eu)xo/menoj Danaoi=si qeopropi/aj a)nafai/neij,
I learned that the participle can be translated as temporal, using when/while or after, depending on the tense in relation to the main verb.
If I do that in Iliad 1:87 I get something like; ...while praying you reveal oracles to the Greeks.
Two translations that I checked have it like; ...you pray while you reveal the oracles to the Greeks.
In this last case I would have expected the first ...