Properties

Conductor 187
Order 16
Real No
Primitive No
Parity Even
Orbit Label 8041.bt

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(8041)
 
sage: chi = H[1506]
 
pari: [g,chi] = znchar(Mod(1506,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 187
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 = 8041.bt
Orbit index = 46

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 ]
 

\(\chi_{8041}(1506,\cdot)\) \(\chi_{8041}(1979,\cdot)\) \(\chi_{8041}(3871,\cdot)\) \(\chi_{8041}(4817,\cdot)\) \(\chi_{8041}(5290,\cdot)\) \(\chi_{8041}(6236,\cdot)\) \(\chi_{8041}(6709,\cdot)\) \(\chi_{8041}(7655,\cdot)\)

Inducing primitive character

\(\chi_{187}(10,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{3}{16}\right),1)\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{3}{16}\right)\)\(i\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{7}{16}\right)\)
value at  e.g. 2

Related number fields

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