# Properties

 Degree 2 Conductor $2^{6} \cdot 3^{2} \cdot 5^{2}$ Sign $unknown$ Motivic weight 0 Primitive yes Self-dual no

# Related objects

(not yet available)

## Dirichlet series

 $L(s,\rho)$  = 1 + 2i·11-s − i·49-s + 2·59-s + 2·61-s + 2i·71-s + 2i·109-s − 3·121-s + 2i·131-s − i·169-s − 2·179-s + 2·181-s − 2i·191-s + 2i·229-s − 2·239-s − 2·241-s + ⋯

## Functional equation

\begin{aligned} \Lambda(s)=\mathstrut & 14400 ^{s/2} \, \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

 $$d$$ = $$2$$ $$N$$ = $$14400$$    =    $$2^{6} \cdot 3^{2} \cdot 5^{2}$$ $$\varepsilon$$ = $unknown$ primitive : yes self-dual : no Selberg data = $(2,\ 14400,\ (1, 1:\ ),\ 0)$

## Euler product

\begin{aligned} L(s,\rho) = \prod_p \ \prod_{j=1}^{2} (1 - \alpha_{j,p}\, p^{-s})^{-1} \end{aligned}

## Particular Values

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

## 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.