We measured the 13C-NMR spectrum and T1 of the quasi-two-dimensional organic superconductor kappa-(BEDT-TTF)2Cu(NCS)_{2} under pressure. This material was thought to show a relationship between T_{c} and the effective cyclotron mass m_{c};{*}, obtained from the Shubnikov-de Haas (SdH) effect. We found that kappa-(BEDT-TTF)2Cu(NCS)_{2} behaved as a Fermi liquid at low temperature under all pressures, and antiferromagnetic fluctuations were expected.
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