Properties

Label 1792.929
Modulus $1792$
Conductor $224$
Order $24$
Real no
Primitive no
Minimal no
Parity odd

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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([0,9,20]))
 
pari: [g,chi] = znchar(Mod(929,1792))
 

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 \(\chi_{224}(61,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1792.bg

\(\chi_{1792}(33,\cdot)\) \(\chi_{1792}(353,\cdot)\) \(\chi_{1792}(481,\cdot)\) \(\chi_{1792}(801,\cdot)\) \(\chi_{1792}(929,\cdot)\) \(\chi_{1792}(1249,\cdot)\) \(\chi_{1792}(1377,\cdot)\) \(\chi_{1792}(1697,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.0.790224330201082600125157415256880139617697792.1

Values on generators

\((1023,1541,1025)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\( \chi_{ 1792 }(929, a) \) \(-1\)\(1\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{1}{8}\right)\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{12}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1792 }(929,a) \;\) at \(\;a = \) e.g. 2