Naga is the third of the four fixed karanas and occupies position 60, the second half of tithi 30. Tithi 30 is Amavasya, so Naga is the final half-tithi of the lunation, ending at the exact moment of the new moon, after which the count restarts at position 1 with Kimstughna.
That makes it the only karana whose end is an astronomical event rather than an arbitrary six degree step. Every other karana boundary falls where the Moon has gained a further six degrees on the Sun from wherever the count began; the boundary at the end of Naga is the conjunction itself, elongation zero, and the whole numbering of tithis and karanas is anchored to it.
The four fixed karanas exist for an arithmetic reason. Sixty karanas cannot be filled by a rotation of seven, but fifty six can, eight times over, so four positions are taken out of the rotation. All four were placed around the conjunction: Shakuni, Chatushpada and Naga at the close of the waning fortnight and Kimstughna at the head of the waxing one. The result is a run of four consecutive half-tithis, roughly two days, in which no movable karana appears, and a seven-fold cycle that runs unbroken from position 2 to position 57 in every lunation.
A karana averages 11 hours and 49 minutes and can be two hours or so shorter or longer depending on the Moon's speed.