LMFDB - Dirichlet character orbit 345.f

Properties

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(254,345))

order = charorder(g,chi)

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

Basic properties

Modulus:	$345$
Conductor:	$15$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$2$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	yes
Primitive:	no, induced from 15.d	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:	$\Q(\sqrt{-15})$

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{345}(254,\cdot)$	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi