  We investigate further the properties of axially symmetric
monopole-antimonopole pair in the standard Weinberg-Salam model. By using a
novel data sampling approach, we have obtained and analyzed 300 numerical
solutions corresponding to physical Higgs self-coupling $\beta=0.7782$ and the
Weinberg angle $\tan\theta_W=0.5358$. We calculate the energy of these
solutions and confirm that they reside in a range of 13.1690 - 21.0221 TeV. In
addition, a unique pattern is shown when the data are arranged according to an
algorithm based on the system's symmetry, which seems to indicate the system is
oscillating. We also calculate numerically the magnetic charge of the solutions
and confirm that their values are indeed $\pm\frac{4\pi}{e}\sin^2\theta_W$.
