LMFDB - Dirichlet character \(\chi

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Show commands: PariGP / SageMath

H = DirichletGroup(3097600)

chi = H[1]

pari: [g,chi] = znchar(Mod(1,3097600))

Basic properties

Modulus:	$3097600$
Conductor:	$1$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$1$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	yes
Primitive:	no, induced from $\chi_{1}(0,\cdot)$	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)

\Q

$(1252351,592901,2354177,2918401)$ → $(1,1,1,1)$

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 3097600 }(1, a)$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$

sage: chi.jacobi_sum(n)

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Classical	Maass
Hilbert	Bianchi