Set of continuum-estimated lattice susceptibilities of order 2 and 4, as well as $T$-derivatives of order 2 susceptibilities, obtained with the 4stout action on lattices with $N_\tau=10, 12, 16, 20, 24$ timeslices with aspect ratio $LT = 4$, except for the $64^4 \times 24$ lattice.All quantities are provided for a range $T = 30 - 800$ MeV, with at step $\Delta T=1$ MeV. Each susceptibility is produced a cubic spline fit of 3 datasets: HRG data with fictitious 5-10% at low temperature cubic-spline spline fitted lattice data at intermediate temperature $1/T$-polynomial fitted of lattice data at high temperature Both lattice-fitted datasets are also continuum-extrapolated using several timeslice lattice simulation results. When using this data, please cite also the following work (contain details about the fitting procedure and the lattice data, respectively): A. Abuali, S. Borsányi, Z. Fodor, J. Jahan, M. Kahangirwe, P. Parotto, A. Pásztor, C. Ratti, H. Shah and S.A. Trabulsi, arXiv:2504.01881 [hep-lat, het-ph] R. Bellwied, S. Borsányi, Z. Fodor, S.D. Katz, A. Pásztor, C. Ratti, K.K. Szabo, Phys.Rev.D 92 (2015) 11, 114505 [hep-lat]