Dirichlet series
| $L(s,f)$ = 1 | + 0.707·2-s + 0.270·3-s + 0.5·4-s − 0.513·5-s + 0.191·6-s − 0.445·7-s + 0.353·8-s − 0.926·9-s − 0.363·10-s + 1.37·11-s + 0.135·12-s − 0.277·13-s − 0.315·14-s − 0.139·15-s + 0.250·16-s + 1.80·17-s − 0.655·18-s + 0.150·19-s − 0.256·20-s − 0.120·21-s + 0.974·22-s − 0.860·23-s + 0.0957·24-s − 0.736·25-s − 0.196·26-s − 0.521·27-s − 0.222·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 26 ^{s/2} \, \Gamma_{\R}(s+(1 + 1.74i)) \, \Gamma_{\R}(s+(1 - 1.74i)) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(26\) = \(2 \cdot 13\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 26,\ (1 + 1.74983899964i, 1 - 1.74983899964i:\ ),\ 1)\) |
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