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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 7625, 'field_bad_primes': [5, 61], 'field_label': '4.4.7625.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.7625.1-20.2-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [2, 5], 'level_ideal': '[20,10,1/2*w^3 - 1/2*w^2 - 7/2*w]', 'level_label': '20.2', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.2-e', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[4,2,1/2*w^3 - 3/2*w^2 - 3/2*w + 4]', 1], ['[5,5,-1/2*w^3 + 3/2*w^2 + 5/2*w - 7]', -1]], 'hecke_eigenvalues': [-1, -1, 1, 4, -4, -6, 2, 0, 0, -2, -10, 12, -12, -10, 8, -8, -16, -8, 2, -10, 6, -18, 6, -14, 2, -14, 2, 2, -12, 4, -24, 0, -10, -2, 0, 24, 0, 8, 24, -8, -12, 20, -6, -6, -22, 18, -8, -8, 16, 0, 4, 12, 18, 18, 18, 2, -24, -16, 16, 24, 26, 18, -26, 22, -24, -16, -12, -20, 2, -14, 0, -24, 26, 2, 4, 4, 28, 12, -6, 26, -6, -6, 6, -18, -20, -36, 6, -10, 0, -24, -32, 0, 14, -2, 38, -34, -36, 28, -30, 2, -22, -22, 14, 14, -2, -2, 6, 6, -26, 22, 32, -24, -30, 10, 10, 26, 0, 8, 34, 18, 22, -42, 30, -34, -22, -38, 28, 28, 10, 10, -18, 30, -2, 30, -42, 54, 28, -20, -42, 6, -54, 36, 20, -12, 20, 18, -14, -14, -14, -10, -18, -38, -48, -16, 56, 32], 'hecke_polynomial': 'x', 'label': '4.4.7625.1-20.2-e'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 7625, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 3/2*w^2 - 3/2*w + 4]', '[4, 2, 1/2*w^3 + 1/2*w^2 - 7/2*w - 5]', '[5, 5, -1/4*w^3 - 3/4*w^2 + 5/4*w + 3]', '[11, 11, -1/4*w^3 + 1/4*w^2 + 9/4*w]', '[11, 11, w - 1]', '[16, 2, 2]', '[16, 4, w]', '[16, 4, -1/4*w^3 + 1/4*w^2 + 9/4*w - 1]', '[20, 10, 1/4*w^3 - 1/4*w^2 - 1/4*w - 1]', '[20, 10, 1/2*w^3 - 1/2*w^2 - 7/2*w]', '[25, 5, -1/2*w^3 + 1/2*w^2 + 5/2*w - 1]', '[29, 29, 1/4*w^3 - 1/4*w^2 - 1/4*w + 2]', '[29, 29, 1/2*w^3 - 1/2*w^2 - 7/2*w + 3]', '[31, 31, -3/4*w^3 - 1/4*w^2 + 19/4*w + 4]', '[31, 31, -3/4*w^3 + 7/4*w^2 + 11/4*w - 5]', '[44, 22, -1/2*w^3 + 3/2*w^2 + 3/2*w - 6]', '[44, 22, 3/4*w^3 - 7/4*w^2 - 15/4*w + 6]', '[44, 22, 1/2*w^3 + 1/2*w^2 - 5/2*w - 4]', '[44, 22, 1/2*w^3 + 1/2*w^2 - 7/2*w - 3]', '[49, 7, -1/2*w^3 + 3/2*w^2 + 5/2*w - 5]', '[49, 7, 1/2*w^3 - 1/2*w^2 - 7/2*w - 1]', '[55, 55, w^2 - 1]', '[55, 55, 1/4*w^3 - 5/4*w^2 - 5/4*w + 9]', '[59, 59, -1/4*w^3 + 5/4*w^2 + 5/4*w - 3]', '[59, 59, w^2 - 7]', '[61, 61, -5/4*w^3 - 7/4*w^2 + 37/4*w + 15]', '[64, 4, w^3 - 3*w^2 - 3*w + 8]', '[64, 4, w^3 + w^2 - 7*w - 10]', '[64, 8, w^2 - 8]', '[64, 8, 1/2*w^3 + 1/2*w^2 - 3/2*w - 3]', '[71, 71, 3/4*w^3 + 9/4*w^2 - 11/4*w - 7]', '[71, 71, 1/4*w^3 - 1/4*w^2 - 13/4*w - 2]', '[79, 79, -1/4*w^3 + 5/4*w^2 + 1/4*w - 7]', '[79, 79, 1/4*w^3 + 3/4*w^2 - 9/4*w - 2]', '[80, 10, -1/2*w^3 - 3/2*w^2 + 5/2*w + 6]', '[80, 20, -3/4*w^3 - 1/4*w^2 + 15/4*w + 2]', '[80, 20, -w^3 + 2*w^2 + 5*w - 8]', '[81, 3, -3]', '[89, 89, -w^2 + 2*w + 1]', '[89, 89, 1/4*w^3 + 3/4*w^2 - 13/4*w - 7]', '[100, 10, w^3 - 8*w - 7]', '[100, 10, 1/2*w^3 - 3/2*w^2 + 1/2*w]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 12]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 9/4*w - 1]', '[109, 109, -5/4*w^3 - 3/4*w^2 + 33/4*w + 7]', '[109, 109, -1/4*w^3 + 5/4*w^2 + 1/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 5/4*w - 9]', '[116, 58, 1/4*w^3 - 5/4*w^2 + 3/4*w]', '[116, 58, -1/2*w^3 - 1/2*w^2 + 9/2*w + 8]', '[116, 58, -3/4*w^3 + 3/4*w^2 + 11/4*w - 1]', '[116, 58, w^3 - w^2 - 6*w + 2]', '[121, 11, -3/4*w^3 + 3/4*w^2 + 15/4*w - 1]', '[121, 11, -3/4*w^3 + 3/4*w^2 + 15/4*w - 2]', '[121, 121, -3/4*w^3 + 3/4*w^2 + 23/4*w - 3]', '[121, 121, 1/4*w^3 - 1/4*w^2 + 3/4*w + 1]', '[124, 62, -1/2*w^3 + 3/2*w^2 + 3/2*w - 7]', '[124, 62, 1/4*w^3 + 3/4*w^2 - 5/4*w - 6]', '[124, 62, 1/2*w^3 - 3/2*w^2 - 5/2*w + 4]', '[124, 62, 1/2*w^3 + 1/2*w^2 - 7/2*w - 2]', '[125, 5, 1/4*w^3 + 3/4*w^2 + 3/4*w - 1]', '[139, 139, 1/2*w^3 + 3/2*w^2 - 9/2*w - 7]', '[139, 139, -1/2*w^3 + 5/2*w^2 + 1/2*w - 11]', '[145, 145, 1/2*w^3 + 1/2*w^2 - 5/2*w - 5]', '[145, 145, -3/4*w^3 + 7/4*w^2 + 15/4*w - 5]', '[151, 151, 7/4*w^3 - 19/4*w^2 - 23/4*w + 14]', '[151, 151, -3/4*w^3 + 11/4*w^2 + 11/4*w - 10]', '[155, 155, 1/4*w^3 - 1/4*w^2 + 3/4*w]', '[155, 155, -3/4*w^3 + 3/4*w^2 + 23/4*w - 2]', '[176, 22, -1/2*w^3 + 1/2*w^2 + 9/2*w]', '[176, 22, 2*w - 2]', '[176, 44, w + 4]', '[176, 44, -w^2 + w + 9]', '[176, 44, w^2 - w]', '[176, 44, 1/4*w^3 - 1/4*w^2 - 9/4*w + 5]', '[181, 181, -3/4*w^3 + 11/4*w^2 + 15/4*w - 12]', '[181, 181, 1/2*w^3 + 3/2*w^2 - 9/2*w - 9]', '[191, 191, 1/4*w^3 + 7/4*w^2 - 13/4*w - 8]', '[191, 191, -1/4*w^3 + 9/4*w^2 - 3/4*w - 10]', '[196, 14, w^3 - 6*w - 3]', '[196, 14, -1/2*w^3 + 3/2*w^2 + 1/2*w]', '[196, 14, 1/2*w^3 - 5/2*w^2 + 5/2*w]', '[196, 14, -3*w^3 - 2*w^2 + 22*w + 25]', '[199, 199, -3/4*w^3 + 11/4*w^2 + 15/4*w - 10]', '[199, 199, 1/4*w^3 + 3/4*w^2 - 5/4*w - 7]', '[199, 199, -1/2*w^3 + 3/2*w^2 + 5/2*w - 3]', '[199, 199, 3/4*w^3 - 3/4*w^2 - 23/4*w - 1]', '[211, 211, -5/4*w^3 + 17/4*w^2 + 13/4*w - 13]', '[211, 211, -1/4*w^3 + 5/4*w^2 - 7/4*w + 2]', '[220, 110, 1/2*w^3 + 1/2*w^2 - 3/2*w - 4]', '[220, 110, w^3 - 2*w^2 - 6*w + 7]', '[220, 110, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1]', '[220, 110, -1/2*w^3 + 3/2*w^2 + 3/2*w - 8]', '[229, 229, -1/4*w^3 + 5/4*w^2 + 9/4*w - 9]', '[229, 229, 1/4*w^3 - 9/4*w^2 + 11/4*w + 1]', '[229, 229, 3/4*w^3 + 1/4*w^2 - 15/4*w - 5]', '[229, 229, 1/2*w^3 + 5/2*w^2 - 1/2*w - 7]', '[236, 118, w^3 - 4*w^2 + 6]', '[236, 118, 5/4*w^3 + 3/4*w^2 - 29/4*w - 7]', '[236, 118, -3/2*w^3 - 3/2*w^2 + 25/2*w + 19]', '[236, 118, -3/2*w^3 + 7/2*w^2 + 13/2*w - 12]', '[239, 239, 5/4*w^3 - 1/4*w^2 - 37/4*w - 6]', '[239, 239, -3/4*w^3 + 7/4*w^2 + 11/4*w - 8]', '[239, 239, w^2 - 2*w - 7]', '[239, 239, -5/2*w^3 - 5/2*w^2 + 37/2*w + 23]', '[244, 122, 5/4*w^3 - 9/4*w^2 - 33/4*w + 8]', '[244, 122, -1/2*w^3 + 3/2*w^2 + 3/2*w - 10]', '[245, 35, 5/4*w^3 + 7/4*w^2 - 29/4*w - 9]', '[245, 35, -3/4*w^3 - 5/4*w^2 + 15/4*w + 3]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 11]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 9]', '[256, 4, 4]', '[256, 8, 2*w]', '[256, 8, -1/2*w^3 + 1/2*w^2 + 9/2*w - 2]', '[256, 16, w^2]', '[256, 16, 1/4*w^3 - 5/4*w^2 - 5/4*w + 10]', '[269, 269, -7/4*w^3 - 1/4*w^2 + 59/4*w + 14]', '[269, 269, -1/2*w^3 - 3/2*w^2 + 7/2*w + 5]', '[269, 269, 3/4*w^3 - 11/4*w^2 + 9/4*w]', '[269, 269, -5/4*w^3 - 7/4*w^2 + 25/4*w + 7]', '[271, 271, 2*w^2 - w - 7]', '[271, 271, -1/4*w^3 + 9/4*w^2 + 1/4*w - 12]', '[271, 271, -1/2*w^3 + 5/2*w^2 + 5/2*w - 11]', '[271, 271, 1/4*w^3 + 7/4*w^2 - 13/4*w - 9]', '[275, 55, -1/4*w^3 - 7/4*w^2 + 9/4*w + 10]', '[275, 55, 1/2*w^3 - 5/2*w^2 - 3/2*w + 9]', '[281, 281, w^3 - 5*w - 3]', '[281, 281, 5/4*w^3 + 3/4*w^2 - 25/4*w - 6]', '[284, 142, -1/2*w^3 + 3/2*w^2 + 7/2*w - 4]', '[284, 142, -3/4*w^3 + 3/4*w^2 + 3/4*w + 1]', '[284, 142, -w^2 - w + 7]', '[284, 142, -1/2*w^3 - 1/2*w^2 + 7/2*w]', '[289, 17, 1/4*w^3 + 7/4*w^2 - 9/4*w - 14]', '[289, 17, -5/4*w^3 - 7/4*w^2 + 45/4*w + 17]', '[295, 295, -5/4*w^3 - 11/4*w^2 + 21/4*w + 8]', '[295, 295, -1/4*w^3 + 1/4*w^2 - 3/4*w - 5]', '[305, 305, 1/4*w^3 - 9/4*w^2 - 5/4*w + 10]', '[311, 311, 1/4*w^3 - 1/4*w^2 - 9/4*w - 4]', '[311, 311, w - 5]', '[316, 158, -7/4*w^3 - 9/4*w^2 + 55/4*w + 21]', '[316, 158, 3/2*w^3 - 11/2*w^2 - 5/2*w + 14]', '[316, 158, -3/4*w^3 - 1/4*w^2 + 31/4*w + 8]', '[316, 158, -w^2 + 4*w - 2]', '[319, 319, -3/4*w^3 + 3/4*w^2 + 7/4*w + 1]', '[319, 319, 5/4*w^3 - 5/4*w^2 - 33/4*w + 1]', '[319, 319, 5/4*w^3 - 13/4*w^2 - 21/4*w + 10]', '[319, 319, -w^3 - w^2 + 6*w + 9]', '[320, 20, 1/2*w^3 - 1/2*w^2 - 1/2*w - 2]', '[320, 20, w^3 - w^2 - 7*w]', '[320, 40, 1/4*w^3 + 3/4*w^2 - 13/4*w]', '[320, 40, w^2 - 2*w - 8]', '[324, 6, -3/2*w^3 + 9/2*w^2 + 9/2*w - 12]', '[324, 6, -3/2*w^3 - 3/2*w^2 + 21/2*w + 15]', '[331, 331, 2*w^2 - w - 11]', '[331, 331, -1/4*w^3 + 9/4*w^2 + 1/4*w - 8]', '[341, 341, -1/4*w^3 - 7/4*w^2 + 9/4*w + 8]', '[341, 341, 1/4*w^3 - 1/4*w^2 - 13/4*w + 7]', '[341, 341, -1/4*w^3 + 1/4*w^2 + 13/4*w + 5]', '[341, 341, 1/2*w^3 - 5/2*w^2 - 3/2*w + 11]', '[349, 349, 1/4*w^3 - 9/4*w^2 + 19/4*w - 2]', '[349, 349, -5/4*w^3 - 3/4*w^2 + 49/4*w + 16]', '[355, 355, -1/2*w^3 + 1/2*w^2 - 1/2*w + 1]', '[355, 355, w^3 - w^2 - 4*w + 3]', '[356, 178, w^3 - 5*w - 2]', '[356, 178, 1/4*w^3 + 7/4*w^2 - 9/4*w - 9]', '[356, 178, 1/2*w^3 - 5/2*w^2 - 3/2*w + 10]', '[356, 178, -5/4*w^3 + 9/4*w^2 + 25/4*w - 8]', '[359, 359, -7/4*w^3 - 5/4*w^2 + 63/4*w + 20]', '[359, 359, 3/4*w^3 + 5/4*w^2 - 19/4*w - 10]', '[361, 19, -1/4*w^3 + 1/4*w^2 + 5/4*w - 5]', '[361, 19, -w^3 + w^2 + 5*w - 3]', '[379, 379, -1/4*w^3 - 3/4*w^2 + 17/4*w - 1]', '[379, 379, -2*w^3 - 2*w^2 + 17*w + 23]', '[379, 379, -1/4*w^3 + 9/4*w^2 + 5/4*w - 16]', '[379, 379, 1/4*w^3 + 3/4*w^2 - 17/4*w - 8]', '[389, 389, -3/2*w^3 - 5/2*w^2 + 13/2*w + 11]', '[389, 389, -5/4*w^3 - 7/4*w^2 + 45/4*w + 19]', '[395, 395, 3/4*w^3 + 5/4*w^2 - 15/4*w - 8]', '[395, 395, -1/2*w^3 - 5/2*w^2 + 1/2*w + 5]', '[400, 10, -w^3 + w^2 + 5*w - 2]', '[400, 20, 1/4*w^3 - 9/4*w^2 - 1/4*w + 11]', '[400, 20, -2*w^2 + w + 8]', '[401, 401, 5/4*w^3 - 5/4*w^2 - 29/4*w + 2]', '[401, 401, w^3 - w^2 - 4*w + 1]', '[404, 202, -3/2*w^3 + 5/2*w^2 + 19/2*w - 14]', '[404, 202, -5/4*w^3 - 7/4*w^2 + 49/4*w + 22]', '[404, 202, -3/4*w^3 - 1/4*w^2 + 7/4*w - 2]', '[404, 202, -1/2*w^3 + 7/2*w^2 - 7/2*w - 2]', '[405, 15, 3/4*w^3 + 9/4*w^2 - 15/4*w - 9]', '[409, 409, -1/4*w^3 + 5/4*w^2 - 3/4*w - 7]', '[409, 409, -3/4*w^3 + 7/4*w^2 + 11/4*w - 9]', '[419, 419, 1/4*w^3 + 3/4*w^2 - 1/4*w - 6]', '[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 7]', '[421, 421, 3/4*w^3 - 11/4*w^2 + 1/4*w + 2]', '[421, 421, 3/2*w^3 + 1/2*w^2 - 19/2*w - 7]', '[431, 431, 1/4*w^3 - 5/4*w^2 + 3/4*w - 1]', '[431, 431, -5/4*w^3 - 3/4*w^2 + 21/4*w + 4]', '[431, 431, -1/2*w^3 - 1/2*w^2 + 9/2*w + 9]', '[431, 431, 1/2*w^3 - 1/2*w^2 - 9/2*w - 5]', '[436, 218, 2*w^3 - 7*w^2 - 4*w + 18]', '[436, 218, 1/2*w^3 - 3/2*w^2 - 9/2*w + 6]', '[436, 218, -1/2*w^3 + 1/2*w^2 + 11/2*w - 6]', '[436, 218, -1/4*w^3 + 1/4*w^2 + 17/4*w + 3]', '[436, 218, -3/4*w^3 + 7/4*w^2 + 15/4*w - 12]', '[436, 218, -9/4*w^3 - 11/4*w^2 + 69/4*w + 26]', '[436, 218, -13/4*w^3 - 11/4*w^2 + 101/4*w + 35]', '[436, 218, -3*w^3 + 8*w^2 + 10*w - 22]', '[445, 445, -1/4*w^3 + 9/4*w^2 + 5/4*w - 5]', '[445, 445, -1/4*w^3 + 9/4*w^2 + 5/4*w - 15]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 4]', '[461, 461, -3/2*w^3 - 1/2*w^2 + 25/2*w + 15]', '[461, 461, -7/4*w^3 - 9/4*w^2 + 55/4*w + 20]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 3]', '[464, 58, 1/2*w^3 - 1/2*w^2 - 1/2*w + 4]', '[464, 58, w^3 - w^2 - 7*w + 6]', '[464, 116, w^2 + w - 8]', '[464, 116, -1/2*w^3 + 3/2*w^2 + 7/2*w - 3]', '[464, 116, 2*w^2 + w - 4]', '[464, 116, -3/4*w^3 + 11/4*w^2 + 19/4*w - 17]', '[484, 22, 5/4*w^3 + 7/4*w^2 - 33/4*w - 14]', '[484, 22, 5/4*w^3 - 1/4*w^2 - 41/4*w - 8]', '[484, 22, 3/2*w^3 - 9/2*w^2 - 11/2*w + 14]', '[484, 22, 1/2*w^3 - 3/2*w^2 + 3/2*w - 2]', '[484, 242, 1/2*w^3 + 3/2*w^2 - 7/2*w - 4]', '[484, 242, 1/2*w^3 + 1/2*w^2 - 3/2*w - 5]', '[484, 242, -3/4*w^3 + 11/4*w^2 + 11/4*w - 15]', '[484, 242, w^3 - 2*w^2 - 6*w + 6]', '[496, 62, -3/2*w^3 - 1/2*w^2 + 19/2*w + 8]', '[496, 62, -3/2*w^3 + 7/2*w^2 + 11/2*w - 10]', '[496, 124, -w^3 - 2*w^2 + 8*w + 15]', '[496, 124, 5/4*w^3 - 17/4*w^2 - 17/4*w + 16]', '[496, 124, w^3 - 4*w^2 - 2*w + 12]', '[496, 124, -w^3 - 2*w^2 + 7*w + 12]', '[499, 499, -1/4*w^3 + 5/4*w^2 - 15/4*w + 5]', '[499, 499, -1/4*w^3 - 3/4*w^2 + 17/4*w - 2]', '[500, 10, 1/2*w^3 + 3/2*w^2 - 7/2*w - 12]', '[500, 10, 3/4*w^3 - 11/4*w^2 - 11/4*w + 7]', '[505, 505, -w^3 - w^2 + 2*w - 3]', '[505, 505, 2*w^3 + 4*w^2 - 7*w - 9]', '[509, 509, 5/4*w^3 + 3/4*w^2 - 33/4*w - 6]', '[509, 509, 1/4*w^3 - 9/4*w^2 + 11/4*w + 3]', '[521, 521, -5/4*w^3 + 1/4*w^2 + 25/4*w - 1]', '[521, 521, 5/4*w^3 - 9/4*w^2 - 21/4*w + 5]', '[529, 23, 5/4*w^3 - 5/4*w^2 - 33/4*w + 6]', '[529, 23, 1/4*w^3 + 7/4*w^2 - 13/4*w - 5]', '[539, 77, 3/4*w^3 - 7/4*w^2 - 11/4*w + 10]', '[539, 77, 3/4*w^3 + 5/4*w^2 - 31/4*w - 14]', '[539, 77, -1/2*w^3 + 3/2*w^2 + 1/2*w - 7]', '[539, 77, 3/2*w^3 - 7/2*w^2 - 11/2*w + 13]', '[541, 541, -5/4*w^3 + 17/4*w^2 + 5/4*w - 6]', '[541, 541, w^2 - 2*w - 11]', '[545, 545, -3/4*w^3 - 1/4*w^2 + 19/4*w - 2]', '[545, 545, 1/4*w^3 + 7/4*w^2 - 17/4*w - 12]', '[545, 545, -3/4*w^3 - 13/4*w^2 + 7/4*w + 8]', '[545, 545, w^3 + 2*w^2 - 5*w - 11]', '[556, 278, 3/2*w^3 - 13/2*w^2 + 7/2*w + 8]', '[556, 278, -3*w^3 - 2*w^2 + 26*w + 31]', '[556, 278, -2*w^3 - 3*w^2 + 17*w + 27]', '[556, 278, 3/2*w^3 - 13/2*w^2 - 1/2*w + 16]', '[569, 569, -3/4*w^3 + 11/4*w^2 + 15/4*w - 9]', '[569, 569, 1/2*w^3 - 3/2*w^2 + 3/2*w - 3]', '[569, 569, -w^3 + w^2 + 7*w + 1]', '[569, 569, 3/4*w^3 - 15/4*w^2 + 9/4*w + 5]', '[580, 290, w^2 - 2*w + 2]', '[580, 290, -1/4*w^3 + 1/4*w^2 + 17/4*w - 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w - 8]', '[9920, 620, 5/2*w^3 - 5/2*w^2 - 37/2*w + 14]', '[9920, 620, w^3 - 3*w^2 - 7*w + 2]', '[9920, 620, 2*w^2 + 2*w - 20]', '[9920, 1240, 3*w^3 - 8*w^2 - 12*w + 24]', '[9920, 1240, 5/2*w^3 + 5/2*w^2 - 31/2*w - 23]', '[9920, 1240, -1/4*w^3 + 9/4*w^2 - 15/4*w - 15]', '[9920, 1240, w^3 + w^2 - 10*w]', '[9929, 9929, -7/4*w^3 - 13/4*w^2 + 47/4*w + 26]', '[9929, 9929, -15/4*w^3 + 43/4*w^2 + 19/4*w - 17]', '[9929, 9929, -3*w^3 - 2*w^2 + 29*w + 37]', '[9929, 9929, -11/2*w^3 - 3/2*w^2 + 83/2*w + 39]', '[9941, 9941, -5/4*w^3 + 17/4*w^2 + 5/4*w - 2]', '[9941, 9941, 7/4*w^3 + 5/4*w^2 - 55/4*w - 23]', '[9949, 9949, -11/4*w^3 - 9/4*w^2 + 79/4*w + 19]', '[9949, 9949, -5/2*w^3 + 15/2*w^2 + 13/2*w - 25]', '[9955, 9955, 7/4*w^3 + 21/4*w^2 - 67/4*w - 39]', '[9955, 9955, -6*w^3 + 16*w^2 + 33*w - 79]', '[9955, 9955, 3/2*w^3 + 11/2*w^2 - 23/2*w - 23]', '[9955, 9955, -1/4*w^3 + 25/4*w^2 + 1/4*w - 20]', '[9980, 4990, 5/2*w^3 - 11/2*w^2 - 35/2*w + 28]', '[9980, 4990, -7/2*w^3 + 15/2*w^2 + 45/2*w - 46]', '[9980, 4990, -5/4*w^3 - 11/4*w^2 + 5/4*w - 1]', '[9980, 4990, -1/2*w^3 - 5/2*w^2 - 5/2*w + 7]', '[10000, 10, 10]', '[10000, 20, 5*w]', '[10000, 20, -5/4*w^3 + 5/4*w^2 + 45/4*w - 5]'], 'label': '4.4.7625.1', 'narrow_class_no': 2, 'primes': ['[4, 2, 1/2*w^3 - 3/2*w^2 - 3/2*w + 4]', '[4, 2, 1/2*w^3 + 1/2*w^2 - 7/2*w - 5]', '[5, 5, -1/4*w^3 - 3/4*w^2 + 5/4*w + 3]', '[11, 11, -1/4*w^3 + 1/4*w^2 + 9/4*w]', '[11, 11, w - 1]', '[29, 29, 1/4*w^3 - 1/4*w^2 - 1/4*w + 2]', '[29, 29, 1/2*w^3 - 1/2*w^2 - 7/2*w + 3]', '[31, 31, -3/4*w^3 - 1/4*w^2 + 19/4*w + 4]', '[31, 31, -3/4*w^3 + 7/4*w^2 + 11/4*w - 5]', '[49, 7, -1/2*w^3 + 3/2*w^2 + 5/2*w - 5]', '[49, 7, 1/2*w^3 - 1/2*w^2 - 7/2*w - 1]', '[59, 59, -1/4*w^3 + 5/4*w^2 + 5/4*w - 3]', '[59, 59, w^2 - 7]', '[61, 61, -5/4*w^3 - 7/4*w^2 + 37/4*w + 15]', '[71, 71, 3/4*w^3 + 9/4*w^2 - 11/4*w - 7]', '[71, 71, 1/4*w^3 - 1/4*w^2 - 13/4*w - 2]', '[79, 79, -1/4*w^3 + 5/4*w^2 + 1/4*w - 7]', '[79, 79, 1/4*w^3 + 3/4*w^2 - 9/4*w - 2]', '[81, 3, -3]', '[89, 89, -w^2 + 2*w + 1]', '[89, 89, 1/4*w^3 + 3/4*w^2 - 13/4*w - 7]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 12]', '[101, 101, -1/4*w^3 + 9/4*w^2 + 5/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 9/4*w - 1]', '[109, 109, -5/4*w^3 - 3/4*w^2 + 33/4*w + 7]', '[109, 109, -1/4*w^3 + 5/4*w^2 + 1/4*w - 8]', '[109, 109, 1/4*w^3 + 3/4*w^2 - 5/4*w - 9]', '[121, 11, -3/4*w^3 + 3/4*w^2 + 15/4*w - 2]', '[139, 139, 1/2*w^3 + 3/2*w^2 - 9/2*w - 7]', '[139, 139, -1/2*w^3 + 5/2*w^2 + 1/2*w - 11]', '[151, 151, 7/4*w^3 - 19/4*w^2 - 23/4*w + 14]', '[151, 151, -3/4*w^3 + 11/4*w^2 + 11/4*w - 10]', '[181, 181, -3/4*w^3 + 11/4*w^2 + 15/4*w - 12]', '[181, 181, 1/2*w^3 + 3/2*w^2 - 9/2*w - 9]', '[191, 191, 1/4*w^3 + 7/4*w^2 - 13/4*w - 8]', '[191, 191, -1/4*w^3 + 9/4*w^2 - 3/4*w - 10]', '[199, 199, -3/4*w^3 + 11/4*w^2 + 15/4*w - 10]', '[199, 199, 1/4*w^3 + 3/4*w^2 - 5/4*w - 7]', '[199, 199, -1/2*w^3 + 3/2*w^2 + 5/2*w - 3]', '[199, 199, 3/4*w^3 - 3/4*w^2 - 23/4*w - 1]', '[211, 211, -5/4*w^3 + 17/4*w^2 + 13/4*w - 13]', '[211, 211, -1/4*w^3 + 5/4*w^2 - 7/4*w + 2]', '[229, 229, -1/4*w^3 + 5/4*w^2 + 9/4*w - 9]', '[229, 229, 1/4*w^3 - 9/4*w^2 + 11/4*w + 1]', '[229, 229, 3/4*w^3 + 1/4*w^2 - 15/4*w - 5]', '[229, 229, 1/2*w^3 + 5/2*w^2 - 1/2*w - 7]', '[239, 239, 5/4*w^3 - 1/4*w^2 - 37/4*w - 6]', '[239, 239, -3/4*w^3 + 7/4*w^2 + 11/4*w - 8]', '[239, 239, w^2 - 2*w - 7]', '[239, 239, -5/2*w^3 - 5/2*w^2 + 37/2*w + 23]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 11]', '[251, 251, -1/4*w^3 + 9/4*w^2 + 5/4*w - 9]', '[269, 269, -7/4*w^3 - 1/4*w^2 + 59/4*w + 14]', '[269, 269, -1/2*w^3 - 3/2*w^2 + 7/2*w + 5]', '[269, 269, 3/4*w^3 - 11/4*w^2 + 9/4*w]', '[269, 269, -5/4*w^3 - 7/4*w^2 + 25/4*w + 7]', '[271, 271, 2*w^2 - w - 7]', '[271, 271, -1/4*w^3 + 9/4*w^2 + 1/4*w - 12]', '[271, 271, -1/2*w^3 + 5/2*w^2 + 5/2*w - 11]', '[271, 271, 1/4*w^3 + 7/4*w^2 - 13/4*w - 9]', '[281, 281, w^3 - 5*w - 3]', '[281, 281, 5/4*w^3 + 3/4*w^2 - 25/4*w - 6]', '[289, 17, 1/4*w^3 + 7/4*w^2 - 9/4*w - 14]', '[289, 17, -5/4*w^3 - 7/4*w^2 + 45/4*w + 17]', '[311, 311, 1/4*w^3 - 1/4*w^2 - 9/4*w - 4]', '[311, 311, w - 5]', '[331, 331, 2*w^2 - w - 11]', '[331, 331, -1/4*w^3 + 9/4*w^2 + 1/4*w - 8]', '[349, 349, 1/4*w^3 - 9/4*w^2 + 19/4*w - 2]', '[349, 349, -5/4*w^3 - 3/4*w^2 + 49/4*w + 16]', '[359, 359, -7/4*w^3 - 5/4*w^2 + 63/4*w + 20]', '[359, 359, 3/4*w^3 + 5/4*w^2 - 19/4*w - 10]', '[361, 19, -1/4*w^3 + 1/4*w^2 + 5/4*w - 5]', '[361, 19, -w^3 + w^2 + 5*w - 3]', '[379, 379, -1/4*w^3 - 3/4*w^2 + 17/4*w - 1]', '[379, 379, -2*w^3 - 2*w^2 + 17*w + 23]', '[379, 379, -1/4*w^3 + 9/4*w^2 + 5/4*w - 16]', '[379, 379, 1/4*w^3 + 3/4*w^2 - 17/4*w - 8]', '[389, 389, -3/2*w^3 - 5/2*w^2 + 13/2*w + 11]', '[389, 389, -5/4*w^3 - 7/4*w^2 + 45/4*w + 19]', '[401, 401, 5/4*w^3 - 5/4*w^2 - 29/4*w + 2]', '[401, 401, w^3 - w^2 - 4*w + 1]', '[409, 409, -1/4*w^3 + 5/4*w^2 - 3/4*w - 7]', '[409, 409, -3/4*w^3 + 7/4*w^2 + 11/4*w - 9]', '[419, 419, 1/4*w^3 + 3/4*w^2 - 1/4*w - 6]', '[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 7]', '[421, 421, 3/4*w^3 - 11/4*w^2 + 1/4*w + 2]', '[421, 421, 3/2*w^3 + 1/2*w^2 - 19/2*w - 7]', '[431, 431, 1/4*w^3 - 5/4*w^2 + 3/4*w - 1]', '[431, 431, -5/4*w^3 - 3/4*w^2 + 21/4*w + 4]', '[431, 431, -1/2*w^3 - 1/2*w^2 + 9/2*w + 9]', '[431, 431, 1/2*w^3 - 1/2*w^2 - 9/2*w - 5]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 4]', '[461, 461, -3/2*w^3 - 1/2*w^2 + 25/2*w + 15]', '[461, 461, -7/4*w^3 - 9/4*w^2 + 55/4*w + 20]', '[461, 461, 1/4*w^3 + 3/4*w^2 - 17/4*w - 3]', '[499, 499, -1/4*w^3 + 5/4*w^2 - 15/4*w + 5]', '[499, 499, -1/4*w^3 - 3/4*w^2 + 17/4*w - 2]', '[509, 509, 5/4*w^3 + 3/4*w^2 - 33/4*w - 6]', '[509, 509, 1/4*w^3 - 9/4*w^2 + 11/4*w + 3]', '[521, 521, -5/4*w^3 + 1/4*w^2 + 25/4*w - 1]', '[521, 521, 5/4*w^3 - 9/4*w^2 - 21/4*w + 5]', '[529, 23, 5/4*w^3 - 5/4*w^2 - 33/4*w + 6]', '[529, 23, 1/4*w^3 + 7/4*w^2 - 13/4*w - 5]', '[541, 541, -5/4*w^3 + 17/4*w^2 + 5/4*w - 6]', '[541, 541, w^2 - 2*w - 11]', '[569, 569, -3/4*w^3 + 11/4*w^2 + 15/4*w - 9]', '[569, 569, 1/2*w^3 - 3/2*w^2 + 3/2*w - 3]', '[569, 569, -w^3 + w^2 + 7*w + 1]', '[569, 569, 3/4*w^3 - 15/4*w^2 + 9/4*w + 5]', '[599, 599, 5/4*w^3 - 1/4*w^2 - 37/4*w - 1]', '[599, 599, -3/4*w^3 + 7/4*w^2 + 3/4*w - 6]', '[601, 601, 1/4*w^3 + 11/4*w^2 - 17/4*w - 11]', '[601, 601, 5/4*w^3 - 5/4*w^2 - 17/4*w + 1]', '[601, 601, 1/4*w^3 - 13/4*w^2 + 7/4*w + 16]', '[601, 601, -7/4*w^3 + 7/4*w^2 + 43/4*w - 3]', '[631, 631, -1/4*w^3 + 1/4*w^2 + 1/4*w - 6]', '[631, 631, -1/2*w^3 + 1/2*w^2 + 7/2*w - 7]', '[641, 641, -1/4*w^3 - 3/4*w^2 + 9/4*w - 2]', '[641, 641, -1/4*w^3 + 5/4*w^2 + 1/4*w - 11]', '[661, 661, -3/4*w^3 - 9/4*w^2 + 27/4*w + 16]', '[661, 661, 1/2*w^3 + 3/2*w^2 - 9/2*w - 15]', '[701, 701, 3/2*w^3 - 3/2*w^2 - 17/2*w + 1]', '[701, 701, -5/4*w^3 + 5/4*w^2 + 21/4*w]', '[709, 709, -3/2*w^3 + 3/2*w^2 + 11/2*w - 7]', '[709, 709, -2*w^3 + 2*w^2 + 12*w - 9]', '[739, 739, -1/4*w^3 + 5/4*w^2 - 3/4*w - 9]', '[739, 739, -1/2*w^3 - 1/2*w^2 + 9/2*w - 1]', '[761, 761, -7/2*w^3 - 7/2*w^2 + 55/2*w + 37]', '[761, 761, 1/2*w^3 + 1/2*w^2 - 5/2*w - 11]', '[769, 769, -1/4*w^3 + 9/4*w^2 - 3/4*w - 14]', '[769, 769, 1/4*w^3 + 7/4*w^2 - 13/4*w - 4]', '[809, 809, 1/4*w^3 + 3/4*w^2 - 21/4*w - 9]', '[809, 809, 1/2*w^3 + 1/2*w^2 - 13/2*w + 3]', '[809, 809, -5/4*w^3 + 9/4*w^2 + 29/4*w - 6]', '[809, 809, 3/4*w^3 + 1/4*w^2 - 11/4*w - 5]', '[811, 811, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5]', '[811, 811, 1/4*w^3 - 1/4*w^2 - 17/4*w - 2]', '[821, 821, -1/4*w^3 - 7/4*w^2 - 7/4*w + 4]', '[821, 821, 7/4*w^3 + 5/4*w^2 - 63/4*w - 22]', '[841, 29, 5/4*w^3 - 5/4*w^2 - 25/4*w + 1]', '[859, 859, -3/4*w^3 - 13/4*w^2 + 3/4*w + 8]', '[859, 859, -1/2*w^3 + 5/2*w^2 + 1/2*w - 13]', '[859, 859, 5/4*w^3 + 11/4*w^2 - 17/4*w - 11]', '[859, 859, 1/2*w^3 + 3/2*w^2 - 9/2*w - 5]', '[881, 881, 5/4*w^3 - 5/4*w^2 - 21/4*w + 4]', '[881, 881, 1/4*w^3 + 3/4*w^2 - 9/4*w - 10]', '[881, 881, -5/4*w^3 + 1/4*w^2 + 45/4*w + 8]', '[881, 881, -1/4*w^3 + 9/4*w^2 + 5/4*w - 18]', '[941, 941, 9/4*w^3 - 33/4*w^2 - 13/4*w + 20]', '[941, 941, -11/4*w^3 - 13/4*w^2 + 87/4*w + 32]', '[961, 31, -1/2*w^3 + 1/2*w^2 + 5/2*w - 7]', '[991, 991, -w^3 + w^2 + 8*w - 3]', '[991, 991, -7/4*w^3 + 15/4*w^2 + 27/4*w - 9]', '[991, 991, -11/4*w^3 + 35/4*w^2 + 31/4*w - 26]', '[991, 991, -1/4*w^3 + 1/4*w^2 - 7/4*w]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [16, 4, -9, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 7625, 'disc_rad': 305, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 1], [1, 2]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 26.115143751039085, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.7625.1', 'local_algs': ['5.4.3.2', '61.2.1.2', '61.2.0.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 61], 'rd': 9.34458377794, 'regulator': {'__RealLiteral__': 0, 'data': '4.88717250406', 'prec': 44}, 'res': {'gal': ['1,0,-29,0,136,0,-29,0,1'], 'sib': ['-4,17,-16,-2,1', '1,0,-29,0,136,0,-29,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{3} - \\frac{1}{4} a^{2} - \\frac{5}{4} a \\)', '\\( \\frac{1}{4} a^{3} + \\frac{3}{4} a^{2} - \\frac{9}{4} a - 6 \\)', '\\( \\frac{1}{4} a^{3} + \\frac{3}{4} a^{2} - \\frac{1}{4} a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/4*a^3 - 1/4*a^2 - 1/4*a']}