Dirichlet series
| $L(s,f)$ = 1 | − 0.568·2-s + 1.52·3-s − 0.676·4-s + 0.748·5-s − 0.868·6-s + 1.10·7-s + 0.953·8-s + 1.33·9-s − 0.425·10-s − 0.496·11-s − 1.03·12-s + 1.33·13-s − 0.630·14-s + 1.14·15-s + 0.134·16-s − 0.242·17-s − 0.758·18-s − 1.21·19-s − 0.506·20-s + 1.69·21-s + 0.282·22-s + 0.544·23-s + 1.45·24-s − 0.440·25-s − 0.756·26-s + 0.511·27-s − 0.750·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 17 ^{s/2} \, \Gamma_{\R}(s+4.28i) \, \Gamma_{\R}(s-4.28i) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(17\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 17,\ (4.2850685348i, -4.2850685348i:\ ),\ 1)\) |
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