Low Degree Fields Ramifying Above {3, 17, 29}

Discriminant class: −1479

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 Over p = 29 2 5 7 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{i} 1_{+} 1_{+} 0 1479  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  2 2  2
C_{2} 28  2 2  2 2
2. 1_{k} 3_{i} 1_{+} 1_{+} 0  3 -111 1^{3} 3_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3  2 2 3 2  3
S_{3}  2 2 3 2 2 3 3
3. 1_{k} 5_{i} 1_{+} 1_{+} 0 27 -39 1^{3} 5_{i} 3∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3 3 2 2 2 3
S_{3}  3 2 2 3 2 2
4. 1_{k} 5_{i} 1_{+} 1_{+} 0 -27 -207 1^{3} 5_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3 3 2 2 3 2
S_{3}  3 2 2 3 2 2 3 3
5. 1_{k} 5_{i} 1_{+} 1_{+} 0 27 -396 1^{3} 5_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  3 2 2 3 2  3
S_{3}  3 2 2  2 2 3 3

Discriminant class: −3

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 Over p = 29 2 5 7 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
6. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -493 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 2 2 3
S_{3} 3  3 2 3 2 2 2 3
7. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -8381 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2 3
S_{3} 6  3 2  2 2 2  3
8. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -1479 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2 3
S_{3} 6  2 3 2 2 2 3
9. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -25143 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  2  3 2
S_{3} 6  3 2 3 2 2 2  3
10. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -42891 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3  2 3
S_{3} 24  2 3 2 2 2  3
11. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -4437 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  2 3 3 2
S_{3} 6  3 2  2 2 2 3

Discriminant class: 17

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 Over p = 29 2 5 7 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
12. 0_{+} 4_{+} 1_{+} 2_{+} 0 -261 -1044 1^{3} 4_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  2 2 2 3  2 2
S_{3}  2 2 3 3  3 2