Low Degree Fields Ramifying Above {7, 17, 29}

Discriminant class: −3451

∞ 7 17 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 29  2 3 5 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{k} 1_{+} 1_{−} 0 3451  1^{2} 1_{k} 7 7 1^{2} 1_{+} 17 17 1^{2} 1_{−} 29∗ 29∗ 2 2  2  2 2
C_{2} 12  2 2  2 2
2. 1_{k} 1_{k} 1_{+} 1_{−} -1  -5 14 1^{2} 1_{k} 7 7 1^{2} 1_{+} 17 17 1^{2} 1_{−} 29∗ 29∗ 2 2 3 3 2 3 2 2
S_{3}  2 2 3 3 2 2 3

Discriminant class: −119

∞ 7 17 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 29 2 3 5 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
3. 1_{k} 1_{k} 1_{−} 2_{+} 1 68 391 1^{2} 1_{k} 7 7 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  3 3 3 2 2 2 2 3
S_{3} 2 3 2 3 2 3 3

Discriminant class: 29

∞ 7 17 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 17 Over p = 29 2 3 5 11 13 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
4. 0_{+} 2_{+} 2_{+} 1_{+} -1 -79 -216 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 2  2 3 2 3 2
S_{3} 6  2 2 2 2  2 3