# Properties

 Degree 1 Conductor $5 \cdot 19$ Sign $unknown$ Motivic weight 0 Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + (0.499 − 0.866i)2-s + (0.499 − 0.866i)3-s + (−0.500 − 0.866i)4-s + (−0.500 − 0.866i)6-s − 7-s − 0.999·8-s + (−0.500 − 0.866i)9-s + 11-s − 0.999·12-s + (0.500 + 0.866i)13-s + (−0.499 + 0.866i)14-s + (−0.499 + 0.866i)16-s + (0.499 − 0.866i)17-s − 0.999·18-s + (−0.499 + 0.866i)21-s + (0.499 − 0.866i)22-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 95 ^{s/2} \, \Gamma_{\R}(s) \, L(s,\rho)\cr =\mathstrut & \epsilon \cdot \overline{\Lambda(1-\overline{s})} \quad (\text{with }\epsilon \text{ not computed}) \end{aligned}

## Invariants

 $$d$$ = $$1$$ $$N$$ = $$95$$    =    $$5 \cdot 19$$ $$\varepsilon$$ = $unknown$ primitive : yes self-dual : no Selberg data = $$(1,\ 95,\ (0:\ ),\ 0)$$

## Euler product

\begin{aligned}L(s,\rho) = \prod_p \ (1 - \alpha_{p}\, p^{-s})^{-1}\end{aligned}

## Particular Values

Not enough information (Dirichlet series coefficients/sign of the functional equation) to compute special values.

## Imaginary part of the first few zeros on the critical line

Zeros not available.

## Graph of the $Z$-function along the critical line

Plot not available.