  We study the sets of radial or nontangential limit points towards $i\infty$
of a Nevanlinna function q. Given a nonempty, closed, and connected subset L of
$C_+$ , we explicitly construct a Hamiltonian H such that the radial- and outer
angular cluster sets towards $i\infty$ of the Weyl coefficient q H are both
equal to L. Our method is based on a study of the continuous group action of
rescaling operators on the set of all Hamiltonians.
