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hmf_forms • Show schema
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{'deg': 4, 'dimension': 2, 'disc': 16225, 'field_bad_primes': [5, 11, 59], 'field_label': '4.4.16225.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.16225.1-4.2-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[4,2,1/3*w^3 + 2/3*w^2 - 10/3*w - 7]', 'level_label': '4.2', 'level_norm': 4, 'parallel_weight': 2, 'short_label': '4.2-b', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[4,2,1/3*w^3 + 2/3*w^2 - 10/3*w - 7]', -1]], 'hecke_eigenvalues': ['e', 1, 3, 'e - 2', -2, '-e - 7', '-2*e - 2', '-e - 7', '-e - 6', '-2*e - 1', '-2*e - 4', '4*e + 4', '-2*e - 3', '-e - 8', '3*e + 13', '-2*e', '5*e + 3', '-5*e - 3', '2*e', '5*e + 4', -9, '3*e + 10', '2*e + 3', '-5*e', '5*e', '-7*e - 10', -6, '3*e + 17', '-e', '11*e + 16', '-4*e - 10', '-e + 13', '-7*e - 16', '-2*e', '-6*e - 21', '3*e + 13', 'e - 11', '3*e + 17', '-3*e - 9', '-4*e - 4', '9*e + 7', '5*e - 11', 17, '-7*e - 24', -18, '4*e', '4*e + 3', '-7*e - 18', '5*e + 8', '-7*e - 8', '-e + 3', '10*e + 24', '3*e + 20', 'e - 8', '4*e - 4', '-7*e - 25', 'e - 17', '4*e + 6', 'e + 3', '3*e + 30', '-6*e', '-2*e - 21', '3*e - 21', '-12*e - 22', '-14*e - 27', '4*e - 2', '-10*e - 18', '13*e + 19', '14*e + 24', '-2*e - 8', -18, '2*e + 34', '8*e + 4', '3*e - 16', '6*e + 7', '3*e - 25', 'e - 13', '-4*e + 10', 'e + 25', '-4*e - 8', '7*e + 13', '-3*e - 14', '4*e + 27', '17*e + 27', '-2*e + 8', '-9*e - 14', '-5*e + 4', '12*e + 6', '-6*e + 20', '14*e + 24', '5*e - 7', '20*e + 29', '-3*e - 8', 'e - 2', -6, '-19*e - 25', '-9*e - 28', '3*e + 20', '-e + 14', '5*e - 28', '-e - 24', 'e + 19', '4*e + 4', '2*e + 8', '4*e - 2', '-10*e + 2', '13*e + 15', '2*e - 6', '-2*e', '5*e + 12', '6*e + 16', '-16*e - 26', '-e + 4', '17*e + 37', '-2*e + 4', '4*e + 26', '9*e - 13', '-2*e - 2', '3*e + 49', '-13*e - 6', '8*e + 38', '-11*e - 16', '10*e + 28', '13*e + 24', '-8*e - 3', '-3*e - 28', '-4*e - 43', '-6*e + 6', '16*e + 10', '-3*e - 1', '7*e - 27', '-e + 13', '4*e + 2', '-17*e - 37', '-2*e - 36', '7*e + 33', '-16*e - 42', '7*e + 20', '12*e + 7', '10*e + 17', '21*e + 26', -10, '12*e + 3', '4*e + 46', '-2*e - 3', '17*e + 41', '-10*e + 14', '-2*e + 12', '-12*e - 42', '-2*e - 8', '-6*e + 12', '-12*e - 34', '-2*e - 8', '-2*e - 24', '17*e + 24', '9*e - 12', '-12*e - 50', '19*e + 21', '-6*e - 6', '12*e + 2', '2*e + 30', '-6*e - 6', '14*e + 5', '9*e + 30', '16*e + 26', '-18*e - 16', '2*e - 40', '2*e + 20', '2*e + 4', '-20*e - 38', '-21*e - 42', '11*e + 10', '-17*e - 24', '-24*e - 43', 'e - 29', '8*e + 36', '-10*e - 26'], 'hecke_polynomial': 'x^2 + 3*x - 2', 'label': '4.4.16225.1-4.2-b'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 16225, 'ideals': ['[1, 1, 1]', '[4, 2, 1/3*w^3 - 4/3*w^2 - 4/3*w + 6]', '[4, 2, -1/3*w^3 - 2/3*w^2 + 10/3*w + 7]', '[9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9]', '[9, 3, 1/3*w^3 + 2/3*w^2 - 7/3*w - 5]', '[11, 11, -1/6*w^3 + 1/6*w^2 + 1/6*w]', '[16, 2, 2]', '[16, 4, -1/3*w^3 + 1/3*w^2 + 10/3*w]', '[16, 4, 1/6*w^3 - 1/6*w^2 - 1/6*w - 1]', '[19, 19, w + 1]', '[19, 19, 1/6*w^3 - 1/6*w^2 - 13/6*w + 2]', '[25, 5, -1/3*w^3 + 1/3*w^2 + 7/3*w - 1]', '[29, 29, -1/6*w^3 + 1/6*w^2 + 13/6*w]', '[29, 29, w - 1]', '[31, 31, 1/3*w^3 - 1/3*w^2 - 10/3*w + 3]', '[31, 31, 1/6*w^3 - 1/6*w^2 - 1/6*w + 2]', '[36, 6, -w]', '[36, 6, -w^2 + w + 4]', '[36, 6, w^2 - w - 9]', '[36, 6, 1/6*w^3 - 1/6*w^2 - 13/6*w + 1]', '[41, 41, -1/2*w^3 - 1/2*w^2 + 9/2*w + 5]', '[41, 41, -1/2*w^3 + 3/2*w^2 + 5/2*w - 8]', '[44, 22, 1/2*w^3 + 1/2*w^2 - 7/2*w - 4]', '[44, 22, 2/3*w^3 - 5/3*w^2 - 14/3*w + 10]', '[59, 59, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1]', '[59, 59, -1/3*w^3 + 4/3*w^2 + 7/3*w - 7]', '[59, 59, 1/2*w^3 - 1/2*w^2 - 5/2*w + 2]', '[64, 4, 2/3*w^3 - 8/3*w^2 - 8/3*w + 12]', '[64, 4, -2/3*w^3 - 4/3*w^2 + 20/3*w + 14]', '[64, 8, -1/3*w^3 + 1/3*w^2 + 10/3*w - 4]', '[64, 8, -1/6*w^3 + 1/6*w^2 + 1/6*w - 3]', '[76, 38, 1/2*w^3 - 3/2*w^2 - 7/2*w + 8]', '[76, 38, -2/3*w^3 + 2/3*w^2 + 17/3*w - 2]', '[76, 38, 1/2*w^3 - 1/2*w^2 - 5/2*w + 1]', '[76, 38, 1/3*w^3 + 2/3*w^2 - 7/3*w - 6]', '[79, 79, w^2 - 11]', '[79, 79, 1/6*w^3 - 7/6*w^2 - 7/6*w + 3]', '[81, 3, 3]', '[81, 9, -1/2*w^3 + 1/2*w^2 + 9/2*w]', '[81, 9, 1/3*w^3 - 1/3*w^2 - 4/3*w - 1]', '[89, 89, -1/6*w^3 + 1/6*w^2 + 19/6*w - 5]', '[89, 89, 1/6*w^3 - 1/6*w^2 - 19/6*w - 3]', '[99, 33, -1/2*w^3 - 3/2*w^2 + 7/2*w + 9]', '[99, 33, 5/6*w^3 - 17/6*w^2 - 35/6*w + 19]', '[100, 10, 1/3*w^3 - 4/3*w^2 + 2/3*w + 2]', '[100, 10, -2/3*w^3 - 1/3*w^2 + 23/3*w + 9]', '[109, 109, -1/6*w^3 + 7/6*w^2 + 1/6*w - 9]', '[109, 109, -7/6*w^3 + 19/6*w^2 + 49/6*w - 20]', '[109, 109, -5/6*w^3 + 17/6*w^2 + 23/6*w - 12]', '[109, 109, 1/6*w^3 + 5/6*w^2 - 13/6*w - 4]', '[116, 58, -2/3*w^3 + 5/3*w^2 + 11/3*w - 8]', '[116, 58, 1/3*w^3 - 4/3*w^2 - 10/3*w + 13]', '[116, 58, -w^2 - w + 2]', '[116, 58, -2/3*w^3 - 1/3*w^2 + 17/3*w + 5]', '[121, 11, 1/6*w^3 - 1/6*w^2 - 7/6*w - 3]', '[121, 11, 1/2*w^3 - 1/2*w^2 - 7/2*w + 1]', '[124, 62, -w - 4]', '[124, 62, 1/6*w^3 - 7/6*w^2 - 7/6*w + 4]', '[124, 62, -w^2 + 10]', '[124, 62, -1/6*w^3 + 1/6*w^2 + 13/6*w - 5]', '[139, 139, 1/3*w^3 - 4/3*w^2 + 5/3*w - 1]', '[139, 139, -5/3*w^3 - 7/3*w^2 + 50/3*w + 29]', '[144, 6, -w^3 + 3*w^2 + 7*w - 18]', '[144, 6, 2/3*w^3 + 4/3*w^2 - 14/3*w - 10]', '[144, 12, w^3 - 2*w^2 - 8*w + 12]', '[144, 12, 2/3*w^3 + 1/3*w^2 - 11/3*w - 3]', '[144, 12, -1/3*w^3 + 4/3*w^2 + 10/3*w - 12]', '[144, 12, w^2 + w - 3]', '[164, 82, -1/3*w^3 + 4/3*w^2 + 7/3*w - 6]', '[164, 82, 5/6*w^3 - 11/6*w^2 - 23/6*w + 8]', '[164, 82, w^3 - 9*w - 4]', '[164, 82, 1/6*w^3 + 5/6*w^2 - 7/6*w - 8]', '[169, 13, w^3 + w^2 - 10*w - 13]', '[169, 13, -5/6*w^3 + 17/6*w^2 + 17/6*w - 12]', '[171, 57, -1/2*w^3 + 5/2*w^2 + 3/2*w - 11]', '[171, 57, 1/2*w^3 - 3/2*w^2 - 5/2*w + 9]', '[171, 57, -1/2*w^3 - 1/2*w^2 + 9/2*w + 4]', '[171, 57, -1/2*w^3 - 3/2*w^2 + 11/2*w + 15]', '[176, 22, -1/3*w^3 + 1/3*w^2 + 1/3*w]', '[176, 44, -1/3*w^3 + 4/3*w^2 + 4/3*w - 9]', '[176, 44, -1/3*w^3 - 2/3*w^2 + 10/3*w + 4]', '[179, 179, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7]', '[179, 179, -2/3*w^3 + 2/3*w^2 + 17/3*w - 5]', '[181, 181, -w^3 + 3*w^2 + 4*w - 13]', '[181, 181, -1/6*w^3 + 7/6*w^2 + 1/6*w - 11]', '[181, 181, 7/6*w^3 + 11/6*w^2 - 79/6*w - 25]', '[181, 181, 1/6*w^3 + 5/6*w^2 - 13/6*w - 2]', '[191, 191, -5/6*w^3 - 1/6*w^2 + 53/6*w + 7]', '[191, 191, 1/6*w^3 + 11/6*w^2 - 19/6*w - 16]', '[209, 209, -1/6*w^3 + 7/6*w^2 - 5/6*w - 1]', '[209, 209, 1/3*w^3 + 2/3*w^2 - 13/3*w - 11]', '[211, 211, -1/6*w^3 + 1/6*w^2 - 5/6*w - 2]', '[211, 211, -1/2*w^3 + 1/2*w^2 + 9/2*w + 2]', '[211, 211, 1/3*w^3 - 1/3*w^2 - 4/3*w - 3]', '[211, 211, -1/2*w^3 + 1/2*w^2 + 11/2*w - 4]', '[225, 15, 1/2*w^3 - 3/2*w^2 - 11/2*w + 15]', '[225, 15, -w^2 - 2*w + 1]', '[229, 229, 5/6*w^3 + 1/6*w^2 - 53/6*w - 9]', '[229, 229, 1/2*w^3 - 3/2*w^2 - 1/2*w + 2]', '[236, 118, w^2 - 2*w - 2]', '[236, 118, 7/3*w^3 + 8/3*w^2 - 70/3*w - 35]', '[236, 118, -4/3*w^3 + 13/3*w^2 + 7/3*w - 12]', '[236, 118, -2/3*w^3 - 1/3*w^2 + 17/3*w + 3]', '[236, 118, 1/3*w^3 - 7/3*w^2 + 8/3*w + 2]', '[236, 118, -1/6*w^3 - 5/6*w^2 - 5/6*w + 2]', '[239, 239, 5/6*w^3 + 7/6*w^2 - 59/6*w - 19]', '[239, 239, 1/2*w^3 - 5/2*w^2 + 1/2*w + 5]', '[241, 241, 1/6*w^3 - 1/6*w^2 - 13/6*w - 4]', '[241, 241, w - 5]', '[256, 4, 4]', '[256, 8, -2/3*w^3 + 2/3*w^2 + 20/3*w]', '[256, 8, 1/3*w^3 - 1/3*w^2 - 1/3*w - 2]', '[256, 16, 2/3*w^3 + 1/3*w^2 - 14/3*w - 4]', '[256, 16, 5/6*w^3 - 11/6*w^2 - 35/6*w + 10]', '[261, 87, 1/2*w^3 - 1/2*w^2 - 11/2*w + 6]', '[261, 87, -2/3*w^3 + 8/3*w^2 + 11/3*w - 15]', '[261, 87, 1/2*w^3 + 3/2*w^2 - 9/2*w - 12]', '[261, 87, 1/6*w^3 - 1/6*w^2 + 5/6*w + 4]', '[269, 269, -1/6*w^3 + 7/6*w^2 + 1/6*w - 2]', '[269, 269, 1/3*w^3 - 7/3*w^2 - 1/3*w + 7]', '[271, 271, 5/3*w^3 + 7/3*w^2 - 47/3*w - 25]', '[271, 271, -5/3*w^3 + 17/3*w^2 + 23/3*w - 27]', '[275, 55, -1/6*w^3 + 13/6*w^2 + 1/6*w - 10]', '[279, 93, -1/3*w^3 + 1/3*w^2 + 13/3*w + 1]', '[279, 93, 5/6*w^3 - 5/6*w^2 - 47/6*w + 5]', '[279, 93, 2*w - 3]', '[279, 93, 1/2*w^3 - 1/2*w^2 - 3/2*w + 3]', '[281, 281, 1/6*w^3 + 5/6*w^2 - 1/6*w - 7]', '[281, 281, -1/2*w^3 + 3/2*w^2 + 9/2*w - 8]', '[304, 38, 2*w + 2]', '[304, 38, 1/3*w^3 - 1/3*w^2 - 13/3*w + 4]', '[304, 76, 5/6*w^3 + 1/6*w^2 - 47/6*w - 4]', '[304, 76, -1/3*w^3 - 2/3*w^2 + 16/3*w + 12]', '[304, 76, -w^2 + 3*w - 1]', '[304, 76, -2/3*w^3 + 5/3*w^2 + 8/3*w - 8]', '[311, 311, 11/6*w^3 + 7/6*w^2 - 113/6*w - 23]', '[311, 311, -4/3*w^3 + 13/3*w^2 + 10/3*w - 13]', '[311, 311, -2/3*w^3 + 5/3*w^2 + 20/3*w - 17]', '[311, 311, 1/6*w^3 + 5/6*w^2 + 5/6*w + 1]', '[316, 158, 5/3*w^3 + 10/3*w^2 - 56/3*w - 41]', '[316, 158, -4/3*w^3 + 19/3*w^2 + 7/3*w - 22]', '[316, 158, 3/2*w^3 + 5/2*w^2 - 27/2*w - 23]', '[316, 158, -5/3*w^3 + 17/3*w^2 + 26/3*w - 30]', '[319, 319, -2/3*w^3 + 2/3*w^2 + 11/3*w - 1]', '[319, 319, -5/6*w^3 + 5/6*w^2 + 41/6*w - 2]', '[324, 6, w^3 - 4*w^2 - 4*w + 18]', '[324, 6, -w^3 - 2*w^2 + 10*w + 21]', '[324, 18, -w^3 + 3*w^2 + 6*w - 18]', '[324, 18, -w^3 + 2*w^2 + 9*w - 16]', '[324, 18, -1/2*w^3 - 3/2*w^2 + 9/2*w + 9]', '[324, 18, 1/3*w^3 + 2/3*w^2 - 16/3*w - 11]', '[341, 341, -1/6*w^3 + 1/6*w^2 - 5/6*w + 4]', '[341, 341, 1/2*w^3 - 1/2*w^2 - 11/2*w - 2]', '[349, 349, -1/2*w^3 + 1/2*w^2 + 11/2*w - 1]', '[349, 349, -5/6*w^3 + 17/6*w^2 + 29/6*w - 14]', '[349, 349, 1/6*w^3 - 1/6*w^2 + 5/6*w - 1]', '[349, 349, -2/3*w^3 - 4/3*w^2 + 17/3*w + 13]', '[356, 178, -5/6*w^3 + 5/6*w^2 + 41/6*w - 3]', '[356, 178, -1/2*w^3 + 7/2*w^2 + 3/2*w - 14]', '[356, 178, -1/3*w^3 - 8/3*w^2 + 13/3*w + 26]', '[356, 178, 2/3*w^3 - 2/3*w^2 - 11/3*w + 2]', '[359, 359, -1/6*w^3 + 13/6*w^2 + 7/6*w - 18]', '[359, 359, -1/6*w^3 - 11/6*w^2 + 13/6*w + 18]', '[361, 19, -2/3*w^3 + 2/3*w^2 + 14/3*w - 3]', '[361, 19, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1]', '[361, 361, 1/6*w^3 + 11/6*w^2 - 1/6*w - 6]', '[361, 361, -2/3*w^3 + 8/3*w^2 + 17/3*w - 23]', '[369, 123, -1/2*w^3 - 1/2*w^2 + 9/2*w + 3]', '[369, 123, -1/2*w^3 + 3/2*w^2 + 5/2*w - 10]', '[369, 123, 1/2*w^3 - 1/2*w^2 - 11/2*w + 3]', '[369, 123, -1/6*w^3 + 1/6*w^2 - 5/6*w - 1]', '[379, 379, 1/2*w^3 + 1/2*w^2 - 7/2*w - 7]', '[379, 379, -5/6*w^3 + 11/6*w^2 + 23/6*w - 7]', '[379, 379, w^3 - 9*w - 5]', '[379, 379, -2/3*w^3 + 5/3*w^2 + 14/3*w - 7]', '[396, 66, -w^2 + w + 12]', '[396, 66, -1/2*w^3 + 3/2*w^2 + 7/2*w - 6]', '[396, 66, w^2 - w - 1]', '[396, 66, 1/3*w^3 + 2/3*w^2 - 7/3*w - 8]', '[400, 10, -2/3*w^3 + 2/3*w^2 + 14/3*w - 2]', '[400, 20, -1/3*w^3 - 5/3*w^2 + 10/3*w + 16]', '[400, 20, 1/2*w^3 - 5/2*w^2 - 5/2*w + 11]', '[401, 401, -1/3*w^3 + 7/3*w^2 + 4/3*w - 17]', '[401, 401, -4/3*w^3 - 8/3*w^2 + 43/3*w + 31]', '[419, 419, 1/6*w^3 - 1/6*w^2 + 5/6*w]', '[419, 419, 1/2*w^3 - 1/2*w^2 - 11/2*w + 2]', '[421, 421, -5/6*w^3 - 7/6*w^2 + 47/6*w + 11]', '[421, 421, 1/3*w^3 - 1/3*w^2 - 19/3*w - 7]', '[431, 431, 5/6*w^3 + 1/6*w^2 - 41/6*w - 6]', '[431, 431, 2/3*w^3 - 8/3*w^2 - 8/3*w + 15]', '[431, 431, 5/6*w^3 - 11/6*w^2 - 29/6*w + 7]', '[431, 431, 1/2*w^3 - 5/2*w^2 + 5/2*w + 2]', '[436, 218, 1/3*w^3 + 2/3*w^2 - 10/3*w - 2]', '[436, 218, -2/3*w^3 - 7/3*w^2 + 23/3*w + 24]', '[436, 218, 3/2*w^3 + 5/2*w^2 - 31/2*w - 31]', '[436, 218, 4/3*w^3 - 16/3*w^2 - 13/3*w + 20]', '[436, 218, -1/6*w^3 + 13/6*w^2 + 1/6*w - 17]', '[436, 218, -1/2*w^3 - 1/2*w^2 + 11/2*w + 4]', '[436, 218, 1/3*w^3 - 4/3*w^2 + 5/3*w - 2]', '[436, 218, 5/6*w^3 + 1/6*w^2 - 59/6*w - 12]', '[439, 439, 5/6*w^3 + 1/6*w^2 - 41/6*w - 4]', '[439, 439, 1/2*w^3 - 1/2*w^2 - 9/2*w + 8]', '[449, 449, 5/6*w^3 - 17/6*w^2 - 29/6*w + 18]', '[449, 449, 11/6*w^3 - 41/6*w^2 - 41/6*w + 29]', '[449, 449, -7/6*w^3 + 31/6*w^2 + 7/6*w - 16]', '[449, 449, 5/3*w^3 + 7/3*w^2 - 56/3*w - 33]', '[451, 451, 2/3*w^3 + 4/3*w^2 - 11/3*w - 9]', '[451, 451, -7/6*w^3 + 19/6*w^2 + 55/6*w - 20]', '[461, 461, -1/6*w^3 + 1/6*w^2 + 19/6*w - 3]', '[461, 461, 1/6*w^3 - 1/6*w^2 - 19/6*w - 1]', '[464, 58, -1/3*w^3 + 1/3*w^2 + 13/3*w]', '[464, 58, 2*w - 2]', '[464, 116, 1/3*w^3 + 5/3*w^2 - 10/3*w - 8]', '[464, 116, 1/2*w^3 - 3/2*w^2 - 3/2*w + 8]', '[464, 116, 2/3*w^3 + 1/3*w^2 - 20/3*w - 4]', '[464, 116, 1/2*w^3 - 5/2*w^2 - 5/2*w + 19]', '[475, 95, -1/3*w^3 - 5/3*w^2 + 10/3*w + 11]', '[475, 95, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16]', '[479, 479, -2*w - 1]', '[479, 479, 1/3*w^3 - 1/3*w^2 - 13/3*w + 3]', '[484, 22, 3/2*w^3 + 5/2*w^2 - 31/2*w - 29]', '[484, 22, 7/6*w^3 + 5/6*w^2 - 79/6*w - 17]', '[484, 22, -4/3*w^3 + 16/3*w^2 + 13/3*w - 22]', '[484, 22, -2/3*w^3 + 8/3*w^2 - 1/3*w - 6]', '[491, 491, 2/3*w^3 + 1/3*w^2 - 14/3*w - 7]', '[491, 491, 5/6*w^3 - 11/6*w^2 - 35/6*w + 7]', '[496, 62, 2/3*w^3 - 2/3*w^2 - 20/3*w + 6]', '[496, 62, 1/3*w^3 - 1/3*w^2 - 1/3*w + 4]', '[496, 124, -1/3*w^3 + 7/3*w^2 + 4/3*w - 12]', '[496, 124, -1/6*w^3 + 1/6*w^2 + 25/6*w - 7]', '[496, 124, -1/3*w^3 + 1/3*w^2 + 16/3*w + 4]', '[496, 124, 1/6*w^3 + 11/6*w^2 - 13/6*w - 15]', '[509, 509, 5/6*w^3 - 11/6*w^2 - 29/6*w + 8]', '[509, 509, 5/6*w^3 + 1/6*w^2 - 41/6*w - 5]', '[521, 521, -1/6*w^3 + 7/6*w^2 - 17/6*w + 1]', '[521, 521, -1/6*w^3 + 7/6*w^2 - 11/6*w - 3]', '[521, 521, -1/6*w^3 + 7/6*w^2 + 19/6*w - 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20]', '[109, 109, -5/6*w^3 + 17/6*w^2 + 23/6*w - 12]', '[109, 109, 1/6*w^3 + 5/6*w^2 - 13/6*w - 4]', '[121, 11, 1/6*w^3 - 1/6*w^2 - 7/6*w - 3]', '[139, 139, 1/3*w^3 - 4/3*w^2 + 5/3*w - 1]', '[139, 139, -5/3*w^3 - 7/3*w^2 + 50/3*w + 29]', '[169, 13, w^3 + w^2 - 10*w - 13]', '[169, 13, -5/6*w^3 + 17/6*w^2 + 17/6*w - 12]', '[179, 179, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7]', '[179, 179, -2/3*w^3 + 2/3*w^2 + 17/3*w - 5]', '[181, 181, -w^3 + 3*w^2 + 4*w - 13]', '[181, 181, -1/6*w^3 + 7/6*w^2 + 1/6*w - 11]', '[181, 181, 7/6*w^3 + 11/6*w^2 - 79/6*w - 25]', '[181, 181, 1/6*w^3 + 5/6*w^2 - 13/6*w - 2]', '[191, 191, -5/6*w^3 - 1/6*w^2 + 53/6*w + 7]', '[191, 191, 1/6*w^3 + 11/6*w^2 - 19/6*w - 16]', '[211, 211, -1/6*w^3 + 1/6*w^2 - 5/6*w - 2]', '[211, 211, -1/2*w^3 + 1/2*w^2 + 9/2*w + 2]', '[211, 211, 1/3*w^3 - 1/3*w^2 - 4/3*w - 3]', '[211, 211, -1/2*w^3 + 1/2*w^2 + 11/2*w - 4]', '[229, 229, 5/6*w^3 + 1/6*w^2 - 53/6*w - 9]', '[229, 229, 1/2*w^3 - 3/2*w^2 - 1/2*w + 2]', '[239, 239, 5/6*w^3 + 7/6*w^2 - 59/6*w - 19]', '[239, 239, 1/2*w^3 - 5/2*w^2 + 1/2*w + 5]', '[241, 241, 1/6*w^3 - 1/6*w^2 - 13/6*w - 4]', '[241, 241, w - 5]', '[269, 269, -1/6*w^3 + 7/6*w^2 + 1/6*w - 2]', '[269, 269, 1/3*w^3 - 7/3*w^2 - 1/3*w + 7]', '[271, 271, 5/3*w^3 + 7/3*w^2 - 47/3*w - 25]', '[271, 271, -5/3*w^3 + 17/3*w^2 + 23/3*w - 27]', '[281, 281, 1/6*w^3 + 5/6*w^2 - 1/6*w - 7]', '[281, 281, -1/2*w^3 + 3/2*w^2 + 9/2*w - 8]', '[311, 311, 11/6*w^3 + 7/6*w^2 - 113/6*w - 23]', '[311, 311, -4/3*w^3 + 13/3*w^2 + 10/3*w - 13]', '[311, 311, -2/3*w^3 + 5/3*w^2 + 20/3*w - 17]', '[311, 311, 1/6*w^3 + 5/6*w^2 + 5/6*w + 1]', '[349, 349, -1/2*w^3 + 1/2*w^2 + 11/2*w - 1]', '[349, 349, -5/6*w^3 + 17/6*w^2 + 29/6*w - 14]', '[349, 349, 1/6*w^3 - 1/6*w^2 + 5/6*w - 1]', '[349, 349, -2/3*w^3 - 4/3*w^2 + 17/3*w + 13]', '[359, 359, -1/6*w^3 + 13/6*w^2 + 7/6*w - 18]', '[359, 359, -1/6*w^3 - 11/6*w^2 + 13/6*w + 18]', '[361, 19, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1]', '[379, 379, 1/2*w^3 + 1/2*w^2 - 7/2*w - 7]', '[379, 379, -5/6*w^3 + 11/6*w^2 + 23/6*w - 7]', '[379, 379, w^3 - 9*w - 5]', '[379, 379, -2/3*w^3 + 5/3*w^2 + 14/3*w - 7]', '[401, 401, -1/3*w^3 + 7/3*w^2 + 4/3*w - 17]', '[401, 401, -4/3*w^3 - 8/3*w^2 + 43/3*w + 31]', '[419, 419, 1/6*w^3 - 1/6*w^2 + 5/6*w]', '[419, 419, 1/2*w^3 - 1/2*w^2 - 11/2*w + 2]', '[421, 421, -5/6*w^3 - 7/6*w^2 + 47/6*w + 11]', '[421, 421, 1/3*w^3 - 1/3*w^2 - 19/3*w - 7]', '[431, 431, 5/6*w^3 + 1/6*w^2 - 41/6*w - 6]', '[431, 431, 2/3*w^3 - 8/3*w^2 - 8/3*w + 15]', '[431, 431, 5/6*w^3 - 11/6*w^2 - 29/6*w + 7]', '[431, 431, 1/2*w^3 - 5/2*w^2 + 5/2*w + 2]', '[439, 439, 5/6*w^3 + 1/6*w^2 - 41/6*w - 4]', '[439, 439, 1/2*w^3 - 1/2*w^2 - 9/2*w + 8]', '[449, 449, 5/6*w^3 - 17/6*w^2 - 29/6*w + 18]', '[449, 449, 11/6*w^3 - 41/6*w^2 - 41/6*w + 29]', '[449, 449, -7/6*w^3 + 31/6*w^2 + 7/6*w - 16]', '[449, 449, 5/3*w^3 + 7/3*w^2 - 56/3*w - 33]', '[461, 461, -1/6*w^3 + 1/6*w^2 + 19/6*w - 3]', '[461, 461, 1/6*w^3 - 1/6*w^2 - 19/6*w - 1]', '[479, 479, -2*w - 1]', '[479, 479, 1/3*w^3 - 1/3*w^2 - 13/3*w + 3]', '[491, 491, 2/3*w^3 + 1/3*w^2 - 14/3*w - 7]', '[491, 491, 5/6*w^3 - 11/6*w^2 - 35/6*w + 7]', '[509, 509, 5/6*w^3 - 11/6*w^2 - 29/6*w + 8]', '[509, 509, 5/6*w^3 + 1/6*w^2 - 41/6*w - 5]', '[521, 521, -1/6*w^3 + 7/6*w^2 - 17/6*w + 1]', '[521, 521, -1/6*w^3 + 7/6*w^2 - 11/6*w - 3]', '[521, 521, -1/6*w^3 + 7/6*w^2 + 19/6*w - 5]', '[521, 521, 2/3*w^3 + 1/3*w^2 - 26/3*w - 11]', '[541, 541, 1/6*w^3 + 5/6*w^2 - 31/6*w - 17]', '[541, 541, 5/6*w^3 - 17/6*w^2 - 47/6*w + 23]', '[541, 541, 3*w^3 + 3*w^2 - 32*w - 47]', '[541, 541, 2/3*w^3 + 4/3*w^2 - 14/3*w - 11]', '[571, 571, -1/3*w^3 + 1/3*w^2 + 13/3*w - 1]', '[571, 571, 2*w - 1]', '[571, 571, -1/3*w^3 + 4/3*w^2 + 7/3*w - 1]', '[571, 571, 1/6*w^3 + 5/6*w^2 - 7/6*w - 13]', '[599, 599, 1/2*w^3 + 1/2*w^2 - 9/2*w - 2]', '[599, 599, -1/6*w^3 + 1/6*w^2 + 19/6*w - 2]', '[599, 599, 1/6*w^3 - 1/6*w^2 - 19/6*w]', '[599, 599, 1/2*w^3 - 3/2*w^2 - 5/2*w + 11]', '[601, 601, 1/6*w^3 + 11/6*w^2 - 7/6*w - 15]', '[601, 601, -1/3*w^3 + 7/3*w^2 - 5/3*w - 5]', '[601, 601, 2/3*w^3 + 4/3*w^2 - 26/3*w - 19]', '[601, 601, 1/2*w^3 - 5/2*w^2 - 7/2*w + 13]', '[659, 659, w^2 - 13]', '[659, 659, -5/6*w^3 + 11/6*w^2 + 29/6*w - 12]', '[659, 659, -1/6*w^3 + 7/6*w^2 + 7/6*w - 1]', '[659, 659, 5/6*w^3 + 1/6*w^2 - 41/6*w - 1]', '[691, 691, 1/2*w^3 - 1/2*w^2 - 11/2*w + 10]', '[691, 691, -1/6*w^3 + 1/6*w^2 - 5/6*w - 8]', '[701, 701, -2*w^2 + w + 11]', '[701, 701, -1/6*w^3 + 13/6*w^2 + 7/6*w - 9]', '[701, 701, -1/6*w^3 + 13/6*w^2 + 1/6*w - 16]', '[701, 701, -w^3 + w^2 + 9*w - 1]', '[709, 709, -2/3*w^3 + 11/3*w^2 + 14/3*w - 21]', '[709, 709, 1/3*w^3 + 5/3*w^2 + 2/3*w - 5]', '[709, 709, 7/6*w^3 - 25/6*w^2 - 43/6*w + 25]', '[709, 709, 2/3*w^3 - 2/3*w^2 - 23/3*w - 1]', '[719, 719, 2*w^2 - 2*w - 19]', '[719, 719, -2*w^2 + 2*w + 7]', '[739, 739, 5/6*w^3 - 5/6*w^2 - 29/6*w + 4]', '[739, 739, -5/6*w^3 + 11/6*w^2 + 53/6*w - 17]', '[739, 739, -1/6*w^3 - 5/6*w^2 - 11/6*w]', '[739, 739, -w^3 + w^2 + 8*w - 5]', '[751, 751, -1/6*w^3 + 1/6*w^2 + 25/6*w + 8]', '[751, 751, -1/3*w^3 + 1/3*w^2 + 16/3*w - 11]', '[761, 761, -2/3*w^3 + 5/3*w^2 + 8/3*w - 9]', '[761, 761, 5/6*w^3 + 1/6*w^2 - 47/6*w - 3]', '[769, 769, 1/3*w^3 - 7/3*w^2 - 7/3*w + 11]', '[769, 769, -4/3*w^3 - 8/3*w^2 + 46/3*w + 33]', '[769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 20]', '[769, 769, 2*w^2 - 17]', '[809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 15]', '[809, 809, -5/6*w^3 - 1/6*w^2 + 35/6*w + 3]', '[809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 9]', '[809, 809, w^3 - 2*w^2 - 7*w + 11]', '[811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w + 7]', '[811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 15]', '[811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w - 4]', '[811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 4]', '[821, 821, -1/2*w^3 - 5/2*w^2 + 13/2*w + 16]', '[821, 821, 1/6*w^3 - 13/6*w^2 - 7/6*w + 21]', '[821, 821, 3/2*w^3 + 1/2*w^2 - 35/2*w - 20]', '[821, 821, -1/6*w^3 + 13/6*w^2 + 7/6*w - 7]', '[829, 829, -1/6*w^3 + 19/6*w^2 - 11/6*w - 23]', '[829, 829, 5/6*w^3 - 17/6*w^2 - 5/6*w + 8]', '[829, 829, -4/3*w^3 - 2/3*w^2 + 43/3*w + 15]', '[829, 829, -1/6*w^3 - 17/6*w^2 + 25/6*w + 16]', '[839, 839, 1/3*w^3 - 7/3*w^2 + 2/3*w + 5]', '[839, 839, 1/2*w^3 + 3/2*w^2 - 13/2*w - 20]', '[841, 29, -5/6*w^3 + 5/6*w^2 + 35/6*w - 4]', '[859, 859, 1/6*w^3 + 5/6*w^2 - 37/6*w + 7]', '[859, 859, 13/6*w^3 + 17/6*w^2 - 127/6*w - 33]', '[881, 881, -2/3*w^3 + 2/3*w^2 + 20/3*w + 5]', '[881, 881, 17/6*w^3 + 19/6*w^2 - 167/6*w - 42]', '[911, 911, -1/6*w^3 + 13/6*w^2 - 11/6*w - 6]', '[911, 911, 3/2*w^3 + 1/2*w^2 - 33/2*w - 17]', '[911, 911, 5/6*w^3 - 17/6*w^2 + 1/6*w + 5]', '[911, 911, 7/6*w^3 - 1/6*w^2 - 61/6*w - 1]', '[929, 929, -7/6*w^3 - 11/6*w^2 + 67/6*w + 22]', '[929, 929, -1/6*w^3 + 1/6*w^2 - 11/6*w + 6]', '[941, 941, 11/6*w^3 + 19/6*w^2 - 107/6*w - 34]', '[941, 941, 4/3*w^3 - 10/3*w^2 - 25/3*w + 19]', '[941, 941, -11/6*w^3 + 41/6*w^2 + 47/6*w - 31]', '[941, 941, 1/2*w^3 + 1/2*w^2 - 13/2*w - 13]', '[961, 31, -1/3*w^3 + 1/3*w^2 + 7/3*w + 5]', '[991, 991, -1/6*w^3 - 5/6*w^2 + 25/6*w + 6]', '[991, 991, 1/6*w^3 + 5/6*w^2 - 25/6*w - 5]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [36, 6, -13, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16225, 'disc_rad': 3245, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[2, 2]]], [5, [0]], [7, [[4, 1]]], [11, [0]], [13, [[2, 2]]], [17, [[4, 1]]], [19, [[2, 1], [1, 2]]], [23, [[4, 1]]], [29, [[2, 1], [1, 2]]], [31, [[2, 1], [1, 2]]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [43, [[2, 2]]], [47, [[4, 1]]], [53, [[2, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 56.96490147450446, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16225.1', 'local_algs': ['5.4.2.1', '11.2.1.2', '11.2.0.1', '59.1.0.1', '59.1.0.1', '59.2.1.2'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [5, 11, 59], 'rd': 11.2861593126, 'regulator': {'__RealLiteral__': 0, 'data': '7.22843244632', 'prec': 44}, 'res': {'gal': ['900,0,-1565,0,724,0,-56,0,1'], 'sib': ['-6,25,-24,-2,1', '900,0,-1565,0,724,0,-56,0,1']}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{6} a^{3} - \\frac{1}{6} a^{2} - \\frac{7}{6} a \\)', '\\( \\frac{1}{6} a^{3} + \\frac{5}{6} a^{2} - \\frac{13}{6} a - 9 \\)', '\\( \\frac{5}{6} a^{3} + \\frac{7}{6} a^{2} - \\frac{47}{6} a - 13 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/6*a^3 - 1/6*a^2 - 1/6*a']}