  We study the topological zeta function Z_{top,f}(s) associated to a
polynomial f with complex coefficients. This is a rational function in one
variable and we want to determine the numbers that can occur as a pole of some
topological zeta function; by definition these poles are negative rational
numbers. We deal with this question in any dimension. Denote P_n := {s_0 |
\exists f in C[x_1,..., x_n] : Z_{top,f}(s) has a pole in s_0}. We show that
{-(n-1)/2-1/i | i in Z_{>1}} is a subset of P_n; for n=2 and n=3, the last two
authors proved before that these are exactly the poles less then -(n-1)/2. As
main result we prove that each rational number in the interval [-(n-1)/2,0) is
contained in P_n.
