# Tables of Octics Containing a Quartic Subfield

## Cases where S contains one prime

 S T1 T2 T4 T6 T7 T8 T10 T12 T13 T14 T16 T17 T19 T20 T21 T23 T27 T28 T30 T38 T40 Total {2} 2 1 2 4 1 2 2 2 4 2 1 1 4 4 4 36 txt gp {3} 0 {5} 0 {7} 0 {11} 0 {13} 0 {17} 1 1 txt gp {19} 0 {23} 0 {29} 0 {31} 0 {37} 0 {41} 1 1 txt gp {43} 0 {47} 0 {53} 0 {59} 1 2 3 txt gp {61} 0 {67} 0 {71} 0 {73} 1 1 txt gp {79} 0 {83} 0 {89} 1 1 txt gp {97} 1 1 txt gp {101} 0 {103} 0 {107} 1 2 3 txt gp {109} 0 {113} 1 1 txt gp {127} 0 {131} 0 {137} 1 1 txt gp {139} 1 2 3 txt gp {149} 0 {151} 0 {157} 0 {163} 2 1 4 7 txt gp {167} 0 {173} 0 {179} 0 {181} 0 {191} 0 {193} 1 1 txt gp {197} 0 {199} 0 {211} 0 {223} 0 {227} 0 {229} 3 6 9 txt gp

## Cases where S contains two primes

• We partition the data into 2 tables, one for old fields and one for new fields.
• If there is no column for a specific type of field that means no fields of that type were found.
• The data files are not partitioned, so they contain all fields.

### Old Fields

 S T2 T3 T4 T9 T10 T13 T14 T18 T24 Total {2,3} 6 1 14 28 8 7 22 24 132 242 txt gp {2,5} 18 1 12 24 24 3 8 18 108 txt gp {3,5} 1 1 2 4 txt gp {2,7} 6 1 20 40 24 7 64 162 txt gp {3,7} 1 1 2 4 txt gp {5,7} 1 1 txt gp {2,11} 6 1 14 28 8 6 24 36 123 txt gp {3,11} 1 3 6 10 txt gp {5,11} 1 2 2 5 txt gp {7,11} 1 1 txt gp {2,13} 18 1 12 24 24 7 10 8 60 164 txt gp {3,13} 1 2 2 1 2 8 txt gp {5,13} 3 3 6 txt gp {7,13} 1 3 4 txt gp {11,13} 1 1 2 4 txt gp {2,17} 18 1 30 60 72 128 309 txt gp {3,17} 1 3 2 4 10 txt gp {5,17} 3 3 txt gp {7,17} 1 1 txt gp {11,17} 1 1 2 4 txt gp {13,17} 3 3 6 12 txt gp {2,19} 6 1 14 28 8 7 13 24 78 179 txt gp {3,19} 1 3 2 4 10 txt gp {5,19} 1 2 2 5 txt gp {7,19} 1 3 4 txt gp {11,19} 1 3 4 txt gp {13,19} 1 1 2 4 txt gp {17,19} 1 2 2 5 txt gp {2,23} 6 1 20 40 24 9 64 54 218 txt gp {3,23} 1 3 6 10 txt gp {5,23} 1 1 2 4 txt gp {7,23} 1 1 2 4 txt gp {11,23} 1 1 2 4 txt gp {13,23} 1 2 2 5 txt gp {17,23} 1 1 2 4 txt gp {19,23} 1 1 2 4 txt gp {2,29} 18 1 12 24 24 17 8 102 206 txt gp {3,29} 1 4 8 13 txt gp {5,29} 3 3 6 12 txt gp {7,29} 1 2 2 3 8 txt gp {11,29} 1 1 2 4 txt gp {13,29} 3 3 6 12 txt gp {17,29} 3 3 txt gp {19,29} 1 1 2 4 txt gp {23,29} 1 2 2 5 txt gp

### New Fields

 S T1 T5 T6 T7 T8 T11 T15 T16 T17 T19 T20 T21 T23 T26 T27 T28 T29 T30 T31 T35 T38 T39 T40 T44 Total {2,3} 4 2 20 6 22 18 42 8 16 8 4 4 128 64 16 16 48 16 16 168 24 168 216 656 1690 txt gp {2,5} 8 20 20 10 18 42 24 72 24 12 12 24 24 48 48 24 48 8 72 24 24 96 702 txt gp {3,5} 1 4 5 txt gp {2,7} 4 60 6 16 12 68 24 48 24 12 12 176 48 48 120 48 40 480 24 1270 txt gp {3,7} 1 4 5 txt gp {5,7} 1 1 txt gp {2,11} 4 2 20 6 22 18 42 8 16 8 4 4 40 64 16 16 48 16 16 168 24 32 240 834 txt gp {3,11} 1 8 9 txt gp {5,11} 2 4 6 txt gp {7,11} 2 2 txt gp {2,13} 8 20 20 10 18 42 24 72 24 12 12 32 24 48 48 24 48 8 72 24 96 144 288 1118 txt gp {3,13} 2 4 4 10 txt gp {5,13} 2 2 txt gp {7,13} 1 1 txt gp {11,13} 1 1 txt gp {2,17} 24 2 84 36 44 36 128 72 192 96 48 48 320 208 208 192 208 64 576 2586 txt gp {3,17} 2 8 10 txt gp {5,17} 4 4 txt gp {7,17} 2 2 txt gp {11,17} 2 2 txt gp {13,17} 4 1 2 2 8 4 2 2 4 4 33 txt gp {2,19} 4 2 20 6 22 18 42 8 16 8 4 4 88 64 16 16 48 16 16 168 24 120 136 480 1346 txt gp {3,19} 1 8 4 8 21 txt gp {5,19} 2 1 2 2 1 1 2 2 4 17 txt gp {7,19} 1 4 5 txt gp {11,19} 1 4 5 txt gp {13,19} 1 1 txt gp {17,19} 2 2 1 1 2 8 txt gp {2,23} 4 60 6 16 12 68 24 48 24 12 12 48 176 48 48 120 48 40 480 48 72 400 1814 txt gp {3,23} 2 8 10 txt gp {5,23} 1 1 txt gp {7,23} 2 2 txt gp {11,23} 1 1 txt gp {13,23} 2 1 2 2 1 1 2 2 4 17 txt gp {17,23} 2 2 txt gp {19,23} 1 1 txt gp {2,29} 8 20 20 10 18 42 24 72 24 12 12 40 24 48 48 24 48 8 72 168 264 416 1422 txt gp {3,29} 1 12 13 txt gp {5,29} 1 8 4 2 2 4 4 25 txt gp {7,29} 2 4 6 txt gp {11,29} 1 4 8 13 txt gp {13,29} 1 2 12 4 2 2 2 2 4 31 txt gp {17,29} 4 4 txt gp {19,29} 1 4 5 txt gp {23,29} 2 4 6 txt gp

## Cases where S contains three primes

• We partition the data into 2 tables, one for old fields and one for new fields.
• If there is no column for a specific type of field that means no fields of that type were found.
• The data files are not partitioned, so they contain all fields.

### Old Fields

 S T2 T3 T4 T9 T10 T13 T14 T18 T24 Total {2,3,5} 84 15 88 528 160 15 143 608 2002 3643 txt gp

### New Fields

 S T1 T5 T6 T7 T8 T11 T15 T16 T17 T19 T20 T21 T22 T23 T26 T27 T28 T29 T30 T31 T35 T38 T39 T40 T44 Total {2,3,5} 16 8 104 88 120 312 928 176 480 192 96 96 204 912 1872 448 448 1296 448 432 5568 112 2496 3872 22944 43668 txt gp