Faraday conversion and rotation in uniformly magnetized relativistic plasmas

We provide precise fitting formulae for Faraday conversion and rotation coefficients in uniformly magnetized relativistic plasmas. The formulae are immediately applicable to rotation measure and circular polarization (CP) production in jets and hot accretion flows. We show the recipe and results for arbitrary isotropic particle distributions, in particular thermal and power law. The exact Faraday conversion coefficient is found to approach zero with the increasing particle energy. The non-linear corrections of Faraday conversion and rotation coefficients are found essential for reliable CP interpretation of Sagittarius A*.