How many polynomials of the form $x^6+a{x}^5+b{x}^4+c{x}^3+d{x}^2+ex+1$, where $a,b,c,d,e$ are real numbers, have the property that whenever $r$ is a root, so is $\frac{-1+i\sqrt{3}}{2}\cdot r$? (Note that $i=\sqrt{-1}$)