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We examine the moments of the number of lattice points in a fixed ball of volume for lattices in Euclidean space which are modules over the ring of integers of a number field . In particular, denoting by the number of roots of unity in , we show that for lattices of large enough dimension the moments of the number of -tuples of lattice points converge to those of a Poisson distribution of mean . This extends work of Rogers for -lattices. What is more, we show that this convergence can also be achieved by increasing the degree of the number field as long as varies within a set of number fields with uniform lower bounds on the absolute Weil height of non-torsion elements.