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!

• try Exclusions->None !Mathematica graphics – Nasser Mar 4 '14 at 10:04
• Have tried that - what's with the grid? Is that part of the plot? Also, no luck on the higher values - still blank. – martin Mar 4 '14 at 10:15

ξ[z_] := ((z - 1) Gamma[z/2 + 1] Zeta[z])/Sqrt[π^z]