Basic invariants
Galois action
Roots of defining polynomial
The roots of
f are computed in
Q181 to precision 5.
Generators of the action on the roots
r1,…,r4
Cycle notation |
(1,2) |
(1,3)(2,4) |
Character values on conjugacy classes
Size | Order | Action on
r1,…,r4
| Character values |
| | |
c1 |
1 |
1 |
() |
2 |
1 |
2 |
(1,2)(3,4) |
−2 |
2 |
2 |
(1,3)(2,4) |
0 |
2 |
2 |
(1,2) |
0 |
2 |
4 |
(1,4,2,3) |
0 |
The blue line marks the conjugacy class containing complex conjugation.