  Many combinatorial and topological invariants of a hyperplane arrangement can
be computed in terms of its Tutte polynomial. Similarly, many invariants of a
hypertoric arrangement can be computed in terms of its arithmetic Tutte
polynomial. We compute the arithmetic Tutte polynomials of the classical root
systems of types A,B,C, and D, with respect to their integer, root, and weight
lattices. We do it in two ways: by introducing a finite field method for
arithmetic Tutte polynomials, and by enumerating signed graphs with respect to
six parameters.
