The Gauss sum for the Dirichlet character modulo 1 is equal to 1, but:
sage: G = DirichletGroup(1)
sage: chi = G.list()[0]
sage: chi.gauss_sum()
0
The output is zero because the gauss_sum function in modular/dirichlet.py,
after some preliminaries, computes the following:
for c in chi.values()[1:]:
z *= zeta
g += L(c)*z
return g
If chi.modulus() > 1, then chi.values()[0] equals 0, so it can be skipped
in the sum above. But in this case, it equals 1 and needs to be included in
the sum
I'm using 8.2 beta 7.
Best,
Nicolás.
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