Label 1.1.1t1.a.a
Dimension 1
Group Trivial
Conductor $1$
Root number 1
Frobenius-Schur indicator 1

Related objects

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Basic invariants

Conductor:$1 $
Artin number field: Splitting field of \(\Q\) defined by $f= x $ over $\Q$
Size of Galois orbit: 1
Smallest containing permutation representation: Trivial
Parity: Even
Corresponding Dirichlet character: \(\chi_{1}(1,\cdot)\)
Projective image: $C_1$
Projective field: \(\Q\)

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 2 }$ to precision 5.
$r_{ 1 }$ $=$ $ 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
The blue line marks the conjugacy class containing complex conjugation.