# Properties

 Label 2-799-799.610-c0-0-2 Degree $2$ Conductor $799$ Sign $-0.762 - 0.647i$ Analytic cond. $0.398752$ Root an. cond. $0.631468$ Motivic weight $0$ Arithmetic yes Rational no Primitive yes Self-dual no Analytic rank $0$

# Related objects

## Dirichlet series

 L(s)  = 1 + (1.34 + 1.34i)2-s + (0.178 + 0.431i)3-s + 2.61i·4-s + (−0.339 + 0.820i)6-s + (−1.40 − 0.581i)7-s + (−2.17 + 2.17i)8-s + (0.552 − 0.552i)9-s + (−1.12 + 0.467i)12-s + (−1.10 − 2.67i)14-s − 3.23·16-s + (0.809 + 0.587i)17-s + 1.48·18-s − 0.710i·21-s + (−1.32 − 0.549i)24-s + (0.707 − 0.707i)25-s + ⋯
 L(s)  = 1 + (1.34 + 1.34i)2-s + (0.178 + 0.431i)3-s + 2.61i·4-s + (−0.339 + 0.820i)6-s + (−1.40 − 0.581i)7-s + (−2.17 + 2.17i)8-s + (0.552 − 0.552i)9-s + (−1.12 + 0.467i)12-s + (−1.10 − 2.67i)14-s − 3.23·16-s + (0.809 + 0.587i)17-s + 1.48·18-s − 0.710i·21-s + (−1.32 − 0.549i)24-s + (0.707 − 0.707i)25-s + ⋯

## Functional equation

\begin{aligned}\Lambda(s)=\mathstrut & 799 ^{s/2} \, \Gamma_{\C}(s) \, L(s)\cr =\mathstrut & (-0.762 - 0.647i)\, \overline{\Lambda}(1-s) \end{aligned}
\begin{aligned}\Lambda(s)=\mathstrut & 799 ^{s/2} \, \Gamma_{\C}(s) \, L(s)\cr =\mathstrut & (-0.762 - 0.647i)\, \overline{\Lambda}(1-s) \end{aligned}

## Invariants

 Degree: $$2$$ Conductor: $$799$$    =    $$17 \cdot 47$$ Sign: $-0.762 - 0.647i$ Analytic conductor: $$0.398752$$ Root analytic conductor: $$0.631468$$ Motivic weight: $$0$$ Rational: no Arithmetic: yes Character: $\chi_{799} (610, \cdot )$ Primitive: yes Self-dual: no Analytic rank: $$0$$ Selberg data: $$(2,\ 799,\ (\ :0),\ -0.762 - 0.647i)$$

## Particular Values

 $$L(\frac{1}{2})$$ $$\approx$$ $$1.791149651$$ $$L(\frac12)$$ $$\approx$$ $$1.791149651$$ $$L(1)$$ not available $$L(1)$$ not available

## Euler product

$$L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1}$$
$p$$F_p(T)$
bad17 $$1 + (-0.809 - 0.587i)T$$
47 $$1 - iT$$
good2 $$1 + (-1.34 - 1.34i)T + iT^{2}$$
3 $$1 + (-0.178 - 0.431i)T + (-0.707 + 0.707i)T^{2}$$
5 $$1 + (-0.707 + 0.707i)T^{2}$$
7 $$1 + (1.40 + 0.581i)T + (0.707 + 0.707i)T^{2}$$
11 $$1 + (0.707 + 0.707i)T^{2}$$
13 $$1 + T^{2}$$
19 $$1 - iT^{2}$$
23 $$1 + (0.707 + 0.707i)T^{2}$$
29 $$1 + (-0.707 + 0.707i)T^{2}$$
31 $$1 + (0.707 - 0.707i)T^{2}$$
37 $$1 + (0.744 + 1.79i)T + (-0.707 + 0.707i)T^{2}$$
41 $$1 + (-0.707 - 0.707i)T^{2}$$
43 $$1 + iT^{2}$$
53 $$1 + (1.26 + 1.26i)T + iT^{2}$$
59 $$1 + (0.437 - 0.437i)T - iT^{2}$$
61 $$1 + (-0.144 - 0.0600i)T + (0.707 + 0.707i)T^{2}$$
67 $$1 - T^{2}$$
71 $$1 + (0.652 + 1.57i)T + (-0.707 + 0.707i)T^{2}$$
73 $$1 + (-0.707 + 0.707i)T^{2}$$
79 $$1 + (0.652 - 1.57i)T + (-0.707 - 0.707i)T^{2}$$
83 $$1 + (1 + i)T + iT^{2}$$
89 $$1 - 1.90iT - T^{2}$$
97 $$1 + (1.84 - 0.763i)T + (0.707 - 0.707i)T^{2}$$
$$L(s) = \displaystyle\prod_p \ \prod_{j=1}^{2} (1 - \alpha_{j,p}\, p^{-s})^{-1}$$