Low Degree Fields Ramifying Above {11, 23, 29}

Discriminant class: 253

∞ 11 23 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 23  Over p = 29 2 3 5 7 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. 0_{+} 1_{k} 1_{i} 2_{+} 0 -58 -145 1^{2} 1_{k} 11 11 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  2 3 2 3 2 3 3
S_{3} 2 2 3 3 2 2

Discriminant class: 7337

∞ 11 23 29 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 23  Over p = 29  2 3 5 7 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. 0_{+} 1_{i} 1_{i} 1_{−} 0 -7337  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{−} 29∗ 29∗  2 2  2 2 2 2
C_{2} 2  2 2 2  2 2