  We describe a method of selective generation and study of polarization
moments of up to the highest rank $\kappa=2F$ possible for a quantum state with
total angular momentum $F$. The technique is based on nonlinear magneto-optical
rotation with frequency-modulated light. Various polarization moments are
distinguished by the periodicity of light-polarization rotation induced by the
atoms during Larmor precession and exhibit distinct light-intensity and
frequency dependences. We apply the method to study polarization moments of
$^{87}$Rb atoms contained in a vapor cell with antirelaxation coating. Distinct
ultra-narrow (1-Hz wide) resonances, corresponding to different multipoles,
appear in the magnetic-field dependence of the optical rotation. The use of the
highest-multipole resonances has important applications in quantum and
nonlinear optics and in magnetometry.
