  We evaluate the number of monic polynomials (of arbitrary degree $N$) the
zeros of which equal their coefficients when these are allowed to take
arbitrary complex values. In the following, we call polynomials with this
property {\em peculiar\/} polynomials. We further show that the problem of
determining the peculiar polynomials of degree $N$ simplifies when any of the
coefficients is either 0 or 1. We proceed to estimate the numbers of peculiar
polynomials of degree $N$ having one coefficient zero, or one coefficient equal
to one, or neither.
