Low Degree Fields Unramified Outside of {∞, 3, 5, 29}

Discriminant class: −435

∞ 3 5 29 a_{1} a_{2} a_{3}  Over p = 3  Over p = 5  Over p = 29  2 7 11 13 17 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_{−} 0 435  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2  2 2 2  2
C_{2} 4  2  2 2 2
2. 1_{k} 3_{i} 1_{−} 1_{−} 0 3 -24 1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 3 2 2 2 3 2
S_{3}  3  2 3 2 2 2
3. 1_{k} 5_{i} 1_{−} 1_{−} 0 27 -48 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2  2 2 2 3 2
S_{3}  3 3 3 2  2 2 2
4. 1_{k} 5_{i} 1_{−} 1_{−} 0 18 -21 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 3 2 2 2  2
S_{3}  3 3 3 2 3 2 2 2
5. 1_{k} 5_{i} 1_{−} 1_{−} 0 -18 -183 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 3 2 2 2 3 2
S_{3}  3 3 2 3 2 2 2

Discriminant class: −87

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 5  Over p = 29  2 7 11 13 17 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} 1_{k} 0_{+} 1_{−} 0 87  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗  2 2 2
C_{2} 6  2  2  2 2 2
7. 1_{k} 1_{k} 0_{+} 1_{−} -1 2  1 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗ 3 3 3 3 3 2 2 2
S_{3}  2  2 3 2 2 2 3
8. 1_{k} 3_{k} 2_{+} 1_{−} 0 15 -15 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 3 3 3 3 3 2 2 2
S_{3} 3  2 3 2 3 2 2 2 3
9. 1_{k} 3_{k} 2_{+} 1_{−} 0 -15 -110 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗  3  3 3 2 2 2
S_{3} 3  2 3 2  2 2 2 3
10. 1_{k} 3_{k} 2_{+} 1_{−} 0 -15 -35 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 3  3  2 2 2
S_{3} 3  2 3 2 3 2 2 2

Discriminant class: −15

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 5 Over p = 29 2 7 11 13 17 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
11. 1_{k} 1_{k} 1_{−} 0_{+} 0 15  1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗  2 2 2
C_{2} 2  2 2 2  2  2
12. 1_{k} 3_{k} 1_{−} 0_{+} 0 3 -1 1^{3} 3_{k} 3  1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 3 2 2 2 3 3 3 3
S_{3}  2 2 2  3 2 3 2
13. 1_{k} 1_{k} 1_{−} 2_{+} -1 10 15 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} ∗  3 2 2 2  3 3 3
S_{3}  2 2 2 3  2 3 2
14. 1_{k} 3_{k} 1_{−} 2_{+} 0 87 -232 1^{3} 3_{k} 3  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} ∗  2 2 2 3 3  3
S_{3} 18  2 2 2 3 3 2  2
15. 1_{k} 3_{k} 1_{−} 2_{+} 0 87 -87 1^{3} 3_{k} 3  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} ∗  3 2 2 2 3  3
S_{3} 9  2 2 2 3 3 2 3 2

Discriminant class: −3

∞ 3 5 29 a_{1} a_{2}  a_{3}  Over p = 3  Over p = 5  Over p = 29 2 7 11 13 17 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
16. 1_{k} 1_{i} 0_{+} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2  2  2  2
C_{2}  2  2 2 2
17. 1_{k} 5_{i} 0_{+} 0_{+} 0 0  -3 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2 3 2 3 2 3 2 3
S_{3}  3 2 3 2 2 2
18. 1_{k} 3_{i} 2_{+} 0_{+} 0 0 -5 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 0_{+} ∗ ∗ 2 3 2 2 3 2 3
S_{3}  3 2 3 2 2 2 3
19. 1_{k} 5_{i} 2_{+} 0_{+} 0 0 -45 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 3 2 3 2  2 3
S_{3}  2  2 2 2 3
20. 1_{k} 5_{i} 2_{+} 0_{+} 0 0 -15 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2  2 3 2 3 2
S_{3} 2  3 2 3 2 2 2 3
21. 1_{k} 3_{i} 0_{+} 2_{+} 0 0 -29 1^{3} 3_{i} 3∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗ 2 2 3 2 3 2
S_{3}  2 3 2 2 2 3 3
22. 1_{k} 1_{i} 2_{+} 2_{+} 0 0 -145 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 3 2 3 2  2 3
S_{3}  3 2  2 2 2  3
23. 1_{k} 5_{i} 0_{+} 2_{+} 0 0 -87 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 3 2 3 2  2 3
S_{3}  3 2  2 2 2 3 3
24. 1_{k} 5_{i} 0_{+} 2_{+} 0 0 -261 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 3 2  2 3 2 3
S_{3}  3 2 3 2 2 2 3 3
25. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -725 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 3 2 3
S_{3} 3  3 2 3 2 2 2 3 3
26. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -2175 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 3 2 3
S_{3} 3  2 3 2 2 2 3 3
27. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -435 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  2 3 2 3 2
S_{3} 3  3 2 3 2 2 2  3
28. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -1305 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 3 2  2 3 2 3
S_{3} 12  2 3 2 2 2  3
29. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -6525 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  2  2  2
S_{3} 3  3 2  2 2 2 3 3

Discriminant class: 1

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 5  Over p = 29 2 7 11 13 17 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
30. 0_{+} 4_{+} 0_{+} 0_{+} 0 -3 1 1^{3} 4_{+} 1  3 0_{+} 1  3 0_{+} 1  3 3 3 3  3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 5

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 5  Over p = 29 2 7 11 13 17 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
31. 0_{+} 0_{+} 1_{+} 0_{+} 1 -1  2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5  2 2  2 2  2
C_{2}  2  2 2 2  2

Discriminant class: 29

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 5  Over p = 29 2 7 11 13 17 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
32. 0_{+} 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗  1^{2} 1_{+} 29 29 2  2  2 2  2
C_{2}  2 2 2 2  2
33. 0_{+} 4_{+} 0_{+} 1_{+} 0 -12 -13 1^{3} 4_{+} ∗  3 0_{+} 1  1^{2} 1_{+} 29 29 2 3 2  2 2 3 2
S_{3}  2 2 2 2 3 3 2 3

Discriminant class: 145

∞ 3 5 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 5  Over p = 29 2 7 11 13 17 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
34. 0_{+} 0_{+} 1_{+} 1_{+} 0 -145  1^{2} 1_{+} 5 5 1^{2} 1_{+} 29 29  2 2 2  2 2 2
C_{2} 4  2  2  2 2