Basic invariants
| Dimension: | $1$ |
| Group: | Trivial |
| Conductor: | $1$ |
| Frobenius-Schur indicator: | $1$ |
| Root number: | $1$ |
| Artin number field: | Galois closure of \(\Q\) |
| Galois orbit size: | $1$ |
| Smallest permutation container: | Trivial |
| Parity: | even |
| Projective image: | $C_1$ |
| Projective field: | Galois closure of \(\Q\) |
Galois action
Roots of defining polynomial
The roots of $f$ are computed in $\Q_{ 2 }$ to precision 5.
Roots:
| $r_{ 1 }$ | $=$ |
\( 0 +O(2^{5})\)
|
Generators of the action on the roots $ r_{ 1 } $
| Cycle notation |
Character values on conjugacy classes
| Size | Order | Action on $ r_{ 1 } $ | Character values |
| $c1$ | |||
| $1$ | $1$ | $()$ | $1$ |