Properties

Degree $1$
Conductor $145$
Sign $unknown$
Motivic weight $0$
Arithmetic yes
Primitive yes
Self-dual no

Related objects

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Normalization:  

(not yet available)

Dirichlet series

$L(s,\rho)$  = 1  + 2-s − 3-s + 4-s − 6-s i·7-s + 8-s + 9-s + i·11-s − 12-s i·13-s i·14-s + 16-s + 17-s + 18-s i·19-s + ⋯

Functional equation

\[\begin{aligned}\Lambda(s)=\mathstrut & 145 ^{s/2} \, \Gamma_{\R}(s) \, L(s,\rho)\cr =\mathstrut & \epsilon \cdot \overline{\Lambda(1-\overline{s})} \quad (\text{with }\epsilon \text{ not computed}) \end{aligned}\]

Invariants

Degree: \(1\)
Conductor: \(145\)    =    \(5 \cdot 29\)
Sign: $unknown$
Arithmetic: yes
Primitive: yes
Self-dual: no
Selberg data: \((1,\ 145,\ (0:\ ),\ 0)\)

Particular Values

Not enough information (Dirichlet series coefficients/sign of the functional equation) to compute special values.

Euler product

\(L(s,\rho) = \displaystyle\prod_p \ (1 - \alpha_{p}\, p^{-s})^{-1}\)

Imaginary part of the first few zeros on the critical line

Zeros not available.

Graph of the $Z$-function along the critical line

Plot not available.