Low Degree Fields Ramifying Above {13, 41}

Discriminant class: 13

∞ 13 41 a_{1} a_{2} a_{3} Over p = 13 Over p = 41 2 3 5 7 11 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 43 47 53 59 61
1. 0_{+} 1_{+} 2_{+} -1 -27 -38 1^{2} 1_{+} 13 13 1^{3} 2_{+} ∗  2 3 2 2 2 3 2 3
S_{3} 3 2 2 3 2 2

Discriminant class: 533

∞ 13 41 a_{1} a_{2} a_{3}  Over p = 13  Over p = 41  2 3 5 7 11 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 29 31 37 43 47 53 59 61
2. 0_{+} 1_{−} 1_{−} 0 -533  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 41∗ 41∗ 2 2 2  2
C_{2} 2  2 2 2  2 2