Low Degree Fields Unramified Outside of {∞, 5, 59}

Discriminant class: −295

∞ 5 59 a_{1} a_{2} a_{3} Over p = 5  Over p = 59  2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 61
1. 1_{k} 1_{+} 1_{i} 0 295  1^{2} 1_{+} 5 5 1^{2} 1_{i} 59∗ 59∗  2 2 2  2
C_{2} 8  2  2 2

Discriminant class: −59

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

Discriminant class: 5

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