Low Degree Fields Ramifying Above {5, 7, 29}

Discriminant class: −1015

∞ 5 7 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 29 2 3 11 13 17 19 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 1015  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 1^{2} 1_{+} 29 29  2 2  2  2
C_{2} 16  2 2 2  2

Discriminant class: −203

∞ 5 7 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 29 2 3 11 13 17 19 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} 2_{+} 1_{i} 1_{+} -1 2 -28 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 2 3 2 2 3 3 3
S_{3}  2  2  3 2 3 3