Low Degree Fields Unramified Outside of {∞, 2, 5, 29}

Discriminant class: −290

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29  3 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_{i} 1_{−} 1_{−} 0 290  1^{2} 3_{i} −2 −2 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗  2  2
C_{2} 20  2 2  2  2

Discriminant class: −145

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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
2. 1_{k} 2_{i} 1_{+} 1_{+} 0 145  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 5 5 1^{2} 1_{+} 29 29 2  2
C_{2} 8  2 2 2 2 2 2

Discriminant class: −58

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29  3 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
3. 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
4. 1_{k} 3_{k} 2_{+} 1_{−} -1 -8 -28 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2 3
S_{3}  3 2 2 3 2 3 3 3

Discriminant class: −29

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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
5. 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
6. 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: −10

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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
7. 1_{k} 3_{k} 1_{−} 0_{+} 0 10  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 2  2  2
C_{2} 2  2  2 2
8. 1_{k} 3_{k} 1_{−} 2_{+} -1 10 102 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} ∗  2  3 3 2  3 2
S_{3}  3 3 2 3 3 3 2 2

Discriminant class: −5

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

Discriminant class: −2

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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} 3_{i} 0_{+} 0_{+} 0 2  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2  2  2 2
C_{2}  2  2 2  2
11. 1_{k} 3_{i} 2_{+} 0_{+} -1 2  2 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 2 3 2 3 3 2 2
S_{3}  2 3  2 2  2 3
12. 1_{k} 3_{i} 0_{+} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  3 2 3 2  3 2 2
S_{3}  2 3 3 2 2  2
13. 1_{k} 3_{i} 2_{+} 2_{+} -1 -48 -188 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 3 2 3  2 2
S_{3} 3  2  3 2 2  2 3
14. 1_{k} 3_{i} 2_{+} 2_{+} -1 97 -333 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  2 3 3 2 2
S_{3} 3  2 3 3 2 2  2 3

Discriminant class: −1

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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
15. 1_{k} 2_{i} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2 2 2  2 2 2
C_{2}  2 2  2  2

Discriminant class: 2

∞ 2 5 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 29 3 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. 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
17. 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: 5

∞ 2 5 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 29 3 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
18. 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: 10

∞ 2 5 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 29 3 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
19. 0_{+} 3_{−} 1_{−} 0_{+} 0 -10  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗  2 2  2 2 2
C_{2} 2  2  2 2

Discriminant class: 29

∞ 2 5 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 29 3 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
20. 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

Discriminant class: 58

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

Discriminant class: 145

∞ 2 5 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 29 3 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
22. 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

Discriminant class: 290

∞ 2 5 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 29  3 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
23. 0_{+} 3_{+} 1_{−} 1_{−} 0 -290  1^{2} 3_{+} 2 2 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 29∗ 29∗ 2 2  2 2
C_{2} 4  2 2 2  2