Properties

Conductor 69
Order 22
Real No
Primitive No
Parity Even
Orbit Label 6003.bm

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(6003)
 
sage: chi = H[494]
 
pari: [g,chi] = znchar(Mod(494,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 69
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 22
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 = 6003.bm
Orbit index = 39

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 ]
 

\(\chi_{6003}(494,\cdot)\) \(\chi_{6003}(755,\cdot)\) \(\chi_{6003}(1538,\cdot)\) \(\chi_{6003}(1799,\cdot)\) \(\chi_{6003}(2321,\cdot)\) \(\chi_{6003}(2843,\cdot)\) \(\chi_{6003}(3365,\cdot)\) \(\chi_{6003}(3626,\cdot)\) \(\chi_{6003}(5192,\cdot)\) \(\chi_{6003}(5714,\cdot)\)

Inducing primitive character

\(\chi_{69}(11,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,e\left(\frac{9}{22}\right),1)\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{3}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{11})\)