LMFDB - Dirichlet character orbit 4655.t

Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4655, base_ring=CyclotomicField(6))

M = H._module

chi = DirichletCharacter(H, M([3,4,4]))

chi.galois_orbit()

[g,chi] = znchar(Mod(4134,4655))

order = charorder(g,chi)

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

Basic properties

Modulus:	$4655$
Conductor:	$665$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$6$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 665.t	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.39112590125.1

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{4655}(4134,\cdot)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{4655}(4244,\cdot)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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