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