Properties

Conductor 261
Order 21
Real No
Primitive No
Parity Even
Orbit Label 6003.bh

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[139]
 
pari: [g,chi] = znchar(Mod(139,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 261
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 21
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.bh
Orbit index = 34

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 ]
 

\(\chi_{6003}(139,\cdot)\) \(\chi_{6003}(277,\cdot)\) \(\chi_{6003}(484,\cdot)\) \(\chi_{6003}(691,\cdot)\) \(\chi_{6003}(1312,\cdot)\) \(\chi_{6003}(2140,\cdot)\) \(\chi_{6003}(3244,\cdot)\) \(\chi_{6003}(4279,\cdot)\) \(\chi_{6003}(4486,\cdot)\) \(\chi_{6003}(4693,\cdot)\) \(\chi_{6003}(5245,\cdot)\) \(\chi_{6003}(5314,\cdot)\)

Inducing primitive character

\(\chi_{261}(139,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{5}{7}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{19}{21}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{11}{21}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{4}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)