### L-functions of signature (0,0,0,0;) with real coefficients

These L-functions satisfy a functional equation with $$\Gamma$$-factors \begin{aligned}\Gamma_\R(s + i \mu_1)\Gamma_\R(s + i \mu_2)\Gamma_\R(s - i \mu_1)\Gamma_\R(s - i \mu_2)\end{aligned} with $$\mu_j$$ real. By renaming and rearranging, we may assume $$0 \le \mu_2 \le \mu_1$$.

#### L-functions of conductor 1

The dots in the plot correspond to L-functions with $$(\mu_1,\mu_2)$$ in the $$\Gamma$$-factors, colored according to the sign of the functional equation (blue indicates $$\epsilon=1$$). Click on any of the dots for detailed information about the L-function.

### L-functions of signature (0,0,0,0;)

These L-functions satisfy a functional equation with $$\Gamma$$-factors \begin{aligned}\Gamma_\R(s + i \mu_1)\Gamma_\R(s + i \mu_2)\Gamma_\R(s + i \mu_3)\Gamma_\R(s + i \mu_4)\end{aligned} with $$\mu_j\in \R$$ and $$\mu_1 + \mu_2 + \mu_3 + \mu_4 = 0$$. By permuting and possibly conjugating, we may assume $$0\le \mu_2 \le \mu_1$$.

#### L-functions of conductor 1

The dots in the plot correspond to L-functions with $$(\mu_1,\mu_2)$$ in the $$\Gamma$$-factors, colored according to the sign of the functional equation (blue indicates $$\epsilon=1$$). Click on any of the dots for detailed information about the L-function.