$\frac{\left(-\left(\sqrt{\frac{3}{2}}+\frac{1}{2}\sqrt{6}i\right)-2+\sqrt{3}i\right)\left(-\left(-1+\sqrt{3}i\right)\left(-\left(\sqrt{\frac{3}{2}}+\frac{1}{2}\sqrt{6}i\right)-1\right)+\left(-\left(\sqrt{\frac{3}{2}}+\frac{1}{2}\sqrt{6}i\right)-1\right)^{2}+\left(-1+\sqrt{3}i\right)^{2}\right)\left(-\left(\left(-1+\sqrt{3}i\right)\left(-\left(\sqrt{\frac{3}{2}}+\frac{1}{2}\sqrt{6}i\right)-1\right)\right)^{3}+\left(-\left(\sqrt{\frac{3}{2}}+\frac{1}{2}\sqrt{6}i\right)-1\right)^{6}+\left(-1+\sqrt{3}i\right)^{6}\right)}{512}\approx 2.564096364+8.438378815i$

$\sqrt{6}\left(\frac{81}{256}+\frac{441}{256}i\right)+\left(\frac{229}{128}+\frac{135}{32}i\right)$