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Within the framework of a method-of-moments algorithm, the natural frequencies and natural modes of a scatterer/antenna can be found by looking for the complex frequencies where the determinant of the impedance matrix becomes zero. However, for nanotopologies, the value of this determinant can easily go beyond the resolution or representation limits available on present-day computers. In this work, we propose a substitute for the matrix determinant that avoids this problem altogether: the characteristic term. A robust numerical procedure for locating natural frequencies using this new target function is outlined. Then, the natural frequencies of three different nanostructures, namely, a gold and nickel nanopatch and a gold nanodimer, are calculated and validated by numerically and experimentally obtained scattering/extinction spectra.