Quartic Fields Unramified Outside of {∞, 7, 29}

Discriminant class: −203

∞ 7 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 29 2 3 5 11 13 17 19 23
G h a_{4} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{k} 3_{−} 2 16 15 1^{2} 1_{k} 7 7 1^{4} 3_{−} 29 29 4 22 2 4 2 22 22 22
D_{4} -9 2 0_{+} ∗ ∗ 22 4 22 4 22 2 22

Discriminant class: −7

∞ 7 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 29 2 3 5 11 13 17 19 23
G h a_{4} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 1_{k} 2_{−} -1 -3 -2 1^{2} 1_{k} 7 7 2^{2} 2_{−} 1 V 22 4 2 22 2 4 4 22
D_{4} 4 2 0_{+} ∗ ∗ 4 22 4 22 4 2 4

Discriminant class: 1

∞ 7 29 a_{1} a_{2} a_{3}  Over p = 7  Over p = 29 2 3 5 11 13 17 19 23
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 2_{−} 2_{−} 2_{+} 0 -11 0 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 22 22 22 22 22 22 22
V_{4} 2 81 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 22 22 22 22 22 22 22
4. 2_{−} 2_{+} 2_{−} -1 5 -6 1^{3} 2_{+} 1  2^{2} 2_{−} 1 V 3 3 3 3 22 3 3 3
A_{4} 2 7 3 3 22 3 3 3 3

Discriminant class: 29

∞ 7 29 a_{1} a_{2} a_{3}  Over p = 7  Over p = 29  2 3 5 11 13 17 19 23
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
5. 2_{−} 0_{+} 3_{−} -1 4 -20  1^{4} 3_{−} 29 29 4 4 22 4 22 4 4
C_{4}  23  4 4 4 4 4  4
6. 0_{+} 2_{−} 3_{−} 1 -54 -154 1^{2} 1_{i} 7∗ 7∗ 1^{4} 3_{−} 29 29 4 4  4  4 4
C_{4}  -35  1^{2} 1_{i} 7∗ 7∗  4 4 4 4 4  22 4
7. 2_{−} 2_{+} 1_{−} 2 2  1 2^{2} 2_{+} 1 V 1^{2} 1_{−} 29∗ 29∗ 2 4 22 2 22 4 4 22
D_{4} 2 2 0_{+} ∗ ∗ 4 2 4 2 4 22 4
8. 2_{−} 2_{+} 3_{−} 0 29  0 2^{2} 2_{+} 1 V 1^{4} 3_{−} 29 29 4 2 22 4 22 2 2 22
D_{4} 4  261  2 4 2 4 2  22 2