The relativistically correct solution of the dispersion relation of linear plasma waves in an isotropic unmagnetized equilibrium electron plasma leads to two new effects unknown from the nonrelativistic dispersion theory. First, the number of damped subluminal modes is limited to a few (mode-limitation effect); secondly, for relativistic plasma temperatures the few individual modes complement each other in the sense that the dispersion relations ωR=ωR(k) continuously match each other (mode-completion effect). The second effect does not occur at nonrelativistic temperatures.