Properties

Label 4928.199
Modulus $4928$
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(4928, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,15,4,0]))
 
pari: [g,chi] = znchar(Mod(199,4928))
 

Basic properties

Modulus: \(4928\)
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 \(\chi_{224}(171,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4928.dp

\(\chi_{4928}(199,\cdot)\) \(\chi_{4928}(551,\cdot)\) \(\chi_{4928}(1431,\cdot)\) \(\chi_{4928}(1783,\cdot)\) \(\chi_{4928}(2663,\cdot)\) \(\chi_{4928}(3015,\cdot)\) \(\chi_{4928}(3895,\cdot)\) \(\chi_{4928}(4247,\cdot)\)

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: 24.24.790224330201082600125157415256880139617697792.1

Values on generators

\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{1}{6}\right),1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 4928 }(199, a) \) \(1\)\(1\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{8}\right)\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{8}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4928 }(199,a) \;\) at \(\;a = \) e.g. 2