# Properties

 Degree $1$ Conductor $1035$ Sign $unknown$ Motivic weight $0$ Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + (0.499 − 0.866i)2-s + (−0.500 − 0.866i)4-s + (−0.499 + 0.866i)7-s − 0.999·8-s + (0.499 − 0.866i)11-s + (0.500 + 0.866i)13-s + (0.500 + 0.866i)14-s + (−0.499 + 0.866i)16-s + 17-s − 19-s + (−0.500 − 0.866i)22-s + 26-s + 0.999·28-s + (−0.499 + 0.866i)29-s + (−0.500 − 0.866i)31-s + (0.500 + 0.866i)32-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 1035 ^{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: $$1035$$    =    $$3^{2} \cdot 5 \cdot 23$$ Sign: $unknown$ Primitive: yes Self-dual: no Selberg data: $$(1,\ 1035,\ (1:\ ),\ 0)$$

## 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.