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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 13025, 'field_bad_primes': [5, 521], 'field_label': '4.4.13025.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.13025.1-5.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [5], 'level_ideal': '[5,5,-1/2*w^3 + w^2 + 4*w - 9/2]', 'level_label': '5.2', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.2-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[5,5,-1/2*w^3 + w^2 + 4*w - 9/2]', -1]], 'hecke_eigenvalues': [1, -3, -2, 1, 4, -4, -2, 6, -2, -10, -6, 10, 6, -2, -8, 0, 2, -6, 10, -2, 14, -6, -14, 4, -4, -12, -20, -18, -10, 8, -16, 8, 8, 2, 2, -20, 4, -10, 22, 24, 0, -24, 0, -8, 8, 6, 6, -8, 16, -14, -22, -12, -4, -26, 30, 8, 0, -24, -16, -6, 26, 24, 0, -24, 8, -20, -12, -2, -18, -24, -24, -8, 0, -6, -20, -20, 12, 28, 22, 6, 10, -38, -14, -6, -26, -26, 14, -26, -16, 8, 0, -32, 24, -8, 14, -18, -20, 28, -2, -2, 10, 10, 10, 14, 22, 38, -2, -6, -38, -8, 24, -20, 4, -20, -20, 8, 24, 0, 8, 18, -6, -42, 38, -12, -28, 52, 20, 24, -16, 42, -22, 34, -30, -30, -46, -20, -36, 28, 28, 54, -10, -34, 46, 24, -56, -48, 8, 2, -54, 50, -30, 2, 10], 'hecke_polynomial': 'x', 'label': '4.4.13025.1-5.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 13025, 'ideals': ['[1, 1, 1]', '[4, 2, 1/2*w^3 - 2*w^2 - 2*w + 15/2]', '[4, 2, -w^2 + w + 8]', '[5, 5, -1/4*w^3 + 1/2*w^2 + 1/2*w - 9/4]', '[5, 5, 1/2*w^3 - w^2 - 4*w + 9/2]', '[16, 2, 2]', '[16, 4, 1/4*w^3 - 1/2*w^2 - 5/2*w + 13/4]', '[16, 4, -w - 1]', '[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4]', '[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 41/4]', '[20, 10, 1/2*w^3 - w^2 - 4*w + 11/2]', '[20, 10, 1/4*w^3 - 1/2*w^2 - 5/2*w + 5/4]', '[20, 10, 1/4*w^3 - 1/2*w^2 - 1/2*w + 13/4]', '[20, 10, -w + 1]', '[25, 5, 1/4*w^3 - 3/2*w^2 - 3/2*w + 21/4]', '[25, 5, 1/2*w^3 - w^2 - 3*w + 7/2]', '[25, 5, 1/2*w^3 - 2*w^2 - 3*w + 25/2]', '[29, 29, w]', '[29, 29, 1/4*w^3 - 1/2*w^2 - 1/2*w + 1/4]', '[29, 29, 1/4*w^3 - 1/2*w^2 - 5/2*w + 9/4]', '[29, 29, -1/2*w^3 + w^2 + 4*w - 5/2]', '[41, 41, 3/4*w^3 - 5/2*w^2 - 7/2*w + 47/4]', '[41, 41, 1/4*w^3 + 1/2*w^2 - 5/2*w - 15/4]', '[61, 61, -3/2*w^3 + 3*w^2 + 11*w - 21/2]', '[61, 61, w^3 - 2*w^2 - 4*w + 6]', '[64, 4, w^3 - 4*w^2 - 4*w + 15]', '[64, 4, -2*w^2 + 2*w + 16]', '[64, 8, 7/4*w^3 - 11/2*w^2 - 15/2*w + 83/4]', '[64, 8, w^3 - 9*w - 8]', '[76, 38, -1/2*w^3 + w^2 + 4*w - 3/2]', '[76, 38, -1/2*w^3 + 2*w^2 + 2*w - 23/2]', '[76, 38, -1/4*w^3 + 1/2*w^2 + 1/2*w + 3/4]', '[76, 38, w^2 - w - 4]', '[79, 79, 3/4*w^3 - 5/2*w^2 - 7/2*w + 27/4]', '[79, 79, 1/4*w^3 + 1/2*w^2 - 5/2*w - 35/4]', '[80, 10, -1/2*w^3 + w^2 + w - 9/2]', '[80, 10, w^3 - 2*w^2 - 8*w + 9]', '[80, 20, -w^2 + w + 10]', '[80, 20, 3/4*w^3 - 3/2*w^2 - 7/2*w + 23/4]', '[80, 20, w^3 - 3*w^2 - 4*w + 12]', '[80, 20, 3/4*w^3 - 1/2*w^2 - 13/2*w - 5/4]', '[81, 3, -3]', '[89, 89, 7/4*w^3 - 11/2*w^2 - 21/2*w + 119/4]', '[89, 89, 1/4*w^3 + 3/2*w^2 - 3/2*w - 23/4]', '[95, 95, -w^3 + 3*w^2 + 6*w - 13]', '[95, 95, w^2 - 2*w - 10]', '[95, 95, -1/4*w^3 + 3/2*w^2 - 1/2*w - 13/4]', '[95, 95, -1/4*w^3 - 1/2*w^2 + 3/2*w + 19/4]', '[100, 10, 3/4*w^3 - 3/2*w^2 - 11/2*w + 15/4]', '[100, 10, -w^3 + 3*w^2 + 3*w - 10]', '[100, 10, -1/4*w^3 + 3/2*w^2 - 1/2*w - 17/4]', '[100, 10, -1/2*w^3 + w^2 + 2*w - 3/2]', '[100, 10, -w^2 + 2*w + 9]', '[100, 10, w^3 - w^2 - 9*w - 1]', '[109, 109, -1/2*w^3 + 3*w^2 + 2*w - 41/2]', '[109, 109, -5/4*w^3 + 7/2*w^2 + 9/2*w - 45/4]', '[116, 58, -3/4*w^3 + 7/2*w^2 + 7/2*w - 87/4]', '[116, 58, 1/2*w^3 - 3*w^2 - 2*w + 23/2]', '[116, 58, -3/2*w^3 + 4*w^2 + 10*w - 37/2]', '[116, 58, 5/4*w^3 - 7/2*w^2 - 11/2*w + 53/4]', '[116, 58, 1/2*w^3 - 2*w - 3/2]', '[116, 58, -w^3 + w^2 + 8*w]', '[116, 58, -1/2*w^3 + 2*w^2 + 2*w - 25/2]', '[116, 58, -w^2 + w + 3]', '[121, 11, -3/4*w^3 + 3/2*w^2 + 9/2*w - 23/4]', '[121, 11, -1/4*w^3 + 1/2*w^2 + 3/2*w - 21/4]', '[125, 5, 1/4*w^3 - 5/2*w^2 - 1/2*w + 41/4]', '[125, 5, w^3 - 4*w^2 - 5*w + 23]', '[125, 25, 1/4*w^3 + 1/2*w^2 - 5/2*w - 11/4]', '[125, 25, 3/4*w^3 - 5/2*w^2 - 7/2*w + 51/4]', '[131, 131, -1/2*w^3 + w^2 + 5*w - 3/2]', '[131, 131, 3/4*w^3 - 1/2*w^2 - 7/2*w - 1/4]', '[139, 139, -5/4*w^3 + 11/2*w^2 + 9/2*w - 73/4]', '[139, 139, -1/4*w^3 + 7/2*w^2 - 3/2*w - 113/4]', '[145, 145, -w - 4]', '[145, 145, -5/4*w^3 + 9/2*w^2 + 11/2*w - 65/4]', '[145, 145, -1/2*w^3 + 2*w^2 + 3*w - 29/2]', '[145, 145, 1/4*w^3 + 3/2*w^2 - 7/2*w - 59/4]', '[145, 145, w^3 - 9*w - 7]', '[145, 145, -1/4*w^3 + 1/2*w^2 + 5/2*w - 25/4]', '[145, 145, -7/4*w^3 + 11/2*w^2 + 15/2*w - 87/4]', '[145, 145, -1/4*w^3 + 3/2*w^2 + 3/2*w - 13/4]', '[149, 149, -1/4*w^3 + 3/2*w^2 + 1/2*w - 49/4]', '[149, 149, 1/4*w^3 - 3/2*w^2 - 1/2*w + 13/4]', '[151, 151, 1/2*w^3 - 3*w^2 - w + 23/2]', '[151, 151, -1/4*w^3 + 3/2*w^2 + 3/2*w - 45/4]', '[151, 151, 3/4*w^3 - 3/2*w^2 - 7/2*w + 11/4]', '[151, 151, -2*w^3 + 6*w^2 + 7*w - 20]', '[164, 82, -9/4*w^3 + 15/2*w^2 + 15/2*w - 97/4]', '[164, 82, 3/2*w^3 - 15*w - 31/2]', '[164, 82, 1/2*w^3 - 3*w^2 - 2*w + 43/2]', '[164, 82, 3/4*w^3 - 7/2*w^2 - 7/2*w + 47/4]', '[169, 13, -1/4*w^3 + 1/2*w^2 + 1/2*w - 25/4]', '[169, 13, 1/2*w^3 - w^2 - 4*w + 17/2]', '[179, 179, -1/4*w^3 + 1/2*w^2 + 7/2*w - 21/4]', '[179, 179, 1/4*w^3 - 1/2*w^2 - 7/2*w - 3/4]', '[181, 181, 1/2*w^3 - 3*w - 7/2]', '[181, 181, -5/4*w^3 + 7/2*w^2 + 15/2*w - 57/4]', '[191, 191, -3/4*w^3 + 5/2*w^2 + 9/2*w - 39/4]', '[191, 191, w^2 - 8]', '[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 43/4]', '[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 81/4]', '[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 75/4]', '[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 49/4]', '[205, 205, -w^3 + 5*w + 3]', '[205, 205, -1/4*w^3 - 3/2*w^2 + 7/2*w + 63/4]', '[205, 205, 5/4*w^3 - 9/2*w^2 - 11/2*w + 61/4]', '[205, 205, 11/4*w^3 - 15/2*w^2 - 35/2*w + 139/4]', '[229, 229, -1/2*w^3 + 2*w^2 + w - 21/2]', '[229, 229, -3/4*w^3 + 5/2*w^2 + 7/2*w - 55/4]', '[239, 239, 3/2*w^3 - 4*w^2 - 9*w + 35/2]', '[239, 239, 3/2*w^3 - 5*w^2 - 7*w + 45/2]', '[241, 241, -5/4*w^3 + 9/2*w^2 + 13/2*w - 93/4]', '[241, 241, -1/4*w^3 - 1/2*w^2 - 1/2*w + 3/4]', '[244, 122, 1/4*w^3 - 1/2*w^2 - 5/2*w - 11/4]', '[244, 122, -w^3 + 3*w^2 + 6*w - 12]', '[244, 122, 1/4*w^3 + 1/2*w^2 - 3/2*w - 23/4]', '[244, 122, w - 5]', '[251, 251, -w^3 + 3*w^2 + 8*w - 13]', '[251, 251, -7/4*w^3 + 13/2*w^2 + 13/2*w - 99/4]', '[256, 4, 4]', '[256, 8, 1/2*w^3 - w^2 - 5*w + 13/2]', '[256, 8, -2*w - 2]', '[256, 16, 1/2*w^3 - 4*w - 1/2]', '[256, 16, w^2 - 2*w - 3]', '[269, 269, -9/4*w^3 + 13/2*w^2 + 15/2*w - 85/4]', '[269, 269, -3/4*w^3 + 5/2*w^2 + 3/2*w - 47/4]', '[271, 271, 5/4*w^3 - 5/2*w^2 - 21/2*w + 53/4]', '[271, 271, 5/4*w^3 - 1/2*w^2 - 23/2*w - 23/4]', '[271, 271, 7/4*w^3 - 11/2*w^2 - 13/2*w + 83/4]', '[271, 271, -1/2*w^3 + w^2 - 13/2]', '[281, 281, 3/4*w^3 - 1/2*w^2 - 13/2*w - 1/4]', '[281, 281, -w^3 + 3*w^2 + 4*w - 13]', '[304, 38, 1/2*w^3 - 3*w^2 - w + 21/2]', '[304, 38, 1/2*w^3 - 3*w^2 - w + 41/2]', '[304, 76, w^3 - 3*w^2 - 3*w + 8]', '[304, 76, -1/2*w^3 - 2*w^2 + 6*w + 37/2]', '[304, 76, -2*w^3 + 7*w^2 + 9*w - 28]', '[304, 76, w^3 - w^2 - 9*w - 3]', '[305, 305, -1/2*w^3 + 5*w + 3/2]', '[305, 305, 1/4*w^3 - 1/2*w^2 + 1/2*w + 9/4]', '[305, 305, -3/4*w^3 + 3/2*w^2 + 13/2*w - 27/4]', '[305, 305, -3/4*w^3 + 5/2*w^2 + 5/2*w - 47/4]', '[311, 311, -1/4*w^3 + 1/2*w^2 - 1/2*w - 5/4]', '[311, 311, 7/4*w^3 - 13/2*w^2 - 19/2*w + 155/4]', '[311, 311, -1/4*w^3 + 7/2*w^2 + 1/2*w - 49/4]', '[311, 311, -3/4*w^3 + 3/2*w^2 + 13/2*w - 23/4]', '[316, 158, -1/2*w^3 + 2*w^2 + 4*w - 33/2]', '[316, 158, w^2 - w - 11]', '[316, 158, -1/2*w^3 + 2*w^2 + 4*w - 7/2]', '[316, 158, 1/2*w^3 - 2*w^2 - 2*w + 9/2]', '[320, 20, w^3 - 2*w^2 - 8*w + 11]', '[320, 20, 1/2*w^3 - w^2 - 5*w + 5/2]', '[320, 20, 1/2*w^3 - w^2 - w + 13/2]', '[320, 20, -2*w + 2]', '[320, 40, w^2 - 1]', '[320, 40, 3/4*w^3 - 5/2*w^2 - 9/2*w + 67/4]', '[320, 40, -w^2 + 9]', '[320, 40, 3/4*w^3 - 5/2*w^2 - 9/2*w + 35/4]', '[324, 6, -3/2*w^3 + 6*w^2 + 6*w - 45/2]', '[324, 6, 3*w^2 - 3*w - 24]', '[331, 331, -3/4*w^3 + 1/2*w^2 + 15/2*w + 5/4]', '[331, 331, -3/4*w^3 + 5/2*w^2 + 3/2*w - 39/4]', '[349, 349, -1/4*w^3 + 1/2*w^2 + 7/2*w - 17/4]', '[349, 349, 1/4*w^3 - 1/2*w^2 - 7/2*w + 1/4]', '[356, 178, -1/4*w^3 - 1/2*w^2 - 1/2*w + 7/4]', '[356, 178, 3/2*w^3 - 4*w^2 - 11*w + 41/2]', '[356, 178, w^3 - w^2 - 7*w + 4]', '[356, 178, 3/2*w^3 - 4*w^2 - 8*w + 39/2]', '[359, 359, -5/4*w^3 - 1/2*w^2 + 25/2*w + 55/4]', '[359, 359, w^2 - 2*w - 2]', '[359, 359, -9/4*w^3 + 15/2*w^2 + 17/2*w - 113/4]', '[359, 359, -1/4*w^3 + 3/2*w^2 - 1/2*w - 45/4]', '[361, 19, -w^3 + 2*w^2 + 6*w - 8]', '[361, 19, -w^3 + 2*w^2 + 6*w - 6]', '[361, 361, 3/4*w^3 - 1/2*w^2 - 15/2*w - 9/4]', '[361, 361, -3/4*w^3 + 5/2*w^2 + 3/2*w - 35/4]', '[379, 379, -5/4*w^3 + 5/2*w^2 + 17/2*w - 37/4]', '[379, 379, -5/4*w^3 + 7/2*w^2 + 9/2*w - 41/4]', '[379, 379, 5/4*w^3 - 3/2*w^2 - 21/2*w - 3/4]', '[379, 379, -w^3 + 2*w^2 + 5*w - 7]', '[380, 190, -2*w^3 + 4*w^2 + 15*w - 17]', '[380, 190, 3/2*w^3 - 4*w^2 - 10*w + 35/2]', '[380, 190, 3/4*w^3 + 5/2*w^2 - 19/2*w - 105/4]', '[380, 190, 1/2*w^3 - 2*w - 5/2]', '[380, 190, -1/4*w^3 - 1/2*w^2 + 7/2*w + 39/4]', '[380, 190, 1/2*w^3 - 2*w^2 - w + 7/2]', '[380, 190, 5/4*w^3 - 5/2*w^2 - 9/2*w + 41/4]', '[380, 190, 5/2*w^3 - 9*w^2 - 10*w + 67/2]', '[389, 389, 9/4*w^3 - 17/2*w^2 - 15/2*w + 117/4]', '[389, 389, -3/4*w^3 - 5/2*w^2 + 21/2*w + 113/4]', '[395, 395, -3/4*w^3 + 7/2*w^2 + 5/2*w - 71/4]', '[395, 395, -7/4*w^3 + 7/2*w^2 + 27/2*w - 63/4]', '[395, 395, -w^3 + 2*w^2 + 3*w - 9]', '[395, 395, -1/4*w^3 + 5/2*w^2 - 1/2*w - 53/4]', '[400, 10, 1/2*w^3 - 3*w^2 - 3*w + 21/2]', '[400, 10, w^3 - 2*w^2 - 6*w + 7]', '[400, 10, w^3 - 4*w^2 - 6*w + 25]', '[400, 20, 5/4*w^3 - 7/2*w^2 - 11/2*w + 61/4]', '[400, 20, 5/4*w^3 - 1/2*w^2 - 21/2*w - 23/4]', '[400, 20, 5/4*w^3 - 9/2*w^2 - 13/2*w + 89/4]', '[400, 20, w^3 - w^2 - 8*w + 2]', '[400, 20, 2*w^3 - 6*w^2 - 9*w + 23]', '[400, 20, -2*w^2 + w + 11]', '[401, 401, -3/4*w^3 - 7/2*w^2 + 23/2*w + 149/4]', '[401, 401, 11/4*w^3 - 21/2*w^2 - 19/2*w + 143/4]', '[405, 15, 3/4*w^3 - 3/2*w^2 - 3/2*w + 27/4]', '[405, 15, -3/2*w^3 + 3*w^2 + 12*w - 27/2]', '[409, 409, -3/4*w^3 + 5/2*w^2 + 9/2*w - 31/4]', '[409, 409, w^2 - 10]', '[421, 421, 5/4*w^3 - 5/2*w^2 - 19/2*w + 49/4]', '[421, 421, -1/4*w^3 + 5/2*w^2 - 1/2*w - 41/4]', '[421, 421, 5/4*w^3 - 5/2*w^2 - 7/2*w + 41/4]', '[421, 421, 9/4*w^3 - 9/2*w^2 - 35/2*w + 77/4]', '[431, 431, 7/4*w^3 - 9/2*w^2 - 11/2*w + 59/4]', '[431, 431, 5/4*w^3 - 9/2*w^2 - 13/2*w + 85/4]', '[431, 431, 5/4*w^3 - 5/2*w^2 - 11/2*w + 33/4]', '[431, 431, -2*w^2 + w + 12]', '[436, 218, -1/2*w^3 + 2*w^2 + 4*w - 13/2]', '[436, 218, -w^3 + 3*w^2 + 5*w - 16]', '[436, 218, 5/4*w^3 - 7/2*w^2 - 15/2*w + 53/4]', '[436, 218, 1/2*w^3 - 2*w^2 - w + 23/2]', '[439, 439, -1/2*w^3 + w^2 + 5*w - 7/2]', '[439, 439, 2*w - 1]', '[445, 445, 1/4*w^3 + 3/2*w^2 - 3/2*w - 11/4]', '[445, 445, 1/4*w^3 - 3/2*w^2 - 5/2*w + 41/4]', '[445, 445, 3/4*w^3 - 5/2*w^2 - 11/2*w + 39/4]', '[445, 445, 7/4*w^3 - 11/2*w^2 - 21/2*w + 131/4]', '[461, 461, -7/4*w^3 + 13/2*w^2 + 21/2*w - 163/4]', '[461, 461, 3/2*w^3 - 5*w^2 - 4*w + 31/2]', '[464, 58, 2*w]', '[464, 58, 1/2*w^3 - w^2 - w + 1/2]', '[464, 58, 1/2*w^3 - w^2 - 5*w + 9/2]', '[464, 58, -w^3 + 2*w^2 + 8*w - 5]', '[464, 116, -1/4*w^3 + 1/2*w^2 + 5/2*w - 29/4]', '[464, 116, w + 5]', '[464, 116, -w^3 + w^2 + 5*w - 2]', '[464, 116, w^3 - 3*w^2 - 7*w + 20]', '[464, 116, -w^2 - w]', '[464, 116, -2*w^2 + w + 7]', '[464, 116, -5/4*w^3 + 9/2*w^2 + 13/2*w - 105/4]', '[464, 116, -2*w^3 + 5*w^2 + 13*w - 22]', '[475, 95, -1/4*w^3 + 1/2*w^2 + 7/2*w - 13/4]', '[475, 95, -5/4*w^3 + 3/2*w^2 + 19/2*w - 9/4]', '[475, 95, -5/4*w^3 + 7/2*w^2 + 9/2*w - 57/4]', '[475, 95, 1/4*w^3 - 1/2*w^2 - 7/2*w + 5/4]', '[475, 95, 5/4*w^3 - 3/2*w^2 - 21/2*w + 13/4]', '[475, 95, 3/2*w^3 - 4*w^2 - 7*w + 31/2]', '[484, 22, -5/4*w^3 + 11/2*w^2 + 11/2*w - 85/4]', '[484, 22, 5/4*w^3 - 7/2*w^2 - 7/2*w + 45/4]', '[484, 22, -3/2*w^3 + 2*w^2 + 13*w - 5/2]', '[484, 22, -1/2*w^3 + 4*w^2 + w - 55/2]', '[491, 491, 5/4*w^3 - 3/2*w^2 - 17/2*w + 21/4]', '[491, 491, -7/4*w^3 + 9/2*w^2 + 19/2*w - 83/4]', '[500, 10, 1/4*w^3 - 5/2*w^2 - 1/2*w + 61/4]', '[500, 10, 1/4*w^3 + 3/2*w^2 - 5/2*w - 27/4]', '[500, 10, w^3 - 4*w^2 - 5*w + 18]', '[500, 10, 3/2*w^3 - 5*w^2 - 8*w + 53/2]', '[500, 50, 3/2*w^3 - w^2 - 14*w - 15/2]', '[500, 50, 1/2*w^3 - 4*w^2 + 59/2]', '[500, 50, -7/4*w^3 + 11/2*w^2 + 11/2*w - 67/4]', '[500, 50, -w^3 + 5*w^2 + 3*w - 17]', '[509, 509, -3/2*w^3 + 4*w^2 + 7*w - 27/2]', '[509, 509, -3/2*w^3 + 3*w^2 + 10*w - 27/2]', '[521, 521, -5/4*w^3 + 3/2*w^2 + 11/2*w - 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1/2]', '[1895, 1895, -5/4*w^3 + 7/2*w^2 + 7/2*w - 33/4]', '[1895, 1895, -2*w + 9]', '[1895, 1895, -3/2*w^3 + 6*w^2 + 7*w - 63/2]', '[1895, 1895, -13/4*w^3 + 25/2*w^2 + 35/2*w - 297/4]', '[1895, 1895, -3/4*w^3 + 15/2*w^2 + 5/2*w - 111/4]', '[1895, 1895, -1/4*w^3 + 7/2*w^2 - 1/2*w - 69/4]', '[1900, 190, -5/2*w^3 + 4*w^2 + 19*w - 23/2]', '[1900, 190, -2*w^2 - w + 3]', '[1900, 190, 1/2*w^3 + w^2 - 4*w - 25/2]', '[1900, 190, -13/4*w^3 + 19/2*w^2 + 27/2*w - 141/4]', '[1900, 190, 1/4*w^3 - 1/2*w^2 + 3/2*w + 5/4]', '[1900, 190, -w^3 + w^2 + 9*w - 4]', '[1900, 190, 7/4*w^3 - 11/2*w^2 - 23/2*w + 139/4]', '[1900, 190, 9/4*w^3 - 11/2*w^2 - 19/2*w + 81/4]', '[1900, 190, 7/4*w^3 - 11/2*w^2 - 19/2*w + 83/4]', '[1900, 190, 5/2*w^3 - 2*w^2 - 21*w - 9/2]', '[1900, 190, w^3 - 3*w^2 - 3*w + 15]', '[1900, 190, w^3 - 2*w^2 - 9*w + 8]', '[1901, 1901, -3/4*w^3 + 5/2*w^2 + 15/2*w - 75/4]', '[1901, 1901, -2*w^3 + 4*w^2 + 16*w - 15]', '[1901, 1901, -7/4*w^3 + 15/2*w^2 + 13/2*w - 155/4]', '[1901, 1901, -7/4*w^3 + 15/2*w^2 + 13/2*w - 115/4]', '[1931, 1931, 3/4*w^3 + 9/2*w^2 - 23/2*w - 181/4]', '[1931, 1931, 9/4*w^3 - 11/2*w^2 - 15/2*w + 69/4]', '[1936, 22, -3/2*w^3 + 3*w^2 + 9*w - 23/2]', '[1936, 22, -1/2*w^3 + w^2 + 3*w - 21/2]', '[1936, 44, -3/2*w^3 + 4*w^2 + 12*w - 45/2]', '[1936, 44, -2*w^3 + 7*w^2 + 11*w - 35]', '[1936, 44, 3*w^2 - w - 16]', '[1936, 44, w^2 + 3*w - 2]', '[1945, 1945, 1/2*w^3 - 2*w^2 + w + 21/2]', '[1945, 1945, -1/4*w^3 + 5/2*w^2 - 3/2*w - 33/4]', '[1945, 1945, -1/2*w^3 + 3*w^2 - 41/2]', '[1945, 1945, 3/4*w^3 - 1/2*w^2 - 17/2*w + 7/4]', '[1949, 1949, 7/4*w^3 - 7/2*w^2 - 17/2*w + 39/4]', '[1949, 1949, -5/4*w^3 + 9/2*w^2 + 15/2*w - 121/4]', '[1964, 982, -1/4*w^3 - 3/2*w^2 - 3/2*w + 27/4]', '[1964, 982, 7/2*w^3 - 4*w^2 - 31*w - 3/2]', '[1964, 982, 13/4*w^3 - 19/2*w^2 - 19/2*w + 117/4]', '[1964, 982, -5/2*w^3 + 7*w^2 + 18*w - 71/2]', '[1975, 395, 3/4*w^3 - 1/2*w^2 - 9/2*w - 25/4]', '[1975, 395, -9/4*w^3 + 11/2*w^2 + 21/2*w - 65/4]', '[1975, 395, -15/4*w^3 + 17/2*w^2 + 51/2*w - 131/4]', '[1975, 395, -3/2*w^3 + 4*w^2 + 9*w - 23/2]', '[1975, 395, -9/4*w^3 + 7/2*w^2 + 21/2*w - 33/4]', '[1975, 395, -9/4*w^3 + 7/2*w^2 + 33/2*w - 21/4]', '[1979, 1979, 3/4*w^3 - 7/2*w^2 - 5/2*w + 35/4]', '[1979, 1979, 1/4*w^3 + 1/2*w^2 + 3/2*w - 15/4]', '[1979, 1979, w^3 - 11*w - 7]', '[1979, 1979, -1/4*w^3 + 5/2*w^2 - 1/2*w - 89/4]', '[1999, 1999, -5/4*w^3 + 7/2*w^2 + 9/2*w - 65/4]', '[1999, 1999, -5/4*w^3 + 3/2*w^2 + 21/2*w - 21/4]', '[2000, 10, 1/2*w^3 - 5*w^2 - w + 41/2]', '[2000, 10, 2*w^3 - 8*w^2 - 10*w + 46]', '[2000, 20, -1/4*w^3 + 5/2*w^2 + 1/2*w - 21/4]', '[2000, 20, 1/4*w^3 - 7/2*w^2 + 5/2*w + 113/4]', '[2000, 20, 2*w^3 - 3*w^2 - 15*w + 6]', '[2000, 20, -w^3 + 5*w^2 + 2*w - 16]', '[2000, 50, 1/2*w^3 + w^2 - 5*w - 11/2]', '[2000, 50, 3/2*w^3 - 5*w^2 - 7*w + 51/2]', '[2000, 100, w^3 - 3*w^2 - 7*w + 9]', '[2000, 100, -w^2 - w + 11]', '[2000, 100, 2*w^3 - 7*w^2 - 11*w + 34]', '[2000, 100, -3*w^2 + w + 17]', '[2005, 2005, 2*w^3 - 4*w^2 - 16*w + 17]', '[2005, 2005, -w^3 + 3*w^2 + 4*w - 17]', '[2005, 2005, 3/4*w^3 - 1/2*w^2 - 13/2*w + 15/4]', '[2005, 2005, w^3 - 2*w^2 - 2*w + 8]', '[2011, 2011, 9/4*w^3 - 15/2*w^2 - 25/2*w + 129/4]', '[2011, 2011, 1/4*w^3 + 5/2*w^2 - 5/2*w - 75/4]', '[2025, 15, -3/4*w^3 + 9/2*w^2 + 9/2*w - 63/4]', '[2025, 15, -3/2*w^3 + 3*w^2 + 9*w - 21/2]', '[2025, 15, -3/2*w^3 + 6*w^2 + 9*w - 75/2]', '[2029, 2029, -1/2*w^3 + 4*w^2 + w - 65/2]', '[2029, 2029, -5/4*w^3 + 11/2*w^2 + 11/2*w - 65/4]', '[2029, 2029, 3/4*w^3 + 1/2*w^2 - 13/2*w - 17/4]', '[2029, 2029, -7/4*w^3 + 11/2*w^2 + 17/2*w - 107/4]', '[2036, 1018, -w^3 + 11*w + 8]', '[2036, 1018, 7*w^3 - 23*w^2 - 25*w + 80]', '[2036, 1018, w^2 + 3*w - 7]', '[2036, 1018, -4*w^3 + 7*w^2 + 32*w - 21]', '[2039, 2039, -3/4*w^3 + 9/2*w^2 + 7/2*w - 107/4]', '[2039, 2039, 7/4*w^3 - 5/2*w^2 - 27/2*w + 35/4]', '[2039, 2039, 5/4*w^3 - 11/2*w^2 - 13/2*w + 97/4]', '[2039, 2039, 7/4*w^3 - 9/2*w^2 - 15/2*w + 79/4]', '[2045, 2045, -7/2*w^3 + 7*w^2 + 27*w - 61/2]', '[2045, 2045, -5/4*w^3 + 11/2*w^2 + 9/2*w - 125/4]', '[2045, 2045, 1/4*w^3 - 7/2*w^2 + 3/2*w + 61/4]', '[2045, 2045, -2*w^3 + 4*w^2 + 6*w - 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3*w^2 - 13*w + 13/2]', '[2105, 2105, -3/4*w^3 + 1/2*w^2 + 7/2*w + 13/4]', '[2105, 2105, -1/2*w^3 + 3*w^2 + 3*w - 43/2]', '[2105, 2105, 7/4*w^3 - 7/2*w^2 - 23/2*w + 47/4]', '[2105, 2105, 21/4*w^3 - 35/2*w^2 - 65/2*w + 409/4]', '[2105, 2105, 11/4*w^3 - 19/2*w^2 - 33/2*w + 231/4]', '[2105, 2105, -3/2*w^3 + 3*w^2 + 8*w - 19/2]', '[2105, 2105, w^3 - 4*w^2 - 6*w + 14]', '[2105, 2105, 7/4*w^3 - 9/2*w^2 - 23/2*w + 67/4]', '[2111, 2111, 11/4*w^3 - 15/2*w^2 - 31/2*w + 139/4]', '[2111, 2111, 7/4*w^3 - 7/2*w^2 - 29/2*w + 79/4]', '[2129, 2129, -3/2*w^3 + 4*w^2 + 11*w - 31/2]', '[2129, 2129, 1/4*w^3 + 1/2*w^2 + 1/2*w - 27/4]', '[2129, 2129, -7/4*w^3 + 7/2*w^2 + 29/2*w - 47/4]', '[2129, 2129, -2*w^3 + 8*w^2 + 8*w - 31]', '[2155, 2155, -1/2*w^3 - 3*w^2 + 3*w + 21/2]', '[2155, 2155, 21/4*w^3 - 29/2*w^2 - 67/2*w + 281/4]', '[2155, 2155, 7/4*w^3 + 1/2*w^2 - 17/2*w - 21/4]', '[2155, 2155, 7/2*w^3 - 11*w^2 - 21*w + 121/2]', '[2155, 2155, 5/2*w^3 - 4*w^2 - 19*w + 21/2]', '[2155, 2155, 1/2*w^3 - w^2 - 6*w + 13/2]', '[2155, 2155, -1/2*w^3 + 4*w^2 + 3*w - 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67/2]', '[2195, 2195, -2*w^3 + 8*w^2 + 11*w - 52]', '[2195, 2195, 3/4*w^3 - 11/2*w^2 - 7/2*w + 67/4]', '[2195, 2195, 1/4*w^3 - 5/2*w^2 - 5/2*w + 17/4]', '[2204, 1102, 1/2*w^3 - 2*w^2 + 29/2]', '[2204, 1102, w^3 - w^2 - 4*w]', '[2204, 1102, 3/2*w^3 - 4*w^2 - 10*w + 29/2]', '[2204, 1102, 2*w^3 - 3*w^2 - 17*w + 7]', '[2204, 1102, 1/4*w^3 - 5/2*w^2 + 3/2*w + 29/4]', '[2204, 1102, -7/4*w^3 + 7/2*w^2 + 23/2*w - 51/4]', '[2204, 1102, -1/2*w^3 + 3*w^2 - 43/2]', '[2204, 1102, -1/2*w^3 + 2*w + 11/2]', '[2204, 1102, -1/2*w^3 - 2*w^2 + 8*w + 51/2]', '[2204, 1102, -9/4*w^3 + 11/2*w^2 + 31/2*w - 89/4]', '[2204, 1102, 3*w^2 - 2*w - 19]', '[2204, 1102, 7/4*w^3 - 13/2*w^2 - 17/2*w + 119/4]', '[2204, 1102, 1/2*w^3 - 6*w + 7/2]', '[2204, 1102, 3/2*w^3 - 6*w^2 - 4*w + 33/2]', '[2204, 1102, 3/2*w^3 - 3*w^2 - 8*w + 21/2]', '[2204, 1102, 3/2*w^3 - 4*w^2 - 4*w + 27/2]', '[2209, 47, -3/4*w^3 + 7/2*w^2 + 3/2*w - 83/4]', '[2209, 47, 5/4*w^3 - 7/2*w^2 - 11/2*w + 73/4]', '[2221, 2221, 3/4*w^3 - 7/2*w^2 - 9/2*w + 31/4]', '[2221, 2221, -7/2*w^3 + 9*w^2 + 23*w - 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10*w^2 - 28*w + 44]', '[10000, 50, -3/2*w^3 + w^2 + 5*w + 1/2]', '[10000, 100, 7/2*w^3 - 6*w^2 - 26*w + 37/2]', '[10000, 100, 2*w^3 - 3*w^2 - 7*w + 15]', '[10000, 100, 4*w^3 - 9*w^2 - 29*w + 44]', '[10000, 100, 3*w^3 - 7*w^2 - 13*w + 25]', '[10000, 100, -2*w^3 + 8*w^2 + 5*w - 21]', '[10000, 100, -3/4*w^3 - 5/2*w^2 + 23/2*w + 137/4]', '[10000, 100, w^3 - 5*w^2 - 2*w + 36]', '[10000, 100, -1/4*w^3 + 7/2*w^2 - 5/2*w - 33/4]'], 'label': '4.4.13025.1', 'narrow_class_no': 1, 'primes': ['[4, 2, 1/2*w^3 - 2*w^2 - 2*w + 15/2]', '[4, 2, -w^2 + w + 8]', '[5, 5, -1/4*w^3 + 1/2*w^2 + 1/2*w - 9/4]', '[5, 5, 1/2*w^3 - w^2 - 4*w + 9/2]', '[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4]', '[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 41/4]', '[29, 29, w]', '[29, 29, 1/4*w^3 - 1/2*w^2 - 1/2*w + 1/4]', '[29, 29, 1/4*w^3 - 1/2*w^2 - 5/2*w + 9/4]', '[29, 29, -1/2*w^3 + w^2 + 4*w - 5/2]', '[41, 41, 3/4*w^3 - 5/2*w^2 - 7/2*w + 47/4]', '[41, 41, 1/4*w^3 + 1/2*w^2 - 5/2*w - 15/4]', '[61, 61, -3/2*w^3 + 3*w^2 + 11*w - 21/2]', '[61, 61, w^3 - 2*w^2 - 4*w + 6]', '[79, 79, 3/4*w^3 - 5/2*w^2 - 7/2*w + 27/4]', '[79, 79, 1/4*w^3 + 1/2*w^2 - 5/2*w - 35/4]', '[81, 3, -3]', '[89, 89, 7/4*w^3 - 11/2*w^2 - 21/2*w + 119/4]', '[89, 89, 1/4*w^3 + 3/2*w^2 - 3/2*w - 23/4]', '[109, 109, -1/2*w^3 + 3*w^2 + 2*w - 41/2]', '[109, 109, -5/4*w^3 + 7/2*w^2 + 9/2*w - 45/4]', '[121, 11, -3/4*w^3 + 3/2*w^2 + 9/2*w - 23/4]', '[121, 11, -1/4*w^3 + 1/2*w^2 + 3/2*w - 21/4]', '[131, 131, -1/2*w^3 + w^2 + 5*w - 3/2]', '[131, 131, 3/4*w^3 - 1/2*w^2 - 7/2*w - 1/4]', '[139, 139, -5/4*w^3 + 11/2*w^2 + 9/2*w - 73/4]', '[139, 139, -1/4*w^3 + 7/2*w^2 - 3/2*w - 113/4]', '[149, 149, -1/4*w^3 + 3/2*w^2 + 1/2*w - 49/4]', '[149, 149, 1/4*w^3 - 3/2*w^2 - 1/2*w + 13/4]', '[151, 151, 1/2*w^3 - 3*w^2 - w + 23/2]', '[151, 151, -1/4*w^3 + 3/2*w^2 + 3/2*w - 45/4]', '[151, 151, 3/4*w^3 - 3/2*w^2 - 7/2*w + 11/4]', '[151, 151, -2*w^3 + 6*w^2 + 7*w - 20]', '[169, 13, -1/4*w^3 + 1/2*w^2 + 1/2*w - 25/4]', '[169, 13, 1/2*w^3 - w^2 - 4*w + 17/2]', '[179, 179, -1/4*w^3 + 1/2*w^2 + 7/2*w - 21/4]', '[179, 179, 1/4*w^3 - 1/2*w^2 - 7/2*w - 3/4]', '[181, 181, 1/2*w^3 - 3*w - 7/2]', '[181, 181, -5/4*w^3 + 7/2*w^2 + 15/2*w - 57/4]', '[191, 191, -3/4*w^3 + 5/2*w^2 + 9/2*w - 39/4]', '[191, 191, w^2 - 8]', '[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 43/4]', '[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 81/4]', '[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 75/4]', '[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 49/4]', '[229, 229, -1/2*w^3 + 2*w^2 + w - 21/2]', '[229, 229, -3/4*w^3 + 5/2*w^2 + 7/2*w - 55/4]', '[239, 239, 3/2*w^3 - 4*w^2 - 9*w + 35/2]', '[239, 239, 3/2*w^3 - 5*w^2 - 7*w + 45/2]', '[241, 241, -5/4*w^3 + 9/2*w^2 + 13/2*w - 93/4]', '[241, 241, -1/4*w^3 - 1/2*w^2 - 1/2*w + 3/4]', '[251, 251, -w^3 + 3*w^2 + 8*w - 13]', '[251, 251, -7/4*w^3 + 13/2*w^2 + 13/2*w - 99/4]', '[269, 269, -9/4*w^3 + 13/2*w^2 + 15/2*w - 85/4]', '[269, 269, -3/4*w^3 + 5/2*w^2 + 3/2*w - 47/4]', '[271, 271, 5/4*w^3 - 5/2*w^2 - 21/2*w + 53/4]', '[271, 271, 5/4*w^3 - 1/2*w^2 - 23/2*w - 23/4]', '[271, 271, 7/4*w^3 - 11/2*w^2 - 13/2*w + 83/4]', '[271, 271, -1/2*w^3 + w^2 - 13/2]', '[281, 281, 3/4*w^3 - 1/2*w^2 - 13/2*w - 1/4]', '[281, 281, -w^3 + 3*w^2 + 4*w - 13]', '[311, 311, -1/4*w^3 + 1/2*w^2 - 1/2*w - 5/4]', '[311, 311, 7/4*w^3 - 13/2*w^2 - 19/2*w + 155/4]', '[311, 311, -1/4*w^3 + 7/2*w^2 + 1/2*w - 49/4]', '[311, 311, -3/4*w^3 + 3/2*w^2 + 13/2*w - 23/4]', '[331, 331, -3/4*w^3 + 1/2*w^2 + 15/2*w + 5/4]', '[331, 331, -3/4*w^3 + 5/2*w^2 + 3/2*w - 39/4]', '[349, 349, -1/4*w^3 + 1/2*w^2 + 7/2*w - 17/4]', '[349, 349, 1/4*w^3 - 1/2*w^2 - 7/2*w + 1/4]', '[359, 359, -5/4*w^3 - 1/2*w^2 + 25/2*w + 55/4]', '[359, 359, w^2 - 2*w - 2]', '[359, 359, -9/4*w^3 + 15/2*w^2 + 17/2*w - 113/4]', '[359, 359, -1/4*w^3 + 3/2*w^2 - 1/2*w - 45/4]', '[361, 19, -w^3 + 2*w^2 + 6*w - 8]', '[379, 379, -5/4*w^3 + 5/2*w^2 + 17/2*w - 37/4]', '[379, 379, -5/4*w^3 + 7/2*w^2 + 9/2*w - 41/4]', '[379, 379, 5/4*w^3 - 3/2*w^2 - 21/2*w - 3/4]', '[379, 379, -w^3 + 2*w^2 + 5*w - 7]', '[389, 389, 9/4*w^3 - 17/2*w^2 - 15/2*w + 117/4]', '[389, 389, -3/4*w^3 - 5/2*w^2 + 21/2*w + 113/4]', '[401, 401, -3/4*w^3 - 7/2*w^2 + 23/2*w + 149/4]', '[401, 401, 11/4*w^3 - 21/2*w^2 - 19/2*w + 143/4]', '[409, 409, -3/4*w^3 + 5/2*w^2 + 9/2*w - 31/4]', '[409, 409, w^2 - 10]', '[421, 421, 5/4*w^3 - 5/2*w^2 - 19/2*w + 49/4]', '[421, 421, -1/4*w^3 + 5/2*w^2 - 1/2*w - 41/4]', '[421, 421, 5/4*w^3 - 5/2*w^2 - 7/2*w + 41/4]', '[421, 421, 9/4*w^3 - 9/2*w^2 - 35/2*w + 77/4]', '[431, 431, 7/4*w^3 - 9/2*w^2 - 11/2*w + 59/4]', '[431, 431, 5/4*w^3 - 9/2*w^2 - 13/2*w + 85/4]', '[431, 431, 5/4*w^3 - 5/2*w^2 - 11/2*w + 33/4]', '[431, 431, -2*w^2 + w + 12]', '[439, 439, -1/2*w^3 + w^2 + 5*w - 7/2]', '[439, 439, 2*w - 1]', '[461, 461, -7/4*w^3 + 13/2*w^2 + 21/2*w - 163/4]', '[461, 461, 3/2*w^3 - 5*w^2 - 4*w + 31/2]', '[491, 491, 5/4*w^3 - 3/2*w^2 - 17/2*w + 21/4]', '[491, 491, -7/4*w^3 + 9/2*w^2 + 19/2*w - 83/4]', '[509, 509, -3/2*w^3 + 4*w^2 + 7*w - 27/2]', '[509, 509, -3/2*w^3 + 3*w^2 + 10*w - 27/2]', '[521, 521, -5/4*w^3 + 3/2*w^2 + 11/2*w - 17/4]', '[521, 521, -5/2*w^3 + 6*w^2 + 17*w - 53/2]', '[521, 521, -1/2*w^3 + 3*w^2 + w - 31/2]', '[541, 541, 9/4*w^3 - 7/2*w^2 - 35/2*w + 37/4]', '[541, 541, w^3 - 2*w^2 - 8*w + 12]', '[541, 541, -1/4*w^3 - 3/2*w^2 + 7/2*w + 35/4]', '[541, 541, -3/4*w^3 + 9/2*w^2 + 5/2*w - 119/4]', '[569, 569, -w^3 + 3*w^2 + 6*w - 7]', '[569, 569, -7/4*w^3 + 9/2*w^2 + 23/2*w - 75/4]', '[599, 599, 1/4*w^3 + 5/2*w^2 - 9/2*w - 95/4]', '[599, 599, -7/4*w^3 + 13/2*w^2 + 15/2*w - 91/4]', '[619, 619, 9/4*w^3 - 13/2*w^2 - 19/2*w + 97/4]', '[619, 619, -7/4*w^3 + 3/2*w^2 + 29/2*w + 9/4]', '[619, 619, -1/4*w^3 + 3/2*w^2 - 3/2*w - 45/4]', '[619, 619, -1/4*w^3 - 1/2*w^2 + 9/2*w - 1/4]', '[631, 631, -9/4*w^3 + 13/2*w^2 + 15/2*w - 93/4]', '[631, 631, -13/4*w^3 + 21/2*w^2 + 39/2*w - 233/4]', '[631, 631, 7/4*w^3 - 9/2*w^2 - 15/2*w + 67/4]', '[631, 631, 1/4*w^3 + 7/2*w^2 - 3/2*w - 51/4]', '[641, 641, -1/4*w^3 + 5/2*w^2 + 1/2*w - 57/4]', '[641, 641, -w^3 + 4*w^2 + 5*w - 19]', '[661, 661, -2*w^3 + 20*w + 19]', '[661, 661, 5/4*w^3 - 11/2*w^2 - 13/2*w + 149/4]', '[691, 691, -5/4*w^3 + 3/2*w^2 + 13/2*w - 9/4]', '[691, 691, -7/4*w^3 + 11/2*w^2 + 23/2*w - 135/4]', '[739, 739, -2*w^3 + 7*w^2 + 10*w - 34]', '[739, 739, 1/4*w^3 + 5/2*w^2 - 7/2*w - 59/4]', '[751, 751, -1/2*w^3 + 3*w^2 + 2*w - 33/2]', '[751, 751, -3/4*w^3 + 7/2*w^2 + 7/2*w - 67/4]', '[761, 761, -w^3 + 4*w^2 + 5*w - 27]', '[761, 761, 7/4*w^3 - 9/2*w^2 - 15/2*w + 63/4]', '[769, 769, -5/4*w^3 + 1/2*w^2 + 25/2*w + 19/4]', '[769, 769, 3/2*w^3 - 5*w^2 - 4*w + 39/2]', '[769, 769, -3*w^3 + 10*w^2 + 11*w - 37]', '[769, 769, -7/4*w^3 + 5/2*w^2 + 27/2*w - 31/4]', '[811, 811, -w^3 + 3*w^2 + 6*w - 9]', '[811, 811, -3/4*w^3 + 7/2*w^2 + 5/2*w - 39/4]', '[811, 811, -1/4*w^3 + 5/2*w^2 - 1/2*w - 85/4]', '[811, 811, -5/4*w^3 + 7/2*w^2 + 17/2*w - 57/4]', '[821, 821, -3/4*w^3 + 3/2*w^2 + 3/2*w - 35/4]', '[821, 821, -5/4*w^3 + 11/2*w^2 + 9/2*w - 121/4]', '[829, 829, 7/4*w^3 - 13/2*w^2 - 19/2*w + 115/4]', '[829, 829, 1/4*w^3 - 7/2*w^2 - 1/2*w + 89/4]', '[839, 839, -3/4*w^3 + 5/2*w^2 + 3/2*w - 51/4]', '[839, 839, -3/4*w^3 + 1/2*w^2 + 15/2*w - 7/4]', '[911, 911, -3/4*w^3 + 1/2*w^2 + 11/2*w - 15/4]', '[911, 911, -3/4*w^3 + 7/2*w^2 + 3/2*w - 75/4]', '[929, 929, 9/4*w^3 - 9/2*w^2 - 35/2*w + 73/4]', '[929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 51/4]', '[929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 91/4]', '[929, 929, 5/2*w^3 - 4*w^2 - 19*w + 25/2]', '[961, 31, -5/4*w^3 + 5/2*w^2 + 15/2*w - 37/4]', '[961, 31, -1/2*w^3 + w^2 + 3*w - 19/2]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [29, 3, -12, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 13025, 'disc_rad': 2605, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [0]], [7, [[4, 1]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[4, 1]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[1, 4]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 51.03920062069938, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.13025.1', 'local_algs': ['5.2.1.1', '5.2.1.1', 'm521.1.1.0', 'm521.1.1.0', 'm521.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 521], 'rd': 10.6830296314, 'regulator': {'__RealLiteral__': 0, 'data': '7.20310202765', 'prec': 44}, 'res': {'gal': ['400,0,-1565,0,636,0,-52,0,1'], 'sib': ['2,23,-22,-2,1', '400,0,-1565,0,636,0,-52,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{3} - \\frac{1}{2} a^{2} - \\frac{3}{2} a + \\frac{5}{4} \\)', '\\( a + 2 \\)', '\\( \\frac{5}{4} a^{3} - \\frac{7}{2} a^{2} - \\frac{9}{2} a + \\frac{49}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/4*a^3 - 1/2*a^2 - 1/2*a + 1/4']}