Root systems in number fields

We classify the types of root systems R in the rings of integers of number fields K such that the Weyl group W(R) lies in the group L(K) generated by Aut(K) and multiplications by the elements of K^*. We also classify the Weyl groups of root systems of rank n which are isomorphic to a subgroup of L(K) for a number field K of degree n over Q.