Low Degree Fields Unramified Outside of {∞, 7, 23, 29}

Discriminant class: −667

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 23  Over p = 29 2 3 5 11 13 17 19 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} 0_{+} 1_{i} 1_{+} 0 667  2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2  2
C_{2} 4  2  2 2  2

Discriminant class: −203

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 23 Over p = 29 2 3 5 11 13 17 19 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} 1_{i} 0_{+} 1_{+} 0 203  1^{2} 1_{i} 7∗ 7∗  1^{2} 1_{+} 29 29 2  2 2 2
C_{2} 4  2  2  2

Discriminant class: −23

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 23  Over p = 29 2 3 5 11 13 17 19 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} 0_{+} 1_{i} 0_{+} 0 23  2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2 2
C_{2} 3  2  2  2  2 2
4. 1_{k} 0_{+} 1_{i} 0_{+} -1 0 1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 3 0_{+} 1  3 3 2 2 3 2 2 3
S_{3} 2 3 2 3 2 2 2

Discriminant class: −7

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 23 Over p = 29 2 3 5 11 13 17 19 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} 1_{i} 0_{+} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗  2 2  2 2 2 2
C_{2}  2  2  2 2

Discriminant class: 1

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 23 Over p = 29 2 3 5 11 13 17 19 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_{+} 0_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3 3 3 3

Discriminant class: 29

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 23 Over p = 29 2 3 5 11 13 17 19 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_{+} 0_{+} 0_{+} 1_{+} 0 -29  1^{2} 1_{+} 29 29 2 2  2  2 2 2
C_{2}  2 2 2 2  2

Discriminant class: 161

∞ 7 23 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 23  Over p = 29 2 3 5 11 13 17 19 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
8. 0_{+} 1_{k} 1_{i} 0_{+} 0 -161  1^{2} 1_{k} 7 7 1^{2} 1_{i} 23∗ 23∗  2  2 2  2
C_{2}  2 2 2 2 2 2  2

Discriminant class: 4669

∞ 7 23 29 a_{1}  a_{2} a_{3} Over p = 7  Over p = 23  Over p = 29 2 3 5 11 13 17 19 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
9. 0_{+} 1_{k} 1_{i} 1_{+} 0 -4669  1^{2} 1_{k} 7 7 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2  2 2 2
C_{2} 8  2 2 2 2