Built a pole barn in the back yard, was going to upgrade the house service and run from there, but thanks to the county I am running separate service.

I have the 3" conduit, I know I need to leave 35' coiled at the bottom of the utility pole, and want to run about 5' inside the barn to get to the main panel.

With a 320' run, and a 400 amp service, what gauge wire should I run?

I'm thinking 0000 aluminum could do it with about a %10 or %11 voltage drop, but I don't know if it will be pushing it on the distance.