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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 10025, 'field_bad_primes': [5, 401], 'field_label': '4.4.10025.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.10025.1-20.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 5], 'level_ideal': '[20, 10, -1/2*w^3 - 1/2*w^2 + 9/2*w]', 'level_label': '20.2', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.2-a', '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 + 1/2*w^2 - 9/2*w - 4]', -1], ['[5, 5, -1/2*w^3 - 3/2*w^2 + 7/2*w + 10]', 1]], 'hecke_eigenvalues': [0, 1, -1, -1, 0, 0, -7, 8, -10, 5, -15, 0, -2, 3, -2, 8, -15, 5, -2, -10, 0, -15, 0, 18, -2, -3, -3, 7, -3, 10, 5, -15, 0, -10, 5, -18, -13, -18, 12, -12, 23, -5, -15, -22, -22, 10, 10, -10, 10, 2, -17, 13, 2, 13, 23, 0, 10, -28, 7, -8, 2, 3, -13, 18, 12, -10, 0, 15, -25, 8, -35, -15, -27, 7, 27, 7, 2, 30, 0, 30, 10, -12, 3, -40, 15, -5, -35, -38, -28, -33, 12, -40, 10, -5, 20, 10, 10, -18, -28, -3, 22, -42, 8, 0, 15, -2, 28, 22, 2, 18, 28, 22, -43, -12, -42, -15, -20, -22, 13, 28, 18, 23, 8, 12, 7, -10, -30, 15, -10, -52, -7, 32, 32, 35, 0, -30, 0, 40, -45, -12, 28, 48, -17, -33, -38, 5, -35, 45, -15, 23, -17, -18, 27, -13, 33, -12, 42, -20, -35, -25, -40, -18, 12, 22, 42, -28, 12, -8, -38, 47, -20, 15, 15, -50, 33, 28, -50, -45, 25, 10, -12, 8, -2, -32, -10, 10, 10, 40, 48, -27, -15, -45, 15, 40, 60, -50, -65, -25, 0, 25, -38, 2, 53, 38, 45, 5, -60, 10, 55, 10, -20, -20, 35, -60, 42, 22, 0, -10, -45, -35, 22, -8, -42, 58, -30, 20, 30, 15, -18, -8, 38, 63, 0, 30, 20, -20, -57, 33, -18, 77, 45, 5, 20, -10, -20, -15, -47, 28, 5, -25, -13, 57, 40, 20, 15, 15, 42, -58, -13, 22, -5, 40, -80, -20, -77, 58, -2, 73, 52, -8, -22, -32, 30, -5, -17, 28, -67, -32, -18, -3, 22, -18, 68, 53, -30, 20, -60, 20, -37, -72, 20, -65, 10, 10], 'hecke_polynomial': 'x', 'label': '4.4.10025.1-20.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 10025, 'ideals': ['[1, 1, 1]', '[4, 2, -w + 2]', '[4, 2, 1/2*w^3 + 1/2*w^2 - 9/2*w - 4]', '[5, 5, -1/2*w^3 - 3/2*w^2 + 7/2*w + 10]', '[5, 5, -1/2*w^3 - 1/2*w^2 + 5/2*w + 3]', '[16, 2, 2]', '[16, 4, w^3 + w^2 - 8*w - 4]', '[16, 4, 3/2*w^3 + 5/2*w^2 - 21/2*w - 11]', '[19, 19, 1/2*w^3 + 1/2*w^2 - 9/2*w - 3]', '[19, 19, w - 1]', '[20, 10, -w^3 - 2*w^2 + 7*w + 10]', '[20, 10, -1/2*w^3 - 1/2*w^2 + 9/2*w]', '[20, 10, -w - 2]', '[20, 10, 1/2*w^3 + 3/2*w^2 - 7/2*w - 9]', '[25, 5, -1/2*w^3 - 1/2*w^2 + 5/2*w + 5]', '[25, 5, w^3 + w^2 - 7*w - 5]', '[25, 5, -w^3 - w^2 + 8*w + 7]', '[31, 31, 1/2*w^3 + 3/2*w^2 - 7/2*w - 6]', '[31, 31, -w^3 - 2*w^2 + 7*w + 13]', '[49, 7, -2*w^3 - 2*w^2 + 15*w + 9]', '[49, 7, 1/2*w^3 + 3/2*w^2 - 9/2*w - 4]', '[59, 59, -3/2*w^3 - 3/2*w^2 + 17/2*w + 8]', '[59, 59, -1/2*w^3 - 5/2*w^2 + 11/2*w + 9]', '[61, 61, -1/2*w^3 - 3/2*w^2 + 9/2*w + 9]', '[61, 61, -3/2*w^3 - 5/2*w^2 + 23/2*w + 12]', '[64, 4, -2*w + 4]', '[64, 4, w^3 + w^2 - 9*w - 8]', '[64, 8, -w^3 - w^2 + 6*w + 4]', '[64, 8, 3/2*w^3 + 3/2*w^2 - 23/2*w - 6]', '[71, 71, -3/2*w^3 - 1/2*w^2 + 23/2*w - 1]', '[71, 71, 3/2*w^3 + 3/2*w^2 - 19/2*w - 9]', '[76, 38, -w^3 - 2*w^2 + 8*w + 14]', '[76, 38, w^3 + 2*w^2 - 8*w - 7]', '[76, 38, -w + 4]', '[76, 38, 1/2*w^3 + 1/2*w^2 - 9/2*w - 6]', '[79, 79, -1/2*w^3 - 3/2*w^2 + 11/2*w + 4]', '[79, 79, -5/2*w^3 - 7/2*w^2 + 37/2*w + 18]', '[80, 10, -w^3 - 3*w^2 + 7*w + 20]', '[80, 10, -w^3 - w^2 + 5*w + 6]', '[80, 20, -w^2 + 2*w]', '[80, 20, 3/2*w^3 + 5/2*w^2 - 21/2*w - 15]', '[80, 20, w^2 - 4]', '[80, 20, -5/2*w^3 - 7/2*w^2 + 39/2*w + 23]', '[81, 3, -3]', '[89, 89, w^3 - 7*w + 1]', '[89, 89, -2*w^3 - 3*w^2 + 14*w + 17]', '[89, 89, 1/2*w^3 - 1/2*w^2 - 7/2*w + 2]', '[89, 89, -5/2*w^3 - 7/2*w^2 + 35/2*w + 18]', '[95, 95, 3/2*w^3 + 3/2*w^2 - 17/2*w - 10]', '[95, 95, 5/2*w^3 + 5/2*w^2 - 39/2*w - 14]', '[95, 95, -5/2*w^3 - 7/2*w^2 + 33/2*w + 17]', '[95, 95, -3/2*w^3 - 1/2*w^2 + 23/2*w]', '[100, 10, -2*w^3 - 2*w^2 + 15*w + 10]', '[100, 10, -2*w^2 + w + 10]', '[100, 10, w^2 - w - 6]', '[100, 10, -1/2*w^3 - 1/2*w^2 + 5/2*w]', '[100, 10, -7/2*w^3 - 11/2*w^2 + 51/2*w + 30]', '[100, 10, -3/2*w^3 - 3/2*w^2 + 19/2*w + 8]', '[101, 101, -2*w^2 + 11]', '[101, 101, 3*w^3 + 5*w^2 - 21*w - 27]', '[121, 11, -3/2*w^3 - 3/2*w^2 + 21/2*w + 7]', '[121, 11, 3/2*w^3 + 3/2*w^2 - 21/2*w - 8]', '[124, 62, -3*w^3 - 4*w^2 + 22*w + 22]', '[124, 62, -w^3 + 8*w - 1]', '[124, 62, -2*w^3 - 3*w^2 + 13*w + 16]', '[124, 62, -w^3 + 6*w + 1]', '[125, 5, 3/2*w^3 + 1/2*w^2 - 25/2*w]', '[125, 5, -3/2*w^3 - 7/2*w^2 + 23/2*w + 15]', '[125, 25, -1/2*w^3 - 3/2*w^2 + 5/2*w + 5]', '[125, 25, -1/2*w^3 - 3/2*w^2 + 5/2*w + 12]', '[131, 131, -3/2*w^3 - 5/2*w^2 + 21/2*w + 16]', '[131, 131, -3/2*w^3 - 5/2*w^2 + 19/2*w + 14]', '[139, 139, -2*w^3 - w^2 + 16*w + 1]', '[139, 139, 1/2*w^3 + 1/2*w^2 - 3/2*w - 8]', '[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 24]', '[149, 149, -w^3 + w^2 + 5*w - 3]', '[149, 149, -5*w^3 - 7*w^2 + 37*w + 39]', '[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 14]', '[155, 155, -1/2*w^3 - 3/2*w^2 + 9/2*w + 10]', '[155, 155, 1/2*w^3 + 1/2*w^2 - 3/2*w - 5]', '[155, 155, 3/2*w^3 + 3/2*w^2 - 25/2*w - 9]', '[155, 155, 3/2*w^3 + 5/2*w^2 - 23/2*w - 11]', '[181, 181, -5/2*w^3 - 9/2*w^2 + 37/2*w + 27]', '[181, 181, -5/2*w^3 - 7/2*w^2 + 33/2*w + 19]', '[181, 181, 3/2*w^3 + 1/2*w^2 - 23/2*w - 2]', '[181, 181, w^3 + 3*w^2 - 8*w - 13]', '[191, 191, 1/2*w^3 + 5/2*w^2 - 7/2*w - 14]', '[191, 191, -5/2*w^3 - 9/2*w^2 + 35/2*w + 24]', '[196, 14, -4*w^3 - 6*w^2 + 27*w + 28]', '[196, 14, -3/2*w^3 - 5/2*w^2 + 17/2*w + 11]', '[196, 14, -w^3 - 2*w^2 + 6*w + 13]', '[196, 14, -w^3 + 2*w^2 + 2]', '[199, 199, -1/2*w^3 - 5/2*w^2 + 7/2*w + 16]', '[199, 199, 5/2*w^3 + 9/2*w^2 - 35/2*w - 22]', '[211, 211, -2*w^3 - 4*w^2 + 14*w + 19]', '[211, 211, -w^3 - 3*w^2 + 7*w + 19]', '[229, 229, 3/2*w^3 + 7/2*w^2 - 21/2*w - 17]', '[229, 229, -3/2*w^3 - 7/2*w^2 + 21/2*w + 21]', '[229, 229, -1/2*w^3 - 3/2*w^2 + 13/2*w + 1]', '[229, 229, 5/2*w^3 + 7/2*w^2 - 41/2*w - 24]', '[236, 118, -w^3 - 2*w^2 + 5*w + 8]', '[236, 118, -2*w^3 - 3*w^2 + 15*w + 14]', '[236, 118, 3/2*w^3 + 3/2*w^2 - 23/2*w - 4]', '[236, 118, -1/2*w^3 + 1/2*w^2 + 11/2*w - 7]', '[241, 241, -1/2*w^3 - 5/2*w^2 + 7/2*w + 12]', '[241, 241, 3/2*w^3 + 3/2*w^2 - 23/2*w - 3]', '[241, 241, w^3 + w^2 - 6*w - 1]', '[241, 241, -5/2*w^3 - 9/2*w^2 + 35/2*w + 26]', '[244, 122, 4*w^3 + 5*w^2 - 31*w - 31]', '[244, 122, 13/2*w^3 + 19/2*w^2 - 95/2*w - 53]', '[244, 122, w^3 - 2*w^2 - 5*w + 8]', '[244, 122, w^3 - 4*w - 6]', '[245, 35, -1/2*w^3 - 5/2*w^2 + 7/2*w + 15]', '[245, 35, -3/2*w^3 - 5/2*w^2 + 23/2*w + 10]', '[245, 35, -3*w^3 - w^2 + 14*w + 13]', '[245, 35, 5/2*w^3 + 9/2*w^2 - 35/2*w - 23]', '[251, 251, 2*w^3 + 2*w^2 - 13*w - 9]', '[251, 251, -5/2*w^3 - 5/2*w^2 + 37/2*w + 11]', '[256, 4, 4]', '[256, 8, 2*w^3 + 2*w^2 - 16*w - 8]', '[256, 8, 3*w^3 + 5*w^2 - 21*w - 22]', '[256, 16, 3*w^3 + 5*w^2 - 22*w - 28]', '[256, 16, 1/2*w^3 + 5/2*w^2 - 9/2*w - 12]', '[269, 269, -2*w^3 - 3*w^2 + 12*w + 17]', '[269, 269, 5/2*w^3 + 11/2*w^2 - 37/2*w - 21]', '[271, 271, 3/2*w^3 + 5/2*w^2 - 23/2*w - 9]', '[271, 271, 1/2*w^3 + 3/2*w^2 - 9/2*w - 12]', '[281, 281, 5/2*w^3 + 9/2*w^2 - 39/2*w - 28]', '[281, 281, 3/2*w^3 + 7/2*w^2 - 25/2*w - 14]', '[284, 142, -4*w^2 + 5*w + 12]', '[284, 142, -1/2*w^3 - 3/2*w^2 + 3/2*w + 13]', '[284, 142, -5*w^3 - 8*w^2 + 36*w + 41]', '[284, 142, -3*w^3 - 4*w^2 + 20*w + 18]', '[295, 295, -1/2*w^3 - 1/2*w^2 + 9/2*w + 7]', '[295, 295, 2*w^3 + 3*w^2 - 14*w - 19]', '[295, 295, 3/2*w^3 + 5/2*w^2 - 19/2*w - 15]', '[295, 295, -w + 5]', '[304, 38, w^3 + w^2 - 9*w - 6]', '[304, 38, 2*w - 2]', '[304, 76, w^3 - w^2 - 8*w + 8]', '[304, 76, -7/2*w^3 - 11/2*w^2 + 47/2*w + 28]', '[304, 76, -2*w^3 - w^2 + 16*w + 4]', '[304, 76, 5/2*w^3 + 7/2*w^2 - 31/2*w - 19]', '[305, 305, -5/2*w^3 - 5/2*w^2 + 39/2*w + 15]', '[305, 305, -2*w^3 - 5*w^2 + 14*w + 35]', '[305, 305, 3*w^3 + 3*w^2 - 18*w - 19]', '[305, 305, 1/2*w^3 - 3/2*w^2 - 3/2*w + 2]', '[311, 311, 1/2*w^3 + 7/2*w^2 - 5/2*w - 24]', '[311, 311, 3*w^3 + 5*w^2 - 22*w - 27]', '[311, 311, 3/2*w^3 + 5/2*w^2 - 17/2*w - 12]', '[311, 311, 1/2*w^3 + 5/2*w^2 - 9/2*w - 13]', '[316, 158, -3*w^3 - 4*w^2 + 24*w + 22]', '[316, 158, 5/2*w^3 + 7/2*w^2 - 35/2*w - 21]', '[316, 158, 3/2*w^3 + 5/2*w^2 - 17/2*w - 13]', '[316, 158, w^3 + 2*w^2 - 6*w - 14]', '[320, 20, -2*w^3 - 4*w^2 + 14*w + 20]', '[320, 20, -w^3 - w^2 + 9*w]', '[320, 20, -2*w - 4]', '[320, 20, w^3 + 3*w^2 - 7*w - 18]', '[320, 40, 3/2*w^3 + 1/2*w^2 - 17/2*w - 5]', '[320, 40, w^3 - 8*w]', '[320, 40, -w^3 - 2*w^2 + 8*w + 16]', '[320, 40, -2*w^3 - 3*w^2 + 13*w + 17]', '[324, 6, 3*w - 6]', '[324, 6, -3/2*w^3 - 3/2*w^2 + 27/2*w + 12]', '[349, 349, 3*w^3 + 4*w^2 - 21*w - 21]', '[349, 349, -3/2*w^3 - 1/2*w^2 + 21/2*w + 2]', '[355, 355, -w^3 - 2*w^2 + 9*w + 5]', '[355, 355, w^3 + w^2 - 9*w - 5]', '[355, 355, 3/2*w^3 + 7/2*w^2 - 21/2*w - 18]', '[355, 355, -5/2*w^3 - 15/2*w^2 + 43/2*w + 28]', '[356, 178, -5/2*w^3 - 9/2*w^2 + 37/2*w + 26]', '[356, 178, w^3 + 2*w^2 - 9*w - 6]', '[356, 178, 17/2*w^3 + 25/2*w^2 - 125/2*w - 68]', '[356, 178, w^3 - 3*w^2 - 4*w + 14]', '[356, 178, w^3 + 3*w^2 - 8*w - 14]', '[356, 178, 4*w^3 + 4*w^2 - 31*w - 22]', '[356, 178, -3/2*w^3 - 5/2*w^2 + 25/2*w + 17]', '[356, 178, 5/2*w^3 + 11/2*w^2 - 35/2*w - 23]', '[359, 359, -w^3 - 3*w^2 + 7*w + 17]', '[359, 359, -2*w^3 - 4*w^2 + 14*w + 21]', '[361, 19, 2*w^3 + 2*w^2 - 14*w - 9]', '[361, 19, -2*w^3 - 2*w^2 + 14*w + 11]', '[361, 361, -7/2*w^3 - 9/2*w^2 + 51/2*w + 23]', '[361, 361, -3/2*w^3 - 1/2*w^2 + 19/2*w + 2]', '[380, 190, w^3 + 2*w^2 - 6*w - 15]', '[380, 190, -2*w^3 - 2*w^2 + 17*w + 16]', '[380, 190, 3/2*w^3 + 1/2*w^2 - 21/2*w - 1]', '[380, 190, 3*w^3 + 4*w^2 - 21*w - 20]', '[380, 190, -w^2 - w + 2]', '[380, 190, -5/2*w^3 - 5/2*w^2 + 37/2*w + 12]', '[380, 190, -1/2*w^3 - 1/2*w^2 + 1/2*w + 10]', '[380, 190, -2*w^3 - 2*w^2 + 13*w + 10]', '[389, 389, -2*w^3 - 2*w^2 + 13*w + 11]', '[389, 389, 5/2*w^3 + 5/2*w^2 - 37/2*w - 13]', '[395, 395, -1/2*w^3 - 1/2*w^2 + 3/2*w]', '[395, 395, 1/2*w^3 - 3/2*w^2 - 7/2*w + 13]', '[395, 395, 1/2*w^3 - 1/2*w^2 - 13/2*w + 10]', '[395, 395, -11/2*w^3 - 17/2*w^2 + 81/2*w + 46]', '[400, 10, -w^3 - w^2 + 5*w + 10]', '[400, 10, 2*w^3 + 2*w^2 - 14*w - 10]', '[400, 10, -2*w^3 - 2*w^2 + 16*w + 14]', '[400, 20, -3*w^3 - 4*w^2 + 20*w + 20]', '[400, 20, -w^3 - 3*w^2 + 8*w + 20]', '[400, 20, 3*w^3 + 3*w^2 - 24*w - 16]', '[400, 20, -3/2*w^3 - 3/2*w^2 + 15/2*w + 10]', '[400, 20, 5/2*w^3 + 7/2*w^2 - 31/2*w - 15]', '[400, 20, -2*w^3 - w^2 + 15*w + 3]', '[401, 401, 3/2*w^3 + 7/2*w^2 - 21/2*w - 19]', '[401, 401, 5/2*w^3 + 9/2*w^2 - 37/2*w - 23]', '[401, 401, -w^3 - 3*w^2 + 8*w + 17]', '[404, 202, 3/2*w^3 + 3/2*w^2 - 19/2*w - 4]', '[404, 202, -2*w^3 - 2*w^2 + 15*w + 6]', '[404, 202, 2*w^3 - 4*w^2 - 11*w + 22]', '[404, 202, -25/2*w^3 - 37/2*w^2 + 181/2*w + 98]', '[405, 15, 3/2*w^3 + 9/2*w^2 - 21/2*w - 30]', '[405, 15, 3/2*w^3 + 3/2*w^2 - 15/2*w - 9]', '[431, 431, 5/2*w^3 + 5/2*w^2 - 29/2*w - 13]', '[431, 431, -15/2*w^3 - 23/2*w^2 + 107/2*w + 61]', '[439, 439, -3/2*w^3 + 1/2*w^2 + 21/2*w - 6]', '[439, 439, -9/2*w^3 - 13/2*w^2 + 63/2*w + 32]', '[445, 445, w + 5]', '[445, 445, 7/2*w^3 + 13/2*w^2 - 51/2*w - 29]', '[445, 445, 5/2*w^3 + 1/2*w^2 - 41/2*w + 5]', '[445, 445, -5/2*w^3 - 9/2*w^2 + 39/2*w + 30]', '[445, 445, 1/2*w^3 + 1/2*w^2 - 9/2*w + 3]', '[445, 445, 6*w^3 + 9*w^2 - 44*w - 51]', '[445, 445, w^3 - w^2 - 3*w + 1]', '[445, 445, 1/2*w^3 - 5/2*w^2 - 3/2*w + 10]', '[449, 449, -w^2 - 2*w + 1]', '[449, 449, -1/2*w^3 - 3/2*w^2 + 3/2*w + 14]', '[461, 461, -2*w^3 - 2*w^2 + 12*w + 9]', '[461, 461, -3*w^3 - 3*w^2 + 23*w + 13]', '[475, 95, 5*w^3 + 7*w^2 - 37*w - 37]', '[475, 95, -1/2*w^3 + 1/2*w^2 + 5/2*w - 5]', '[475, 95, -5/2*w^3 - 9/2*w^2 + 37/2*w + 25]', '[475, 95, -5/2*w^3 - 7/2*w^2 + 37/2*w + 16]', '[475, 95, w^3 + 3*w^2 - 8*w - 15]', '[475, 95, w^3 - w^2 - 5*w + 5]', '[479, 479, 7/2*w^3 + 9/2*w^2 - 47/2*w - 26]', '[479, 479, 3/2*w^3 + 5/2*w^2 - 27/2*w - 16]', '[479, 479, -7/2*w^3 - 9/2*w^2 + 51/2*w + 24]', '[479, 479, 3/2*w^3 + 1/2*w^2 - 19/2*w - 3]', '[484, 22, 3*w^2 - w - 16]', '[484, 22, -3*w^2 + 2*w + 14]', '[484, 22, 5*w^3 + 8*w^2 - 36*w - 43]', '[484, 22, -11/2*w^3 - 17/2*w^2 + 81/2*w + 47]', '[491, 491, 2*w^3 + 4*w^2 - 15*w - 23]', '[491, 491, -7/2*w^3 - 7/2*w^2 + 53/2*w + 17]', '[491, 491, -1/2*w^3 - 5/2*w^2 + 11/2*w + 6]', '[491, 491, -3/2*w^3 - 7/2*w^2 + 23/2*w + 17]', '[496, 62, w^3 + 3*w^2 - 7*w - 12]', '[496, 62, -2*w^3 - 4*w^2 + 14*w + 26]', '[496, 124, w^3 + 3*w^2 - 8*w - 16]', '[496, 124, w^2 - 3*w + 3]', '[496, 124, -3*w^3 - 4*w^2 + 24*w + 28]', '[496, 124, 5/2*w^3 + 9/2*w^2 - 37/2*w - 24]', '[499, 499, 3*w^2 - 19]', '[499, 499, 3/2*w^3 + 5/2*w^2 - 19/2*w - 16]', '[499, 499, -9/2*w^3 - 15/2*w^2 + 63/2*w + 38]', '[499, 499, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1]', '[500, 10, -4*w^3 - 6*w^2 + 29*w + 30]', '[500, 10, -w^3 - 2*w^2 + 5*w + 10]', '[500, 10, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5]', '[500, 10, -1/2*w^3 + 3/2*w^2 + 5/2*w - 10]', '[500, 50, 7/2*w^3 + 7/2*w^2 - 55/2*w - 20]', '[500, 50, w^3 - 5*w]', '[500, 50, -2*w^3 - 2*w^2 + 11*w + 14]', '[500, 50, 7/2*w^3 + 9/2*w^2 - 53/2*w - 23]', '[505, 505, 5/2*w^3 + 1/2*w^2 - 25/2*w - 7]', '[505, 505, -13/2*w^3 - 21/2*w^2 + 89/2*w + 49]', '[505, 505, 5/2*w^3 - 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1/2*w^2 - 19/2*w + 7]', '[1919, 1919, 5*w^3 + 7*w^2 - 36*w - 33]', '[1931, 1931, -2*w^3 + w^2 + 10*w + 1]', '[1931, 1931, 17/2*w^3 + 23/2*w^2 - 127/2*w - 66]', '[1936, 22, -3*w^3 - 3*w^2 + 21*w + 14]', '[1936, 22, 3*w^3 + 3*w^2 - 21*w - 16]', '[1936, 44, w^3 + 4*w^2 - 8*w - 28]', '[1936, 44, -2*w^3 - 5*w^2 + 16*w + 32]', '[1936, 44, -9/2*w^3 - 13/2*w^2 + 57/2*w + 28]', '[1936, 44, 3*w^3 + 4*w^2 - 18*w - 17]', '[1945, 1945, -3/2*w^3 - 1/2*w^2 + 27/2*w]', '[1945, 1945, -5/2*w^3 - 11/2*w^2 + 39/2*w + 26]', '[1945, 1945, 7/2*w^3 + 19/2*w^2 - 57/2*w - 37]', '[1945, 1945, 6*w^3 + 4*w^2 - 48*w - 15]', '[1949, 1949, -w^3 - 2*w^2 + 3*w + 17]', '[1949, 1949, -4*w^2 + 2*w + 17]', '[1949, 1949, -w^3 - 5*w^2 + 7*w + 27]', '[1949, 1949, -5*w^3 - 9*w^2 + 35*w + 49]', '[1951, 1951, -13/2*w^3 - 17/2*w^2 + 103/2*w + 52]', '[1951, 1951, 11/2*w^3 + 13/2*w^2 - 87/2*w - 41]', '[1964, 982, -2*w^3 + w^2 + 13*w - 6]', '[1964, 982, -21/2*w^3 - 29/2*w^2 + 157/2*w + 82]', '[1964, 982, -3/2*w^3 - 5/2*w^2 + 17/2*w + 19]', '[1964, 982, 5/2*w^3 + 1/2*w^2 - 37/2*w + 2]', '[1964, 982, -5*w^3 - 7*w^2 + 34*w + 34]', '[1964, 982, w^3 - 9*w - 4]', '[1964, 982, 7*w^3 + 10*w^2 - 50*w - 53]', '[1964, 982, 2*w^3 - 2*w^2 - 9*w + 4]', '[1975, 395, 11/2*w^3 + 13/2*w^2 - 85/2*w - 40]', '[1975, 395, -5/2*w^3 - 11/2*w^2 + 41/2*w + 28]', '[1975, 395, -1/2*w^3 + 5/2*w^2 - 1/2*w - 10]', '[1975, 395, -1/2*w^3 - 7/2*w^2 + 9/2*w + 14]', '[1975, 395, -5/2*w^3 - 11/2*w^2 + 35/2*w + 30]', '[1975, 395, 3/2*w^3 + 5/2*w^2 - 27/2*w - 20]', '[1979, 1979, -15/2*w^3 - 19/2*w^2 + 119/2*w + 59]', '[1979, 1979, 9/2*w^3 + 17/2*w^2 - 61/2*w - 47]', '[1984, 124, -6*w^3 - 8*w^2 + 44*w + 44]', '[1984, 124, -2*w^3 + 16*w - 2]', '[1984, 124, -4*w^3 - 6*w^2 + 26*w + 32]', '[1984, 124, -2*w^3 + 12*w + 2]', '[1984, 248, 6*w^3 + 7*w^2 - 46*w - 36]', '[1984, 248, w^3 + w^2 - 10*w - 4]', '[1984, 248, 1/2*w^3 + 1/2*w^2 - 13/2*w - 2]', '[1984, 248, -5/2*w^3 - 3/2*w^2 + 27/2*w + 9]', '[1996, 998, -w^3 - 2*w^2 + 12*w - 2]', '[1996, 998, -7/2*w^3 - 7/2*w^2 + 51/2*w + 16]', '[1996, 998, -w^3 + 2*w^2 + 5*w - 12]', '[1996, 998, -13/2*w^3 - 19/2*w^2 + 95/2*w + 49]', '[1996, 998, 13/2*w^3 + 19/2*w^2 - 83/2*w - 43]', '[1996, 998, 3*w^3 + 4*w^2 - 26*w - 31]', '[1996, 998, 2*w^3 + 6*w^2 - 15*w - 42]', '[1996, 998, 3*w^3 + 3*w^2 - 20*w - 14]', '[1999, 1999, 3*w^3 + 3*w^2 - 20*w - 17]', '[1999, 1999, 7/2*w^3 + 7/2*w^2 - 51/2*w - 19]', '[2000, 10, 3*w^3 + w^2 - 25*w]', '[2000, 10, -3*w^3 - 7*w^2 + 23*w + 30]', '[2000, 20, 2*w^3 + 3*w^2 - 12*w - 20]', '[2000, 20, -2*w^3 + w^2 + 10*w]', '[2000, 20, 17/2*w^3 + 23/2*w^2 - 127/2*w - 65]', '[2000, 20, -3/2*w^3 - 1/2*w^2 + 25/2*w + 5]', '[2000, 50, -w^3 - 3*w^2 + 5*w + 10]', '[2000, 50, -w^3 - 3*w^2 + 5*w + 24]', '[2000, 100, 5/2*w^3 + 3/2*w^2 - 35/2*w - 5]', '[2000, 100, -4*w^3 - 7*w^2 + 30*w + 40]', '[2000, 100, -4*w^3 - 5*w^2 + 28*w + 24]', '[2000, 100, 3/2*w^3 + 9/2*w^2 - 25/2*w - 21]', '[2005, 2005, -9/2*w^3 - 11/2*w^2 + 57/2*w + 28]', '[2005, 2005, 3*w^3 + 5*w^2 - 23*w - 35]', '[2005, 2005, -5/2*w^3 - 1/2*w^2 + 27/2*w + 9]', '[2005, 2005, -11/2*w^3 - 13/2*w^2 + 69/2*w + 36]', '[2005, 2005, 4*w^2 + w - 35]', '[2005, 2005, 3/2*w^3 + 13/2*w^2 - 19/2*w - 50]', '[2011, 2011, -1/2*w^3 - 5/2*w^2 + 1/2*w + 23]', '[2011, 2011, -4*w^3 - 4*w^2 + 32*w + 17]', '[2020, 1010, -5/2*w^3 + 1/2*w^2 + 43/2*w - 19]', '[2020, 1010, 3*w^3 + 4*w^2 - 23*w - 10]', '[2020, 1010, 1/2*w^3 - 1/2*w^2 - 3/2*w + 13]', '[2020, 1010, -5*w^3 - 8*w^2 + 31*w + 30]', '[2020, 1010, 2*w^3 + 4*w^2 - 11*w - 22]', '[2020, 1010, -3/2*w^3 + 13/2*w^2 + 19/2*w - 40]', '[2020, 1010, -14*w^3 - 22*w^2 + 99*w + 114]', '[2020, 1010, 1/2*w^3 - 3/2*w^2 - 13/2*w + 10]', '[2025, 15, 3/2*w^3 + 3/2*w^2 - 15/2*w - 15]', '[2025, 15, -3*w^3 - 3*w^2 + 21*w + 15]', '[2025, 15, 3*w^3 + 3*w^2 - 24*w - 21]', '[2029, 2029, 4*w^3 + 6*w^2 - 27*w - 33]', '[2029, 2029, 3/2*w^3 - 1/2*w^2 - 23/2*w + 3]', '[2036, 1018, -2*w^3 + 5*w^2 + 5*w - 14]', '[2036, 1018, -1/2*w^3 - 1/2*w^2 + 1/2*w - 2]', '[2036, 1018, -17*w^3 - 24*w^2 + 128*w + 137]', '[2036, 1018, -2*w^3 - 2*w^2 + 17*w + 4]', '[2039, 2039, -11/2*w^3 - 13/2*w^2 + 83/2*w + 32]', '[2039, 2039, 19/2*w^3 + 27/2*w^2 - 139/2*w - 73]', '[2081, 2081, 5/2*w^3 + 13/2*w^2 - 37/2*w - 29]', '[2081, 2081, -1/2*w^3 - 1/2*w^2 - 5/2*w + 17]', '[2084, 1042, 7/2*w^3 + 11/2*w^2 - 51/2*w - 24]', '[2084, 1042, 1/2*w^3 + 3/2*w^2 - 7/2*w - 1]', '[2084, 1042, -w^3 - 2*w^2 + 7*w + 18]', '[2084, 1042, 3*w^3 + 4*w^2 - 24*w - 18]', '[2089, 2089, -7/2*w^3 - 9/2*w^2 + 51/2*w + 18]', '[2089, 2089, -3/2*w^3 - 1/2*w^2 + 19/2*w - 3]', '[2096, 262, -3*w^3 - 5*w^2 + 21*w + 32]', '[2096, 262, -3*w^3 - 5*w^2 + 19*w + 28]', '[2096, 524, -w^3 - 2*w^2 + 4*w + 9]', '[2096, 524, 5*w^3 + 5*w^2 - 40*w - 24]', '[2096, 524, -8*w^3 - 13*w^2 + 51*w + 61]', '[2096, 524, w^3 - 10*w + 4]', '[2099, 2099, -w^3 + 2*w^2 + 7*w - 11]', '[2099, 2099, -2*w^3 - 2*w^2 + 13*w + 1]', '[2099, 2099, 11/2*w^3 + 17/2*w^2 - 77/2*w - 46]', '[2099, 2099, -w^2 + 2*w - 3]', '[2111, 2111, 13/2*w^3 + 17/2*w^2 - 103/2*w - 57]', '[2111, 2111, 5/2*w^3 + 3/2*w^2 - 23/2*w - 12]', '[2129, 2129, 1/2*w^3 + 3/2*w^2 - 1/2*w - 6]', '[2129, 2129, -1/2*w^3 + 1/2*w^2 + 13/2*w - 7]', '[2131, 2131, -3*w^3 - 7*w^2 + 20*w + 43]', '[2131, 2131, 21/2*w^3 + 29/2*w^2 - 157/2*w - 83]', '[2131, 2131, 5/2*w^3 + 13/2*w^2 - 33/2*w - 31]', '[2131, 2131, 2*w^3 - 2*w^2 - 9*w + 3]', '[2141, 2141, -3*w^2 + 2*w + 7]', '[2141, 2141, 2*w^3 + 6*w^2 - 13*w - 41]', '[2155, 2155, -w - 7]', '[2155, 2155, -1/2*w^3 - 1/2*w^2 + 9/2*w - 5]', '[2155, 2155, -2*w^3 - 4*w^2 + 12*w + 25]', '[2155, 2155, 2*w^2 + 2*w - 9]', '[2164, 1082, 5/2*w^3 + 3/2*w^2 - 35/2*w - 7]', '[2164, 1082, 11/2*w^3 + 17/2*w^2 - 69/2*w - 37]', '[2164, 1082, -2*w^3 + 19*w - 14]', '[2164, 1082, -w^3 - 5*w^2 + 8*w + 34]', '[2164, 1082, 4*w^3 + 5*w^2 - 28*w - 26]', '[2164, 1082, 2*w^3 + 5*w^2 - 13*w - 33]', '[2164, 1082, -23/2*w^3 - 31/2*w^2 + 175/2*w + 88]', '[2164, 1082, w^3 + w^2 - 10*w - 14]', '[2179, 2179, -7/2*w^3 - 13/2*w^2 + 51/2*w + 33]', '[2179, 2179, 3/2*w^3 + 9/2*w^2 - 23/2*w - 26]', '[2195, 2195, 3/2*w^3 + 1/2*w^2 - 23/2*w + 7]', '[2195, 2195, -5/2*w^3 - 7/2*w^2 + 33/2*w + 10]', '[2195, 2195, 1/2*w^3 - 7/2*w^2 - 7/2*w + 20]', '[2195, 2195, -13/2*w^3 - 21/2*w^2 + 91/2*w + 56]', '[2201, 2201, -1/2*w^3 + 3/2*w^2 + 9/2*w - 7]', '[2201, 2201, 3/2*w^3 + 1/2*w^2 - 23/2*w - 7]', '[2201, 2201, 2*w^3 + 4*w^2 - 16*w - 11]', '[2201, 2201, 5*w^3 + 5*w^2 - 29*w - 31]', '[2209, 47, -7/2*w^3 - 11/2*w^2 + 53/2*w + 26]', '[2209, 47, -5/2*w^3 - 5/2*w^2 + 39/2*w + 7]', '[2221, 2221, -5*w^3 - 7*w^2 + 39*w + 37]', '[2221, 2221, -5/2*w^3 - 5/2*w^2 + 31/2*w + 9]', '[2224, 278, -4*w^3 - 2*w^2 + 32*w + 2]', '[2224, 278, w^3 + w^2 - 3*w - 16]', '[2224, 556, w^3 - 4*w^2 - 2*w + 12]', '[2224, 556, 7/2*w^3 + 7/2*w^2 - 51/2*w - 18]', '[2224, 556, 11*w^3 + 16*w^2 - 82*w - 93]', '[2224, 556, 3*w^3 + 3*w^2 - 20*w - 16]', '[2225, 445, 3*w^3 + 5*w^2 - 21*w - 33]', '[2225, 445, -7*w^3 - 8*w^2 + 55*w + 45]', '[2225, 445, -w^2 - 2*w + 15]', '[2225, 445, w^3 - 9*w - 5]', '[2225, 445, -1/2*w^3 + 1/2*w^2 + 5/2*w + 5]', '[2225, 445, -10*w^3 - 14*w^2 + 74*w + 79]', '[2225, 445, 2*w^3 - 2*w^2 - 10*w + 5]', '[2225, 445, 5/2*w^3 + 7/2*w^2 - 37/2*w - 26]', '[2225, 445, -3/2*w^3 - 5/2*w^2 + 17/2*w + 20]', '[2225, 445, -1/2*w^3 - 3/2*w^2 + 3/2*w]', '[2225, 445, -7/2*w^3 - 11/2*w^2 + 45/2*w + 30]', '[2225, 445, -5/2*w^3 - 3/2*w^2 + 23/2*w + 14]', '[2239, 2239, -7/2*w^3 - 15/2*w^2 + 51/2*w + 47]', '[2239, 2239, 3*w^3 + 7*w^2 - 22*w - 31]', '[2245, 2245, -2*w^3 + w^2 + 12*w - 5]', '[2245, 2245, -15/2*w^3 - 21/2*w^2 + 109/2*w + 56]', '[2245, 2245, 3/2*w^3 + 7/2*w^2 - 17/2*w - 24]', '[2245, 2245, -1/2*w^3 - 5/2*w^2 + 3/2*w + 10]', '[2251, 2251, -19/2*w^3 - 29/2*w^2 + 135/2*w + 73]', '[2251, 2251, -3*w^3 - 7*w^2 + 21*w + 29]', '[2269, 2269, -2*w^3 - w^2 + 16*w + 7]', '[2269, 2269, 5/2*w^3 + 7/2*w^2 - 31/2*w - 22]', '[2276, 1138, -3*w^3 - 5*w^2 + 20*w + 18]', '[2276, 1138, 1/2*w^3 - 5/2*w^2 - 7/2*w + 13]', '[2276, 1138, -5*w^3 - 8*w^2 + 35*w + 44]', '[2276, 1138, 1/2*w^3 - 3/2*w^2 - 9/2*w + 18]', '[2284, 1142, -2*w^3 + 2*w^2 + 15*w - 22]', '[2284, 1142, -2*w^3 - 2*w^2 + 19*w - 6]', '[2284, 1142, 1/2*w^3 + 1/2*w^2 - 17/2*w - 16]', '[2284, 1142, -15/2*w^3 - 23/2*w^2 + 103/2*w + 52]', '[2299, 209, -4*w^3 - 7*w^2 + 30*w + 39]', '[2299, 209, 7/2*w^3 + 13/2*w^2 - 51/2*w - 36]', '[2299, 209, -3/2*w^3 - 9/2*w^2 + 23/2*w + 23]', '[2299, 209, 3/2*w^3 + 9/2*w^2 - 25/2*w - 22]', '[2305, 2305, -5/2*w^3 - 3/2*w^2 + 31/2*w + 10]', '[2305, 2305, 3/2*w^3 + 9/2*w^2 - 17/2*w - 30]', '[2305, 2305, 7/2*w^3 + 11/2*w^2 - 47/2*w - 31]', '[2305, 2305, 11/2*w^3 + 27/2*w^2 - 83/2*w - 53]', '[2309, 2309, 2*w^3 + 6*w^2 - 14*w - 39]', '[2309, 2309, 3/2*w^3 + 3/2*w^2 - 13/2*w - 9]', '[2311, 2311, 1/2*w^3 + 5/2*w^2 - 5/2*w - 9]', '[2311, 2311, 2*w^3 + 4*w^2 - 13*w - 27]', '[2339, 2339, 5*w^3 + 5*w^2 - 37*w - 21]', '[2339, 2339, 4*w^3 + 4*w^2 - 26*w - 17]', '[2341, 2341, -3*w^3 - 7*w^2 + 21*w + 33]', '[2341, 2341, -3*w^3 - 7*w^2 + 21*w + 43]', '[2351, 2351, w^3 + 5*w^2 - 9*w - 29]', '[2351, 2351, -9/2*w^3 - 1/2*w^2 + 73/2*w - 7]', '[2351, 2351, -3/2*w^3 - 3/2*w^2 + 29/2*w - 4]', '[2351, 2351, -6*w^3 - 10*w^2 + 44*w + 51]', '[2356, 1178, -3*w^3 - 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11/2*w^2 + 59/2*w + 24]', '[1409, 1409, -3/2*w^3 - 1/2*w^2 + 15/2*w + 3]', '[1409, 1409, -5*w^3 - 6*w^2 + 39*w + 31]', '[1409, 1409, 7/2*w^3 + 13/2*w^2 - 51/2*w - 27]', '[1409, 1409, 1/2*w^3 + 5/2*w^2 - 9/2*w - 21]', '[1429, 1429, -1/2*w^3 - 1/2*w^2 + 13/2*w - 1]', '[1429, 1429, 7/2*w^3 + 13/2*w^2 - 49/2*w - 34]', '[1429, 1429, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17]', '[1429, 1429, 11/2*w^3 + 17/2*w^2 - 79/2*w - 42]', '[1439, 1439, -17/2*w^3 - 25/2*w^2 + 125/2*w + 71]', '[1439, 1439, 9/2*w^3 + 17/2*w^2 - 65/2*w - 51]', '[1451, 1451, 3/2*w^3 - 3/2*w^2 - 15/2*w + 7]', '[1451, 1451, -7/2*w^3 - 5/2*w^2 + 47/2*w + 7]', '[1459, 1459, 3/2*w^3 + 11/2*w^2 - 25/2*w - 18]', '[1459, 1459, -7/2*w^3 - 9/2*w^2 + 55/2*w + 22]', '[1459, 1459, 3*w^3 + 5*w^2 - 22*w - 21]', '[1459, 1459, w^3 + 7*w^2 - 5*w - 53]', '[1471, 1471, -1/2*w^3 - 9/2*w^2 + 7/2*w + 37]', '[1471, 1471, -21/2*w^3 - 31/2*w^2 + 151/2*w + 82]', '[1481, 1481, -11/2*w^3 - 15/2*w^2 + 81/2*w + 38]', '[1481, 1481, 3/2*w^3 - 1/2*w^2 - 17/2*w + 4]', '[1489, 1489, -7/2*w^3 - 7/2*w^2 + 45/2*w + 22]', '[1489, 1489, 9/2*w^3 + 9/2*w^2 - 67/2*w - 26]', '[1499, 1499, 7/2*w^3 + 9/2*w^2 - 45/2*w - 26]', '[1499, 1499, 7*w^3 + 11*w^2 - 49*w - 53]', '[1511, 1511, -7/2*w^3 - 9/2*w^2 + 51/2*w + 19]', '[1511, 1511, -3/2*w^3 - 1/2*w^2 + 19/2*w - 2]', '[1511, 1511, -5*w^3 - 3*w^2 + 39*w + 9]', '[1511, 1511, 1/2*w^3 - 9/2*w^2 - 5/2*w + 26]', '[1559, 1559, -9/2*w^3 - 13/2*w^2 + 65/2*w + 31]', '[1559, 1559, -3/2*w^3 - 5/2*w^2 + 27/2*w + 4]', '[1559, 1559, -6*w^3 - 8*w^2 + 43*w + 37]', '[1559, 1559, w^3 - w^2 - 6*w + 9]', '[1571, 1571, 9/2*w^3 + 17/2*w^2 - 65/2*w - 39]', '[1571, 1571, -2*w^3 - 6*w^2 + 15*w + 39]', '[1601, 1601, -3*w^3 - 5*w^2 + 24*w + 33]', '[1601, 1601, -7/2*w^3 - 9/2*w^2 + 51/2*w + 14]', '[1609, 1609, 4*w^3 + 5*w^2 - 28*w - 23]', '[1609, 1609, -3/2*w^3 - 3/2*w^2 + 13/2*w + 8]', '[1609, 1609, -13/2*w^3 - 19/2*w^2 + 91/2*w + 48]', '[1609, 1609, -5/2*w^3 - 3/2*w^2 + 35/2*w + 4]', '[1619, 1619, 5/2*w^3 + 7/2*w^2 - 29/2*w - 14]', '[1619, 1619, -11/2*w^3 - 17/2*w^2 + 75/2*w + 44]', '[1621, 1621, 2*w^3 + 2*w^2 - 16*w - 3]', '[1621, 1621, w^3 + w^2 - 5*w + 1]', '[1669, 1669, -6*w^3 - 6*w^2 + 46*w + 31]', '[1669, 1669, -1/2*w^3 - 9/2*w^2 + 15/2*w + 11]', '[1681, 41, 3*w^3 + 3*w^2 - 21*w - 13]', '[1681, 41, 3*w^3 + 3*w^2 - 21*w - 17]', '[1699, 1699, 7/2*w^3 + 7/2*w^2 - 39/2*w - 23]', '[1699, 1699, -7/2*w^3 - 17/2*w^2 + 49/2*w + 56]', '[1709, 1709, -1/2*w^3 + 1/2*w^2 + 13/2*w - 1]', '[1709, 1709, 1/2*w^3 + 3/2*w^2 - 1/2*w - 12]', '[1721, 1721, 5/2*w^3 + 9/2*w^2 - 39/2*w - 19]', '[1721, 1721, -3*w^3 - 3*w^2 + 23*w + 11]', '[1741, 1741, 5/2*w^3 + 9/2*w^2 - 31/2*w - 26]', '[1741, 1741, -3*w^3 - 5*w^2 + 21*w + 31]', '[1759, 1759, w^3 + 5*w^2 - 6*w - 33]', '[1759, 1759, 9/2*w^3 + 17/2*w^2 - 61/2*w - 41]', '[1789, 1789, 5/2*w^3 + 11/2*w^2 - 35/2*w - 28]', '[1789, 1789, 2*w^3 + 5*w^2 - 14*w - 29]', '[1801, 1801, w^3 + 3*w^2 - 4*w - 23]', '[1801, 1801, 3/2*w^3 + 9/2*w^2 - 21/2*w - 26]', '[1801, 1801, 3*w^3 + 6*w^2 - 21*w - 31]', '[1801, 1801, 11/2*w^3 + 17/2*w^2 - 79/2*w - 48]', '[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 1]', '[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 16]', '[1831, 1831, -9/2*w^3 - 13/2*w^2 + 63/2*w + 37]', '[1831, 1831, -w^3 - 3*w^2 + 5*w + 23]', '[1849, 43, 6*w^3 + 8*w^2 - 44*w - 43]', '[1849, 43, 1/2*w^3 - 3/2*w^2 + 1/2*w - 3]', '[1861, 1861, 5/2*w^3 + 7/2*w^2 - 33/2*w - 23]', '[1861, 1861, 5/2*w^3 + 9/2*w^2 - 33/2*w - 27]', '[1861, 1861, -2*w^3 + 13*w - 1]', '[1861, 1861, 2*w^3 + 3*w^2 - 12*w - 7]', '[1871, 1871, 3/2*w^3 + 5/2*w^2 - 15/2*w - 14]', '[1871, 1871, 3/2*w^3 + 1/2*w^2 - 27/2*w - 1]', '[1901, 1901, -4*w^3 - 5*w^2 + 28*w + 27]', '[1901, 1901, 5/2*w^3 + 3/2*w^2 - 35/2*w - 8]', '[1931, 1931, -2*w^3 + w^2 + 10*w + 1]', '[1931, 1931, 17/2*w^3 + 23/2*w^2 - 127/2*w - 66]', '[1949, 1949, -w^3 - 2*w^2 + 3*w + 17]', '[1949, 1949, -4*w^2 + 2*w + 17]', '[1949, 1949, -w^3 - 5*w^2 + 7*w + 27]', '[1949, 1949, -5*w^3 - 9*w^2 + 35*w + 49]', '[1951, 1951, -13/2*w^3 - 17/2*w^2 + 103/2*w + 52]', '[1951, 1951, 11/2*w^3 + 13/2*w^2 - 87/2*w - 41]', '[1979, 1979, -15/2*w^3 - 19/2*w^2 + 119/2*w + 59]', '[1979, 1979, 9/2*w^3 + 17/2*w^2 - 61/2*w - 47]', '[1999, 1999, 3*w^3 + 3*w^2 - 20*w - 17]', '[1999, 1999, 7/2*w^3 + 7/2*w^2 - 51/2*w - 19]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [20, 10, -11, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 10025, 'disc_rad': 2005, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[4, 1]]], [17, [[4, 1]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[2, 2]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 44.77722635447622, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.10025.1', 'local_algs': ['5.2.1.1', '5.2.1.1', 'm401.1.1.0', 'm401.1.1.0', 'm401.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 401], 'rd': 10.0062441492, 'regulator': {'__RealLiteral__': 0, 'data': '6.14918012369', 'prec': 44}, 'res': {'gal': ['1,0,-45,0,408,0,-45,0,1'], 'sib': ['10,21,-20,-2,1', '1,0,-45,0,408,0,-45,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} + \\frac{1}{2} a^{2} - \\frac{7}{2} a - 3 \\)', '\\( \\frac{3}{2} a^{3} + \\frac{5}{2} a^{2} - \\frac{19}{2} a - 11 \\)', '\\( \\frac{5}{2} a^{3} + \\frac{7}{2} a^{2} - \\frac{39}{2} a - 22 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a']}