Low Degree Fields Unramified Outside of {∞, 31}

Discriminant class: −31

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

Discriminant class: 1

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