Properties

Label 1.1.1t1.1c1
Dimension 1
Group Trivial
Conductor $1$
Root number 1
Frobenius-Schur indicator 1

Related objects

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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
Corresponding Dirichlet character: \(\chi_{1}(1,\cdot)\)

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 2 }$ to precision 5.
Roots: \[ \begin{aligned} r_{ 1 } &= 0 +O\left(2^{ 5 }\right) \\ \end{aligned}\]

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.