Low Degree Fields Ramifying Above {83}

Discriminant class: −83

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