Basic invariants
| Dimension: | $1$ |
| Group: | Trivial |
| Conductor: | $1 $ |
| Artin number field: | Splitting field of $f= x $ over $\Q$ |
| Size of Galois orbit: | 1 |
| Smallest containing permutation representation: | Trivial |
| Parity: | Even |
Galois action
Roots of defining polynomial
The roots of $f$ are computed in $\Q_{ 2 }$ to precision 5.
Roots:
| $r_{ 1 }$ | $=$ | $ 0 +O\left(2^{ 5 }\right)$ |
Generators of the action on the roots $ r_{ 1 } $
| Cycle notation |
Character values on conjugacy classes
| Size | Order | Action on $ r_{ 1 } $ | Character values |
| $c1$ | |||
| $1$ | $1$ | $()$ | $1$ |