Dear all`

I have the following function, I copy the code in Mathematica

F[x_, y_] = (1/Abs[x + I y])1.12554 Im[Sqrt[x + I y]] Re[Sqrt[x + I y]] (BesselJ[-(1/4), 0.45 Re[Sqrt[x + I y]]^2]^2 BesselJ[3/4, 
     0.45 Im[Sqrt[x + I y]]^2]^2 Im[Sqrt[x + I y]]^2 + BesselJ[-(1/4), 0.45 Im[Sqrt[x + I y]]^2]^2 BesselJ[3/4,  0.45 Re[Sqrt[x + I y]]^2]^2 Re[Sqrt[x + I y]]^2)

gr = Plot3D[Re[F[x, y]], {x, -L, L}, {y, -L, L},  PlotRange -> Full, PlotPoints -> 300]

I obtain the following 3Dplot, I see not function in some region, How can i solve this problem ?

Or it is possible somehow to put the same color of the graph itself. ? In advance thank you