# Properties

 Degree 1 Conductor 23 Sign $unknown$ Motivic weight 0 Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + (−0.959 + 0.281i)2-s + (−0.654 − 0.755i)3-s + (0.841 − 0.540i)4-s + (−0.142 − 0.989i)5-s + (0.841 + 0.540i)6-s + (0.415 − 0.909i)7-s + (−0.654 + 0.755i)8-s + (−0.142 + 0.989i)9-s + (0.415 + 0.909i)10-s + (−0.959 − 0.281i)11-s + (−0.959 − 0.281i)12-s + (0.415 + 0.909i)13-s + (−0.142 + 0.989i)14-s + (−0.654 + 0.755i)15-s + (0.415 − 0.909i)16-s + (0.841 + 0.540i)17-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 23 ^{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

 $$d$$ = $$1$$ $$N$$ = $$23$$ $$\varepsilon$$ = $unknown$ primitive : yes self-dual : no Selberg data = $(1,\ 23,\ (0:\ ),\ 0)$

## 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.