# Properties

 Label 1.3233.2t1.a.a Dimension $1$ Group $C_2$ Conductor $3233$ Root number $1$ Indicator $1$

# Related objects

## Basic invariants

 Dimension: $1$ Group: $C_2$ Conductor: $$3233$$$$\medspace = 53 \cdot 61$$ Frobenius-Schur indicator: $1$ Root number: $1$ Artin number field: Galois closure of $$\Q(\sqrt{3233})$$ Galois orbit size: $1$ Smallest permutation container: $C_2$ Parity: even Dirichlet character: $$\displaystyle\left(\frac{3233}{\bullet}\right)$$ Projective image: $C_1$ Projective field: $$\Q$$

## Defining polynomial

 $f(x)$ $=$ $x^{2} - x - 808$.

The roots of $f$ are computed in $\Q_{ 13 }$ to precision 5.

Roots:
 $r_{ 1 }$ $=$ $2 + 12\cdot 13 + 9\cdot 13^{2} + 6\cdot 13^{3} + 13^{4} +O\left(13^{ 5 }\right)$ $r_{ 2 }$ $=$ $12 + 3\cdot 13^{2} + 6\cdot 13^{3} + 11\cdot 13^{4} +O\left(13^{ 5 }\right)$

## 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.