Properties

Conductor 64
Order 16
Real No
Primitive No
Parity Even
Orbit Label 2432.bd

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[2281]
 
pari: [g,chi] = znchar(Mod(2281,2432))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 64
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 16
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 2432.bd
Orbit index = 30

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 ]
 

\(\chi_{2432}(153,\cdot)\) \(\chi_{2432}(457,\cdot)\) \(\chi_{2432}(761,\cdot)\) \(\chi_{2432}(1065,\cdot)\) \(\chi_{2432}(1369,\cdot)\) \(\chi_{2432}(1673,\cdot)\) \(\chi_{2432}(1977,\cdot)\) \(\chi_{2432}(2281,\cdot)\)

Inducing primitive character

\(\chi_{64}(45,\cdot)\)

Values on generators

\((1407,2053,1921)\) → \((1,e\left(\frac{7}{16}\right),1)\)

Values

-113579111315172123
\(1\)\(1\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(-i\)\(i\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{1}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{16})\)