Hi, I created a numberfield:
K.<w>=NumberField(x^2+x+1)
Then I wanted to know the following residue symbol:
K.ideal(-1-3*w).residue_symbol(5,3)
Sage said the answer is:
-w-1

My problem is: What is meant by the element w? 
Does it mean w=e^(2pi*i/3) or is it w=e^(2pi*i/3)^2?
Which one of the roots of unity does sage use as w? I dont know, how to find it 
out. It is really important for me, so it would be great if anyone could help 
me.
I cannot use the forum, because I am not allowed to ask questions.
Please help me!

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