Quintic Fields Ramifying Above {151}

Discriminant class: −151

∞ 151 a_{1} a_{2} a_{3}  Over p = 151  2 3 5 7 11 13 17 19
G h a_{4} a_{5}  f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 3_{i} -2 -1 7 1^{3} 2_{+} 1  5 32 3 4 5 4 3 3
S_{5} -13 7 1^{2} 1_{i} 151∗ 151∗ 4 5 3 5 32 22 3 4

Discriminant class: 1

∞ 151 a_{1} a_{2} a_{3} Over p = 151 2 3 5 7 11 13 17 19
G h a_{4} a_{5} f^{e} c_{w} d s 23 29 31 37 41 43 47 53
2. 0_{+} 4_{+} 1 -60 -12 1^{5} 4_{+} 1  5 5 5 5 5 5
C_{5}  784 128  5 5 5 5 5 5 5