(* Created with the Wolfram Language : www.wolfram.com *)
{z1^(1 - \[Epsilon])*C[1], 0, 0, (C[2] - (-1 + \[Epsilon])*C[1]*Log[z1/z2])/
  (z1^\[Epsilon]*z2), (2*((-1 + \[Epsilon])*C[1] - \[Epsilon]*C[2] + 
    (-1 + \[Epsilon])*\[Epsilon]*C[1]*Log[z1/z2]))/
  (z1^\[Epsilon]*z2*\[Epsilon])}
