Low Degree Fields Ramifying Above {7, 83}

Discriminant class: −7

∞ 7 83 a_{1} a_{2} a_{3} Over p = 7 Over p = 83 2 3 5 11 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 28 -123 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 2 2 3 2 2 2 3
S_{3} 3 2 2 3 2 3 2

Discriminant class: 581

∞ 7 83 a_{1} a_{2} a_{3} Over p = 7 Over p = 83 2 3 5 11 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 -581  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 83 83 2 2  2
C_{2}  2  2 2  2 2