Q: Breaks in plot & blank plots Almost as a follow on from this old question, I am having similar problems again, with slight difference, that if the values are small enough, a completely blank plot is produced.
ξ[z_] := ((z - 1) Gamma[z/2 + 1] Zeta[z])/Sqrt[π^z]

ContourPlot[{Im[ξ[σ + b I]], Re[ξ[σ + b I]]}, {σ, -2, 3}, {b, 100, 120},
            PlotPoints -> 500]


Even with PlotPoints->500 there are still breaks in the plot. I know I am dealing with very small numbers here, but is there anything I can do to create a clean plot?
The plot above is not too bad, but I would really like to look at plots for values of {b,7000,7010} - but it just produces a blank plot above 1000. Is there anything I can to to avoid this?
Update
Have tried Exclusions->None but creates a plot that is just wrong!


A: I'm not sure this is on the right track, if so OP just comment and I'll delete. I've found that plotting can get finicky with very large/very small values, and have in the past "helped" by lifting values into a more "reasonable" range. E.G. (I picked a scaling for a "middle" value of the plot range):
ξ[z_] := ((z - 1) Gamma[z/2 + 1] Zeta[z])/Sqrt[π^z]
ContourPlot[{Im[ξ[σ + b I]]*10^2380,  Re[ξ[σ + b I]]*10^2380}, 
             {σ, -2, 3}, {b, 7000, 7010}, PlotPoints -> 100, MaxRecursion -> 2, 
             PerformanceGoal -> "Speed", Contours -> 20, PlotRange -> Automatic]


