Low Degree Fields Unramified Outside of {∞, 83, 89}

Discriminant class: −7387

∞ 83 89 a_{1} a_{2} a_{3}  Over p = 83  Over p = 89  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} 1_{k} 1_{−} 0 7387  1^{2} 1_{k} 83 83 1^{2} 1_{−} 89∗ 89∗ 2 2 2 2
C_{2} 10 2 2 2 2 2 2 2

Discriminant class: −83

∞ 83 89 a_{1} a_{2}  a_{3}  Over p = 83  Over p = 89 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
2. 1_{k} 1_{i} 0_{+} 0 83  1^{2} 1_{i} 83∗ 83∗ 2 0_{+} ∗ ∗ 2  2  2  2
C_{2} 3  2 2 2
3. 1_{k} 1_{i} 0_{+} -1 1  -2 1^{2} 1_{i} 83∗ 83∗ 2 0_{+} ∗ ∗ 2 3 2 3 3 2 3 2
S_{3}  3 3 3  2 2 2
4. 1_{k} 1_{i} 2_{+} 0 89 -534 1^{2} 1_{i} 83∗ 83∗ 1^{3} 2_{+} ∗  2  2 3 3 2 3 2
S_{3} 3  3  3 2 2 2
5. 1_{k} 1_{i} 2_{+} -1 208 412 1^{2} 1_{i} 83∗ 83∗ 1^{3} 2_{+} ∗  2 3 2 3 3 2  2
S_{3} 3  3  3 3 2 2 2
6. 1_{k} 1_{i} 2_{+} -1 119 -1012 1^{2} 1_{i} 83∗ 83∗ 1^{3} 2_{+} ∗  2 3 2  2 3 2
S_{3} 3  3 3 3 3 2 2 2

Discriminant class: 89

∞ 83 89 a_{1} a_{2} a_{3} Over p = 83  Over p = 89 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
7. 0_{+} 0_{+} 1_{+} 0 -89 2 0_{+} ∗ ∗ 1^{2} 1_{+} 89 89 2 2 2 2
C_{2}  2 2 2 2 2 2
8. 0_{+} 2_{+} 1_{+} 0 -83 -249 1^{3} 2_{+} ∗  1^{2} 1_{+} 89 89 3 2 3 2  2 3 2
S_{3}  2 2 2 2 2 2  3