Low Degree Fields Ramifying Above {2, 17, 29}

Discriminant class: −986

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 5 7 11 13 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_{k} 1_{−} 1_{+} 0 986  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{+} 29 29  2 2  2
C_{2} 44  2  2  2  2

Discriminant class: −493

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29  3 5 7 11 13 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_{i} 1_{−} 1_{−} 0 493  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 2  2  2
C_{2} 12  2  2
3. 1_{k} 2_{i} 1_{−} 1_{−} 0 10 -12 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 3 2 3 3  2
S_{3} 5  3 3 3 3 3 2 3 2

Discriminant class: −58

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29  3 5 7 11 13 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} 3_{k} 2_{+} 1_{−} -1 -11 -97 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2
S_{3} 13  3 2 2 3 2 3 3 3

Discriminant class: −17

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 5 7 11 13 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. 1_{k} 2_{i} 1_{+} 2_{+} 0 29 -174 1^{2} 2_{i} −1 −1 1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  2 3 3 3 2 3
S_{3}  2 2 2 2 3 2 2 2

Discriminant class: 29

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 17 Over p = 29 3 5 7 11 13 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_{+} 2_{+} 2_{+} 1_{+} -1 -45 -97 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 3 3 2 3 2 3 2
S_{3}  2 2 2 2 3  2 3

Discriminant class: 986

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 5 7 11 13 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
7. 0_{+} 3_{−} 1_{−} 1_{+} 0 -986  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{+} 29 29 2  2 2 2  2
C_{2} 4  2  2 2 2 2 2