Properties

Label 1.1.1t1.a.a
Dimension $1$
Group Trivial
Conductor $1$
Root number $1$
Indicator $1$

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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
Dirichlet character: \(\chi_{1}(1,\cdot)\)
Projective image: $C_1$
Projective field: \(\Q\)

Defining polynomial

$f(x)$$=$$ x $.

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

SizeOrderAction on $ r_{ 1 } $ Character value
$1$$1$$()$$1$

The blue line marks the conjugacy class containing complex conjugation.