Complex sentence: The Ayutthaya Chronicle says the army was sent in 960 ME (April 1598 to April 99) but per the "Nan Chronicle" (Ratchasomphan 1994: 68), the siege of Chiang Mai began in January 1599.
Split into simpler sentences: The Ayutthaya Chronicle says the army was sent in 960 ME (April 1598 to April 99). The "Nan Chronicle" (Ratchasomphan 1994: 68) gives a more specific date, that the siege of Chiang Mai began in January 1599.