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The required size of a conduit raceway for a 3-5000 mcm wire is 300 kcmil. It maximizes the limits on the wire fill for raceways.
Using the AWG for wire sizes only goes up to 4/0. After that the increases use MCM to size the wire. So your 262 MCM wire size will be same in AWG. There is no 262 MCM in the North American market place. It goes in 50 MCM increments starting at 250 MCM , 300 MCM, 350 MCM, 400 MCM right up to 2000 MCM cable.
250 mcm
This size service can be wired in a few combinations. Two parallel runs of 1250 MCM, three parallel runs of 600 MCM, four parallel runs of 350 MCM. Of the three choices the four runs of 350 MCM wires would be the easiest to handle if there are any bends in the service entrance conduit.
There are different combination to obtain a current capacity of 1250 amps. A parallel run of #1250 MCM wires. A triple run of #600 MCM wire. The most flexible run would be with a quad run of #350 MCM wire.