Dirichlet series
| $L(s,f)$ = 1 | − 0.220·2-s − 0.458·3-s − 0.951·4-s + 1.35·5-s + 0.101·6-s + 1.29·7-s + 0.431·8-s − 0.789·9-s − 0.299·10-s + 0.592·11-s + 0.436·12-s + 0.595·13-s − 0.285·14-s − 0.622·15-s + 0.855·16-s + 0.242·17-s + 0.174·18-s + 1.69·19-s − 1.29·20-s − 0.592·21-s − 0.130·22-s − 1.17·23-s − 0.197·24-s + 0.841·25-s − 0.131·26-s + 0.821·27-s − 1.22·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 17 ^{s/2} \, \Gamma_{\R}(s+(1 + 4.55i)) \, \Gamma_{\R}(s+(1 - 4.55i)) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(17\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 17,\ (1 + 4.55176008183i, 1 - 4.55176008183i:\ ),\ 1)\) |
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