complex number roots

Find all values of the real number $a$ so that the four complex roots of \[z^4 - 6z^3 + 11az^2 - 3(2a^2 + 3a - 3) z + 1 = 0\]
form the vertices of a parallelogram in the complex plane. Enter all the values, separated by commas.

 

I have already tried 1,3 and that was wrong... 

Thanks

 

mercurym999