  An new method of calculating the energy spectrum of neutrinos and
antineutrinos produced in the electron-positron annihilation processes in hot
stellar plasma is presented. Detection of these neutrinos, produced copiously
in the presupernova which is evolutionary advanced neutrino-cooled star, may
serve in future as a trigger of pre-collapse early warning system. Also,
observation of neutrinos will probe final stages of thermonuclear burning in
the presupernova.
  The spectra obtained with the new method are compared to Monte Carlo
simulations. To achieve high accuracy in the energy range of interest,
determined by neutrino detector thresholds, differential cross-section for
production of the antineutrino, previously unknown in an explicit form, is
calculated as a function of energy in the plasma rest frame. Neutrino spectrum
is obtained as a 3-dimensional integral, computed with the use of the Cuhre
algorithm of at least 5% accuracy. Formulae for the mean neutrino energy and
its dispersion are given as a combination of Fermi-Dirac integrals. Also,
useful analytical approximations of the whole spectrum are shown.
