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hmf_forms • Show schema
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{'deg': 4, 'dimension': 2, 'disc': 13888, 'field_bad_primes': [2, 7, 31], 'field_label': '4.4.13888.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.13888.1-23.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [23], 'level_ideal': '[23, 23, -1/3*w^3 + 2/3*w^2 + 1/3*w - 2]', 'level_label': '23.1', 'level_norm': 23, 'parallel_weight': 2, 'short_label': '23.1-c', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[23, 23, -1/3*w^3 + 2/3*w^2 + 1/3*w - 2]', -1]], 'hecke_eigenvalues': [1, '-e', 0, 'e', 'e', '-1/2*e', 1, -6, -6, '-7/2*e', 0, '-1/2*e', '7/2*e', '-2*e', -2, 14, 0, 0, '-7/2*e', '-3*e', '5*e', 4, 14, '-3/2*e', '-13/2*e', '9/2*e', '2*e', 0, 20, -22, -2, -12, 0, '-3*e', '-6*e', '1/2*e', '3*e', '2*e', '3/2*e', 12, -28, -16, 0, -18, '3*e', -26, 6, '10*e', '-1/2*e', -26, 10, -28, 12, -22, 4, 20, 0, -6, -14, '-5/2*e', '8*e', '-15/2*e', 0, '-2*e', -6, '-3*e', -26, 38, '-21/2*e', -8, '-10*e', 12, -36, '-8*e', '13*e', '-2*e', '-11/2*e', -34, '27/2*e', '-3/2*e', 2, '-3/2*e', -18, 34, 0, '29/2*e', '9/2*e', -24, 24, '9/2*e', '19/2*e', '-7*e', '-23/2*e', -6, -32, -32, -16, -22, 0, 8, -22, 10, 'e', '-5/2*e', '15/2*e', '-7*e', '-17/2*e', '14*e', '27/2*e', '9*e', '5*e', '8*e', 8, 30, 22, '27/2*e', '-15*e', '-16*e', '-19/2*e', -6, '35/2*e', '31/2*e', -24, 14, -30, 0, -26, 16, -4, '14*e', '-3/2*e', '-e', '15*e', '-13/2*e', '-11/2*e', '-25/2*e', '7*e', -42, -42, '7*e', '35/2*e', 48, '-29/2*e', '-31/2*e', -18, '7/2*e', '-15*e', -20, -48, 36, -32, '-13/2*e', '17/2*e', 6, -8, 48, 24, -30, -12, -22, 44, 54, 18, -22, 36, '15*e', '-e', 4, '3/2*e', '17/2*e'], 'hecke_polynomial': 'x^2 - 8', 'label': '4.4.13888.1-23.1-c'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 13888, 'ideals': ['[1, 1, 1]', '[4, 2, -1/3*w^3 + 2/3*w^2 + 4/3*w - 1]', '[7, 7, 1/3*w^3 - 2/3*w^2 - 7/3*w + 1]', '[7, 7, w - 2]', '[7, 7, w - 1]', '[9, 3, w]', '[9, 3, -1/3*w^3 + 2/3*w^2 + 7/3*w - 2]', '[16, 2, 2]', '[23, 23, -1/3*w^3 + 2/3*w^2 + 1/3*w - 2]', '[23, 23, -2/3*w^3 + 4/3*w^2 + 11/3*w - 4]', '[28, 14, w^2 - w - 5]', '[28, 14, 2/3*w^3 - 7/3*w^2 - 5/3*w + 5]', '[28, 14, 1/3*w^3 - 5/3*w^2 - 1/3*w + 4]', '[31, 31, -2/3*w^3 + 1/3*w^2 + 14/3*w + 2]', '[36, 6, -w^2 + w + 3]', '[36, 6, 1/3*w^3 - 5/3*w^2 - 1/3*w + 6]', '[41, 41, -1/3*w^3 + 5/3*w^2 + 4/3*w - 7]', '[41, 41, -1/3*w^3 + 5/3*w^2 + 4/3*w - 4]', '[47, 47, 1/3*w^3 - 5/3*w^2 - 1/3*w + 5]', '[47, 47, w^2 - w - 4]', '[49, 7, -2/3*w^3 + 4/3*w^2 + 11/3*w - 5]', '[49, 7, -1/3*w^3 + 2/3*w^2 + 1/3*w - 3]', '[49, 7, -2/3*w^3 + 4/3*w^2 + 8/3*w - 1]', '[49, 7, -2/3*w^3 + 4/3*w^2 + 8/3*w - 3]', '[49, 49, -2/3*w^3 + 7/3*w^2 + 5/3*w - 8]', '[49, 49, -1/3*w^3 - 1/3*w^2 + 7/3*w + 1]', '[63, 21, -w - 3]', '[63, 21, w^2 - 2*w - 6]', '[63, 21, w^2 - 2*w - 1]', '[63, 21, -w^3 + 2*w^2 + 5*w - 3]', '[63, 21, 2/3*w^3 - 4/3*w^2 - 5/3*w + 1]', '[63, 21, 1/3*w^3 - 2/3*w^2 - 7/3*w + 5]', '[64, 4, -2/3*w^3 + 4/3*w^2 + 8/3*w - 2]', '[73, 73, -w^3 + 3*w^2 + 4*w - 8]', '[73, 73, -2/3*w^3 + 7/3*w^2 - 1/3*w - 4]', '[73, 73, -w^3 + w^2 + 7*w + 1]', '[73, 73, 2/3*w^3 - 4/3*w^2 - 14/3*w + 5]', '[79, 79, w^2 - 5]', '[79, 79, -2/3*w^3 + 7/3*w^2 + 8/3*w - 6]', '[81, 3, 3]', '[81, 9, w^2 - 3*w]', '[81, 9, 2/3*w^3 - 1/3*w^2 - 11/3*w]', '[92, 46, 1/3*w^3 + 1/3*w^2 - 7/3*w]', '[92, 46, 2/3*w^3 - 7/3*w^2 - 5/3*w + 9]', '[97, 97, -2/3*w^3 + 7/3*w^2 + 5/3*w - 4]', '[97, 97, 1/3*w^3 + 1/3*w^2 - 7/3*w - 5]', '[103, 103, w^3 - 3*w^2 - 2*w + 5]', '[103, 103, -4/3*w^3 + 11/3*w^2 + 13/3*w - 10]', '[112, 14, 2/3*w^3 - 4/3*w^2 - 14/3*w + 2]', '[112, 14, 2*w - 4]', '[112, 14, 2*w - 2]', '[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 3]', '[113, 113, w^3 - 2*w^2 - 5*w + 1]', '[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 1]', '[113, 113, -1/3*w^3 + 5/3*w^2 + 4/3*w - 10]', '[124, 62, -1/3*w^3 - 1/3*w^2 + 13/3*w + 6]', '[127, 127, -2/3*w^3 + 1/3*w^2 + 14/3*w + 1]', '[127, 127, -2/3*w^3 + 7/3*w^2 + 2/3*w - 6]', '[137, 137, -1/3*w^3 + 5/3*w^2 - 2/3*w - 6]', '[137, 137, 1/3*w^3 + 1/3*w^2 - 10/3*w - 1]', '[144, 6, 2*w]', '[144, 6, -2/3*w^3 + 4/3*w^2 + 14/3*w - 4]', '[151, 151, -w^3 + 2*w^2 + 3*w - 5]', '[151, 151, 1/3*w^3 + 1/3*w^2 - 10/3*w - 7]', '[161, 161, -2/3*w^3 + 4/3*w^2 + 14/3*w - 3]', '[161, 161, w^3 - 3*w^2 - 3*w + 5]', '[161, 161, 2/3*w^3 - 1/3*w^2 - 11/3*w - 4]', '[161, 161, -1/3*w^3 + 5/3*w^2 + 4/3*w - 9]', '[161, 161, -2*w + 1]', '[161, 161, 1/3*w^3 - 5/3*w^2 - 4/3*w + 2]', '[164, 82, w^3 - 3*w^2 - 5*w + 8]', '[164, 82, -w^2 - w + 5]', '[169, 13, -2/3*w^3 + 7/3*w^2 + 5/3*w - 2]', '[169, 13, 1/3*w^3 + 1/3*w^2 - 7/3*w - 7]', '[188, 94, -1/3*w^3 + 2/3*w^2 + 10/3*w - 3]', '[188, 94, 1/3*w^3 - 2/3*w^2 - 10/3*w + 1]', '[191, 191, 1/3*w^3 - 2/3*w^2 + 2/3*w - 2]', '[191, 191, 2*w - 5]', '[191, 191, -w^3 + 2*w^2 + 6*w - 2]', '[191, 191, 2/3*w^3 - 4/3*w^2 - 14/3*w - 1]', '[196, 14, w^3 - 3*w^2 - 3*w + 10]', '[196, 14, 2/3*w^3 - 1/3*w^2 - 11/3*w + 1]', '[196, 14, 1/3*w^3 - 2/3*w^2 - 4/3*w + 5]', '[196, 14, -1/3*w^3 + 2/3*w^2 + 4/3*w + 3]', '[196, 98, w^3 - 2*w^2 - 6*w + 7]', '[196, 98, 1/3*w^3 - 2/3*w^2 + 2/3*w + 3]', '[207, 69, w^3 - 4*w^2 - w + 9]', '[207, 69, 2/3*w^3 - 7/3*w^2 - 8/3*w + 5]', '[207, 69, -2/3*w^3 - 2/3*w^2 + 17/3*w + 7]', '[207, 69, -w^2 + 6]', '[217, 217, w^3 - 3*w^2 - 4*w + 7]', '[217, 217, -1/3*w^3 - 1/3*w^2 + 4/3*w + 4]', '[217, 217, 1/3*w^3 - 2/3*w^2 - 10/3*w + 2]', '[239, 239, 1/3*w^3 - 2/3*w^2 - 7/3*w - 3]', '[239, 239, w - 5]', '[241, 241, 1/3*w^3 + 1/3*w^2 - 10/3*w]', '[241, 241, 4/3*w^3 - 17/3*w^2 + 2/3*w + 9]', '[241, 241, -1/3*w^3 + 5/3*w^2 - 2/3*w - 7]', '[241, 241, -4/3*w^3 + 14/3*w^2 + 13/3*w - 14]', '[252, 42, w^3 - w^2 - 5*w]', '[252, 42, w^3 - w^2 - 7*w]', '[252, 42, -2/3*w^3 + 7/3*w^2 - 1/3*w - 5]', '[252, 42, -w^2 + w + 9]', '[252, 42, 1/3*w^3 - 5/3*w^2 - 1/3*w]', '[252, 42, -4/3*w^3 + 11/3*w^2 + 13/3*w - 9]', '[256, 4, 4]', '[257, 257, -w - 4]', '[257, 257, -1/3*w^3 + 2/3*w^2 + 7/3*w - 6]', '[263, 263, -4/3*w^3 + 11/3*w^2 + 16/3*w - 8]', '[263, 263, 2/3*w^3 - 1/3*w^2 - 8/3*w - 3]', '[279, 93, 2*w^2 - w - 5]', '[279, 93, w^3 - 4*w^2 - 3*w + 15]', '[281, 281, -1/3*w^3 - 1/3*w^2 + 10/3*w - 2]', '[281, 281, -1/3*w^3 + 5/3*w^2 - 5/3*w - 5]', '[281, 281, -1/3*w^3 + 5/3*w^2 - 2/3*w - 9]', '[281, 281, -2/3*w^3 + 1/3*w^2 + 17/3*w]', '[287, 287, 4/3*w^3 - 8/3*w^2 - 19/3*w + 10]', '[287, 287, 4/3*w^3 - 8/3*w^2 - 10/3*w + 7]', '[287, 287, 5/3*w^3 - 13/3*w^2 - 23/3*w + 17]', '[287, 287, 5/3*w^3 - 13/3*w^2 - 14/3*w + 11]', '[287, 287, -2*w^3 + 4*w^2 + 10*w - 11]', '[287, 287, -w^3 + 2*w^2 + 3*w - 8]', '[289, 17, -w^3 + 2*w^2 + 4*w - 4]', '[289, 17, w^3 - 2*w^2 - 4*w + 2]', '[292, 146, 2/3*w^3 - 7/3*w^2 - 11/3*w + 11]', '[292, 146, -1/3*w^3 + 8/3*w^2 - 8/3*w - 3]', '[292, 146, -1/3*w^3 - 4/3*w^2 + 16/3*w + 11]', '[292, 146, -w^3 + 4*w^2 + 2*w - 13]', '[311, 311, -2/3*w^3 + 10/3*w^2 - 4/3*w - 9]', '[311, 311, -2/3*w^3 - 2/3*w^2 + 20/3*w + 5]', '[313, 313, -1/3*w^3 + 5/3*w^2 - 2/3*w - 8]', '[313, 313, -1/3*w^3 - 1/3*w^2 + 10/3*w - 1]', '[313, 313, w^3 - 4*w^2 - 2*w + 10]', '[313, 313, 1/3*w^3 + 4/3*w^2 - 10/3*w - 8]', '[316, 158, 2/3*w^3 - 7/3*w^2 - 11/3*w + 5]', '[316, 158, 1/3*w^3 - 5/3*w^2 - 7/3*w + 8]', '[324, 6, -w^3 + 2*w^2 + 4*w - 3]', '[324, 18, -w^3 + 4*w^2 - 9]', '[324, 18, -1/3*w^3 + 2/3*w^2 - 2/3*w - 5]', '[329, 329, -5/3*w^3 + 16/3*w^2 + 11/3*w - 13]', '[329, 329, w^3 - 2*w^2 - 3*w + 4]', '[329, 329, 4/3*w^3 - 8/3*w^2 - 19/3*w + 6]', '[329, 329, -4/3*w^3 + 11/3*w^2 + 10/3*w - 8]', '[329, 329, w^3 - 3*w^2 - 2*w + 8]', '[329, 329, -4/3*w^3 + 5/3*w^2 + 22/3*w - 1]', '[337, 337, -4/3*w^3 + 5/3*w^2 + 19/3*w + 4]', '[337, 337, 5/3*w^3 - 13/3*w^2 - 17/3*w + 5]', '[343, 7, -1/3*w^3 + 5/3*w^2 - 8/3*w - 1]', '[343, 7, w^3 - 7*w - 8]', '[343, 7, -w^3 + w^2 + 8*w + 2]', '[343, 49, 1/3*w^3 + 4/3*w^2 - 13/3*w - 9]', '[343, 49, -4/3*w^3 + 8/3*w^2 + 22/3*w - 3]', '[343, 49, -2/3*w^3 + 7/3*w^2 - 4/3*w + 1]', '[343, 49, 2/3*w^3 - 10/3*w^2 + 1/3*w + 7]', '[343, 49, -2/3*w^3 + 4/3*w^2 + 2/3*w + 1]', '[343, 343, -4/3*w^3 + 8/3*w^2 + 25/3*w - 7]', '[343, 343, -1/3*w^3 + 2/3*w^2 - 5/3*w - 1]', '[353, 353, -4/3*w^3 + 8/3*w^2 + 25/3*w - 3]', '[353, 353, -1/3*w^3 - 1/3*w^2 + 16/3*w + 6]', '[353, 353, -2/3*w^3 + 10/3*w^2 + 2/3*w - 13]', '[353, 353, -5/3*w^3 + 7/3*w^2 + 29/3*w - 3]', '[367, 367, -5/3*w^3 + 4/3*w^2 + 35/3*w + 4]', '[367, 367, 2/3*w^3 - 7/3*w^2 - 8/3*w + 4]', '[367, 367, -4/3*w^3 + 14/3*w^2 + 1/3*w - 8]', '[367, 367, w^2 - 7]', '[368, 46, -2/3*w^3 + 4/3*w^2 + 2/3*w - 4]', '[368, 46, -4/3*w^3 + 8/3*w^2 + 22/3*w - 8]', '[369, 123, w^3 - w^2 - 2*w + 3]', '[369, 123, 7/3*w^3 - 17/3*w^2 - 34/3*w + 18]', '[369, 123, 4/3*w^3 - 11/3*w^2 - 13/3*w + 12]', '[369, 123, w^3 - w^2 - 5*w + 3]', '[383, 383, 4/3*w^3 - 14/3*w^2 - 10/3*w + 15]', '[383, 383, -5/3*w^3 + 13/3*w^2 + 20/3*w - 12]', '[383, 383, 2*w^2 - 2*w - 13]', '[383, 383, w^3 - w^2 - 8*w - 1]', '[388, 194, -1/3*w^3 + 2/3*w^2 - 2/3*w + 3]', '[388, 194, w^3 - 2*w^2 - 6*w + 1]', '[401, 401, -4/3*w^3 + 11/3*w^2 + 22/3*w - 11]', '[401, 401, 5/3*w^3 - 10/3*w^2 - 29/3*w + 5]', '[409, 409, -w^3 + 2*w^2 + 3*w - 2]', '[409, 409, -1/3*w^3 + 8/3*w^2 - 2/3*w - 6]', '[409, 409, 1/3*w^3 - 8/3*w^2 + 2/3*w + 12]', '[409, 409, 4/3*w^3 - 8/3*w^2 - 19/3*w + 4]', '[412, 206, 1/3*w^3 - 5/3*w^2 + 5/3*w - 2]', '[412, 206, w^3 - 2*w^2 - 6*w + 11]', '[423, 141, w^3 - w^2 - 4*w]', '[423, 141, -5/3*w^3 + 13/3*w^2 + 20/3*w - 11]', '[423, 141, 4/3*w^3 - 8/3*w^2 - 19/3*w + 5]', '[423, 141, -w^3 + 2*w^2 + 3*w - 3]', '[433, 433, -w^3 + 3*w^2 - 1]', '[433, 433, -1/3*w^3 + 5/3*w^2 - 8/3*w - 5]', '[433, 433, -w^3 + w^2 + 8*w - 2]', '[433, 433, 5/3*w^3 - 7/3*w^2 - 32/3*w - 2]', '[439, 439, w^2 - 10]', '[439, 439, -2/3*w^3 + 4/3*w^2 + 17/3*w - 7]', '[441, 21, -2/3*w^3 + 1/3*w^2 + 11/3*w + 6]', '[441, 21, -1/3*w^3 - 4/3*w^2 + 10/3*w + 6]', '[441, 21, w^3 - 4*w^2 - 2*w + 12]', '[441, 21, 1/3*w^3 - 8/3*w^2 + 5/3*w + 10]', '[441, 21, w^3 - 4*w^2 - 3*w + 14]', '[441, 21, w^3 - 3*w^2 - 3*w + 3]', '[441, 21, -2*w^2 + 3*w + 6]', '[441, 21, -2*w^2 + w + 6]', '[441, 147, 2/3*w^3 - 1/3*w^2 - 20/3*w - 3]', '[441, 147, w^2 - 4*w]', '[441, 147, w^3 - 3*w^2 - 4*w + 6]', '[441, 147, -1/3*w^3 - 1/3*w^2 + 4/3*w + 5]', '[448, 28, 2*w^2 - 2*w - 10]', '[448, 28, 4/3*w^3 - 14/3*w^2 - 10/3*w + 10]', '[448, 28, 2/3*w^3 - 10/3*w^2 - 2/3*w + 8]', '[449, 449, -2/3*w^3 + 4/3*w^2 + 11/3*w - 8]', '[449, 449, -4/3*w^3 + 5/3*w^2 + 22/3*w + 2]', '[452, 226, -1/3*w^3 - 1/3*w^2 + 1/3*w + 4]', '[452, 226, 2/3*w^3 - 1/3*w^2 - 11/3*w - 7]', '[452, 226, -w^3 + w^2 + 3*w + 2]', '[452, 226, 2*w^3 - 5*w^2 - 9*w + 11]', '[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 6]', '[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 9]', '[463, 463, w^3 - 3*w^2 - 6*w + 11]', '[463, 463, -1/3*w^3 + 5/3*w^2 + 10/3*w - 4]', '[479, 479, -1/3*w^3 + 5/3*w^2 - 2/3*w + 1]', '[479, 479, 5/3*w^3 - 10/3*w^2 - 23/3*w + 9]', '[487, 487, -2/3*w^3 + 7/3*w^2 + 2/3*w - 8]', '[487, 487, -2/3*w^3 + 1/3*w^2 + 14/3*w - 1]', '[496, 62, -4/3*w^3 + 2/3*w^2 + 28/3*w + 4]', '[503, 503, w^3 - 4*w^2 - 2*w + 16]', '[503, 503, -1/3*w^3 + 5/3*w^2 - 2/3*w - 11]', '[508, 254, -w^2 + 3*w + 7]', '[508, 254, 1/3*w^3 + 1/3*w^2 - 13/3*w + 2]', '[511, 511, 3*w^3 - 9*w^2 - 10*w + 25]', '[511, 511, -2/3*w^3 + 7/3*w^2 + 8/3*w - 3]', '[511, 511, 5/3*w^3 - 22/3*w^2 + 1/3*w + 10]', '[511, 511, w^3 - 4*w^2 - 3*w + 19]', '[511, 511, 4/3*w^3 + 4/3*w^2 - 37/3*w - 20]', '[511, 511, -2/3*w^3 + 4/3*w^2 + 17/3*w - 11]', '[511, 511, 7/3*w^3 - 29/3*w^2 + 2/3*w + 14]', '[511, 511, -w^2 + 8]', '[511, 511, -5/3*w^3 + 16/3*w^2 + 17/3*w - 20]', '[511, 511, -4/3*w^3 + 8/3*w^2 + 31/3*w - 16]', '[511, 511, 2*w^3 - 6*w^2 - 6*w + 17]', '[511, 511, w^3 - 2*w^2 - 7*w + 7]', '[521, 521, -4/3*w^3 + 11/3*w^2 + 10/3*w - 7]', '[521, 521, 4/3*w^3 - 5/3*w^2 - 22/3*w]', '[529, 23, -1/3*w^3 + 2/3*w^2 + 4/3*w - 6]', '[529, 23, -1/3*w^3 + 2/3*w^2 + 4/3*w + 4]', '[529, 529, -1/3*w^3 - 1/3*w^2 + 13/3*w - 3]', '[529, 529, w^2 - 3*w - 8]', '[548, 274, 2/3*w^3 - 1/3*w^2 - 17/3*w + 1]', '[548, 274, -1/3*w^3 + 5/3*w^2 - 5/3*w - 6]', '[553, 553, w^3 - w^2 - 5*w + 5]', '[553, 553, 5/3*w^3 - 13/3*w^2 - 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3]', '[367, 367, -5/3*w^3 + 4/3*w^2 + 35/3*w + 4]', '[367, 367, 2/3*w^3 - 7/3*w^2 - 8/3*w + 4]', '[367, 367, -4/3*w^3 + 14/3*w^2 + 1/3*w - 8]', '[367, 367, w^2 - 7]', '[383, 383, 4/3*w^3 - 14/3*w^2 - 10/3*w + 15]', '[383, 383, -5/3*w^3 + 13/3*w^2 + 20/3*w - 12]', '[383, 383, 2*w^2 - 2*w - 13]', '[383, 383, w^3 - w^2 - 8*w - 1]', '[401, 401, -4/3*w^3 + 11/3*w^2 + 22/3*w - 11]', '[401, 401, 5/3*w^3 - 10/3*w^2 - 29/3*w + 5]', '[409, 409, -w^3 + 2*w^2 + 3*w - 2]', '[409, 409, -1/3*w^3 + 8/3*w^2 - 2/3*w - 6]', '[409, 409, 1/3*w^3 - 8/3*w^2 + 2/3*w + 12]', '[409, 409, 4/3*w^3 - 8/3*w^2 - 19/3*w + 4]', '[433, 433, -w^3 + 3*w^2 - 1]', '[433, 433, -1/3*w^3 + 5/3*w^2 - 8/3*w - 5]', '[433, 433, -w^3 + w^2 + 8*w - 2]', '[433, 433, 5/3*w^3 - 7/3*w^2 - 32/3*w - 2]', '[439, 439, w^2 - 10]', '[439, 439, -2/3*w^3 + 4/3*w^2 + 17/3*w - 7]', '[449, 449, -2/3*w^3 + 4/3*w^2 + 11/3*w - 8]', '[449, 449, -4/3*w^3 + 5/3*w^2 + 22/3*w + 2]', '[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 6]', '[457, 457, 2/3*w^3 - 7/3*w^2 - 14/3*w + 9]', '[463, 463, w^3 - 3*w^2 - 6*w + 11]', '[463, 463, -1/3*w^3 + 5/3*w^2 + 10/3*w - 4]', '[479, 479, -1/3*w^3 + 5/3*w^2 - 2/3*w + 1]', '[479, 479, 5/3*w^3 - 10/3*w^2 - 23/3*w + 9]', '[487, 487, -2/3*w^3 + 7/3*w^2 + 2/3*w - 8]', '[487, 487, -2/3*w^3 + 1/3*w^2 + 14/3*w - 1]', '[503, 503, w^3 - 4*w^2 - 2*w + 16]', '[503, 503, -1/3*w^3 + 5/3*w^2 - 2/3*w - 11]', '[521, 521, -4/3*w^3 + 11/3*w^2 + 10/3*w - 7]', '[521, 521, 4/3*w^3 - 5/3*w^2 - 22/3*w]', '[529, 23, -1/3*w^3 + 2/3*w^2 + 4/3*w - 6]', '[569, 569, -1/3*w^3 + 8/3*w^2 + 1/3*w - 10]', '[569, 569, -2/3*w^3 + 10/3*w^2 + 5/3*w - 10]', '[577, 577, -2/3*w^3 + 10/3*w^2 + 5/3*w - 12]', '[577, 577, -1/3*w^3 + 8/3*w^2 + 1/3*w - 8]', '[593, 593, w^3 - w^2 - 5*w - 5]', '[593, 593, 4/3*w^3 - 11/3*w^2 - 13/3*w + 4]', '[599, 599, 2*w^2 - 3*w - 7]', '[599, 599, 2/3*w^3 - 1/3*w^2 - 8/3*w - 4]', '[599, 599, -1/3*w^3 + 8/3*w^2 - 5/3*w - 9]', '[599, 599, -4/3*w^3 + 11/3*w^2 + 16/3*w - 7]', '[607, 607, 4/3*w^3 - 8/3*w^2 - 22/3*w + 9]', '[607, 607, -2/3*w^3 + 4/3*w^2 + 2/3*w - 5]', '[625, 5, -5]', '[631, 631, -1/3*w^3 + 2/3*w^2 + 13/3*w - 5]', '[631, 631, -2/3*w^3 + 4/3*w^2 + 17/3*w - 1]', '[641, 641, -2/3*w^3 + 7/3*w^2 + 14/3*w - 7]', '[641, 641, 2/3*w^3 - 7/3*w^2 - 14/3*w + 8]', '[647, 647, -2/3*w^3 - 5/3*w^2 + 26/3*w + 8]', '[647, 647, -1/3*w^3 + 8/3*w^2 + 1/3*w - 9]', '[647, 647, -2/3*w^3 + 10/3*w^2 + 5/3*w - 11]', '[647, 647, -2/3*w^3 + 13/3*w^2 - 10/3*w - 13]', '[673, 673, -4/3*w^3 + 5/3*w^2 + 25/3*w - 2]', '[673, 673, -w^3 + 3*w^2 + w - 7]', '[727, 727, -2/3*w^3 + 7/3*w^2 + 2/3*w - 11]', '[727, 727, -2/3*w^3 + 1/3*w^2 + 14/3*w - 4]', '[743, 743, w^2 - w - 10]', '[743, 743, 1/3*w^3 - 5/3*w^2 - 1/3*w - 1]', '[769, 769, -w^3 + 2*w^2 + 7*w - 4]', '[769, 769, 3*w - 2]', '[809, 809, -1/3*w^3 + 8/3*w^2 - 2/3*w - 8]', '[809, 809, -1/3*w^3 + 8/3*w^2 - 2/3*w - 10]', '[823, 823, -w^3 + 2*w^2 + 7*w - 5]', '[823, 823, 3*w - 1]', '[839, 839, 4/3*w^3 - 2/3*w^2 - 25/3*w - 8]', '[839, 839, 2/3*w^3 - 7/3*w^2 - 14/3*w + 12]', '[857, 857, -1/3*w^3 + 5/3*w^2 - 5/3*w - 7]', '[857, 857, -2/3*w^3 + 1/3*w^2 + 17/3*w - 2]', '[863, 863, -2/3*w^3 + 7/3*w^2 - 7/3*w - 2]', '[863, 863, 5/3*w^3 - 7/3*w^2 - 35/3*w + 1]', '[881, 881, -2/3*w^3 + 1/3*w^2 + 14/3*w + 8]', '[881, 881, -2/3*w^3 + 13/3*w^2 - 4/3*w - 18]', '[881, 881, -5/3*w^3 + 7/3*w^2 + 35/3*w + 3]', '[881, 881, -2/3*w^3 + 7/3*w^2 + 2/3*w + 1]', '[887, 887, -1/3*w^3 + 11/3*w^2 - 8/3*w - 7]', '[887, 887, -1/3*w^3 + 11/3*w^2 - 8/3*w - 18]', '[911, 911, 5/3*w^3 - 4/3*w^2 - 29/3*w - 3]', '[911, 911, 2*w^3 - 6*w^2 - 5*w + 13]', '[929, 929, 2*w^3 - 4*w^2 - 9*w + 2]', '[929, 929, 5/3*w^3 - 10/3*w^2 - 17/3*w]', '[929, 929, -4/3*w^3 + 14/3*w^2 + 13/3*w - 11]', '[929, 929, 1/3*w^3 + 4/3*w^2 - 7/3*w - 9]', '[937, 937, -w^3 + 4*w^2 + w - 13]', '[937, 937, 2/3*w^3 + 2/3*w^2 - 17/3*w - 3]', '[953, 953, -2*w^3 + w^2 + 15*w + 8]', '[953, 953, -5/3*w^3 + 19/3*w^2 - 1/3*w - 11]', '[961, 31, 4/3*w^3 - 8/3*w^2 - 16/3*w + 5]', '[967, 967, -4/3*w^3 + 2/3*w^2 + 31/3*w + 11]', '[967, 967, 7/3*w^3 - 5/3*w^2 - 46/3*w - 9]', '[977, 977, 2*w^3 - 5*w^2 - 8*w + 10]', '[977, 977, -w^3 + 3*w^2 + 2*w - 14]', '[977, 977, -4/3*w^3 + 8/3*w^2 + 25/3*w - 11]', '[977, 977, -w^3 + w^2 + 6*w - 7]', '[983, 983, -5/3*w^3 + 16/3*w^2 + 8/3*w - 12]', '[983, 983, -1/3*w^3 + 11/3*w^2 - 11/3*w - 15]', '[983, 983, 3*w^2 - 2*w - 16]', '[983, 983, -5/3*w^3 + 16/3*w^2 + 11/3*w - 14]', '[991, 991, 4/3*w^3 - 8/3*w^2 - 22/3*w + 1]', '[991, 991, 2/3*w^3 - 4/3*w^2 - 2/3*w - 3]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 6, -7, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 13888, 'disc_rad': 434, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 2]]], [5, [[4, 1]]], [7, [0]], [11, [[4, 1]]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[4, 1]]], [23, [[2, 1], [1, 2]]], [29, [[4, 1]]], [31, [0]], [37, [[4, 1]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 41.66533331199932, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.13888.1', 'local_algs': ['2.4.6.1', '7.1.0.1', '7.1.0.1', '7.2.1.2', '31.2.0.1', '31.2.1.2'], 'monogenic': -1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 7, 31], 'rd': 10.8557523416, 'regulator': {'__RealLiteral__': 0, 'data': '6.51385459818', 'prec': 44}, 'res': {'gal': ['576,0,-824,0,313,0,-38,0,1'], 'sib': ['2,0,-15,0,1', '576,0,-824,0,313,0,-38,0,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{3} - \\frac{2}{3} a^{2} - \\frac{4}{3} a \\)', '\\( a + 1 \\)', '\\( \\frac{2}{3} a^{3} - \\frac{4}{3} a^{2} - \\frac{11}{3} a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 + 1/3*a^2 - 1/3*a']}