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hmf_forms • Show schema
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{'deg': 4, 'dimension': 2, 'disc': 7225, 'field_bad_primes': [5, 17], 'field_label': '4.4.7225.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.7225.1-9.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [3], 'level_ideal': '[9,3,-1/3*w^3 + 11/3*w]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[9,3,-1/3*w^3 + 11/3*w]', 1]], 'hecke_eigenvalues': ['e', '-e', -1, 4, '2*e + 2', 2, 2, '-2*e + 2', 0, 12, -2, '2*e + 6', '2*e - 8', '-2*e - 8', '-2*e + 6', '-2*e - 10', '2*e + 4', '-2*e + 4', '2*e - 10', '-2*e + 2', '2*e - 12', '-2*e - 12', '2*e + 2', '6*e + 2', '-6*e + 2', '8*e + 2', '-4*e - 12', '4*e - 12', '-8*e + 2', '-2*e', '2*e', '-2*e', '2*e', '2*e - 6', '-2*e - 6', '-4*e - 6', '4*e + 8', '-4*e + 8', '4*e - 6', '2*e - 14', '6*e', '-6*e', '-2*e - 14', '2*e + 12', '2*e - 16', '-2*e - 16', '-2*e + 12', 8, -6, -6, 8, '-2*e - 2', '-2*e + 12', '2*e + 12', '2*e - 2', '4*e', '4*e - 14', '-4*e - 14', '-4*e', '4*e + 12', '4*e - 2', '-4*e - 2', '-4*e + 12', -10, '-2*e + 18', '-4*e + 18', '4*e + 18', '2*e + 18', '-8*e + 10', 10, 10, '8*e + 10', '4*e + 20', '-4*e + 20', '4*e + 20', '-4*e + 20', '10*e - 10', '4*e - 10', '-4*e - 10', '-10*e - 10', 4, '-4*e - 24', '4*e - 24', 4, 16, '8*e + 2', '-8*e + 2', 16, '-12*e + 6', '-8*e + 6', '8*e + 6', '12*e + 6', '4*e - 4', '-4*e - 4', '4*e - 4', '-4*e - 4', '-6*e + 14', -28, -28, '6*e + 14', -34, -20, '12*e + 2', '-12*e - 12', '12*e - 12', '-12*e + 2', '12*e - 10', '-10*e + 4', '10*e + 4', '-12*e - 10', '14*e + 4', '-2*e - 24', '2*e - 24', '-14*e + 4', '4*e + 24', '12*e - 18', '-12*e - 18', '-4*e + 24', 38, '8*e - 18', '-8*e - 18', 38, '-4*e + 22', '14*e - 6', '-14*e - 6', '4*e + 22', '2*e - 4', '-2*e + 24', '2*e + 24', '-2*e - 4', '2*e - 30', '-2*e + 12', '2*e + 12', '-2*e - 30', '14*e - 16', '2*e + 40', '-2*e + 40', '-14*e - 16', 30, -26, -26, 30, '-8*e + 18', '8*e + 18', 4, 4, 4, 4, '-6*e + 24', '14*e - 4', '-14*e - 4', '6*e + 24', '-2*e - 28', '2*e - 28', '8*e', 0, 0, '-8*e'], 'hecke_polynomial': 'x^2 - 7', 'label': '4.4.7225.1-9.1-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 7225, 'ideals': ['[1, 1, 1]', '[4, 2, 1/6*w^3 - 7/3*w - 3/2]', '[4, 2, 1/6*w^3 - 7/3*w + 3/2]', '[9, 3, -1/3*w^3 + 11/3*w]', '[9, 3, w]', '[16, 2, 2]', '[16, 4, 1/6*w^3 - 7/3*w + 1/2]', '[16, 4, 1/6*w^3 - 7/3*w - 1/2]', '[19, 19, w + 2]', '[19, 19, -1/3*w^3 + 11/3*w - 2]', '[19, 19, -1/3*w^3 + 11/3*w + 2]', '[19, 19, -w + 2]', '[25, 5, 1/3*w^3 - 8/3*w]', '[36, 6, 1/2*w^2 - 1/2*w - 9/2]', '[36, 6, -1/2*w^2 - 1/2*w + 9/2]', '[36, 6, -1/6*w^3 + 1/3*w - 3/2]', '[36, 6, -1/6*w^3 + 1/3*w + 3/2]', '[49, 7, 2/3*w^3 - 19/3*w]', '[49, 7, -1/3*w^3 + 5/3*w]', '[59, 59, 1/6*w^3 + 1/2*w^2 - 11/6*w]', '[59, 59, 1/2*w^2 + 1/2*w - 11/2]', '[59, 59, 1/2*w^2 - 1/2*w - 11/2]', '[59, 59, 1/6*w^3 - 1/2*w^2 - 11/6*w]', '[64, 4, 1/3*w^3 - 14/3*w - 3]', '[64, 4, 1/3*w^3 - 14/3*w + 3]', '[64, 8, 1/6*w^3 - 7/3*w + 7/2]', '[64, 8, -1/6*w^3 + 7/3*w + 7/2]', '[76, 38, 1/3*w^3 - 1/2*w^2 - 19/6*w + 3/2]', '[76, 38, 1/3*w^3 - 1/2*w^2 - 13/6*w + 7/2]', '[76, 38, -1/2*w^3 - 1/2*w^2 + 9/2*w + 2]', '[76, 38, 1/6*w^3 + 1/2*w^2 - 5/6*w - 4]', '[76, 38, -1/2*w^3 + 1/2*w^2 + 9/2*w - 2]', '[76, 38, -1/6*w^3 + 1/2*w^2 + 5/6*w - 4]', '[76, 38, 1/3*w^3 + 1/2*w^2 - 19/6*w - 3/2]', '[76, 38, -1/3*w^3 - 1/2*w^2 + 13/6*w + 7/2]', '[81, 3, 3]', '[81, 9, w^2 - 2]', '[81, 9, w^2 - 9]', '[89, 89, 2/3*w^3 + 1/2*w^2 - 35/6*w - 7/2]', '[89, 89, -5/6*w^3 + 26/3*w - 3/2]', '[89, 89, 1/6*w^3 - 1/2*w^2 + 1/6*w - 2]', '[89, 89, -1/6*w^3 - w^2 + 7/3*w + 5/2]', '[100, 10, -1/2*w^3 - w^2 + 4*w + 11/2]', '[100, 10, 1/2*w^3 - w^2 - 4*w + 11/2]', '[101, 101, 1/6*w^3 + 1/2*w^2 - 17/6*w + 1]', '[101, 101, -1/3*w^3 - 1/2*w^2 + 25/6*w + 13/2]', '[101, 101, -1/3*w^3 + 1/2*w^2 + 25/6*w - 13/2]', '[101, 101, 1/6*w^3 - 1/2*w^2 - 17/6*w - 1]', '[121, 11, 1/2*w^3 - 4*w - 1/2]', '[121, 11, -1/2*w^3 + 4*w - 1/2]', '[144, 6, -2/3*w^3 + 22/3*w]', '[144, 6, 2*w]', '[144, 12, -1/2*w^2 + 1/2*w - 3/2]', '[144, 12, -1/2*w^2 - 1/2*w - 3/2]', '[144, 12, -1/6*w^3 + 1/2*w^2 + 11/6*w - 7]', '[144, 12, 1/6*w^3 + 1/2*w^2 - 11/6*w - 7]', '[149, 149, 1/6*w^3 + 1/2*w^2 - 5/6*w - 5]', '[149, 149, -1/3*w^3 + 1/2*w^2 + 19/6*w - 1/2]', '[149, 149, 1/3*w^3 + 1/2*w^2 - 19/6*w - 1/2]', '[149, 149, -1/6*w^3 + 1/2*w^2 + 5/6*w - 5]', '[151, 151, -5/6*w^3 - 1/2*w^2 + 49/6*w + 3]', '[151, 151, 1/3*w^3 + w^2 - 8/3*w - 7]', '[151, 151, 1/2*w^3 + 1/2*w^2 - 13/2*w - 1]', '[151, 151, 5/6*w^3 - 1/2*w^2 - 49/6*w + 3]', '[169, 13, -1/3*w^3 + 14/3*w + 2]', '[169, 13, -1/3*w^3 + 14/3*w - 2]', '[171, 57, -2/3*w^3 + 22/3*w + 3]', '[171, 57, -1/2*w^3 + 6*w - 3/2]', '[171, 57, -1/6*w^3 + 10/3*w + 3/2]', '[171, 57, -2*w + 3]', '[171, 57, 2*w + 3]', '[171, 57, 1/6*w^3 - 10/3*w + 3/2]', '[171, 57, 1/2*w^3 - 6*w - 3/2]', '[171, 57, -2/3*w^3 + 22/3*w - 3]', '[179, 179, -1/3*w^3 + 17/3*w - 6]', '[179, 179, -2/3*w^3 + 25/3*w + 6]', '[179, 179, -2/3*w^3 + 25/3*w - 6]', '[179, 179, -1/3*w^3 + 17/3*w + 6]', '[191, 191, 1/2*w^3 + 1/2*w^2 - 9/2*w - 1]', '[191, 191, 1/3*w^3 + 1/2*w^2 - 13/6*w - 9/2]', '[191, 191, -1/3*w^3 + 1/2*w^2 + 13/6*w - 9/2]', '[191, 191, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1]', '[196, 14, w^3 - 3/2*w^2 - 19/2*w + 25/2]', '[196, 14, -w^3 - 3/2*w^2 + 19/2*w + 25/2]', '[196, 14, 1/2*w^3 - 3/2*w^2 - 5/2*w + 4]', '[196, 14, -1/2*w^3 - 3/2*w^2 + 5/2*w + 4]', '[225, 15, w^2 - 8]', '[225, 15, w^2 - 3]', '[229, 229, 5/6*w^3 - 1/2*w^2 - 43/6*w + 2]', '[229, 229, -2/3*w^3 - 1/2*w^2 + 29/6*w + 7/2]', '[229, 229, 2/3*w^3 - 1/2*w^2 - 29/6*w + 7/2]', '[229, 229, 5/6*w^3 + 1/2*w^2 - 43/6*w - 2]', '[236, 118, 1/2*w^2 - 7/2*w + 7/2]', '[236, 118, -1/2*w^3 - w^2 + 2*w + 7/2]', '[236, 118, -7/6*w^3 + 1/2*w^2 + 77/6*w - 9]', '[236, 118, -7/6*w^3 - w^2 + 34/3*w + 15/2]', '[236, 118, -7/6*w^3 - 1/2*w^2 + 77/6*w + 9]', '[236, 118, -7/6*w^3 + w^2 + 34/3*w - 15/2]', '[236, 118, 1/2*w^2 + 7/2*w + 7/2]', '[236, 118, 1/2*w^3 - w^2 - 2*w + 7/2]', '[239, 239, -1/3*w^3 + w^2 + 11/3*w - 7]', '[239, 239, 1/6*w^3 + w^2 - 7/3*w - 9/2]', '[239, 239, w^2 - w - 4]', '[239, 239, -1/3*w^3 - w^2 + 11/3*w + 7]', '[251, 251, 1/3*w^3 + w^2 - 8/3*w - 5]', '[251, 251, 1/3*w^3 + w^2 - 8/3*w - 6]', '[251, 251, -1/3*w^3 + w^2 + 8/3*w - 6]', '[251, 251, -1/3*w^3 + w^2 + 8/3*w - 5]', '[256, 4, 4]', '[256, 8, 1/3*w^3 - 14/3*w + 1]', '[256, 8, 1/3*w^3 - 14/3*w - 1]', '[256, 16, 1/6*w^3 - 7/3*w + 9/2]', '[256, 16, -1/6*w^3 + 7/3*w + 9/2]', '[271, 271, 1/6*w^3 + w^2 - 7/3*w - 19/2]', '[271, 271, 2/3*w^3 - 3/2*w^2 - 29/6*w + 17/2]', '[271, 271, -w^3 + w^2 + 8*w - 4]', '[271, 271, w^3 - 10*w - 2]', '[281, 281, 5/6*w^3 - 1/2*w^2 - 37/6*w + 5]', '[281, 281, -1/6*w^3 - 2/3*w - 5/2]', '[281, 281, 1/3*w^3 + 1/2*w^2 - 25/6*w - 17/2]', '[281, 281, 5/6*w^3 - 26/3*w + 5/2]', '[289, 17, 1/6*w^3 + w^2 - 7/3*w - 11/2]', '[304, 38, 2*w + 4]', '[304, 38, -2/3*w^3 + 22/3*w - 4]', '[304, 38, -2/3*w^3 + 22/3*w + 4]', '[304, 38, -2*w + 4]', '[304, 76, 1/3*w^3 - 1/2*w^2 - 25/6*w - 1/2]', '[304, 76, 1/3*w^3 - 1/2*w^2 - 31/6*w - 5/2]', '[304, 76, -1/2*w^3 + 1/2*w^2 + 13/2*w - 8]', '[304, 76, -1/6*w^3 + 1/2*w^2 + 17/6*w - 6]', '[304, 76, 1/6*w^3 + 1/2*w^2 - 17/6*w - 6]', '[304, 76, 1/2*w^3 + 1/2*w^2 - 13/2*w - 8]', '[304, 76, 1/3*w^3 + 1/2*w^2 - 25/6*w + 1/2]', '[304, 76, 1/3*w^3 + 1/2*w^2 - 31/6*w + 5/2]', '[324, 6, 1/2*w^3 - 7*w - 9/2]', '[324, 6, 1/2*w^3 - 7*w + 9/2]', '[324, 18, 1/3*w^3 - 1/2*w^2 - 13/6*w + 11/2]', '[324, 18, 1/2*w^3 - 1/2*w^2 - 11/2*w + 1]', '[324, 18, -1/2*w^3 - 1/2*w^2 + 9/2*w]', '[324, 18, 1/2*w^2 + 3/2*w - 9/2]', '[331, 331, -5/6*w^3 + 32/3*w + 17/2]', '[331, 331, -2*w + 5]', '[331, 331, -2*w - 5]', '[331, 331, -2/3*w^3 + 22/3*w + 5]', '[349, 349, 5/6*w^3 - 1/2*w^2 - 43/6*w]', '[349, 349, w^3 - 11*w + 2]', '[349, 349, 1/3*w^3 - w^2 - 2/3*w + 4]', '[349, 349, -5/6*w^3 - 1/2*w^2 + 43/6*w]', '[356, 178, 1/6*w^3 - w^2 - 4/3*w + 13/2]', '[356, 178, -11/6*w^3 - 5/2*w^2 + 97/6*w + 17]', '[356, 178, w^3 + 3/2*w^2 - 19/2*w - 29/2]', '[356, 178, -3/2*w^3 + 3/2*w^2 + 33/2*w - 19]', '[356, 178, 1/2*w^3 - 5*w - 11/2]', '[356, 178, -1/3*w^3 - 1/2*w^2 + 31/6*w + 7/2]', '[356, 178, 7/6*w^3 + 3/2*w^2 - 47/6*w - 8]', '[356, 178, 2/3*w^3 - 3/2*w^2 - 5/6*w - 1/2]', '[359, 359, -w - 5]', '[359, 359, -1/3*w^3 + 11/3*w - 5]', '[359, 359, 1/3*w^3 - 11/3*w - 5]', '[359, 359, w - 5]', '[361, 19, 1/3*w^3 - 14/3*w - 6]', '[361, 19, -1/3*w^3 + 14/3*w - 6]', '[361, 19, -w^2 + 4]', '[361, 19, -w^2 + 7]', '[361, 19, -2/3*w^3 + 16/3*w + 1]', '[361, 19, -2/3*w^3 + 16/3*w - 1]', '[361, 361, -1/6*w^3 - w^2 + 7/3*w + 1/2]', '[361, 361, -1/6*w^3 + w^2 + 7/3*w - 21/2]', '[361, 361, -1/6*w^3 - w^2 + 7/3*w + 21/2]', '[361, 361, 1/6*w^3 - w^2 - 7/3*w + 1/2]', '[389, 389, -w^3 - 1/2*w^2 + 21/2*w + 5/2]', '[389, 389, -7/6*w^3 + w^2 + 31/3*w - 13/2]', '[389, 389, 7/6*w^3 + w^2 - 31/3*w - 13/2]', '[389, 389, 5/6*w^3 - w^2 - 17/3*w + 9/2]', '[400, 10, 2/3*w^3 - 16/3*w]', '[400, 20, -1/6*w^3 - w^2 + 4/3*w + 11/2]', '[400, 20, 1/6*w^3 - w^2 - 4/3*w + 11/2]', '[404, 202, 1/2*w^3 + w^2 - 4*w - 5/2]', '[404, 202, -1/3*w^3 - 1/2*w^2 + 7/6*w + 7/2]', '[404, 202, 5/6*w^3 - 1/2*w^2 - 49/6*w + 2]', '[404, 202, 11/6*w^3 + w^2 - 62/3*w - 35/2]', '[404, 202, -5/6*w^3 - 1/2*w^2 + 49/6*w + 2]', '[404, 202, -11/6*w^3 + w^2 + 62/3*w - 35/2]', '[404, 202, -1/6*w^3 + w^2 + 22/3*w + 13/2]', '[404, 202, 1/3*w^3 - 1/2*w^2 - 7/6*w + 7/2]', '[409, 409, -3/2*w^3 - 3/2*w^2 + 27/2*w + 11]', '[409, 409, 1/3*w^3 + w^2 - 8/3*w - 11]', '[409, 409, -2/3*w^3 + 25/3*w + 8]', '[409, 409, -3/2*w^3 + 3/2*w^2 + 27/2*w - 11]', '[421, 421, 1/6*w^3 + 1/2*w^2 + 1/6*w - 4]', '[421, 421, 1/3*w^3 + 1/2*w^2 - 13/6*w - 13/2]', '[421, 421, -1/3*w^3 + 1/2*w^2 + 13/6*w - 13/2]', '[421, 421, 1/2*w^3 + 1/2*w^2 - 9/2*w + 1]', '[441, 21, 2*w^2 - 19]', '[441, 21, 2*w^2 - 3]', '[441, 21, w^2 - 6]', '[441, 21, w^2 - 5]', '[461, 461, 2/3*w^3 - 1/2*w^2 - 23/6*w - 1/2]', '[461, 461, 1/6*w^3 - 1/2*w^2 - 11/6*w + 8]', '[461, 461, -1/6*w^3 - 1/2*w^2 + 11/6*w + 8]', '[461, 461, 2/3*w^3 - 13/3*w - 2]', '[475, 95, 2/3*w^3 + w^2 - 16/3*w - 3]', '[475, 95, -2/3*w^3 + w^2 + 16/3*w - 8]', '[475, 95, 2/3*w^3 + w^2 - 16/3*w - 8]', '[475, 95, 2/3*w^3 - w^2 - 16/3*w + 3]', '[484, 22, 2/3*w^3 - 3/2*w^2 - 29/6*w + 15/2]', '[484, 22, -5/6*w^3 + 3/2*w^2 + 43/6*w - 9]', '[484, 22, -5/6*w^3 - 3/2*w^2 + 43/6*w + 9]', '[484, 22, 2/3*w^3 + 3/2*w^2 - 29/6*w - 15/2]', '[491, 491, 7/6*w^3 + 2*w^2 - 28/3*w - 21/2]', '[491, 491, 1/6*w^3 - 10/3*w - 13/2]', '[491, 491, 7/6*w^3 + 2*w^2 - 28/3*w - 23/2]', '[491, 491, -7/6*w^3 + 2*w^2 + 28/3*w - 21/2]', '[509, 509, 1/2*w^3 - w^2 - 5*w + 7/2]', '[509, 509, -2/3*w^3 + w^2 + 25/3*w - 4]', '[509, 509, -5/6*w^3 + 26/3*w - 7/2]', '[509, 509, 1/3*w^3 + w^2 - 17/3*w - 7]', '[529, 23, -2/3*w^3 + 1/2*w^2 + 53/6*w - 19/2]', '[529, 23, 7/6*w^3 - 3/2*w^2 - 59/6*w + 11]', '[531, 177, 1/2*w^3 + 1/2*w^2 - 11/2*w]', '[531, 177, 1/2*w^2 + 3/2*w - 11/2]', '[531, 177, 11/6*w^3 - 56/3*w + 3/2]', '[531, 177, 1/2*w^3 - 3/2]', '[531, 177, -1/2*w^3 - 3/2]', '[531, 177, 11/6*w^3 - 56/3*w - 3/2]', '[531, 177, 1/2*w^2 - 3/2*w - 11/2]', '[531, 177, 1/2*w^3 - 1/2*w^2 - 11/2*w]', '[569, 569, w^3 - w^2 - 9*w + 5]', '[569, 569, 2/3*w^3 - w^2 - 13/3*w + 6]', '[569, 569, 2/3*w^3 + w^2 - 13/3*w - 6]', '[569, 569, w^3 + w^2 - 9*w - 5]', '[576, 12, w^2 - w - 9]', '[576, 12, -w^2 - w + 9]', '[576, 12, -1/3*w^3 + 2/3*w - 3]', '[576, 12, -1/3*w^3 + 2/3*w + 3]', '[576, 24, 1/2*w^3 + w^2 - 6*w - 21/2]', '[576, 24, -w^3 + 1/2*w^2 + 19/2*w - 3/2]', '[576, 24, -1/2*w^3 + 1/2*w^2 + 5/2*w - 4]', '[576, 24, -1/6*w^3 + w^2 + 10/3*w - 1/2]', '[596, 298, -5/6*w^3 + 29/3*w - 11/2]', '[596, 298, -4/3*w^3 - 3/2*w^2 + 73/6*w + 19/2]', '[596, 298, 1/6*w^3 - 13/3*w - 11/2]', '[596, 298, -5/6*w^3 + 3/2*w^2 + 31/6*w - 7]', '[596, 298, 1/6*w^3 - 13/3*w + 11/2]', '[596, 298, -5/6*w^3 - 3/2*w^2 + 31/6*w + 7]', '[596, 298, -5/6*w^3 + 29/3*w + 11/2]', '[596, 298, -4/3*w^3 + 3/2*w^2 + 73/6*w - 19/2]', '[599, 599, 2/3*w^3 - 1/2*w^2 - 23/6*w + 3/2]', '[599, 599, -7/6*w^3 + 1/2*w^2 + 65/6*w - 4]', '[599, 599, -7/6*w^3 - 1/2*w^2 + 65/6*w + 4]', '[599, 599, 2/3*w^3 + 1/2*w^2 - 23/6*w - 3/2]', '[604, 302, -1/2*w^3 + w^2 + 6*w - 23/2]', '[604, 302, 2*w^3 + 5/2*w^2 - 37/2*w - 41/2]', '[604, 302, -13/6*w^3 - 5/2*w^2 + 113/6*w + 16]', '[604, 302, -7/6*w^3 + 1/2*w^2 + 65/6*w - 5]', '[604, 302, 1/3*w^3 + 1/2*w^2 - 49/6*w + 21/2]', '[604, 302, -7/6*w^3 - w^2 + 34/3*w + 27/2]', '[604, 302, -1/2*w^3 - w^2 + 6*w + 23/2]', '[604, 302, 2*w^3 - 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19/3*w - 4]', '[739, 739, 1/3*w^3 - 17/3*w - 3]', '[739, 739, 2/3*w^3 - 25/3*w + 3]', '[739, 739, 2/3*w^3 - 25/3*w - 3]', '[739, 739, -1/3*w^3 + 17/3*w - 3]', '[761, 761, -1/2*w^3 + w^2 + 3*w - 13/2]', '[761, 761, 5/6*w^3 - w^2 - 23/3*w + 9/2]', '[761, 761, 5/6*w^3 + w^2 - 23/3*w - 9/2]', '[761, 761, 1/2*w^3 + w^2 - 3*w - 13/2]', '[769, 769, 2/3*w^3 + 1/2*w^2 - 35/6*w + 5/2]', '[769, 769, 1/2*w^3 + 1/2*w^2 - 7/2*w - 8]', '[769, 769, -1/2*w^3 + 1/2*w^2 + 7/2*w - 8]', '[769, 769, 2/3*w^3 - 1/2*w^2 - 35/6*w - 5/2]', '[829, 829, w^2 + w - 10]', '[829, 829, 1/3*w^3 + w^2 - 11/3*w - 1]', '[829, 829, -1/3*w^3 + w^2 + 11/3*w - 1]', '[829, 829, w^2 - w - 10]', '[841, 29, 5/6*w^3 - 20/3*w - 3/2]', '[841, 29, 5/6*w^3 - 20/3*w + 3/2]', '[859, 859, 1/6*w^3 + 1/2*w^2 - 23/6*w - 6]', '[859, 859, -2/3*w^3 - 1/2*w^2 + 47/6*w - 1/2]', '[859, 859, -2/3*w^3 + 1/2*w^2 + 47/6*w + 1/2]', '[859, 859, -1/6*w^3 + 1/2*w^2 + 23/6*w - 6]', '[919, 919, 1/2*w^3 + w^2 - 5*w - 5/2]', '[919, 919, 1/6*w^3 + w^2 - 1/3*w - 17/2]', '[919, 919, -1/6*w^3 + w^2 + 1/3*w - 17/2]', '[919, 919, -1/2*w^3 + w^2 + 5*w - 5/2]', '[961, 31, 1/3*w^3 - 8/3*w - 6]', '[961, 31, 5/6*w^3 - 20/3*w - 1/2]', '[971, 971, 1/2*w^3 + 3/2*w^2 - 7/2*w - 8]', '[971, 971, 2/3*w^3 - 3/2*w^2 - 35/6*w + 17/2]', '[971, 971, 1/3*w^3 - 1/2*w^2 - 37/6*w - 3/2]', '[971, 971, 1/2*w^3 - 3/2*w^2 - 7/2*w + 8]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 0, -11, 0, 1], 'conductor': 85, 'degree': 4, 'dirichlet_group': [16, 1, 84, 69], 'disc_abs': 7225, 'disc_rad': 85, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[2, 2]]], [5, [0]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [0]], [19, [[1, 4]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[1, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 9.219544457292887, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.7225.1', 'local_algs': ['5.4.2.1', '17.4.2.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [5, 17], 'rd': 9.21954445729, 'regulator': {'__RealLiteral__': 0, 'data': '4.45404695945', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-4.-1.1', '-1.-1.1', '-21.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{6} a^{3} - \\frac{4}{3} a - \\frac{1}{2} \\)', '\\( \\frac{1}{6} a^{3} - \\frac{1}{2} a^{2} - \\frac{5}{6} a + 1 \\)', '\\( \\frac{1}{3} a^{3} - \\frac{1}{2} a^{2} - \\frac{19}{6} a + \\frac{9}{2} \\)'], 'unitsGmodule': [[14, 1]], 'unitsType': 'Type IV', 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a - 1/2', '1/6*a^3 - 1/3*a - 1/2']}