  Spectroscopic tools are fundamental for the understanding of complex quantum
systems. Here we demonstrate high-precision multi-band spectroscopy in a
graphene-like lattice using ultracold fermionic atoms. From the measured band
structure, we characterize the underlying lattice potential with a relative
error of 1.2 10^(-3). Such a precise characterization of complex lattice
potentials is an important step towards precision measurements of quantum
many-body systems. Furthermore, we explain the excitation strengths into the
different bands with a model and experimentally study their dependency on the
symmetry of the perturbation operator. This insight suggests the excitation
strengths as a suitable observable for interaction effects on the eigenstates.
