Septic Fields Ramifying Above {7}

Discriminant class: −7

∞  7 a_{1} a_{2} a_{3} a_{4}  Over p = 7  2 3 5 11 13 17 19 23
G  h a_{5} a_{6} a_{7}  f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 3_{i} 9_{k} 0 0 0 7 1^{7} 9_{k} 7∗  7 222 222 7 222 222 222 7
D_{7} -7 7 1 7 222 7 222 7 222 7 222
2. 3_{i} 11_{k} 0 0 -14 7 1^{7} 11_{k} 7∗  33 6 6 33 222 6 6 33
F_{7} 28 21 8 7 6 33 222 7 6 33 6
3. 3_{i} 13_{k} 0 0 0 0 1^{7} 13_{k} 7∗  33 6 6 33 222 6 6 33
F_{7} 0 0 -7 7 6 33 222 6 33 6

Discriminant class: 1

∞  7 a_{1} a_{2} a_{3} a_{4}  Over p = 7 2 3 5 11 13 17 19 23
G  h a_{5} a_{6} a_{7}  f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 12_{+} 0 -21 -21 91 1^{7} 12_{+} 1  7 7 7 7 7 7  7
C_{7}  112 -84 -97  7  7 7 7 7 7 7