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An algorithm is described that approximates complex numbers by elements of the algebraic integers of with integer coordinates of at most a prescribed size. The motivating application is to reduce the dynamic range requirements of residue number system implementations of the discrete Fourier transform. The closest points to zero of gor any integer are determined. A particular sequence of such points forms the basis of the algorithm. An example of -bit - approximations of the 128th roots of unity is considered. The algorithm yields with scaling is reduced to .