Quintic Fields Unramified Outside of {∞, 5}

Discriminant class: 1

∞ 5 a_{1} a_{2} a_{3} Over p = 5 2 3 7 11 13 17 19 23
G h a_{4} a_{5}  f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 0_{+} 8_{+} 0 -10 -5 1^{5} 8_{+} 1  5 5  5 5 5 5 5
C_{5}  10 -1  5 5 5 5  5 5 5

Discriminant class: 5

∞ 5 a_{1} a_{2} a_{3} Over p = 5 2 3 7 11 13 17 19 23
G h a_{4} a_{5}  f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 2_{−} 7_{−} 0 5 0 1^{5} 7_{−} 5  4 4 4 5 4 4 22 4
F_{5} 5 -1 22 5 4 5 4 4 4 22
3. 2_{−} 9_{−} 0 0 0 1^{5} 9_{−} 5  4 4 4 5 4 4 22 4
F_{5}  0 -5  22  4 5 4 4 4 22