If  $\omega$ is the non-real cube root of unity such that  $|\left(\sum _{r=1}^n(r.\sum _{p=1}^r\left({\omega }^{p-1}\right))\right)-155\omega |=\left(\sum _{r=1}^n(r.\sum _{p=1}^r\left({\omega }^{p-1}\right))\right)-155\omega$, then n can be equal to 

$$\begin{gathered} \sum _{r=1}^n(r.\sum _{p=1}^r\left({\omega }^{P-1}\right))-155\omega \\ =\sum _{r=1}^n(r.({\omega }^0+{\omega }^1+{\omega }^2+\mathrm{....}+{\omega }^{r-1}))-155\omega \\ =1.{\omega }^0+2({\omega }^0+{\omega }^0)+3({\omega }^0+{\omega }^1+{\omega }^2)+4({\omega }^0+{\omega }^1+{\omega }^2+{\omega }^3)\mathrm{.....} \\ n({\omega }^0+{\omega }^1+{\omega }^2+\mathrm{.....}+{\omega }^{4-1})-155\omega \\ =1+2(-{\omega }^2)+3\left(0\right)+4\left(1\right)+5(-{\omega }^2)+\mathrm{...} \end{gathered}$$

Upto n terms  $-155\omega$
Will be real if  $n=29,30,31$