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

Discriminant class: −58

∞ 2 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 29  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 3_{k} 1_{−} 0 58  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2 2
C_{2} 2 2 2 2

Discriminant class: −29

∞ 2 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 29 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 2_{i} 1_{+} 0 29  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 29 29  2  2  2
C_{2} 6  2 2  2 2
3. 1_{k} 2_{i} 1_{+} -1 0 -2 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 29 29 3 3 2 3 3 2  2
S_{3}  3 2 2 3 3 3 2 2

Discriminant class: −2

∞ 2 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 29 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 1_{k} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗  2 2  2  2
C_{2}  2 2  2 2  2
5. 1_{k} 3_{i} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  3 2 2 3 2  3 2
S_{3}  2 2 3 3 2 2  2

Discriminant class: −1

∞ 2 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 29 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
6. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2  2 2  2 2
C_{2}  2  2 2  2

Discriminant class: 2

∞ 2 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 29 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
7. 0_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2  2  2 2 2
8. 0_{+} 3_{+} 2_{+} -1 -19 15 1^{2} 3_{+} 2 2 1^{3} 2_{+} ∗  2 2 3 2 2 3 2 3
S_{3}  3 2  2 3 2 2 2

Discriminant class: 29

∞ 2 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 29 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
9. 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2  2  2 2
C_{2}  2 2 2 2 2  2

Discriminant class: 58

∞ 2 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 29  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
10. 0_{+} 3_{−} 1_{−} 0 -58  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 2  2  2  2 2 2