Low degree fields ramifying above {19}

Discriminant class: −19

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

Discriminant class: 1

∞ 19 a_{1} a_{2} a_{3} Over p = 19 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 2_{+} -1 -6 7 1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3 3 3