Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
At the head of these stood Gnaeus Naevius, the first Roman who deserves to be called a poet, and, so far as the accounts preserved regarding him and the few fragments of his works allow us to form an opinion, to all appearance as regards talent one of the most remarkable and most important names in the whole range of Roman literature.
He was a younger contemporary of Andronicus--his poetical activity began considerably before, and probably did not end till after, the Hannibalic war--and felt in a general sense his influence; he was, as is usually the case in artificial literatures, a worker in all the forms of art produced by his predecessor, in epos, tragedy, and comedy, and closely adhered to him in the matter of metres. Nevertheless, an immense chasm separates the poets and their poems. Naevius was neither freedman, schoolmaster, nor actor, but a citizen of unstained character although not of rank, belonging probably to one of the Latin communities of Campania, and a soldier in the first Punic war.(28)
28. The personal notices of Naevius are sadly confused. Seeing that he fought in the first Punic war, he cannot have been born later than 495. Dramas, probably the first, were exhibited by him in 519 (Gell. xii. 21. 45). That he had died as early as 550, as is usually stated, was doubted by Varro (ap. Cic. Brut. 15, 60), and certainly with reason; if it were true, he must have made his escape during the Hannibalic war to the soil of the enemy. The sarcastic verses on Scipio (p. 150) cannot have been written before the battle of Zama.
We may place his life between 490 and 560, so that he was a contemporary of the two Scipios who fell in 543 (Cic. de Rep. iv. 10), ten years younger than Andronicus, and perhaps ten years older than Plautus. His Campanian origin is indicated by Gellius, and his Latin nationality, if proof of it were needed, by himself in his epitaph. The hypothesis that he was not a Roman citizen, but possibly a burgess of Cales or of some other Latin town in Campania, renders the fact that the Roman police treated him so unscrupulously the more easy of explanation. At any rate he was not an actor, for he served in the army.
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Reference address : https://www.ellopos.net/elpenor/rome/3-14-literature-art.asp?pg=46