Luke 7:3

3. The elders of the Jews Presbyters. The word literally signifies the older men. But as it became an official epithet, it acquired the official sense. The elders of Israel were anciently the heads of the tribes, chosen for their age and wisdom. In latter times, subsequent to the restoration from the captivity, a part of the Sanhedrim consisted, with the chief priests and the scribes, also of the elders. Similarly the courts of the individual towns, consisting of seven judges, were composed of the elders of Israel. In the present case the elders were of this last class. The centurion, feeling that as a Gentile and a sinner he might have little hope of a favourable reception from the holy and divine prophet of the Jews, the wonderful Jesus, sends the most weighty men and magistrates of Jewish Capernaum.

Beseeching The Greek word for beseeching, here, is a participle, agreeing with the centurion. So that even according to Luke’s language, the words were those of the centurion.