Yes, says the OED: the adverb inadvertently does have an antonym, advertently, and it’s in current use.

So read on below to page 3, think about the difference between “listed inadvertently” and “inadvertently listed,” acknowledge that tone-deafness and inadvertency are inescapable, and then consider that that inescapability is one more of the murderous reasons why Zionism is necessary.