How Can You Accurately Draw the Riemann Xi Function Curve?

[zetafunction]

how to draw this curve ??

$$Arg\xi (1/2+iz)$$

however i am a bit ashamed because the Riemann Xi function is real for real 'z' so for ALL the real numbers the argument of the $$\xi(1/2+iz)$$ should be 0 ¡¡

 

[Bill Simpson]

http://www.wolframalpha.com/input/?i=plot+1%2f2(1%2f2%2bI+z)((1%2f2%2bI+z)-1)Gamma((1%2f2%2bI+z)%2f2)%2fPi^((1%2f2%2bI+z)%2f2)Zeta((1%2f2%2bI+z))&incParTime=true

In the graph in the middle you can barely see the hint of the orange horizontal line for the complex part that is lying on the x axis.

 

[zetafunction]

thanks a lot Bill... :)