  We consider polynomials orthogonal on the unit circle with respect to the
complex-valued measure $z^{\omega-1}\mathrm{d} z$, where
$\omega\in\mathbb{R}\setminus\{0\}$. We derive their explicit form, a
generating function and several recurrence relations. These polynomials possess
an intriguing pattern of zeros which, as $\omega$ varies, are reminiscent of a
firework explosion. We prove this pattern in a rigorous manner.
