>>594
　z　= ζ + ζ^2 + ζ^4　とおく。
　z* = ζ^6 + ζ^5 + ζ^3,

　z + z* = (1 + ζ + ζ^2 + ζ^3 + ζ^4 + ζ^5 + ζ^6) -1 = -1,
　zz* = (1 + ζ + ζ^2 + ζ^3 + ζ^4 + ζ^5 + ζ^6) + 2 = 2,

　Z^2 + Z +2 = 0,
∴　z　= {-1 + (√7)ｉ}/2,