New Sextic Fields Unramified Outside of {∞, 3, 7}

Discriminant class: −7

∞  3 7 a_{1} a_{2} a_{3}  Over p = 3  Over p = 7  2 5 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 3_{i}  10_{+} 1_{k} 0 3 1 1^{6} 10_{+} ∗  1^{2} 1_{k} 7 7 42 6 42 32 6 32 42 42
C_{3}^{2}.D_{4}  9 -3 1  2 0_{+} ∗ ∗ 32 22 222 22 6 42 6 32
2. 1_{k}  10_{+} 3_{i} 0 -6 -1 1^{6} 10_{+} ∗  2^{2} 2_{+} 1 V 42 32 42 6 32 6 42 42
C_{3}^{2}.D_{4}  9 3 -5  1^{2} 1_{i} 7∗ 7∗ 6 22 2 22 32 42 32 6

Discriminant class: 1

∞  3 7 a_{1} a_{2} a_{3}  Over p = 3  Over p = 7  2 5 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 2_{−} 8_{−} 4_{+} 3 3 -9 1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 5 5 42 5 42 42 5 5
A_{6} -18 9 18 1^{3} 3_{i} 3∗ 1^{2} 1_{i} 7∗ 7∗ 5 33 42 42 33 42 5 3
4. 2_{−} 10_{−} 4_{+} 3 6 -17 1^{3} 5_{i} 3∗  1^{4} 3_{i} 7 7∗ 5 5 42 5 42 42 5 5
A_{6}  -57 -69 -47 1^{3} 5_{i} 3∗  1^{2} 1_{k} 7 7 5 3 42 42 3 42 5 33