Low Degree Fields Unramified Outside of {∞, 13, 59}

Discriminant class: −767

∞ 13 59 a_{1} a_{2} a_{3}  Over p = 13  Over p = 59 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 61
1. 1_{k} 1_{−} 1_{k} 0 767  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 59 59  2 2  2 2
C_{2} 22  2 2  2

Discriminant class: −59

∞ 13 59 a_{1} a_{2} a_{3} Over p = 13  Over p = 59  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 61
2. 1_{k} 0_{+} 1_{i} 0 59  2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗ 2  2  2
C_{2} 3  2 2  2 2  2
3. 1_{k} 0_{+} 1_{i} 0 2 -1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗ 2 3 3 3 2  3 2
S_{3}  3 2 2 3 2 2 3 2

Discriminant class: 1

∞ 13 59 a_{1} a_{2} a_{3} Over p = 13 Over p = 59 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 61
4. 0_{+} 2_{+} 0_{+} -1 -4 -1 1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3 3
C_{3}  3  3 3 3  3

Discriminant class: 13

∞ 13 59 a_{1} a_{2} a_{3} Over p = 13 Over p = 59 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 61
5. 0_{+} 1_{+} 0_{+} 1 -3  1^{2} 1_{+} 13 13 2 0_{+} ∗ ∗ 2  2 2 2  2
C_{2}  2 2 2  2