We propose to investigate field-induced exotic ordered magnetic states of coupled Tomonaga-Luttinger liquids (TLL) by single crystal neutron diffraction on the quasi-1D S=1/2 XXZ antiferromagnet SrCo2V2O8. A sequence of three field-induced ordered states (AFM-II: 3.7-7 T; AFM-III: 7-25 T, and AFM-IV: 25-32 T) is evident from the bulk measurements. The first field-induced state (AFM-II) was found to be an incommensurate longitudinal spin density wave (columnar SDW) from neutron diffraction. Recent nuclear magnetic resonance measurements on the related compound BaCo2V2O8 revealed longitudinal spin correlations also for the AFM-III and AFM-IV states (ferromagnetic SDW and checker-board SDW, respectively) in contrast to the theoretical prediction of a crossover of spin correlations from the longitudinal to transverse component. This proposal is intended to investigate the magnetic structures of the AFM-III and AFM-IV phases to verify the theoretical and experimental predictions.