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Let $\chi$ be the trivial Dirichlet character mod $N$. What is the primitive Dirichlet character associated to $\chi$? Is it just the character on $\mathbb{Z}$ that sends all integers to 1?

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Yes, exactly. :)

Here are more characters to meet the minimum.

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    Maaaaan.... this software situation is not ... useful... Sorry if my responses are [obstructed-by] ...2011-12-08