Dirichlet series
| $L(s,f)$ = 1 | − 0.247·2-s + 1.81·3-s − 0.938·4-s − 0.431·5-s − 0.449·6-s − 0.768·7-s + 0.480·8-s + 2.29·9-s + 0.106·10-s + 0.334·11-s − 1.70·12-s − 0.0685·13-s + 0.190·14-s − 0.784·15-s + 0.819·16-s + 0.242·17-s − 0.569·18-s + 0.196·19-s + 0.405·20-s − 1.39·21-s − 0.0826·22-s − 0.298·23-s + 0.871·24-s − 0.813·25-s + 0.0169·26-s + 2.35·27-s + 0.721·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 17 ^{s/2} \, \Gamma_{\R}(s+(1 + 1.97i)) \, \Gamma_{\R}(s+(1 - 1.97i)) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(17\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 17,\ (1 + 1.97928209991i, 1 - 1.97928209991i:\ ),\ 1)\) |
Euler product
\(L(s,f) = \displaystyle\prod_{p\ \mathrm{bad}} (1- a(p) p^{-s})^{-1} \prod_{p\ \mathrm{good}} (1- a(p) p^{-s} + \chi(p)p^{-2s})^{-1}\)
Imaginary part of the first few zeros on the critical line