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hmf_forms • Show schema
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{'deg': 4, 'dimension': 3, 'disc': 4913, 'field_bad_primes': [17], 'field_label': '4.4.4913.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.4913.1-47.3-h', 'label_nsuffix': 7, 'label_suffix': 'h', 'level_bad_primes': [47], 'level_ideal': '[47,47,3/2*w^3 - w^2 - 10*w - 3/2]', 'level_label': '47.3', 'level_norm': 47, 'parallel_weight': 2, 'short_label': '47.3-h', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[47,47,3/2*w^3 - w^2 - 10*w - 3/2]', 1]], 'hecke_eigenvalues': ['e', 'e', '1/2*e^2 - 1/2*e - 2', '-e^2 - e + 4', '-1/2*e^2 + 3/2*e + 5', '-3/2*e^2 + 1/2*e + 7', 2, 'e^2 - e', '-2*e^2 - 2*e + 12', -1, '1/2*e^2 - 1/2*e + 4', '4*e', '-5/2*e^2 + 1/2*e + 10', '3/2*e^2 - 1/2*e - 1', '-5/2*e^2 + 1/2*e + 10', '-3/2*e^2 - 1/2*e + 8', '3/2*e^2 + 5/2*e - 10', '-2*e', '-2*e^2 + 8', '-1/2*e^2 + 7/2*e + 7', 'e^2 - 3*e - 12', '1/2*e^2 + 5/2*e - 13', '-2*e^2 + 2*e + 2', 2, 0, '-5/2*e^2 + 3/2*e + 5', 'e^2 - 5*e - 4', '-e^2 - 5*e + 6', '3/2*e^2 + 5/2*e - 2', '-1/2*e^2 - 3/2*e - 4', '-e^2 + 3*e - 4', '7/2*e^2 + 5/2*e - 4', '3/2*e^2 - 9/2*e - 19', '1/2*e^2 - 3/2*e + 3', '4*e^2 - 14', 'e^2 + e + 12', '3*e^2 + 3*e - 16', '7/2*e^2 - 7/2*e - 22', '1/2*e^2 + 7/2*e - 2', '-6*e^2 - 2*e + 22', '-3/2*e^2 - 3/2*e + 7', '4*e^2 + 6*e - 18', 'e^2 - e', -16, '9/2*e^2 + 5/2*e - 19', '3/2*e^2 + 3/2*e + 9', '-3/2*e^2 - 5/2*e + 8', '-7/2*e^2 - 5/2*e + 26', '7/2*e^2 + 1/2*e - 12', '2*e^2 + 6*e - 20', '-4*e^2 - 8*e + 24', '-e^2 - 5*e - 6', '4*e + 4', '5*e^2 - e - 20', '9/2*e^2 + 5/2*e - 27', 8, '6*e^2 - 2*e - 30', '5/2*e^2 - 3/2*e - 15', '-3/2*e^2 - 19/2*e + 13', '-7/2*e^2 - 9/2*e + 2', 'e^2 - 11*e - 2', '5/2*e^2 - 3/2*e - 25', '-9/2*e^2 + 3/2*e + 27', '6*e^2 + 6*e - 16', '-11/2*e^2 - 11/2*e + 25', '3/2*e^2 - 13/2*e - 5', 'e^2 - 3*e + 12', '7*e^2 + 5*e - 18', '2*e^2 - 2*e - 22', '5/2*e^2 + 21/2*e - 7', '7*e^2 - e - 28', '-11/2*e^2 - 3/2*e + 21', '-3*e^2 - e + 22', '-5*e^2 - e', '1/2*e^2 - 5/2*e', '9/2*e^2 + 13/2*e - 5', '-2*e^2 + 12*e + 16', '-1/2*e^2 - 13/2*e - 11', '-2*e^2 + 8*e + 12', '10*e^2 - 40', '4*e^2 - 26', '-11/2*e^2 - 1/2*e + 28', '-2*e^2 + 2*e + 4', '3*e^2 - 3*e - 36', '3/2*e^2 + 13/2*e - 8', '-4*e^2 - 6*e + 6', '-6*e^2 + 2*e + 12', '2*e^2 - 8*e - 26', '6*e^2 + 8*e - 14', '-2*e^2 + 2*e - 8', '-5*e^2 + 11*e + 32', '3*e^2 + 5*e - 18', 'e^2 + e + 20', '7/2*e^2 - 15/2*e - 34', '-5*e^2 - 5*e + 14', 'e^2 + 11*e + 8', '5/2*e^2 + 19/2*e - 12', '11/2*e^2 + 1/2*e + 2', '3/2*e^2 - 5/2*e - 33', '-7/2*e^2 - 13/2*e + 32', '-21/2*e^2 - 3/2*e + 42', '-3*e^2 + e + 28', '-1/2*e^2 - 17/2*e + 3', '3*e^2 + 5*e - 10', '1/2*e^2 - 9/2*e + 6', '13/2*e^2 - 7/2*e - 33', '-1/2*e^2 + 1/2*e + 12', 'e^2 - 9*e + 16', '-6*e^2 + 2*e + 36', '9/2*e^2 + 9/2*e - 29', '-e^2 + 3*e + 12', '-7*e^2 - e + 22', '1/2*e^2 - 3/2*e + 19', '-19/2*e^2 - 1/2*e + 36', '-5*e^2 + 9*e + 38', '-15/2*e^2 - 21/2*e + 30', '-e^2 + 9*e', '15/2*e^2 - 19/2*e - 34', '-4*e + 20', '3*e^2 + 5*e + 4', '8*e + 12', '15/2*e^2 - 19/2*e - 46', '-9/2*e^2 - 7/2*e + 24', '-21/2*e^2 + 9/2*e + 52', '7/2*e^2 - 7/2*e - 18', '9*e^2 - e - 30', '11/2*e^2 - 7/2*e - 12', '-16*e + 8', '9*e^2 + e - 26', '-2*e^2 - 2*e + 4', '-13/2*e^2 - 25/2*e + 31', '-19/2*e^2 - 15/2*e + 51', '7*e^2 + e - 10', '2*e^2 - 8*e - 36', '12*e^2 - 4*e - 50', '-3*e^2 - e + 10', '-4*e^2 + 10*e + 32', '-5*e^2 - 5*e + 32', 'e^2 - 5*e + 18', '-19/2*e^2 - 3/2*e + 37', '-2*e^2 - 2*e - 14', '-5*e^2 - 5*e + 48', '-4*e^2 - 2*e + 52', '8*e^2 + 12*e - 52', '-2*e^2 - 12*e + 14', '-13/2*e^2 + 5/2*e + 8', '-5/2*e^2 - 21/2*e + 9', '-11*e^2 + 7*e + 64', '8*e^2 - 14*e - 38', '-13/2*e^2 - 7/2*e + 18', '5/2*e^2 + 15/2*e - 2', '4*e^2 + 4*e - 16', '-10*e + 18', '-3*e^2 + 5*e + 54', '-7/2*e^2 - 27/2*e + 21', '5/2*e^2 - 9/2*e - 28', '-13*e^2 + e + 58', '-7*e^2 - e + 46', '2*e^2 - 8*e + 4'], 'hecke_polynomial': 'x^3 + x^2 - 6*x - 4', 'label': '4.4.4913.1-47.3-h'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 4913, 'ideals': ['[1, 1, 1]', '[4, 2, -1/2*w^3 + 3*w + 5/2]', '[4, 2, w^3 - w^2 - 6*w]', '[13, 13, -1/2*w^3 + w^2 + 3*w - 1/2]', '[13, 13, 1/2*w^3 - w^2 - 3*w + 7/2]', '[13, 13, -1/2*w^3 + 4*w - 1/2]', '[13, 13, -1/2*w^3 + 4*w + 5/2]', '[16, 2, 2]', '[16, 4, w^3 - w^2 - 5*w]', '[16, 4, w^3 - w^2 - 5*w + 1]', '[17, 17, 1/2*w^3 - w^2 - w + 3/2]', '[47, 47, -w^2 + 2]', '[47, 47, -w^3 + 2*w^2 + 5*w - 5]', '[47, 47, -3/2*w^3 + w^2 + 10*w + 3/2]', '[47, 47, -1/2*w^3 + 5*w - 1/2]', '[52, 26, -w^3 + 2*w^2 + 5*w - 4]', '[52, 26, -w^3 + w^2 + 7*w - 2]', '[52, 26, w^2 - w - 4]', '[52, 26, w^3 - w^2 - 7*w]', '[52, 26, -w^2 + w + 2]', '[52, 26, -3/2*w^3 + w^2 + 10*w + 1/2]', '[52, 26, -w^2 + 3]', '[52, 26, 1/2*w^3 - 5*w - 1/2]', '[64, 4, -w^3 + 6*w + 5]', '[64, 4, 2*w^3 - 2*w^2 - 12*w]', '[64, 8, w^3 - w^2 - 5*w + 4]', '[64, 8, -w^3 + w^2 + 5*w + 3]', '[67, 67, 3/2*w^3 - 2*w^2 - 8*w + 3/2]', '[67, 67, 1/2*w^3 - 2*w - 5/2]', '[67, 67, -1/2*w^3 + w^2 + w - 5/2]', '[67, 67, -3/2*w^3 + w^2 + 9*w - 1/2]', '[68, 34, -w^2 + w + 3]', '[68, 34, w^3 - w^2 - 7*w + 1]', '[81, 3, -3]', '[89, 89, w^2 - 2*w - 4]', '[89, 89, 3/2*w^3 - 2*w^2 - 9*w + 3/2]', '[89, 89, -1/2*w^3 + w^2 + 4*w - 7/2]', '[89, 89, -w^3 + 7*w + 1]', '[101, 101, -1/2*w^3 + 3*w - 5/2]', '[101, 101, -1/2*w^3 + w^2 + 2*w - 11/2]', '[101, 101, -w^3 + w^2 + 6*w + 3]', '[101, 101, w - 4]', '[103, 103, 3/2*w^3 - 3*w^2 - 7*w + 7/2]', '[103, 103, -w^2 + 8]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 11/2]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 13/2]', '[137, 137, 1/2*w^3 - 2*w - 7/2]', '[137, 137, -1/2*w^3 + w^2 + w - 7/2]', '[137, 137, 3/2*w^3 - 2*w^2 - 8*w + 1/2]', '[137, 137, -3/2*w^3 + w^2 + 9*w - 3/2]', '[149, 149, 3/2*w^3 - 9*w - 13/2]', '[149, 149, 7/2*w^3 - 3*w^2 - 21*w - 3/2]', '[149, 149, 2*w^3 - 2*w^2 - 12*w - 1]', '[149, 149, -w^2 + 6]', '[157, 157, -5/2*w^3 + 3*w^2 + 13*w - 9/2]', '[157, 157, -2*w^3 + 3*w^2 + 12*w - 4]', '[157, 157, 1/2*w^3 - 2*w^2 - 2*w + 15/2]', '[157, 157, 5/2*w^3 - 2*w^2 - 14*w - 3/2]', '[169, 13, -5/2*w^3 + 2*w^2 + 14*w + 1/2]', '[169, 13, 3/2*w^3 - w^2 - 7*w - 1/2]', '[169, 13, -3/2*w^3 + 2*w^2 + 6*w - 3/2]', '[169, 13, 5/2*w^3 - 3*w^2 - 13*w + 7/2]', '[169, 13, -2*w^3 + 2*w^2 + 10*w + 1]', '[169, 13, -2*w^3 + 2*w^2 + 10*w - 3]', '[169, 169, 3/2*w^3 - 2*w^2 - 10*w + 5/2]', '[169, 169, -1/2*w^3 - w^2 + 5*w + 7/2]', '[169, 169, 3/2*w^3 - 2*w^2 - 10*w + 7/2]', '[169, 169, -1/2*w^3 - w^2 + 5*w + 9/2]', '[188, 94, 2*w^3 - 3*w^2 - 11*w + 4]', '[188, 94, 1/2*w^3 - w^2 - 4*w + 9/2]', '[188, 94, -3/2*w^3 + 2*w^2 + 9*w - 1/2]', '[188, 94, w^2 - 3*w - 3]', '[188, 94, w^2 + w - 4]', '[188, 94, -2*w^3 + w^2 + 13*w + 1]', '[188, 94, -w^3 + 7*w]', '[188, 94, w^2 - 2*w - 5]', '[191, 191, 3/2*w^3 - 2*w^2 - 8*w - 1/2]', '[191, 191, -3/2*w^3 + w^2 + 9*w - 5/2]', '[191, 191, 1/2*w^3 - 2*w - 9/2]', '[191, 191, -1/2*w^3 + w^2 + w - 9/2]', '[208, 26, -w^3 + 2*w^2 + 6*w - 1]', '[208, 26, w^3 - 2*w^2 - 6*w + 7]', '[208, 26, -w^3 + 8*w - 1]', '[208, 26, -w^3 + 8*w + 5]', '[208, 52, -w^3 + 9*w]', '[208, 52, 1/2*w^3 - w - 5/2]', '[208, 52, -w^3 + 2*w^2 + 3*w - 4]', '[208, 52, 5/2*w^3 - 3*w^2 - 14*w + 5/2]', '[208, 52, 2*w^3 - w^2 - 12*w - 1]', '[208, 52, -3/2*w^3 + 3*w^2 + 8*w - 15/2]', '[208, 52, 2*w^3 - w^2 - 14*w - 3]', '[208, 52, 1/2*w^3 - 2*w^2 - 3*w + 7/2]', '[221, 221, w + 4]', '[221, 221, -w^3 + w^2 + 6*w - 5]', '[221, 221, 1/2*w^3 - 3*w - 11/2]', '[221, 221, -1/2*w^3 + w^2 + 2*w + 5/2]', '[239, 239, -5/2*w^3 + 2*w^2 + 16*w + 1/2]', '[239, 239, 2*w^3 - 13*w - 8]', '[239, 239, -7/2*w^3 + 3*w^2 + 20*w - 1/2]', '[239, 239, -1/2*w^3 + 4*w + 11/2]', '[251, 251, -5/2*w^3 + 3*w^2 + 13*w - 1/2]', '[251, 251, -2*w^3 + w^2 + 14*w + 2]', '[251, 251, 3/2*w^3 - w^2 - 7*w - 7/2]', '[251, 251, -w^3 + 9*w + 1]', '[256, 4, 4]', '[256, 8, 2*w^3 - 2*w^2 - 10*w]', '[256, 8, 2*w^3 - 2*w^2 - 10*w + 2]', '[256, 16, -w^3 + w^2 + 5*w + 4]', '[256, 16, w^3 - w^2 - 5*w + 5]', '[268, 134, -3*w^3 + 2*w^2 + 17*w + 2]', '[268, 134, 7/2*w^3 - 3*w^2 - 20*w - 1/2]', '[268, 134, w^3 + w^2 - 7*w - 9]', '[268, 134, -w^2 + w + 8]', '[268, 134, 2*w^3 - w^2 - 13*w - 7]', '[268, 134, 1/2*w^3 + w^2 - 4*w - 11/2]', '[268, 134, -4*w^3 + 3*w^2 + 25*w + 3]', '[268, 134, -2*w^3 + 2*w^2 + 13*w - 1]', '[271, 271, -w^3 + 7*w - 1]', '[271, 271, -3/2*w^3 + 2*w^2 + 9*w + 1/2]', '[271, 271, w^2 - 2*w - 6]', '[271, 271, -1/2*w^3 + w^2 + 4*w - 11/2]', '[272, 34, w^3 - 2*w^2 - 2*w + 3]', '[272, 68, 1/2*w^3 + w^2 - 6*w + 1/2]', '[272, 68, w^3 - 2*w^2 - 7*w]', '[289, 17, 2*w^3 - 2*w^2 - 10*w + 1]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 13/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w - 3/2]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 7/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w + 3/2]', '[307, 307, w^3 - w^2 - 8*w + 1]', '[307, 307, 2*w^3 - 2*w^2 - 13*w + 2]', '[307, 307, -1/2*w^3 + 2*w^2 + w - 9/2]', '[307, 307, -1/2*w^3 - w^2 + 4*w + 9/2]', '[324, 6, 3/2*w^3 - 9*w - 15/2]', '[324, 6, -3*w^3 + 3*w^2 + 18*w]', '[353, 353, -3/2*w^3 + 2*w^2 + 8*w - 15/2]', '[353, 353, 11/2*w^3 - 4*w^2 - 34*w - 7/2]', '[353, 353, 6*w^3 - 4*w^2 - 36*w - 7]', '[353, 353, 9/2*w^3 - 3*w^2 - 26*w - 5/2]', '[356, 178, -w^2 + 2*w + 9]', '[356, 178, 5/2*w^3 - 17*w - 21/2]', '[356, 178, 4*w^3 - 3*w^2 - 23*w - 1]', '[356, 178, -1/2*w^3 + w^2 + 2*w - 13/2]', '[356, 178, -4*w^3 + 3*w^2 + 25*w + 2]', '[356, 178, -3*w^3 + 3*w^2 + 16*w - 4]', '[356, 178, 7/2*w^3 - 2*w^2 - 23*w - 11/2]', '[356, 178, -2*w^3 + 13*w + 7]', '[361, 19, 1/2*w^3 + w^2 - 3*w - 15/2]', '[361, 19, -2*w^3 + 2*w^2 + 10*w - 7]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 9/2]', '[373, 373, -3/2*w^3 + w^2 + 11*w + 1/2]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 11/2]', '[373, 373, 3/2*w^3 - w^2 - 11*w + 1/2]', '[404, 202, -5*w^3 + 5*w^2 + 30*w - 2]', '[404, 202, -4*w^3 + 4*w^2 + 23*w - 1]', '[404, 202, w^2 + w - 5]', '[404, 202, 3/2*w^3 + w^2 - 10*w - 25/2]', '[404, 202, -9/2*w^3 + 2*w^2 + 27*w + 21/2]', '[404, 202, -2*w^3 + 3*w^2 + 12*w - 3]', '[404, 202, 4*w^3 - 3*w^2 - 25*w - 6]', '[404, 202, 3/2*w^3 - 9*w - 19/2]', '[409, 409, 2*w^3 - 3*w^2 - 10*w + 2]', '[409, 409, -w^3 + 5*w + 5]', '[409, 409, -1/2*w^3 + w^2 - 7/2]', '[409, 409, 5/2*w^3 - 2*w^2 - 15*w + 5/2]', '[412, 206, 2*w^3 - 2*w^2 - 11*w + 7]', '[412, 206, 8*w^3 - 7*w^2 - 47*w]', '[412, 206, 5/2*w^3 - 3*w^2 - 12*w + 9/2]', '[412, 206, -7/2*w^3 + 23*w + 39/2]', '[412, 206, w^3 - w^2 - 3*w + 5]', '[412, 206, 2*w^3 - w^2 - 11*w + 1]', '[412, 206, 5/2*w^3 - 2*w^2 - 13*w + 3/2]', '[412, 206, w^3 - w^2 - 4*w + 6]', '[421, 421, -2*w^3 + w^2 + 12*w]', '[421, 421, 5/2*w^3 - 3*w^2 - 14*w + 3/2]', '[421, 421, -w^3 + 2*w^2 + 3*w - 5]', '[421, 421, 1/2*w^3 - w - 7/2]', '[443, 443, 5/2*w^3 - 3*w^2 - 15*w + 3/2]', '[443, 443, 1/2*w^3 - w^2 - 5*w + 9/2]', '[443, 443, -1/2*w^3 + 2*w^2 - 13/2]', '[443, 443, -3/2*w^3 + 10*w + 3/2]', '[463, 463, 4*w^3 - 4*w^2 - 22*w + 5]', '[463, 463, 3*w^3 - 4*w^2 - 14*w + 2]', '[463, 463, -5/2*w^3 + 2*w^2 + 14*w - 7/2]', '[463, 463, 3/2*w^3 - w^2 - 7*w - 9/2]', '[509, 509, -7/2*w^3 + 2*w^2 + 20*w + 3/2]', '[509, 509, 5/2*w^3 - w^2 - 16*w - 5/2]', '[509, 509, -5/2*w^3 + 4*w^2 + 10*w - 13/2]', '[509, 509, 9/2*w^3 - 5*w^2 - 25*w + 7/2]', '[523, 523, 3*w^3 - 3*w^2 - 16*w + 3]', '[523, 523, 2*w^3 - 2*w^2 - 9*w + 2]', '[523, 523, 5/2*w^3 - 3*w^2 - 12*w + 3/2]', '[523, 523, -5/2*w^3 + 2*w^2 + 13*w + 3/2]', '[548, 274, -w^3 + 7*w + 8]', '[548, 274, 5/2*w^3 - w^2 - 16*w - 19/2]', '[548, 274, w^3 + w^2 - 7*w - 8]', '[548, 274, 4*w^3 - 3*w^2 - 23*w - 3]', '[548, 274, -4*w^3 + 3*w^2 + 23*w + 2]', '[548, 274, -3*w^3 + 3*w^2 + 19*w - 1]', '[548, 274, -7/2*w^3 + 3*w^2 + 22*w + 1/2]', '[548, 274, 2*w^2 - w - 9]', '[557, 557, 3*w^3 - 3*w^2 - 16*w + 1]', '[557, 557, 5/2*w^3 - 2*w^2 - 13*w + 1/2]', '[557, 557, -2*w^3 + 2*w^2 + 9*w]', '[557, 557, -5/2*w^3 + 3*w^2 + 12*w - 7/2]', '[577, 577, -w^3 - w^2 + 6*w + 9]', '[577, 577, 7/2*w^3 - 3*w^2 - 21*w - 7/2]', '[577, 577, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[577, 577, -5/2*w^3 + 3*w^2 + 13*w - 19/2]', '[596, 298, -w - 5]', '[596, 298, -5/2*w^3 + 2*w^2 + 13*w + 1/2]', '[596, 298, 3*w^3 - 3*w^2 - 16*w + 2]', '[596, 298, w^3 - w^2 - 6*w + 6]', '[596, 298, -1/2*w^3 + 3*w + 13/2]', '[596, 298, -1/2*w^3 + w^2 + 2*w + 7/2]', '[596, 298, 5/2*w^3 - 3*w^2 - 12*w + 5/2]', '[596, 298, 2*w^3 - 2*w^2 - 9*w + 1]', '[599, 599, -4*w^3 + 4*w^2 + 22*w - 1]', '[599, 599, w^3 + w^2 - 8*w - 7]', '[599, 599, -5/2*w^3 + 3*w^2 + 16*w - 11/2]', '[599, 599, 3/2*w^3 - w^2 - 7*w - 13/2]', '[611, 611, -3/2*w^3 + 3*w^2 + 6*w - 17/2]', '[611, 611, 3*w^3 - 2*w^2 - 18*w]', '[611, 611, w^3 - 4*w - 4]', '[611, 611, -3/2*w^3 + w^2 + 7*w + 11/2]', '[611, 611, 3*w^3 - 4*w^2 - 16*w + 4]', '[611, 611, -5/2*w^3 + 3*w^2 + 13*w + 3/2]', '[611, 611, -1/2*w^3 + 2*w^2 + 4*w - 13/2]', '[611, 611, 5/2*w^3 - 2*w^2 - 14*w + 9/2]', '[611, 611, w^3 - 2*w^2 - 2*w + 4]', '[611, 611, -3/2*w^3 + 9*w + 1/2]', '[611, 611, -3*w + 4]', '[611, 611, -5/2*w^3 + w^2 + 17*w + 3/2]', '[611, 611, -3*w^3 + 3*w^2 + 18*w + 1]', '[611, 611, 3/2*w^3 - 2*w^2 - 6*w + 13/2]', '[611, 611, -5/2*w^3 + 4*w^2 + 14*w - 11/2]', '[611, 611, -1/2*w^3 - w^2 + 7*w + 9/2]', '[613, 613, w^3 - 5*w - 9]', '[613, 613, -2*w^3 + 3*w^2 + 10*w + 2]', '[613, 613, -1/2*w^3 + w^2 - 15/2]', '[613, 613, -5/2*w^3 + 2*w^2 + 15*w - 13/2]', '[625, 5, -5]', '[628, 314, -2*w^3 + 4*w^2 + 11*w - 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6]', '[676, 26, 2*w^3 - w^2 - 12*w + 1]', '[676, 338, -2*w^3 + w^2 + 10*w + 5]', '[676, 338, 3/2*w^3 - 2*w^2 - 5*w + 9/2]', '[676, 338, 3/2*w^3 - 2*w^2 - 11*w + 5/2]', '[676, 338, 7/2*w^3 - 3*w^2 - 20*w + 7/2]', '[676, 338, 5/2*w^3 - 3*w^2 - 16*w + 9/2]', '[676, 338, -w^3 - w^2 + 8*w + 6]', '[676, 338, 3*w^3 - 4*w^2 - 15*w + 2]', '[676, 338, -2*w^2 + 3*w + 5]', '[701, 701, 3*w^3 - 2*w^2 - 18*w - 8]', '[701, 701, 7/2*w^3 - 3*w^2 - 21*w - 9/2]', '[701, 701, -1/2*w^3 - 2*w^2 + 3*w + 19/2]', '[701, 701, 15/2*w^3 - 5*w^2 - 45*w - 19/2]', '[727, 727, 2*w^3 - 3*w^2 - 12*w + 2]', '[727, 727, w^3 - 2*w^2 - 7*w + 7]', '[727, 727, 1/2*w^3 + w^2 - 6*w - 13/2]', '[727, 727, 3/2*w^3 - 11*w - 1/2]', '[752, 94, -2*w^2 + 4]', '[752, 94, -2*w^3 + 4*w^2 + 10*w - 10]', '[752, 94, -3*w^3 + 2*w^2 + 20*w + 3]', '[752, 94, -w^3 + 10*w - 1]', '[752, 188, -w^3 + w^2 + 3*w + 5]', '[752, 188, w^3 - w^2 - 9*w]', '[752, 188, -3*w^3 + 3*w^2 + 19*w - 4]', '[752, 188, -2*w^3 + w^2 + 11*w - 3]', '[752, 188, -3*w^3 + 3*w^2 + 17*w + 3]', '[752, 188, -2*w^3 + 3*w^2 + 9*w - 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6*w - 15/2]', '[1937, 1937, -1/2*w^3 - 2*w^2 + 6*w + 13/2]', '[1937, 1937, -1/2*w^3 - 2*w^2 + 4*w + 19/2]', '[1937, 1937, w^3 - 11*w + 1]', '[1937, 1937, 4*w^3 - 3*w^2 - 26*w - 2]', '[1937, 1937, -3*w^2 + 4*w + 4]', '[1937, 1937, 5/2*w^3 - 3*w^2 - 17*w + 7/2]', '[1937, 1937, -5/2*w^3 + 5*w^2 + 12*w - 23/2]', '[1937, 1937, -1/2*w^3 - 2*w^2 + 3*w + 11/2]', '[1937, 1937, -7/2*w^3 + 4*w^2 + 23*w - 19/2]', '[1937, 1937, -3/2*w^3 + 4*w^2 + 6*w - 13/2]', '[1951, 1951, -7/2*w^3 + 3*w^2 + 20*w - 13/2]', '[1951, 1951, 2*w^3 - w^2 - 10*w - 8]', '[1951, 1951, 3*w^3 - 4*w^2 - 15*w - 1]', '[1951, 1951, -3/2*w^3 + 2*w^2 + 5*w - 15/2]', '[1973, 1973, 5/2*w^3 - w^2 - 14*w + 3/2]', '[1973, 1973, 4*w^3 - 4*w^2 - 23*w - 2]', '[1973, 1973, w^3 - w^2 - 2*w - 5]', '[1973, 1973, 5/2*w^3 - 4*w^2 - 11*w + 21/2]', '[1993, 1993, 5/2*w^3 - w^2 - 15*w + 1/2]', '[1993, 1993, 7/2*w^3 - 4*w^2 - 20*w + 1/2]', '[1993, 1993, -3/2*w^3 + 3*w^2 + 5*w - 17/2]', '[1993, 1993, 1/2*w^3 - 11/2]', '[2027, 2027, -6*w^3 + 6*w^2 + 37*w - 2]', '[2027, 2027, 3/2*w^3 - 4*w^2 - 8*w + 21/2]', '[2027, 2027, 7/2*w^3 - w^2 - 22*w - 31/2]', '[2027, 2027, 13/2*w^3 - 4*w^2 - 38*w - 19/2]', '[2036, 1018, 5*w^3 - 31*w - 20]', '[2036, 1018, -10*w^3 + 7*w^2 + 63*w + 13]', '[2036, 1018, -4*w^3 + 5*w^2 + 25*w - 10]', '[2036, 1018, 17/2*w^3 - 5*w^2 - 54*w - 27/2]', '[2036, 1018, -w^3 - 3*w^2 + 9*w + 25]', '[2036, 1018, -5/2*w^3 + 5*w^2 + 12*w - 21/2]', '[2036, 1018, -5*w^3 + w^2 + 32*w + 16]', '[2036, 1018, 11*w^3 - 9*w^2 - 65*w - 4]', '[2039, 2039, 13/2*w^3 - 3*w^2 - 41*w - 21/2]', '[2039, 2039, 7*w^3 - 4*w^2 - 44*w - 8]', '[2039, 2039, 6*w^3 - 5*w^2 - 34*w + 4]', '[2039, 2039, -9/2*w^3 + 4*w^2 + 25*w - 13/2]', '[2041, 2041, 3/2*w^3 - 3*w^2 - 11*w + 17/2]', '[2041, 2041, 5/2*w^3 - w^2 - 10*w + 15/2]', '[2041, 2041, 5/2*w^3 - 3*w^2 - 18*w + 15/2]', '[2041, 2041, -9*w^3 + 12*w^2 + 50*w - 22]', '[2041, 2041, -17/2*w^3 + 10*w^2 + 46*w - 39/2]', '[2041, 2041, -11/2*w^3 + 8*w^2 + 30*w - 27/2]', '[2041, 2041, 7/2*w^3 - 5*w^2 - 21*w + 11/2]', '[2041, 2041, 7/2*w^3 - 6*w^2 - 15*w + 23/2]', '[2041, 2041, 5/2*w^3 - 5*w^2 - 13*w + 21/2]', '[2041, 2041, -1/2*w^3 + 3*w^2 + 3*w - 15/2]', '[2041, 2041, -5*w^3 + 6*w^2 + 28*w - 6]', '[2041, 2041, -4*w^3 + 3*w^2 + 24*w - 2]', '[2041, 2041, -7/2*w^3 + 4*w^2 + 23*w - 3/2]', '[2041, 2041, 7/2*w^3 - 2*w^2 - 14*w + 11/2]', '[2041, 2041, 5/2*w^3 - 4*w^2 - 13*w + 5/2]', '[2041, 2041, -13/2*w^3 + 8*w^2 + 35*w - 41/2]', '[2053, 2053, 7/2*w^3 - 2*w^2 - 21*w - 1/2]', '[2053, 2053, 4*w^3 - 5*w^2 - 22*w + 4]', '[2053, 2053, -3/2*w^3 + 3*w^2 + 4*w - 13/2]', '[2053, 2053, w^3 - 3*w - 5]', '[2087, 2087, -1/2*w^3 + 2*w^2 - 2*w - 11/2]', '[2087, 2087, -7/2*w^3 + 5*w^2 + 19*w - 11/2]', '[2087, 2087, 7/2*w^3 - 2*w^2 - 22*w - 1/2]', '[2087, 2087, 1/2*w^3 + w^2 - w - 13/2]', '[2092, 1046, -3*w^2 + w + 16]', '[2092, 1046, -2*w^2 - w + 9]', '[2092, 1046, 13/2*w^3 - 6*w^2 - 39*w - 1/2]', '[2092, 1046, 7/2*w^3 - 4*w^2 - 21*w + 1/2]', '[2092, 1046, 11/2*w^3 - 5*w^2 - 32*w - 5/2]', '[2092, 1046, -7*w^3 + 5*w^2 + 43*w + 10]', '[2092, 1046, -w^3 - w^2 + 6*w + 12]', '[2092, 1046, 4*w^3 - w^2 - 24*w - 13]', '[2129, 2129, -3*w^3 + 3*w^2 + 20*w - 1]', '[2129, 2129, -1/2*w^3 + 3*w^2 - 19/2]', '[2129, 2129, -2*w^3 + 2*w^2 + 15*w - 4]', '[2129, 2129, 1/2*w^3 + 2*w^2 - 5*w - 11/2]', '[2141, 2141, -2*w^3 + 2*w^2 + 15*w]', '[2141, 2141, -1/2*w^3 + 3*w^2 - 11/2]', '[2141, 2141, -3*w^3 + 3*w^2 + 20*w - 5]', '[2141, 2141, 1/2*w^3 + 2*w^2 - 5*w - 19/2]', '[2143, 2143, 4*w^3 - 5*w^2 - 26*w + 12]', '[2143, 2143, 3/2*w^3 + 2*w^2 - 13*w - 29/2]', '[2143, 2143, 1/2*w^3 + 3*w^2 - 8*w - 9/2]', '[2143, 2143, -3*w^3 + 4*w^2 + 21*w - 1]', '[2192, 274, w^3 - 4*w - 7]', '[2192, 274, -w^3 + 2*w^2 + 2*w - 7]', '[2192, 274, 3*w^3 - 4*w^2 - 16*w + 1]', '[2192, 274, -3*w^3 + 2*w^2 + 18*w - 3]', '[2192, 548, -w^2 - 2*w + 7]', '[2192, 548, -7/2*w^3 + 4*w^2 + 19*w + 3/2]', '[2192, 548, -5/2*w^3 + w^2 + 16*w - 1/2]', '[2192, 548, -3/2*w^3 + w^2 + 6*w + 13/2]', '[2192, 548, -3*w^3 + 4*w^2 + 17*w - 2]', '[2192, 548, -3*w^3 + 2*w^2 + 17*w - 4]', '[2192, 548, -1/2*w^3 + 2*w^2 - w - 15/2]', '[2192, 548, -2*w^3 + 3*w^2 + 8*w - 9]', '[2197, 13, -9/2*w^3 + 5*w^2 + 25*w - 3/2]', '[2197, 13, -7/2*w^3 + 2*w^2 + 20*w - 1/2]', '[2197, 13, 5/2*w^3 - 4*w^2 - 10*w + 17/2]', '[2197, 13, -3/2*w^3 + w^2 + 5*w + 9/2]', '[2197, 169, 7/2*w^3 - 3*w^2 - 21*w + 13/2]', '[2197, 169, 2*w^3 - w^2 - 16*w + 2]', '[2197, 169, -w^3 + 2*w^2 + 8*w - 8]', '[2197, 169, 3*w^3 - 4*w^2 - 18*w + 2]', '[2197, 169, -1/2*w^3 + w^2 - w - 13/2]', '[2197, 169, -3*w^3 + 2*w^2 + 21*w + 3]', '[2197, 169, -2*w^2 + 4*w + 9]', '[2197, 169, 3/2*w^3 - 4*w^2 - 7*w + 23/2]', '[2197, 169, 3/2*w^3 - 8*w - 19/2]', '[2197, 169, 5/2*w^3 - 4*w^2 - 12*w + 1/2]', '[2197, 169, -1/2*w^3 + 3*w^2 + 2*w - 11/2]', '[2197, 169, -2*w^3 + 14*w + 1]', '[2197, 2197, -4*w^3 + 4*w^2 + 21*w - 4]', '[2197, 2197, 3*w^3 - 3*w^2 - 14*w + 3]', '[2197, 2197, -7/2*w^3 + 4*w^2 + 17*w - 3/2]', '[2197, 2197, 7/2*w^3 - 3*w^2 - 18*w - 3/2]', '[2209, 47, 7/2*w^3 - 3*w^2 - 23*w - 1/2]', '[2209, 47, -3/2*w^3 + 4*w^2 + 6*w - 21/2]', '[2209, 47, -3/2*w^3 + w^2 + 13*w - 5/2]', '[2209, 47, -1/2*w^3 - 2*w^2 + 4*w + 11/2]', '[2209, 47, -2*w^3 + 2*w^2 + 10*w + 7]', '[2209, 47, -2*w^3 + 2*w^2 + 10*w - 9]', '[2209, 2209, 5/2*w^3 - 4*w^2 - 16*w + 5/2]', '[2209, 2209, -3/2*w^3 - w^2 + 13*w + 21/2]', '[2209, 2209, 3/2*w^3 + w^2 - 13*w - 3/2]', '[2209, 2209, 5/2*w^3 - 4*w^2 - 16*w + 23/2]', '[2228, 1114, -2*w^3 - w^2 + 13*w + 16]', '[2228, 1114, -2*w^3 - w^2 + 12*w + 13]', '[2228, 1114, 15/2*w^3 - 6*w^2 - 45*w - 11/2]', '[2228, 1114, 6*w^3 - 5*w^2 - 37*w - 5]', '[2228, 1114, -w^3 + 3*w^2 + 6*w - 12]', '[2228, 1114, -9/2*w^3 + 4*w^2 + 27*w + 9/2]', '[2228, 1114, 2*w^3 - 11*w - 9]', '[2228, 1114, -9/2*w^3 + 5*w^2 + 26*w - 5/2]', '[2243, 2243, -9/2*w^3 + 4*w^2 + 26*w - 11/2]', '[2243, 2243, 6*w^3 - 4*w^2 - 35*w - 2]', '[2243, 2243, 15/2*w^3 - 5*w^2 - 46*w - 11/2]', '[2243, 2243, 9/2*w^3 - 2*w^2 - 28*w - 11/2]', '[2308, 1154, 7/2*w^3 - 3*w^2 - 18*w + 3/2]', '[2308, 1154, 12*w^3 - 7*w^2 - 73*w - 19]', '[2308, 1154, -7*w^3 + 9*w^2 + 41*w - 13]', '[2308, 1154, 7/2*w^3 - 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4]', '[103, 103, 3/2*w^3 - 3*w^2 - 7*w + 7/2]', '[103, 103, -w^2 + 8]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 11/2]', '[103, 103, -1/2*w^3 - w^2 + 3*w + 13/2]', '[137, 137, 1/2*w^3 - 2*w - 7/2]', '[137, 137, -1/2*w^3 + w^2 + w - 7/2]', '[137, 137, 3/2*w^3 - 2*w^2 - 8*w + 1/2]', '[137, 137, -3/2*w^3 + w^2 + 9*w - 3/2]', '[149, 149, 3/2*w^3 - 9*w - 13/2]', '[149, 149, 7/2*w^3 - 3*w^2 - 21*w - 3/2]', '[149, 149, 2*w^3 - 2*w^2 - 12*w - 1]', '[149, 149, -w^2 + 6]', '[157, 157, -5/2*w^3 + 3*w^2 + 13*w - 9/2]', '[157, 157, -2*w^3 + 3*w^2 + 12*w - 4]', '[157, 157, 1/2*w^3 - 2*w^2 - 2*w + 15/2]', '[157, 157, 5/2*w^3 - 2*w^2 - 14*w - 3/2]', '[191, 191, 3/2*w^3 - 2*w^2 - 8*w - 1/2]', '[191, 191, -3/2*w^3 + w^2 + 9*w - 5/2]', '[191, 191, 1/2*w^3 - 2*w - 9/2]', '[191, 191, -1/2*w^3 + w^2 + w - 9/2]', '[239, 239, -5/2*w^3 + 2*w^2 + 16*w + 1/2]', '[239, 239, 2*w^3 - 13*w - 8]', '[239, 239, -7/2*w^3 + 3*w^2 + 20*w - 1/2]', '[239, 239, -1/2*w^3 + 4*w + 11/2]', '[251, 251, -5/2*w^3 + 3*w^2 + 13*w - 1/2]', '[251, 251, -2*w^3 + w^2 + 14*w + 2]', '[251, 251, 3/2*w^3 - w^2 - 7*w - 7/2]', '[251, 251, -w^3 + 9*w + 1]', '[271, 271, -w^3 + 7*w - 1]', '[271, 271, -3/2*w^3 + 2*w^2 + 9*w + 1/2]', '[271, 271, w^2 - 2*w - 6]', '[271, 271, -1/2*w^3 + w^2 + 4*w - 11/2]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 13/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w - 3/2]', '[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 7/2]', '[293, 293, -3/2*w^3 + w^2 + 11*w + 3/2]', '[307, 307, w^3 - w^2 - 8*w + 1]', '[307, 307, 2*w^3 - 2*w^2 - 13*w + 2]', '[307, 307, -1/2*w^3 + 2*w^2 + w - 9/2]', '[307, 307, -1/2*w^3 - w^2 + 4*w + 9/2]', '[353, 353, -3/2*w^3 + 2*w^2 + 8*w - 15/2]', '[353, 353, 11/2*w^3 - 4*w^2 - 34*w - 7/2]', '[353, 353, 6*w^3 - 4*w^2 - 36*w - 7]', '[353, 353, 9/2*w^3 - 3*w^2 - 26*w - 5/2]', '[361, 19, 1/2*w^3 + w^2 - 3*w - 15/2]', '[361, 19, -2*w^3 + 2*w^2 + 10*w - 7]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 9/2]', '[373, 373, -3/2*w^3 + w^2 + 11*w + 1/2]', '[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 11/2]', '[373, 373, 3/2*w^3 - w^2 - 11*w + 1/2]', '[409, 409, 2*w^3 - 3*w^2 - 10*w + 2]', '[409, 409, -w^3 + 5*w + 5]', '[409, 409, -1/2*w^3 + w^2 - 7/2]', '[409, 409, 5/2*w^3 - 2*w^2 - 15*w + 5/2]', '[421, 421, -2*w^3 + w^2 + 12*w]', '[421, 421, 5/2*w^3 - 3*w^2 - 14*w + 3/2]', '[421, 421, -w^3 + 2*w^2 + 3*w - 5]', '[421, 421, 1/2*w^3 - w - 7/2]', '[443, 443, 5/2*w^3 - 3*w^2 - 15*w + 3/2]', '[443, 443, 1/2*w^3 - w^2 - 5*w + 9/2]', '[443, 443, -1/2*w^3 + 2*w^2 - 13/2]', '[443, 443, -3/2*w^3 + 10*w + 3/2]', '[463, 463, 4*w^3 - 4*w^2 - 22*w + 5]', '[463, 463, 3*w^3 - 4*w^2 - 14*w + 2]', '[463, 463, -5/2*w^3 + 2*w^2 + 14*w - 7/2]', '[463, 463, 3/2*w^3 - w^2 - 7*w - 9/2]', '[509, 509, -7/2*w^3 + 2*w^2 + 20*w + 3/2]', '[509, 509, 5/2*w^3 - w^2 - 16*w - 5/2]', '[509, 509, -5/2*w^3 + 4*w^2 + 10*w - 13/2]', '[509, 509, 9/2*w^3 - 5*w^2 - 25*w + 7/2]', '[523, 523, 3*w^3 - 3*w^2 - 16*w + 3]', '[523, 523, 2*w^3 - 2*w^2 - 9*w + 2]', '[523, 523, 5/2*w^3 - 3*w^2 - 12*w + 3/2]', '[523, 523, -5/2*w^3 + 2*w^2 + 13*w + 3/2]', '[557, 557, 3*w^3 - 3*w^2 - 16*w + 1]', '[557, 557, 5/2*w^3 - 2*w^2 - 13*w + 1/2]', '[557, 557, -2*w^3 + 2*w^2 + 9*w]', '[557, 557, -5/2*w^3 + 3*w^2 + 12*w - 7/2]', '[577, 577, -w^3 - w^2 + 6*w + 9]', '[577, 577, 7/2*w^3 - 3*w^2 - 21*w - 7/2]', '[577, 577, 1/2*w^3 - 2*w^2 - 3*w + 17/2]', '[577, 577, -5/2*w^3 + 3*w^2 + 13*w - 19/2]', '[599, 599, -4*w^3 + 4*w^2 + 22*w - 1]', '[599, 599, w^3 + w^2 - 8*w - 7]', '[599, 599, -5/2*w^3 + 3*w^2 + 16*w - 11/2]', '[599, 599, 3/2*w^3 - w^2 - 7*w - 13/2]', '[613, 613, w^3 - 5*w - 9]', '[613, 613, -2*w^3 + 3*w^2 + 10*w + 2]', '[613, 613, -1/2*w^3 + w^2 - 15/2]', '[613, 613, -5/2*w^3 + 2*w^2 + 15*w - 13/2]', '[625, 5, -5]', '[647, 647, 2*w^3 - 3*w^2 - 8*w + 6]', '[647, 647, -3*w^3 + 2*w^2 + 17*w - 1]', '[647, 647, 3/2*w^3 - w^2 - 6*w - 7/2]', '[647, 647, -7/2*w^3 + 4*w^2 + 19*w - 3/2]', '[659, 659, w^3 + w^2 - 6*w - 5]', '[659, 659, -2*w^3 + 4*w^2 + 9*w - 8]', '[659, 659, -7/2*w^3 + 3*w^2 + 22*w - 1/2]', '[659, 659, 1/2*w^3 - 7*w + 1/2]', '[701, 701, 3*w^3 - 2*w^2 - 18*w - 8]', '[701, 701, 7/2*w^3 - 3*w^2 - 21*w - 9/2]', '[701, 701, -1/2*w^3 - 2*w^2 + 3*w + 19/2]', '[701, 701, 15/2*w^3 - 5*w^2 - 45*w - 19/2]', '[727, 727, 2*w^3 - 3*w^2 - 12*w + 2]', '[727, 727, w^3 - 2*w^2 - 7*w + 7]', '[727, 727, 1/2*w^3 + w^2 - 6*w - 13/2]', '[727, 727, 3/2*w^3 - 11*w - 1/2]', '[761, 761, 3*w^3 - 4*w^2 - 18*w + 4]', '[761, 761, -w^3 + 2*w^2 + 8*w - 6]', '[761, 761, 2*w^2 - 4*w - 7]', '[761, 761, -2*w^3 + 14*w + 3]', '[769, 769, 5/2*w^3 - 3*w^2 - 15*w + 1/2]', '[769, 769, -1/2*w^3 + w^2 + 5*w - 11/2]', '[769, 769, 3/2*w^3 - 10*w - 1/2]', '[769, 769, -1/2*w^3 + 2*w^2 - 15/2]', '[829, 829, 7/2*w^3 - 4*w^2 - 20*w + 5/2]', '[829, 829, -5/2*w^3 + 4*w^2 + 12*w - 7/2]', '[829, 829, 7/2*w^3 - 3*w^2 - 21*w + 7/2]', '[829, 829, 3/2*w^3 - 3*w^2 - 5*w + 13/2]', '[863, 863, 3*w^3 - 2*w^2 - 19*w + 1]', '[863, 863, w^2 - 4*w - 4]', '[863, 863, -5/2*w^3 + 4*w^2 + 13*w - 9/2]', '[863, 863, 1/2*w^3 + w^2 - 2*w - 13/2]', '[883, 883, -4*w^3 + 4*w^2 + 22*w - 3]', '[883, 883, 3*w^3 - 2*w^2 - 16*w - 2]', '[883, 883, -3*w^3 + 4*w^2 + 14*w - 4]', '[883, 883, 2*w^3 - 2*w^2 - 8*w + 1]', '[919, 919, 1/2*w^3 - w - 11/2]', '[919, 919, -5/2*w^3 + 3*w^2 + 14*w + 1/2]', '[919, 919, w^3 - 2*w^2 - 3*w + 7]', '[919, 919, -2*w^3 + w^2 + 12*w - 2]', '[953, 953, 7/2*w^3 - 3*w^2 - 19*w + 3/2]', '[953, 953, 5/2*w^3 - 2*w^2 - 12*w - 3/2]', '[953, 953, 7/2*w^3 - 4*w^2 - 18*w + 5/2]', '[953, 953, -5/2*w^3 + 3*w^2 + 11*w - 7/2]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, -6, -1, 1], 'conductor': 17, 'degree': 4, 'dirichlet_group': [16, 1, 4, 13], 'disc_abs': 4913, 'disc_rad': 17, 'disc_sign': 1, 'frobs': [[2, [[2, 2]]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[4, 1]]], [11, [[4, 1]]], [13, [[1, 4]]], [17, [0]], [19, [[2, 2]]], [23, [[4, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[4, 1]]], [41, [[4, 1]]], [43, [[2, 2]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '4T1', 'galt': 1, 'grd': 8.37214402859269, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.4913.1', 'local_algs': ['17.4.3.1'], 'monogenic': -1, 'num_ram': 1, 'r2': 0, 'ramps': [17], 'rd': 8.37214402859, 'regulator': {'__RealLiteral__': 0, 'data': '3.46198873228', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{3} - 3 a - \\frac{3}{2} \\)', '\\( a \\)', '\\( \\frac{1}{2} a^{3} - a^{2} - 3 a + \\frac{5}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2']}