三十七角形
λ 1 = 2 cos  2 π 37 + 2 cos  12 π 37 + 2 cos  16 π 37 + 2 cos  20 π 37 + 2 cos  22 π 37 + 2 cos  28 π 37 = − 1 3 + 37 3 − 11 + 3 3 i 2 37 3 ω 2 + 37 3 − 11 − 3 3 i 2 37 3 ω λ 2 = 2 cos  4 π 37 + 2 cos  18 π 37 + 2 cos  24 π 37 + 2 cos  30 π 37 + 2 cos  32 π 37 + 2 cos  34 π 37 = − 1 3 + 37 3 − 11 + 3 3 i 2 37 3 ω + 37 3 − 11 − 3 3 i 2 37 3 ω 2 λ 3 = 2 cos  6 π 37 + 2 cos  8 π 37 + 2 cos  10 π 37 + 2 cos  14 π 37 + 2 cos  26 π 37 + 2 cos  36 π 37 = − 1 3 + 37 3 − 11 + 3 3 i 2 37 3 + 37 3 − 11 − 3 3 i 2 37 3 {\displaystyle {\begin{aligned}\lambda _{1}=&2\cos {\frac {2\pi }{37}}+2\cos {\frac {12\pi }{37}}+2\cos {\frac {16\pi }{37}}+2\cos {\frac {20\pi }{37}}+2\cos {\frac {22\pi }{37}}+2\cos {\frac {28\pi }{37}}=-{\frac {1}{3}}+{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11+3{\sqrt {3}}i}{2{\sqrt {37}}}}}\omega ^{2}+{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11-3{\sqrt {3}}i}{2{\sqrt {37}}}}}\omega \\\lambda _{2}=&2\cos {\frac {4\pi }{37}}+2\cos {\frac {18\pi }{37}}+2\cos {\frac {24\pi }{37}}+2\cos {\frac {30\pi }{37}}+2\cos {\frac {32\pi }{37}}+2\cos {\frac {34\pi }{37}}=-{\frac {1}{3}}+{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11+3{\sqrt {3}}i}{2{\sqrt {37}}}}}\omega +{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11-3{\sqrt {3}}i}{2{\sqrt {37}}}}}\omega ^{2}\\\lambda _{3}=&2\cos {\frac {6\pi }{37}}+2\cos {\frac {8\pi }{37}}+2\cos {\frac {10\pi }{37}}+2\cos {\frac {14\pi }{37}}+2\cos {\frac {26\pi }{37}}+2\cos {\frac {36\pi }{37}}=-{\frac {1}{3}}+{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11+3{\sqrt {3}}i}{2{\sqrt {37}}}}}+{\frac {\sqrt {37}}{3}}{\sqrt[{3}]{\frac {-11-3{\sqrt {3}}i}{2{\sqrt {37}}}}}\\\end{aligned}}}