Properties

Conductor 288
Order 24
Real no
Primitive no
Minimal no
Parity even
Orbit label 4032.gl

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4032)
 
sage: chi = H[407]
 
pari: [g,chi] = znchar(Mod(407,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 288
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 24
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4032.gl
Orbit index = 168

Galois orbit

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

\(\chi_{4032}(407,\cdot)\) \(\chi_{4032}(743,\cdot)\) \(\chi_{4032}(1415,\cdot)\) \(\chi_{4032}(1751,\cdot)\) \(\chi_{4032}(2423,\cdot)\) \(\chi_{4032}(2759,\cdot)\) \(\chi_{4032}(3431,\cdot)\) \(\chi_{4032}(3767,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{1}{6}\right),1)\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{11}{24}\right)\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{24})\)