Hamiltonian character of the motion of the zeros of a polynomial whose coefficients oscillate over time

A Hamiltonian is explicitly exhibited, whose equations of motion yield the time evolution of the n zeros, z(j)(t), of a polynomial of degree n in z, P-n(z, t) = z(n) + Sigma(m=1)(n) c(m)(t)z(n-m), when its coefficients c(m)(t) oscillate, c(m)(t) = c(m)(+)exp(i omega(m)t) + c(m)((-))exp(-i omega(m)t), or evolve in some other Hamiltonian manner.