Low Degree Fields Unramified Outside of {∞, 29, 31}

Discriminant class: −899

∞ 29 31 a_{1} a_{2} a_{3}  Over p = 29  Over p = 31 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 37 41 43 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 899  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 31 31 2  2  2
C_{2} 14  2  2  2 2

Discriminant class: −31

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

Discriminant class: 1

∞ 29 31 a_{1} a_{2} a_{3} Over p = 29 Over p = 31 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 37 41 43 47 53 59 61
4. 0_{+} 0_{+} 2_{+} 1 -10 -8  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3 3  3 3

Discriminant class: 29

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