Low Degree Fields Unramified Outside of {∞, 2, 83}

Discriminant class: −166

∞ 2 83 a_{1} a_{2} a_{3} Over p = 2 Over p = 83 3 5 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} 3_{−} 1_{k} 0 166  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 83 83 2  2
C_{2} 10  2  2  2  2

Discriminant class: −83

∞ 2 83 a_{1} a_{2} a_{3} Over p = 2  Over p = 83  3 5 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∗ 3 2 3 3 2 3 2
S_{3} 3 3 3 2 2 2 3

Discriminant class: −2

∞ 2 83 a_{1} a_{2} a_{3}  Over p = 2  Over p = 83 3 5 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
4. 1_{k} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 2  2  2
C_{2}  2 2 2  2 2

Discriminant class: −1

∞ 2 83 a_{1} a_{2} a_{3}  Over p = 2  Over p = 83 3 5 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
5. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 2  2 2  2 2
C_{2}  2  2 2  2
6. 1_{k} 2_{i} 2_{+} -1 28 -40 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2  2 2 3 3 2 2
S_{3} 2  2 3 3 2 2 3 2

Discriminant class: 2

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

Discriminant class: 83

∞ 2 83 a_{1} a_{2} a_{3}  Over p = 2  Over p = 83 3 5 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
8. 0_{+} 2_{i} 1_{k} 0 -83  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 83 83 2 2 2 2 2  2
C_{2}  2  2 2

Discriminant class: 166

∞ 2 83 a_{1} a_{2} a_{3}  Over p = 2  Over p = 83  3 5 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
9. 0_{+} 3_{k} 1_{i} 0 -166  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 83∗ 83∗  2  2 2
C_{2}  2 2 2  2