Properties

Label 896.bi
Modulus $896$
Conductor $224$
Order $24$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(896, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,9,20]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(47,896))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(896\)
Conductor: \(224\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 224.be
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.790224330201082600125157415256880139617697792.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{896}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{896}(143,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{896}(271,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{896}(367,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{896}(495,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{896}(591,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{896}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{896}(815,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\)