# Properties

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

# Related objects

## Dirichlet series

 $L(s,f)$  = 1 − 1.06·2-s − 0.456·3-s + 0.141·4-s − 0.290·5-s + 0.487·6-s − 0.744·7-s + 0.917·8-s − 0.791·9-s + 0.310·10-s + 0.166·11-s − 0.0644·12-s − 0.586·13-s + 0.795·14-s + 0.132·15-s − 1.12·16-s + 0.570·17-s + 0.845·18-s − 0.981·19-s − 0.0410·20-s + 0.339·21-s − 0.177·22-s + 0.662·23-s − 0.418·24-s − 0.915·25-s + 0.626·26-s + 0.817·27-s − 0.105·28-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s,f)=\mathstrut &\Gamma_{\R}(s+(1 + 9.53i)) \, \Gamma_{\R}(s+(1 - 9.53i)) \, L(s,f)\cr=\mathstrut & -\,\Lambda(1-s,f)\end{aligned}

## Invariants

 $$d$$ = $$2$$ $$N$$ = $$1$$ $$\varepsilon$$ = $-1$ primitive : yes self-dual : yes Selberg data = $$(2,\ 1,\ (1 + 9.53369526135i, 1 - 9.53369526135i:\ ),\ -1)$$

## Euler product

\begin{aligned}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}\end{aligned}