We report ^{115}In nuclear magnetic resonance (NMR) measurements in the heavy-fermion superconductor CeCoIn_5 as a function of temperature in different magnetic fields applied parallel to the $(hat a, hat b)$ plane. The measurements probe a part of the phase diagram in the vicinity of the superconducting critical field H_{c2} where a possible inhomogeneous superconducting state, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), is stabilized. We have identified clear NMR signatures of two phase transitions occurring in this part of the phase diagram. The first order phase transitions are characterized by the sizable discontinuity of the shift. We find that a continuous second order phase transition from the superconducting to the FFLO state occurs at temperature below which the shift becomes temperature independent. We have compiled the first phase diagram of CeCoIn_5 in the vicinity of H_{c2} from NMR data and found that it is in agreement with the one determined by thermodynamic measurements.
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