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    $\begingroup$ Mathematica doesn't like Mathieu functions $\endgroup$ Commented Aug 27, 2014 at 18:30
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    $\begingroup$ Definitely trust the one done with WorkingPrecision other than the default, which is MachinePrecision. In other words, precision tracking is off by default for Plot. This is a very bad thing for numerically sensitive functions such as the Mathieu functions. $\endgroup$ Commented May 16, 2015 at 17:20