Examples of zero modes of the Faddeev–Popov operator for the $SU(2)$ gauge field

We construct zeros of the Faddeev–Popov operator for the $SU(2)$ gauge field in the Coulomb gauge parametrized by expressions with a simple interaction of components of spacial and internal symmetries. The radial component of the gauge field is taken in the form of rational expression with negative poles of the first and the second order.