Properties

Label 6048.3365
Modulus $6048$
Conductor $2016$
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(6048, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,20,20]))
 
pari: [g,chi] = znchar(Mod(3365,6048))
 

Basic properties

Modulus: \(6048\)
Conductor: \(2016\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2016}(5,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6048.hk

\(\chi_{6048}(341,\cdot)\) \(\chi_{6048}(1277,\cdot)\) \(\chi_{6048}(1853,\cdot)\) \(\chi_{6048}(2789,\cdot)\) \(\chi_{6048}(3365,\cdot)\) \(\chi_{6048}(4301,\cdot)\) \(\chi_{6048}(4877,\cdot)\) \(\chi_{6048}(5813,\cdot)\)

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: 24.24.118608432644346900933171742046091098112592780299359440267640832.2

Values on generators

\((4159,3781,3809,2593)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\( \chi_{ 6048 }(3365, a) \) \(1\)\(1\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{5}{24}\right)\)\(-1\)\(e\left(\frac{19}{24}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6048 }(3365,a) \;\) at \(\;a = \) e.g. 2