Low Degree Fields Ramifying Above {53, 83}

Discriminant class: −4399

∞ 53 83 a_{1} a_{2} a_{3}  Over p = 53  Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 59
1. 1_{k} 1_{−} 1_{k} 0 4399  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 83 83  2  2
C_{2} 50  2  2  2 2 2

Discriminant class: 53

∞ 53 83 a_{1} a_{2} a_{3} Over p = 53 Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 59
2. 0_{+} 1_{+} 2_{+} -1 -55 126 1^{2} 1_{+} 53 53 1^{3} 2_{+} ∗  2 2 2  3 3  2
S_{3}  2 3 2 3 2  3 3