Low Degree Fields Ramifying Above {3, 73}

Discriminant class: −219

∞ 3 73 a_{1} a_{2} a_{3} Over p = 3 Over p = 73 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{i} 1_{+} 0 219  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 73 73 2  2  2  2
C_{2} 4  2  2 2
2. 1_{k} 3_{i} 1_{+} 0 -9 -20 1^{3} 3_{i} 3∗  1^{2} 1_{+} 73 73 2  2 3 2 3 3 2
S_{3}  3 2 3 2 2 3 3 3
3. 1_{k} 5_{i} 1_{+} 0 -36 -87 1^{3} 5_{i} 3∗  1^{2} 1_{+} 73 73 2 3 2 3 2 3 3 2
S_{3}  2 3 2 2 3  3
4. 1_{k} 5_{i} 1_{+} 0 9 -102 1^{3} 5_{i} 3∗  1^{2} 1_{+} 73 73 2 3 2 3 2  2
S_{3}  3 2 3 2 2 3 3
5. 1_{k} 5_{i} 1_{+} 0 -18 -39 1^{3} 5_{i} 3∗  1^{2} 1_{+} 73 73 2 3 2  2 3 3 2
S_{3} 2  3 2  2 2  3 3

Discriminant class: −3

∞ 3 73 a_{1} a_{2} a_{3} Over p = 3 Over p = 73 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
6. 1_{k} 1_{i} 2_{+} 0 0 -73 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} 1  2 2 3 2  2 3 2
S_{3} 3  2 3  2 3 2 2 2
7. 1_{k} 5_{i} 2_{+} 0 0 -657 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2  2 3 2  2
S_{3} 27  2 3 3 2 3 2 2 2
8. 1_{k} 5_{i} 2_{+} 0 0 -219 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2 3 2 3 2
S_{3} 18  2  3 2  2 2 2

Discriminant class: 1

∞ 3 73 a_{1} a_{2} a_{3} Over p = 3 Over p = 73 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
9. 0_{+} 4_{+} 2_{+} 0 -219 -1241 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3
C_{3} 9  3  3 3 3  3
10. 0_{+} 4_{+} 2_{+} 0 -219 -730 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3  3
C_{3} 9  3 3  3 3 3 3