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I have a function defined in cylindrical coordinates

rho[r_, z_] :=  2 E^(-(z^2/200))BesselJ[0,0.16 r] (-0.025 + 1/100 (1 +2 Log[E^(-(z^2/200)) BesselJ[0, 0.16 r]]));

This function is defined in a system with azimuthal symmetry, thus the system has no theta dependence. How will I plot such function in mathematica

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