Low Degree Fields Ramifying Above {7, 19, 23}

Discriminant class: −3059

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 23  2 3 5 11 13 17 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{k} 1_{i} 1_{i} 0 3059  1^{2} 1_{k} 7 7 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 2  2  2
C_{2} 24  2 2
2. 1_{k} 1_{k} 1_{i} 1_{i} 0 11 -16 1^{2} 1_{k} 7 7 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 2 3 3 2 3 3 2
S_{3}  3  2 2 3 3 3