Liddel and Scott
Greek Lexicon

ἀ-, as insep. Prefix in compos.:

I α στερητικόν (Sch. Od. 3.279, etc., cf. Eust. 985.16), expressing want or absence (cf. Arist. Metaph. 1022b32), as σοφός wise, ἄσοφος unwise: for n^, the weak form of the negative ne, commonly used in the formation of adjs. and advbs., very rarely in that of vbs. and substs., cf. ἀδώτης, ἀτιμάω, ἀτίω. Before a vowel it usu. appears as ἀν- (exc. where f or spiritus asper has been lost, as ἄ-οινος, ἄ-υπνος, when it sts. coalesces with the following vowel, as ἀργός = ἀ-fεργός): the forms ἀνάεδνος, ἀνάελπτος are probably misspelt for ἀν-έfεδνος, -έfελπτος. Adjs. formed with it freq. take gen., esp. in Trag., cf. ἀλαμπὲς ἡλίου, = ἄνευ λάμψεως ἡλίου, S. Tr. 691. [ᾰ, exc. in adjs. which begin with three short syllables, which have a_ in Ep., and freq. also in Lyr., Trag., and Com.; ἀθάνατος invariably has ᾱθ.]

II α ἀθροιστικόν ( Eust. 641.61; τὸ ἄλφα σημαίνει πολλαχοῦ τὸ ὁμοῦ Pl. Cra. 405c), properly ἁ-since it represents sm- (cf. ἅμα, εἷς = sems), and so in ἁπλόος, ἁθρόος: but freq. ἀ- by dissimilation from following aspirate, as ἄ-λοχος, and hence by analogy in ἄ-κοιτις, etc., q.v.: sts. in the form ὀ-, as in ὄπατρος, ὀγάστριος, ὄζυξ. [ᾰ.]

III α ἐπιτατικόν ( Eust. 641.61), strengthening the force of compds., as ἀ-τενής; prob. identical in etymology with 11, from which it is distinguished by Gramm., who sts. confuse it with 1; v. ἀδάκρυτος. [ᾰ.]