Will my PSU work with a 6770?

Hello,

I am currently running the following build:


- FX 4100

- Diamond ATX Mid Tower Computer Case with 400W Power Supply

- GA-78LMT-S2P Socket AM3+ 760G mATX AMD Motherboard

- 60GB 2.5" SATA III 6Gb/s Pyro Solid State Drives (SSD) with SandForce 2281 Controller

- Extreme Performance Sector 5 G Series 4GB DDR3-1333 (PC3-10666) Enhanced Latency Dual Channel Desktop Memory Kit (Two 2GB Memory Modules)


I know that the 400w power supply that came with the case is not the best, but I figured that it would not be a problem without a graphics card.

Will this PSU still be sufficient if I add a Gigabyte 6770 1GB?

And if not, what is a good PSU that I can add, that is incredibly cheap as possible?

Thanks so much for all the help.