# Properties

 Degree $6$ Conductor $9037905787$ Sign $unknown$ Motivic weight $0$ Arithmetic yes Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + i·2-s + i·3-s − 4-s − i·5-s − 6-s − i·7-s − i·8-s − 9-s + 10-s − i·12-s + 14-s + 15-s + 16-s + 17-s − i·18-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut &\left(2083^{3}\right)^{s/2} \, \Gamma_{\R}(s)^{3} \, \Gamma_{\R}(s+1)^{3} \, L(s,\rho)\cr=\mathstrut & \epsilon \cdot \overline{\Lambda(1-\overline{s})}\quad (\text{with }\epsilon \text{ unknown})\end{aligned}

## Invariants

 Degree: $$6$$ Conductor: $$2083^{3}$$ Sign: $unknown$ Arithmetic: yes Primitive: yes Self-dual: no Selberg data: $$(6,\ 2083^{3} ,\ ( 0, 0, 0, 1, 1, 1 : \ ),\ 0 )$$

## Particular Values

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

## Euler product

$$L(s,\rho) = \displaystyle\prod_p \ \prod_{j=1}^{6} (1 - \alpha_{j,p}\, p^{-s})^{-1}$$

## 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.