Low Degree Fields Ramifying Above {5, 19, 29}

Discriminant class: −2755

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29  2 3 7 11 13 17 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_{+} 1_{k} 1_{−} 0 2755  1^{2} 1_{+} 5 5 1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗ 2 2 2 2  2
C_{2} 8  2  2 2

Discriminant class: −95

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29 2 3 7 11 13 17 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} 1_{+} 1_{i} 2_{+} -1 10 -275 1^{2} 1_{+} 5 5 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  3 3 2  3 2 2 2
S_{3}  3 2 2 2  2