# Properties

 Degree $3$ Conductor $14462809$ Sign $unknown$ Motivic weight $0$ Primitive yes Self-dual no

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## Dirichlet series

 $L(s,\rho)$  = 1 + (−0.500 + 1.32i)2-s + (−0.500 + 1.32i)3-s − 1.00·4-s + 5-s + (−1.5 − 1.32i)6-s + (−0.499 − 1.32i)8-s − 1.00·9-s + (−0.500 + 1.32i)10-s + (0.500 − 1.32i)12-s + (−0.500 + 1.32i)13-s + (−0.500 + 1.32i)15-s + 1.00·16-s + (0.500 − 1.32i)18-s + (−0.499 − 1.32i)19-s − 1.00·20-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 14462809 ^{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: $$14462809$$    =    $$3803^{2}$$ Sign: $unknown$ Primitive: yes Self-dual: no Selberg data: $$(3,\ 14462809,\ (0, 1, 1:\ ),\ 0)$$

## 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.