Āgama and Pāñcarātra
आगमāgamaपाञ्चरात्रpāñcarātraĀgama is a word for what has 'come down' (it also means a coming, an arrival): a teaching received through a line of teachers, and, in the later use, the books that lay down how the Lord is to be worshipped. For the Vaiṣṇavas the chief of these is the Pāñcarātra, a body of texts called saṃhitās, among them the Sātvata, the Pauṣkara and the Jayākhya, which teach the worship of the Lord, the making and care of His image, and the forms in which He is known. The name Pāñcarātra is read as 'five nights', but its sense is not settled and has been taken in more than one way.
Pāñcarātra speaks of the Lord as Vāsudēva in His supreme form, with three emanations from Him, Saṅkarṣaṇa, Pradyumna and Aniruddha; and it speaks of five ways in which He is present to souls: in His supreme state, in the emanations, in His descents, as the Lord within the heart, and in the temple image. It has been a major influence on Śrīvaiṣṇava thought, and Parāśara Bhaṭṭar finds the same fivefold order in the thousand names, the first run of them describing the supreme form. Some temples are tied to particular saṃhitās, Śrīraṅgam among them.
The hymn has the word in the name Kṛtāgamaḥ, which stands twice (664 and 798). At its first place He is the Giver of the sacred teaching, who in mercy makes known the way to Himself. At its second, since āgama also means a coming, He is the One whose every coming into the world is His own doing and not the result of past deeds, and who likewise made the teaching by which souls learn to worship Him.
SourcesMonier-Williams Sanskrit-English Dictionary, āgama (Cologne Digital Sanskrit Dictionaries)Pancharatra (Wikipedia)Vishnu Sahasranama, introduction to Parāśara Bhaṭṭar's commentary (sadagopan.org)