sibyllic

/sɪˈbɪlɪk/
adjective
  1. Relating to or characteristic of a sibyl; prophetic, oracular (variant spelling of sibylic).
    • Her sibyllic advice often turned out to be surprisingly accurate.
    • The painting had a sibyllic quality, as if the figure knew secrets of the future.
    • The sibyllic utterances of the fortune-teller were hard to understand.