On numbers of the form n=x2+Ny2 and the Hecke groups

We consider the Hecke groups , N⩾2 integer, to get some results about the problem when a natural number n can be represented in the form n=x2+Ny2. Given a natural number n, we give an algorithm that computes the integers x and y satisfying the equation n=x2+Ny2 for all N⩾2.