三十七角形
λ 1 = ( 2 cos  30 π 37 ⋅ 2 cos  32 π 37 ) + ( 2 cos  4 π 37 ⋅ 2 cos  24 π 37 ) + ( 2 cos  18 π 37 ⋅ 2 cos  34 π 37 ) = u 1 + u 2 + u 3 λ 2 = ( 2 cos  10 π 37 ⋅ 2 cos  14 π 37 ) + ( 2 cos  6 π 37 ⋅ 2 cos  36 π 37 ) + ( 2 cos  8 π 37 ⋅ 2 cos  26 π 37 ) = v 1 + v 2 + v 3 λ 3 = ( 2 cos  2 π 37 ⋅ 2 cos  12 π 37 ) + ( 2 cos  16 π 37 ⋅ 2 cos  22 π 37 ) + ( 2 cos  20 π 37 ⋅ 2 cos  28 π 37 ) = w 1 + w 2 + w 3 {\displaystyle {\begin{aligned}\lambda _{1}=&\left(2\cos {\frac {30\pi }{37}}\cdot 2\cos {\frac {32\pi }{37}}\right)+\left(2\cos {\frac {4\pi }{37}}\cdot 2\cos {\frac {24\pi }{37}}\right)+\left(2\cos {\frac {18\pi }{37}}\cdot 2\cos {\frac {34\pi }{37}}\right)=u_{1}+u_{2}+u_{3}\\\lambda _{2}=&\left(2\cos {\frac {10\pi }{37}}\cdot 2\cos {\frac {14\pi }{37}}\right)+\left(2\cos {\frac {6\pi }{37}}\cdot 2\cos {\frac {36\pi }{37}}\right)+\left(2\cos {\frac {8\pi }{37}}\cdot 2\cos {\frac {26\pi }{37}}\right)=v_{1}+v_{2}+v_{3}\\\lambda _{3}=&\left(2\cos {\frac {2\pi }{37}}\cdot 2\cos {\frac {12\pi }{37}}\right)+\left(2\cos {\frac {16\pi }{37}}\cdot 2\cos {\frac {22\pi }{37}}\right)+\left(2\cos {\frac {20\pi }{37}}\cdot 2\cos {\frac {28\pi }{37}}\right)=w_{1}+w_{2}+w_{3}\\\end{aligned}}}