Low Degree Fields Ramifying Above {7, 41}

Discriminant class: −287

∞ 7 41 a_{1} a_{2} a_{3} Over p = 7  Over p = 41  2 3 5 11 13 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. 1_{k} 1_{k} 1_{−} 0 287  1^{2} 1_{k} 7 7 1^{2} 1_{−} 41∗ 41∗  2 2
C_{2} 14  2 2  2 2 2

Discriminant class: −7

∞ 7 41 a_{1} a_{2} a_{3} Over p = 7 Over p = 41 2 3 5 11 13 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. 1_{k} 1_{i} 2_{+} -1 14 3 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 2 2 3 2 2 2 3
S_{3}  3 2  3 2 3 2 2