Finding coefficients in linear combination

["Swati, NoFirstName" <S10@email.sc.edu>]

Hello all,

I am trying to look for an efficient way to compute the coefficients a_{i} in the linear combination of  the form 

\Delta^{129} \mid T_{17} \equiv \sum{j = 1}^{i} a_{i} \Delta^{i} \pmod{3} 

using pari/gp. 

I figured out if I compute the LHS first and accordingly, keep subtracting terms from RHS, it takes way longer time. Could someone refer to a better way for performing this computation?

Thank you for your time and help.

Regards,

Swati