七十角形
( 2 cos  2 π 70 + ω ⋅ 2 cos  22 π 70 + ω 2 ⋅ 2 cos  38 π 70 ) 3 = 3 x 1 + x 2 + 6 x 3 + 12 cos  2 π 10 + 3 ω ( 2 x 1 + x 2 + x 3 ) + 3 ω 2 ( 2 x 1 + x 4 + 6 cos  6 π 10 ) = 5 − 47 5 − 15 14 ( 5 + 5 ) + 4 14 ( 5 − 5 ) + 3 3 ( − 7 + 7 5 − 14 ( 5 + 5 ) + 2 14 ( 5 − 5 ) ) i 8 ( 2 cos  2 π 70 + ω 2 ⋅ 2 cos  22 π 70 + ω ⋅ 2 cos  38 π 70 ) 3 = 3 x 1 + x 2 + 6 x 3 + 12 cos  2 π 10 + 3 ω 2 ( 2 x 1 + x 2 + x 3 ) + 3 ω ( 2 x 1 + x 4 + 6 cos  6 π 10 ) = 5 − 47 5 − 15 14 ( 5 + 5 ) + 4 14 ( 5 − 5 ) − 3 3 ( − 7 + 7 5 − 14 ( 5 + 5 ) + 2 14 ( 5 − 5 ) ) i 8 {\displaystyle {\begin{aligned}\left(2\cos {\frac {2\pi }{70}}+\omega \cdot 2\cos {\frac {22\pi }{70}}+\omega ^{2}\cdot 2\cos {\frac {38\pi }{70}}\right)^{3}=&3x_{1}+x_{2}+6x_{3}+12\cos {\frac {2\pi }{10}}+3\omega (2x_{1}+x_{2}+x_{3})+3\omega ^{2}(2x_{1}+x_{4}+6\cos {\frac {6\pi }{10}})\\=&{\tfrac {{5-47{\sqrt {5}}-15{\sqrt {14\left(5+{\sqrt {5}}\right)}}+4{\sqrt {14\left(5-{\sqrt {5}}\right)}}}+3{\sqrt {3}}\left(-7+7{\sqrt {5}}-{\sqrt {14\left(5+{\sqrt {5}}\right)}}+2{\sqrt {14\left(5-{\sqrt {5}}\right)}}\right)i}{8}}\\\left(2\cos {\frac {2\pi }{70}}+\omega ^{2}\cdot 2\cos {\frac {22\pi }{70}}+\omega \cdot 2\cos {\frac {38\pi }{70}}\right)^{3}=&3x_{1}+x_{2}+6x_{3}+12\cos {\frac {2\pi }{10}}+3\omega ^{2}(2x_{1}+x_{2}+x_{3})+3\omega (2x_{1}+x_{4}+6\cos {\frac {6\pi }{10}})\\=&{\tfrac {{5-47{\sqrt {5}}-15{\sqrt {14\left(5+{\sqrt {5}}\right)}}+4{\sqrt {14\left(5-{\sqrt {5}}\right)}}}-3{\sqrt {3}}\left(-7+7{\sqrt {5}}-{\sqrt {14\left(5+{\sqrt {5}}\right)}}+2{\sqrt {14\left(5-{\sqrt {5}}\right)}}\right)i}{8}}\\\end{aligned}}}
2 cos  2 π 70 + 2 cos  22 π 70 + 2 cos  38 π 70 = 1 4 ( − 1 + 5 + 14 ( 5 + 5 ) ) = x 1 2 cos  6 π 70 + 2 cos  66 π 70 + 2 cos  26 π 70 = 1 4 ( − 1 − 5 + 14 ( 5 − 5 ) ) = x 2 2 cos  18 π 70 + 2 cos  58 π 70 + 2 cos  62 π 70 = 1 4 ( − 1 + 5 − 14 ( 5 + 5 ) ) = x 3 2 cos  54 π 70 + 2 cos  34 π 70 + 2 cos  46 π 70 = 1 4 ( − 1 − 5 − 14 ( 5 − 5 ) ) = x 4 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{70}}+2\cos {\frac {22\pi }{70}}+2\cos {\frac {38\pi }{70}}={\frac {1}{4}}\left(-1+{\sqrt {5}}+{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)=x_{1}\\2\cos {\frac {6\pi }{70}}+2\cos {\frac {66\pi }{70}}+2\cos {\frac {26\pi }{70}}={\frac {1}{4}}\left(-1-{\sqrt {5}}+{\sqrt {14\left(5-{\sqrt {5}}\right)}}\right)=x_{2}\\2\cos {\frac {18\pi }{70}}+2\cos {\frac {58\pi }{70}}+2\cos {\frac {62\pi }{70}}={\frac {1}{4}}\left(-1+{\sqrt {5}}-{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)=x_{3}\\2\cos {\frac {54\pi }{70}}+2\cos {\frac {34\pi }{70}}+2\cos {\frac {46\pi }{70}}={\frac {1}{4}}\left(-1-{\sqrt {5}}-{\sqrt {14\left(5-{\sqrt {5}}\right)}}\right)=x_{4}\\\end{aligned}}}