Low Degree Fields Unramified Outside of {∞, 11, 53}

Discriminant class: −583

∞ 11 53 a_{1} a_{2} a_{3}  Over p = 11  Over p = 53 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 59 61
1. 1_{k} 1_{i} 1_{+} 0 583  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 53 53  2 2 2 2 2  2
C_{2} 8  2 2  2

Discriminant class: −11

∞ 11 53 a_{1} a_{2} a_{3}  Over p = 11  Over p = 53 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 59 61
2. 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: 53

∞ 11 53 a_{1} a_{2} a_{3} Over p = 11  Over p = 53 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 59 61
3. 0_{+} 0_{+} 1_{+} 0 -53  1^{2} 1_{+} 53 53 2 2 2  2 2
C_{2}  2  2  2