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This paper of dispersion relations in relativistic plasma with Maxwell distribution is based on the kinetic (Vlasov Maxwell equations) and linear dispersion relations of plasma theory.the dispersion equations are numerically evaluated.The Electromagnetic instabilities ( Weibel instability) in ultraintense laser-plasma interactions is a transverse electromagnetic instability driven by temperature or electrons moment anisotropy ( Weibel) or two counter streams ( Fried).Apart from its basic theoretical interest,the electromagnetic instability has attracted much attention in the recent years in the plasma community.This paper research by using electromagnetic relativistic pacticle-in cell simulation ultraintense laser-plasma interactions is produced in electromagnetic instability of the occurrence and linear saturated process.Discusses the linear and nonlinear saturation of electromagnetic instability.There results may be important for understanding the spontaneous magnetic field generation and fast electron propagation in fast iginition phisics.