Dirichlet series
| $L(s,f)$ = 1 | + 1.81·2-s − 1.17·3-s + 2.30·4-s − 0.336·5-s − 2.13·6-s − 1.43·7-s + 2.36·8-s + 0.381·9-s − 0.611·10-s − 0.572·11-s − 2.70·12-s + 1.55·13-s − 2.60·14-s + 0.395·15-s + 1.99·16-s + 1.80·17-s + 0.693·18-s − 0.400·19-s − 0.774·20-s + 1.68·21-s − 1.03·22-s − 0.520·23-s − 2.77·24-s − 0.886·25-s + 2.83·26-s + 0.726·27-s − 3.30·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 293 ^{s/2} \, \Gamma_{\R}(s+0.850i) \, \Gamma_{\R}(s-0.850i) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(293\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 293,\ (0.850490920380i, -0.850490920380i:\ ),\ 1)\) |
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