Properties

Label 4928.219
Modulus $4928$
Conductor $4928$
Order $48$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4928, base_ring=CyclotomicField(48))
 
M = H._module
 
chi = DirichletCharacter(H, M([24,27,16,24]))
 
pari: [g,chi] = znchar(Mod(219,4928))
 

Basic properties

Modulus: \(4928\)
Conductor: \(4928\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4928.et

\(\chi_{4928}(219,\cdot)\) \(\chi_{4928}(571,\cdot)\) \(\chi_{4928}(835,\cdot)\) \(\chi_{4928}(1187,\cdot)\) \(\chi_{4928}(1451,\cdot)\) \(\chi_{4928}(1803,\cdot)\) \(\chi_{4928}(2067,\cdot)\) \(\chi_{4928}(2419,\cdot)\) \(\chi_{4928}(2683,\cdot)\) \(\chi_{4928}(3035,\cdot)\) \(\chi_{4928}(3299,\cdot)\) \(\chi_{4928}(3651,\cdot)\) \(\chi_{4928}(3915,\cdot)\) \(\chi_{4928}(4267,\cdot)\) \(\chi_{4928}(4531,\cdot)\) \(\chi_{4928}(4883,\cdot)\)

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: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{1}{3}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 4928 }(219, a) \) \(1\)\(1\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{15}{16}\right)\)\(-i\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{9}{16}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4928 }(219,a) \;\) at \(\;a = \) e.g. 2