Quintic Fields Ramifying Above {17, 19}

Discriminant class: −19

∞ 17 19 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  2 3 5 7 11 13 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} 2_{+} 3_{i} -2 0 8 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  32 4 22 5 5 32 22 32
S_{5}  1 -3  2 0_{+} ∗ ∗ 1^{2} 1_{i} 19∗ 19∗ 2 4 4 5 3 4 4 5