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Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form satisfying theRamanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be aprimitive Dirichlet character modulo $M$, which we assume to be prime forsimplicity. We will prove the following subconvex bound $$L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon}M^{\frac{3}{4}-\frac{1}{1612}+\varepsilon}. $$

The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B