Properties

Label 1792.bh
Modulus $1792$
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(1792, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,21,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(289,1792))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1792\)
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.bd
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: 24.24.329123002999201416128761938882499016916992.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1792}(417,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1792}(737,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1792}(865,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1792}(1185,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1792}(1313,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1792}(1633,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1792}(1761,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)