Quintic Fields Ramifying Above {∞, 131}

Discriminant class: 1

∞ 131 a_{1} a_{2} a_{3}  Over p = 131  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. 0_{+} 4_{+} -1 -52 89 1^{5} 4_{+} 1  5 5 5 5 5 5 5
C_{5} 109 -193 5 5 5 5 5 5 5
2. 2_{−} 2_{−} -1  2 -1 1^{2} 1_{i} 131∗ 131∗ 22 5 5 5 5 5 22 22
D_{5}  1  2  1^{2} 1_{i} 131∗ 131∗ 22 22 22 22 5 5 22