十九角形
cos  2 π 19 = 1 6 ( − 1 + ω 2 133 + 57 3 i 2 3 + ω 133 − 57 3 i 2 3 3 + 38 + ( 10 + 6 ω 2 ) 133 + 57 3 i 2 3 + ( 10 − 3 ω ) 133 − 57 3 i 2 3 3 3 + 38 + ( 10 − 3 ω 2 ) 133 + 57 3 i 2 3 + ( 10 + 6 ω ) 133 − 57 3 i 2 3 3 3 ) {\displaystyle {\begin{aligned}\cos {\frac {2\pi }{19}}=&{\frac {1}{6}}\left({\tfrac {-1+\omega ^{2}{\sqrt[{3}]{\frac {133+57{\sqrt {3}}i}{2}}}+\omega {\sqrt[{3}]{\frac {133-57{\sqrt {3}}i}{2}}}}{3}}+{\sqrt[{3}]{\tfrac {38+(10+6\omega ^{2}){\sqrt[{3}]{\frac {133+57{\sqrt {3}}i}{2}}}+(10-3\omega ){\sqrt[{3}]{\frac {133-57{\sqrt {3}}i}{2}}}}{3}}}+{\sqrt[{3}]{\tfrac {38+(10-3\omega ^{2}){\sqrt[{3}]{\frac {133+57{\sqrt {3}}i}{2}}}+(10+6\omega ){\sqrt[{3}]{\frac {133-57{\sqrt {3}}i}{2}}}}{3}}}\right)\\\end{aligned}}}