  A magnetic atomic impurity inside a superconductor locally distorts
superconductivity. They scatter Cooper pairs as a potential with broken
time-reversal symmetry, what leads to localized bound states with subgap
excitation energies, named hereon Shiba states. Most conventional approaches to
study Shiba states treat magnetic impurities as point scatterers with an
isotropic exchange interaction, while the complex internal structure of
magnetic impurities is usually neglected. Here, we show that the number and the
shape of Shiba states are correlated to the spin-polarized atomic orbitals of
the impurity, hybridized with the superconducting host, as supported by Density
Functional Theory simulations. Using high-resolution scanning tunneling
spectroscopy, we spatially map the five Shiba excitations found on sub-surface
chromium atoms in Pb(111), resolving both their particle and hole components.
While the maps of particle components resemble the \textit{d} orbitals of
embedded Cr atoms, the hole components differ strongly from them. The orbital
fingerprints of Shiba states thus unveil the magnetic ground state of the
impurity, and identify scattering channels and interactions, all valuable tools
for designing atomic-scale superconducting devices.
