1の冪根
以下、i は虚数単位である。
ξ 2 = − 1 {\displaystyle \xi _{2}=-1}
ξ 3 = − 1 ± 3 i 2 {\displaystyle \xi _{3}={\frac {-1\pm {\sqrt {3}}\,i}{2}}} (しばしば ω と書かれる)
ξ 4 = ± i {\displaystyle \xi _{4}=\pm i}
ξ 5 = − 1 + 5 ± i 10 + 2 5 4 , − 1 − 5 ± i 10 − 2 5 4 {\displaystyle \xi _{5}={\frac {-1+{\sqrt {5}}\pm i{\sqrt {10+2{\sqrt {5}}}}}{4}},{\frac {-1-{\sqrt {5}}\pm i{\sqrt {10-2{\sqrt {5}}}}}{4}}}
ξ 6 = 1 ± 3 i 2 {\displaystyle \xi _{6}={\frac {1\pm {\sqrt {3}}\,i}{2}}}
ξ 8 = 2 ± 2 i 2 , − 2 ± 2 i 2 {\displaystyle \xi _{8}={\frac {{\sqrt {2}}\pm {\sqrt {2}}\,i}{2}},{\frac {-{\sqrt {2}}\pm {\sqrt {2}}\,i}{2}}}