Unlikely this is run from a domestic supply it would require whole of the supply just for the compressor plus the voltage dip on start would likely upset all neighbours. So assuming industrial we have insurance to consider, if you can't work out cable sizes I would assume you would not be able to satisfy an insurance company you have the skill required?
Start method will likely have a huge bearing on the supply required. Direct on line (unlikely), star delta, resistor, auto transformer, electronic soft start, inverter, all will have different start loads which could mean a different cable is required.
Also the de-loading method, often the motor runs after de-loading and only stops after it has been de-loaded for a set time. Rotary Screw compressors don't have the same start load as reciprocating all which has to be considered.
I would guess with that size rotary screw type? In the main manufacturers are very good giving details of the supply required. I would have expected to see a mini um recommended cable size in their technical spec. However often this needs to be exceeded to reduce volt drop. Never seen resistor or auto transformer start on a compressor, but nothing to stop it. With most compressors the start system is linked to the de-load valve so one has to use as supplied.