the only way to get the remaining fuel quantity at 1/4 tank.
Since we don't know the exact shape of the fuel cell or blockage
design inside for baffles, vents, sender, etc.
I believe the manual tells you what the tank holds, total.
It also says when fuel warning goes on you have X miles to go,
Run it near dry and stop for gas, put a little in and wait for gauge to
stabilize. Add as needed via stop and visually check gauge to 1/4 tank.
How many gallons to get 1/4 tank. is your answer. That also should be
very close since you were almost dry.
You will never know the exact amount unless you can find BMW's
tank fill calibration figures. They put in a specific quantity of fuel in
at factory and verify fuel sender accuracy on gauge.