Eisenstein integers

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Eisenstein integers are complex numbers of the form

$z=a+b\,\omega ,\,$

where

a

and

b

are integers and

$\omega =e^{2\pi i/3}=\cos \left({\frac {2\pi }{3}}\right)+i\sin \left({\frac {2\pi }{3}}\right)=-{\frac {1}{2}}+i{\frac {\sqrt {3}}{2}}\,$

is a primitive (non-real) cube root of unity.