Real (black solid line) and imaginary part (dashed lines) of the dispersion relation obtained by solving Equation (16), in the case where the background is pair plasma. The growth rates from the corresponding simulation are plotted using blue and red solid lines for right- and left-handed modes), respectively. The fit was not performed on kR_L,cr > 50 modes as being strongly affected by thermal noise. The black dot-dashed and dotted lines correspond to Doppler-shifted cyclotron resonance of background thermal plasma: ω = Ω_ce − kυ_th,e and ω = Ω_ce − 3kυ_th,e, respectively.