Low Degree Fields Ramifying Above {5, 23, 29}

Discriminant class: −3335

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 23 Over p = 29 2 3 7 11 13 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_{k} 1_{+} 0 3335 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 23 23 1^{2} 1_{+} 29 29 2 2 2
C_{2} 64  2 2 2

Discriminant class: −667

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 23  Over p = 29 2 3 7 11 13 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 7 72 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 3 3 3 3 2
S_{3}  2 3 2 2 3  2