Low Degree Fields Unramified Outside of {∞, 5, 83}

Discriminant class: −415

∞ 5 83 a_{1} a_{2} a_{3} Over p = 5 Over p = 83 2 3 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_{−} 1_{k} 0 415 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 83 83 2 2 2 2 2
C_{2} 10  2

Discriminant class: −83

∞ 5 83 a_{1} a_{2} a_{3} Over p = 5  Over p = 83  2 3 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
2. 1_{k} 0_{+} 1_{i} 0 83  2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2  2  2
C_{2} 3  2 2 2
3. 1_{k} 0_{+} 1_{i} -1 1 -2 2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2 3 3 3 2 3 2
S_{3}  3 3 3  2 2 2 3
4. 1_{k} 2_{+} 1_{i} -1 -3 -8 1^{3} 2_{+} ∗  1^{2} 1_{i} 83∗ 83∗ 2 3  2 3 2 3
S_{3} 3  3 3 3 3 2 2 2 3
5. 1_{k} 2_{+} 1_{i} 0 -10 -15 1^{3} 2_{+} ∗ 1^{2} 1_{i} 83∗ 83∗ 2 3 3 2 3 2 3
S_{3} 3  3 3 3 3 2 2 2
6. 1_{k} 2_{+} 1_{i} -1 7 -8 1^{3} 2_{+} ∗ 1^{2} 1_{i} 83∗ 83∗ 2 3 3 3 2 2 3
S_{3} 3  3 2 2 2 3

Discriminant class: 5

∞ 5 83 a_{1} a_{2} a_{3} Over p = 5  Over p = 83 2 3 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
7. 0_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2}  2  2 2 2