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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 12544, 'field_bad_primes': [2, 7], 'field_label': '4.4.12544.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.12544.1-16.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [2], 'level_ideal': '[16, 2, 2]', 'level_label': '16.1', 'level_norm': 16, 'parallel_weight': 2, 'short_label': '16.1-g', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2,2,1/3*w^3+w^2-2/3*w-2]', 1]], 'hecke_eigenvalues': [0, 4, 4, -2, -2, -2, -2, 8, 8, 8, 8, 0, 0, 0, 0, -4, -4, -4, -4, -18, -18, -18, -18, 10, 10, -6, -6, -6, -6, 12, 12, 12, 12, 14, 14, -2, -2, -2, -2, -20, -20, -20, -20, 16, 16, 16, 16, -6, -6, -6, -6, 8, 8, 8, 8, -6, -6, -6, -6, 34, 34, 12, 12, 12, 12, 14, 14, 14, 14, -34, -34, -8, -8, -8, -8, -24, -24, -24, -24, 30, 30, 30, 30, 28, 28, 28, 28, -30, -30, -30, -30, -34, -34, -34, -34, -24, -24, -24, -24, -36, -36, -36, -36, 34, 34, -18, -18, -18, -18, 16, 16, 16, 16, -18, -18, -18, -18, 30, 30, 30, 30, 12, 12, 12, 12, -14, -14, -14, -14, 48, 48, 48, 48, -28, -28, -28, -28, 30, 30, 30, 30, 12, 12, 12, 12, -22, -22, -12, -12, -12, -12, -6, -6, -6, -6, -30, -30, -30, -30, 36, 36, 36, 36], 'hecke_polynomial': 'x', 'label': '4.4.12544.1-16.1-g'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 12544, 'ideals': ['[1, 1, 1]', '[2, 2, 1/3*w^3 + w^2 - 2/3*w - 2]', '[4, 2, -1/3*w^3 + 5/3*w]', '[7, 7, 1/3*w^3 - 8/3*w + 2]', '[7, 7, -w + 2]', '[8, 2, -1/3*w^3 - w^2 - 1/3*w + 1]', '[9, 3, w]', '[9, 3, -1/3*w^3 + 8/3*w]', '[14, 14, 2/3*w^3 - 13/3*w + 1]', '[14, 14, 1/3*w^3 - 2/3*w - 1]', '[16, 2, 2]', '[18, 6, 2/3*w^3 + w^2 - 7/3*w - 2]', '[18, 6, -w - 3]', '[25, 5, 1/3*w^3 - w^2 - 5/3*w + 4]', '[25, 5, -1/3*w^3 - w^2 + 5/3*w + 4]', '[28, 14, -2/3*w^3 + w^2 + 10/3*w - 5]', '[28, 14, -2/3*w^3 + w^2 + 10/3*w - 3]', '[31, 31, 1/3*w^3 + w^2 - 5/3*w - 2]', '[31, 31, 1/3*w^3 + w^2 - 5/3*w - 6]', '[31, 31, 1/3*w^3 - w^2 - 5/3*w + 6]', '[31, 31, 1/3*w^3 - w^2 - 5/3*w + 2]', '[32, 4, 2/3*w^3 + 2*w^2 - 4/3*w - 4]', '[36, 6, -w^2 + 5]', '[36, 6, -w^2 + 3]', '[47, 47, 1/3*w^3 + w^2 - 8/3*w - 3]', '[47, 47, -w^2 - w + 5]', '[47, 47, w^2 - w - 5]', '[47, 47, -1/3*w^3 + w^2 + 8/3*w - 3]', '[49, 7, -w^2 + 4]', '[49, 7, 2/3*w^3 - 10/3*w - 1]', '[49, 7, 2/3*w^3 - 10/3*w + 1]', '[50, 10, -2/3*w^3 + 7/3*w - 1]', '[50, 10, -1/3*w^3 - w^2 + 2/3*w]', '[56, 14, 1/3*w^3 - w^2 - 5/3*w + 1]', '[56, 14, -1/3*w^3 + w^2 + 5/3*w - 7]', '[62, 62, 2/3*w^3 - w^2 - 13/3*w + 4]', '[62, 62, 1/3*w^3 - w^2 - 2/3*w + 4]', '[62, 62, 1/3*w^3 + w^2 - 2/3*w - 4]', '[62, 62, 2/3*w^3 + w^2 - 13/3*w - 4]', '[63, 21, -2/3*w^3 + 16/3*w + 3]', '[63, 21, w^2 + 2*w]', '[63, 21, -2*w - 3]', '[63, 21, 2/3*w^3 + w^2 - 16/3*w - 8]', '[64, 4, -2/3*w^3 + 10/3*w]', '[72, 6, w^3 + w^2 - 5*w - 3]', '[72, 6, -1/3*w^3 - w^2 - 1/3*w - 1]', '[81, 3, 3]', '[81, 9, -w^3 + 6*w]', '[81, 9, -2/3*w^3 + 7/3*w]', '[94, 94, 1/3*w^3 + 2*w^2 + 4/3*w - 1]', '[94, 94, -2/3*w^3 - w^2 + 7/3*w + 4]', '[94, 94, -4/3*w^3 - 3*w^2 + 5/3*w + 2]', '[94, 94, 5/3*w^3 + 4*w^2 - 10/3*w - 5]', '[98, 14, -2/3*w^3 - 2*w^2 + 1/3*w + 1]', '[98, 14, 4/3*w^3 - w^2 - 29/3*w + 8]', '[98, 14, w^3 - 2*w^2 - 6*w + 11]', '[100, 10, -1/3*w^3 + 11/3*w - 2]', '[100, 10, -1/3*w^3 + 11/3*w + 2]', '[103, 103, 2/3*w^3 + w^2 - 10/3*w - 2]', '[103, 103, -2/3*w^3 + w^2 + 10/3*w - 6]', '[103, 103, 2/3*w^3 + w^2 - 10/3*w - 6]', '[103, 103, 1/3*w^3 + 2*w^2 + 7/3*w - 1]', '[112, 14, 2/3*w^3 - 16/3*w + 4]', '[112, 14, -2*w + 4]', '[113, 113, -2/3*w^3 + 16/3*w + 1]', '[113, 113, 2*w - 1]', '[113, 113, -2*w - 1]', '[113, 113, 2/3*w^3 - 16/3*w + 1]', '[121, 11, 1/3*w^3 - 11/3*w + 5]', '[121, 11, -w^3 + w^2 + 5*w - 4]', '[124, 62, -1/3*w^3 - 1/3*w - 2]', '[124, 62, w^3 - 7*w - 2]', '[124, 62, -w^3 + 7*w - 2]', '[124, 62, 1/3*w^3 + 1/3*w - 2]', '[126, 42, w^2 - w - 6]', '[126, 42, 1/3*w^3 - w^2 - 8/3*w + 2]', '[126, 42, 1/3*w^3 + w^2 - 8/3*w - 2]', '[126, 42, w^2 + w - 6]', '[128, 4, -2/3*w^3 - 2*w^2 - 2/3*w + 2]', '[137, 137, -w - 4]', '[137, 137, 1/3*w^3 - 8/3*w - 4]', '[137, 137, -1/3*w^3 + 8/3*w - 4]', '[137, 137, w - 4]', '[144, 6, 2*w]', '[144, 6, -2/3*w^3 + 16/3*w]', '[162, 6, w^3 + 3*w^2 - 2*w - 6]', '[162, 18, 2/3*w^3 + 2*w^2 - 7/3*w - 7]', '[162, 18, -w^2 - 3*w]', '[167, 167, -4/3*w^3 + w^2 + 23/3*w - 3]', '[167, 167, -w^3 + w^2 + 4*w - 5]', '[167, 167, w^3 + w^2 - 4*w - 5]', '[167, 167, 4/3*w^3 + w^2 - 23/3*w - 3]', '[169, 13, 1/3*w^3 - 11/3*w + 1]', '[169, 13, -1/3*w^3 + 11/3*w + 1]', '[175, 35, -1/3*w^3 - w^2 + 2/3*w + 5]', '[175, 35, 2/3*w^3 - w^2 - 13/3*w + 3]', '[175, 35, 1/3*w^3 - w^2 - 2/3*w + 5]', '[175, 35, 2/3*w^3 + w^2 - 13/3*w - 3]', '[188, 94, w^2 - 2*w - 5]', '[188, 94, -2/3*w^3 + w^2 + 16/3*w - 3]', '[188, 94, 2/3*w^3 + w^2 - 16/3*w - 3]', '[188, 94, -w^2 - 2*w + 5]', '[193, 193, 2/3*w^3 + 2*w^2 - 7/3*w - 6]', '[193, 193, 4/3*w^3 + 4*w^2 - 8/3*w - 7]', '[193, 193, -5/3*w^3 - 5*w^2 + 7/3*w + 8]', '[193, 193, -w^3 - 3*w^2 + 2*w + 7]', '[196, 14, -1/3*w^3 + 11/3*w]', '[196, 14, -1/3*w^3 + 5/3*w - 4]', '[196, 14, 1/3*w^3 - 5/3*w - 4]', '[199, 199, 1/3*w^3 + w^2 - 8/3*w - 1]', '[199, 199, w^2 + w - 7]', '[199, 199, w^2 - w - 7]', '[199, 199, -1/3*w^3 + w^2 + 8/3*w - 1]', '[200, 10, 1/3*w^3 + w^2 - 5/3*w + 1]', '[200, 10, w^3 + w^2 - 3*w - 1]', '[206, 206, -w^2 - w + 8]', '[206, 206, 2/3*w^3 + 2*w^2 + 5/3*w + 1]', '[206, 206, -2/3*w^3 - 2*w^2 + 1/3*w + 5]', '[206, 206, w^2 - w - 8]', '[217, 217, -1/3*w^3 + w^2 - 4/3*w - 1]', '[217, 217, w^2 + w + 1]', '[217, 217, -4/3*w^3 + w^2 + 29/3*w - 7]', '[217, 217, -1/3*w^3 + w^2 + 8/3*w - 9]', '[217, 217, -1/3*w^3 - w^2 + 8/3*w + 9]', '[217, 217, 4/3*w^3 + w^2 - 29/3*w - 7]', '[217, 217, w^2 - w + 1]', '[217, 217, -1/3*w^3 - w^2 - 4/3*w + 1]', '[223, 223, -w^3 + w^2 + 7*w - 4]', '[223, 223, 2/3*w^3 + w^2 - 10/3*w]', '[223, 223, -2/3*w^3 + w^2 + 10/3*w]', '[223, 223, -w^3 - w^2 + 7*w + 4]', '[224, 28, 4/3*w^3 - 26/3*w + 2]', '[224, 28, 2/3*w^3 - 4/3*w - 2]', '[225, 15, -w^3 + w^2 + 4*w - 3]', '[225, 15, -w^3 - w^2 + 4*w + 3]', '[225, 15, -4/3*w^3 - w^2 + 23/3*w + 5]', '[225, 15, -4/3*w^3 + w^2 + 23/3*w - 5]', '[226, 226, -7/3*w^3 - 5*w^2 + 14/3*w + 8]', '[226, 226, -w^3 - w^2 + 4*w + 2]', '[226, 226, 5/3*w^3 + 3*w^2 - 16/3*w - 6]', '[226, 226, 5/3*w^3 + 3*w^2 - 10/3*w - 4]', '[233, 233, w^3 - 4*w - 2]', '[233, 233, -4/3*w^3 + 23/3*w - 2]', '[233, 233, 4/3*w^3 - 23/3*w - 2]', '[233, 233, w^3 - 4*w + 2]', '[242, 22, 1/3*w^3 - w^2 + 4/3*w + 2]', '[242, 22, -1/3*w^3 + 2*w^2 + 8/3*w - 11]', '[248, 62, -1/3*w^3 + w^2 + 11/3*w - 7]', '[248, 62, -1/3*w^3 - w^2 + 11/3*w + 1]', '[248, 62, 1/3*w^3 - w^2 - 11/3*w + 1]', '[248, 62, 1/3*w^3 + w^2 - 11/3*w - 7]', '[252, 42, -w^3 - 2*w^2 + 5*w + 10]', '[252, 42, -w^3 - 2*w^2 + 3*w + 6]', '[252, 42, w^3 + 2*w^2 - 5*w - 6]', '[252, 42, 5/3*w^3 + 2*w^2 - 31/3*w - 10]', '[256, 4, 4]', '[271, 271, -5/3*w^3 - 4*w^2 + 13/3*w + 7]', '[271, 271, -2/3*w^3 - w^2 + 1/3*w - 1]', '[271, 271, -5/3*w^3 - 4*w^2 + 10/3*w + 8]', '[271, 271, 2/3*w^3 + 3*w^2 + 2/3*w - 4]', '[274, 274, -2*w^3 - 5*w^2 + 5*w + 10]', '[274, 274, -1/3*w^3 - 2*w^2 + 2/3*w + 5]', '[274, 274, -7/3*w^3 - 6*w^2 + 14/3*w + 11]', '[274, 274, -2/3*w^3 - 3*w^2 + 1/3*w + 6]', '[279, 93, 2/3*w^3 + w^2 - 7/3*w - 5]', '[279, 93, -w^3 + w^2 + 6*w - 3]', '[279, 93, w^3 - 7*w - 3]', '[279, 93, -1/3*w^3 - 1/3*w - 3]', '[279, 93, -1/3*w^3 - 1/3*w + 3]', '[279, 93, w^3 - 7*w + 3]', '[279, 93, w^3 + w^2 - 6*w - 3]', '[279, 93, -2/3*w^3 + w^2 + 7/3*w - 5]', '[281, 281, -1/3*w^3 + w^2 + 2/3*w - 11]', '[281, 281, -2/3*w^3 + w^2 + 16/3*w - 10]', '[281, 281, 2/3*w^3 + w^2 - 16/3*w - 10]', '[281, 281, 1/3*w^3 + w^2 - 2/3*w - 11]', '[288, 12, 4/3*w^3 + 2*w^2 - 14/3*w - 4]', '[288, 12, -2*w - 6]', '[289, 17, -w^3 + 5*w - 1]', '[289, 17, w^3 - 5*w - 1]', '[311, 311, -4/3*w^3 - 3*w^2 + 2/3*w + 2]', '[311, 311, 2/3*w^3 + 3*w^2 + 5/3*w - 3]', '[311, 311, -w^3 - 2*w^2 + 4*w + 4]', '[311, 311, -5/3*w^3 - 4*w^2 + 7/3*w + 7]', '[324, 6, -w^3 + 5*w]', '[324, 18, w^2 + 1]', '[324, 18, -w^2 + 9]', '[329, 329, -1/3*w^3 + w^2 - 1/3*w + 2]', '[329, 329, 5/3*w^3 - 2*w^2 - 37/3*w + 13]', '[329, 329, -1/3*w^3 + 2*w^2 - 7/3*w - 3]', '[329, 329, w^3 - w^2 - 7*w + 10]', '[329, 329, -5/3*w^3 + 2*w^2 + 25/3*w - 7]', '[329, 329, -5/3*w^3 + 3*w^2 + 31/3*w - 14]', '[329, 329, -w^3 + 3*w^2 + 3*w - 10]', '[329, 329, -5/3*w^3 + 2*w^2 + 25/3*w - 9]', '[334, 334, -5/3*w^3 - 4*w^2 + 4/3*w + 7]', '[334, 334, -2/3*w^3 + w^2 + 13/3*w - 2]', '[334, 334, 2/3*w^3 + w^2 - 13/3*w - 2]', '[334, 334, -7/3*w^3 - 6*w^2 + 2/3*w + 5]', '[337, 337, w^3 - w^2 - 8*w + 7]', '[337, 337, -1/3*w^3 - 2*w^2 - 10/3*w]', '[337, 337, w^2 + 3*w - 1]', '[337, 337, -w^3 - w^2 + 8*w + 7]', '[338, 26, -4/3*w^3 - 2*w^2 + 11/3*w + 3]', '[338, 26, 2*w^3 + 4*w^2 - 5*w - 7]', '[343, 7, 4/3*w^3 - 2*w^2 - 23/3*w + 8]', '[343, 7, w^3 - 2*w^2 - 4*w + 8]', '[343, 49, -2/3*w^3 - w^2 + 19/3*w + 9]', '[343, 49, 1/3*w^3 - w^2 - 14/3*w - 1]', '[350, 70, w^3 + 2*w^2 - 2*w - 5]', '[350, 70, 2*w^3 - 2*w^2 - 13*w + 11]', '[350, 70, 4/3*w^3 - 29/3*w + 3]', '[350, 70, -1/3*w^3 - 4/3*w - 3]', '[361, 19, 2*w^2 - 11]', '[361, 19, -2*w^2 + 5]', '[367, 367, -4/3*w^3 - w^2 + 20/3*w + 8]', '[367, 367, 7/3*w^3 + 5*w^2 - 14/3*w - 9]', '[367, 367, 2*w^3 + 4*w^2 - 3*w - 4]', '[367, 367, 4/3*w^3 - w^2 - 20/3*w + 8]', '[376, 94, -5/3*w^3 - 3*w^2 + 13/3*w + 7]', '[376, 94, 7/3*w^3 + 5*w^2 - 17/3*w - 7]', '[376, 94, -1/3*w^3 + w^2 + 11/3*w + 1]', '[376, 94, -7/3*w^3 - 5*w^2 + 11/3*w + 5]', '[383, 383, 4/3*w^3 + 3*w^2 - 11/3*w - 3]', '[383, 383, -w^3 - w^2 + 5*w - 2]', '[383, 383, w^3 - w^2 - 5*w - 2]', '[383, 383, w^3 + w^2 - 5*w - 10]', '[386, 386, w^3 - 4*w + 1]', '[386, 386, 4/3*w^3 - 23/3*w + 1]', '[386, 386, -4/3*w^3 + 23/3*w + 1]', '[386, 386, -w^3 + 4*w + 1]', '[392, 14, 5/3*w^3 + 3*w^2 - 13/3*w - 5]', '[392, 14, -5/3*w^3 + w^2 + 37/3*w - 9]', '[392, 14, -5/3*w^3 + 3*w^2 + 31/3*w - 17]', '[398, 398, -4/3*w^3 - 3*w^2 + 11/3*w + 8]', '[398, 398, 7/3*w^3 + 6*w^2 - 14/3*w - 9]', '[398, 398, w^3 + 4*w^2 - 5]', '[398, 398, 2/3*w^3 + w^2 - 1/3*w + 2]', '[400, 10, 2/3*w^3 - 2*w^2 - 10/3*w + 8]', '[400, 10, -2/3*w^3 - 2*w^2 + 10/3*w + 8]', '[401, 401, 2/3*w^3 + 2*w^2 - 13/3*w - 10]', '[401, 401, -1/3*w^3 - w^2 + 14/3*w + 5]', '[401, 401, 1/3*w^3 - w^2 - 14/3*w + 5]', '[401, 401, -2/3*w^3 + 2*w^2 + 13/3*w - 10]', '[412, 206, -1/3*w^3 - 1/3*w - 4]', '[412, 206, w^3 - 7*w + 4]', '[412, 206, w^3 - 7*w - 4]', '[412, 206, -5/3*w^3 - 4*w^2 + 13/3*w + 10]', '[423, 141, w^3 - 3*w - 3]', '[423, 141, w^3 + w^2 - 5*w - 8]', '[423, 141, -5/3*w^3 + 31/3*w - 3]', '[423, 141, -w^3 - w^2 + 5*w]', '[423, 141, w^3 - w^2 - 5*w]', '[423, 141, 5/3*w^3 - 31/3*w - 3]', '[423, 141, w^3 - w^2 - 5*w + 8]', '[423, 141, w^3 - 3*w + 3]', '[434, 434, w + 5]', '[434, 434, -1/3*w^3 - 2*w^2 + 2/3*w + 7]', '[434, 434, -1/3*w^3 + 8/3*w - 5]', '[434, 434, -2/3*w^3 - 2*w^2 + 13/3*w + 9]', '[434, 434, 2/3*w^3 - 2*w^2 - 13/3*w + 9]', '[434, 434, -1/3*w^3 + 8/3*w + 5]', '[434, 434, -1/3*w^3 + 2*w^2 + 2/3*w - 7]', '[434, 434, -w + 5]', '[439, 439, -4/3*w^3 - 2*w^2 + 26/3*w + 9]', '[439, 439, -2/3*w^3 - 2*w^2 + 4/3*w + 7]', '[439, 439, 2/3*w^3 - 2*w^2 - 4/3*w + 7]', '[439, 439, 4/3*w^3 - 2*w^2 - 26/3*w + 9]', '[441, 21, -w^3 + 4*w]', '[441, 21, 1/3*w^3 + 2*w^2 - 8/3*w - 10]', '[441, 21, -1/3*w^3 + 2*w^2 + 8/3*w - 10]', '[441, 21, -4/3*w^3 + 23/3*w]', '[441, 21, 2*w^2 - w - 6]', '[441, 21, 2*w^2 + w - 6]', '[446, 446, 8/3*w^3 + 8*w^2 - 7/3*w - 11]', '[446, 446, 1/3*w^3 - w^2 - 14/3*w - 2]', '[446, 446, 5/3*w^3 + 3*w^2 - 16/3*w - 4]', '[446, 446, -4/3*w^3 - 4*w^2 + 11/3*w + 7]', '[448, 28, -4/3*w^3 + 2*w^2 + 20/3*w - 10]', '[448, 28, -4/3*w^3 + 2*w^2 + 20/3*w - 6]', '[449, 449, -5/3*w^3 + w^2 + 28/3*w - 3]', '[449, 449, -4/3*w^3 + w^2 + 17/3*w - 5]', '[449, 449, 4/3*w^3 + w^2 - 17/3*w - 5]', '[449, 449, 5/3*w^3 + w^2 - 28/3*w - 3]', '[450, 30, 2*w^2 - w - 9]', '[450, 30, w^2 - 3*w - 2]', '[450, 30, -w^3 - w^2 + 8*w + 6]', '[450, 30, -1/3*w^3 - 2*w^2 + 8/3*w + 7]', '[452, 226, -1/3*w^3 - 2*w^2 + 5/3*w + 10]', '[452, 226, 1/3*w^3 - 2*w^2 - 5/3*w + 6]', '[452, 226, 1/3*w^3 + 2*w^2 - 5/3*w - 6]', '[452, 226, -1/3*w^3 + 2*w^2 + 5/3*w - 10]', '[457, 457, 2/3*w^3 + 3*w^2 - 1/3*w - 7]', '[457, 457, -3*w^3 - 8*w^2 + 5*w + 13]', '[457, 457, 2/3*w^3 + 3*w^2 - 4/3*w - 6]', '[457, 457, -5/3*w^3 - 4*w^2 + 16/3*w + 10]', '[466, 466, -w^3 - 4*w^2 - 2*w + 5]', '[466, 466, 8/3*w^3 + 7*w^2 - 7/3*w - 10]', '[466, 466, 4/3*w^3 + 3*w^2 + 1/3*w - 2]', '[466, 466, -1/3*w^3 + 14/3*w + 3]', '[479, 479, 1/3*w^3 + 2*w^2 - 11/3*w - 5]', '[479, 479, -1/3*w^3 - 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7/3*w - 12]', '[1828, 914, -w^3 - 2*w^2 - w + 2]', '[1828, 914, 2/3*w^3 + 3*w^2 + 14/3*w + 1]', '[1847, 1847, -3*w^2 - 3*w + 5]', '[1847, 1847, 7/3*w^3 - 44/3*w + 4]', '[1847, 1847, -7/3*w^3 + 44/3*w + 4]', '[1847, 1847, 1/3*w^3 + 3*w^2 - 11/3*w - 18]', '[1849, 43, 5/3*w^3 - w^2 - 25/3*w + 4]', '[1849, 43, -5/3*w^3 - w^2 + 25/3*w + 4]', '[1854, 618, -w^3 - w^2 + 8*w]', '[1854, 618, -8/3*w^3 + 55/3*w - 3]', '[1854, 618, w^3 - w^2 - 4*w + 12]', '[1854, 618, -1/3*w^3 + 2*w^2 + 26/3*w + 5]', '[1854, 618, -5/3*w^3 - 2*w^2 + 22/3*w + 1]', '[1854, 618, -3*w^3 - 5*w^2 + 16*w + 24]', '[1854, 618, 8/3*w^3 - 55/3*w - 3]', '[1854, 618, w^3 - w^2 - 8*w]', '[1864, 466, -7/3*w^3 - 7*w^2 + 17/3*w + 13]', '[1864, 466, 7/3*w^3 + 7*w^2 - 11/3*w - 15]', '[1864, 466, -w^3 - 3*w^2 + 5*w + 11]', '[1864, 466, -11/3*w^3 - 11*w^2 + 13/3*w + 17]', '[1873, 1873, -4/3*w^3 + w^2 + 29/3*w - 13]', '[1873, 1873, -7/3*w^3 + 2*w^2 + 38/3*w - 12]', '[1873, 1873, 7/3*w^3 + 2*w^2 - 38/3*w - 12]', '[1873, 1873, 4/3*w^3 + w^2 - 29/3*w - 13]', '[1879, 1879, -5/3*w^3 + 2*w^2 + 28/3*w - 6]', '[1879, 1879, -4/3*w^3 - 2*w^2 + 17/3*w + 10]', '[1879, 1879, -7/3*w^3 - 5*w^2 + 8/3*w + 1]', '[1879, 1879, 8/3*w^3 - 4*w^2 - 43/3*w + 20]', '[1897, 1897, -1/3*w^3 - 3*w^2 + 5/3*w + 8]', '[1897, 1897, -5/3*w^3 + 16/3*w + 2]', '[1897, 1897, 2/3*w^3 - w^2 + 5/3*w + 1]', '[1897, 1897, 2/3*w^3 - 2*w^2 - 4/3*w - 1]', '[1897, 1897, -8/3*w^3 + 49/3*w - 2]', '[1897, 1897, -1/3*w^3 - 3*w^2 + 5/3*w + 16]', '[1897, 1897, 4/3*w^3 - 2*w^2 - 26/3*w + 17]', '[1897, 1897, 7/3*w^3 - w^2 - 50/3*w + 7]', '[1906, 1906, -2/3*w^3 + 3*w^2 + 13/3*w - 10]', '[1906, 1906, -3*w^3 - 10*w^2 + 2*w + 17]', '[1906, 1906, -7/3*w^3 - 6*w^2 + 26/3*w + 15]', '[1906, 1906, 2/3*w^3 + 3*w^2 - 13/3*w - 10]', '[1913, 1913, -2/3*w^3 - w^2 + 22/3*w + 2]', '[1913, 1913, -2/3*w^3 + w^2 + 22/3*w - 6]', '[1913, 1913, 2/3*w^3 + w^2 - 22/3*w - 6]', '[1913, 1913, 2/3*w^3 - w^2 - 22/3*w + 2]', '[1916, 958, -1/3*w^3 + 2*w^2 - 7/3*w - 8]', '[1916, 958, -5/3*w^3 - 2*w^2 + 37/3*w + 8]', '[1916, 958, -5/3*w^3 + 2*w^2 + 37/3*w - 8]', '[1916, 958, -1/3*w^3 - 2*w^2 - 7/3*w + 8]', '[1918, 1918, -4/3*w^3 - 2*w^2 + 11/3*w + 7]', '[1918, 1918, -w^3 + w^2 + 2]', '[1918, 1918, -5/3*w^3 - w^2 + 16/3*w + 6]', '[1918, 1918, -4/3*w^3 + 2*w^2 + 5/3*w + 1]', '[1918, 1918, -8/3*w^3 - w^2 + 49/3*w + 2]', '[1918, 1918, -3*w^3 + 2*w^2 + 20*w - 17]', '[1918, 1918, -7/3*w^3 - 2*w^2 + 44/3*w + 9]', '[1918, 1918, -8/3*w^3 + w^2 + 55/3*w - 10]', '[1922, 62, w^3 + 2*w^2 - 6*w - 17]', '[1922, 62, 1/3*w^3 - w^2 - 14/3*w + 14]', '[1922, 62, w^3 + 3*w^2 + 2*w - 2]', '[1922, 62, 8/3*w^3 + w^2 - 49/3*w - 8]', '[1922, 62, 7/3*w^3 + 4*w^2 - 20/3*w - 7]', '[1922, 62, -4/3*w^3 - 4*w^2 + 17/3*w + 11]', '[1922, 1922, 1/3*w^3 + 3*w^2 - 8/3*w - 16]', '[1922, 1922, -3*w^2 + w + 8]', '[1922, 1922, -3*w^2 - w + 8]', '[1922, 1922, -1/3*w^3 + 3*w^2 + 8/3*w - 16]', '[1936, 22, 2/3*w^3 - 22/3*w + 10]', '[1936, 22, -2*w^3 + 2*w^2 + 10*w - 8]', '[1951, 1951, -2*w^3 + 3*w^2 + 9*w - 13]', '[1951, 1951, 2*w^3 - 3*w^2 - 11*w + 17]', '[1951, 1951, -7/3*w^3 + 3*w^2 + 38/3*w - 11]', '[1951, 1951, 5/3*w^3 - 3*w^2 - 22/3*w + 7]', '[1953, 651, 1/3*w^3 - w^2 + 1/3*w - 4]', '[1953, 651, w^3 - 9*w + 3]', '[1953, 651, -1/3*w^3 + 17/3*w + 3]', '[1953, 651, -5/3*w^3 + w^2 + 22/3*w - 5]', '[1953, 651, 2*w^3 - w^2 - 11*w + 3]', '[1953, 651, -2/3*w^3 + 3*w^2 + 7/3*w - 9]', '[1953, 651, -w^3 - 3*w^2 + 6*w + 15]', '[1953, 651, w^3 - w^2 - 7*w + 12]', '[1953, 651, w^3 + w^2 - 7*w - 12]', '[1953, 651, w^3 - 3*w^2 - 6*w + 15]', '[1953, 651, -2/3*w^3 - 3*w^2 + 7/3*w + 9]', '[1953, 651, 2*w^3 + w^2 - 11*w - 3]', '[1953, 651, 5/3*w^3 + w^2 - 22/3*w - 5]', '[1953, 651, -1/3*w^3 + 17/3*w - 3]', '[1953, 651, -w^3 + 9*w + 3]', '[1953, 651, -1/3*w^3 - w^2 - 1/3*w - 4]', '[1954, 1954, 7/3*w^3 - 50/3*w - 1]', '[1954, 1954, -2/3*w^3 - 3*w^2 + 13/3*w + 16]', '[1954, 1954, 2/3*w^3 - 3*w^2 - 13/3*w + 16]', '[1954, 1954, -1/3*w^3 + 3*w^2 + 2/3*w - 8]', '[1966, 1966, 5/3*w^3 + 5*w^2 + 8/3*w]', '[1966, 1966, 1/3*w^3 - 2*w^2 - 2/3*w + 15]', '[1966, 1966, w^3 - 3*w^2 - 4*w + 4]', '[1966, 1966, -w^3 - 3*w^2 + 8]', '[1967, 1967, -5/3*w^3 + 4*w^2 + 37/3*w - 25]', '[1967, 1967, -14/3*w^3 + 4*w^2 + 103/3*w - 36]', '[1967, 1967, -2*w^3 + 13*w - 4]', '[1967, 1967, -1/3*w^3 + 29/3*w - 19]', '[1967, 1967, -13/3*w^3 + 3*w^2 + 83/3*w - 24]', '[1967, 1967, -7/3*w^3 + 2*w^2 + 62/3*w - 26]', '[1967, 1967, 1/3*w^3 + 2*w^2 - 2/3*w - 14]', '[1967, 1967, -3*w^3 + w^2 + 25*w - 20]', '[1984, 124, -2/3*w^3 - 2/3*w - 4]', '[1984, 124, 2*w^3 - 14*w - 4]', '[1984, 124, -2*w^3 + 14*w - 4]', '[1984, 124, 2/3*w^3 + 2/3*w - 4]', '[2007, 669, -w^3 + 2*w^2 - 6]', '[2007, 669, -w^3 - w^2 + 4*w + 9]', '[2007, 669, 4/3*w^3 - 3*w^2 - 23/3*w + 21]', '[2007, 669, 2*w^2 + 3*w - 10]', '[2007, 669, 2*w^2 - 3*w - 10]', '[2007, 669, -4/3*w^3 - 3*w^2 + 23/3*w + 21]', '[2007, 669, w^3 - w^2 - 4*w + 9]', '[2007, 669, w^3 + 2*w^2 - 6]', '[2012, 1006, -2/3*w^3 + w^2 + 4/3*w - 7]', '[2012, 1006, 4/3*w^3 + w^2 - 26/3*w - 1]', '[2012, 1006, 4/3*w^3 - w^2 - 26/3*w + 1]', '[2012, 1006, -2/3*w^3 - w^2 + 4/3*w + 7]', '[2016, 84, 2*w^2 - 2*w - 12]', '[2016, 84, 2/3*w^3 - 2*w^2 - 16/3*w + 4]', '[2016, 84, 2/3*w^3 + 2*w^2 - 16/3*w - 4]', '[2016, 84, 2*w^2 + 2*w - 12]', '[2017, 2017, 5/3*w^3 + 6*w^2 + 2/3*w - 4]', '[2017, 2017, -7/3*w^3 - w^2 + 35/3*w + 10]', '[2017, 2017, -7/3*w^3 + w^2 + 35/3*w - 10]', '[2017, 2017, -8/3*w^3 - 7*w^2 + 13/3*w + 7]', '[2018, 2018, -10/3*w^3 - 9*w^2 + 17/3*w + 10]', '[2018, 2018, -1/3*w^3 + 8/3*w + 7]', '[2018, 2018, 7/3*w^3 + 6*w^2 - 2/3*w - 1]', '[2018, 2018, 4/3*w^3 + 4*w^2 + 7/3*w + 3]', '[2023, 119, -7/3*w^3 + 3*w^2 + 38/3*w - 17]', '[2023, 119, 5/3*w^3 - 3*w^2 - 22/3*w + 13]', '[2023, 119, 2*w^3 - 3*w^2 - 9*w + 7]', '[2023, 119, -2*w^3 + 3*w^2 + 11*w - 11]', '[2025, 15, w^3 - 3*w^2 - 5*w + 12]', '[2025, 15, -w^3 - 3*w^2 + 5*w + 12]', '[2025, 45, -2*w^3 - w^2 + 15*w + 9]', '[2025, 45, -2*w^3 + w^2 + 15*w - 9]', '[2025, 45, 1/3*w^3 + w^2 + 10/3*w + 1]', '[2025, 45, 1/3*w^3 - w^2 + 10/3*w - 1]', '[2034, 678, 2*w^2 + 7*w + 3]', '[2034, 678, -8/3*w^3 - 7*w^2 + 19/3*w + 14]', '[2034, 678, -2/3*w^3 - 3*w^2 + 7/3*w + 12]', '[2034, 678, -2*w^3 + 15*w + 3]', '[2034, 678, 2*w^3 - 17*w - 9]', '[2034, 678, 2*w^3 + 5*w^2 - 7*w - 16]', '[2034, 678, 4/3*w^3 + 5*w^2 - 5/3*w - 10]', '[2034, 678, -2*w^2 - 5*w + 3]', '[2048, 8, -4/3*w^3 - 4*w^2 - 4/3*w + 4]', '[2063, 2063, -2/3*w^3 - 2*w^2 + 19/3*w + 14]', '[2063, 2063, -1/3*w^3 + 2*w^2 + 14/3*w - 2]', '[2063, 2063, -10/3*w^3 - 7*w^2 + 29/3*w + 13]', '[2063, 2063, -2/3*w^3 + 2*w^2 + 19/3*w - 14]', '[2066, 2066, 5/3*w^3 + 4*w^2 + 2/3*w - 3]', '[2066, 2066, 4/3*w^3 + 5*w^2 + 7/3*w - 6]', '[2066, 2066, -w^2 - 5*w - 2]', '[2066, 2066, -3*w^3 - 8*w^2 + 2*w + 11]', '[2078, 2078, -2*w^3 - 7*w^2 - w + 8]', '[2078, 2078, -7/3*w^3 - 6*w^2 + 8/3*w + 11]', '[2078, 2078, 5/3*w^3 + 4*w^2 + 2/3*w - 1]', '[2078, 2078, -4/3*w^3 - 3*w^2 + 17/3*w + 6]', '[2081, 2081, -w^3 + 2*w^2 + 7*w - 17]', '[2081, 2081, 8/3*w^3 + w^2 - 49/3*w - 5]', '[2081, 2081, -8/3*w^3 + w^2 + 49/3*w - 5]', '[2081, 2081, w^3 + 2*w^2 - 7*w - 17]', '[2097, 699, 2/3*w^3 + 3*w^2 - 16/3*w - 12]', '[2097, 699, -3*w^2 - 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1]', '[113, 113, -2*w - 1]', '[113, 113, 2/3*w^3 - 16/3*w + 1]', '[121, 11, 1/3*w^3 - 11/3*w + 5]', '[121, 11, -w^3 + w^2 + 5*w - 4]', '[137, 137, -w - 4]', '[137, 137, 1/3*w^3 - 8/3*w - 4]', '[137, 137, -1/3*w^3 + 8/3*w - 4]', '[137, 137, w - 4]', '[167, 167, -4/3*w^3 + w^2 + 23/3*w - 3]', '[167, 167, -w^3 + w^2 + 4*w - 5]', '[167, 167, w^3 + w^2 - 4*w - 5]', '[167, 167, 4/3*w^3 + w^2 - 23/3*w - 3]', '[169, 13, 1/3*w^3 - 11/3*w + 1]', '[169, 13, -1/3*w^3 + 11/3*w + 1]', '[193, 193, 2/3*w^3 + 2*w^2 - 7/3*w - 6]', '[193, 193, 4/3*w^3 + 4*w^2 - 8/3*w - 7]', '[193, 193, -5/3*w^3 - 5*w^2 + 7/3*w + 8]', '[193, 193, -w^3 - 3*w^2 + 2*w + 7]', '[199, 199, 1/3*w^3 + w^2 - 8/3*w - 1]', '[199, 199, w^2 + w - 7]', '[199, 199, w^2 - w - 7]', '[199, 199, -1/3*w^3 + w^2 + 8/3*w - 1]', '[223, 223, -w^3 + w^2 + 7*w - 4]', '[223, 223, 2/3*w^3 + w^2 - 10/3*w]', '[223, 223, -2/3*w^3 + w^2 + 10/3*w]', '[223, 223, -w^3 - w^2 + 7*w + 4]', '[233, 233, w^3 - 4*w - 2]', '[233, 233, -4/3*w^3 + 23/3*w - 2]', '[233, 233, 4/3*w^3 - 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13/3*w - 1]', '[503, 503, -1/3*w^3 + w^2 + 2/3*w - 7]', '[503, 503, 1/3*w^3 + w^2 - 2/3*w - 7]', '[503, 503, -2/3*w^3 + w^2 + 13/3*w - 1]', '[529, 23, -1/3*w^3 + 5/3*w - 5]', '[529, 23, 1/3*w^3 - 5/3*w - 5]', '[569, 569, 2*w^2 + w - 8]', '[569, 569, 1/3*w^3 + 2*w^2 - 8/3*w - 8]', '[569, 569, -1/3*w^3 + 2*w^2 + 8/3*w - 8]', '[569, 569, 2*w^2 - w - 8]', '[607, 607, -2/3*w^3 - w^2 + 13/3*w - 1]', '[607, 607, 1/3*w^3 - w^2 - 2/3*w + 9]', '[607, 607, -1/3*w^3 - w^2 + 2/3*w + 9]', '[607, 607, 2/3*w^3 - w^2 - 13/3*w - 1]', '[617, 617, 1/3*w^3 + 2*w^2 - 5/3*w - 9]', '[617, 617, -1/3*w^3 + 2*w^2 + 5/3*w - 7]', '[617, 617, 1/3*w^3 + 2*w^2 - 5/3*w - 7]', '[617, 617, -1/3*w^3 + 2*w^2 + 5/3*w - 9]', '[641, 641, -2*w^3 - 6*w^2 + 3*w + 10]', '[641, 641, 4/3*w^3 + 4*w^2 - 8/3*w - 9]', '[641, 641, -w^3 - 3*w^2 + 3*w + 8]', '[641, 641, 5/3*w^3 + 5*w^2 - 10/3*w - 9]', '[647, 647, 2/3*w^3 + 2*w^2 - 22/3*w - 5]', '[647, 647, -5/3*w^3 - 3*w^2 + 19/3*w + 10]', '[647, 647, 4/3*w^3 + 2*w^2 - 8/3*w + 1]', '[647, 647, -2/3*w^3 + 2*w^2 + 22/3*w - 5]', '[673, 673, 1/3*w^3 + w^2 - 5/3*w - 10]', '[673, 673, -1/3*w^3 - w^2 + 5/3*w - 2]', '[673, 673, 1/3*w^3 - w^2 - 5/3*w - 2]', '[673, 673, -1/3*w^3 + w^2 + 5/3*w - 10]', '[719, 719, 5/3*w^3 - 2*w^2 - 31/3*w + 9]', '[719, 719, 5/3*w^3 - 3*w^2 - 25/3*w + 10]', '[719, 719, -w^3 + 2*w^2 + 3*w - 7]', '[719, 719, -5/3*w^3 - 2*w^2 + 31/3*w + 9]', '[727, 727, -w^3 + 2*w^2 + 4*w - 2]', '[727, 727, 4/3*w^3 - 2*w^2 - 23/3*w + 14]', '[727, 727, 4/3*w^3 + 2*w^2 - 23/3*w - 14]', '[727, 727, w^3 + 2*w^2 - 4*w - 2]', '[809, 809, -4/3*w^3 - 5*w^2 + 2/3*w + 10]', '[809, 809, 5/3*w^3 + w^2 - 37/3*w - 8]', '[809, 809, -5/3*w^3 + w^2 + 37/3*w - 8]', '[809, 809, -5/3*w^3 - 4*w^2 + 19/3*w + 11]', '[839, 839, 5/3*w^3 + 2*w^2 - 25/3*w - 11]', '[839, 839, 2/3*w^3 + w^2 - 22/3*w + 2]', '[839, 839, -5/3*w^3 + 2*w^2 + 25/3*w - 5]', '[839, 839, -5/3*w^3 + 2*w^2 + 25/3*w - 11]', '[841, 29, -w^2 - 2]', '[841, 29, w^2 - 10]', '[887, 887, w^3 + w^2 - 7*w - 2]', '[887, 887, 1/3*w^3 + w^2 + 1/3*w - 6]', '[887, 887, -1/3*w^3 + w^2 - 1/3*w - 6]', '[887, 887, -w^3 + w^2 + 7*w - 2]', '[953, 953, 4/3*w^3 - 23/3*w - 8]', '[953, 953, -3*w^3 - 6*w^2 + 7*w + 11]', '[953, 953, -8/3*w^3 - 5*w^2 + 16/3*w + 6]', '[953, 953, -4/3*w^3 + 23/3*w - 8]', '[977, 977, 5/3*w^3 + 2*w^2 - 19/3*w - 3]', '[977, 977, -2*w + 7]', '[977, 977, 8/3*w^3 - 3*w^2 - 46/3*w + 16]', '[977, 977, 2*w^3 + 3*w^2 - 8*w - 8]', '[983, 983, 4/3*w^3 + 2*w^2 - 20/3*w - 11]', '[983, 983, 4/3*w^3 - 2*w^2 - 20/3*w + 5]', '[983, 983, -2*w^3 + 3*w^2 + 10*w - 14]', '[983, 983, -4/3*w^3 + 2*w^2 + 20/3*w - 11]']}
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 0, -8, 0, 1], 'conductor': 56, 'degree': 4, 'dirichlet_group': [1, 27, 29, 55], 'disc_abs': 12544, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [[2, 2]]], [7, [0]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[1, 4]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[2, 2]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[2, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 10.583005244258363, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.12544.1', 'local_algs': ['2.4.8.2', '7.2.1.1', '7.2.1.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 7], 'rd': 10.5830052443, 'regulator': {'__RealLiteral__': 0, 'data': '8.29696504576', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-14.0.1', '-2.0.1', '-7.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{3} - \\frac{5}{3} a + 1 \\)', '\\( \\frac{1}{3} a^{3} - \\frac{2}{3} a \\)', '\\( \\frac{2}{3} a^{3} - a^{2} - \\frac{10}{3} a + 4 \\)'], 'unitsGmodule': [[1, 1], [2, 1], [3, 1]], 'unitsType': 'Type I (iii)', 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 + 1/3*a']}