Properties

Conductor 3021
Order 12
Real No
Primitive No
Parity Even
Orbit Label 6042.x

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(6042)
 
sage: chi = H[83]
 
pari: [g,chi] = znchar(Mod(83,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 12
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 = 6042.x
Orbit index = 24

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 ]
 

\(\chi_{6042}(83,\cdot)\) \(\chi_{6042}(1037,\cdot)\) \(\chi_{6042}(2249,\cdot)\) \(\chi_{6042}(3203,\cdot)\)

Inducing primitive character

\(\chi_{3021}(83,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{3}\right),i)\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{7}{12}\right)\)\(-1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(i\)\(e\left(\frac{1}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)