Low Degree Fields Ramifying Above {19, 59}

Discriminant class: −19

∞ 19 59 a_{1} a_{2} a_{3}  Over p = 19  Over p = 59 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 61
1. 1_{k} 1_{i} 2_{+} -1 -39 -94 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3  3 2 3 3
S_{3}  2 2 2 2 3  2 3

Discriminant class: 1121

∞ 19 59 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 59 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 61
2. 0_{+} 1_{i} 1_{k} 0 -1121  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 59 59  2  2  2
C_{2}  2  2 2 2 2 2