Low Degree Fields Ramifying Above {11, 83}

Discriminant class: −11

∞ 11 83 a_{1} a_{2} a_{3}  Over p = 11  Over p = 83 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{i} 2_{+} -1 -55 -206 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2  3 2 2 2 2 3
S_{3}  2 3 3 2 2 3  3

Discriminant class: 913

∞ 11 83 a_{1} a_{2} a_{3}  Over p = 11  Over p = 83 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 1_{i} 1_{k} 0 -913  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{k} 83 83  2 2  2
C_{2}  2  2  2 2