Low Degree Fields Ramifying Above {67, 89}

Discriminant class: −5963

∞ 67 89 a_{1} a_{2} a_{3}  Over p = 67  Over p = 89 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{i} 1_{+} 0 5963  1^{2} 1_{i} 67∗ 67∗ 1^{2} 1_{+} 89 89 2  2  2  2
C_{2} 24  2 2  2  2
2. 1_{k} 1_{i} 1_{+} -1 11 -10 1^{2} 1_{i} 67∗ 67∗ 1^{2} 1_{+} 89 89 2 3 2 3 2 3 3 2
S_{3} 4  2 2 3 2  3 2