What is the most exact translation of the Greek word δωρεάν?

Question

I came across this word most notably when reading the book of John where it says

But this is to fulfill what is written in their Law: ‘They hated Me without reason.’ John 15:25 BSB

The word δωρεάν here is translated to "without a cause" or "without cause". Yet in other passages, δωρεάν, is translated to "in vain" or, in another case, "freely". Εxamples among others are Galatians 2:21, Matthew 10:8, and Revelation 22:17. Are all these uses just a result of the context surrounding the word usage?

Answer 1

δωρεάν, like its Hebrew equivalent חִנָּם (chinnam), possesses positive and negative connotations; its meaning is dependent on the context.

It can mean “freely,” as in Numbers 11:5:

We remember the fish that we ate in Egypt freely...
...זָכַרְנוּ אֶת הַדָּגָה אֲשֶׁר נֹאכַל בְּמִצְרַיִם חִנָּם
ἐμνήσθημεν τοὺς ἰχθύας οὓς ἠσθίομεν ἐν Αἰγύπτῳ δωρεάν

It can also mean “without cause,” as in Job 1:9:

Then Satan answered Yahveh and said, “Does Job fear God for no reason?”
וַיַּעַן הַשָּׂטָן אֶת יָהְוֶה וַיֹּאמַר הַחִנָּם יָרֵא אִיּוֹב אֱלֹהִים
ἀπεκρίθη δὲ ὁ διάβολος καὶ εἶπεν ἐναντίον τοῦ κυρίου μὴ δωρεὰν σέβεται Ιωβ τὸν θεόν

If there were one English word that could possibly capture the entire range of meaning, it would be “gratuitously.”

According to the Oxford English Dictionary, gratuitously:

1. Without cost to the recipient; without any claim or merit on his part; free of charge.
   
2. Without sufficient cause, reason, or ground; unjustifiably, unwarrantably, unnecessarily.

Answer 2

According to BDAG, δωρεάν is the accusative of δωρεά.

δωρεάν is used as an adverb with the following meanings (according to BDAG):

1. "Pertaining to being freely given, as a gift, without payment, gratis", eg, Matt 10:8, Rev 21:6, 22:7, 2 Cor 11:7, Rom 3:24.
2. "Pertaining to being without contributory fault, undeservedly, without reason/cause", eg, John 15:15 (alluding to Ps 34:19, 68:5 LXX ref) See also, PsSol7:1, cp Ps 118:161, etc.
3. "Pertaining to being without purpose, in vain, to no purpose", eg, Gal 2:21, Job 1:9, Ps 34:7 (LXX ref).

My Analytical lexicon of the Greek New Testament by Friberg et al gives similar results.