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The mean field vortex phase diagram of a quasi two dimensional superconductorwith a nodal d-wave pairing and with strong Pauli spin depairing is examined inthe parallel field case in order to examine an effect of gap nodes (or minima)on the stability of a FFLO-like vortex lattice. We find through a heuristicargument and a model calculation with a four-fold anisotropic Fermi velocitythat the FFLO-like state is relatively suppressed as the field approaches anodal direction. When taking account of a couple of experimental resultsaltogether, the present result strongly suggests that a node or gap minimum ofthe pairing function of CeCoIn$_5$ is located along the [100]-direction.Comment: 5 pages, 2 figures, References were added. To appear in Phys. Rev.

Modulated vortex lattice in high fields and gap nodes