Low Degree Fields Ramifying Above {17, 31}

Discriminant class: −527

∞ 17 31 a_{1} a_{2} a_{3}  Over p = 17  Over p = 31 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 527  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 31 31  2 2  2
C_{2} 18  2 2  2
2. 1_{k} 1_{−} 1_{k} 0 5 -1 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 31 31 3 3 2 2 3 2  3
S_{3}  3 2 2 3 2 3 3