Verb hēgemoneuō (to govern) in the Gospels-Acts

(Translation from NRSV with a few modifications for a more literal meaning)

Luke

2: 2This was the first registration and was taken while Quirinius was governing (hēgemoneuō) of Syria.
3: 1In the fifteenth year of the reign of Emperor Tiberius, when Pontius Pilate was governing (hēgemoneuō) Judea, and Herod was ruler of Galilee, and his brother Philip ruler of the region of Ituraea and Trachonitis, and Lysanias ruler of Abilene,