LMFDB - Dirichlet character orbit 5850.z

Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5850, base_ring=CyclotomicField(6))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(1699,5850))

order = charorder(g,chi)

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

Basic properties

Modulus:	$5850$
Conductor:	$585$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$6$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 585.bl	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:	6.6.23423590125.2

Character	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{5850}(1699,\cdot)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$
$\chi_{5850}(1849,\cdot)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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