Relating to omens, auspices, or bird divination; favorable or propitious.
From 'auspice' + '-ial' (adjective-forming suffix), ultimately from Latin 'auspicium.' A rare, archaic adjective.
This adjective is so uncommon that spell-checkers probably flag it—it's what you'd use if you wanted to sound like someone writing in the style of a 19th-century novel about ancient Rome.
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