In a manner that shows connivance; with secret cooperation or tacit approval of something improper.
From 'connivant' plus the adverbial suffix '-ly.' This creates an adverb from the rare adjective, making it a doubly rare word in modern English.
This might be the rarest word on this list—it's technically grammatically correct but so obscure that even searching major corpora gives almost no results. It's a word that probably exists in principle but is rarely said aloud!
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