Data on the polarization observables T, P, and H for the reaction γp→pπ0 are reported. Compared to earlier data from other experiments, our
data are more precise and extend the covered range in energy and angle
substantially. The results were extracted from azimuthal asymmetries measured
using a transversely polarized target and linearly polarized photons. The data
were taken at the Bonn electron stretcher accelerator ELSA with the CBELSA/TAPS
detector. Within the Bonn-Gatchina partial wave analysis, the new polarization
data lead to a significant narrowing of the error band for the multipoles for
neutral-pion photoproduction