Low Degree Fields Ramifying Above {7, 89}

Discriminant class: −623

∞ 7 89 a_{1} a_{2} a_{3} Over p = 7  Over p = 89  2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 623  1^{2} 1_{k} 7 7 1^{2} 1_{−} 89∗ 89∗  2  2  2
C_{2} 22  2  2  2 2

Discriminant class: −7

∞ 7 89 a_{1} a_{2} a_{3} Over p = 7 Over p = 89 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 1_{k} 1_{i} 2_{+} -1 30 56 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  2 2 3 2 2 2 3
S_{3}  3 2 3 2  2 3 2