Perseus analyses of θεσπεσίοιο:

θεσπέσιος (divinely sounding, divinely sweet): masc/neut gen sg (epic)
θεσπέσιος (divinely sounding, divinely sweet): masc/fem/neut gen sg (epic)

LSJ entry

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θεσπέσιος

θεσπέσιος, α, ον, also ος, ον E. Andr. 296 (lyr.), Luc. Sacr. 13: (perh. for θεσ-σπέσιος, cf. θεός, ἔσπον ):—prop. of the voice,

A. divinely sounding, divinely sweet, ἀοιδή Il. 2.600; Σειρῆνες Od. 12.158; ἔπεα Pi. I. 4(3).39; ἀχέτας Ar. Av. 1095 (lyr.).

2. divinely uttered or decreed, dat. sg. fem. θεσπεσίῃ as Adv., Il. 2.367.

b. oracular, γένος Pi. P. 12.13 (of the Graiae); δάφνα E. l.c.; θ. ὁδός the way of divination, of Cassandra, A. Ag. 1154 (lyr.); εὐχαῖς ὑπὸ θ. with prayers to the gods, Pi. I. 6(5).44.

c. = θεῖος, βηλός Il. 1.591; ἄντρον Od. 13.363.