Low Degree Fields Unramified Outside of {∞, 13, 83}

Discriminant class: −1079

∞ 13 83 a_{1} a_{2} a_{3}  Over p = 13  Over p = 83 2 3 5 7 11 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 1079  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 83 83  2 2
C_{2} 34  2 2 2 2  2 2

Discriminant class: −83

∞ 13 83 a_{1} a_{2} a_{3} Over p = 13  Over p = 83  2 3 5 7 11 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 2 3 3 3 2
S_{3} 3 3 3 2 2 2 3

Discriminant class: 1

∞ 13 83 a_{1} a_{2} a_{3} Over p = 13 Over p = 83 2 3 5 7 11 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
4. 0_{+} 2_{+} 0_{+} -1 -4 -1 1^{3} 2_{+} 1  3 3  3 3 3 3 3
C_{3}  3  3 3 3  3

Discriminant class: 13

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