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hmf_forms • Show schema
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{'deg': 4, 'dimension': 1, 'disc': 8768, 'field_bad_primes': [2, 137], 'field_label': '4.4.8768.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.8768.1-49.10-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [7], 'level_ideal': '[49,49,w^3 - 3*w^2 - w + 7]', 'level_label': '49.10', 'level_norm': 49, 'parallel_weight': 2, 'short_label': '49.10-d', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[7,7,-w]', -1]], 'hecke_eigenvalues': [2, 0, -4, 4, -4, 4, -8, -8, -4, 6, -6, 0, 4, 4, 8, 16, 16, 8, 0, 6, -10, -16, -2, -4, -16, -8, -12, -20, 8, 8, 16, 0, 0, 0, 4, 0, -12, -14, 2, -20, -24, 4, -20, 6, 26, -28, 24, -8, 16, 18, 0, -30, -30, 0, -4, -24, 12, -16, 20, -10, -24, 0, -4, -12, 12, 4, -22, -16, 2, -18, 28, 12, -20, 20, -10, 4, -8, 4, 12, -32, 6, -22, -32, -16, -4, 24, -20, -28, 10, -20, -24, 0, 24, 28, -4, 20, -40, -42, 14, 44, 24, -8, 24, 4, 44, -10, -4, 20, 32, -20, -32, -46, -24, -2, 16, -24, 20, 12, -12, -30, -30, -12, 12, -12, -20, 20, -28, 48, 28, -4, 4, -16, -28, -36, 4, 0, -28, -4, 28, -6, 32, 16, -32, 16, -20, 36, 20, -16, -32, 52, 26, -20, -4, 48, -16, 32, -8, -4, -44, -36, 18, 42, -44, -26, 14, -36, 36, 44, -56, -52, -36, 48, 16, 12, -28, 24, -32, 56], 'hecke_polynomial': 'x', 'label': '4.4.8768.1-49.10-d'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 8768, 'ideals': ['[1, 1, 1]', '[4, 2, -w^2 + w + 3]', '[7, 7, w]', '[7, 7, -w^2 + 2*w + 1]', '[7, 7, w^2 - 2]', '[7, 7, w - 1]', '[16, 2, 2]', '[23, 23, -w^3 + w^2 + 3*w - 1]', '[23, 23, w^3 - 2*w^2 - 2*w + 2]', '[28, 14, -w^3 + w^2 + 3*w]', '[28, 14, -w^3 + 3*w^2 + w - 4]', '[28, 14, -w^3 + 4*w + 1]', '[28, 14, -w^3 + 2*w^2 + 2*w - 3]', '[31, 31, w^2 - 5]', '[31, 31, -w^2 + 2*w + 4]', '[41, 41, -w^3 + 2*w^2 + 2*w - 6]', '[41, 41, w^3 - w^2 - 3*w - 3]', '[47, 47, w^2 - 2*w - 5]', '[47, 47, w^2 - 6]', '[49, 7, -2*w^2 + 3*w + 7]', '[49, 7, w^3 - 2*w^2 - 3*w + 7]', '[49, 7, -2*w^2 + 2*w + 7]', '[49, 7, -2*w^2 + 2*w + 5]', '[49, 7, w^3 - w^2 - 2*w + 2]', '[49, 7, -w^3 + w^2 + 4*w + 3]', '[49, 49, -w^3 + 4*w + 4]', '[49, 49, -w^3 + 5*w + 2]', '[49, 49, -w^3 + 3*w^2 + 2*w - 6]', '[49, 49, w^3 - 3*w^2 - w + 7]', '[64, 4, -2*w^2 + 2*w + 6]', '[71, 71, -w^3 + 2*w^2 + 3*w - 1]', '[71, 71, -w^3 + w^2 + 4*w - 3]', '[79, 79, -w - 3]', '[79, 79, w - 4]', '[81, 3, -3]', '[89, 89, w^2 - 3*w - 2]', '[89, 89, w^2 + w - 4]', '[92, 46, w^2 + w - 3]', '[92, 46, w^2 - 3*w - 1]', '[97, 97, 2*w^3 - 5*w^2 - 4*w + 9]', '[97, 97, -2*w^3 + w^2 + 8*w + 2]', '[112, 14, 2*w]', '[112, 14, -2*w^2 + 4*w + 2]', '[112, 14, 2*w^2 - 4]', '[112, 14, 2*w - 2]', '[113, 113, w^3 - 2*w^2 - 4*w + 2]', '[113, 113, w^3 - w^2 - 5*w + 3]', '[121, 11, 2*w^2 - w - 9]', '[121, 11, -2*w^2 + 3*w + 8]', '[124, 62, -w^3 + 3*w^2 + w - 8]', '[124, 62, -w^3 + 4*w + 5]', '[127, 127, w^3 - 3*w^2 - 2*w + 5]', '[127, 127, w^3 - 5*w - 1]', '[137, 137, 2*w - 1]', '[161, 161, w^3 - 3*w^2 + 6]', '[161, 161, -w^3 + 5*w^2 - 2*w - 9]', '[161, 161, -w^3 - w^2 + 6*w + 4]', '[161, 161, -3*w^2 + 2*w + 8]', '[161, 161, 3*w^2 - 4*w - 7]', '[161, 161, w^3 - 4*w^2 - w + 8]', '[161, 161, -w^3 - 2*w^2 + 5*w + 7]', '[161, 161, w^3 - 3*w - 4]', '[164, 82, 3*w^2 - w - 11]', '[164, 82, 3*w^2 - 5*w - 9]', '[167, 167, 2*w^3 - 2*w^2 - 7*w - 2]', '[167, 167, w^3 - 7*w - 4]', '[167, 167, 2*w^3 - w^2 - 9*w - 2]', '[167, 167, 2*w^3 - 4*w^2 - 5*w + 9]', '[188, 94, w^3 + w^2 - 5*w - 8]', '[188, 94, -w^3 + 4*w^2 - 11]', '[191, 191, 2*w^3 - 4*w^2 - 5*w + 5]', '[191, 191, -2*w^3 + 2*w^2 + 7*w - 2]', '[193, 193, -2*w^3 + 3*w^2 + 6*w - 6]', '[193, 193, -2*w^3 + 2*w^2 + 7*w - 4]', '[193, 193, -2*w^3 + 4*w^2 + 5*w - 3]', '[193, 193, 2*w^3 - 3*w^2 - 6*w + 1]', '[196, 14, w^2 - w + 1]', '[196, 14, -w^3 - w^2 + 3*w + 6]', '[196, 14, -w^3 - 2*w^2 + 8*w + 9]', '[196, 14, -w^3 + 4*w + 7]', '[196, 14, w^3 - 5*w^2 - w + 14]', '[196, 14, -w^2 + w + 7]', '[196, 98, -w^2 + 3*w + 5]', '[196, 98, -w^3 + 2*w^2 + 4*w - 1]', '[196, 98, -w^3 + w^2 + 5*w - 4]', '[196, 98, -w^2 - w + 7]', '[199, 199, -w^3 - 2*w^2 + 6*w + 10]', '[199, 199, -w^3 + 5*w^2 - w - 13]', '[217, 217, w^3 - w^2 - 6*w - 1]', '[217, 217, 2*w^3 - 11*w - 6]', '[217, 217, -w^3 + 3*w^2 + 2*w - 4]', '[217, 217, -3*w^2 + 2*w + 9]', '[217, 217, 3*w^2 - 4*w - 8]', '[217, 217, w^3 - 5*w]', '[217, 217, -2*w^3 + 6*w^2 + 5*w - 15]', '[217, 217, -w^3 + 2*w^2 + 5*w - 7]', '[223, 223, -w^3 + 2*w^2 + 3*w - 8]', '[223, 223, w^3 - w^2 - 4*w - 4]', '[233, 233, -w^2 - 1]', '[233, 233, w^2 - 2*w + 2]', '[239, 239, 3*w^2 - 2*w - 13]', '[239, 239, 3*w^2 - 4*w - 12]', '[241, 241, w^3 - w^2 - 6*w + 3]', '[241, 241, w^3 - 2*w^2 - 5*w + 3]', '[256, 4, 4]', '[257, 257, -w^3 + 3*w^2 + 4*w - 9]', '[257, 257, -2*w^3 + 4*w^2 + 8*w - 11]', '[257, 257, -w^3 + 2*w^2 + 4]', '[257, 257, w^3 - 7*w - 3]', '[263, 263, -w^3 + w^2 + 3*w + 5]', '[263, 263, w^3 - 5*w^2 + 12]', '[263, 263, -w^3 - 2*w^2 + 7*w + 8]', '[263, 263, -w^3 + 7*w + 2]', '[271, 271, -w^3 + 3*w^2 + 2*w - 3]', '[271, 271, w^3 - 5*w + 1]', '[284, 142, -w^3 - w^2 + 7*w + 4]', '[284, 142, -w^3 + 4*w^2 + 2*w - 9]', '[287, 287, -w^3 - 4*w^2 + 3*w + 12]', '[287, 287, w^3 + 2*w^2 - 9*w - 7]', '[287, 287, 2*w^3 - 4*w^2 - 5*w + 8]', '[287, 287, 3*w^2 - 6*w - 4]', '[287, 287, -3*w^2 + 7]', '[287, 287, 2*w^3 - 2*w^2 - 7*w - 1]', '[287, 287, w^3 - 5*w^2 - 2*w + 13]', '[287, 287, -w^3 + 7*w^2 - 8*w - 10]', '[289, 17, 3*w^2 - 3*w - 8]', '[289, 17, 3*w^2 - 3*w - 10]', '[311, 311, -2*w^3 + 2*w^2 + 7*w - 1]', '[311, 311, -w^3 + 5*w^2 - w - 11]', '[311, 311, w^3 + 2*w^2 - 6*w - 8]', '[311, 311, -2*w^3 + 4*w^2 + 5*w - 6]', '[316, 158, w^3 + 2*w^2 - 6*w - 9]', '[316, 158, -w^3 + 5*w^2 - w - 12]', '[324, 6, 3*w^2 - 3*w - 9]', '[329, 329, 2*w^3 - 3*w^2 - 6*w + 2]', '[329, 329, 2*w^2 - 6*w + 1]', '[329, 329, w^3 - 2*w^2 - 5*w]', '[329, 329, w^3 - 6*w]', '[329, 329, w^3 - 3*w^2 - 3*w + 5]', '[329, 329, w^3 - w^2 - 6*w + 6]', '[329, 329, -2*w^2 - 2*w + 3]', '[329, 329, 2*w^3 - 3*w^2 - 6*w + 5]', '[337, 337, w^3 - w^2 - 2*w - 4]', '[337, 337, 2*w^3 - 9*w - 4]', '[337, 337, 2*w^3 - 6*w^2 - 3*w + 11]', '[337, 337, -w^3 + 2*w^2 + w - 6]', '[343, 7, -w^3 + w^2 + 6*w]', '[343, 7, -2*w^3 + w^2 + 8*w]', '[343, 7, -2*w^3 + 5*w^2 + 4*w - 7]', '[343, 7, -w^3 + 2*w^2 + 5*w - 6]', '[343, 49, -2*w^3 + 2*w^2 + 7*w]', '[343, 49, -w^3 + 3*w^2]', '[343, 49, -2*w^3 + 3*w^2 + 7*w]', '[343, 49, -w^3 + 7*w - 1]', '[343, 49, w^3 - 5*w^2 + 14]', '[343, 49, -w^3 + 3*w + 5]', '[343, 49, w^3 - 3*w^2 + 7]', '[343, 49, -w^3 + 3*w^2 + 4*w - 5]', '[343, 49, -w^3 - 2*w^2 + 7*w + 10]', '[343, 49, -2*w^3 + 4*w^2 + 5*w - 7]', '[343, 49, w^3 - 3*w + 2]', '[343, 49, -2*w^3 + 3*w^2 + 7*w - 8]', '[343, 343, -w^3 + 2*w^2 + 2*w + 2]', '[343, 343, -w^3 - w^2 + 6*w + 3]', '[343, 343, -w^3 + 4*w^2 + w - 7]', '[343, 343, w^3 - w^2 - 3*w + 5]', '[353, 353, -w^3 + 4*w^2 - 12]', '[353, 353, w^3 + w^2 - 5*w - 9]', '[356, 178, -2*w^3 + 3*w^2 + 5*w - 1]', '[356, 178, -2*w^3 + 3*w^2 + 5*w - 5]', '[359, 359, 2*w^3 - 4*w^2 - 6*w + 5]', '[359, 359, 2*w^3 - 2*w^2 - 8*w + 3]', '[361, 19, -w^3 + 5*w^2 - 13]', '[361, 19, w^3 + 2*w^2 - 7*w - 9]', '[367, 367, 2*w^3 - 10*w - 5]', '[367, 367, w^3 - w^2 - 6*w + 2]', '[367, 367, -w^3 + 2*w^2 + 5*w - 4]', '[367, 367, 2*w^3 - 6*w^2 - 4*w + 13]', '[368, 46, -2*w^3 + 2*w^2 + 6*w - 2]', '[368, 46, 2*w^3 - 4*w^2 - 4*w + 4]', '[388, 194, w^3 - w^2 - 7*w + 6]', '[388, 194, w^3 - 2*w^2 - 6*w + 1]', '[401, 401, -w^3 + 2*w^2 + 5*w - 5]', '[401, 401, -w^3 + w^2 + 6*w - 1]', '[409, 409, 2*w^3 - 3*w^2 - 6*w + 4]', '[409, 409, 3*w^3 - 3*w^2 - 12*w + 1]', '[409, 409, -3*w^3 + 6*w^2 + 9*w - 11]', '[409, 409, -2*w^3 + 3*w^2 + 6*w - 3]', '[431, 431, 3*w^2 - 5*w - 10]', '[431, 431, w^3 + w^2 - 8*w - 3]', '[448, 28, -2*w^3 + 2*w^2 + 6*w]', '[448, 28, -2*w^3 + 6*w^2 + 2*w - 8]', '[448, 28, -2*w^3 + 8*w + 2]', '[448, 28, -2*w^3 + 4*w^2 + 4*w - 6]', '[452, 226, 2*w^3 - w^2 - 9*w - 1]', '[452, 226, 2*w^3 - 5*w^2 - 5*w + 9]', '[457, 457, -2*w^3 + 4*w^2 + 4*w - 5]', '[457, 457, -2*w^3 + 2*w^2 + 6*w - 1]', '[463, 463, -2*w^3 + 7*w^2 + w - 16]', '[463, 463, 3*w^3 - 6*w^2 - 8*w + 8]', '[484, 22, -w^3 + 4*w^2 - 13]', '[484, 22, -w^3 - w^2 + 5*w + 10]', '[496, 62, 2*w^2 - 10]', '[496, 62, -2*w^2 + 4*w + 8]', '[497, 497, w^2 + w + 2]', '[497, 497, -w^3 - 4*w^2 + 5*w + 13]', '[497, 497, w^3 - 4*w^2 + 2*w + 8]', '[497, 497, -2*w^2 + 5*w + 7]', '[497, 497, -2*w^2 - w + 10]', '[497, 497, -w^3 - w^2 + 3*w + 7]', '[497, 497, w^3 - 7*w^2 + 6*w + 13]', '[497, 497, w^2 - 3*w + 4]', '[503, 503, -w^3 + 3*w^2 + 2*w - 12]', '[503, 503, -w^3 + 4*w^2 + 4*w - 10]', '[508, 254, -w^3 + 6*w - 1]', '[508, 254, w^3 - 3*w^2 - 3*w + 4]', '[521, 521, w^3 + w^2 - 6*w - 2]', '[521, 521, -w^3 + 4*w^2 + w - 6]', '[529, 23, -w^2 + w - 2]', '[529, 23, w^2 - w - 8]', '[529, 529, -w^2 + 4*w + 2]', '[529, 529, w^2 + 2*w - 5]', '[548, 274, -2*w^3 + 3*w^2 + 5*w - 3]', '[553, 553, w^2 - 4*w]', '[553, 553, -w^2 - 3*w]', '[553, 553, -w^3 + 6*w^2 - 7*w - 4]', '[553, 553, w^3 + w^2 - 7*w - 3]', '[553, 553, w^3 - 4*w^2 - 2*w + 8]', '[553, 553, -w^3 - 3*w^2 + 2*w + 6]', '[553, 553, w^2 - 5*w + 4]', '[553, 553, -w^2 - 2*w + 3]', '[567, 21, -3*w]', '[567, 21, 3*w^2 - 6*w - 3]', '[567, 21, -3*w^2 + 6]', '[567, 21, -3*w + 3]', '[569, 569, w^3 - 3*w - 6]', '[569, 569, -w^3 + 3*w^2 - 8]', '[577, 577, -w^3 + 4*w^2 - w - 10]', '[577, 577, w^3 + w^2 - 4*w - 8]', '[593, 593, -w^3 + 3*w^2 - 12]', '[593, 593, w^3 - 3*w - 10]', '[599, 599, w^3 + 3*w^2 - 7*w - 9]', '[599, 599, -w^3 + 3*w^2 + 3*w - 13]', '[601, 601, w^2 + 2*w - 4]', '[601, 601, w^2 - 4*w - 1]', '[607, 607, 2*w^2 - 13]', '[607, 607, w^3 + 2*w^2 - 7*w - 5]', '[607, 607, 2*w^3 - 3*w^2 - 8*w + 8]', '[607, 607, 2*w^2 - 4*w - 11]', '[617, 617, w^3 + w^2 - 9*w - 1]', '[617, 617, w^3 - w^2 - 4*w - 5]', '[617, 617, -w^3 + 2*w^2 + 3*w - 9]', '[617, 617, -w^3 + 4*w^2 + 4*w - 8]', '[623, 623, w^3 - 5*w + 4]', '[623, 623, 3*w^3 - w^2 - 8*w + 1]', '[623, 623, -w^3 + 2*w^2 - w + 3]', '[623, 623, -w^3 + 4*w^2 - w - 2]', '[623, 623, w^3 + w^2 - 4*w]', '[623, 623, w^3 - w^2 + 3]', '[623, 623, -3*w^3 + 8*w^2 + w - 5]', '[623, 623, -w^3 + 3*w^2 + 2*w]', '[625, 5, -5]', '[631, 631, -w^3 + 5*w^2 - 2*w - 13]', '[631, 631, w^3 + 2*w^2 - 5*w - 11]', '[641, 641, w^2 - 2*w + 3]', '[641, 641, -w^3 + 6*w - 2]', '[641, 641, -w^3 + 3*w^2 + 3*w - 3]', '[641, 641, -w^2 - 2]', '[644, 322, -w^3 + w^2 + w + 4]', '[644, 322, w^3 - 4*w^2 + 2*w + 1]', '[644, 322, -w^3 + 3*w^2 + 3*w - 2]', '[644, 322, w^3 - 4*w + 3]', '[644, 322, w^3 - 3*w^2 - w]', '[644, 322, w^3 - 6*w + 3]', '[644, 322, w^3 + w^2 - 3*w]', '[644, 322, -w^3 + 2*w^2 - 5]', '[647, 647, -2*w^3 + 5*w^2 + 4*w - 6]', '[647, 647, 2*w^3 - 4*w^2 - 5*w - 1]', '[647, 647, 3*w^3 - 7*w^2 - 7*w + 13]', '[647, 647, -2*w^3 + w^2 + 8*w - 1]', '[656, 82, -2*w^3 + 4*w^2 + 4*w - 12]', '[656, 82, 2*w^3 - 2*w^2 - 6*w - 6]', '[668, 334, w^3 + w^2 - 9*w - 6]', '[668, 334, 3*w^3 - 2*w^2 - 12*w - 5]', '[668, 334, 2*w^3 - 3*w^2 - 9*w + 1]', '[668, 334, -w^3 + 4*w^2 + 4*w - 13]', '[673, 673, -w^3 + 7*w - 2]', '[673, 673, -w^3 + 3*w^2 + 4*w - 4]', '[679, 679, 2*w^2 - 11]', '[679, 679, 3*w^3 + 2*w^2 - 14*w - 14]', '[679, 679, -4*w^3 + 15*w^2 - 2*w - 26]', '[679, 679, w^3 + 3*w^2 - 6*w - 12]', '[679, 679, -w^3 + 6*w^2 - 3*w - 14]', '[679, 679, 4*w^3 + 3*w^2 - 16*w - 17]', '[679, 679, -3*w^3 + 11*w^2 + w - 23]', '[679, 679, 2*w^2 - 4*w - 9]', '[713, 713, -2*w^3 + 9*w + 3]', '[713, 713, -w^3 + 5*w^2 - 3*w - 11]', '[713, 713, w^3 + 2*w^2 - 4*w - 10]', '[713, 713, -2*w^3 + 6*w^2 + 3*w - 10]', '[719, 719, -2*w^3 + 5*w^2 + 3*w - 12]', '[719, 719, 4*w^2 - 5*w - 10]', '[719, 719, -4*w^2 + 3*w + 11]', '[719, 719, 2*w^3 - w^2 - 7*w - 6]', '[727, 727, -w - 5]', '[727, 727, w - 6]', '[743, 743, w^2 + 2*w - 11]', '[743, 743, w^3 + 4*w^2 - 11*w - 11]', '[751, 751, -2*w^2 + w + 13]', '[751, 751, 2*w^2 - 3*w - 12]', '[752, 94, 2*w^2 - 4*w - 10]', '[752, 94, 2*w^2 - 12]', '[764, 382, w^3 - 8*w + 1]', '[764, 382, w^3 - 3*w^2 - 5*w + 6]', '[769, 769, 2*w^3 - 6*w^2 - 3*w + 17]', '[769, 769, 3*w^3 - 2*w^2 - 11*w + 2]', '[772, 386, -w^3 + 4*w^2 + 4*w - 11]', '[772, 386, -w^3 + 5*w^2 + 3*w - 12]', '[772, 386, -w^3 - 2*w^2 + 10*w + 5]', '[772, 386, w^3 + w^2 - 9*w - 4]', '[784, 14, -4*w^2 + 6*w + 14]', '[784, 14, 2*w^3 - 4*w^2 - 6*w + 14]', '[784, 14, -4*w^2 + 4*w + 14]', '[784, 14, -4*w^2 + 4*w + 10]', '[784, 14, 2*w^3 - 2*w^2 - 4*w + 4]', '[784, 14, -2*w^3 + 2*w^2 + 8*w + 6]', '[784, 98, -2*w^3 + 8*w + 8]', '[784, 98, -2*w^3 + 10*w + 4]', '[784, 98, -2*w^3 + 6*w^2 + 4*w - 12]', '[784, 98, 2*w^3 - 6*w^2 - 2*w + 14]', '[791, 791, w^2 + 2*w - 10]', '[791, 791, 4*w^2 - 5*w - 12]', '[791, 791, w^3 - 3*w - 7]', '[791, 791, -w^3 + w - 4]', '[791, 791, w^3 - 3*w^2 + 2*w - 4]', '[791, 791, -w^3 + 3*w^2 - 9]', '[791, 791, 4*w^2 - 3*w - 13]', '[791, 791, w^2 - 4*w - 7]', '[796, 398, -w^2 + 3*w + 9]', '[796, 398, w^2 + w - 11]', '[809, 809, w^3 + 3*w^2 - 6*w - 11]', '[809, 809, -3*w^3 + 5*w^2 + 8*w - 11]', '[823, 823, -w^3 + w^2 + 2*w - 6]', '[823, 823, 4*w^2 - 5*w - 11]', '[823, 823, -4*w^2 + 3*w + 12]', '[823, 823, -w^3 + 4*w^2 + 4*w - 12]', '[839, 839, -2*w^3 + w^2 + 6*w + 5]', '[839, 839, -3*w^3 + 8*w^2 + 7*w - 17]', '[839, 839, 3*w^3 - w^2 - 14*w - 5]', '[839, 839, -2*w^3 + 5*w^2 + 2*w - 10]', '[847, 77, -2*w^3 + 3*w^2 + 8*w]', '[847, 77, 2*w^3 - w^2 - 9*w]', '[847, 77, -3*w^3 + 6*w^2 + 7*w - 6]', '[847, 77, w^3 - w^2 - 7*w + 5]', '[847, 77, -w^3 + 2*w^2 + 6*w - 2]', '[847, 77, 3*w^3 - 3*w^2 - 10*w + 4]', '[847, 77, 2*w^3 - 3*w^2 - 8*w + 9]', '[847, 77, -2*w^3 + 5*w^2 + 5*w - 8]', '[857, 857, w^3 + w^2 - 8*w - 2]', '[857, 857, -w^3 + 4*w^2 + 3*w - 8]', '[863, 863, -w^3 + w^2 - w - 1]', '[863, 863, w^3 - 2*w^2 + 2*w - 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10]', '[1697, 1697, 2*w^3 - 2*w^2 - 5*w - 5]', '[1721, 1721, 4*w^2 - 7*w - 3]', '[1721, 1721, -w^3 + 2*w^2 - w - 6]', '[1721, 1721, w^3 - w^2 - 6]', '[1721, 1721, 3*w^3 - w^2 - 14*w - 4]', '[1724, 862, 2*w^3 - w^2 - 7*w - 9]', '[1724, 862, 3*w^3 - 6*w^2 - 8*w + 5]', '[1753, 1753, w^2 + 3*w - 6]', '[1753, 1753, -2*w^3 + 5*w^2 + 5*w - 18]', '[1753, 1753, 6*w^2 - 8*w - 13]', '[1753, 1753, w^2 - 5*w - 2]', '[1759, 1759, -2*w^3 + w^2 + 10*w - 1]', '[1759, 1759, w^3 - 5*w^2 + 6*w + 8]', '[1759, 1759, w^3 + 2*w^2 - w - 10]', '[1759, 1759, -2*w^3 + 5*w^2 + 6*w - 8]', '[1783, 1783, -4*w^3 + 6*w^2 + 14*w - 13]', '[1783, 1783, w^3 + 2*w^2 - 5*w - 13]', '[1783, 1783, -w^3 + 5*w^2 - 2*w - 15]', '[1783, 1783, -2*w^3 + 7*w^2 + 2*w - 23]', '[1792, 28, 4*w]', '[1792, 28, -4*w^2 + 8*w + 4]', '[1792, 28, 4*w^2 - 8]', '[1792, 28, 4*w - 4]', '[1799, 1799, -2*w^2 + w + 14]', '[1799, 1799, -3*w^3 + 6*w^2 + 7*w - 8]', '[1799, 1799, w^3 - 2*w^2 - 2*w - 4]', '[1799, 1799, 4*w^3 - 18*w^2 + 13*w + 18]', '[1799, 1799, w^2 - 5*w - 8]', '[1799, 1799, -5*w^2 + 10*w + 7]', '[1799, 1799, 3*w^3 - 5*w^2 - 6*w - 3]', '[1799, 1799, 2*w^3 - 4*w^2 - 7*w + 16]', '[1799, 1799, 2*w^3 - 2*w^2 - 9*w - 7]', '[1799, 1799, 3*w^3 - 4*w^2 - 7*w + 11]', '[1799, 1799, 2*w^3 - 6*w^2 - 7*w + 25]', '[1799, 1799, -w^2 - 3*w + 12]', '[1799, 1799, 2*w^3 - 7*w^2 - 2*w + 22]', '[1799, 1799, w^3 - w^2 - 3*w + 7]', '[1799, 1799, -w^2 - 4*w + 17]', '[1799, 1799, w^3 - 7*w^2 + 10*w + 3]', '[1801, 1801, 2*w^3 - 11*w - 3]', '[1801, 1801, -2*w^3 + 6*w^2 + 5*w - 12]', '[1808, 226, 2*w^3 - 4*w^2 - 8*w + 4]', '[1808, 226, 2*w^3 - 2*w^2 - 10*w + 6]', '[1817, 1817, -3*w^3 + 3*w^2 + 10*w + 1]', '[1817, 1817, -4*w^3 + 11*w^2 + 4*w - 15]', '[1817, 1817, 4*w^3 - w^2 - 14*w - 4]', '[1817, 1817, 3*w^3 - 6*w^2 - 7*w + 11]', '[1823, 1823, -2*w^3 + 7*w^2 + w - 18]', '[1823, 1823, 2*w^3 + w^2 - 9*w - 12]', '[1828, 914, -w^2 + 5*w - 1]', '[1828, 914, w^2 + 3*w - 3]', '[1831, 1831, 2*w^2 + 3*w - 3]', '[1831, 1831, -3*w^3 + 4*w^2 + 9*w - 6]', '[1831, 1831, -3*w^3 + 5*w^2 + 8*w - 4]', '[1831, 1831, -2*w^2 + 7*w - 2]', '[1841, 1841, -3*w^3 + 8*w^2 + 4*w - 6]', '[1841, 1841, w^3 - 9*w^2 + 12*w + 12]', '[1841, 1841, -3*w^3 + 4*w^2 + 7*w - 1]', '[1841, 1841, -3*w^3 + 6*w^2 + 4*w + 2]', '[1841, 1841, -3*w^2 + 8*w + 2]', '[1841, 1841, -4*w^3 + 14*w^2 + w - 23]', '[1841, 1841, -w^3 + 2*w^2 + w + 5]', '[1841, 1841, -4*w^3 + 10*w^2 + 6*w - 19]', '[1841, 1841, -4*w^3 + 2*w^2 + 14*w + 7]', '[1841, 1841, -w^3 - 2*w^2 + 11*w + 7]', '[1841, 1841, -4*w^3 - 2*w^2 + 17*w + 12]', '[1841, 1841, -2*w^3 + 2*w^2 + 8*w + 7]', '[1841, 1841, -2*w^3 + 4*w^2 + 7*w - 3]', '[1841, 1841, -3*w^3 + 5*w^2 + 6*w - 7]', '[1841, 1841, -2*w^2 + 5*w + 10]', '[1841, 1841, -3*w^3 + w^2 + 11*w - 3]', '[1847, 1847, w^3 + w^2 - 4*w - 13]', '[1847, 1847, -w^3 + 4*w^2 - w - 15]', '[1852, 926, w^2 + 3*w - 13]', '[1852, 926, 2*w^3 - w^2 - 13*w + 3]', '[1863, 69, 3*w^3 - 3*w^2 - 9*w + 3]', '[1863, 69, -3*w^3 + 6*w^2 + 6*w - 6]', '[1871, 1871, -4*w^2 + 9*w + 8]', '[1871, 1871, -4*w^2 - w + 13]', '[1873, 1873, -w^3 + 3*w^2 - w - 9]', '[1873, 1873, w^3 - 2*w - 8]', '[1889, 1889, 5*w^2 - 6*w - 16]', '[1889, 1889, 5*w^2 - 4*w - 17]', '[1897, 1897, 2*w^3 - 6*w^2 + w + 10]', '[1897, 1897, w^3 + 2*w^2 - 3*w - 1]', '[1897, 1897, 2*w^3 - 11*w^2 + 7*w + 18]', '[1897, 1897, w^3 - 3*w^2 + 3*w + 7]', '[1897, 1897, w^3 - 8]', '[1897, 1897, 2*w^3 + 5*w^2 - 9*w - 16]', '[1897, 1897, w^3 - 5*w^2 + 4*w + 1]', '[1897, 1897, 2*w^3 - 5*w - 7]', '[1913, 1913, -3*w^3 + 9*w^2 + 4*w - 22]', '[1913, 1913, 3*w^3 - 13*w - 12]', '[1927, 1927, 3*w^3 - 3*w^2 - 9*w - 1]', '[1927, 1927, 4*w^3 - 8*w^2 - 11*w + 12]', '[1927, 1927, -2*w^3 + 10*w - 5]', '[1927, 1927, -3*w^3 + 6*w^2 + 6*w - 10]', '[1936, 22, 4*w^2 - 2*w - 18]', '[1936, 22, -4*w^2 + 6*w + 16]', '[1951, 1951, -3*w^3 + 5*w^2 + 7*w - 3]', '[1951, 1951, 3*w^3 - 4*w^2 - 8*w + 6]', '[1984, 124, -2*w^3 + 6*w^2 + 2*w - 16]', '[1984, 124, -2*w^3 + 8*w + 10]', '[1988, 994, -2*w^3 - 3*w^2 + 11*w + 13]', '[1988, 994, 3*w^3 - w^2 - 9*w + 4]', '[1988, 994, -2*w^3 + 3*w^2 + 3*w + 3]', '[1988, 994, -3*w^3 + 2*w^2 + 10*w + 7]', '[1988, 994, 3*w^3 - 7*w^2 - 5*w + 16]', '[1988, 994, 2*w^3 - 3*w^2 - 3*w + 7]', '[1988, 994, -3*w^3 + 8*w^2 + 2*w - 3]', '[1988, 994, 2*w^3 - 9*w^2 + w + 19]', '[1993, 1993, 3*w^3 - 17*w - 8]', '[1993, 1993, -3*w^3 + 9*w^2 + 8*w - 22]', '[2009, 287, -7*w^3 + 15*w^2 + 18*w - 42]', '[2009, 287, w^3 + 4*w^2 - 4*w - 16]', '[2009, 287, -w^3 + 8*w^2 - 28]', '[2009, 287, 2*w^2 - 5*w - 11]', '[2009, 287, -w^3 + 5*w^2 - 21]', '[2009, 287, -5*w^3 + 2*w^2 + 15*w - 5]', '[2009, 287, 2*w^2 + w - 14]', '[2009, 287, 5*w^2 - 6*w - 13]', '[2009, 287, -w^3 + 7*w^2 - 7*w - 15]', '[2009, 287, 2*w^3 + 7*w^2 - 22*w - 28]', '[2009, 287, 7*w^3 - 6*w^2 - 27*w - 16]', '[2009, 287, w^3 + 5*w^2 - 13*w - 21]', '[2009, 2009, 2*w^3 + 4*w^2 - 10*w - 17]', '[2009, 2009, 4*w^3 - 3*w^2 - 14*w + 2]', '[2009, 2009, 4*w^3 - 3*w^2 - 17*w - 12]', '[2009, 2009, 3*w^3 + w^2 - 20*w - 13]', '[2009, 2009, 3*w^3 - 10*w^2 - 9*w + 29]', '[2009, 2009, -4*w^3 + 9*w^2 + 11*w - 28]', '[2009, 2009, 4*w^3 - 9*w^2 - 8*w + 11]', '[2009, 2009, -2*w^3 + 10*w^2 - 4*w - 21]', '[2012, 1006, -w^3 + 7*w^2 - w - 22]', '[2012, 1006, -4*w^3 + 5*w^2 + 13*w - 9]', '[2017, 2017, -3*w^3 + 3*w^2 + 10*w - 1]', '[2017, 2017, -w^3 + 3*w^2 - w - 13]', '[2017, 2017, -w^3 + 2*w + 12]', '[2017, 2017, -3*w^3 + 6*w^2 + 7*w - 9]', '[2023, 119, 3*w^3 - 3*w^2 - 10*w]', '[2023, 119, 3*w^3 - 3*w^2 - 8*w]', '[2023, 119, 3*w^3 - 8*w^2 - 5*w + 11]', '[2023, 119, 3*w^3 - 10*w^2 - w + 13]', '[2023, 119, 3*w^3 + w^2 - 12*w - 5]', '[2023, 119, 3*w^3 - w^2 - 12*w - 1]', '[2023, 119, 3*w^3 - 6*w^2 - 7*w + 10]', '[2023, 119, 3*w^3 - 6*w^2 - 5*w + 8]', '[2032, 254, -2*w^3 + 6*w^2 + 4*w - 10]', '[2032, 254, 2*w^3 - 10*w - 2]', '[2039, 2039, 2*w^2 - 3*w + 2]', '[2039, 2039, -2*w^3 + 10*w^2 - 3*w - 24]', '[2039, 2039, -2*w^3 - 4*w^2 + 11*w + 19]', '[2039, 2039, -2*w^2 + w - 1]', '[2047, 2047, -w^3 - 4*w^2 + 8*w + 12]', '[2047, 2047, -w^3 - 6*w^2 + 6*w + 18]', '[2047, 2047, -w^3 + 9*w^2 - 9*w - 17]', '[2047, 2047, -w^3 + 7*w^2 - 3*w - 15]', '[2081, 2081, 2*w^3 + 3*w^2 - 14*w - 16]', '[2081, 2081, 2*w^3 - 9*w^2 - 2*w + 25]', '[2084, 1042, w^3 - 5*w^2 - w + 8]', '[2084, 1042, -w^3 - 2*w^2 + 8*w + 3]', '[2089, 2089, w^3 - 9*w + 3]', '[2089, 2089, 4*w - 1]', '[2089, 2089, 4*w - 3]', '[2089, 2089, -3*w^3 + 5*w^2 + 11*w - 17]', '[2113, 2113, w^3 + 5*w^2 - 10*w - 13]', '[2113, 2113, -2*w^3 + 5*w^2 + 6*w - 19]', '[2116, 46, 5*w^2 - 5*w - 17]', '[2116, 46, 5*w^2 - 5*w - 13]', '[2116, 1058, -3*w^3 + 4*w^2 + 8*w - 1]', '[2116, 1058, -3*w^3 + 5*w^2 + 7*w - 8]', '[2137, 2137, 5*w^2 - 6*w - 15]', '[2137, 2137, 5*w^2 - 4*w - 16]', '[2153, 2153, 2*w^3 - 2*w^2 - 5*w - 6]', '[2153, 2153, w^3 - 4*w^2 - 4*w + 6]', '[2153, 2153, -w^3 - w^2 + 9*w - 1]', '[2153, 2153, -2*w^3 + 4*w^2 + 3*w - 11]', '[2161, 2161, 3*w^2 - 4*w - 17]', '[2161, 2161, 3*w^2 - 2*w - 18]', '[2177, 2177, -w^3 - 2*w^2 + 4*w + 12]', '[2177, 2177, 2*w^3 - 9*w + 1]', '[2177, 2177, 5*w^3 + 2*w^2 - 19*w - 12]', '[2177, 2177, -5*w^2 + 6*w + 14]', '[2177, 2177, -3*w^3 - 3*w^2 + 12*w + 16]', '[2177, 2177, 3*w^3 - 6*w^2 - 5*w + 7]', '[2177, 2177, 4*w^3 - 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6]', '[71, 71, -w^3 + 2*w^2 + 3*w - 1]', '[71, 71, -w^3 + w^2 + 4*w - 3]', '[79, 79, -w - 3]', '[79, 79, w - 4]', '[81, 3, -3]', '[89, 89, w^2 - 3*w - 2]', '[89, 89, w^2 + w - 4]', '[97, 97, 2*w^3 - 5*w^2 - 4*w + 9]', '[97, 97, -2*w^3 + w^2 + 8*w + 2]', '[113, 113, w^3 - 2*w^2 - 4*w + 2]', '[113, 113, w^3 - w^2 - 5*w + 3]', '[121, 11, 2*w^2 - w - 9]', '[121, 11, -2*w^2 + 3*w + 8]', '[127, 127, w^3 - 3*w^2 - 2*w + 5]', '[127, 127, w^3 - 5*w - 1]', '[137, 137, 2*w - 1]', '[167, 167, 2*w^3 - 2*w^2 - 7*w - 2]', '[167, 167, w^3 - 7*w - 4]', '[167, 167, 2*w^3 - w^2 - 9*w - 2]', '[167, 167, 2*w^3 - 4*w^2 - 5*w + 9]', '[191, 191, 2*w^3 - 4*w^2 - 5*w + 5]', '[191, 191, -2*w^3 + 2*w^2 + 7*w - 2]', '[193, 193, -2*w^3 + 3*w^2 + 6*w - 6]', '[193, 193, -2*w^3 + 2*w^2 + 7*w - 4]', '[193, 193, -2*w^3 + 4*w^2 + 5*w - 3]', '[193, 193, 2*w^3 - 3*w^2 - 6*w + 1]', '[199, 199, -w^3 - 2*w^2 + 6*w + 10]', '[199, 199, -w^3 + 5*w^2 - w - 13]', '[223, 223, -w^3 + 2*w^2 + 3*w - 8]', '[223, 223, w^3 - w^2 - 4*w - 4]', '[233, 233, -w^2 - 1]', '[233, 233, w^2 - 2*w + 2]', '[239, 239, 3*w^2 - 2*w - 13]', '[239, 239, 3*w^2 - 4*w - 12]', '[241, 241, w^3 - w^2 - 6*w + 3]', '[241, 241, w^3 - 2*w^2 - 5*w + 3]', '[257, 257, -w^3 + 3*w^2 + 4*w - 9]', '[257, 257, -2*w^3 + 4*w^2 + 8*w - 11]', '[257, 257, -w^3 + 2*w^2 + 4]', '[257, 257, w^3 - 7*w - 3]', '[263, 263, -w^3 + w^2 + 3*w + 5]', '[263, 263, w^3 - 5*w^2 + 12]', '[263, 263, -w^3 - 2*w^2 + 7*w + 8]', '[263, 263, -w^3 + 7*w + 2]', '[271, 271, -w^3 + 3*w^2 + 2*w - 3]', '[271, 271, w^3 - 5*w + 1]', '[289, 17, 3*w^2 - 3*w - 8]', '[289, 17, 3*w^2 - 3*w - 10]', '[311, 311, -2*w^3 + 2*w^2 + 7*w - 1]', '[311, 311, -w^3 + 5*w^2 - w - 11]', '[311, 311, w^3 + 2*w^2 - 6*w - 8]', '[311, 311, -2*w^3 + 4*w^2 + 5*w - 6]', '[337, 337, w^3 - w^2 - 2*w - 4]', '[337, 337, 2*w^3 - 9*w - 4]', '[337, 337, 2*w^3 - 6*w^2 - 3*w + 11]', '[337, 337, -w^3 + 2*w^2 + w - 6]', '[353, 353, -w^3 + 4*w^2 - 12]', '[353, 353, w^3 + w^2 - 5*w - 9]', '[359, 359, 2*w^3 - 4*w^2 - 6*w + 5]', '[359, 359, 2*w^3 - 2*w^2 - 8*w + 3]', '[361, 19, -w^3 + 5*w^2 - 13]', '[361, 19, w^3 + 2*w^2 - 7*w - 9]', '[367, 367, 2*w^3 - 10*w - 5]', '[367, 367, w^3 - w^2 - 6*w + 2]', '[367, 367, -w^3 + 2*w^2 + 5*w - 4]', '[367, 367, 2*w^3 - 6*w^2 - 4*w + 13]', '[401, 401, -w^3 + 2*w^2 + 5*w - 5]', '[401, 401, -w^3 + w^2 + 6*w - 1]', '[409, 409, 2*w^3 - 3*w^2 - 6*w + 4]', '[409, 409, 3*w^3 - 3*w^2 - 12*w + 1]', '[409, 409, -3*w^3 + 6*w^2 + 9*w - 11]', '[409, 409, -2*w^3 + 3*w^2 + 6*w - 3]', '[431, 431, 3*w^2 - 5*w - 10]', '[431, 431, w^3 + w^2 - 8*w - 3]', '[457, 457, -2*w^3 + 4*w^2 + 4*w - 5]', '[457, 457, -2*w^3 + 2*w^2 + 6*w - 1]', '[463, 463, -2*w^3 + 7*w^2 + w - 16]', '[463, 463, 3*w^3 - 6*w^2 - 8*w + 8]', '[503, 503, -w^3 + 3*w^2 + 2*w - 12]', '[503, 503, -w^3 + 4*w^2 + 4*w - 10]', '[521, 521, w^3 + w^2 - 6*w - 2]', '[521, 521, -w^3 + 4*w^2 + w - 6]', '[529, 23, w^2 - w - 8]', '[569, 569, w^3 - 3*w - 6]', '[569, 569, -w^3 + 3*w^2 - 8]', '[577, 577, -w^3 + 4*w^2 - w - 10]', '[577, 577, w^3 + w^2 - 4*w - 8]', '[593, 593, -w^3 + 3*w^2 - 12]', '[593, 593, w^3 - 3*w - 10]', '[599, 599, w^3 + 3*w^2 - 7*w - 9]', '[599, 599, -w^3 + 3*w^2 + 3*w - 13]', '[601, 601, w^2 + 2*w - 4]', '[601, 601, w^2 - 4*w - 1]', '[607, 607, 2*w^2 - 13]', '[607, 607, w^3 + 2*w^2 - 7*w - 5]', '[607, 607, 2*w^3 - 3*w^2 - 8*w + 8]', '[607, 607, 2*w^2 - 4*w - 11]', '[617, 617, w^3 + w^2 - 9*w - 1]', '[617, 617, w^3 - w^2 - 4*w - 5]', '[617, 617, -w^3 + 2*w^2 + 3*w - 9]', '[617, 617, -w^3 + 4*w^2 + 4*w - 8]', '[625, 5, -5]', '[631, 631, -w^3 + 5*w^2 - 2*w - 13]', '[631, 631, w^3 + 2*w^2 - 5*w - 11]', '[641, 641, w^2 - 2*w + 3]', '[641, 641, -w^3 + 6*w - 2]', '[641, 641, -w^3 + 3*w^2 + 3*w - 3]', '[641, 641, -w^2 - 2]', '[647, 647, -2*w^3 + 5*w^2 + 4*w - 6]', '[647, 647, 2*w^3 - 4*w^2 - 5*w - 1]', '[647, 647, 3*w^3 - 7*w^2 - 7*w + 13]', '[647, 647, -2*w^3 + w^2 + 8*w - 1]', '[673, 673, -w^3 + 7*w - 2]', '[673, 673, -w^3 + 3*w^2 + 4*w - 4]', '[719, 719, -2*w^3 + 5*w^2 + 3*w - 12]', '[719, 719, 4*w^2 - 5*w - 10]', '[719, 719, -4*w^2 + 3*w + 11]', '[719, 719, 2*w^3 - w^2 - 7*w - 6]', '[727, 727, -w - 5]', '[727, 727, w - 6]', '[743, 743, w^2 + 2*w - 11]', '[743, 743, w^3 + 4*w^2 - 11*w - 11]', '[751, 751, -2*w^2 + w + 13]', '[751, 751, 2*w^2 - 3*w - 12]', '[769, 769, 2*w^3 - 6*w^2 - 3*w + 17]', '[769, 769, 3*w^3 - 2*w^2 - 11*w + 2]', '[809, 809, w^3 + 3*w^2 - 6*w - 11]', '[809, 809, -3*w^3 + 5*w^2 + 8*w - 11]', '[823, 823, -w^3 + w^2 + 2*w - 6]', '[823, 823, 4*w^2 - 5*w - 11]', '[823, 823, -4*w^2 + 3*w + 12]', '[823, 823, -w^3 + 4*w^2 + 4*w - 12]', '[839, 839, -2*w^3 + w^2 + 6*w + 5]', '[839, 839, -3*w^3 + 8*w^2 + 7*w - 17]', '[839, 839, 3*w^3 - w^2 - 14*w - 5]', '[839, 839, -2*w^3 + 5*w^2 + 2*w - 10]', '[857, 857, w^3 + w^2 - 8*w - 2]', '[857, 857, -w^3 + 4*w^2 + 3*w - 8]', '[863, 863, -w^3 + w^2 - w - 1]', '[863, 863, w^3 - 2*w^2 + 2*w - 2]', '[911, 911, -w^3 + 3*w^2 - 11]', '[911, 911, w^3 - 3*w - 9]', '[919, 919, -2*w^3 + w^2 + 8*w - 2]', '[919, 919, -2*w^3 + 5*w^2 + 4*w - 5]', '[929, 929, -2*w^3 + 2*w^2 + 9*w - 4]', '[929, 929, 2*w^3 - 9*w - 12]', '[929, 929, 2*w^3 - 6*w^2 - 3*w + 19]', '[929, 929, -2*w^3 + 4*w^2 + 7*w - 5]', '[937, 937, -w^3 + 2*w^2 - 6]', '[937, 937, -w^3 + 3*w^2 - 10]', '[937, 937, w^3 - 3*w - 8]', '[937, 937, w^3 - w^2 - w - 5]', '[953, 953, 2*w^3 - 6*w^2 - 3*w + 18]', '[953, 953, -3*w^3 + 3*w^2 + 11*w - 5]', '[961, 31, 4*w^2 - 4*w - 11]', '[967, 967, -w^3 + 7*w - 3]', '[967, 967, -2*w^3 + 2*w^2 + 11*w + 2]', '[967, 967, -w^3 - 4*w^2 + 9*w + 9]', '[967, 967, -w^3 + 3*w^2 + 4*w - 3]', '[977, 977, 2*w^2 - 5*w - 8]', '[977, 977, -w^3 + 2*w^2 - w + 6]', '[977, 977, -w^3 + w^2 - 6]', '[977, 977, 2*w^2 + w - 11]', '[983, 983, -w^3 + 6*w^2 - 2*w - 16]', '[983, 983, w^3 + 3*w^2 - 7*w - 13]']}
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nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [7, 6, -5, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 8768, 'disc_rad': 274, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1]]], [5, [[4, 1]]], [7, [[1, 4]]], [11, [[2, 2]]], [13, [[4, 1]]], [17, [[2, 2]]], [19, [[2, 2]]], [23, [[2, 1], [1, 2]]], [29, [[4, 1]]], [31, [[2, 1], [1, 2]]], [37, [[2, 2]]], [41, [[2, 1], [1, 2]]], [43, [[4, 1]]], [47, [[2, 1], [1, 2]]], [53, [[4, 1]]], [59, [[2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 33.1058907144937, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.8768.1', 'local_algs': ['2.4.6.1', '137.2.1.2', '137.2.0.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 137], 'rd': 9.67665227678, 'regulator': {'__RealLiteral__': 0, 'data': '4.92588435923', 'prec': 44}, 'res': {'gal': ['196,0,-620,0,261,0,-34,0,1'], 'sib': ['8,0,-13,0,1', '196,0,-620,0,261,0,-34,0,1']}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a - 2 \\)', '\\( a^{2} - 3 \\)', '\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}