Low Degree Fields Ramifying Above {3, 29}

Discriminant class: −87

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

Discriminant class: −3

∞ 3 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 29 2 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
3. 1_{k} 3_{i} 2_{+} 0 0 -29 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 2 3 2 3 2
S_{3}  2 3 2 2 2 3
4. 1_{k} 5_{i} 2_{+} 0 0 -261 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 3 2 2 3 2
S_{3}  3 3 2 3 2 2 2 3
5. 1_{k} 5_{i} 2_{+} 0 0 -87 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2 3 2  2
S_{3}  3 3 2  2 2 2 3

Discriminant class: 29

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