How are the IVs of SHA-512/256 and SHA-512/224 calculated?
Those are calculated using the "SHA-512/t IV Generation Function", as described in FIPS-180 (pdf, see 5.3.6), the Secure Hash Standard.

The procedure is to first modify the normal SHA-512 IV, then calculate the hash of a string describing the truncation mode used, and use that as the IV. Those IVs are essentially just predefined hash outputs and so not any particularly nice numbers.

The reason it is done like this is to allow arbitrary truncation lengths below 512 (except 384, which has its own hash which was defined earlier).