Analysis of the well-known dispersion relation for electromagnetic waves propagating in an uniform electron plasma with a magnetic field shows unexpected results near the cyclotron harmonics nΩ when the electron energies are relativistic. In particular, it can be shown that gain for waves propagating across the magnetic field will exist up to the harmonic number nmax = 0.1 A3γ6 , where A is the normalized transit-time 2ΩT for the interacting electrons and γ is the relativistic energy factor. For n < nmax , gain falls slowly with harmonic number, i.e. as n-1/3. Similar results can be inferred from relativistic quantum theory. Numerical solutions of the reduced dispersion relation substantiate the analytical approximations. The starting current for a quasi-optical synchrotron resonance maser oscillator is derived, and examples using a 2 megavolt electron beam are discussed.