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Not necessarily just a singular weird animal either. Sometimes a breeding pair was given. Take this interesting excerpt about Plato's stepbrother:

By 413, Demos had inherited his father's peacocks, descendants of an original breeding pair given to Pyrilampes s.v. on one of his embassies to the Persian court. They were such beautiful εὐόφθαλμος and expensive birds—a pair valued at a thousand drachmae (Ael. NA 5.21)--that visitors would arrive from Sparta and Thessaly to see them, and in hopes of obtaining some of their eggs. Apparently Demos continued the tradition his father had begun, more than thirty years previously, of admitting the public on the first day of each month to view the birds.