Quintic Fields Ramifying Above {13, 19}

Discriminant class: −19

∞ 13 19 a_{1} a_{2} a_{3} Over p = 13  Over p = 19  2 3 5 7 11 17 23 29
G h  a_{4} a_{5}  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 4_{+} 3_{i} -1 -23 67 1^{5} 4_{+} ∗  1^{4} 3_{i} 19∗ 19 4 4 3 3 3 22 22 32
S_{5}  5 -34  32 4 4 5 5 4 2 5