# Properties

 Degree 2 Conductor 3 Sign $1$ Self-dual yes

# Nearby objects

 previous $L(s,f_{\text prev}$) next $L(s,f_{\text next})$

## Dirichlet series

 $L(s,f)$  = 1 + 1.342·2-s − 0.577·3-s + 0.802·4-s − 0.062·5-s − 0.775·6-s + 0.753·7-s − 0.265·8-s + 0.333·9-s − 0.083·10-s − 0.408·11-s − 0.463·12-s + 0.527·13-s + 1.011·14-s + 0.036·15-s − 1.158·16-s − 0.967·17-s + 0.447·18-s + 1.560·19-s − 0.050·20-s − 0.435·21-s − 0.548·22-s + 0.285·23-s + 0.153·24-s − 0.996·25-s + 0.708·26-s − 0.192·27-s + 0.604·28-s + ⋯

## Functional equation

\begin{align} \Lambda(s,f)=\mathstrut & 3 ^{s/2} \Gamma_{\R}(s+5.098i) \Gamma_{\R}(s-5.098 i) \cdot L(s,f)\cr =\mathstrut & \Lambda(1-s,f) \end{align}

## Invariants

 $d$ = $2$ $N$ = $3$ $\varepsilon$ = $1$ primitive : yes self-dual : yes Selberg data = $(2,\ 3,\ (5.098741908729592i, -5.098741908729592i:\ ),\ 1)$

## Euler product

$$$L(s,f) = \prod_{p\ \mathrm{bad}} (1- a(p) p^{-s})^{-1} \prod_{p\ \mathrm{good}} (1- a(p) p^{-s} + \chi(p)p^{-2s})^{-1}$$$