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We present a study of the Seebeck and Nernst coefficients of FeTeSe extended up to 28 T. The large magnitude of the Seebeck coefficient in the optimally doped sample tracks a remarkably low normalized Fermi temperature, which, like other correlated superconductors, is only one order of magnitude larger than T. We combine our data with other experimentally measured coefficients of the system to extract a set of self-consistent parameters, which identify FeTeSe as a low-density correlated superconductor barely in the clean limit. The system is subject to strong superconducting fluctuations with a sizeable vortex Nernst signal in a wide temperature window.

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