LMFDB - Dirichlet character orbit 720.bo

Properties

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([2,1,0,0]))

chi.galois_orbit()

[g,chi] = znchar(Mod(91,720))

order = charorder(g,chi)

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

Basic properties

Modulus:	$720$
Conductor:	$16$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$4$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 16.f	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage: chi.is_odd() pari: zncharisodd(g,chi)

Field of values:	$\mathbb{Q}(i)$
Fixed field:	4.0.2048.2

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{720}(91,\cdot)$	$-1$	$1$	$1$	$-i$	$-i$	$1$	$i$	$1$	$-i$	$-1$	$i$	$-1$
$\chi_{720}(451,\cdot)$	$-1$	$1$	$1$	$i$	$i$	$1$	$-i$	$1$	$i$	$-1$	$-i$	$-1$

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi