Would a Roman officer have had the means to finance the construction of a synagogue in the lakeshore town of Capernaum?
The Appearance of Jesus: Hairstyles and Beards in Bible Times

No one knows for sure how Jesus looked in the eyes of his contemporaries. However, there is evidence that suggests the hair of Jesus may have been rather short—black or dark in color—and his beard closely trimmed.
The Centurion and the Synagogue

A Roman centurion’s concern for his slave focuses our attention on the presence of non-Jews in the land of Israel in the first century. A modern Jewish authority on the history of the period provides the story’s background.