Properties

Label 4928.41
Modulus $4928$
Conductor $2464$
Order $40$
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(40))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,35,20,12]))
 
pari: [g,chi] = znchar(Mod(41,4928))
 

Basic properties

Modulus: \(4928\)
Conductor: \(2464\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(40\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2464}(1581,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4928.ep

\(\chi_{4928}(41,\cdot)\) \(\chi_{4928}(601,\cdot)\) \(\chi_{4928}(937,\cdot)\) \(\chi_{4928}(1161,\cdot)\) \(\chi_{4928}(1273,\cdot)\) \(\chi_{4928}(1833,\cdot)\) \(\chi_{4928}(2169,\cdot)\) \(\chi_{4928}(2393,\cdot)\) \(\chi_{4928}(2505,\cdot)\) \(\chi_{4928}(3065,\cdot)\) \(\chi_{4928}(3401,\cdot)\) \(\chi_{4928}(3625,\cdot)\) \(\chi_{4928}(3737,\cdot)\) \(\chi_{4928}(4297,\cdot)\) \(\chi_{4928}(4633,\cdot)\) \(\chi_{4928}(4857,\cdot)\)

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: \(\Q(\zeta_{40})\)
Fixed field: Number field defined by a degree 40 polynomial

Values on generators

\((4159,1541,2817,3137)\) → \((1,e\left(\frac{7}{8}\right),-1,e\left(\frac{3}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)\(27\)
\( \chi_{ 4928 }(41, a) \) \(1\)\(1\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{37}{40}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{21}{40}\right)\)\(i\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{23}{40}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4928 }(41,a) \;\) at \(\;a = \) e.g. 2