We present the results of processing of magnetograms which were obtained with Solar
and Heliospheric Observatory (SOHO). The results confirm the basic properties of
long-period oscillations of sunspots established by authors earlier and reveal the new
ones. It is shown that a limiting (lowest) eigen mode of low-frequency oscillations of a
sunspot as a whole structure is the mode with the period of 10 to 22 hrs (depending on
sunspot's magnetic field strength). Lower mode with the period of about 1.5-2 days
normally observed in a power spectrum of sunspots, apparently, is not the eigen mode
of a sunspot because its period does not depend on the magnetic field of the sunspot.
Perhaps, it reflects the quasi-periodical perturbations of sunspot caused by the
supergranulation cells surrounding it. The artifacts of MDI (SOHO) device, which may
affect the low-frequency power spectra of sunspots, are analyzed.