We report detailed $^{75}$As-NQR investigations of the locally non-centrosymmetric superconductor SrPtAs. The spin-lattice relaxation studies prove weakly coupled multi-gap superconductivity. The Hebel-Slichter peak, a hallmark of conventional superconductivity, is strongly suppressed, which points to an unconventional superconducting state. The observed behavior excludes a superconducting order parameter with line nodes and is consistent with proposed $f$-wave and chiral $d$-wave order parameters.
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