Perseus analyses of θεοῖο:

θεάομαι (gaze at, behold): pres opt mp 2nd sg (attic epic doric ionic)
θεάω (gaze at, behold): pres opt mp 2nd sg (attic epic doric ionic)
θεός (God, the Deity): masc gen sg (epic)

LSJ entries

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θεάομαι

θεάομαι, Ep. and Ion. θηέομαι (v. infr.), Dor. θᾱέομαι, *θάομαι (qq. v.), imper. θεῶ Ar. Ach. 262; opt. θηοῖο (for Att. θεῷο) Il. 24.418; part. θηεύμενος Hdt. 7.146: Ion. impf. ἐθηεῖτο, ἐθηεῦντο, Id. 1.10, 3.136; Ep. θηεῖτο Od. 5.75, etc., θηεῦντο Il. 7.444, al., ἐθηεύμεσθα Od. 9.218, ἐθεῆτο Hp. Nat.Puer. 13, θηέσκετο Poet. ap. Parth. 21.2: fut. θεάσομαι [ᾱ], Ion. -ήσομαι: aor. ἐθεᾱσάμην, Ep. opt. θηήσαιο, θηήσαιτο, Od. 17.315, 5.74; 3pl. ἐθηήσαντο Euph. 51.15; Ion. inf. θεήσασθαι (v.l. θεάσ-) Hdt. 1.8: Att. pf. τεθέαμαι X. Cyr. 7.5.7: codd. of Hdt. vary betw. θεη- and θηη-: a rare Ion. contr. of θηη- to θη- is found in θησαίατʼ Od. 18.191, θησάμενος IG 12.826:—

2. of the mind, contemplate, τὸ ἀληθές Pl. Phd. 84b, al.

3. view as spectators, esp. in the theatre, Isoc. 4.44; οἱ θεώμενοι the spectators, Ar. Ra. 2, cf.Nu. 518, al. (but also, onlookers, bystanders, Antipho 3.3.7): metaph., θ. τὸν πόλεμον to be spectators of the war, Hdt. 8.116.

4. θ. τὸ στράτευμα to review it, X. Cyr. 5.5.1.

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θεός

θεός, ὁ, Boeot. θιός, Lacon. σιός (v. infr.), Cypr., Cret. θιός Inscr.Cypr. 135.27 H., Leg.Gort. 1.1, Dor. also θεύς Call. Cer. 58; acc. θεῦν v.l. ib.130; voc. (only late) θεός, also θεέ LXXDe. 3.24, Ev.Matt. 27.46, PMag.Lond. 121.529, etc.; but classical in compd. names, Ἀμφίθεε, Τιμόθεε:—

A. God, the Deity, in general sense, both sg. and pl. (εἰ καὶ ἐπὶ θεοὺς καὶ ἔτι μᾶλλον ἐπὶ θεὸν ἁρμόζει μεταφέρειν Plot. 6.8.1), θ. δὲ τὸ μὲν δώσει τὸ δʼ ἐάσει God will grant . . , Od. 14.444; οὐδέ κεν ἄλλως οὐδὲ θ. τεύξειε 8.177, cf. 3.231, Il. 13.730 (also θεὸς Ζεύς Od. 4.236, 14.327); θ. καὶ ἀγαθὴ τύχη Pl. Lg. 757e, cf. Timocl. 3 D.; σὺν θεῷ Il. 9.49, S. Aj. 765, etc. (less freq. ξὺν τῷ θ. ib.383); σὺν θ. εἰρημένον Hdt. 1.86, cf. 3.153; σὺν θ. εἰπεῖν Pl. Prt. 317b: so in pl., σύν γε θεοῖσιν Il. 24.430; οὔ τοι ἄνευ θεοῦ Od. 2.372; οὐ θεῶν ἄτερ pi.P. 5.76; ἐκ θεόφι Il. 17.101; ὑπὲρ θεόν against his will, 17.327; ἂν θ. θέλῃ Alex. 231; θ. θέλοντος Men. Mon. 671: in pl., ἂν θεοὶ θέλωσιν Alex. 247; θεῶν συνεθελόντων, βουλομένων, X. Eq.Mag. 9.8, Luc. Macr. 29; εἰ ὀρθῶς ἢ μή, θ. οἶδε Pl. Phdr. 266b, cf.R. 517b, etc.; in oaths, θ. ἴστω S. OC 522 (lyr.), etc.; πρὸς θεῶν Hdt. 5.49, D. 1.15, etc.: τοὺς θεούς σοι bless you! good heavens! for heavenʼs sake! M.Ant. 7.17, Arr. Epict. 2.19.15, al.; τὸν θ. σοι ib.3.7.19, al.: qualified by τις, Od. 9.142, etc.; οὐκ ἄνευ θεῶν τινος A. Pers. 164 (troch.), E. Ba. 764; κατὰ θεόν τινα Id. IA 411, Pl. Euthd. 272e; κατὰ θεόν πως εἰρημένα Id. Lg. 682a: doubled in poets, θεὸν θεόν τις ἀγλαϊζέτω B. 3.21, cf. Diagor. 1; θεοὶ θεοὶ τῶν ἀδίκων μέλουσι E. HF 772, cf. Paus.Gr. Fr. 203; θεοί (Cret. θιοί) as an opening formula in Inscrr. (sc. τύχην ἀγαθὴν διδοῖεν), Leg.Gort. 1.1, IG 12.52, etc.: sg., θ. τύχη ib.5(2).1, etc.: in Prose also with the Art., ὁ θ. πάντων ἂν εἴη αἴτιος Pl. R. 379c, cf. Lg. 716c, etc.; τὰ πρὸς τοὺς θ., τὰ παρὰ τῶν θ., X. Mem. 1.3.1, 2.6.8.

e. Astrol., θεοί,= ἀστέρες, Jul. Laod. in Cat.Cod.Astr. 8(4).252.

f. θεός (sc. Ἥλιος), name of the 9th τόπος, Rhetor.ib.163, etc.

b. = Lat. Divus, Mon.Anc.Gr. 10.4, Str. 4.1.1, etc.; οἱ ἐν θεοῖς αὐτοκράτορες,= divi Imperatores, IG 12(1).786 (Rhodes).

c. generally of the dead, καὶ ζῶντός σου καὶ εἰς θεοὺς ἀπελθόντος PPetr. 2p.45 (iii B.C.); θεοῖς χθονίοις,= Lat. Dis Manibus, IG 14.30,al.

4. one set in authority, judge, τὸ κριτήριον τοῦ θ., ἐνώπιον τοῦ θ., LXXEx. 21.6, 22.8; θεοὺς οὐ κακολογήσεις ib.22.28(27).