Reproduce general tensor perturbation result

[Chao]

Hi all,

I am new to this program and I tried to put some code to reproduce the result in Weinberg's Cosmology textbook.

It seems that if I interpret my normal vector as n^\mu=(-1,0,0,0) then the result will not recover the correct coefficient of factors associated with h_ii and h_ii dot.

Could anyone help me check if my code is correct or it is just my calculation based on that could be wrong? Thanks!