Properties

Label 6048.5363
Modulus $6048$
Conductor $288$
Order $24$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6048)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([12,21,20,0]))
 
pari: [g,chi] = znchar(Mod(5363,6048))
 

Basic properties

Modulus: \(6048\)
Conductor: \(288\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{288}(275,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6048.hz

\(\chi_{6048}(827,\cdot)\) \(\chi_{6048}(1331,\cdot)\) \(\chi_{6048}(2339,\cdot)\) \(\chi_{6048}(2843,\cdot)\) \(\chi_{6048}(3851,\cdot)\) \(\chi_{6048}(4355,\cdot)\) \(\chi_{6048}(5363,\cdot)\) \(\chi_{6048}(5867,\cdot)\)

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

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),1)\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{19}{24}\right)\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{7}{8}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.1486465269728735333725176976133731985582456832.1