Low Degree Fields Unramified Outside of {∞, 29, 83}

Discriminant class: −2407

∞ 29 83 a_{1} a_{2} a_{3}  Over p = 29  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 31 37 41 43 47 53 59
1. 1_{k} 1_{+} 1_{i} 0 2407  1^{2} 1_{+} 29 29 1^{2} 1_{i} 83∗ 83∗  2 2  2 2 2
C_{2} 20  2 2 2  2

Discriminant class: −83

∞ 29 83 a_{1} a_{2} a_{3} Over p = 29  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 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 3 2
S_{3} 3 3 2 2 2 3

Discriminant class: 29

∞ 29 83 a_{1} a_{2} a_{3} Over p = 29 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 31 37 41 43 47 53 59
4. 0_{+} 1_{+} 0_{+} 0 -29 1^{2} 1_{+} 29 29 2 2 2 2 2
C_{2}  2 2 2 2 2