>>134

A^3
=A(2-ω)B
=(2-ω)(2ω+3)C
=(2-ω)(2ω+3)√-7
=(-2ω^2+ω+6)√-7
=(3ω+8)√-7
=(-3√(-7)-3√21)/2+16√-7/2
=(13√(-7)-3√21)/2

E^3
=E(3+ω)D
=(3+ω)(-2ω+1)F
=(-2ω^2-5ω+3)F
=(-3ω+5)√5
=(3√(-7)+3√21)/2+10√-7/2
=(13√(-7)+3√21)/2

C=√(-7)
A=((13√(-7)/2-3√21)/2)^(1/3)
E=((13√(-7)/2+3√21)/2)^(1/3)

ζ7 -ζ7^6=1/3(C+  A+  E)
ζ7^2-ζ7^5=1/3(C+ω^2A+ω E)
ζ7^4-ζ7^3=1/3(C+ω A+ω^2E)