  Many measurements of quarkonium suppression at the LHC, e.g. the nuclear
modification factor $R_{AA}$ of $J/\Psi$, are well described by a multitude of
different models. Thus pinpointing the underlying physics aspects is difficult
and guidance based on first principles is needed. Here we present the current
status of our ongoing high precision study of in-medium spectral properties of
both bottomonium and charmonium based on NRQCD on the lattice. This effective
field theory allows us to capture the physics of quarkonium without modeling
assumptions in a thermal QCD medium. In our study a first principles and
realistic description of the QCD medium is provided by state-of-the-art
lattices of the HotQCD collaboration at almost physical pion mass. Our updated
results corroborate a picture of sequential modification of states with respect
to their vacuum binding energy. Using a novel low-gain variant of the Bayesian
BR method for reconstructing spectral functions we find that remnant features
of the Upsilon may survive up to $T\sim400$MeV, while the $\chi_b$ signal
disappears around $T\sim270$MeV. The $c\bar{c}$ analysis hints at melting of
$\chi_c$ below $T\sim190$MeV while some $J/\Psi$ remnant feature might survive
up to $T\sim245$MeV. An improved understanding of the numerical artifacts in
the Bayesian approach and the availability of increased statistics have made
possible a first quantitative study of the in-medium ground state masses, which
tend to lower values as $T$ increases, consistent with lattice potential based
studies.
