I have an ODE

V''[z] + ( (I z0^2 w)/(3 (z - z0)^2) + (2 - (4 I z0 w)/9)/(z - z0)) V'[z] + 
 (-(12/41) I z0 w + (23 z0^2 w^2)/369)/(z - z0)^2 V[z] == 0

Mathematica can solve this exactly. But I just need the asymptotic behavior of the solution near z = z0. I have tried Series near z = z0, but the solution still looks messy. Is there any way to directly obtain the asymptotic behavior in Mathematica?