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[en] The full energy shift of a massive Dirac neutrino in magnetized electron-positron plasma was investigated using the Matsubara imaginary time and real time formalisms. The neutrino dispersion in the magnetized medium was analyzed as a function of the neutrino spin and mass. It was shown that in a superstrong magnetic field the CP-symmetric plasma contribution to the neutrino energy greatly exceeds the analogous correction in the field-free case. The contribution of plasma to the anomalous magnetic moment of a neutrino was obtained.