Low Degree Fields Unramified Outside of {∞, 3, 23}

Discriminant class: −23

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

Discriminant class: −3

∞ 3 23 a_{1} a_{2} a_{3} Over p = 3 Over p = 23 2 5 7 11 13 17 19 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 1_{k} 1_{i} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 2 2  2  2  2
C_{2}  2  2 2 2
4. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 2 3 2 3 2 3 2
S_{3}  3 3 2 3 2 2 2
5. 1_{k} 3_{i} 2_{+} 0 0 -23 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 3 2 3 2 3 2
S_{3}  2 3 2 2 2
6. 1_{k} 5_{i} 2_{+} 0 0 -69 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 2 3 2 2
S_{3}  3 3 2 3 2 2 2
7. 1_{k} 5_{i} 2_{+} 0 0 -207 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2  2 3 2
S_{3} 8  3 3 2  2 2 2

Discriminant class: 1

∞ 3 23 a_{1} a_{2} a_{3} Over p = 3  Over p = 23 2 5 7 11 13 17 19 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
8. 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

Discriminant class: 69

∞ 3 23 a_{1} a_{2} a_{3} Over p = 3 Over p = 23 2 5 7 11 13 17 19 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
9. 0_{+} 1_{i} 1_{k} 0 -69  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 23 23 2  2  2 2
C_{2}  2 2 2 2  2 2
10. 0_{+} 3_{i} 1_{k} 0 -6 -3 1^{3} 3_{i} 3∗  1^{2} 1_{k} 23 23 2 3 2 3 3 3 2 2
S_{3}  3 2 2 2 2 3 2 2