LMFDB - Dirichlet character orbit 101.c

Properties

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Show commands: PariGP / SageMath

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(101, base_ring=CyclotomicField(4))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(10,101))

order = charorder(g,chi)

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

Basic properties

Modulus:	$101$
Conductor:	$101$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$4$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	yes	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:	4.0.1030301.1

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{101}(10,\cdot)$	$-1$	$1$	$i$	$i$	$-1$	$1$	$-1$	$i$	$-i$	$-1$	$i$	$i$
$\chi_{101}(91,\cdot)$	$-1$	$1$	$-i$	$-i$	$-1$	$1$	$-1$	$-i$	$i$	$-1$	$-i$	$-i$

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