Perseus analysis of ὀμοῦμαι:

ὄμνυμι (swear): fut ind mid 1st sg (attic epic doric)

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ὄμνῡμι

ὄμνυμι, Pi. P. 4.166, etc. ; imper. ὄμνῠθι Il. 23.585, ὄμνῡ S. Tr. 1185, E. Med. 746, cf. Orac. ap. Hdt. 6.86.γʹ; 3sg. ὀμνύτω IG 12.134.5 ; 3pl. ὀμνύντων. Foed. ap. Th. 5.47, IG 12.87.24 : impf. ὤμνυν Ar. Av. 520, Ec. 823, D. 17.10, etc. : also (from pres. ὀμνύω) 3sg. imper. ὀμνῠέτω Il. 19.175 ; part. ὀμνύουσα Hyp. Ath. 2 : impf. ὤμνῠον Il. 14.278, Foed. ap.Th. 5.19,24, IG 22.236.14, etc. (for pres. ind. the Trag. and Ar. use only ὄμνυμι, Hdt. and Att. Prose writers also ὀμνύω, which also occurs in Com., Pherecr. 143.9, Amphis 42, Diph. 101, Antiph. 241.1, Alex. 160 ; in Hdt. 1.153 ὀμνύντες is restored for the dub. form ὀμοῦντες) : fut. ὀμοῦμαι, εῖ , εῖται , Il. 1.233,9.274, Hes. Op. 194, Ar. Nu. 246, Lys. 193, X. HG 1.3.11, etc. ; Dor. 1pl. ὀμιώμεθα Ar. Lys. 183 ; later fut. ὀμόσω AP 12.201 (Strat.), Plu. Cic. 23, etc. : aor. ὤμοσα Od. 4.253, etc. ; Ep. ὤμοσσα Il. 20.313 ; Ep. also without augm. ὄμοσα, -οσσα, 19.113,10.328 : pf. ὀμώμοκα E. Hipp. 612, Ar. Ra. 1471, etc. : plpf. ὠμωμόκειν X. HG 5.1.35, D. 9.16, 19.318 :—Med., Paus. 10.26.3, aor. part. ὀμοσάμενος SIG 531.28 (Dyme, iii B. C.), IG 5(2).357.11 (Stymphalus), also in compds. ἀντ-, ἀπ-, δι-, ὑπ- :—Pass., fut. ὀμοσθήσομαι And. 3.34 : aor. ὠμόσθην X. HG 7.4.10, (ὑπ-) Hyp. Fr. 202 ; but ὠμόθην Is. 2.40, (ὑπ-) D. 48.25 : pf. 3sg. ὀμώμοται A. Ag. 1284, ὀμώμοσται E. Rh. 816, Arist. Rh. 1377a11 ; 3pl. ὀμώμονται Lex ap.And. 1.98 ; part. ὀμωμοσμένος D. 7.10, 22.4, Arist. Rh. 1377b7 (ὠμοσμένος v. l. in App. Pun. 83, etc.) :—

II. swear to a thing, affirm or confirm by oath,

2. folld. by fut. inf., swear that one will . . , Il. 21.373, etc., cf. S. Ph. 623,941 (pres. inf., D. 21.188 codd.) : freq. with ἦ μέν, Att. ἦ μήν, preceding the inf., καί μοι ὄμοσσον ἦ μέν μοι . . ἀρήξειν Il. 1.76, cf. 10.321, Lys. 31.1, X. HG 5.3.26, etc. : also by aor. inf. and ἄν, Id. An. 7.7.40 : by pres. inf., swear that one does . . , S. Ph. 357 : by pf. inf., swear that one has . . , D. 21.119 ; ὤμνυς μὴ γεγονέναι Magn. 6 : by aor. inf., swear that one did . . , ὀμνύουσι μὴ ʼκπιεῖν ἀλλʼ ἢ μίαν Pherecr. 143.9, cf. Hdt. 2.179 (aor. inf. is perh. used, without ἄν, in fut. sense, D. 23.170 (s. v. l.)) : sts. a clause follows in the ind., ὀμνύω . . , ἦ μὴν ἐγὼ ἐθυόμην X. An. 6.1.31 ; ὄμνυμί σοι . . , οὐκ ἤθελον . . Theoc. Adon. 22.

3. abs., εἶπον ὀμόσας ἄν I would have given my word of honour, Pl. Smp. 215d.

III. with acc. of the person or thing sworn by, swear by, νῦν μοι ὄμοσσον ἀάατον Στυγὸς ὕδωρ Il. 14.271 ; γαιήοχον ἐννοσίγαιον ὄμνυθι 23.585, cf. 15.40, Hdt. 5.7, A. Th. 529, S. Tr. 1185, etc. ; ὀμωμοκὼς τοὺς θεούς D. 18.217 ; ὄμνυμι θεοὺς καὶ θεάς folld. by inf., X. An. 6.6.17, cf. 6.1.31 : rarely c. dat., τῷ γὰρ ὄμνυτʼ; ἢ σιδαρέοισι; Ar. Nu. 248 : in Prose also with Preps., ὀ. καθʼ ἱερῶν τελείων Lex ap.And. 1.97, Th. 5.47 ; κατʼ ἐξωλείας D. 21.119 ; κατὰ τῆς Πολιάδος Luc. Symp. 32 ; εἰς τὸν Οὐιτέλλιον Plu. Oth. 18 ; ἐπὶ τῶν ἱερῶν Plb. 38.20.5 ; ἐν Κυρίῳ LXXJd. 21.7 ; ἐν τῷ ναῷ Ev.Matt. 23.16 :—Pass., ὀμώμοσται Ζεύς Zeus has been sworn by, adjured, E. Rh. 816, cf. Ar. Nu. 1241.