Low Degree Fields Ramifying Above {13, 23, 29}

Discriminant class: −8671

∞ 13 23 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{i} 1_{+} 0 8671  1^{2} 1_{+} 13 13 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29  2  2  2
C_{2} 64  2  2 2

Discriminant class: −667

∞ 13 23 29 a_{1} a_{2} a_{3} Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{+} 1_{i} 1_{+} -1 22 116 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2 3 3 3 2
S_{3} 6  2  2 2 3 3 2