Fields are organized by the set S.

## Cases where S contains 1 prime

 S S3 C3 C2 Total gp dvi {2} 3 3 gp dvi {3} 1 1 1 3 gp dvi {5} 1 1 gp dvi {7} 1 1 2 gp dvi {11} 1 1 gp dvi {13} 1 1 2 gp dvi {17} 1 1 gp dvi {19} 1 1 2 gp dvi {23} 1 1 2 gp dvi {29} 1 1 gp dvi {31} 1 1 1 3 gp dvi {37} 1 1 2 gp dvi {41} 1 1 gp dvi {43} 1 1 2 gp dvi {47} 1 1 gp dvi {53} 1 1 gp dvi {59} 1 1 2 gp dvi {61} 1 1 2 gp dvi {67} 1 1 2 gp dvi {71} 1 1 gp dvi {73} 1 1 2 gp dvi {79} 1 1 2 gp dvi {83} 1 1 2 gp dvi {89} 1 1 gp dvi {97} 1 1 2 gp dvi {101} 1 1 gp dvi {103} 1 1 2 gp dvi {107} 1 1 2 gp dvi {109} 1 1 2 gp dvi {113} 1 1 gp dvi {127} 1 1 2 gp dvi {131} 1 1 gp dvi {137} 1 1 gp dvi {139} 1 1 1 3 gp dvi {149} 1 1 gp dvi {151} 1 1 2 gp dvi {157} 1 1 2 gp dvi {163} 1 1 2 gp dvi {167} 1 1 gp dvi {173} 1 1 gp dvi {179} 1 1 gp dvi {181} 1 1 2 gp dvi {191} 1 1 gp dvi {193} 1 1 2 gp dvi {197} 1 1 gp dvi {199} 1 1 1 3

## Cases where S contains 2 primes

 S S3 C3 C2 Total gp dvi {2,3} 7 3 10 gp dvi {2,5} 1 3 4 gp dvi {3,5} 4 1 5 gp dvi {2,7} 3 3 gp dvi {3,7} 4 2 1 7 gp dvi {5,7} 1 1 2 gp dvi {2,11} 2 3 5 gp dvi {3,11} 5 1 6 gp dvi {5,11} 1 1 gp dvi {7,11} 1 1 gp dvi {2,13} 2 3 5 gp dvi {3,13} 7 2 1 10 gp dvi {5,13} 1 1 gp dvi {7,13} 2 1 3 gp dvi {11,13} 1 1 2 gp dvi {2,17} 3 3 gp dvi {3,17} 4 1 5 gp dvi {5,17} 1 1 gp dvi {7,17} 1 1 2 gp dvi {11,17} 2 1 3 gp dvi {13,17} 1 1 gp dvi {2,19} 3 3 6 gp dvi {3,19} 4 2 1 7 gp dvi {5,19} 1 1 gp dvi {7,19} 1 2 1 4 gp dvi {11,19} 1 1 gp dvi {13,19} 1 2 1 4 gp dvi {17,19} 1 1 gp dvi {2,23} 2 3 5 gp dvi {3,23} 4 1 5 gp dvi {5,23} 1 1 gp dvi {7,23} 1 1 gp dvi {11,23} 1 1 gp dvi {13,23} 1 1 gp dvi {17,23} 1 1 gp dvi {19,23} 1 1 gp dvi {2,29} 3 3 6 gp dvi {3,29} 5 1 6 gp dvi {5,29} 1 1 gp dvi {7,29} 1 1 gp dvi {11,29} 1 1 2 gp dvi {13,29} 1 1 gp dvi {17,29} 1 1 gp dvi {19,29} 1 1 2 gp dvi {23,29} 1 1 gp dvi {2,31} 3 3 gp dvi {3,31} 4 2 1 7 gp dvi {5,31} 1 1 gp dvi {7,31} 2 1 3 gp dvi {11,31} 1 1 2 gp dvi {13,31} 2 1 3 gp dvi {17,31} 1 1 2 gp dvi {19,31} 2 1 3 gp dvi {23,31} 1 1 gp dvi {29,31} 1 1 gp dvi {2,37} 2 3 5 gp dvi {3,37} 7 2 1 10 gp dvi {5,37} 1 1 gp dvi {7,37} 1 2 1 4 gp dvi {11,37} 1 1 2 gp dvi {13,37} 2 1 3 gp dvi {17,37} 1 1 gp dvi {19,37} 2 1 3 gp dvi {23,37} 1 1 gp dvi {29,37} 1 1 gp dvi {31,37} 1 2 1 4 gp dvi {2,41} 3 3 gp dvi {3,41} 4 1 5 gp dvi {5,41} 1 1 gp dvi {7,41} 1 1 2 gp dvi {11,41} 2 1 3 gp dvi {13,41} 1 1 2 gp dvi {17,41} 2 1 3 gp dvi {19,41} 1 1 2 gp dvi {23,41} 1 1 gp dvi {29,41} 1 1 2 gp dvi {31,41} 1 1 gp dvi {37,41} 1 1 gp dvi {2,43} 2 3 5 gp dvi {3,43} 4 2 1 7 gp dvi {5,43} 1 1 2 gp dvi {7,43} 1 2 1 4 gp dvi {11,43} 1 1 2 gp dvi {13,43} 1 2 1 4 gp dvi {17,43} 1 1 2 gp dvi {19,43} 1 2 1 4 gp dvi {23,43} 1 1 gp dvi {29,43} 1 1 2 gp dvi {31,43} 1 2 1 4 gp dvi {37,43} 2 1 3 gp dvi {41,43} 1 1 2 gp dvi {2,47} 2 3 5 gp dvi {3,47} 5 1 6 gp dvi {5,47} 2 1 3 gp dvi {7,47} 2 1 3 gp dvi {11,47} 1 1 2 gp dvi {13,47} 1 1 gp dvi {17,47} 1 1 gp dvi {19,47} 1 1 gp dvi {23,47} 1 1 2 gp dvi {29,47} 2 1 3 gp dvi {31,47} 1 1 gp dvi {37,47} 1 1 2 gp dvi {41,47} 2 1 3 gp dvi {43,47} 1 1 2 gp dvi {2,53} 3 3 6 gp dvi {3,53} 4 1 5 gp dvi {5,53} 1 1 gp dvi {7,53} 1 1 2 gp dvi {11,53} 1 1 gp dvi {13,53} 1 1 gp dvi {17,53} 1 1 gp dvi {19,53} 2 1 3 gp dvi {23,53} 2 1 3 gp dvi {29,53} 1 1 gp dvi {31,53} 3 1 4 gp dvi {37,53} 1 1 gp dvi {41,53} 1 1 gp dvi {43,53} 1 1 2 gp dvi {47,53} 1 1 2 gp dvi {2,59} 3 3 6 gp dvi {3,59} 4 1 5 gp dvi {5,59} 1 1 gp dvi {7,59} 4 1 5 gp dvi {11,59} 1 1 gp dvi {13,59} 1 1 gp dvi {17,59} 1 1 gp dvi {19,59} 1 1 2 gp dvi {23,59} 1 1 gp dvi {29,59} 1 1 gp dvi {31,59} 1 1 gp dvi {37,59} 1 1 2 gp dvi {41,59} 1 1 gp dvi {43,59} 1 1 gp dvi {47,59} 1 1 gp dvi {53,59} 1 1 2 gp dvi {2,61} 2 3 5 gp dvi {3,61} 7 2 1 10 gp dvi {5,61} 1 1 gp dvi {7,61} 2 1 3 gp dvi {11,61} 1 1 2 gp dvi {13,61} 1 2 1 4 gp dvi {17,61} 1 1 gp dvi {19,61} 1 2 1 4 gp dvi {23,61} 1 1 2 gp dvi {29,61} 1 1 gp dvi {31,61} 2 1 3 gp dvi {37,61} 2 1 3 gp dvi {41,61} 1 1 gp dvi {43,61} 2 1 3 gp dvi {47,61} 2 1 3 gp dvi {53,61} 1 1 2 gp dvi {59,61} 1 1 2 gp dvi {2,67} 2 3 5 gp dvi {3,67} 4 2 1 7 gp dvi {5,67} 2 1 3 gp dvi {7,67} 2 2 1 5 gp dvi {11,67} 2 1 3 gp dvi {13,67} 2 1 3 gp dvi {17,67} 1 1 gp dvi {19,67} 1 2 1 4 gp dvi {23,67} 1 1 gp dvi {29,67} 1 1 gp dvi {31,67} 2 1 3 gp dvi {37,67} 2 2 1 5 gp dvi {41,67} 2 1 3 gp dvi {43,67} 1 2 1 4 gp dvi {47,67} 1 1 gp dvi {53,67} 1 1 2 gp dvi {59,67} 1 1 gp dvi {61,67} 1 2 1 4 gp dvi {2,71} 3 3 6 gp dvi {3,71} 5 1 6 gp dvi {5,71} 1 1 gp dvi {7,71} 1 1 gp dvi {11,71} 1 1 2 gp dvi {13,71} 1 1 gp dvi {17,71} 2 1 3 gp dvi {19,71} 2 1 3 gp dvi {23,71} 1 1 2 gp dvi {29,71} 1 1 gp dvi {31,71} 1 1 gp dvi {37,71} 2 1 3 gp dvi {41,71} 3 1 4 gp dvi {43,71} 2 1 3 gp dvi {47,71} 1 1 2 gp dvi {53,71} 3 1 4 gp dvi {59,71} 1 1 2 gp dvi {61,71} 1 1 2 gp dvi {67,71} 1 1 gp dvi {2,73} 2 3 5 gp dvi {3,73} 7 2 1 10 gp dvi {5,73} 1 1 2 gp dvi {7,73} 2 1 3 gp dvi {11,73} 1 1 gp dvi {13,73} 2 1 3 gp dvi {17,73} 1 1 gp dvi {19,73} 1 2 1 4 gp dvi {23,73} 1 1 gp dvi {29,73} 1 1 gp dvi {31,73} 2 1 3 gp dvi {37,73} 1 2 1 4 gp dvi {41,73} 1 1 2 gp dvi {43,73} 2 1 3 gp dvi {47,73} 1 1 2 gp dvi {53,73} 1 1 gp dvi {59,73} 1 1 2 gp dvi {61,73} 2 1 3 gp dvi {67,73} 1 2 1 4 gp dvi {71,73} 1 1 2 gp dvi {2,79} 2 3 5 gp dvi {3,79} 4 2 1 7 gp dvi {5,79} 1 1 gp dvi {7,79} 1 2 1 4 gp dvi {11,79} 1 1 gp dvi {13,79} 2 2 1 5 gp dvi {17,79} 1 1 2 gp dvi {19,79} 1 2 1 4 gp dvi {23,79} 1 1 gp dvi {29,79} 2 1 3 gp dvi {31,79} 1 2 1 4 gp dvi {37,79} 1 2 1 4 gp dvi {41,79} 1 1 2 gp dvi {43,79} 1 2 1 4 gp dvi {47,79} 2 1 3 gp dvi {53,79} 1 1 2 gp dvi {59,79} 1 1 2 gp dvi {61,79} 1 2 1 4 gp dvi {67,79} 1 2 1 4 gp dvi {71,79} 2 1 3 gp dvi {73,79} 3 2 1 6 gp dvi {2,83} 1 3 4 gp dvi {3,83} 4 1 5 gp dvi {5,83} 3 1 4 gp dvi {7,83} 1 1 2 gp dvi {11,83} 1 1 2 gp dvi {13,83} 1 1 gp dvi {17,83} 1 1 gp dvi {19,83} 1 1 gp dvi {23,83} 3 1 4 gp dvi {29,83} 1 1 gp dvi {31,83} 1 1 gp dvi {37,83} 1 1 gp dvi {41,83} 1 1 gp dvi {43,83} 1 1 2 gp dvi {47,83} 1 1 gp dvi {53,83} 1 1 2 gp dvi {59,83} 1 1 gp dvi {61,83} 4 1 5 gp dvi {67,83} 1 1 gp dvi {71,83} 1 1 gp dvi {73,83} 1 1 gp dvi {79,83} 1 1 2 gp dvi {2,89} 1 3 4 gp dvi {3,89} 4 1 5 gp dvi {5,89} 1 1 gp dvi {7,89} 1 1 2 gp dvi {11,89} 1 1 gp dvi {13,89} 1 1 gp dvi {17,89} 1 1 gp dvi {19,89} 2 1 3 gp dvi {23,89} 1 1 2 gp dvi {29,89} 1 1 2 gp dvi {31,89} 1 1 2 gp dvi {37,89} 1 1 2 gp dvi {41,89} 1 1 gp dvi {43,89} 1 1 2 gp dvi {47,89} 1 1 gp dvi {53,89} 1 1 gp dvi {59,89} 1 1 gp dvi {61,89} 1 1 2 gp dvi {67,89} 1 1 2 gp dvi {71,89} 1 1 gp dvi {73,89} 1 1 gp dvi {79,89} 1 1 2 gp dvi {83,89} 4 1 5 gp dvi {2,97} 2 3 5 gp dvi {3,97} 7 2 1 10 gp dvi {5,97} 1 1 gp dvi {7,97} 1 2 1 4 gp dvi {11,97} 2 1 3 gp dvi {13,97} 2 1 3 gp dvi {17,97} 1 1 gp dvi {19,97} 1 2 1 4 gp dvi {23,97} 1 1 2 gp dvi {29,97} 1 1 2 gp dvi {31,97} 4 2 1 7 gp dvi {37,97} 2 1 3 gp dvi {41,97} 1 1 gp dvi {43,97} 1 2 1 4 gp dvi {47,97} 2 1 3 gp dvi {53,97} 1 1 gp dvi {59,97} 1 1 2 gp dvi {61,97} 2 1 3 gp dvi {67,97} 2 1 3 gp dvi {71,97} 1 1 2 gp dvi {73,97} 2 1 3 gp dvi {79,97} 1 2 1 4 gp dvi {83,97} 1 1 gp dvi {89,97} 1 1

## Cases where S contains 3 primes

 S S3 C3 C2 Total gp dvi {2,3,5} 18 3 21 gp dvi {2,3,7} 18 3 21 gp dvi {2,5,7} 4 3 7 gp dvi {3,5,7} 10 1 11 gp dvi {2,3,11} 20 3 23 gp dvi {2,5,11} 4 3 7 gp dvi {3,5,11} 13 1 14 gp dvi {2,7,11} 3 3 6 gp dvi {3,7,11} 9 1 10 gp dvi {5,7,11} 1 1 2 gp dvi {2,3,13} 13 3 16 gp dvi {2,5,13} 3 3 6 gp dvi {3,5,13} 8 1 9 gp dvi {2,7,13} 4 3 7 gp dvi {3,7,13} 7 4 1 12 gp dvi {5,7,13} 1 1 2 gp dvi {2,11,13} 4 3 7 gp dvi {3,11,13} 8 1 9 gp dvi {5,11,13} 2 1 3 gp dvi {7,11,13} 2 1 3 gp dvi {2,3,17} 23 3 26 gp dvi {2,5,17} 5 3 8 gp dvi {3,5,17} 13 1 14 gp dvi {2,7,17} 4 3 7 gp dvi {3,7,17} 10 1 11 gp dvi {5,7,17} 2 1 3 gp dvi {2,11,17} 5 3 8 gp dvi {3,11,17} 9 1 10 gp dvi {5,11,17} 1 1 2 gp dvi {7,11,17} 2 1 3 gp dvi {2,13,17} 1 3 4 gp dvi {3,13,17} 20 1 21 gp dvi {5,13,17} 1 1 2 gp dvi {7,13,17} 2 1 3 gp dvi {11,13,17} 1 1 2 gp dvi {2,3,19} 19 3 22 gp dvi {2,5,19} 4 3 7 gp dvi {3,5,19} 13 1 14 gp dvi {2,7,19} 3 3 6 gp dvi {3,7,19} 13 4 1 18 gp dvi {5,7,19} 1 1 2 gp dvi {2,11,19} 5 3 8 gp dvi {3,11,19} 8 1 9 gp dvi {5,11,19} 1 1 gp dvi {7,11,19} 1 1 gp dvi {2,13,19} 1 3 4 gp dvi {3,13,19} 7 4 1 12 gp dvi {5,13,19} 2 1 3 gp dvi {7,13,19} 1 4 1 6 gp dvi {11,13,19} 1 1 2 gp dvi {2,17,19} 2 3 5 gp dvi {3,17,19} 13 1 14 gp dvi {5,17,19} 5 1 6 gp dvi {7,17,19} 1 1 gp dvi {11,17,19} 1 1 2 gp dvi {13,17,19} 1 1 2 gp dvi {2,3,23} 22 3 25 gp dvi {2,5,23} 5 3 8 gp dvi {3,5,23} 11 1 12 gp dvi {2,7,23} 3 3 gp dvi {3,7,23} 8 1 9 gp dvi {5,7,23} 2 1 3 gp dvi {2,11,23} 3 3 6 gp dvi {3,11,23} 17 1 18 gp dvi {5,11,23} 5 1 6 gp dvi {7,11,23} 1 1 gp dvi {2,13,23} 4 3 7 gp dvi {3,13,23} 23 1 24 gp dvi {5,13,23} 4 1 5 gp dvi {7,13,23} 1 1 2 gp dvi {11,13,23} 3 1 4 gp dvi {2,17,23} 3 3 6 gp dvi {3,17,23} 11 1 12 gp dvi {5,17,23} 6 1 7 gp dvi {7,17,23} 2 1 3 gp dvi {11,17,23} 4 1 5 gp dvi {13,17,23} 6 1 7 gp dvi {2,19,23} 6 3 9 gp dvi {3,19,23} 8 1 9 gp dvi {5,19,23} 2 1 3 gp dvi {7,19,23} 1 1 2 gp dvi {11,19,23} 1 1 2 gp dvi {13,19,23} 1 1 2 gp dvi {17,19,23} 2 1 3 gp dvi {2,3,29} 16 3 19 gp dvi {2,5,29} 4 3 7 gp dvi {3,5,29} 16 1 17 gp dvi {2,7,29} 3 3 6 gp dvi {3,7,29} 12 1 13 gp dvi {5,7,29} 1 1 2 gp dvi {2,11,29} 4 3 7 gp dvi {3,11,29} 9 1 10 gp dvi {5,11,29} 1 1 2 gp dvi {7,11,29} 3 1 4 gp dvi {2,13,29} 1 3 4 gp dvi {3,13,29} 19 1 20 gp dvi {5,13,29} 1 1 gp dvi {7,13,29} 1 1 2 gp dvi {11,13,29} 3 1 4 gp dvi {2,17,29} 4 3 7 gp dvi {3,17,29} 11 1 12 gp dvi {5,17,29} 2 1 3 gp dvi {7,17,29} 3 1 4 gp dvi {11,17,29} 3 1 4 gp dvi {13,17,29} 2 1 3 gp dvi {2,19,29} 4 3 7 gp dvi {3,19,29} 10 1 11 gp dvi {5,19,29} 1 1 2 gp dvi {7,19,29} 4 1 5 gp dvi {11,19,29} 2 1 3 gp dvi {13,19,29} 1 1 gp dvi {17,19,29} 2 1 3 gp dvi {2,23,29} 5 3 8 gp dvi {3,23,29} 13 1 14 gp dvi {5,23,29} 1 1 2 gp dvi {7,23,29} 1 1 gp dvi {11,23,29} 1 1 2 gp dvi {13,23,29} 1 1 2 gp dvi {17,23,29} 3 1 4 gp dvi {19,23,29} 1 1 2

## Cases where S contains 4 primes

 S S3 C3 C2 Total gp dvi {2,3,5,7} 36 3 39

John Jones