Perseus analyses of πέμψω:

πέμπω (send): aor subj act 1st sg
πέμπω (send): aor ind mid 2nd sg (epic ionic)
πέμπω (send): fut ind act 1st sg

LSJ entry

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πέμπω

πέμπω, Ep. inf. -έμεναι, -έμεν, Od. 13.48, 10.18 : Ion. impf. πέμπεσκε Hdt. 7.106 : fut. πέμψω Od. 5.167, etc.; Dor. πεμψῶ Theoc. 5.141; Ep.inf. πεμψέμεναι Od. 10.484: aor. ἔπεμψα, Ep. πέμψα Il. 1.442, 21.43, etc.: pf. πέπομφα Th. 7.12, X. Cyr. 6.2.10, D. 4.48 : plpf. ἐπεμπόμφει, Ion. -εε, X. Cyr. 6.2.9, Hdt. 1.85 :—Med. (not in early Prose, exc. in compds. ἀπο-, μετα-, προ-πέμπομαι), fut. πέμψομαι only f.l. in E. Or. 111 : aor. ἐπεμψάμην Id. Hec. 977 :—Pass., fut. πεμφθήσομαι Str. 1.1.4, Plu. Demetr. 27 : aor. ἐπέμφθην Pi. N. 3.59, S. El. 1163, etc.: 3sg. pf. πέπεμπται A. Th. 473, (προ-) Th. 7.77; part. πεπεμμένος D. 23.159, Luc. Alex. 32, D.C. 50.13: plpf. ἐπέπεμπτο Id. 36.18, (προὐπ-) Th. 8.79 (cj.) :—

A. send, freq. of persons, as messengers, spies, etc., Il. 3.116, A. Th. 37, Hdt. 7.15, etc.; of troops, A. Pers. 34 (anap.), Th. 470 : c. dupl. acc., ὁδὸν π. τινά send one on a journey, S. Aj. 739, cf.El. 1163 (Pass.); also of things, πέμψω δέ τοι οὖρον ὄπισθεν Od. 5.167, etc.; π. γράμματα, ἐπιστολήν, Pl. Ep. 310d, 323b; in letters, in the epistolary aorist, Th. 1.129, X. An. 1.9.25, LXX2 Es. 4.14; π. κακόν τινι send one evil, Il. 15.109; π. παραβᾶσιν Ἐρινύν A. Ag. 59 (anap.); ποινάς, ζημίαν, Id. Eu. 203 (dub.), E. Fr. 506; ψόφον π. ἔσω Id. IT 1308; ὕπνον, ὀνείρατα, S. Ph. 19, El. 460; freq. of omens, π. οἰωνόν, τέρατα, Il. 24.310, X. Mem. 1.4.15, cf. Smp. 4.48; μαντείας S. OT 149; also ἱκεσίους π. λιτάς Id. Ph. 495 ; π. ἀρωγάς, ἀλκάν, A. Eu. 598, S. OT 189 (lyr.) :—Constr.:

1. c. acc. of place to which, π. τινὰ Θήβας, ἀγρούς, Id. OC 1770 (anap.), OT 761 : also c. dat., Ἀΐδᾳ E. IT 159 (anap.): but usu. with Preps., ἐς Τροίην, φίλην ἐς πατρίδα γαῖαν, etc., Il. 6.207, Od. 5.37, etc.; π. εἰς Ἀΐδαο Il. 21.48 ; δόμον Ἄϊδος εἴσω Od. 9.524; π. εἰς διδασκάλων send to school, Pl. Prt. 325d (so πέμπειν alone, Ar. Fr. 216); π. ἐπʼ εὐρέα νῶτα θαλάσσης over. . , Od. 4.560, etc. ; π.ἐπὶ Θρῃκῶν ἵππους to them, Il. 10.464; but πέμπειν ἐπί τι send for a purpose, ἐπʼ ὕδωρ Hdt. 5.12 ; ἐπὶ κατασκοπήν X. Cyr. 6.2.9 (π. εἰς κ. S. Ph. 45); π. ἀρωγὴν ἐπὶ νίκην A. Ch. 477 codd. (anap.); π. ἐπί τινι send to him, Il. 2.6; against. . , A. Ag. 61 (anap.), etc.; for a purpose, ἐπὶ πολέμῳ X. HG 4.8.17; περί τινος about something, Th. 1.91, X. Cyr. 6.2.10; ὑπέρ τινος Epist. Philipp. ap.D. 12.12; παρά or πρός τινα to some one, Th. 2.81, X. An. 5.2.6; ὥς τινα Th. 8.50.

5. send forward, nominate a person for a post, ὀνόματα Wilcken Chr. 28.20 (ii A.D.) :—Pass., ib.392.7 (ii A.D.).

II. send forth or away, dismiss, send home, τὸν ξεῖνον Od. 7.227, al.: less freq. in Il., as 24.780; χρὴ ξεῖνον παρεόντα φιλεῖν, ἐθέλοντα δὲ πέμπειν ‘welcome the coming, speed the parting guest’, Od. 15.74 ; ὑπέδεκτο καὶ πέμπε 23.315 ; of the father who sends off his daughter to go to her husband, c. dat., 4.5 ; π. τινὰ ἄποικον S. OT 1518, etc.

3. of words, send forth, utter, A. Th. 443, S. Ph. 846 (lyr.), 1445 (anap.).

2. πομπὴν π. conduct, or take part in, a procession, Hdt. 5.56, Ar. Ec. 757, Th. 6.56, Lys. 13.80, D. 4.26, etc.; π. χορούς move in dancing procession, E. El. 434 (lyr.); Παναθήναια π. Men. 494, Philostr. VA 4.22 :—Pass., φαλλὸς Διονύσῳ πεμπόμενος carried in procession in his honour, Hdt. 2.49, cf. Plu. Aem. 32, Demetr. 12; τῆς πομπῆς ὅπως ἂν ὡς κάλλισταπεμφθῇ IG 12.84.27; χορὸς ὁ εἰς Δῆλον πεμπόμενος X. Mem. 3.3.12.

IV. send as a present, εἵματα, σῖτον, Od. 16.83,4.623; π. δῶρα, σκῦλα, ξένια, Hdt. 7.106 (Act. and Pass.), S. Ph. 1429, X. Cyr. 3.1.42.

V. send up, produce, ὅσα πέμπει βιόδωρος αἶα S. Ph. 1162 (lyr.).

B. Med., πέμπεσθαί τινα send for one, S. OC 602, ubiv. Sch.; τί χρῆμʼ ἐπέμψω τὸν ἐμὸν ἐκ δόμων πόδα; E. Hec. 977.

II. send in oneʼs own service or cause to be sent, S. OT 556, Luc. Tox. 14.