# Properties

 Degree $1$ Conductor $36$ Sign $unknown$ Motivic weight $0$ Arithmetic yes Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + (−0.499 + 0.866i)5-s + (0.500 + 0.866i)7-s + (0.500 + 0.866i)11-s + (−0.499 + 0.866i)13-s + 17-s − 19-s + (0.499 − 0.866i)23-s + (−0.500 − 0.866i)25-s + (−0.500 − 0.866i)29-s + (0.499 − 0.866i)31-s − 35-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 36 ^{s/2} \, \Gamma_{\R}(s+1) \, L(s,\rho)\cr =\mathstrut & \epsilon \cdot \overline{\Lambda(1-\overline{s})} \quad (\text{with }\epsilon \text{ not computed}) \end{aligned}

## Invariants

 Degree: $$1$$ Conductor: $$36$$    =    $$2^{2} \cdot 3^{2}$$ Sign: $unknown$ Arithmetic: yes Primitive: yes Self-dual: no Selberg data: $$(1,\ 36,\ (1:\ ),\ 0)$$

## Particular Values

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

## Euler product

$$L(s,\rho) = \displaystyle\prod_p \ (1 - \alpha_{p}\, p^{-s})^{-1}$$

## 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.