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We present a computationally efficient way to compute the modal Green's function arising in the electric-field integral equation for a body of revolution. The computation of this function is time consuming due to its singular and oscillating nature, especially for high Fourier-mode indices. Efficient and accurate computation of this function is important to arrive at a fast numerical method for analyzing the scattering problem of a body of revolution. We compute the modal Green's function up to machine precision in a well-controlled way with limited effort, even for large bodies.