$\left\{\begin{matrix}z=\frac{442^{\frac{2}{3}}\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{-\frac{1}{3}}\left(663\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}+442^{\frac{2}{3}}\left(-290-812i\right)\right)}{293046}\approx 0.017240937+0.000001237i\text{, }a=-\frac{5}{2}-5i=-2.5-5i\text{, }&\sqrt[3]{442}\left(-\frac{290}{663}-\frac{812}{663}i\right)\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{-\frac{1}{3}}+\frac{442^{\frac{2}{3}}\sqrt[3]{442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)}}{442}\neq 0\\z=-\frac{442^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{-\frac{1}{3}}\left(-663\left(1+\sqrt{3}i\right)\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}+442^{\frac{2}{3}}\left(-580-1624i\right)\right)}{1172184}\approx -1.14641155+1.614622767i\text{, }a=-\frac{5}{2}-5i=-2.5-5i\text{, }&\sqrt[3]{442}\left(1+\sqrt{3}i\right)\left(-\frac{3}{2}\sqrt{3}\sqrt[3]{442}i\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}-\frac{3\sqrt[3]{442}\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}}{2}+\left(-580-1624i\right)\right)\neq 0\\z=\frac{442^{\frac{2}{3}}\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{-\frac{1}{3}}\left(-\sqrt{3}i+1\right)\left(663\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)+442^{\frac{2}{3}}\left(580+1624i\right)\right)}{1172184}\approx 1.129170613-1.614624004i\text{, }a=-\frac{5}{2}-5i=-2.5-5i\text{, }&\left(-\sqrt{3}i+1\right)\left(663\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)+442^{\frac{2}{3}}\left(580+1624i\right)\right)\neq 0\text{ and }\sqrt[3]{442}\left(-\sqrt{3}i+1\right)\left(\frac{3}{2}\sqrt{3}\sqrt[3]{442}i\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}-\frac{3\sqrt[3]{442}\left(442\sqrt{-\frac{2197981477}{1165736988}-\frac{330310883}{291434247}i}+\left(5+14i\right)\right)^{\frac{2}{3}}}{2}+\left(-580-1624i\right)\right)\neq 0\end{matrix}\right.$