Hi,

it's me again, sorry for reporting another (possible) bug within 24 hours... 

sage: CC = ComplexField(332)
sage: 
X=CC(1.357903630374279963068269401271673391959119893809138669904789002836753985101796915789954726170961844+0.08656877927962875916843133406339412225470973123970623802678766038896195993916712945561867677105668213*I)
sage: X
1.35790363037427996850681211071787402033805847167968750000000000000000000000000000000000000000000000
 + 
0.0865687792796287600323446032035690222983248531818389892578125000000000000000000000000000000000000000*I

If we compare this numbers, 

IN  1.357903630374279963068...
OUT 1.357903630374279968506...
                      
IN  0.086568779279628759168...*I
OUT 0.086568779279628760032...*I
                   
we see that they differ already after 16 digits. It seems like a bug.

Best,
Marek


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