  Let (X, \omega) be an affine symplectic variety. Assume that X has a
C^*-action with positive weights and \omega is homogeneous with respect to the
C^*-action. We prove that the algebraic fundamental group of the smooth locus
X_{reg} is finite. This is a collorary to a more general theorem:
  If an affine variety X has a C^*action with positive weights and the log pair
(X, 0) has klt singularities, then the algebraic fundamental group of X_{reg}
is finite.
