Low Degree Fields Ramifying Above {3, 59}

Discriminant class: −3

∞ 3 59 a_{1} a_{2} a_{3} Over p = 3 Over p = 59 2 5 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} 3_{i} 2_{+} 0 0 -59 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2 3 2 3 2
S_{3}  2 3 3 2  2 2 3
2. 1_{k} 5_{i} 2_{+} 0 0 -177 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2  2 3 2
S_{3}  2 3  2 3 2 2 3
3. 1_{k} 5_{i} 2_{+} 0 0 -531 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2  2 3 2  2
S_{3}  2  3 2 3 2 2 3

Discriminant class: 177

∞ 3 59 a_{1} a_{2} a_{3} Over p = 3 Over p = 59 2 5 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_{i} 1_{k} 0 -177  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 59 59  2  2 2
C_{2}  2 2 2 2 2  2 2
5. 0_{+} 3_{i} 1_{k} 0 -9 -7 1^{3} 3_{i} 3∗  1^{2} 1_{k} 59 59 3 2  3 2 2 3 3
S_{3}  2 2 2 2 2 3 2 2