Low Degree Fields Unramified Outside of {∞, 59, 67}

Discriminant class: −67

∞ 59 67 a_{1} a_{2} a_{3} Over p = 59  Over p = 67  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 0_{+} 1_{i} 0 67  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2
C_{2} 2 2 2 2

Discriminant class: −59

∞ 59 67 a_{1} a_{2} a_{3}  Over p = 59  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
2. 1_{k} 1_{i} 0_{+} 0 59  1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2  2 2
C_{2} 3  2  2 2  2 2
3. 1_{k} 1_{i} 0_{+} 0 2 -1 1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2 3 3 3 2 2  3
S_{3}  2 3 2 2 3 2 2 3

Discriminant class: 1

∞ 59 67 a_{1} a_{2} a_{3} Over p = 59 Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
4. 0_{+} 0_{+} 2_{+} -1 -22 -5  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3}  3 3 3 3 3  3

Discriminant class: 3953

∞ 59 67 a_{1}  a_{2} a_{3}  Over p = 59  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
5. 0_{+} 1_{i} 1_{k} 0 -3953  1^{2} 1_{i} 59∗ 59∗ 1^{2} 1_{k} 67 67  2 2 2
C_{2}  2  2 2  2 2