Low Degree Fields Unramified Outside of {∞, 3, 53}

Discriminant class: −159

∞ 3 53 a_{1} a_{2} a_{3} Over p = 3  Over p = 53  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 59 61
1. 1_{k} 1_{k} 1_{−} 0 159  1^{2} 1_{k} 3 3 1^{2} 1_{−} 53∗ 53∗  2  2 2
C_{2} 10  2 2  2 2 2
2. 1_{k} 3_{k} 1_{−} 0 3 -7 1^{3} 3_{k} 3  1^{2} 1_{−} 53∗ 53∗ 3 3  2 3 2 2
S_{3}  2 2 3 3  2 2 2

Discriminant class: −3

∞ 3 53 a_{1} a_{2} a_{3} Over p = 3 Over p = 53 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 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}  2 3 3 2 3 2 2
5. 1_{k} 1_{i} 2_{+} 0 0 -53 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗ 2 2 3 2 2 3 2
S_{3}  2 3 3 2 3 2 2
6. 1_{k} 5_{i} 2_{+} 0 0 -159 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2 3 2  2
S_{3} 3  2  2 3 2 2
7. 1_{k} 5_{i} 2_{+} 0 0 -477 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2  2 3 2 3 2
S_{3} 9  2 3 3 2  2 2

Discriminant class: 1

∞ 3 53 a_{1} a_{2} a_{3} Over p = 3  Over p = 53 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 59 61
8. 0_{+} 4_{+} 0_{+} 0 -3 1 1^{3} 4_{+} 1  3 3 3 3 3  3
C_{3}  3 3  3 3 3 3 3

Discriminant class: 53

∞ 3 53 a_{1} a_{2} a_{3} Over p = 3  Over p = 53 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 59 61
9. 0_{+} 0_{+} 1_{+} 0 -53  2 0_{+} ∗ ∗ 1^{2} 1_{+} 53 53 2 2  2 2
C_{2}  2  2  2