Question

Suppose the character table of a finite group G has the following
two rows:
g1 g2 g3 g4 g5 g6 g7
μ 1 1 1 ω2 ω ω2 ω
ν 2 −2 0 −1 −1 1 1
where ω = e^2πi/3. Determine the rest of the character table.