David,

I was looking at DualAbelianGroup.  I'm very surprised you made it map to
floating point complex numbers, at least for finite groups.  It would make
way more sense to make to a cyclotomic field instead, since everything  
would
be exact then.  That's how I define Dirichlet characters, which are the
dual group of (Z/nZ)^*.   (Actually, with Dirichlet characters, one can  
also
map to CC if desired -- it's an option.)

William


sage: G.<a> = DirichletGroup(11)
sage: a(2)
zeta10

sage: parent(a(2))
Cyclotomic Field of order 10 and degree 4

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