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In particle accelerators, pumping holes in a vacuum chamber can be a source of unwanted broadband coupling impedance, leading to beam instabilities. Analytical methods have been previously developed to estimate the impedance of holes in circularlike chambers, e.g., the beam screen of the Large Hadron Collider (LHC). More sophisticated chamber designs like that of the High Energy LHC and the Future Circular Collider (the hadron-hadron option) call for a different way to calculate the impedance. We propose using the decomposition of the wakefield into synchronous traveling waves and employing a numerical solver to find the impedance of each wave. This method is compared to the direct time domain wakefield calculation method, and its greater sensitivity to small impedances is shown.