LMFDB - Dirichlet character orbit 1640.bl

Properties

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1640, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([0,0,3,1]))

chi.galois_orbit()

[g,chi] = znchar(Mod(73,1640))

order = charorder(g,chi)

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

Basic properties

Modulus:	$1640$
Conductor:	$205$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$4$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 205.i	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:	4.0.8615125.2

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1640}(73,\cdot)$	$-1$	$1$	$1$	$-1$	$1$	$-i$	$1$	$1$	$-i$	$-1$	$i$	$1$
$\chi_{1640}(337,\cdot)$	$-1$	$1$	$1$	$-1$	$1$	$i$	$1$	$1$	$i$	$-1$	$-i$	$1$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi