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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 8112, 'field_bad_primes': [2, 3, 13], 'field_label': '4.4.8112.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.8112.1-9.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [3], 'level_ideal': '[9, 3, -w^2 + 3]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-c', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3, 3, w]', 1]], 'hecke_eigenvalues': [0, 4, 4, -2, -2, -6, -6, 6, 6, 2, 2, 6, 6, -8, -8, -12, -12, -10, -10, -6, -12, -12, -6, 6, 6, -14, -14, 4, 4, 6, -12, -12, 6, 20, 20, -24, -24, -18, 12, 12, -18, 4, 4, 16, 16, 6, 6, 0, 0, 24, -18, -18, 24, 6, 6, -16, 26, 26, -16, 4, 4, 2, -14, -2, -2, -14, 22, 10, 10, 22, 8, 8, -14, -14, -14, -14, 18, 18, -24, 12, 12, -24, 8, 8, 12, 36, 36, 12, -30, -12, -12, -30, 18, 18, -4, -4, -4, 38, -28, -28, -36, 24, 24, -36, 24, 24, 40, 40, 24, -6, -6, 24, -2, 46, 46, -2, 38, 38, 32, -18, -18, -18, -12, -12, -18, 6, 6, -6, -6, -30, -30, -44, -44, -40, -40, -18, -18, -30, -30, -16, -16, 50, 12, 12, -56, -56, 18, 18, 16, 16, 28, 28, -20, -20, 6, 6, -16, -16, -28, -58, -58, -28], 'hecke_polynomial': 'x', 'label': '4.4.8112.1-9.1-c'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 8112, 'ideals': ['[1, 1, 1]', '[3, 3, w]', '[4, 2, w^2 - w - 1]', '[9, 3, -w^2 + 3]', '[9, 3, -w^2 + 2]', '[12, 6, w^2 - w - 3]', '[13, 13, w^3 - 4*w + 2]', '[13, 13, -w^3 + 4*w + 2]', '[16, 2, 2]', '[17, 17, w^3 - 3*w - 1]', '[17, 17, -w^3 + 3*w - 1]', '[27, 3, -w^3 + 5*w]', '[27, 9, -w^3 + 3*w]', '[29, 29, w^3 + w^2 - 4*w - 2]', '[29, 29, w^3 - w^2 - 4*w + 2]', '[36, 6, w^3 + w^2 - 5*w - 2]', '[36, 6, w^3 + w^2 - 3*w]', '[39, 39, w + 3]', '[39, 39, w - 3]', '[43, 43, w^2 + w - 4]', '[43, 43, w^2 - w - 4]', '[48, 6, 2*w]', '[51, 51, w^3 + w^2 - 4*w - 6]', '[51, 51, w^3 - w^2 - 4*w + 6]', '[52, 26, w^3 + w^2 - 3*w - 4]', '[52, 26, w^3 - w^2 - 3*w + 4]', '[53, 53, w^3 - 2*w - 2]', '[53, 53, -w^3 + 2*w - 2]', '[64, 4, 2*w^2 - 2*w - 2]', '[68, 34, -w^2 + w + 5]', '[68, 34, w^2 + w - 5]', '[79, 79, w^3 - w^2 - 4*w + 1]', '[79, 79, -w^3 - w^2 + 4*w + 1]', '[81, 3, 3]', '[81, 9, w^2 + 1]', '[81, 9, -w^2 + 6]', '[87, 87, -w^3 - 2*w^2 + 4*w + 6]', '[87, 87, w^3 - 2*w^2 - 4*w + 6]', '[101, 101, -w^3 + w^2 + 3*w - 5]', '[101, 101, w^3 + w^2 - 3*w - 5]', '[103, 103, 2*w^2 - w - 4]', '[103, 103, 2*w^2 + w - 4]', '[107, 107, 2*w^2 + w - 5]', '[107, 107, 3*w^2 - 3*w - 4]', '[107, 107, 2*w^2 - 2*w - 1]', '[107, 107, 2*w^2 - w - 5]', '[108, 6, w^3 - 2*w - 3]', '[108, 18, w^3 + w^2 - 3*w - 6]', '[113, 113, w^3 - w^2 - 5*w + 1]', '[113, 113, -w^3 - w^2 + 5*w + 1]', '[116, 58, -w^3 + 2*w^2 + 2*w - 5]', '[116, 58, w^3 + 2*w^2 - 2*w - 5]', '[117, 39, -2*w^3 - w^2 + 7*w + 2]', '[117, 39, w^2 + 3*w]', '[117, 39, 2*w^3 - w^2 - 7*w + 2]', '[117, 39, w^2 - 3*w]', '[121, 11, w^3 - 2*w^2 - 3*w + 2]', '[121, 11, -2*w^3 + w^2 + 7*w - 4]', '[127, 127, -2*w^3 + 7*w - 2]', '[127, 127, 2*w^3 - 7*w - 2]', '[129, 129, w^3 - w^2 - 4*w]', '[129, 129, w^3 + w^2 - 4*w]', '[131, 131, w^3 - w^2 - 1]', '[131, 131, -w^3 + w^2 + 4*w + 1]', '[131, 131, -2*w^3 + 3*w^2 + 4*w - 2]', '[131, 131, -2*w^3 + w^2 + 4*w + 2]', '[139, 139, w^2 - 2*w - 4]', '[139, 139, w^2 + 2*w - 4]', '[144, 6, -2*w^2 + 6]', '[144, 6, -2*w^2 + 4]', '[153, 51, w^2 - 3*w - 2]', '[153, 51, w^3 + w^2 - 6*w - 3]', '[153, 51, w^2 + 3*w - 2]', '[153, 51, -w^3 + w^2 + 6*w - 3]', '[156, 78, -2*w^3 + w^2 + 7*w - 3]', '[156, 78, 2*w^3 + w^2 - 7*w - 3]', '[159, 159, 3*w^2 - 2*w - 3]', '[159, 159, -3*w^2 - 2*w + 3]', '[169, 13, 2*w^2 - 5]', '[169, 13, 2*w^2 + w - 8]', '[169, 13, 2*w^2 - w - 8]', '[172, 86, -w^2 + 3*w + 1]', '[172, 86, -2*w^3 + w^2 + 5*w + 1]', '[173, 173, 2*w^2 - 3*w - 5]', '[173, 173, 2*w^2 + 3*w - 5]', '[179, 179, -w^2 - 3*w + 4]', '[179, 179, 2*w^3 - w^2 - 9*w + 2]', '[179, 179, -2*w^3 - w^2 + 9*w + 2]', '[179, 179, w^2 - 3*w - 4]', '[192, 12, 2*w^2 - 2*w - 6]', '[199, 199, -3*w^3 + w^2 + 12*w - 4]', '[199, 199, -3*w^3 - w^2 + 12*w + 4]', '[204, 102, -w^3 + w^2 + 5*w]', '[204, 102, w^3 + w^2 - 5*w]', '[208, 26, 2*w^3 - 8*w + 4]', '[208, 26, -2*w^3 + 8*w + 4]', '[211, 211, 2*w^3 - 7*w + 1]', '[211, 211, -2*w^3 + 7*w + 1]', '[212, 106, 2*w^3 - 5*w^2 + w + 5]', '[212, 106, -2*w^3 + w^2 + 3*w - 1]', '[221, 221, -w^3 - w^2 + 2*w + 4]', '[221, 221, w^3 - w^2 - 4*w + 7]', '[221, 221, -w^3 - w^2 + 4*w + 7]', '[221, 221, w^3 - w^2 - 2*w + 4]', '[233, 233, -w^2 - w - 2]', '[233, 233, -w^2 + w - 2]', '[237, 237, -w^3 + w^2 + w - 3]', '[237, 237, w^3 + w^2 - w - 3]', '[243, 9, 3*w]', '[243, 9, -2*w^3 + 7*w]', '[243, 27, -w^3 + 6*w]', '[256, 4, 4]', '[257, 257, -3*w^2 - w + 10]', '[257, 257, 3*w^2 - w - 10]', '[261, 87, w^3 - w^2 - 5*w - 1]', '[261, 87, 2*w^3 - 9*w - 3]', '[261, 87, w^3 + w^2 - 5*w + 1]', '[261, 87, 2*w^3 - 9*w + 3]', '[263, 263, -w^3 + w^2 + 6*w + 1]', '[263, 263, w^2 + 2*w - 5]', '[263, 263, w^2 - 2*w - 5]', '[263, 263, w^3 + w^2 - 6*w + 1]', '[269, 269, -2*w^3 - w^2 + 6*w + 1]', '[269, 269, 2*w^3 - w^2 - 6*w + 1]', '[272, 34, 2*w^3 - 6*w - 2]', '[272, 34, -2*w^3 + 6*w - 2]', '[277, 277, w^3 - w^2 - 2]', '[277, 277, -w^3 + 2*w^2 + 3*w - 8]', '[277, 277, w^3 + 2*w^2 - 3*w - 8]', '[277, 277, -w^3 - w^2 - 2]', '[283, 283, -2*w^3 + w^2 + 8*w - 1]', '[283, 283, 2*w^3 + w^2 - 8*w - 1]', '[289, 17, -w^2 - 2]', '[289, 17, w^2 - 7]', '[289, 289, -w^3 + 2*w^2 + 6*w - 8]', '[289, 289, w^3 + 2*w^2 - 6*w - 8]', '[303, 303, w^3 + 2*w^2 - 5*w - 3]', '[303, 303, w^3 - 2*w^2 - 5*w + 3]', '[309, 309, 2*w^3 - w^2 - 4*w]', '[309, 309, 2*w^3 + w^2 - 4*w]', '[313, 313, w^3 + 2*w^2 - 4*w - 2]', '[313, 313, 2*w^3 - w^2 - 6*w + 2]', '[313, 313, -2*w^3 - w^2 + 6*w + 2]', '[313, 313, -w^3 + 2*w^2 + 4*w - 2]', '[316, 158, w^3 - 4*w^2 + 5]', '[316, 158, -w^3 + 2*w^2 + 2*w + 1]', '[321, 321, 2*w^3 + w^2 - 5*w]', '[321, 321, w^3 + 3*w^2 - 7*w - 9]', '[321, 321, -w^3 + 2*w^2 + 2*w - 6]', '[321, 321, 2*w^3 - w^2 - 5*w]', '[324, 6, 3*w^2 - 3*w - 3]', '[324, 18, 2*w^3 - w^2 - 7*w - 1]', '[324, 18, w^3 + 2*w^2 - 6*w - 3]', '[337, 337, -w^3 - 2*w^2 + 7*w + 2]', '[337, 337, -2*w^3 + 4*w + 1]', '[337, 337, 2*w^3 - 4*w + 1]', '[337, 337, -w^3 + 2*w^2 + 7*w - 2]', '[339, 339, -w^3 + w + 3]', '[339, 339, -w^3 + w - 3]', '[348, 174, -3*w^3 + w^2 + 11*w - 6]', '[348, 174, -3*w^3 - w^2 + 11*w + 6]', '[351, 39, -w^3 - 3*w^2 + 2*w + 6]', '[351, 39, -w^3 + 3*w^2 + 2*w - 6]', '[351, 117, -2*w^3 + w^2 + 6*w - 6]', '[351, 117, -2*w^3 - w^2 + 6*w + 6]', '[363, 33, -2*w^3 + 2*w^2 + 2*w - 3]', '[363, 33, w^3 - 3*w^2 - 4*w + 6]', '[367, 367, -w^3 + 3*w^2 - 2*w - 5]', '[367, 367, 2*w^3 - 3*w^2 - 2*w + 4]', '[373, 373, -2*w^3 + 10*w + 1]', '[373, 373, -3*w^3 - w^2 + 14*w + 5]', '[373, 373, 3*w^3 - w^2 - 14*w + 5]', '[373, 373, 2*w^3 - 10*w + 1]', '[377, 377, w^3 - 2*w^2 + 4]', '[377, 377, w^3 - 3*w + 5]', '[377, 377, w^3 - 3*w - 5]', '[377, 377, w^3 + 2*w^2 - 4]', '[381, 381, 3*w^2 - 2*w - 6]', '[381, 381, -3*w^2 - 2*w + 6]', '[387, 129, -w^3 + 2*w^2 + 3*w - 9]', '[387, 129, -w^3 + w^2 + 2*w - 5]', '[387, 129, w^3 + 2*w^2 - 3*w - 9]', '[387, 129, w^3 + w^2 - 2*w - 5]', '[389, 389, 2*w^3 - 6*w - 1]', '[389, 389, -2*w^3 + 6*w - 1]', '[393, 393, 2*w^3 - 2*w^2 - 7*w + 3]', '[393, 393, -2*w^3 - 2*w^2 + 7*w + 9]', '[393, 393, -w^3 + w + 6]', '[393, 393, -3*w^3 + 11*w + 6]', '[404, 202, -2*w^3 + w^2 + 5*w - 1]', '[404, 202, -3*w^2 + 5*w + 5]', '[412, 206, -3*w^3 + 5*w^2 + 5*w - 2]', '[412, 206, -w^3 + 3*w^2 + 3*w - 2]', '[417, 417, w^3 - 2*w^2 - 4*w]', '[417, 417, w^3 + 2*w^2 - 4*w]', '[419, 419, 2*w^3 - 11*w - 4]', '[419, 419, 2*w^2 - 2*w - 7]', '[419, 419, 2*w^2 + 2*w - 7]', '[419, 419, -2*w^3 + 11*w - 4]', '[428, 214, -w^3 + 2*w^2 + 4*w - 1]', '[428, 214, -w^3 + 4*w + 5]', '[428, 214, w^3 - 4*w + 5]', '[428, 214, -3*w^3 + 4*w^2 + 6*w - 1]', '[432, 6, -2*w^3 + 10*w]', '[432, 18, -2*w^3 + 6*w]', '[439, 439, 3*w^2 - w - 14]', '[439, 439, -3*w^2 - w + 14]', '[443, 443, w^3 + 3*w^2 - 4*w - 10]', '[443, 443, 3*w^3 + w^2 - 14*w - 4]', '[443, 443, 3*w^3 - w^2 - 14*w + 4]', '[443, 443, -w^3 + 3*w^2 + 4*w - 10]', '[452, 226, -3*w^2 + w + 5]', '[452, 226, 2*w^3 - 3*w^2 - 3*w - 1]', '[459, 51, w^3 + 3*w^2 - 5*w - 9]', '[459, 51, w^3 - 3*w^2 - 5*w + 9]', '[459, 153, w^3 - w^2 - 3*w - 3]', '[459, 153, w^3 + w^2 - 3*w + 3]', '[464, 58, 2*w^3 + 2*w^2 - 8*w - 4]', '[464, 58, 2*w^3 - 2*w^2 - 8*w + 4]', '[468, 78, w^2 - 3*w - 5]', '[468, 78, w^3 + 2*w^2 - 6*w - 9]', '[468, 78, w^3 - 2*w^2 - 6*w + 9]', '[468, 78, -w^2 - 3*w + 5]', '[477, 159, -w^3 + 2*w^2 - w - 4]', '[477, 159, 2*w^2 - 3*w - 6]', '[477, 159, w^3 + 2*w^2 + w - 4]', '[477, 159, 2*w^2 + 3*w - 6]', '[484, 22, 3*w^3 - 8*w^2 - 2*w + 7]', '[484, 22, -2*w^3 + 3*w^2 + 3*w - 5]', '[493, 493, -w^2 + w + 8]', '[493, 493, -w^3 + w + 4]', '[493, 493, -w^3 + w - 4]', '[493, 493, w^2 + w - 8]', '[503, 503, -w - 5]', '[503, 503, 3*w^3 + w^2 - 12*w - 1]', '[503, 503, 3*w^3 - w^2 - 12*w + 1]', '[503, 503, w - 5]', '[507, 39, 2*w^3 + w^2 - 8*w]', '[507, 39, 2*w^3 - w^2 - 8*w]', '[507, 39, 2*w^3 - 5*w]', '[508, 254, -w^3 + w^2 + w - 4]', '[508, 254, w^3 - 5*w^2 + 3*w + 8]', '[516, 258, -2*w^3 - w^2 + 7*w + 9]', '[516, 258, -3*w^2 + w + 9]', '[519, 519, 2*w^3 - 3*w^2 - 5*w]', '[519, 519, 2*w^3 + 3*w^2 - 5*w]', '[521, 521, w^3 + 2*w^2 - 5*w - 2]', '[521, 521, -w^3 + 2*w^2 + 5*w - 2]', '[523, 523, 3*w^2 - 2*w - 10]', '[523, 523, w^3 + 3*w^2 - 6*w - 11]', '[524, 262, -w^3 + w^2 + 7*w - 4]', '[524, 262, w^3 + 3*w^2 - 3*w - 8]', '[524, 262, -w^3 + 3*w^2 + 3*w - 8]', '[524, 262, w^3 + w^2 - 7*w - 4]', '[529, 23, 2*w^2 - 11]', '[529, 23, 3*w^2 - 10]', '[537, 537, -w^3 - 3*w^2 + 4*w]', '[537, 537, -w^3 + w^2 + 2*w - 6]', '[537, 537, -w^3 - w^2 + 2*w + 6]', '[537, 537, w^3 - 3*w^2 - 4*w]', '[547, 547, -2*w^3 + w^2 + 6*w - 7]', '[547, 547, 2*w^3 + w^2 - 6*w - 7]', '[556, 278, -3*w^3 + 2*w^2 + 6*w + 1]', '[556, 278, w^3 - 2*w^2 + 2*w + 1]', '[559, 559, 3*w^3 + w^2 - 11*w - 5]', '[559, 559, 3*w^3 + 3*w^2 - 15*w - 11]', '[559, 559, -3*w^3 + 3*w^2 + 15*w - 11]', '[559, 559, -3*w^3 + w^2 + 11*w - 5]', '[563, 563, -2*w^3 + w^2 + 4*w - 4]', '[563, 563, -3*w^3 + 10*w - 4]', '[563, 563, 3*w^3 - 10*w - 4]', '[563, 563, 2*w^3 + w^2 - 4*w - 4]', '[569, 569, w^3 + 2*w^2 - 6*w - 10]', '[569, 569, -w^3 + 2*w^2 + 6*w - 10]', '[571, 571, -2*w^3 + 3*w^2 + 5*w - 2]', '[571, 571, -2*w^3 + 2*w^2 + 6*w + 1]', '[576, 12, 2*w^3 + 2*w^2 - 10*w - 4]', '[576, 12, 2*w^3 + 2*w^2 - 6*w]', '[597, 597, w^3 - 3*w^2 - 4*w + 9]', '[597, 597, -w^3 - 3*w^2 + 4*w + 9]', '[599, 599, 3*w^3 - 11*w - 2]', '[599, 599, 2*w^3 + w^2 - 6*w - 8]', '[599, 599, 2*w^3 - w^2 - 6*w + 8]', '[599, 599, 3*w^3 - 11*w + 2]', '[601, 601, -w^3 - 2*w^2 + 6*w + 2]', '[601, 601, 4*w^3 - w^2 - 16*w + 5]', '[601, 601, 4*w^3 + w^2 - 16*w - 5]', '[601, 601, w^3 - 2*w^2 - 6*w + 2]', '[607, 607, -w^3 + w^2 + 4*w - 8]', '[607, 607, -w^3 - w^2 + 4*w + 8]', '[612, 102, w^3 + 3]', '[612, 102, -w^3 - 2*w^2 + 2*w + 7]', '[612, 102, w^3 - 3]', '[612, 102, -w^3 + 2*w^2 + 2*w - 7]', '[624, 78, 2*w + 6]', '[624, 78, 2*w - 6]', '[625, 5, -5]', '[633, 633, 3*w^2 + w - 6]', '[633, 633, -3*w^2 + w + 6]', '[636, 318, -5*w^2 + 5*w + 9]', '[636, 318, w^2 - w + 3]', '[641, 641, w^2 + 4*w - 1]', '[641, 641, w^2 - 4*w - 1]', '[647, 647, w^3 + 3*w^2 - 4*w - 8]', '[647, 647, -w^3 + 7*w + 2]', '[647, 647, w^3 - 7*w + 2]', '[647, 647, -w^3 + 3*w^2 + 4*w - 8]', '[653, 653, 2*w^3 - 3*w^2 - 12*w + 10]', '[653, 653, 2*w^3 + 3*w^2 - 12*w - 10]', '[663, 663, -w^3 + w^2 + 7*w - 3]', '[663, 663, -3*w^3 + 13*w + 3]', '[663, 663, -3*w^3 + 13*w - 3]', '[663, 663, -w^3 - w^2 + 7*w + 3]', '[676, 26, -w^3 + w^2 + 7*w - 2]', '[676, 26, -w^3 - w^2 + 7*w + 2]', '[676, 26, -2*w^3 + 3*w^2 + 5*w - 1]', '[677, 677, 3*w^2 + w - 8]', '[677, 677, 3*w^2 - w - 8]', '[688, 86, 2*w^2 + 2*w - 8]', '[688, 86, 2*w^2 - 2*w - 8]', '[689, 689, -4*w^3 + 12*w - 7]', '[689, 689, 4*w - 1]', '[689, 689, -4*w - 1]', '[689, 689, 4*w^3 - 12*w - 7]', '[692, 346, -5*w^3 + 6*w^2 + 8*w - 1]', '[692, 346, w^3 + 2*w - 1]', '[699, 699, -w^3 - w^2 - 2*w]', '[699, 699, -w^3 + w^2 - 2*w]', '[701, 701, 2*w^3 - 2*w^2 - 7*w + 2]', '[701, 701, -2*w^3 - 2*w^2 + 7*w + 2]', '[711, 237, w^3 + 2*w^2 - 5*w - 1]', '[711, 237, 2*w^3 + w^2 - 9*w]', '[711, 237, w^3 - 2*w^2 - 5*w + 1]', '[711, 237, 2*w^3 - w^2 - 9*w]', '[716, 358, -2*w^3 + 3*w^2 - w - 1]', '[716, 358, -3*w^2 + w + 7]', '[716, 358, 2*w^3 - w^2 - 5*w - 5]', '[716, 358, -4*w^3 + 3*w^2 + 7*w + 1]', '[727, 727, -2*w^3 - 2*w^2 + 11*w + 7]', '[727, 727, -2*w^3 + 2*w^2 + 11*w - 7]', '[729, 9, -3*w^2 + 9]', '[729, 9, -3*w^2 + 6]', '[729, 27, w^2 + 3]', '[729, 27, -w^2 + 8]', '[731, 731, 2*w^3 - 3*w^2 - 10*w + 7]', '[731, 731, 2*w^3 + w^2 - 8*w + 1]', '[731, 731, -2*w^3 + w^2 + 8*w + 1]', '[731, 731, -2*w^3 - 3*w^2 + 10*w + 7]', '[751, 751, -4*w^2 + 3*w + 7]', '[751, 751, w^3 - 2*w^2 - w - 2]', '[768, 12, 4*w]', '[771, 771, -3*w^3 - w^2 + 10*w]', '[771, 771, 3*w^3 - w^2 - 10*w]', '[783, 87, w^3 - 5*w + 6]', '[783, 87, -w^3 + 5*w + 6]', '[783, 261, w^2 + 3*w - 6]', '[783, 261, w^2 - 3*w - 6]', '[789, 789, w^3 + w^2 + w + 3]', '[789, 789, w^3 - 2*w^2 - 5*w]', '[789, 789, w^3 + 2*w^2 - 5*w]', '[789, 789, w^3 - w^2 + w - 3]', '[796, 398, -w^3 + 3*w^2 + w - 8]', '[796, 398, w^3 + 3*w^2 - 7*w - 10]', '[797, 797, 3*w^3 - 11*w + 1]', '[797, 797, 3*w^3 - 11*w - 1]', '[807, 807, -w^3 - 4*w^2 + w + 6]', '[807, 807, -w^3 + 4*w^2 + w - 6]', '[809, 809, -w^3 + 7*w - 1]', '[809, 809, w^3 - 7*w - 1]', '[816, 102, 2*w^3 + 2*w^2 - 8*w - 12]', '[816, 102, 2*w^3 - 2*w^2 - 8*w + 12]', '[823, 823, -2*w^3 + 4*w^2 + 9*w - 14]', '[823, 823, 2*w^3 + 4*w^2 - 9*w - 14]', '[831, 831, -w^3 + 5*w^2 - 2*w - 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6]', '[1521, 39, -w^3 + 2*w^2 + 2*w - 10]', '[1521, 39, w^3 + 2*w^2 - 2*w - 10]', '[1521, 39, w^2 - 9]', '[1524, 762, -3*w^3 - 5*w^2 + 17*w + 12]', '[1524, 762, 3*w^3 + w^2 - 13*w]', '[1531, 1531, 4*w^3 - 2*w^2 - 18*w + 5]', '[1531, 1531, -4*w^3 - 2*w^2 + 18*w + 5]', '[1537, 1537, -w^3 + 2*w^2 + 9*w - 7]', '[1537, 1537, -3*w^3 - 2*w^2 + 7*w + 1]', '[1537, 1537, -3*w^3 + 2*w^2 + 7*w - 1]', '[1537, 1537, -w^3 - 2*w^2 + 9*w + 7]', '[1543, 1543, -w^3 + w^2 + 8*w - 4]', '[1543, 1543, w^3 + w^2 - 8*w - 4]', '[1548, 258, -3*w^3 - w^2 + 15*w + 2]', '[1548, 258, -w^3 + 3*w^2 + 9*w - 6]', '[1548, 258, -5*w^3 - w^2 + 19*w + 8]', '[1548, 258, -3*w^3 - w^2 + 9*w]', '[1556, 778, 2*w^3 - 5*w^2 + w + 7]', '[1556, 778, -2*w^3 + 3*w^2 + w - 5]', '[1557, 519, 3*w^3 - w^2 - 6*w - 4]', '[1557, 519, 3*w^3 + w^2 - 9*w - 9]', '[1557, 519, -3*w^3 - w^2 + 6*w - 4]', '[1557, 519, -3*w^3 + w^2 + 9*w - 9]', '[1563, 1563, 2*w^3 - 2*w - 3]', '[1563, 1563, 2*w^3 - 2*w + 3]', '[1569, 1569, 3*w^3 - w^2 - 11*w - 3]', '[1569, 1569, 3*w^3 - 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6]', '[1797, 1797, 4*w^2 + 2*w - 9]', '[1803, 1803, -2*w^3 + w^2 + 2*w + 3]', '[1803, 1803, -w^3 + 4*w^2 + 5*w - 12]', '[1803, 1803, w^3 + 4*w^2 - 5*w - 12]', '[1803, 1803, -2*w^3 - w^2 + 2*w - 3]', '[1807, 1807, -3*w^3 + 9*w - 2]', '[1807, 1807, -3*w^3 + 4*w^2 + 17*w - 14]', '[1807, 1807, 3*w^3 + 4*w^2 - 17*w - 14]', '[1807, 1807, 3*w^3 - 9*w - 2]', '[1808, 226, 2*w^3 - 2*w^2 - 10*w + 2]', '[1808, 226, -2*w^3 - 2*w^2 + 10*w + 2]', '[1819, 1819, -w^3 + 8*w + 2]', '[1819, 1819, -2*w^3 - 3*w^2 + 11*w + 14]', '[1819, 1819, 2*w^3 - 2*w^2 - 6*w + 11]', '[1819, 1819, w^3 - 4*w^2 - 10*w + 8]', '[1819, 1819, -w^3 - 4*w^2 + 10*w + 8]', '[1819, 1819, 2*w^3 + 2*w^2 - 6*w - 11]', '[1819, 1819, -2*w^3 + 3*w^2 + 11*w - 14]', '[1819, 1819, w^3 - 8*w + 2]', '[1821, 1821, w^3 - w^2 - 8*w + 3]', '[1821, 1821, -w^3 - w^2 + 8*w + 3]', '[1836, 102, -2*w^3 - 3*w^2 + 7*w + 3]', '[1836, 102, 2*w^3 - 3*w^2 - 7*w + 3]', '[1836, 306, -3*w^3 - 2*w^2 + 12*w + 3]', '[1836, 306, 3*w^3 - 2*w^2 - 12*w + 3]', '[1849, 43, 4*w^2 - 7]', '[1849, 43, 4*w^2 - 13]', '[1849, 1849, -2*w^3 + 2*w^2 + 8*w - 13]', '[1849, 1849, 2*w^3 + 2*w^2 - 8*w - 13]', '[1856, 116, -2*w^3 + 4*w^2 + 4*w - 10]', '[1856, 116, 2*w^3 + 4*w^2 - 4*w - 10]', '[1871, 1871, 4*w^3 - 2*w^2 - 19*w + 8]', '[1871, 1871, 2*w^3 + w^2 - 5*w - 8]', '[1871, 1871, -2*w^3 + w^2 + 5*w - 8]', '[1871, 1871, 4*w^3 + 2*w^2 - 19*w - 8]', '[1872, 78, -4*w^3 - 2*w^2 + 14*w + 4]', '[1872, 78, 2*w^2 + 6*w]', '[1872, 78, 4*w^3 - 2*w^2 - 14*w + 4]', '[1872, 78, 2*w^2 - 6*w]', '[1875, 15, -5*w]', '[1889, 1889, w^3 - 3*w - 7]', '[1889, 1889, -w^3 + 3*w - 7]', '[1899, 633, w^3 - w^2 - 8*w + 2]', '[1899, 633, 3*w^3 - w^2 - 15*w + 3]', '[1899, 633, -w^3 - w^2 + 8*w + 2]', '[1899, 633, -3*w^3 - w^2 + 15*w + 3]', '[1901, 1901, -w^3 + 4*w^2 - 2*w - 8]', '[1901, 1901, w^3 + 4*w^2 + 2*w - 8]', '[1908, 318, w^3 + w^2 + 3*w]', '[1908, 318, -w^3 - 5*w^2 + 11*w + 10]', '[1908, 318, -5*w^3 - 5*w^2 + 9*w]', '[1908, 318, -3*w^3 + w^2 + 9*w - 2]', '[1921, 1921, -2*w^3 - 2*w^2 + 5*w + 8]', '[1921, 1921, 4*w^2 - 5*w - 10]', '[1921, 1921, 4*w^2 + 5*w - 10]', '[1921, 1921, 2*w^3 - 2*w^2 - 5*w + 8]', '[1923, 1923, w^3 - 4*w^2 - w]', '[1923, 1923, w^3 + 4*w^2 - w]', '[1936, 22, 2*w^3 - 4*w^2 - 6*w + 4]', '[1936, 22, -4*w^3 + 2*w^2 + 14*w - 8]', '[1941, 1941, 3*w^3 + w^2 - 8*w - 3]', '[1941, 1941, -2*w^2 + 2*w - 3]', '[1941, 1941, 2*w^2 + 2*w + 3]', '[1941, 1941, 3*w^3 - w^2 - 8*w + 3]', '[1949, 1949, 4*w^3 - w^2 - 15*w + 4]', '[1949, 1949, 4*w^3 + w^2 - 15*w - 4]', '[1951, 1951, -w^3 + 4*w^2 + 5*w - 10]', '[1951, 1951, w^3 + 4*w^2 - 5*w - 10]', '[1959, 1959, -3*w^3 - 2*w^2 + 10*w - 6]', '[1959, 1959, 3*w^3 - 2*w^2 - 10*w - 6]', '[1972, 986, 2*w^3 + 3*w^2 - 9*w - 5]', '[1972, 986, 3*w^3 - w^2 - 15*w + 4]', '[1972, 986, -3*w^3 - w^2 + 15*w + 4]', '[1972, 986, -2*w^3 + 3*w^2 + 9*w - 5]', '[1973, 1973, -4*w^3 + 17*w - 4]', '[1973, 1973, 4*w^3 - 17*w - 4]', '[1989, 663, w^3 - w^2 + w + 5]', '[1989, 663, -2*w^2 + 3*w + 9]', '[1989, 663, w^3 - 4*w^2 - 5*w + 11]', '[1989, 663, w^3 + 2*w^2 - 3*w + 3]', '[1989, 663, -w^3 - 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5]', '[5212, 2606, -w^3 + 3*w^2 - 3*w - 8]', '[5212, 2606, 3*w^3 - 7*w^2 - w + 10]', '[5227, 5227, 2*w^3 - 13*w + 4]', '[5227, 5227, -2*w^3 + 13*w + 4]', '[5252, 2626, -5*w^3 - 3*w^2 + 21*w + 20]', '[5252, 2626, -w^3 + 5*w^2 + 3*w - 14]', '[5252, 2626, -w^3 - 5*w^2 + 3*w + 14]', '[5252, 2626, -5*w^3 + 3*w^2 + 21*w - 20]', '[5253, 5253, -w^3 - 5*w^2 + 4*w + 15]', '[5253, 5253, -3*w^3 + 7*w^2 + 16*w - 21]', '[5253, 5253, -3*w^3 - 7*w^2 + 16*w + 21]', '[5253, 5253, -w^3 + 5*w^2 + 4*w - 15]', '[5261, 5261, -2*w^3 + 4*w^2 + 9*w - 5]', '[5261, 5261, 2*w^3 + 4*w^2 - 9*w - 5]', '[5268, 2634, -w^3 - 5*w^2 + 5*w + 12]', '[5268, 2634, 3*w^3 - 3*w^2 - 5*w - 6]', '[5277, 5277, w^3 - 4*w^2 - 7*w]', '[5277, 5277, w^3 + 4*w^2 - 7*w]', '[5279, 5279, 3*w^3 - 8*w^2 - w + 2]', '[5279, 5279, 4*w^3 + w^2 - 17*w + 2]', '[5279, 5279, -4*w^3 + w^2 + 17*w + 2]', '[5279, 5279, -8*w^2 + 5*w + 11]', '[5303, 5303, w^3 - w - 10]', '[5303, 5303, w^3 + w^2 - 10*w + 2]', '[5303, 5303, -w^3 + w^2 + 10*w + 2]', '[5303, 5303, -w^3 + w - 10]', '[5308, 2654, -3*w^3 + w^2 + 7*w + 10]', '[5308, 2654, -w^3 - 5*w^2 + 5*w + 14]', '[5316, 2658, -w^3 - 4*w^2 + 8*w + 3]', '[5316, 2658, -5*w^3 - 5*w^2 + 19*w + 24]', '[5316, 2658, -w^3 - 3*w^2 + w + 18]', '[5316, 2658, -w^3 - 6*w^2 + 10*w + 9]', '[5321, 5321, -w^3 - 3*w^2 - 4*w + 8]', '[5321, 5321, 3*w^3 - w^2 - 4*w - 4]', '[5321, 5321, -2*w^3 - w^2 + 9*w - 8]', '[5321, 5321, -2*w^3 + 3*w^2 + 3*w + 4]', '[5321, 5321, 2*w^3 + 3*w^2 - 3*w + 4]', '[5321, 5321, 2*w^3 - w^2 - 9*w - 8]', '[5321, 5321, -3*w^3 - w^2 + 4*w - 4]', '[5321, 5321, w^3 - 3*w^2 + 4*w + 8]', '[5329, 73, 4*w^3 + w^2 - 15*w - 14]', '[5329, 73, -4*w^3 + w^2 + 15*w - 14]', '[5331, 5331, -w^3 - 3*w^2 + w - 3]', '[5331, 5331, w^2 - 5*w - 12]', '[5331, 5331, -w^2 - 5*w + 12]', '[5331, 5331, -w^3 + 3*w^2 + w + 3]', '[5333, 5333, -7*w^3 + 27*w - 5]', '[5333, 5333, 3*w^3 - w^2 - 17*w - 7]', '[5347, 5347, 3*w^3 - 18*w + 8]', '[5347, 5347, -3*w^3 + 18*w + 8]', '[5353, 5353, 5*w^2 + w - 10]', '[5353, 5353, -4*w^3 - w^2 + 13*w - 10]', '[5353, 5353, 4*w^3 - w^2 - 13*w - 10]', '[5353, 5353, 5*w^2 - w - 10]', '[5356, 2678, -w^3 + 4*w^2 + 10*w - 13]', '[5356, 2678, w^3 + 2*w - 7]', '[5356, 2678, w^3 + 2*w + 7]', '[5356, 2678, -w^3 - 4*w^2 + 10*w + 13]', '[5372, 2686, -5*w^3 + 2*w^2 + 18*w - 5]', '[5372, 2686, -3*w^3 + 16*w - 1]', '[5372, 2686, 3*w^3 - 16*w - 1]', '[5372, 2686, 5*w^3 + 2*w^2 - 18*w - 5]', '[5373, 597, w^3 - 5*w + 9]', '[5373, 597, -w^3 + 5*w + 9]', '[5373, 1791, 2*w^3 - 3*w^2 - 9*w + 18]', '[5373, 1791, -2*w^3 - 3*w^2 + 9*w + 18]', '[5381, 5381, w^3 + 5*w^2 - 4*w - 11]', '[5381, 5381, -w^3 + 5*w^2 + 4*w - 11]', '[5391, 1797, 2*w^3 + 2*w^2 - 13*w - 4]', '[5391, 1797, 4*w^3 - 2*w^2 - 9*w]', '[5391, 1797, 5*w^2 - 6*w - 13]', '[5391, 1797, 2*w^3 + 6*w^2 - 12*w - 21]', '[5391, 1797, -5*w^2 - 6*w + 13]', '[5391, 1797, 2*w^3 - 6*w^2 - 12*w + 21]', '[5391, 1797, 2*w^3 - 2*w^2 - 13*w + 4]', '[5391, 1797, 4*w^3 + 2*w^2 - 9*w]', '[5392, 674, 2*w^3 + 4*w^2 - 14*w - 4]', '[5392, 674, -4*w^3 + 8*w + 2]', '[5392, 674, 4*w^3 - 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13*w + 1]', '[5524, 2762, 2*w^3 - 9*w^2 + 3*w + 7]', '[5547, 129, 4*w^3 - 7*w]', '[5547, 129, 4*w^3 - 13*w]', '[5547, 5547, 2*w^3 - 2*w^2 - 13*w + 6]', '[5547, 5547, 2*w^3 + 2*w^2 - 13*w - 6]', '[5563, 5563, 6*w^3 + 2*w^2 - 23*w - 10]', '[5563, 5563, -6*w^3 + 2*w^2 + 23*w - 10]', '[5564, 2782, -3*w^3 + 2*w^2 + 12*w + 1]', '[5564, 2782, 7*w^3 - 2*w^2 - 28*w + 19]', '[5564, 2782, -2*w^3 + 5*w^2 + 13*w - 17]', '[5564, 2782, w^2 + 5*w - 11]', '[5564, 2782, -w^2 + 5*w + 11]', '[5564, 2782, -2*w^3 - 5*w^2 + 13*w + 17]', '[5564, 2782, -7*w^3 - 2*w^2 + 28*w + 19]', '[5564, 2782, 3*w^3 + 2*w^2 - 12*w + 1]', '[5568, 348, -6*w^3 + 2*w^2 + 22*w - 12]', '[5568, 348, -6*w^3 - 2*w^2 + 22*w + 12]', '[5573, 5573, -4*w^3 + 2*w^2 + 18*w - 17]', '[5573, 5573, 4*w^3 + 2*w^2 - 18*w - 17]', '[5581, 5581, -w^3 + 4*w^2 - 2*w - 10]', '[5581, 5581, -w^3 + 3*w^2 + w - 13]', '[5581, 5581, w^3 + 3*w^2 - w - 13]', '[5581, 5581, w^3 - 5*w^2 + 3*w + 11]', '[5591, 5591, w^3 + 5*w^2 - 8*w - 17]', '[5591, 5591, 3*w^3 + 6*w^2 - 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20]', '[5651, 5651, 3*w^3 + 6*w^2 - 13*w - 20]', '[5651, 5651, 7*w^3 - 28*w + 2]', '[5659, 5659, -w^3 + 5*w^2 + 3*w - 13]', '[5659, 5659, w^3 + 5*w^2 - 3*w - 13]', '[5667, 5667, -2*w^2 - 7*w + 3]', '[5667, 5667, 2*w^2 - 7*w - 3]', '[5669, 5669, -3*w^3 - w^2 + 15*w - 5]', '[5669, 5669, 3*w^3 - w^2 - 15*w - 5]', '[5671, 5671, 2*w^3 - 2*w^2 - 13*w + 5]', '[5671, 5671, w^3 + w^2 + 2*w - 7]', '[5671, 5671, -2*w^3 + 3*w^2 + 2*w - 8]', '[5671, 5671, 6*w^3 - 3*w^2 - 25*w + 8]', '[5671, 5671, 6*w^3 + 3*w^2 - 25*w - 8]', '[5671, 5671, 2*w^3 + 3*w^2 - 2*w - 8]', '[5671, 5671, -w^3 + w^2 - 2*w - 7]', '[5671, 5671, -2*w^3 - 2*w^2 + 13*w + 5]', '[5693, 5693, 5*w^3 + w^2 - 21*w + 1]', '[5693, 5693, -5*w^3 + w^2 + 21*w + 1]', '[5697, 633, -w^3 + 6*w^2 + 5*w - 21]', '[5697, 633, -w^3 - 6*w^2 + 5*w + 21]', '[5697, 1899, -w^3 + 3*w - 9]', '[5697, 1899, -w^3 + 3*w + 9]', '[5703, 5703, 4*w^3 - 7*w^2 - 8*w + 3]', '[5703, 5703, 4*w^3 + 7*w^2 - 8*w - 3]', '[5707, 5707, -4*w^3 + w^2 + 18*w + 2]', '[5707, 5707, 6*w^3 - 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9]', '[10000, 10, -10]'], 'label': '4.4.8112.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w]', '[4, 2, w^2 - w - 1]', '[9, 3, -w^2 + 2]', '[13, 13, w^3 - 4*w + 2]', '[13, 13, -w^3 + 4*w + 2]', '[17, 17, w^3 - 3*w - 1]', '[17, 17, -w^3 + 3*w - 1]', '[29, 29, w^3 + w^2 - 4*w - 2]', '[29, 29, w^3 - w^2 - 4*w + 2]', '[43, 43, w^2 + w - 4]', '[43, 43, w^2 - w - 4]', '[53, 53, w^3 - 2*w - 2]', '[53, 53, -w^3 + 2*w - 2]', '[79, 79, w^3 - w^2 - 4*w + 1]', '[79, 79, -w^3 - w^2 + 4*w + 1]', '[101, 101, -w^3 + w^2 + 3*w - 5]', '[101, 101, w^3 + w^2 - 3*w - 5]', '[103, 103, 2*w^2 - w - 4]', '[103, 103, 2*w^2 + w - 4]', '[107, 107, 2*w^2 + w - 5]', '[107, 107, 3*w^2 - 3*w - 4]', '[107, 107, 2*w^2 - 2*w - 1]', '[107, 107, 2*w^2 - w - 5]', '[113, 113, w^3 - w^2 - 5*w + 1]', '[113, 113, -w^3 - w^2 + 5*w + 1]', '[121, 11, w^3 - 2*w^2 - 3*w + 2]', '[121, 11, -2*w^3 + w^2 + 7*w - 4]', '[127, 127, -2*w^3 + 7*w - 2]', '[127, 127, 2*w^3 - 7*w - 2]', '[131, 131, w^3 - w^2 - 1]', '[131, 131, -w^3 + w^2 + 4*w + 1]', '[131, 131, -2*w^3 + 3*w^2 + 4*w - 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4*w - 2]', '[313, 313, 2*w^3 - w^2 - 6*w + 2]', '[313, 313, -2*w^3 - w^2 + 6*w + 2]', '[313, 313, -w^3 + 2*w^2 + 4*w - 2]', '[337, 337, -w^3 - 2*w^2 + 7*w + 2]', '[337, 337, -2*w^3 + 4*w + 1]', '[337, 337, 2*w^3 - 4*w + 1]', '[337, 337, -w^3 + 2*w^2 + 7*w - 2]', '[367, 367, -w^3 + 3*w^2 - 2*w - 5]', '[367, 367, 2*w^3 - 3*w^2 - 2*w + 4]', '[373, 373, -2*w^3 + 10*w + 1]', '[373, 373, -3*w^3 - w^2 + 14*w + 5]', '[373, 373, 3*w^3 - w^2 - 14*w + 5]', '[373, 373, 2*w^3 - 10*w + 1]', '[389, 389, 2*w^3 - 6*w - 1]', '[389, 389, -2*w^3 + 6*w - 1]', '[419, 419, 2*w^3 - 11*w - 4]', '[419, 419, 2*w^2 - 2*w - 7]', '[419, 419, 2*w^2 + 2*w - 7]', '[419, 419, -2*w^3 + 11*w - 4]', '[439, 439, 3*w^2 - w - 14]', '[439, 439, -3*w^2 - w + 14]', '[443, 443, w^3 + 3*w^2 - 4*w - 10]', '[443, 443, 3*w^3 + w^2 - 14*w - 4]', '[443, 443, 3*w^3 - w^2 - 14*w + 4]', '[443, 443, -w^3 + 3*w^2 + 4*w - 10]', '[503, 503, -w - 5]', '[503, 503, 3*w^3 + w^2 - 12*w - 1]', '[503, 503, 3*w^3 - w^2 - 12*w + 1]', '[503, 503, w - 5]', '[521, 521, w^3 + 2*w^2 - 5*w - 2]', '[521, 521, -w^3 + 2*w^2 + 5*w - 2]', '[523, 523, 3*w^2 - 2*w - 10]', '[523, 523, w^3 + 3*w^2 - 6*w - 11]', '[529, 23, 2*w^2 - 11]', '[529, 23, 3*w^2 - 10]', '[547, 547, -2*w^3 + w^2 + 6*w - 7]', '[547, 547, 2*w^3 + w^2 - 6*w - 7]', '[563, 563, -2*w^3 + w^2 + 4*w - 4]', '[563, 563, -3*w^3 + 10*w - 4]', '[563, 563, 3*w^3 - 10*w - 4]', '[563, 563, 2*w^3 + w^2 - 4*w - 4]', '[569, 569, w^3 + 2*w^2 - 6*w - 10]', '[569, 569, -w^3 + 2*w^2 + 6*w - 10]', '[571, 571, -2*w^3 + 3*w^2 + 5*w - 2]', '[571, 571, -2*w^3 + 2*w^2 + 6*w + 1]', '[599, 599, 3*w^3 - 11*w - 2]', '[599, 599, 2*w^3 + w^2 - 6*w - 8]', '[599, 599, 2*w^3 - w^2 - 6*w + 8]', '[599, 599, 3*w^3 - 11*w + 2]', '[601, 601, -w^3 - 2*w^2 + 6*w + 2]', '[601, 601, 4*w^3 - w^2 - 16*w + 5]', '[601, 601, 4*w^3 + w^2 - 16*w - 5]', '[601, 601, w^3 - 2*w^2 - 6*w + 2]', '[607, 607, -w^3 + w^2 + 4*w - 8]', '[607, 607, -w^3 - w^2 + 4*w + 8]', '[625, 5, -5]', '[641, 641, w^2 + 4*w - 1]', '[641, 641, w^2 - 4*w - 1]', '[647, 647, w^3 + 3*w^2 - 4*w - 8]', '[647, 647, -w^3 + 7*w + 2]', '[647, 647, w^3 - 7*w + 2]', '[647, 647, -w^3 + 3*w^2 + 4*w - 8]', '[653, 653, 2*w^3 - 3*w^2 - 12*w + 10]', '[653, 653, 2*w^3 + 3*w^2 - 12*w - 10]', '[677, 677, 3*w^2 + w - 8]', '[677, 677, 3*w^2 - w - 8]', '[701, 701, 2*w^3 - 2*w^2 - 7*w + 2]', '[701, 701, -2*w^3 - 2*w^2 + 7*w + 2]', '[727, 727, -2*w^3 - 2*w^2 + 11*w + 7]', '[727, 727, -2*w^3 + 2*w^2 + 11*w - 7]', '[751, 751, -4*w^2 + 3*w + 7]', '[751, 751, w^3 - 2*w^2 - w - 2]', '[797, 797, 3*w^3 - 11*w + 1]', '[797, 797, 3*w^3 - 11*w - 1]', '[809, 809, -w^3 + 7*w - 1]', '[809, 809, w^3 - 7*w - 1]', '[823, 823, -2*w^3 + 4*w^2 + 9*w - 14]', '[823, 823, 2*w^3 + 4*w^2 - 9*w - 14]', '[841, 29, 3*w^2 - 7]', '[857, 857, w^3 + w^2 - w - 5]', '[857, 857, -w^3 + w^2 + w - 5]', '[859, 859, 5*w^3 + w^2 - 20*w - 2]', '[859, 859, -5*w^3 + w^2 + 20*w - 2]', '[881, 881, w^3 + 3*w^2 - 2*w - 10]', '[881, 881, -w^3 + 3*w^2 + 2*w - 10]', '[883, 883, 2*w^3 - w^2 - 8*w - 2]', '[883, 883, 2*w^3 + w^2 - 8*w + 2]', '[907, 907, 3*w^3 - 2*w^2 - 13*w + 5]', '[907, 907, 3*w^3 + 2*w^2 - 13*w - 5]', '[919, 919, 3*w^3 - w^2 - 15*w + 1]', '[919, 919, 3*w^3 + 3*w^2 - 10*w - 5]', '[953, 953, w^3 + 2*w^2 - 2*w - 8]', '[953, 953, -w^3 + 2*w^2 + 2*w - 8]', '[991, 991, -w^3 - w^2 + 4*w - 4]', '[991, 991, w^3 - w^2 - 4*w - 4]', '[997, 997, w^3 + 4*w^2 - 3*w - 16]', '[997, 997, -3*w^3 + 3*w^2 + 11*w - 13]', '[997, 997, 3*w^3 + 3*w^2 - 11*w - 13]', '[997, 997, w^3 - 4*w^2 - 3*w + 16]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3, 0, -5, 0, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 8112, 'disc_rad': 78, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[2, 2]]], [13, [0]], [17, [[2, 1], [1, 2]]], [19, [[4, 1]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[4, 1]]], [37, [[2, 2]]], [41, [[4, 1]]], [43, [[2, 1], [1, 2]]], [47, [[2, 2]]], [53, [[2, 1], [1, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 17.663521732655695, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '4.4.8112.1', 'local_algs': ['2.4.4.4', '3.2.1.2', '3.2.0.1', '13.2.1.1', '13.2.1.1'], 'minimal_sibling': [1, 2, -4, -2, 1], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 13], 'rd': 9.49034467201, 'regulator': {'__RealLiteral__': 0, 'data': '5.2034416884', 'prec': 40}, 'res': {'gal': ['1,6,-14,-26,35,26,-12,-4,1'], 'sib': ['1,2,-4,-2,1', '1,6,-14,-26,35,26,-12,-4,1']}, 'subfield_mults': [1], 'subfields': ['-3.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a + 1 \\)', '\\( a^{2} - a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}