2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224879We find explicit formulae for the circular spectral measures of $E_7,E_8$. This leads to a number of general observations regarding the ADE circular measures: these are linear combinations of measures supported by the roots of unity, with real density given by certain degree 3 polynomials.23 pagesQuantum AlgebraCyclotomic expansion of exceptional spectral measurestext