LMFDB - Dirichlet character orbit 72.h

Properties

Learn more

Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(53,72))

order = charorder(g,chi)

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

Basic properties

Modulus:	$72$
Conductor:	$24$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$2$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	yes
Primitive:	no, induced from 24.h	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage: chi.is_odd() pari: zncharisodd(g,chi)

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{-6})$

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{72}(53,\cdot)$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi