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How do I "tidy up" error terms in a matrix?

Hi - I have some calculation results in the form of a complex Gram matrix which are all supposed to be integers (or "obvious" algebraic numbers which I know about). However inevitably in the course of creating them as inner products, some "error" terms arise which are of a size of the order of 10^-16 (real and/or complex). Is there an easy way to "clean up" my matrix with some sort of threshold, so that things which differ from a user-specified list of algebraic numbers by less than a tiny amount like 10^-15, are assumed to be the relevant algebraic number? At the moment I'm having to do it by a bunch of hideous if-statement contortions but I'm sure there's a better way! Many thanks in advance for any help.