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Pion photoproduction in the $\vec{\gamma }\vec{p}\to {\pi }^{0}p$reaction has been measured in the FROzen Spin Target (FROST) experiment at the Thomas Jefferson National Accelerator Facility. In this experiment, circularly polarized photons with energies up to 3.082 GeV impinged on a transversely polarized frozen-spin target. Final-state protons were detected in the Continuous Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer. The polarization observables $T$and $F$have been extracted for $W$from 1445 to 2525 MeV, of which the energy range is much broader, and the precision is better than the existing measurements in higher $W$ranges. The data generally agree with predictions of present partial-wave analyses but also show marked differences for higher $W$ranges. By incorporating the present data into the databases, the Scattering Analysis Interactive Data (SAID) fits have been improved with relatively small ${\chi }^2$and significant changes in the parameters of the $\mathrm{\Delta }\left(1910\right)1/2^{+}$and $N\left(2190\right)7/2^{-}$have been found with the JüBo model.