Properties

 Label 1.1609.2t1.1c1 Dimension 1 Group $C_2$ Conductor $1609$ Root number 1 Frobenius-Schur indicator 1

Related objects

Basic invariants

 Dimension: $1$ Group: $C_2$ Conductor: $1609$ Artin number field: Splitting field of $f=x^{2} - x - 402$ over $\Q$ Size of Galois orbit: 1 Smallest containing permutation representation: 2T1 Parity: Even Corresponding Dirichlet character: $\displaystyle\left(\frac{1609}{\bullet}\right)$

Galois action

Roots of defining polynomial

The roots of $f$ are computed in $\Q_{ 3 }$ to precision 5.
Roots: \begin{aligned} r_{ 1 } &= 66 +O\left(3^{ 5 }\right) \\ r_{ 2 } &= -65 +O\left(3^{ 5 }\right) \\ \end{aligned}

Generators of the action on the roots $r_{ 1 }, r_{ 2 }$

 Cycle notation $(1,2)$

Character values on conjugacy classes

 Size Order Action on $r_{ 1 }, r_{ 2 }$ Character value $1$ $1$ $()$ $1$ $1$ $2$ $(1,2)$ $-1$
The blue line marks the conjugacy class containing complex conjugation.