In a manner suggesting an omen or serving as a sign; ominously or portentously.
From 'boding' (noun/adjective) plus the adverb suffix '-ly'. This formation creates an adverb describing how something happens in the manner of a boding or omen.
The adverb 'bodingly' is almost never used in modern English, but it represents a linguistic lost art—when writers could take any noun and turn it into an adverb to describe how something was done, like describing a sky that darkened 'bodingly' before a storm.
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