Perseus analyses of ἧκε:

ἥκω (to have come, be present): imperf ind act 3rd sg
ἥκω (to have come, be present): pres imperat act 2nd sg
ἥκω (to have come, be present): imperf ind act 3rd sg (homeric ionic)
ἵημι (release, let go): aor ind act 3rd sg
ἵημι (release, let go): aor ind act 3rd sg (homeric ionic)

LSJ entries

ἥκω

ἥκω, Il. 5.478: impf. ἧκον (v. infr.): fut. ἥξω (v. infr.); Dor. ἡξῶ Theoc. 4.47, Call. Fr. 1.65 P. (in Dor. and Hom. more commonly ἵκω): all other tenses late; aor. 1 part. ἥξας Paus. 2.11.5, Gal. 6.56, 10.609: pf. ἧκα Philostr. VA 3.24, Scymn. 62, 1pl. ἥκαμεν UPZ 72.9 (ii B.C.), CIG 4762 (Egypt, i A.D.), Dor. ἥκαμες f.l. in Plu. 2.225b, 2pl. ἥκατε PGrenf. 2.36.18 (i B.C.), 3pl. ἥκασι LXX4 Ki. 20.14, Ev.Marc. 8.3; inf. ἡκέναι UPZ 6.30 (ii B.C.): plpf. ἥκεσαν J. AJ 19.1.14: —Med., pres. subj. ἥκηται Aret. SD 2.1: fut. ἥξομαι v.l. in M.Ant. 2.4:—

A. to have come, be present, prop. in a pf. sense, with impf. ἧκον as plpf., I had come, and fut. ἥξω as fut. pf., I shall have come, μάλα τηλόθεν ἥκω Il. 5.478, cf. Od. 13.325, Pi. O. 4.12 (ἵκω codd. vett.): impf. ἧκον A. Pr. 661, Th. 1.91, al., Pl. R. 327c, Hdt. 8.50, etc.: fut. ἥξω A. Pr. 103, al., E. Andr. 738, Ar. Pax 265, Orac. ap. Th. 2.54, etc.; ἧκε imper., S. Aj. 1116, Ar. Pax 275, X. Cyr. 4.5.25; ἡκέτω E. Rh. 337 :—Constr. mostly with εἰς, Hdt. 8.50, A. Ch. 3, etc.; παρά τινα Hdt. 7.157, Th. 1.137; πρός τινα A. Ch. 659; πρὸς δαίμονα S. Fr. 770; esp. in worship, ἥκω πρὸς τὴν κυρίαν Ἶσιν OGI 186.6 (Egypt, i B.C.), cf. Ev.Jo. 6.37; πρὸς πόλιν S. OC 734; ἐπί τινα to set upon, attack, Pl. R. 336b, Aeschin. 2.178; but ἥ. ἐπὶ τὸ στράτευμα to have come to fetch the army, X. An. 7.6.2; οἱ ἐπὶ ταῦθʼ ἥκοντες D. 18.28; ἐπʼ ὀλέθρῳ E. IA 886 (troch.); περὶ σπονδῶν X. An. 2.3.4: c. acc., ἥξεις ποταμόν A. Pr. 717, cf. 724, 730; ἥ. δῆμον τὸν Λυρκείου S. Fr. 271.6, cf. E. Ba. 1; ἥκουσιν αὐτῷ ἄγγελοι X. Cyr. 5.3.26; ἐς ταὐτὸν ἥ. to have come to the same point, to agree, E. Hec. 748, Hipp. 273: with Adv. of motion, ἥ. ἐνθάδε, δεῦρο, S. Ph. 377, D. 19.58; βῆναι κεῖθεν ὅθενπερ ἥκει S. OC 1227: c. neut. Pron., αὐτὰ ταῦτα ἥκω παρά σε Pl. Prt. 310e; ἐρωτώμενοι ὅ τι ἥκοιεν for what they had come, X. HG 4.5.9: c. acc. cogn., ὁδὸν μακρὰν ἥκειν Id. Cyr. 5.5.42: c.inf., μανθάνειν γὰρ ἥκομεν we are here to learn, S. OC 12.

b. διὰ μάχης, διʼ ὀργῆς ἥκειν, A. Supp. 475, S. OC 905 ; cf. διά A. IV.

c. with an Adv. folld. by gen., οὕτω πόρρω σοφίας ἥκεις Pl. Euthd. 294e; εὖ ἥκειν τινός to be well off for a thing, have plenty of it, τοῦ βίου, χρημάτων, Hdt. 1.30, 5.62; ἑωυτῶν Id. 1.102; θεῶν χρηστῶν Id. 8.111; πιθανότητος Demetr.Magn. ap.D.H. Din. 1; οὐκ ὁμοίως ἥ. τινός not to be equally well off in respect of . . , Hdt. 1.149; πῶς ἀγῶνος ἥκομεν; how have we sped in the contest? E. El. 751; ὧδε γένους ἥ. τινί to be this degree of kin to him, Id. Heracl. 213; ὡς δυνάμεως ἥκεις Paus. 4.21.10; ἐς μῆκος εὖ ἥκων Ael. NA 4.34: abs., εὖ ἥκειν to be flourishing, Hdt. 1.30: rarely c. gen. only, σὺ δὲ δυνάμιος ἥκεις μεγάλης thou art in great power, Id. 7.157 (nisi leg. μεγάλως).

3. to have come back, returned, D. 20.73; from exile, And. 2.13; αὐτίκα ἥξω I shall be back in a moment, X. An. 2.1.9; ἧκέ νυν ταχύ come back soon, Ar. Pax 275; ἄψορρον ἥξεις A. Pr. 1021; ἄψορρον ἥξομεν πάλιν S. El. 53.

4. c. part., ἥκω φέρων I have come bringing (i.e. with), Id. OC 579, cf. 357, Ar. Pax 265, Eup. 22 D., Pl. Grg. 518d; ἧκεν ἄγων Id. Phd. 117a; ἕτερόν τι ἥκεις ἕχων Id. Grg. 491c, etc.: c. fut. part., like ἔρχομαι, ἥκω φράσων, ἀγγελῶν, etc., I am going, I intend to say, E. Ph. 706, 1075, etc.

4. c. inf., ἧκέ μοι γένει . . πενθεῖν it has come to me by birth . . , my birth lays it on me . . , S. OC 738, cf. Ichn. 356; καλῶς αὐτοῖς κατθανεῖν ἧκον βίου it being well for them at their age to die, E. Alc. 291.

5. c. part., ὃ καὶ νῦν ἥκει γινόμενον which commonly happens even now, Plb. 24.9.11 codd. (v.l. γενόμενον). (Prob. from same root as ἵκω.)

ἵημι

ἵημι, ἵης (v.l. ἵεις S. El. 596, Castorio 2), ἵησι, 3pl. ἱᾶσι, Ion. and Ep. ἱεῖσι; imper. ἵει Il. 21.338, E. El. 593 (lyr.); subj. ἱῶ; opt. ἱείην (also ἀφ-ίοιμι, X. HG 6.4.3); inf. ἱέναι; part. ἱείς :—thematic forms of the pres. (as if from ἱέω) are also found, esp. in compds., cf. μεθίημι, σύνιημι: also, as if from ἵω, 3sg. pres. ἵει A.R. 4.634, imper. ξύν-ιε Thgn. 1240b codd.: impf. 3sg. ἵει Il. 1.479, Dor. ἀν-ίη SIG 1 (Abu Simbel, vi B.C.); 3pl. ἵεσαν E. Ba. 1099, ἵεν Il. 12.33, ξύν-ιεν (v.l. -ιον) 1.273; also 2sg. ἵεις Ar. V. 355; Ion. impf. ἵεσκε (ἀν-) Hes. Th. 157: fut. ἥσω Il. 17.515, etc.: aor. 1 ind. ἧκα Il. 5.125, etc., Ep. ἕηκα 1.48 (mostly in compds.); 3sg. subj. ᾗσι 15.359; 3sg. opt. εἵη 3.221; inf. εἷναι Ar. Ra. 133, Ep. ἐξ-έμεναι Od. 11.531: pf. εἷκα, only in compds. (ἀφ-, καθ-, παρ-, συν-), also ἕωκα (ἀφ-) PCair.Zen. 502.4 (iii B.C.), Hdn.Gr.2.236:—Med., pres. ἵεμαι Od. 2.327, etc.; also 3pl. προ-ίονται PCair.Zen. 151.4 (iii B.C.): impf. ἱέμην Ar. Eq. 625, etc.: fut. ἥσομαι (μετ-) Hdt. 5.35, (προ-) D. 1.12, (ἐξαν-) E. Andr. 718: aor. 1 ἡκάμην (only in compds. προσ-, προ-): aor. 2 εἵμην, Ep. and Ion. ἕμην, of which we find εἷτο (ἐφ-) S. Ph. 619, (ἀφ-) X. Hier. 7.11, ἕτο (συν-) Od. 4.76, ἕντο (ἐξ-) Il. 9.92, etc.; imper. ἕο (ἐξ-) Hdt. 5.39, οὗ (ἀφ-) S. OT 1521; subj. ὧμαι (συν-) Il. 13.381; opt. εἵμην (ἀφ-) Ar. Av. 628, or οἵμην (προ-) Pl. Grg. 520c; inf. ἕσθαι (προσ-) Ar. V. 742; part. ἕμενος (προ-) Th. 6.78, Isoc. 4.164, etc.:— Pass., fut. ἑθήσομαι (ἀν-) Th. 8.63: aor. εἵθην (only in compds. ἀφ-, καθ-, παρ-): pf. εἷμαι (only in compds.); also ἕωμαι in compds. ἀν-, ἀφ-, ἐφ- (q.v.): plpf. εἵμην (only in compds.).—Of the Pass. and Med. Hom. has only pres., impf., and 3pl. aor. 2 Med. ἕντο .—For varieties peculiar to special compds., v. ἀν-, ἀφ-, ὑφ-ίημι. (Perh. cogn. with Lat. Ja-c-io or with Lat. sēmen:—Med. ἵεμαι prob. from ϝῑ-, cf. εἴσομαι II, Skt. véti (pl. vyánti) ‘press forward, desire’, Lat. vīs (2sg.), invitus.) [ῐ generally in Hom. and Ep., ῑ in Att.; sts. ῑ in Hom., ἵει Il. 16.152, etc.; ἱεῖσαι Od. 12.192; also in inf. ἱέμεν, ἱέμεναι, part. ἱέμενος, etc., ξυν-ῑετε Archil. 50: ῐ sts. in Trag., ῐησι A. Th. 309 (lyr.), ῐέντα ib.493, ῐείς, ῐεῖσα, E. IT 298, IA 1101, Hec. 338; ῐεῖσαν Id. Supp. 281; in Com., συνῐημι Ar. Av. 946 (s. v.l.), Strato Com. 1.3: with variation of quantity, πλεῖστον οὖλον ἵει [ῐ], ἴουλον ἵει [ῑ] Carm.Pop. 1.]:—

2. of sounds, utter, ὄπα Il. 3.152, Od. 12.192; ἔπεα Il. 3.221; γλῶσσαν Hdt. 1.57; Ἑλλάδα γλῶσσαν ἱ. to speak Greek, Id. 9.16; Δωρίδα, Ἀττικὴν γλῶσσαν, Th. 3.112, Sol. 36.10; φωνὴν Παρνησίδα A. Ch. 563; δύσθροα βάγματα Id. Pers. 636 (lyr.); ἐκ στηθέων ἄλγος Id. Th. 865 (lyr.); μέγαν κωκυτόν S. Aj. 851, etc.; but πᾶσαν γλῶσσαν ἱ. to let loose every kind of speech, Id. El. 596; πᾶσαν (τὸ λεγόμενον) φωνὴν ἱέντα Pl. Lg. 890d; τὸ τᾶς εὐφάμου στόμα φροντίδος ἱέντες, i.e. speaking not in words, but in silent thought, S. OC 133 (lyr.); ἧκε abs. (sc. φωνήν), Plu. 2.973e; of instruments, ἄλλα μέλη τῶν χορδῶν ἱεισῶν Pl. Lg. 812d.

2. metaph., to be eager, desire to do a thing, c. inf., ἵετο γὰρ βαλέειν Il. 16.383; βαλέειν δέ ἑ ἵετο θυμός 8.301; ἵετο θυμῷ τείσασθαι . . 2.589: c. gen., to be set upon, long for a thing, in part., ἱέμενοι πόλιος, νίκης, 11.168, 23.371; νόστοιο Od. 15.69; λεχέων S. Tr. 514 (lyr.); ἱέμενος ποταμοῖο ῥοάων setting thyself toward, Od. 10.529: abs. in part., ἱέμενός περ eager though he was, 1.6, etc.