LMFDB - Dirichlet character orbit 728.b

Properties

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(363,728))

order = charorder(g,chi)

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

Kronecker symbol representation

sage: kronecker_character(728)

pari: znchartokronecker(g,chi)

$\displaystyle\left(\frac{728}{\bullet}\right)$

Modulus:	$728$
Conductor:	$728$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$2$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	yes
Primitive:	yes	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{182})$

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{728}(363,\cdot)$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi