αἰσχυνομένως
From LSJ
Ἀμήχανον δὲ παντὸς ἀνδρὸς ἐκμαθεῖν ψυχήν τε καὶ φρόνημα καὶ γνώμην πρὶν ἂν ἀρχαῖς τε καὶ νόμοισιν ἐντριβὴς φανῇ → It is impossible to know the spirit, thought, and mind of any man before he be versed in sovereignty and the laws
English (LSJ)
Adv.
A modestly, shamefacedly, D.H. 7.50.