Low Degree Fields Ramifying Above {199}

Discriminant class: −199

∞ 199 a_{1} a_{2} a_{3}  Over p = 199  2 3 5 7 11 13 17 19
G  h  f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{i} 0 199  1^{2} 1_{i} 199∗ 199∗  2  2  2 2
C_{2} 9  2 2
2. 1_{k} 1_{i} -1 4 -1 1^{2} 1_{i} 199∗ 199∗ 3 2 3  2 3 2 2
S_{3} 3 3 2 2 3 3 3

Discriminant class: 1

∞ 199 a_{1} a_{2} a_{3} Over p = 199 2 3 5 7 11 13 17 19
G  h  f^{e} c_{w} d s 23 29 31 37 41 43 47 53
3. 0_{+} 2_{+} 1 -66 59 1^{3} 2_{+} 1  3 3  3  3  3
C_{3}  3 3 3 3 3 3 3 3