Low Degree Fields Unramified Outside of {∞, 23, 29}

Discriminant class: −667

∞ 23 29 a_{1} a_{2} a_{3}  Over p = 23  Over p = 29 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{i} 1_{+} 0 667  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2
C_{2} 4 2 2 2 2

Discriminant class: −23

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

Discriminant class: 29

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