In the following we describe the method for interpolating the value of the reference solution at any grid point while preserving spectral accuracy and double precision. To get values of the reference solution at a given location $(x,y)$, first download the archive file refsolcyl.tgz and extract the files and directory. The directory should contain the program interpol.m and the data directory containing the reference solution values. In a file named grid.dat, report the couples of values (x,y) where the reference solution has to be interpolated. Then, execute the software Octave or Matlab and enter the command interpol. The solution at each selected locations (x,y) is stored in files named U.dat, V.dat (velocity components), P.dat (pressure) and vort.dat (vorticity). Please note that, because of the lack of physical boundary conditions for the pressure, the pressure has been extrapolated with a spline method on the cylinder and on the exterior boundary. Thus a strictly spectral accuracy cannot be warranty for the pressure. For points inside the cylinder, the value is arbitrarily zero, while for points exterior to the domain (i.e. r_\infty>40), the velocity is arbitrarily set to a uniform streamwise flow. For example the interpolation on the point (x=3,~ y=3) should give the values: U=1.0670111347099145e+00 V=1.5134054077428072e-02 P=-7.0794830815655407e-02 vort=-6.5845796777125321e-06 Small variations starting from to the fourteenth decimal can be observed, depending on the computer used. ================================================================================ We kindly require that you cite the following paper where all details about these data are documented: R. Gautier, D. Biau, E. Lamballais, 2012, A reference solution of the flow over a circular cylinder at Re=40, Computers & Fluids, 10.1016/j.compfluid.2012.12.017 ================================================================================