Low Degree Fields Ramifying Above {3, 11, 29}

Discriminant class: −319

∞ 3 11 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 29  2 5 7 13 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 4_{+} 1_{k} 1_{−} 0 -3 -31 1^{3} 4_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗ 3 3 2 2 3 3 3 2
S_{3} 2 3 3 2 3 3 3

Discriminant class: −11

∞ 3 11 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 29 2 5 7 13 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
2. 1_{k} 4_{+} 1_{i} 2_{+} 0 87 -116 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 2 3 3
S_{3} 3  2 2 3 3 3 2 3
3. 1_{k} 4_{+} 1_{i} 2_{+} 0 -174 -899 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 2 3
S_{3} 3  3 2 2 3  2

Discriminant class: −3

∞ 3 11 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 Over p = 29 2 5 7 13 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
4. 1_{k} 1_{i} 2_{+} 2_{+} -1 -106 508 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 2 3 2 3
S_{3}  2 3 2 2 2 3
5. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -319 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 3 2 3
S_{3} 3  2 3 2 2 2 3 3
6. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -2871 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 2 3 2 3
S_{3} 6  3 2 3 2 2 2 3 3
7. 1_{k} 5_{i} 2_{+} 2_{+} 0  0 -10527 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  3 2  2 3
S_{3} 126  3 2  2 2 2 3
8. 1_{k} 5_{i} 2_{+} 2_{+} 0  0 -27753 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 3 2 3 2
S_{3} 18  3 2 3 2 2 2 3
9. 1_{k} 5_{i} 2_{+} 2_{+} 0  0 -957 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3  2  2
S_{3} 3  3 2  2 2 2 3 3

Discriminant class: 957

∞ 3 11 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 29 2 5 7 13 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
10. 0_{+} 1_{k} 1_{i} 1_{+} 0 -957  1^{2} 1_{k} 3 3 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 29 29 2 2 2 2 2  2 2
C_{2} 2  2 2  2 2