LMFDB - Dirichlet character \(\chi

Properties

Related objects

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

M = H._module

chi = DirichletCharacter(H, M([1,0,1,0]))

pari: [g,chi] = znchar(Mod(647,1224))

Basic properties

Modulus:	$1224$
Conductor:	$12$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$2$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	yes
Primitive:	no, induced from $\chi_{12}(11,\cdot)$	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)

sage: chi.galois_orbit()

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{3})$

$(919,613,137,649)$ → $(-1,1,-1,1)$

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 1224 }(647, a)$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$

sage: chi.jacobi_sum(n)

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi