  The Tutte polynomial is originally a bivariate polynomial which enumerates
the colorings of a graph and of its dual graph. Ardila extended in 2007 the
definition of the Tutte polynomial on the real hyperplane arrangements. He
particularly computed the Tutte polynomials of the hyperplane arrangements
associated to the classical Weyl groups. Those associated to the exceptional
Weyl groups were computed by De Concini and Procesi one year later. This
article has two objectives: On one side, we extend the Tutte polynomial
computing to the complex hyperplane arrangements. On the other side, we
introduce a wider class of hyperplane arrangements which is that of the
symmetric hyperplane arrangements. Computing the Tutte polynomial of a
symmetric hyperplane arrangement permits us to deduce the Tutte polynomials of
some hyperplane arrangements, particularly of those associated to the
imprimitive reflection groups.
