  Microscopic details such as interactions and Fermiology determine the
structure of superconducting pairing beyond the spatial symmetry classification
along irreducible point group representations. From the effective pairing
vertex, the pairing wave function related to superconducting order unfolds in
its orbital-resolved Fourier profile which we call the harmonic fingerprint
(HFP). The HFP allows to formulate a concise connection between microsopic
parameter changes and their impact on superconductivity. From a random phase
approximation analysis of twisted bilayer graphene (TBG) involving $d+id$,
$s_{\pm}$, and $f$-wave order, we find that nonlocal interactions, which
unavoidably enter the low-energy electronic description of TBG, not only
increase the weight of higher lattice harmonics but also have a significant
effect on the orbital structure of these pairing states. For gapped
unconventional superconducting order such as $s_{\pm}$ and $d+id$, a change in
HPF induces enhanced gap anisotropies. Experimental implications to distinguish
the different gaps and HPFs are also discussed.
