# Properties

 Degree $3$ Conductor $3857296$ Sign $unknown$ Motivic weight $0$ Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + (−0.499 − 1.32i)3-s + (−0.500 + 1.32i)5-s + (−0.499 − 1.32i)7-s − 1.00·9-s + (−0.500 + 1.32i)11-s + 13-s + 2·15-s + (−0.499 − 1.32i)17-s + (−1.50 + 1.32i)21-s − 1.00·25-s + (−0.500 + 1.32i)27-s + (−0.500 + 1.32i)29-s + 2·33-s + 2·35-s + (−0.499 − 1.32i)39-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 3857296 ^{s/2} \, \Gamma_{\R}(s) \, \Gamma_{\R}(s+1)^{2} \, L(s,\rho)\cr =\mathstrut & \epsilon \cdot \overline{\Lambda(1-\overline{s})} \quad (\text{with }\epsilon \text{ unknown}) \end{aligned}

## Invariants

 Degree: $$3$$ Conductor: $$3857296$$    =    $$2^{4} \cdot 491^{2}$$ Sign: $unknown$ Primitive: yes Self-dual: no Selberg data: $$(3,\ 3857296,\ (0, 1, 1:\ ),\ 0)$$

## Particular Values

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

## Euler product

$$L(s,\rho) = \displaystyle\prod_p \ \prod_{j=1}^{3} (1 - \alpha_{j,p}\, p^{-s})^{-1}$$

## 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.