Low Degree Fields Unramified Outside of {∞, 11, 59}

Discriminant class: −59

∞ 11 59 a_{1} a_{2} a_{3} Over p = 11  Over p = 59  2 3 5 7 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 61
1. 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
2. 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: −11

∞ 11 59 a_{1} a_{2} a_{3}  Over p = 11  Over p = 59 2 3 5 7 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 61
3. 1_{k} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗  2  2 2 2 2
C_{2}  2  2 2  2

Discriminant class: 649

∞ 11 59 a_{1} a_{2} a_{3}  Over p = 11  Over p = 59  2 3 5 7 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 61
4. 0_{+} 1_{k} 1_{i} 0 -649  1^{2} 1_{k} 11 11 1^{2} 1_{i} 59∗ 59∗  2  2 2 2
C_{2}  2 2 2 2  2