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SHA-3 hash
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For the like-named file downloaded from sqlite.org, I get a 256 bit SHA3 hash of d669a92271ad31bbefe4ba827c3d6621179b1964b5dd1f27c6fbaa9c4cf6a082 and a 512 bit SHA3 hash of 429f5cb2eb6eddaac55599b755bf50513ab1b83a065d83ff24b3873a745e0e138443012d7ee401802f80300ce946e4c2e492dfc9a64181d2133383d7ebbae622 .  The former matches what you claim the website says and the latter is the same length as the "quickhash" result you report but with a different value.  Based on this, I think you have a genuine, uncorrupted .zip file and a strange SHA3 hash calculator.

What happens if you ask Quickhash for the SHA-3 (256 bit) hash? (And what is a "sha-e hash"?)