Properties

Conductor 667
Order 28
Real No
Primitive No
Parity Even
Orbit Label 6003.bq

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[298]
 
pari: [g,chi] = znchar(Mod(298,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 667
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 28
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.bq
Orbit index = 43

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 ]
 

\(\chi_{6003}(298,\cdot)\) \(\chi_{6003}(1540,\cdot)\) \(\chi_{6003}(1954,\cdot)\) \(\chi_{6003}(2161,\cdot)\) \(\chi_{6003}(2368,\cdot)\) \(\chi_{6003}(2782,\cdot)\) \(\chi_{6003}(2989,\cdot)\) \(\chi_{6003}(3403,\cdot)\) \(\chi_{6003}(3610,\cdot)\) \(\chi_{6003}(3817,\cdot)\) \(\chi_{6003}(4231,\cdot)\) \(\chi_{6003}(5473,\cdot)\)

Inducing primitive character

\(\chi_{667}(298,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((1,-1,e\left(\frac{3}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{3}{7}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{28})\)