Low Degree Fields Unramified Outside of {∞, 2, 3, 29}

Discriminant class: −174

∞ 2 3 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 3 Over p = 29 5 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} 3_{+} 1_{i} 1_{+} 0 174 1^{2} 3_{+} 2 2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 29 29 2 2 2 2
C_{2} 12  2
2. 1_{k} 3_{+} 1_{i} 1_{+} -1 -2  6 1^{2} 3_{+} 2 2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 29 29 3 3 2 2 3 3 2 2
S_{3}  3 3 3 3  3  2
3. 1_{k} 3_{+} 5_{i} 1_{+} 0 -18 -96 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 29 29 3 3 2 2  3 2 2
S_{3} 3  3  3 3 3  2
4. 1_{k} 3_{+} 5_{i} 1_{+} 0 27 -126 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 29 29 3  2 2 3 3 2 2
S_{3} 3  3 3  3 3  2
5. 1_{k} 3_{+} 5_{i} 1_{+} 0 27 -222 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 29 29  3 2 2 3  2 2
S_{3} 12  3 3 3 3 3  2

Discriminant class: −87

∞ 2 3 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 29  5 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} 0_{+} 1_{k} 1_{−} 0 87  1^{2} 1_{k} 3 3 1^{2} 1_{−} 29∗ 29∗ 2  2 2 2
C_{2} 6  2  2  2 2 2
7. 1_{k} 0_{+} 1_{k} 1_{−} -1 2 1 3 0_{+} 1  1^{2} 1_{k} 3 3 1^{2} 1_{−} 29∗ 29∗ 2 3 3 3 3 2 2 2
S_{3} 2 2 3 2 2 2 3

Discriminant class: −58

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29  5 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
8. 1_{k} 3_{k} 0_{+} 1_{−} 0 58  1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2
C_{2} 2 2 2 2
9. 1_{k} 3_{k} 4_{+} 1_{−} 0 15 -14 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2
S_{3}  3 2 2 3 2 3 3 3

Discriminant class: −29

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
10. 1_{k} 2_{i} 0_{+} 1_{+} 0 29  1^{2} 2_{i} −∗ −∗  1^{2} 1_{+} 29 29  2  2  2
C_{2} 6  2 2  2 2 2
11. 1_{k} 2_{i} 0_{+} 1_{+} -1 0 -2 1^{2} 2_{i} −∗ −∗ 3 0_{+} 1  1^{2} 1_{+} 29 29 3 2 3 3 2  2 3
S_{3}  2 2 3 3 3 2 2 2

Discriminant class: −6

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
12. 1_{k} 3_{−} 1_{k} 0_{+} 0 6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3  2 2 2 2
C_{2} 2  2 2 2 2  2 2
13. 1_{k} 3_{−} 3_{k} 0_{+} 0 3 -2 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  3 3 3 2 2 2 2 3
S_{3}  2 2 2 2 3  2 2

Discriminant class: −3

∞ 2 3 29 a_{1} a_{2}  a_{3} Over p = 2  Over p = 3  Over p = 29 5 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
14. 1_{k} 0_{+} 1_{i} 0_{+} 1 1  2 0_{+} ∗ ∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 2  2  2  2
C_{2}  2  2 2 2
15. 1_{k} 2_{+} 3_{i} 0_{+} 0 0  -2 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 0_{+} ∗ ∗ 2 3 2 3 2 3 2
S_{3}  3 2  2 2 2 3 3
16. 1_{k} 0_{+} 5_{i} 0_{+} 0 0  -3 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 3 2 3 2 3 2 3
S_{3}  3 2 3 2 2 2
17. 1_{k} 2_{+} 5_{i} 0_{+} 0 0 -6 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 2 2 3 2 3 2 3
S_{3}  2 3 2 2 2 3 3
18. 1_{k} 2_{+} 5_{i} 0_{+} 0 0 -12 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 2 3 2 2 2 3
S_{3}  3 2 3 2 2 2 3 3
19. 1_{k} 2_{+} 1_{i} 2_{+} -1 -19 73 1^{3} 2_{+} ∗ 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗ 2 3 2 2 3 2
S_{3}  3 2 3 2 2 2 3 3
20. 1_{k} 0_{+} 3_{i} 2_{+} 0 0 -29 2 0_{+} ∗ ∗ 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 3 2 3 2
S_{3}  2 3 2 2 2 3 3
21. 1_{k} 2_{+} 3_{i} 2_{+} 0 0 -58 1^{3} 2_{+} ∗ 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 2
S_{3} 6  3 2 3 2 2 2
22. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -87 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 2  2 3
S_{3}  3 2  2 2 2 3 3
23. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -261 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2  2 3 2 3
S_{3}  3 2 3 2 2 2 3 3
24. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -1044 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 3 2 2 3
S_{3} 3  2 3 2 2 2 3 3
25. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -174 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2  2 3 2 3
S_{3} 12  2  2 2 2
26. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -522 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 2 3 2 3
S_{3} 3  3 2 3 2 2 2
27. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -348 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 2 3 2 3
S_{3} 3  3 2  2 2 2 3 3

Discriminant class: −2

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
28. 1_{k} 3_{i} 0_{+} 0_{+} 0  2  1^{2} 3_{i} −2 −2  2 0_{+} ∗ ∗ 2 2  2  2 2
C_{2}  2  2 2  2
29. 1_{k} 3_{i} 4_{+} 0_{+} 0 -3 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  2 0_{+} ∗ ∗ 2 2 3 2 3 3 2 2
S_{3} 3  2 3 3 2 2 3 2 3

Discriminant class: −2 (continued)

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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. 1_{k} 3_{i} 0_{+} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2 3 0_{+} 1  1^{3} 2_{+} ∗  2 2 3 2  3 2 2
S_{3}  2 3 3 2 2  2
31. 1_{k} 3_{i} 4_{+} 2_{+} 0 -174 -928 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 2 3 2 3 3 2 2
S_{3} 6  2 3 3 2 2 3 2 3
32. 1_{k} 3_{i} 4_{+} 2_{+} 0 87 -638 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 2  2 3  2 2
S_{3} 3  2  2 2 3 2 3

Discriminant class: −1

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
33. 1_{k} 2_{i} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗  2 2  2 2 2
C_{2}  2 2  2  2
34. 1_{k} 2_{i} 4_{+} 0_{+} 0 -3 -4 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  3 0_{+} 1  3 2 2 3 3 2 2 2
S_{3}  3  2 2  2 3 2

Discriminant class: 1

∞ 2 3 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 29 5 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
35. 0_{+} 0_{+} 4_{+} 0_{+} 0 -3 1 3 0_{+} 1  1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3  3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 2

∞ 2 3 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 29 5 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
36. 0_{+} 3_{+} 0_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2  2  2 2 2 2
37. 0_{+} 3_{+} 0_{+} 2_{+} -1 -19 15 1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 3 2 2 3 2 3 3
S_{3}  2  2 3 2 2 2 2

Discriminant class: 3

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
38. 0_{+} 2_{i} 1_{k} 0_{+} 0 -3  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2 2  2  2
39. 0_{+} 2_{i} 3_{k} 2_{+} 0 -87 116 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 2 3 3 2 2 3 2
S_{3}  3 2 2  2  3 2

Discriminant class: 6

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
40. 0_{+} 3_{k} 1_{i} 0_{+} 0 -6  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗  2 2 2 2  2
C_{2}  2 2  2 2
41. 0_{+} 3_{k} 5_{i} 0_{+} 0 -9 -6 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  3 2 2 2 2 3 3 2
S_{3}  2 2  3 3 2 2 3

Discriminant class: 29

∞ 2 3 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 29 5 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
42. 0_{+} 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29  2  2 2  2
C_{2}  2 2 2 2  2
43. 0_{+} 0_{+} 4_{+} 1_{+} 0 -12 -13 2 0_{+} ∗ ∗ 1^{3} 4_{+} ∗  1^{2} 1_{+} 29 29 3 3 2  2 2 3 2
S_{3}  2 2 2 2 3 3 2 3

Discriminant class: 58

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29  5 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
44. 0_{+} 3_{−} 0_{+} 1_{−} 0 -58  1^{2} 3_{−} 2∗ 2∗  1^{2} 1_{−} 29∗ 29∗ 2  2 2  2
C_{2} 2  2  2 2 2  2
45. 0_{+} 3_{−} 4_{+} 1_{−} 0 -21 -26 1^{2} 3_{−} 2∗ 2∗ 1^{3} 4_{+} 1  1^{2} 1_{−} 29∗ 29∗ 2 3 3 2 2 3  2
S_{3} 3  2 3 2 2 2 3 2

Discriminant class: 87

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29  5 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
46. 0_{+} 2_{i} 1_{i} 1_{−} 0 -87  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2
C_{2} 2 2 2 2 2 2
47. 0_{+} 2_{i} 3_{i} 1_{−} 0 -15 -6 1^{2} 2_{i} −1 −1 1^{3} 3_{i} 3∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 3 3 3 3 3
S_{3}  2 3 3 2 2 3 2 2

Discriminant class: 174

∞ 2 3 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 29 5 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
48. 0_{+} 3_{i} 1_{k} 1_{+} 0 -174  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3 1^{2} 1_{+} 29 29  2  2  2
C_{2} 2  2 2  2