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The Prime Extragalactic Areas for Reionization and Lensing Science, a James Webb Space Telescope (JWST) GTO program, obtained a set of unique NIRCam observations that have enabled us to significantly improve the default photometric calibration across both NIRCam modules. The observations consisted of three epochs of 4-band (F150W, F200W, F356W, and F444W) NIRCam imaging in the Spitzer IRAC Dark Field (IDF). The three epochs were six months apart and spanned the full duration of Cycle 1. As the IDF is in the JWST continuous viewing zone, we were able to design the observations such that the two modules of NIRCam, modules A and B, were flipped by 180° and completely overlapped each other's footprints in alternate epochs. We were therefore able to directly compare the photometry of the same objects observed with different modules and detectors, and we found significant photometric residuals up to ∼0.05 mag in some detectors and filters, for the default version of the calibration files that we used (jwst_1039.pmap). Moreover, there are multiplicative gradients present in the data obtained in the two long-wavelength bands. The problem is less severe in the data reduced using the latest pmap (jwst_1130.pmap as of 2023 September), but it is still present, and is non-negligible. We provide a recipe to correct for this systematic effect to bring the two modules onto a more consistent calibration, to a photometric precision better than ∼0.02 mag. [ABSTRACT FROM AUTHOR]