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We have observed 69 K-Li interspecies Feshbach resonances including 13 elastic p-wave resonances and 6 broad d-wave resonances of K atoms in different spin-state combinations at fields up to 600~G. Multi-channel quantum defect theory calculation is performed to assign these resonances and the results show perfect agreement with experimental values after improving input parameters. The observed broad p- and d- wave resonances display a full resolved multiplet structure. They may serve as important simulators to nonzero partial wave dominated physics.

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