Low Degree Fields Ramifying Above {31, 89}

Discriminant class: −2759

∞ 31 89 a_{1} a_{2} a_{3}  Over p = 31  Over p = 89  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 2759  1^{2} 1_{k} 31 31 1^{2} 1_{−} 89∗ 89∗  2 2  2 2
C_{2} 54  2  2 2
2. 1_{k} 1_{k} 1_{−} -1  4 -11 1^{2} 1_{k} 31 31 1^{2} 1_{−} 89∗ 89∗ 3 3 3 2 2 3 2 2
S_{3}  3 3 3 2 3 3 2 2