The eigenvalues and eigenfunctions of the finite Fourier transform corresponding to parameter c = 10 pi, 15 pi, 20 pi, and 25 pi are computed and tabulated. The computational details are given and discussed. An antenna pattern synthesis technique that makes use of these eigenelements is illustrated by examples. When the superdirective ratio is constrained to reasonable values, the number of eigenfunctions that contribute significantly to the pattern is found to be approximately equal to twice the number of wavelengths in the aperture. A pattern synthesized with the above eigenfunctions is compared with the pattern obtained by Woodward's method.