On any well-organized website, you will get many 404 errors from poorly written scanners, poorly written anti-virus software cache servers and browser bar add-ons, as each of them tries to guess which URLs lead from the page. Often they misinterpret embedded Javascript, trying to figure out which pages it may link to.
BUT I have never seen a single character in it. This means that you have ~ on the page, which means that you have the literal ~ / Default.aspx found somewhere on the page. Can you find the page in question and look at the source on it to see if there is anywhere on it?
If you change the page content according to the user agent, can you reproduce the same request and look at the source?
Have you launched a link to your site?
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