Dirichlet series
| $L(s,f)$ = 1 | − 0.707·2-s + 1.46·3-s + 0.5·4-s + 1.11·5-s − 1.03·6-s − 1.32·7-s − 0.353·8-s + 1.13·9-s − 0.789·10-s − 0.848·11-s + 0.730·12-s + 0.277·13-s + 0.940·14-s + 1.63·15-s + 0.250·16-s + 0.0591·17-s − 0.800·18-s − 1.14·19-s + 0.558·20-s − 1.94·21-s + 0.600·22-s + 0.708·23-s − 0.516·24-s + 0.248·25-s − 0.196·26-s + 0.192·27-s − 0.664·28-s + ⋯ |
Functional equation
\[\begin{aligned}\Lambda(s,f)=\mathstrut & 26 ^{s/2} \, \Gamma_{\R}(s+(1 + 1.97i)) \, \Gamma_{\R}(s+(1 - 1.97i)) \, L(s,f)\cr =\mathstrut & \, \Lambda(1-s,f) \end{aligned}\]
Invariants
| Degree: | \(2\) |
| Conductor: | \(26\) = \(2 \cdot 13\) |
| Sign: | $1$ |
| Arithmetic: | no |
| Primitive: | yes |
| Self-dual: | yes |
| Selberg data: | \((2,\ 26,\ (1 + 1.9732685967i, 1 - 1.9732685967i:\ ),\ 1)\) |
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