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### Understanding Output in SageMath Regarding Dirichlet Characters

 p=7
G = DirichletGroup(p); G

m=3; n=ZZ((p-1)/m); print m,n

c=G[1]

c1=c^n;c1


The output is:

Dirichlet character modulo 7 of conductor 7 mapping 3 |--> zeta6 - 1


Can anyone explain what zeta6 is? Is this the Riemann-Zeta function? Is this the whole group of units? Is there a relation to the Eisenstein primes? I'm still a bit weak in this material and am having trouble grasping some of these sage outputs. Thank you in advance!

 2 retagged FrédéricC 5141 ●3 ●43 ●112

### Understanding Output in SageMath Regarding Dirichlet Characters

 p=7
G = DirichletGroup(p); G

m=3; n=ZZ((p-1)/m); print m,n

c=G[1]

c1=c^n;c1


The output is:

Dirichlet character modulo 7 of conductor 7 mapping 3 |--> zeta6 - 1


Can anyone explain what zeta6 is? Is this the Riemann-Zeta function? Is this the whole group of units? Is there a relation to the Eisenstein primes? I'm still a bit weak in this material and am having trouble grasping some of these sage outputs. Thank you in advance!