + w^2 + 9*w - 2]', '[256, 4, 4]', '[259, 259, 2*w^3 - 3*w^2 - 6*w + 8]', '[259, 259, 2*w^3 - 10*w - 3]', '[260, 130, w^3 - 2*w^2 - 3*w]', '[263, 263, w^2 - 3*w - 1]', '[263, 263, -w^3 + 2*w^2 + 2*w - 8]', '[266, 266, -w^2 - w + 6]', '[268, 134, 2*w^3 - 3*w^2 - 8*w + 11]', '[269, 269, 2*w^3 - 2*w^2 - 10*w + 3]', '[271, 271, 2*w^3 - 3*w^2 - 8*w + 4]', '[271, 271, 2*w^3 - w^2 - 7*w + 1]', '[277, 277, w^2 + w - 7]', '[280, 70, w^3 - w^2 - w + 5]', '[283, 283, w^3 - 4*w^2 - 2*w + 6]', '[287, 287, 2*w^3 - w^2 - 8*w + 4]', '[289, 17, -2*w^3 + 3*w^2 + 5*w - 7]', '[289, 17, -w^3 + 3*w^2 + 2*w - 11]', '[290, 290, 2*w^3 - w^2 - 7*w]', '[290, 290, 2*w^3 - 5*w^2 - 5*w + 10]', '[292, 146, -3*w^3 + 4*w^2 + 9*w - 6]', '[295, 295, w^3 - 5*w^2 - 7*w + 10]', '[296, 74, 3*w^3 - 5*w^2 - 11*w + 9]', '[296, 74, -w^3 + 3*w^2 + w - 9]', '[298, 298, -3*w^2 + w + 6]', '[298, 298, w^3 - 3*w^2 - 2*w + 12]', '[302, 302, -w^3 + 2*w^2 + 6*w - 7]', '[302, 302, -3*w^3 + 3*w^2 + 14*w - 6]', '[304, 38, 2*w^3 - 2*w^2 - 10*w + 4]', '[307, 307, 2*w^3 - 5*w^2 - 9*w + 13]', '[307, 307, 4*w^3 - 5*w^2 - 13*w + 11]', '[311, 311, -2*w^3 + 5*w^2 + 5*w - 11]', '[313, 313, -3*w - 2]', '[314, 314, 2*w^2 + w - 7]', '[314, 314, -w^2 + 3*w + 4]', '[314, 314, -4*w^3 + 5*w^2 + 17*w - 16]', '[314, 314, -5*w^3 + 6*w^2 + 20*w - 11]', '[316, 158, -2*w^3 + w^2 + 6*w - 1]', '[320, 20, -2*w^2 + 10]', '[324, 6, 3*w^3 - 6*w^2 - 9*w + 12]', '[325, 325, w^3 - 3*w - 5]', '[326, 326, 3*w^3 - 4*w^2 - 14*w + 9]', '[326, 326, -3*w^3 + 3*w^2 + 12*w - 2]', '[328, 82, -w^3 - w^2 + 5*w + 3]', '[329, 329, 2*w^3 - w^2 - 3*w + 1]', '[329, 329, -w^3 + 2*w^2 + 7*w - 7]', '[335, 335, 2*w^2 - 3*w - 10]', '[338, 338, -w^3 - w^2 + 2*w + 4]', '[343, 7, -2*w^3 + 3*w^2 + 4*w - 2]', '[343, 343, -4*w^3 + 5*w^2 + 15*w - 11]', '[346, 346, 3*w^3 - 2*w^2 - 12*w + 3]', '[347, 347, 3*w^2 - w - 9]', '[350, 350, -3*w^2 + w + 10]', '[358, 358, 3*w^3 - 5*w^2 - 14*w + 14]', '[361, 361, 3*w^2 - 8]', '[362, 362, 2*w^3 - 3*w^2 - 9*w + 12]', '[364, 182, -2*w^3 + 5*w^2 + 6*w - 9]', '[365, 365, -2*w^2 - w]', '[367, 367, 2*w^2 - 2*w - 3]', '[367, 367, 2*w^3 - w^2 - 11*w - 3]', '[370, 370, 4*w^3 - 5*w^2 - 15*w + 10]', '[370, 370, 4*w^3 - 5*w^2 - 17*w + 10]', '[376, 94, -3*w^3 + 3*w^2 + 7*w - 3]', '[376, 94, -w^3 + w^2 + w + 1]', '[377, 377, -3*w^3 + 5*w^2 + 10*w - 7]', '[377, 377, -w^3 + 2*w^2 + w - 7]', '[379, 379, w^2 - 3*w - 3]', '[379, 379, -2*w^3 + 4*w^2 + 4*w - 9]', '[380, 190, -2*w^3 + w^2 + 10*w + 5]', '[383, 383, 2*w^3 - 9*w - 2]', '[388, 194, w^3 - 4*w^2 + w + 8]', '[389, 389, w^3 + w^2 - 4*w - 9]', '[389, 389, -2*w^3 + 5*w^2 + 6*w - 14]', '[389, 389, 2*w^3 - 4*w^2 - 6*w + 3]', '[392, 98, 3*w^3 - 3*w^2 - 11*w + 3]', '[394, 394, -6*w^3 + 10*w^2 + 25*w - 27]', '[394, 394, 5*w^3 - 9*w^2 - 20*w + 28]', '[395, 395, -2*w^3 + 2*w^2 + 9*w]', '[397, 397, w^3 - 4*w^2 - w + 7]', '[397, 397, -2*w^3 + 11*w + 4]', '[400, 50, 2*w^3 - 2*w^2 - 10*w]', '[404, 202, -6*w^3 + 7*w^2 + 26*w - 19]', '[404, 202, 3*w^2 - 2*w - 7]', '[405, 15, -3*w]', '[406, 406, -3*w - 1]', '[406, 406, -2*w^3 + 4*w^2 + 5*w - 3]', '[409, 409, w^2 - 8]', '[410, 410, -2*w^3 + 11*w + 5]', '[412, 206, 3*w^3 - 2*w^2 - 15*w + 4]', '[412, 206, 2*w^3 - w^2 - 10*w + 3]', '[413, 413, 3*w^3 - 8*w + 6]', '[416, 52, -2*w^3 + 4*w^2 + 8*w - 6]', '[419, 419, -3*w^2 - 2*w + 8]', '[422, 422, w^3 - 3*w^2 - 4*w + 14]', '[428, 214, 4*w^3 - 7*w^2 - 16*w + 19]', '[428, 214, -3*w^3 + 2*w^2 + 13*w - 4]', '[431, 431, -w^3 + 4*w^2 + 3*w - 13]', '[433, 433, 2*w^3 - w^2 - 9*w + 3]', '[436, 218, -w^3 + 4*w^2 + 3*w - 8]', '[436, 218, w^2 - 4*w + 1]', '[443, 443, -3*w^3 + 3*w^2 + 11*w - 6]', '[446, 446, 5*w^3 - 5*w^2 - 20*w + 12]', '[448, 28, 2*w^3 - 4*w^2 - 6*w + 12]', '[449, 449, w^3 - 2*w^2 - w + 11]', '[449, 449, -w^2 - 2]', '[452, 226, -2*w^3 + 5*w^2 + 2*w - 7]', '[454, 454, -6*w^3 + 9*w^2 + 23*w - 24]', '[454, 454, -w^2 + w + 8]', '[455, 455, -2*w^3 + 4*w^2 + 5*w - 10]', '[457, 457, w^3 + w^2 - 6*w - 3]', '[463, 463, -3*w^3 + 6*w^2 + 11*w - 17]', '[464, 58, -2*w^2 - 2*w + 6]', '[464, 58, 2*w^2 - 2*w - 2]', '[469, 469, w^3 + w^2 - 3*w - 6]', '[470, 470, -2*w^3 + 3*w^2 + 7*w]', '[470, 470, -w + 5]', '[472, 118, -w^3 - w^2 + w - 3]', '[475, 475, 2*w^3 - 2*w^2 - 5*w]', '[478, 478, 2*w^3 - 2*w^2 - 9*w + 9]', '[479, 479, -3*w^3 + 2*w^2 + 14*w - 4]', '[479, 479, 2*w^3 - 3*w^2 - 8*w + 2]', '[481, 481, -w^3 + 2*w^2 - 4]', '[481, 481, -3*w^3 + 4*w^2 + 13*w - 7]', '[484, 22, 3*w^3 - 6*w^2 - 7*w + 12]', '[484, 22, -5*w^3 + 4*w^2 + 23*w - 6]', '[485, 485, -w^3 + 4*w^2 + 2*w - 10]', '[490, 490, w + 5]', '[491, 491, -3*w^3 + 4*w^2 + 8*w - 2]', '[494, 494, 3*w^3 - 3*w^2 - 10*w + 2]', '[500, 10, 4*w^3 - 5*w^2 - 14*w + 7]', '[500, 250, -w^2 - 2*w + 5]', '[502, 502, -w^3 + 4*w^2 + 2*w - 11]', '[502, 502, -2*w^3 + 2*w^2 + 9*w + 1]', '[503, 503, 3*w^3 - 3*w^2 - 11*w + 4]', '[505, 505, 3*w^3 - 2*w^2 - 12*w]', '[505, 505, w^3 + 2*w^2 - 8*w - 10]', '[508, 254, -2*w^3 + 3*w^2 + 4*w - 1]', '[511, 511, -w^3 + 5*w^2 + 5*w - 8]', '[512, 8, 4*w^3 - 4*w^2 - 16*w + 8]', '[515, 515, 2*w^3 - 5*w^2 - 7*w + 15]', '[515, 515, 2*w^3 - 3*w^2 - 6*w + 10]', '[518, 518, 2*w^3 - 2*w^2 - 11*w + 7]', '[518, 518, w^3 - 4*w - 7]', '[520, 130, -3*w^3 + 3*w^2 + 11*w - 5]', '[521, 521, -3*w^3 + w^2 + 14*w + 1]', '[521, 521, -3*w^3 + 2*w^2 + 12*w - 2]', '[526, 526, 4*w^3 - 7*w^2 - 15*w + 18]', '[526, 526, -4*w^3 + 3*w^2 + 17*w - 6]', '[532, 266, -w^3 - 2*w^2 + 5*w + 6]', '[533, 533, 3*w^3 + w^2 - 14*w - 9]', '[535, 535, 3*w^3 + w^2 - 13*w - 10]', '[535, 535, w^3 + 2*w^2 - 4*w - 10]', '[536, 134, w^3 - 3*w^2 + w + 3]', '[538, 538, 5*w^3 - 9*w^2 - 20*w + 26]', '[542, 542, 2*w^3 - 4*w^2 - 9*w + 13]', '[542, 542, 2*w^3 - 3*w^2 - 7*w + 12]', '[545, 545, 2*w^3 - 5*w^2 - 8*w + 10]', '[545, 545, -w^3 + 3*w^2 + w - 10]', '[551, 551, w^3 - 5*w - 7]', '[551, 551, w^3 - 2*w^2 - 6*w + 8]', '[553, 553, -w^3 - w^2 + 5*w + 2]', '[554, 554, -6*w^3 + 7*w^2 + 25*w - 14]', '[560, 70, 2*w^3 - 8*w]', '[565, 565, 2*w^3 - 5*w^2 - 6*w + 10]', '[566, 566, -2*w^3 + 3*w^2 + 5*w - 8]', '[567, 21, 3*w^3 - 3*w^2 - 9*w + 6]', '[569, 569, 4*w^3 - 4*w^2 - 16*w + 7]', '[574, 574, -3*w^3 + 2*w^2 + 12*w - 1]', '[578, 34, -2*w^3 + w^2 + 9*w - 4]', '[578, 34, -5*w^3 + 4*w^2 + 22*w - 7]', '[580, 290, w^3 - 2*w^2 - 3*w + 10]', '[580, 290, w^3 - 7*w]', '[584, 146, w^3 - 5*w^2 - 3*w + 9]', '[587, 587, -3*w^3 + 4*w^2 + 12*w - 6]', '[587, 587, -2*w^3 + 2*w^2 + 4*w - 1]', '[590, 590, 3*w^2 + w - 10]', '[592, 74, -2*w^2 + 4*w + 4]', '[592, 74, -2*w^3 + 10*w + 2]', '[593, 593, -3*w^3 + 3*w^2 + 12*w - 1]', '[593, 593, -w^3 - w^2 + 5*w - 2]', '[596, 298, -w^3 + 2*w^2 + w - 8]', '[596, 298, 6*w^3 - 5*w^2 - 26*w + 9]', '[604, 302, -7*w^3 + 10*w^2 + 29*w - 24]', '[604, 302, -w^3 + 2*w^2 + w + 2]', '[605, 55, 5*w^3 + w^2 - 25*w - 20]', '[605, 55, 3*w^2 - w - 5]', '[607, 607, -3*w^3 + 6*w^2 + 10*w - 18]', '[608, 76, -2*w - 6]', '[611, 611, 2*w^3 + w^2 - 6*w - 6]', '[611, 611, 2*w^2 + w - 8]', '[613, 613, -2*w^2 + w + 12]', '[613, 613, 3*w^3 - 5*w^2 - 11*w + 8]', '[614, 614, 8*w^3 - 11*w^2 - 35*w + 26]', '[614, 614, 6*w^3 - 7*w^2 - 25*w + 22]', '[622, 622, -2*w^3 + w^2 + 11*w - 2]', '[625, 5, 5]', '[625, 625, w^3 - 2*w^2 - 4*w + 10]', '[626, 626, w^3 - 4*w^2 - 4*w + 11]', '[628, 314, -4*w^3 + 5*w^2 + 18*w - 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10*w - 12]', '[1652, 826, -6*w^3 + 5*w^2 + 24*w - 13]', '[1663, 1663, -2*w^3 + 6*w^2 + 5*w - 22]', '[1663, 1663, w^3 + 2*w^2 - 2*w - 8]', '[1664, 52, 2*w^3 - 6*w^2 - 6*w + 18]', '[1667, 1667, -w^3 + 4*w^2 + 6*w - 12]', '[1673, 1673, 2*w^3 - 7*w^2 - 4*w + 6]', '[1675, 1675, 2*w^3 - 3*w^2 - 10*w]', '[1676, 838, -3*w^3 + 4*w^2 + 9*w - 12]', '[1681, 1681, -2*w^3 + 6*w^2 + 5*w - 14]', '[1682, 58, -w^3 - w^2 + 8*w - 2]', '[1682, 58, -3*w^3 + 4*w^2 + 12*w - 3]', '[1682, 1682, -w^3 + 2*w^2 - 11]', '[1682, 1682, 2*w^2 - 5*w - 13]', '[1688, 422, -5*w^3 + 7*w^2 + 15*w - 3]', '[1690, 1690, -2*w^3 + 6*w^2 + 5*w - 15]', '[1694, 154, w^3 - 4*w^2 + 2*w + 11]', '[1694, 154, w^3 - 8*w + 1]', '[1699, 1699, 2*w^3 + 2*w^2 - 6*w - 9]', '[1709, 1709, w^3 - 8*w - 4]', '[1711, 1711, -4*w^3 + 3*w^2 + 12*w - 12]', '[1711, 1711, -2*w^3 + 9*w^2 + 16*w - 14]', '[1712, 214, 2*w^3 - 6*w^2 - 6*w + 12]', '[1712, 214, -4*w^2 + 2*w + 8]', '[1714, 1714, -w^2 - w - 4]', '[1715, 35, -w^3 + 5*w^2 + 2*w - 15]', '[1715, 1715, -5*w^3 + 8*w^2 + 16*w - 10]', '[1718, 1718, -2*w^3 + 13*w + 9]', '[1721, 1721, -w^3 + 2*w^2 + 2*w - 12]', '[1721, 1721, w^3 - w^2 - 3]', '[1723, 1723, 5*w^3 - 4*w^2 - 22*w + 2]', '[1723, 1723, 3*w^3 + w^2 - 17*w - 12]', '[1724, 862, 2*w^3 - 5*w^2 - 10*w + 7]', '[1726, 1726, -5*w^3 + 9*w^2 + 20*w - 24]', '[1729, 1729, w^3 - 2*w^2 - 8*w + 2]', '[1730, 1730, -2*w^3 + 6*w^2 + 9*w - 15]', '[1732, 866, -6*w^3 + 9*w^2 + 22*w - 17]', '[1733, 1733, 3*w^3 - 5*w^2 - 12*w + 7]', '[1733, 1733, 2*w^3 - w^2 - 5*w - 3]', '[1735, 1735, 3*w^3 - w^2 - 9*w]', '[1739, 1739, -4*w^3 + 8*w^2 + 9*w - 16]', '[1739, 1739, -w^3 + 5*w^2 + 2*w - 13]', '[1739, 1739, -6*w^3 + 10*w^2 + 20*w - 23]', '[1739, 1739, -5*w^3 + 9*w^2 + 19*w - 24]', '[1741, 1741, 2*w^3 + w^2 - 7*w - 9]', '[1741, 1741, w^3 + 3*w^2 - 5*w - 18]', '[1742, 1742, w^3 - 6*w - 9]', '[1744, 218, -4*w^3 + 8*w^2 + 10*w - 8]', '[1744, 218, -4*w^3 + 4*w^2 + 14*w - 8]', '[1747, 1747, 5*w^3 - 3*w^2 - 24*w + 1]', '[1747, 1747, 2*w^3 - 2*w^2 - 4*w - 1]', '[1750, 70, 2*w^3 - 7*w - 9]', '[1750, 1750, -3*w^3 + w^2 + 10*w]', '[1754, 1754, 3*w^3 - 2*w^2 - 14*w + 7]', '[1757, 1757, 3*w^3 - 8*w^2 - 11*w + 9]', '[1757, 1757, 2*w^3 + 3*w^2 - 11*w - 13]', '[1759, 1759, -6*w^3 + 8*w^2 + 19*w - 18]', '[1759, 1759, 2*w^3 + w^2 - 8*w - 2]', '[1762, 1762, 6*w^3 - 11*w^2 - 19*w + 22]', '[1762, 1762, -6*w^3 + 8*w^2 + 27*w - 19]', '[1772, 886, w^3 - 9*w + 4]', '[1774, 1774, -6*w^3 + 10*w^2 + 25*w - 31]', '[1774, 1774, 5*w^3 - 9*w^2 - 18*w + 22]', '[1777, 1777, w^3 - 5*w^2 + 9]', '[1778, 1778, -4*w^3 + 4*w^2 + 13*w - 3]', '[1783, 1783, -w^3 + 9*w + 7]', '[1783, 1783, 4*w^3 - 6*w^2 - 14*w + 7]', '[1784, 446, 3*w^3 - w^2 - 9*w + 1]', '[1786, 1786, -3*w^3 + 5*w^2 + 14*w - 8]', '[1786, 1786, -w^3 + 4*w^2 + 8*w - 1]', '[1787, 1787, w^3 + w^2 - 5*w - 12]', '[1787, 1787, -5*w^3 + 6*w^2 + 23*w - 13]', '[1789, 1789, -2*w^3 + 5*w^2 + 5*w - 17]', '[1789, 1789, -3*w^3 + 11*w - 1]', '[1790, 1790, -w^3 + 3*w^2 + 2*w]', '[1792, 28, -4*w^3 + 4*w^2 + 12*w - 8]', '[1796, 898, w^2 - 6*w + 7]', '[1796, 898, 5*w^3 - 10*w^2 - 15*w + 18]', '[1801, 1801, 4*w^3 - 8*w^2 - 13*w + 18]', '[1805, 1805, -w^3 - w^2 + 3*w + 10]', '[1808, 226, -4*w^3 + 4*w^2 + 14*w - 4]', '[1810, 1810, -4*w^3 + 5*w^2 + 11*w]', '[1811, 1811, -w^3 + w^2 + 2*w - 9]', '[1811, 1811, w^3 + 5*w^2 - 7*w - 18]', '[1813, 1813, -3*w^3 + 5*w^2 + 9*w - 14]', '[1813, 1813, -2*w^3 + 6*w^2 + 8*w - 17]', '[1814, 1814, w^3 + 3*w^2 - 4*w - 14]', '[1814, 1814, -4*w^3 + 6*w^2 + 15*w - 21]', '[1814, 1814, -5*w^3 + 7*w^2 + 18*w - 22]', '[1814, 1814, 4*w^3 - 9*w^2 - 15*w + 28]', '[1816, 454, -5*w^3 + 9*w^2 + 13*w - 17]', '[1816, 454, -3*w^3 + 5*w^2 + 11*w - 1]', '[1820, 910, -w^3 - 2*w^2 + 3*w + 10]', '[1822, 1822, -5*w^3 + 7*w^2 + 22*w - 14]', '[1822, 1822, -3*w^3 + 7*w^2 + 10*w - 6]', '[1822, 1822, w^3 - 5*w^2 - 2*w + 14]', '[1822, 1822, 3*w^3 - 4*w^2 - 12*w + 1]', '[1825, 1825, w^3 - w^2 + w + 10]', '[1828, 914, -6*w^3 + 9*w^2 + 20*w - 13]', '[1831, 1831, -w^3 + 5*w^2 + 4*w - 11]', '[1835, 1835, 2*w^3 - 2*w^2 - 3*w]', '[1835, 1835, -w^3 + w^2 + w - 10]', '[1838, 1838, -6*w^3 + 7*w^2 + 27*w - 16]', '[1841, 1841, 2*w^3 + w^2 - 7*w + 1]', '[1841, 1841, -5*w^3 + 10*w^2 + 16*w - 18]', '[1843, 1843, w^3 - 6*w^2 - w + 21]', '[1850, 1850, -5*w^3 + 9*w^2 + 18*w - 20]', '[1850, 1850, 4*w^3 - 3*w^2 - 15*w]', '[1852, 926, 3*w^3 - 4*w^2 - 15*w + 18]', '[1856, 116, -4*w^3 + 6*w^2 + 12*w - 14]', '[1856, 116, -2*w^3 + 4*w^2 + 10*w - 4]', '[1861, 1861, 2*w^3 - 5*w^2 - 11*w + 7]', '[1861, 1861, -w^3 - 3*w^2 + 3*w + 12]', '[1862, 1862, -4*w^3 + 7*w^2 + 15*w - 12]', '[1867, 1867, -4*w^3 + w^2 + 15*w + 7]', '[1871, 1871, -2*w^3 + 4*w^2 + 5*w - 14]', '[1874, 1874, -4*w^2 + 3*w + 9]', '[1876, 938, 3*w^3 - 6*w^2 - 7*w + 14]', '[1877, 1877, 2*w^3 - 12*w - 3]', '[1879, 1879, -5*w^3 + 7*w^2 + 17*w - 2]', '[1880, 470, w^3 + 5*w^2 - 5*w - 15]', '[1880, 470, -w^3 + 5*w^2 + 3*w - 15]', '[1883, 1883, -3*w^3 + 7*w^2 + 13*w - 16]', '[1885, 1885, 2*w^3 - 12*w - 5]', '[1885, 1885, -2*w^3 + 2*w^2 + 6*w + 5]', '[1888, 236, -8*w^3 + 10*w^2 + 30*w - 32]', '[1889, 1889, -w^3 + 2*w^2 + 8*w - 4]', '[1889, 1889, -2*w^3 + 6*w^2 + 7*w - 18]', '[1895, 1895, w^3 - 3*w^2 - 3*w]', '[1895, 1895, -2*w^3 - w^2 + 11*w + 15]', '[1897, 1897, -w^3 - 2*w^2 + 2*w - 2]', '[1897, 1897, w^3 + w - 3]', '[1898, 1898, -3*w^3 + 2*w^2 + 6*w - 7]', '[1900, 950, -3*w^3 + 6*w^2 + 13*w - 20]', '[1906, 1906, -4*w^3 + 6*w^2 + 11*w - 13]', '[1912, 478, -5*w^3 + 11*w^2 + 13*w - 13]', '[1913, 1913, -w^3 + 6*w^2 - 18]', '[1913, 1913, w^3 - 3*w^2 - 6*w + 11]', '[1915, 1915, -3*w^2 - 2*w + 10]', '[1916, 958, 8*w^3 - 11*w^2 - 30*w + 21]', '[1916, 958, 3*w^3 - 8*w^2 - 5*w + 12]', '[1919, 1919, 4*w - 7]', '[1919, 1919, 2*w^2 - 5*w - 14]', '[1924, 962, 2*w^3 + w^2 - 8*w - 13]', '[1924, 962, 3*w^3 - 2*w^2 - 15*w + 8]', '[1927, 1927, w^3 + 2*w^2 - 4*w - 14]', '[1927, 1927, -w^3 + w^2 + 8*w + 1]', '[1933, 1933, 2*w^2 - 5*w - 8]', '[1933, 1933, 2*w^3 - 4*w^2 - 13*w + 4]', '[1934, 1934, 6*w^3 - 12*w^2 - 23*w + 37]', '[1934, 1934, -4*w^3 + 8*w^2 + 13*w - 23]', '[1936, 22, 2*w^3 - 6*w - 6]', '[1936, 22, -4*w^2 + 6*w + 12]', '[1937, 1937, -3*w^3 + 3*w^2 + 13*w + 2]', '[1937, 1937, w^3 - 7*w^2 - 2*w + 29]', '[1939, 1939, 5*w^3 - 8*w^2 - 18*w + 14]', '[1940, 970, 6*w^3 - w^2 - 28*w - 15]', '[1942, 1942, -6*w^3 + 7*w^2 + 23*w - 16]', '[1943, 1943, 5*w^3 - 6*w^2 - 17*w + 7]', '[1943, 1943, -5*w^2 + 3*w + 17]', '[1945, 1945, w^3 + 2*w^2 - 7*w - 5]', '[1945, 1945, 5*w^3 - 6*w^2 - 18*w + 10]', '[1945, 1945, -3*w^2 + 5*w + 15]', '[1949, 1949, 3*w^3 - w^2 - 13*w + 2]', '[1951, 1951, -2*w^3 + 6*w^2 + 9*w - 6]', '[1954, 1954, -4*w^3 + 6*w^2 + 17*w - 11]', '[1954, 1954, 4*w^3 - 6*w^2 - 15*w + 9]', '[1957, 1957, -6*w^3 + 13*w^2 + 22*w - 42]', '[1957, 1957, -5*w^3 + 9*w^2 + 18*w - 29]', '[1960, 490, -3*w^3 + 7*w^2 + 9*w - 15]', '[1963, 1963, 2*w^3 + w^2 - 13*w - 11]', '[1963, 1963, -6*w^3 + 9*w^2 + 22*w - 24]', '[1964, 982, 3*w^3 - 6*w^2 - 13*w + 22]', '[1966, 1966, -w^2 + w - 4]', '[1970, 1970, -2*w^3 + 4*w^2 + 5*w - 15]', '[1970, 1970, -w^3 - 3*w^2 + 6*w + 20]', '[1973, 1973, 4*w^3 - 4*w^2 - 13*w + 8]', '[1975, 1975, 2*w^3 - 3*w^2 - 4*w + 10]', '[1976, 494, -w^3 - w^2 + 9*w + 9]', '[1979, 1979, -w^3 + 5*w^2 + 3*w - 12]', '[1979, 1979, w^3 - 6*w^2 - 5*w + 17]', '[1981, 1981, -5*w - 4]', '[1982, 1982, -5*w^2 + 3*w + 12]', '[1985, 1985, 4*w^3 - 17*w - 10]', '[1985, 1985, -w^2 + 10]', '[1987, 1987, -3*w^3 + 7*w^2 + 11*w - 14]', '[1997, 1997, -2*w^3 + 6*w^2 + 7*w - 12]', '[2000, 10, -2*w^3 + 12*w + 4]', '[2000, 250, -2*w^3 + 2*w^2 + 4*w - 10]', '[2003, 2003, -3*w^3 + 7*w^2 + 9*w - 16]', '[2008, 502, -3*w^3 + 5*w^2 + 7*w - 1]', '[2008, 502, -5*w^3 + 9*w^2 + 17*w - 7]', '[2009, 2009, -4*w^3 + 6*w^2 + 20*w - 11]', '[2011, 2011, -2*w^3 + 2*w^2 + 3*w - 8]', '[2012, 1006, w^3 - 4*w^2 + 3*w + 4]', '[2020, 1010, -3*w^2 + 6*w + 5]', '[2020, 1010, -5*w^3 - 2*w^2 + 23*w + 20]', '[2023, 119, 2*w^3 - 9*w + 2]', '[2023, 119, -w^3 + 6*w^2 + 2*w - 6]', '[2025, 75, -3*w^3 + 3*w^2 + 15*w]', '[2026, 2026, 3*w^2 + w - 12]', '[2026, 2026, -5*w^3 + 3*w^2 + 22*w - 4]', '[2029, 2029, w^2 + 6*w + 4]', '[2029, 2029, w^3 + 2*w^2 - 5*w - 3]', '[2030, 2030, -w^3 + 4*w^2 - 15]', '[2030, 2030, -5*w^3 + 7*w^2 + 18*w - 10]', '[2032, 254, -2*w^3 + 4*w^2 + 4*w - 12]', '[2033, 2033, w^3 + w^2 - 2*w - 7]', '[2033, 2033, 4*w^3 - 4*w^2 - 14*w + 7]', '[2038, 2038, -4*w^3 + 4*w^2 + 17*w - 3]', '[2038, 2038, -3*w^3 + 16*w + 3]', '[2039, 2039, 5*w^3 - 3*w^2 - 21*w + 2]', '[2041, 2041, -4*w^3 + 2*w^2 + 16*w + 3]', '[2041, 2041, 5*w^3 - 3*w^2 - 21*w - 6]', '[2041, 2041, -2*w^3 + 5*w^2 + 5*w - 19]', '[2041, 2041, w^2 + 4]', '[2044, 1022, 3*w^3 - 4*w^2 - 13*w + 4]', '[2045, 2045, w^3 - 8*w]', '[2048, 8, 4*w^3 - 4*w^2 - 12*w + 4]', '[2050, 2050, -w^2 + w + 10]', '[2053, 2053, 2*w^3 - 5*w^2 - 9*w + 17]', '[2053, 2053, 3*w^3 - 4*w^2 - 9*w + 13]', '[2054, 2054, -w^3 + 8*w + 3]', '[2060, 1030, -10*w^3 + 5*w^2 + 46*w + 5]', '[2060, 1030, -7*w^3 + 4*w^2 + 31*w]', '[2062, 2062, 2*w^3 - 5*w^2 - 5*w + 18]', '[2062, 2062, -8*w^3 + 11*w^2 + 31*w - 34]', '[2065, 2065, -5*w^3 + 2*w^2 + 13*w - 15]', '[2066, 2066, -5*w^3 + 6*w^2 + 18*w - 11]', '[2066, 2066, -5*w^3 + 5*w^2 + 20*w - 18]', '[2071, 2071, -6*w^3 + 7*w^2 + 15*w - 9]', '[2071, 2071, -5*w^3 + 9*w^2 + 20*w - 23]', '[2072, 518, -w^3 + 5*w^2 + w - 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5*w - 3]', '[2119, 2119, 5*w^3 - 2*w^2 - 22*w - 12]', '[2119, 2119, -w^3 + w^2 + 9*w + 4]', '[2126, 2126, 5*w^3 - 12*w^2 - 20*w + 37]', '[2126, 2126, -2*w^3 + 4*w^2 + 7*w - 17]', '[2128, 266, 4*w^3 - 6*w^2 - 14*w + 6]', '[2129, 2129, w^3 + w^2 + w - 4]', '[2132, 1066, -4*w^3 + 3*w^2 + 18*w + 1]', '[2137, 2137, 4*w^3 - 2*w^2 - 20*w - 1]', '[2137, 2137, -3*w^3 + 6*w^2 + 13*w - 21]', '[2138, 2138, -7*w^3 + 13*w^2 + 30*w - 36]', '[2138, 2138, -9*w^3 + 11*w^2 + 38*w - 24]', '[2140, 1070, -w^3 - 2*w^2 + 9*w + 10]', '[2140, 1070, 2*w^3 - 5*w^2 - 4*w + 15]', '[2141, 2141, w^3 - 4*w^2 + 2*w + 8]', '[2144, 268, 4*w^3 - 4*w^2 - 14*w + 6]', '[2146, 2146, -w^3 - w^2 + 4*w - 4]', '[2146, 2146, -5*w^3 + 8*w^2 + 18*w - 23]', '[2146, 2146, w^2 - 5*w - 6]', '[2146, 2146, -2*w^3 + 4*w^2 + 5*w - 1]', '[2147, 2147, -3*w^3 + 7*w^2 + 10*w - 19]', '[2149, 2149, -w^3 - 4*w^2 + 6*w - 2]', '[2149, 2149, -3*w^3 + 8*w^2 + 18*w - 16]', '[2152, 538, w^3 - 5*w^2 - 3*w + 13]', '[2153, 2153, 3*w^3 - 7*w^2 - 11*w + 8]', '[2155, 2155, 4*w^3 - 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9*w + 1]', '[5333, 5333, 7*w^3 - 11*w^2 - 27*w + 22]', '[5333, 5333, -w^3 + 2*w^2 - 3*w - 13]', '[5341, 5341, -2*w^3 + 7*w^2 + 13*w - 17]', '[5341, 5341, 4*w^3 - 9*w^2 - 15*w + 13]', '[5345, 5345, 3*w^3 - w^2 - 14*w + 5]', '[5345, 5345, 5*w^3 - 3*w^2 - 14*w + 15]', '[5347, 5347, -3*w^3 + 8*w^2 + 9*w - 21]', '[5350, 5350, -3*w^3 + 2*w^2 + 18*w + 5]', '[5350, 5350, 3*w^3 - 5*w^2 - 8*w + 20]', '[5351, 5351, -2*w^3 + 3*w^2 + 13*w - 3]', '[5356, 2678, 9*w^2 - 6*w - 37]', '[5356, 2678, -w^3 + 6*w^2 - w - 24]', '[5360, 670, 4*w^2 - 6*w - 20]', '[5362, 5362, w^3 + w^2 - 6*w - 14]', '[5365, 5365, 2*w^3 - 8*w^2 - 4*w + 25]', '[5365, 5365, w^2 - 6*w]', '[5365, 5365, -w^3 - w + 5]', '[5365, 5365, 2*w^3 - w^2 - 6*w + 10]', '[5366, 5366, -9*w^3 + 14*w^2 + 34*w - 43]', '[5366, 5366, 3*w^3 - w^2 - 18*w - 8]', '[5369, 5369, -2*w^3 + 7*w^2 + 9*w - 23]', '[5374, 5374, 5*w^3 - 11*w^2 - 20*w + 36]', '[5377, 5377, 2*w^3 - w^2 - 3*w - 3]', '[5380, 2690, 8*w^3 - 5*w^2 - 36*w + 5]', '[5381, 5381, -2*w^3 + 10*w + 13]', '[5383, 5383, 5*w^3 - 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3*w - 3]', '[379, 379, -2*w^3 + 4*w^2 + 4*w - 9]', '[383, 383, 2*w^3 - 9*w - 2]', '[389, 389, w^3 + w^2 - 4*w - 9]', '[389, 389, -2*w^3 + 5*w^2 + 6*w - 14]', '[389, 389, 2*w^3 - 4*w^2 - 6*w + 3]', '[397, 397, w^3 - 4*w^2 - w + 7]', '[397, 397, -2*w^3 + 11*w + 4]', '[409, 409, w^2 - 8]', '[419, 419, -3*w^2 - 2*w + 8]', '[431, 431, -w^3 + 4*w^2 + 3*w - 13]', '[433, 433, 2*w^3 - w^2 - 9*w + 3]', '[443, 443, -3*w^3 + 3*w^2 + 11*w - 6]', '[449, 449, w^3 - 2*w^2 - w + 11]', '[449, 449, -w^2 - 2]', '[457, 457, w^3 + w^2 - 6*w - 3]', '[463, 463, -3*w^3 + 6*w^2 + 11*w - 17]', '[479, 479, -3*w^3 + 2*w^2 + 14*w - 4]', '[479, 479, 2*w^3 - 3*w^2 - 8*w + 2]', '[491, 491, -3*w^3 + 4*w^2 + 8*w - 2]', '[503, 503, 3*w^3 - 3*w^2 - 11*w + 4]', '[521, 521, -3*w^3 + w^2 + 14*w + 1]', '[521, 521, -3*w^3 + 2*w^2 + 12*w - 2]', '[569, 569, 4*w^3 - 4*w^2 - 16*w + 7]', '[587, 587, -3*w^3 + 4*w^2 + 12*w - 6]', '[587, 587, -2*w^3 + 2*w^2 + 4*w - 1]', '[593, 593, -3*w^3 + 3*w^2 + 12*w - 1]', '[593, 593, -w^3 - w^2 + 5*w - 2]', '[607, 607, -3*w^3 + 6*w^2 + 10*w - 18]', '[613, 613, -2*w^2 + w + 12]', '[613, 613, 3*w^3 - 5*w^2 - 11*w + 8]', '[631, 631, w^3 - 4*w^2 - 3*w + 9]', '[631, 631, w^3 - 7*w - 3]', '[641, 641, -3*w^3 + 6*w^2 + 10*w - 14]', '[643, 643, w^3 - w^2 - 3*w - 4]', '[643, 643, -w^3 + 3*w^2 + 4*w - 1]', '[659, 659, -2*w^3 + w^2 + 10*w - 4]', '[661, 661, w^3 + 2*w^2 - 7*w - 7]', '[673, 673, -2*w^3 + 3*w^2 + 9*w - 3]', '[673, 673, w^3 + w^2 - 6*w + 3]', '[677, 677, 3*w^2 - 3*w - 7]', '[677, 677, -3*w^3 + 5*w^2 + 12*w - 9]', '[683, 683, -3*w^3 + 3*w^2 + 10*w - 3]', '[691, 691, 2*w^3 - 2*w^2 - 10*w - 1]', '[709, 709, 2*w^3 - 5*w^2 - 6*w + 12]', '[719, 719, -w^3 + 2*w^2 - 8]', '[727, 727, -w^3 + 5*w^2 + w - 16]', '[727, 727, -3*w^3 + 6*w^2 + 10*w - 8]', '[733, 733, 4*w^3 - 5*w^2 - 14*w + 8]', '[739, 739, -w^3 + 4*w^2 + 3*w - 11]', '[739, 739, 3*w^3 - w^2 - 12*w - 1]', '[743, 743, 3*w^3 - 6*w^2 - 11*w + 13]', '[761, 761, -3*w^3 + 5*w^2 + 9*w - 12]', '[769, 769, -3*w^3 + 4*w^2 + 11*w - 3]', '[773, 773, 4*w^3 - 7*w^2 - 10*w + 6]', '[787, 787, w^2 + 2*w - 6]', '[787, 787, 3*w^2 - 2*w - 6]', '[787, 787, -3*w^3 + 3*w^2 + 9*w - 4]', '[787, 787, -w^3 + 7*w + 9]', '[811, 811, -2*w^3 - w^2 + 10*w + 6]', '[811, 811, 3*w^3 - 2*w^2 - 15*w + 3]', '[823, 823, 2*w^3 - 3*w^2 - 4*w + 8]', '[823, 823, -3*w^3 + 2*w^2 + 6*w - 2]', '[823, 823, -2*w^3 + 2*w^2 + 11*w + 2]', '[823, 823, -w^2 - w - 3]', '[841, 29, -2*w^3 - w^2 + 12*w + 8]', '[857, 857, 2*w^3 - 3*w^2 - 12*w + 2]', '[859, 859, w^3 + 4*w^2 - 5*w - 13]', '[863, 863, -w^3 + w^2 + 7*w - 2]', '[877, 877, 3*w^3 - 5*w^2 - 8*w + 11]', '[881, 881, -w^3 + 5*w^2 - 17]', '[881, 881, -2*w^3 + 5*w^2 + 8*w - 12]', '[887, 887, -4*w^3 + 5*w^2 + 16*w - 8]', '[887, 887, -w^3 + 3*w^2 - w - 4]', '[907, 907, -2*w^3 + 2*w^2 + 10*w + 3]', '[907, 907, 2*w^3 - w^2 - 11*w - 1]', '[907, 907, -3*w^3 + 2*w^2 + 11*w - 3]', '[907, 907, -2*w^3 + 8*w - 1]', '[911, 911, 2*w^2 + 2*w - 7]', '[911, 911, w^2 + 5*w + 3]', '[911, 911, -w^3 + 3*w^2 - w - 8]', '[911, 911, -4*w^3 + 4*w^2 + 11*w - 2]', '[919, 919, -2*w^3 + 5*w^2 + 7*w - 13]', '[937, 937, -w^3 - 3*w^2 + 4*w + 13]', '[953, 953, 3*w^3 - 8*w^2 - 7*w + 11]', '[967, 967, 3*w^3 - 2*w^2 - 15*w + 1]', '[967, 967, -3*w^2 + 4*w + 6]', '[971, 971, -w^2 + w - 3]', '[977, 977, -3*w^3 + 4*w^2 + 7*w - 3]', '[977, 977, w^3 - w - 3]', '[983, 983, -4*w^3 + 5*w^2 + 11*w - 7]', '[991, 991, -3*w^3 + 6*w^2 + 4*w - 14]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [5, -2, -6, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 6224, 'disc_rad': 778, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[3, 1], [1, 1]]], [7, [[3, 1], [1, 1]]], [11, [[2, 2]]], [13, [[3, 1], [1, 1]]], [17, [[2, 2]]], [19, [[3, 1], [1, 1]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[2, 1], [1, 2]]], [41, [[3, 1], [1, 1]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 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': 44.27682411416183, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.6224.1', 'local_algs': ['2.4.4.5', 'm389.1.1.0', 'm389.1.1.0', 'm389.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 389], 'rd': 8.88213553675, 'regulator': {'__RealLiteral__': 0, 'data': '5.46622407668', 'prec': 44}, 'res': {'gal': ['16,0,-1104,0,21280,0,-138416,0,391776,0,-578624,0,488616,0,-245092,0,73188,0,-12656,0,1196,0,-56,0,1'], 'sib': ['-9,28,23,-52,-35,-2,1', '1,0,-149,0,814,0,-801,0,262,0,-29,0,1', '1,8,2,-72,-31,216,-26,-188,73,38,-18,-2,1', '1132,1092,-1052,-604,278,92,-28,-4,1', '2,-6,-2,14,-6,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 3 \\)', '\\( a^{3} - a^{2} - 4 a + 1 \\)', '\\( a^{3} - 5 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}