Low Degree Fields Ramifying Above {2, 7, 29}

Discriminant class: −406

∞ 2 7 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 29  3 5 11 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} 3_{−} 1_{i} 1_{−} 0 406  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{−} 29∗ 29∗ 2  2
C_{2} 16  2  2 2

Discriminant class: −203

∞ 2 7 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 29 3 5 11 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} 2_{+} 1_{i} 1_{+} -1 -7 -7 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 3 2 2 2  3 3
S_{3}  2 3 2 3 3 2  3

Discriminant class: −14

∞ 2 7 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 29 3 5 11 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
3. 1_{k} 3_{+} 1_{i} 2_{+} 0 29 -58 1^{2} 3_{+} 2 2 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 3 2 3 2 3 3 2
S_{3} 2 2 2 2 2 2 3 2

Discriminant class: 29

∞ 2 7 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 29 3 5 11 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. 0_{+} 2_{+} 2_{+} 1_{+} 0 -14 -14 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{+} 29 29 2 3 2 3 2 2  2
S_{3} 3  2 2 2 2 3  2

Discriminant class: 203

∞ 2 7 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 29 3 5 11 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
5. 0_{+} 2_{i} 1_{k} 1_{+} 0 -203  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 7 7 1^{2} 1_{+} 29 29 2 2  2  2 2 2
C_{2} 2  2  2  2

Discriminant class: 406

∞ 2 7 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 29  3 5 11 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
6. 0_{+} 3_{k} 1_{k} 1_{−} 0 -406  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 7 7 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 2  2 2 2 2 2