Low Degree Fields Unramified Outside of {∞, 3, 97}

Discriminant class: −291

∞ 3 97 a_{1} a_{2} a_{3} Over p = 3 Over p = 97 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_{+} 0 291  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 97 97 2  2 2 2  2
C_{2} 4  2  2 2
2. 1_{k} 3_{i} 1_{+} 0 6 -29 1^{3} 3_{i} 3∗  1^{2} 1_{+} 97 97 2 3 2 2 2 3 2
S_{3} 2  2 3 3 2 2
3. 1_{k} 5_{i} 1_{+} 0 27 24 1^{3} 5_{i} 3∗  1^{2} 1_{+} 97 97 2 3 2 2 2 3 2 3
S_{3}  3 3 2 3  2 2
4. 1_{k} 5_{i} 1_{+} 0 -9 -60 1^{3} 5_{i} 3∗  1^{2} 1_{+} 97 97 2  2 2 2  2 3
S_{3}  3 3 2 3 3 2 2
5. 1_{k} 5_{i} 1_{+} 0 18 -3 1^{3} 5_{i} 3∗  1^{2} 1_{+} 97 97 2 3 2 2 2 3 2 3
S_{3} 4 3 3 2 3 2 2

Discriminant class: −3

∞ 3 97 a_{1} a_{2} a_{3} Over p = 3 Over p = 97 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} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗  2 2  2  2  2
C_{2}  2  2  2 2 2
7. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 3 2 3 2 3 2
S_{3}  2 3 3 2 3 2 2 2
8. 1_{k} 3_{i} 2_{+} 0 0 -97 1^{3} 3_{i} 3∗  1^{3} 2_{+} 1  2 2  2 3 2 3 2
S_{3} 3  2  2  2 2 2
9. 1_{k} 5_{i} 2_{+} 0 0 -873 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2 3 2  2
S_{3} 12  2 3 3 2 3 2 2 2
10. 1_{k} 5_{i} 2_{+} 0 0 -291 1^{3} 5_{i} 3∗ 1^{3} 2_{+} 1 2 2 3 2 2 3 2
S_{3} 6  2 3 3 2 3 2 2 2

Discriminant class: 1

∞ 3 97 a_{1} a_{2} a_{3} Over p = 3  Over p = 97 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
11. 0_{+} 4_{+} 0_{+} 0 -3  1 1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3 3  3
C_{3}  3 3  3 3 3  3
12. 0_{+} 0_{+} 2_{+} -1 -32 79 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3 3  3 3
13. 0_{+} 4_{+} 2_{+} 0 -291 485 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3  3  3  3
C_{3} 3  3  3  3 3 3
14. 0_{+} 4_{+} 2_{+} 0 -291 1358 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3  3 3 3
C_{3} 3  3 3 3  3 3 3

Discriminant class: 97

∞ 3 97 a_{1} a_{2} a_{3} Over p = 3  Over p = 97 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
15. 0_{+} 0_{+} 1_{+} 0 -97  1^{2} 1_{+} 97 97  2 2  2 2 2 2
C_{2}  2  2 2  2