Low Degree Fields Unramified Outside of {∞, 17, 83}

Discriminant class: −1411

∞ 17 83 a_{1} a_{2} a_{3}  Over p = 17  Over p = 83  2 3 5 7 11 13 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_{i} 0 1411  1^{2} 1_{+} 17 17 1^{2} 1_{i} 83∗ 83∗ 2 2  2 2 2 2 2
C_{2} 4  2 2 2 2 2 2 2

Discriminant class: −83

∞ 17 83 a_{1} a_{2} a_{3} Over p = 17  Over p = 83  2 3 5 7 11 13 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  1^{2} 1_{i} 83∗ 83∗ 2  2  2 2
C_{2} 3  2 2 2
3. 1_{k} 0_{+} 1_{i} -1 1 -2 3 0_{+} 1  1^{2} 1_{i} 83∗ 83∗ 2 3 2 3 3 2 2
S_{3} 3 3 3 2 2 2 3

Discriminant class: 17

∞ 17 83 a_{1} a_{2} a_{3} Over p = 17 Over p = 83 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 1_{+} 0_{+} 1 -4 1^{2} 1_{+} 17 17 2 2 2 2 2
C_{2}  2 2 2 2