Properties

Conductor 2432
Order 32
Real No
Primitive Yes
Parity Even
Orbit Label 2432.bv

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2432)
 
sage: chi = H[683]
 
pari: [g,chi] = znchar(Mod(683,2432))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2432
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 32
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 2432.bv
Orbit index = 48

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 ]
 

\(\chi_{2432}(75,\cdot)\) \(\chi_{2432}(227,\cdot)\) \(\chi_{2432}(379,\cdot)\) \(\chi_{2432}(531,\cdot)\) \(\chi_{2432}(683,\cdot)\) \(\chi_{2432}(835,\cdot)\) \(\chi_{2432}(987,\cdot)\) \(\chi_{2432}(1139,\cdot)\) \(\chi_{2432}(1291,\cdot)\) \(\chi_{2432}(1443,\cdot)\) \(\chi_{2432}(1595,\cdot)\) \(\chi_{2432}(1747,\cdot)\) \(\chi_{2432}(1899,\cdot)\) \(\chi_{2432}(2051,\cdot)\) \(\chi_{2432}(2203,\cdot)\) \(\chi_{2432}(2355,\cdot)\)

Values on generators

\((1407,2053,1921)\) → \((-1,e\left(\frac{29}{32}\right),-1)\)

Values

-113579111315172123
\(1\)\(1\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{29}{32}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{3}{32}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{9}{32}\right)\)\(e\left(\frac{3}{16}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{32})\)