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Query: /api/artin_reps/?_offset=0
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  1. Baselabel: 1.1.1t1.a
    {'BadPrimes': [], 'Baselabel': '1.1.1t1.a', 'CharacterField': 1, 'Conductor': 1, 'Container': '1t1', 'Dets': ['1.1'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 1, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1]], 'GalOrbIndex': 1, 'HardFactors': [], 'LocalFactors': [[[1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '1T1', 'Galt': 1, 'HardPrimes': [], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [0, 1], 'NumBadPrimes': 0, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  2. Baselabel: 1.3.2t1.a
    {'BadPrimes': [3], 'Baselabel': '1.3.2t1.a', 'CharacterField': 1, 'Conductor': 3, 'Container': '2t1', 'Dets': ['3.2'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [3], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  3. Baselabel: 1.4.2t1.a
    {'BadPrimes': [2], 'Baselabel': '1.4.2t1.a', 'CharacterField': 1, 'Conductor': 4, 'Container': '2t1', 'Dets': ['4.3'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  4. Baselabel: 1.5.4t1.a
    {'BadPrimes': [5], 'Baselabel': '1.5.4t1.a', 'CharacterField': 4, 'Conductor': 5, 'Container': '4t1', 'Dets': ['5.3', '5.2'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [5], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  5. Baselabel: 1.5.2t1.a
    {'BadPrimes': [5], 'Baselabel': '1.5.2t1.a', 'CharacterField': 1, 'Conductor': 5, 'Container': '2t1', 'Dets': ['5.4'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [5], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  6. Baselabel: 1.7.3t1.a
    {'BadPrimes': [7], 'Baselabel': '1.7.3t1.a', 'CharacterField': 3, 'Conductor': 7, 'Container': '3t1', 'Dets': ['7.2', '7.4'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  7. Baselabel: 1.7.6t1.a
    {'BadPrimes': [7], 'Baselabel': '1.7.6t1.a', 'CharacterField': 3, 'Conductor': 7, 'Container': '6t1', 'Dets': ['7.3', '7.5'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [7], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 1, -1, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  8. Baselabel: 1.7.2t1.a
    {'BadPrimes': [7], 'Baselabel': '1.7.2t1.a', 'CharacterField': 1, 'Conductor': 7, 'Container': '2t1', 'Dets': ['7.6'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [7], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  9. Baselabel: 1.8.2t1.a
    {'BadPrimes': [2], 'Baselabel': '1.8.2t1.a', 'CharacterField': 1, 'Conductor': 8, 'Container': '2t1', 'Dets': ['8.5'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-2, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  10. Baselabel: 1.8.2t1.b
    {'BadPrimes': [2], 'Baselabel': '1.8.2t1.b', 'CharacterField': 1, 'Conductor': 8, 'Container': '2t1', 'Dets': ['8.5'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  11. Baselabel: 1.9.3t1.a
    {'BadPrimes': [3], 'Baselabel': '1.9.3t1.a', 'CharacterField': 3, 'Conductor': 9, 'Container': '3t1', 'Dets': ['9.7', '9.4'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -3, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  12. Baselabel: 1.9.6t1.a
    {'BadPrimes': [3], 'Baselabel': '1.9.6t1.a', 'CharacterField': 3, 'Conductor': 9, 'Container': '6t1', 'Dets': ['9.5', '9.2'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [3], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, -1, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  13. Baselabel: 1.11.2t1.a
    {'BadPrimes': [11], 'Baselabel': '1.11.2t1.a', 'CharacterField': 1, 'Conductor': 11, 'Container': '2t1', 'Dets': ['11.10'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [11], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [3, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  14. Baselabel: 1.11.5t1.a
    {'BadPrimes': [11], 'Baselabel': '1.11.5t1.a', 'CharacterField': 5, 'Conductor': 11, 'Container': '5t1', 'Dets': ['11.3', '11.9', '11.5', '11.4'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 5, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 3, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 3, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [5, 3, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [5, 3, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '5T1', 'Galt': 1, 'HardPrimes': [2, 3, 11], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 3, 3, -4, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  15. Baselabel: 1.11.10t1.a
    {'BadPrimes': [11], 'Baselabel': '1.11.10t1.a', 'CharacterField': 5, 'Conductor': 11, 'Container': '10t1', 'Dets': ['11.7', '11.6', '11.2', '11.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [10, 4, 8, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [10, 4, 8, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [10, 4, 8, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 4, 'HardFactors': [10, 4, 8, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 7, 11], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  16. Baselabel: 1.12.2t1.a
    {'BadPrimes': [2, 3], 'Baselabel': '1.12.2t1.a', 'CharacterField': 1, 'Conductor': 12, 'Container': '2t1', 'Dets': ['12.11'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  17. Baselabel: 1.13.2t1.a
    {'BadPrimes': [13], 'Baselabel': '1.13.2t1.a', 'CharacterField': 1, 'Conductor': 13, 'Container': '2t1', 'Dets': ['13.12'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [13], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-3, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  18. Baselabel: 1.13.3t1.a
    {'BadPrimes': [13], 'Baselabel': '1.13.3t1.a', 'CharacterField': 3, 'Conductor': 13, 'Container': '3t1', 'Dets': ['13.3', '13.9'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -4, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  19. Baselabel: 1.13.4t1.a
    {'BadPrimes': [13], 'Baselabel': '1.13.4t1.a', 'CharacterField': 4, 'Conductor': 13, 'Container': '4t1', 'Dets': ['13.8', '13.5'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [3, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [3, 4, 2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  20. Baselabel: 1.13.6t1.a
    {'BadPrimes': [13], 'Baselabel': '1.13.6t1.a', 'CharacterField': 3, 'Conductor': 13, 'Container': '6t1', 'Dets': ['13.10', '13.4'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 1, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [13], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -3, 6, 4, -5, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  21. Baselabel: 1.15.2t1.a
    {'BadPrimes': [3, 5], 'Baselabel': '1.15.2t1.a', 'CharacterField': 1, 'Conductor': 15, 'Container': '2t1', 'Dets': ['15.14'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [3, 5], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [4, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  22. Baselabel: 1.15.4t1.a
    {'BadPrimes': [3, 5], 'Baselabel': '1.15.4t1.a', 'CharacterField': 4, 'Conductor': 15, 'Container': '4t1', 'Dets': ['15.8', '15.2'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [3, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, 4, -4, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  23. Baselabel: 1.16.4t1.b
    {'BadPrimes': [2], 'Baselabel': '1.16.4t1.b', 'CharacterField': 4, 'Conductor': 16, 'Container': '4t1', 'Dets': ['16.11', '16.3'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [2, 0, 4, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  24. Baselabel: 1.16.4t1.a
    {'BadPrimes': [2], 'Baselabel': '1.16.4t1.a', 'CharacterField': 4, 'Conductor': 16, 'Container': '4t1', 'Dets': ['16.5', '16.13'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [2, 0, -4, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  25. Baselabel: 1.17.2t1.a
    {'BadPrimes': [17], 'Baselabel': '1.17.2t1.a', 'CharacterField': 1, 'Conductor': 17, 'Container': '2t1', 'Dets': ['17.16'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [17], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-4, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  26. Baselabel: 1.17.4t1.a
    {'BadPrimes': [17], 'Baselabel': '1.17.4t1.a', 'CharacterField': 4, 'Conductor': 17, 'Container': '4t1', 'Dets': ['17.4', '17.13'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 17], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, 1, -6, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  27. Baselabel: 1.17.8t1.a
    {'BadPrimes': [17], 'Baselabel': '1.17.8t1.a', 'CharacterField': 8, 'Conductor': 17, 'Container': '8t1', 'Dets': ['17.8', '17.2', '17.9', '17.15'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [17, 31], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, 4, -10, -10, 15, 6, -7, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  28. Baselabel: 1.19.2t1.a
    {'BadPrimes': [19], 'Baselabel': '1.19.2t1.a', 'CharacterField': 1, 'Conductor': 19, 'Container': '2t1', 'Dets': ['19.18'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [19], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [5, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  29. Baselabel: 1.19.3t1.a
    {'BadPrimes': [19], 'Baselabel': '1.19.3t1.a', 'CharacterField': 3, 'Conductor': 19, 'Container': '3t1', 'Dets': ['19.7', '19.11'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 19], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [7, -6, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  30. Baselabel: 1.19.6t1.a
    {'BadPrimes': [19], 'Baselabel': '1.19.6t1.a', 'CharacterField': 3, 'Conductor': 19, 'Container': '6t1', 'Dets': ['19.12', '19.8'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 1, 1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 1, 1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [3, 7, 11, 19], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [7, -5, -1, 8, 2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  31. Baselabel: 1.19.9t1.a
    {'BadPrimes': [19], 'Baselabel': '1.19.9t1.a', 'CharacterField': 9, 'Conductor': 19, 'Container': '9t1', 'Dets': ['19.9', '19.5', '19.6', '19.16', '19.4', '19.17'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [6, 4, 5, 10, 9, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '9T1', 'Galt': 1, 'HardPrimes': [2, 5, 13, 19, 23, 79], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 5, 10, -20, -15, 21, 7, -8, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  32. Baselabel: 1.20.2t1.a
    {'BadPrimes': [2, 5], 'Baselabel': '1.20.2t1.a', 'CharacterField': 1, 'Conductor': 20, 'Container': '2t1', 'Dets': ['20.19'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [5, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  33. Baselabel: 1.20.4t1.a
    {'BadPrimes': [2, 5], 'Baselabel': '1.20.4t1.a', 'CharacterField': 4, 'Conductor': 20, 'Container': '4t1', 'Dets': ['20.7', '20.3'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [5, 0, -5, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  34. Baselabel: 1.21.2t1.a
    {'BadPrimes': [3, 7], 'Baselabel': '1.21.2t1.a', 'CharacterField': 1, 'Conductor': 21, 'Container': '2t1', 'Dets': ['21.20'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [3, 7], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-5, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  35. Baselabel: 1.21.6t1.a
    {'BadPrimes': [3, 7], 'Baselabel': '1.21.6t1.a', 'CharacterField': 3, 'Conductor': 21, 'Container': '6t1', 'Dets': ['21.11', '21.2'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [3, 7, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -2, 5, 0, 3, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  36. Baselabel: 1.21.6t1.b
    {'BadPrimes': [3, 7], 'Baselabel': '1.21.6t1.b', 'CharacterField': 3, 'Conductor': 21, 'Container': '6t1', 'Dets': ['21.17', '21.5'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -8, 8, 6, -6, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  37. Baselabel: 1.23.2t1.a
    {'BadPrimes': [23], 'Baselabel': '1.23.2t1.a', 'CharacterField': 1, 'Conductor': 23, 'Container': '2t1', 'Dets': ['23.22'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [23], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [6, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  38. Baselabel: 1.23.22t1.a
    {'BadPrimes': [23], 'Baselabel': '1.23.22t1.a', 'CharacterField': 11, 'Conductor': 23, 'Container': '22t1', 'Dets': ['23.10', '23.15', '23.11', '23.5', '23.19', '23.17', '23.14', '23.21', '23.20', '23.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 22, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, -1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 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12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 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-1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 5, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 6, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, -1]], 'GalOrbIndex': 7, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, -1], [0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 8, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 9, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 0, -1], [0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 10, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '22T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 13, 23], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  39. Baselabel: 1.23.11t1.a
    {'BadPrimes': [23], 'Baselabel': '1.23.11t1.a', 'CharacterField': 11, 'Conductor': 23, 'Container': '11t1', 'Dets': ['23.3', '23.9', '23.4', '23.12', '23.13', '23.16', '23.2', '23.6', '23.18', '23.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 11, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 7, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 8, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 9, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 10, 'HardFactors': [6, 8, 9, 10, 7, 11, 12, 5, 6, 2, 7], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '11T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 11, 19, 23, 61, 163, 167, 241], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  40. Baselabel: 1.24.2t1.a
    {'BadPrimes': [2, 3], 'Baselabel': '1.24.2t1.a', 'CharacterField': 1, 'Conductor': 24, 'Container': '2t1', 'Dets': ['24.11'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  41. Baselabel: 1.24.2t1.b
    {'BadPrimes': [2, 3], 'Baselabel': '1.24.2t1.b', 'CharacterField': 1, 'Conductor': 24, 'Container': '2t1', 'Dets': ['24.11'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  42. Baselabel: 1.25.5t1.a
    {'BadPrimes': [5], 'Baselabel': '1.25.5t1.a', 'CharacterField': 5, 'Conductor': 25, 'Container': '5t1', 'Dets': ['25.11', '25.21', '25.6', '25.16'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 5, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 4, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 4, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [5, 4, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [5, 4, 6, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '5T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 10, -5, -10, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  43. Baselabel: 1.25.10t1.a
    {'BadPrimes': [5], 'Baselabel': '1.25.10t1.a', 'CharacterField': 5, 'Conductor': 25, 'Container': '10t1', 'Dets': ['25.4', '25.9', '25.14', '25.19'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [10, 11, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [10, 11, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 3, 'HardFactors': [10, 11, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [10, 11, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 5, 29], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -5, 25, 5, -50, -1, 35, 0, -10, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  44. Baselabel: 1.25.20t1.a
    {'BadPrimes': [5], 'Baselabel': '1.25.20t1.a', 'CharacterField': 20, 'Conductor': 25, 'Container': '20t1', 'Dets': ['25.2', '25.3', '25.8', '25.12', '25.13', '25.17', '25.22', '25.23'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 20, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, -1], [0, -1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, -1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, -1], [0, 0, -1], [-1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1], [0, -1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 1, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [14, 13, 21, 19, 20, 18], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [-1, 0, 1, 0, -1, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 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-1]], [[1], [0, -1]], [[1], [0, 1, 0, -1, 0, 1, 0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '20T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 13, 17, 23], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  45. Baselabel: 1.27.9t1.a
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  46. Baselabel: 1.27.18t1.a
    {'BadPrimes': [3], 'Baselabel': '1.27.18t1.a', 'CharacterField': 9, 'Conductor': 27, 'Container': '18t1', 'Dets': ['27.5', '27.2', '27.23', '27.20', '27.14', '27.11'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 18, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, -1], [0, 0, -1], [0, 0, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 4, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 5, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '18T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  47. Baselabel: 1.28.2t1.a
    {'BadPrimes': [2, 7], 'Baselabel': '1.28.2t1.a', 'CharacterField': 1, 'Conductor': 28, 'Container': '2t1', 'Dets': ['28.27'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 7], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-7, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  48. Baselabel: 1.28.6t1.a
    {'BadPrimes': [2, 7], 'Baselabel': '1.28.6t1.a', 'CharacterField': 3, 'Conductor': 28, 'Container': '6t1', 'Dets': ['28.11', '28.23'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 6, 0, 5, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  49. Baselabel: 1.28.6t1.b
    {'BadPrimes': [2, 7], 'Baselabel': '1.28.6t1.b', 'CharacterField': 3, 'Conductor': 28, 'Container': '6t1', 'Dets': ['28.19', '28.3'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-7, 0, 14, 0, -7, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  50. Baselabel: 1.29.2t1.a
    {'BadPrimes': [29], 'Baselabel': '1.29.2t1.a', 'CharacterField': 1, 'Conductor': 29, 'Container': '2t1', 'Dets': ['29.28'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [29], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-7, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  51. Baselabel: 1.29.4t1.a
    {'BadPrimes': [29], 'Baselabel': '1.29.4t1.a', 'CharacterField': 4, 'Conductor': 29, 'Container': '4t1', 'Dets': ['29.17', '29.12'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [7, 29], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [23, -20, 4, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  52. Baselabel: 1.29.7t1.a
    {'BadPrimes': [29], 'Baselabel': '1.29.7t1.a', 'CharacterField': 7, 'Conductor': 29, 'Container': '7t1', 'Dets': ['29.25', '29.16', '29.23', '29.24', '29.20', '29.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [5, 7, 5, 7, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '7T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 17, 29], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -9, -14, 28, 7, -12, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  53. Baselabel: 1.31.2t1.a
    {'BadPrimes': [31], 'Baselabel': '1.31.2t1.a', 'CharacterField': 1, 'Conductor': 31, 'Container': '2t1', 'Dets': ['31.30'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [31], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [8, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  54. Baselabel: 1.31.3t1.a
    {'BadPrimes': [31], 'Baselabel': '1.31.3t1.a', 'CharacterField': 3, 'Conductor': 31, 'Container': '3t1', 'Dets': ['31.5', '31.25'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 31], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [8, -10, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  55. Baselabel: 1.31.5t1.a
    {'BadPrimes': [31], 'Baselabel': '1.31.5t1.a', 'CharacterField': 5, 'Conductor': 31, 'Container': '5t1', 'Dets': ['31.8', '31.2', '31.16', '31.4'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 5, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [4, 3, 1, 2, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [4, 3, 1, 2, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [4, 3, 1, 2, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [4, 3, 1, 2, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '5T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 17, 31], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-5, 1, 21, -12, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  56. Baselabel: 1.31.6t1.a
    {'BadPrimes': [31], 'Baselabel': '1.31.6t1.a', 'CharacterField': 3, 'Conductor': 31, 'Container': '6t1', 'Dets': ['31.26', '31.6'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 31], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [32, -36, 44, -11, 3, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  57. Baselabel: 1.31.10t1.a
    {'BadPrimes': [31], 'Baselabel': '1.31.10t1.a', 'CharacterField': 5, 'Conductor': 31, 'Container': '10t1', 'Dets': ['31.29', '31.27', '31.23', '31.15'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 4, 'HardFactors': [6, 1, 5, 9, 11, 1, 7, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 5, 7, 17, 31, 67, 199, 229], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [25, -20, 63, -6, 43, 11, -9, 16, 2, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  58. Baselabel: 1.32.8t1.b
    {'BadPrimes': [2], 'Baselabel': '1.32.8t1.b', 'CharacterField': 8, 'Conductor': 32, 'Container': '8t1', 'Dets': ['32.3', '32.27', '32.19', '32.11'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [9, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [9, 7, 6], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [2, 3, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [2, 0, 16, 0, 20, 0, 8, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  59. Baselabel: 1.32.8t1.a
    {'BadPrimes': [2], 'Baselabel': '1.32.8t1.a', 'CharacterField': 8, 'Conductor': 32, 'Container': '8t1', 'Dets': ['32.13', '32.21', '32.29', '32.5'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 7, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 7, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [9, 7, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [9, 7, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [2, 3, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  60. Baselabel: 1.33.2t1.a
    {'BadPrimes': [3, 11], 'Baselabel': '1.33.2t1.a', 'CharacterField': 1, 'Conductor': 33, 'Container': '2t1', 'Dets': ['33.32'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [3, 11], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-8, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  61. Baselabel: 1.33.10t1.a
    {'BadPrimes': [3, 11], 'Baselabel': '1.33.10t1.a', 'CharacterField': 5, 'Conductor': 33, 'Container': '10t1', 'Dets': ['33.26', '33.5', '33.20', '33.14'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 11, 8, 4, 11, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [9, 11, 8, 4, 11, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [9, 11, 8, 4, 11, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [9, 11, 8, 4, 11, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 11, 67, 199], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -3, 12, 1, 20, -7, 16, -2, 5, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  62. Baselabel: 1.33.10t1.b
    {'BadPrimes': [3, 11], 'Baselabel': '1.33.10t1.b', 'CharacterField': 5, 'Conductor': 33, 'Container': '10t1', 'Dets': ['33.29', '33.17', '33.2', '33.8'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 11, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 11, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [3, 11, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [3, 11, 11], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 11], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  63. Baselabel: 1.35.2t1.a
    {'BadPrimes': [5, 7], 'Baselabel': '1.35.2t1.a', 'CharacterField': 1, 'Conductor': 35, 'Container': '2t1', 'Dets': ['35.34'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [5, 7], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [9, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  64. Baselabel: 1.35.4t1.a
    {'BadPrimes': [5, 7], 'Baselabel': '1.35.4t1.a', 'CharacterField': 4, 'Conductor': 35, 'Container': '4t1', 'Dets': ['35.27', '35.13'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [5, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [11, 9, -9, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  65. Baselabel: 1.35.6t1.b
    {'BadPrimes': [5, 7], 'Baselabel': '1.35.6t1.b', 'CharacterField': 3, 'Conductor': 35, 'Container': '6t1', 'Dets': ['35.9', '35.4'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [5, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -2, 7, 2, -7, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  66. Baselabel: 1.35.6t1.a
    {'BadPrimes': [5, 7], 'Baselabel': '1.35.6t1.a', 'CharacterField': 3, 'Conductor': 35, 'Container': '6t1', 'Dets': ['35.19', '35.24'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 5, 7, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [29, -22, 22, -8, 8, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  67. Baselabel: 1.35.12t1.a
    {'BadPrimes': [5, 7], 'Baselabel': '1.35.12t1.a', 'CharacterField': 12, 'Conductor': 35, 'Container': '12t1', 'Dets': ['35.2', '35.23', '35.32', '35.18'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1], [0, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1], [0, 0, 1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [1, 0, -1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [1, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '12T1', 'Galt': 1, 'HardPrimes': [5, 7, 181], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -2, 5, -11, 25, 1, 12, 2, 9, -4, 3, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  68. Baselabel: 1.36.6t1.b
    {'BadPrimes': [2, 3], 'Baselabel': '1.36.6t1.b', 'CharacterField': 3, 'Conductor': 36, 'Container': '6t1', 'Dets': ['36.7', '36.31'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 9, 0, 6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  69. Baselabel: 1.36.6t1.a
    {'BadPrimes': [2, 3], 'Baselabel': '1.36.6t1.a', 'CharacterField': 3, 'Conductor': 36, 'Container': '6t1', 'Dets': ['36.23', '36.11'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-3, 0, 9, 0, -6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  70. Baselabel: 1.37.2t1.a
    {'BadPrimes': [37], 'Baselabel': '1.37.2t1.a', 'CharacterField': 1, 'Conductor': 37, 'Container': '2t1', 'Dets': ['37.36'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [37], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-9, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  71. Baselabel: 1.37.3t1.a
    {'BadPrimes': [37], 'Baselabel': '1.37.3t1.a', 'CharacterField': 3, 'Conductor': 37, 'Container': '3t1', 'Dets': ['37.10', '37.26'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 37], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-11, -12, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  72. Baselabel: 1.37.4t1.a
    {'BadPrimes': [37], 'Baselabel': '1.37.4t1.a', 'CharacterField': 4, 'Conductor': 37, 'Container': '4t1', 'Dets': ['37.31', '37.6'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 1, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [3, 7, 37], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [49, -7, 5, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  73. Baselabel: 1.37.6t1.a
    {'BadPrimes': [37], 'Baselabel': '1.37.6t1.a', 'CharacterField': 3, 'Conductor': 37, 'Container': '6t1', 'Dets': ['37.27', '37.11'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [11, 37], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -38, 15, 28, -15, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  74. Baselabel: 1.37.9t1.a
    {'BadPrimes': [37], 'Baselabel': '1.37.9t1.a', 'CharacterField': 9, 'Conductor': 37, 'Container': '9t1', 'Dets': ['37.16', '37.34', '37.9', '37.33', '37.12', '37.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, 1], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [4, 9, 7, 1, 10, 1], 'LocalFactors': [[[1], [-1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '9T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 31, 37, 43], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 7, 7, -73, -32, 66, 11, -16, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  75. Baselabel: 1.39.2t1.a
    {'BadPrimes': [3, 13], 'Baselabel': '1.39.2t1.a', 'CharacterField': 1, 'Conductor': 39, 'Container': '2t1', 'Dets': ['39.38'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [3, 13], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [10, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  76. Baselabel: 1.39.4t1.a
    {'BadPrimes': [3, 13], 'Baselabel': '1.39.4t1.a', 'CharacterField': 4, 'Conductor': 39, 'Container': '4t1', 'Dets': ['39.5', '39.8'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [3, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [3, -9, -11, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  77. Baselabel: 1.39.6t1.a
    {'BadPrimes': [3, 13], 'Baselabel': '1.39.6t1.a', 'CharacterField': 3, 'Conductor': 39, 'Container': '6t1', 'Dets': ['39.35', '39.29'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [3, 13, 79], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 4, 15, 6, 5, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  78. Baselabel: 1.39.6t1.b
    {'BadPrimes': [3, 13], 'Baselabel': '1.39.6t1.b', 'CharacterField': 3, 'Conductor': 39, 'Container': '6t1', 'Dets': ['39.23', '39.17'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 7, 1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 7, 1, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 13], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [25, 10, 6, -9, 8, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  79. Baselabel: 1.40.2t1.b
    {'BadPrimes': [2, 5], 'Baselabel': '1.40.2t1.b', 'CharacterField': 1, 'Conductor': 40, 'Container': '2t1', 'Dets': ['40.29'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [10, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  80. Baselabel: 1.40.2t1.a
    {'BadPrimes': [2, 5], 'Baselabel': '1.40.2t1.a', 'CharacterField': 1, 'Conductor': 40, 'Container': '2t1', 'Dets': ['40.29'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-10, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  81. Baselabel: 1.40.4t1.a
    {'BadPrimes': [2, 5], 'Baselabel': '1.40.4t1.a', 'CharacterField': 4, 'Conductor': 40, 'Container': '4t1', 'Dets': ['40.3', '40.27'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [20, 0, -10, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  82. Baselabel: 1.40.4t1.b
    {'BadPrimes': [2, 5], 'Baselabel': '1.40.4t1.b', 'CharacterField': 4, 'Conductor': 40, 'Container': '4t1', 'Dets': ['40.13', '40.37'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [20, 0, 10, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  83. Baselabel: 1.41.2t1.a
    {'BadPrimes': [41], 'Baselabel': '1.41.2t1.a', 'CharacterField': 1, 'Conductor': 41, 'Container': '2t1', 'Dets': ['41.40'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [41], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-10, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  84. Baselabel: 1.41.5t1.a
    {'BadPrimes': [41], 'Baselabel': '1.41.5t1.a', 'CharacterField': 5, 'Conductor': 41, 'Container': '5t1', 'Dets': ['41.16', '41.10', '41.37', '41.18'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 5, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [4, 1, 3, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [4, 1, 3, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [4, 1, 3, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [4, 1, 3, 5, 6], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '5T1', 'Galt': 1, 'HardPrimes': [2, 3, 7, 11, 41], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [9, 21, -5, -16, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  85. Baselabel: 1.41.4t1.a
    {'BadPrimes': [41], 'Baselabel': '1.41.4t1.a', 'CharacterField': 4, 'Conductor': 41, 'Container': '4t1', 'Dets': ['41.32', '41.9'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 41], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-4, -18, -15, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  86. Baselabel: 1.41.8t1.a
    {'BadPrimes': [41], 'Baselabel': '1.41.8t1.a', 'CharacterField': 8, 'Conductor': 41, 'Container': '8t1', 'Dets': ['41.27', '41.3', '41.14', '41.38'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 8, 1, 9, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [3, 8, 1, 9, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [3, 8, 1, 9, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [3, 8, 1, 9, 1, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [2, 3, 37, 41, 83, 139], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [59, 160, 153, 53, 44, -11, 3, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  87. Baselabel: 1.43.2t1.a
    {'BadPrimes': [43], 'Baselabel': '1.43.2t1.a', 'CharacterField': 1, 'Conductor': 43, 'Container': '2t1', 'Dets': ['43.42'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [43], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [11, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  88. Baselabel: 1.43.3t1.a
    {'BadPrimes': [43], 'Baselabel': '1.43.3t1.a', 'CharacterField': 3, 'Conductor': 43, 'Container': '3t1', 'Dets': ['43.36', '43.6'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 3, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [-1, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 4], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 4], 'LocalFactors': [[[1], [-1]], [[1], [1, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '3T1', 'Galt': 1, 'HardPrimes': [2, 43], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-8, -14, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  89. Baselabel: 1.43.6t1.a
    {'BadPrimes': [43], 'Baselabel': '1.43.6t1.a', 'CharacterField': 3, 'Conductor': 43, 'Container': '6t1', 'Dets': ['43.7', '43.37'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [2, 1, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [2, 1, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 11, 43, 47], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [44, 50, 67, 23, 4, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  90. Baselabel: 1.43.7t1.a
    {'BadPrimes': [43], 'Baselabel': '1.43.7t1.a', 'CharacterField': 7, 'Conductor': 43, 'Container': '7t1', 'Dets': ['43.41', '43.4', '43.35', '43.16', '43.11', '43.21'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 7, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 1], [0, 0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, 0, 0, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 1]], 'GalOrbIndex': 4, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 1], [0, 0, 1]], 'GalOrbIndex': 5, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1]], 'GalOrbIndex': 6, 'HardFactors': [7, 2, 1, 8], 'LocalFactors': [[[1], [-1]], [[1], [1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '7T1', 'Galt': 1, 'HardPrimes': [2, 3, 7, 43], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [49, 7, -104, 38, 35, -18, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  91. Baselabel: 1.44.2t1.a
    {'BadPrimes': [2, 11], 'Baselabel': '1.44.2t1.a', 'CharacterField': 1, 'Conductor': 44, 'Container': '2t1', 'Dets': ['44.43'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3, 3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [2, 11], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-11, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  92. Baselabel: 1.44.10t1.a
    {'BadPrimes': [2, 11], 'Baselabel': '1.44.10t1.a', 'CharacterField': 5, 'Conductor': 44, 'Container': '10t1', 'Dets': ['44.3', '44.31', '44.27', '44.15'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [11, 8, 9, 11, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [11, 8, 9, 11, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [11, 8, 9, 11, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 4, 'HardFactors': [11, 8, 9, 11, 8], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 7, 11, 19], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 15, 0, 35, 0, 28, 0, 9, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  93. Baselabel: 1.44.10t1.b
    {'BadPrimes': [2, 11], 'Baselabel': '1.44.10t1.b', 'CharacterField': 5, 'Conductor': 44, 'Container': '10t1', 'Dets': ['44.7', '44.39', '44.35', '44.19'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, 0, 1], [0, 0, 0, 1], [-1, -1, -1, -1], [0, 0, 0, -1], [1, 1, 1, 1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [11, 7, 6, 11, 8, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [-1, -1, -1, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1], [0, 0, -1], [1, 1, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [11, 7, 6, 11, 8, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [0, 1], [-1, -1, -1, -1], [0, 0, 1], [1, 1, 1, 1], [0, 0, -1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [11, 7, 6, 11, 8, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, -1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [1, 1, 1, 1], [0, 0, 0, -1]], 'GalOrbIndex': 4, 'HardFactors': [11, 7, 6, 11, 8, 10], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1]], [[1], [0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '10T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 11, 61, 191], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  94. Baselabel: 1.45.6t1.a
    {'BadPrimes': [3, 5], 'Baselabel': '1.45.6t1.a', 'CharacterField': 3, 'Conductor': 45, 'Container': '6t1', 'Dets': ['45.34', '45.4'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [1, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [0, -1], [1, 1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [3, 5, 19], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, 3, 9, -4, -9, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  95. Baselabel: 1.45.6t1.b
    {'BadPrimes': [3, 5], 'Baselabel': '1.45.6t1.b', 'CharacterField': 3, 'Conductor': 45, 'Container': '6t1', 'Dets': ['45.29', '45.14'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 1, 'HardFactors': [4, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [4, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 17], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [19, -12, 9, -4, 6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  96. Baselabel: 1.45.12t1.a
    {'BadPrimes': [3, 5], 'Baselabel': '1.45.12t1.a', 'CharacterField': 12, 'Conductor': 45, 'Container': '12t1', 'Dets': ['45.7', '45.43', '45.22', '45.13'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1], [0, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1], [0, 0, 1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [1, 0, -1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [1, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [12, 13, 13, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '12T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 701], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 3, 9, 26, 75, 18, 28, 9, 9, -1, 3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  97. Baselabel: 1.45.12t1.b
    {'BadPrimes': [3, 5], 'Baselabel': '1.45.12t1.b', 'CharacterField': 12, 'Conductor': 45, 'Container': '12t1', 'Dets': ['45.38', '45.2', '45.23', '45.32'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1], [1, 0, -1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [12, 13, 13], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 1], [0, 0, 1], [1, 0, -1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [12, 13, 13], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 1]], [[1], [0, -1, 0, 1]], [[1], [0, -1]], [[1], [0, 1, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, -1], [0, 0, 1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 3, 'HardFactors': [12, 13, 13], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [-1, 0, 1], [0, 0, 0, -1], [0, 0, 0, 1], [1, 0, -1], [0, 0, 1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [12, 13, 13], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1, 0, 1]], [[1], [0, 1]], [[1], [0, 1, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '12T1', 'Galt': 1, 'HardPrimes': [2, 3, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  98. Baselabel: 1.47.2t1.a
    {'BadPrimes': [47], 'Baselabel': '1.47.2t1.a', 'CharacterField': 1, 'Conductor': 47, 'Container': '2t1', 'Dets': ['47.46'], 'Dim': 1, 'GalConjSigns': [1], 'Galn': 2, 'GaloisConjugates': [{'Sign': 1, 'Character': [[1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [3], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '2T1', 'Galt': 1, 'HardPrimes': [47], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [12, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  99. Baselabel: 1.48.4t1.b
    {'BadPrimes': [2, 3], 'Baselabel': '1.48.4t1.b', 'CharacterField': 4, 'Conductor': 48, 'Container': '4t1', 'Dets': ['48.5', '48.29'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [18, 0, 12, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
  100. Baselabel: 1.48.4t1.a
    {'BadPrimes': [2, 3], 'Baselabel': '1.48.4t1.a', 'CharacterField': 4, 'Conductor': 48, 'Container': '4t1', 'Dets': ['48.35', '48.11'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 3], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [18, 0, -12, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}