  We study the evolution of hypermagnetic fields (HMFs) in random plasma in the
symmetric phase of the early universe. The system of kinetic equations for the
spectra of the energy density and the helicity, as well as the particles
asymmetries is derived. We also formulate the initial condition which involve
the Kazantsev and Kolmogorov spectra of the seed HMFs. This system is solved
numerically. We predict the energy spectrum of primeval gravitational waves
which are produced by these HMFs. Additionally, the baryon asymmetry of the
universe, generated by the lepton asymmetries, is obtained. These results allow
us to constrain the strength of seed HMFs.
