L-functions of degree 1 are associated to Dirichlet characters and they are called Dirichlet L-functions. These L-functions have a functional equation of the form \[ \Lambda(s,\chi) = q^{s/2} \Gamma_{\R} (s+a) L(s,\chi) = \varepsilon \Lambda(1-s,\overline{\chi}), \] where $q$ is the conductor of $\chi$, $\varepsilon$ is the sign and $a$ is 1 (or 0) when $\chi$ is odd (or even). In particular, the only Dirichlet L-function with conductor 1 is the Riemann zeta function. Degree 1 L-functions can also be obtained from Artin representations of dimension 1.

The plot below shows the primitive characters arranged by the conductor and the order of the character, with color indicating the parity (blue is even) of the Dirichlet character. Clicking on an entry will take you to the associated Dirichlet L-function.

Conductor range: