Dirichlet series
| $L(s,f)$ = 1 | + 1.44·2-s + 0.0800·3-s + 1.09·4-s + 1.62·5-s + 0.115·6-s + 0.556·7-s + 0.133·8-s − 0.993·9-s + 2.34·10-s + 1.18·11-s + 0.0874·12-s − 0.838·13-s + 0.804·14-s + 0.130·15-s − 0.899·16-s − 0.242·17-s − 1.43·18-s − 0.466·19-s + 1.77·20-s + 0.0445·21-s + 1.70·22-s − 0.677·23-s + 0.0106·24-s + 1.63·25-s − 1.21·26-s − 0.159·27-s + 0.607·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 17 ^{s/2} \, \Gamma_{\R}(s+4.69i) \, \Gamma_{\R}(s-4.69i) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(17\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 17,\ (4.69933935i, -4.69933935i:\ ),\ 1)\) |
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