Low Degree Fields Unramified Outside of {∞, 79, 83}

Discriminant class: −83

∞ 79 83 a_{1} a_{2} a_{3} Over p = 79  Over p = 83  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 0_{+} 1_{i} 0 83  2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2  2  2  2
C_{2} 3  2 2 2
2. 1_{k} 0_{+} 1_{i} -1 1 -2 2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2 3 2 3 3 2 3 2
S_{3} 3 3 3 2 2 2

Discriminant class: −79

∞ 79 83 a_{1} a_{2} a_{3}  Over p = 79  Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
3. 1_{k} 1_{i} 0_{+} 0 79  1^{2} 1_{i} 79∗ 79∗  2  2  2
C_{2} 5  2  2 2 2 2 2

Discriminant class: 1

∞ 79 83 a_{1} a_{2} a_{3} Over p = 79 Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
4. 0_{+} 2_{+} 0_{+} 1 -26 41 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3  3 3 3

Discriminant class: 6557

∞ 79 83 a_{1}  a_{2} a_{3}  Over p = 79  Over p = 83  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
5. 0_{+} 1_{k} 1_{i} 0 -6557  1^{2} 1_{k} 79 79 1^{2} 1_{i} 83∗ 83∗ 2 2 2 2  2 2 2
C_{2} 3  2  2 2
6. 0_{+} 1_{k} 1_{i} -1 -13 -6 1^{2} 1_{k} 79 79 1^{2} 1_{i} 83∗ 83∗ 2 2 2 2 3 2 2 2
S_{3}  3 2 3 2 2 3 3 3