Properties

Conductor 667
Order 44
Real No
Primitive No
Parity Even
Orbit Label 6003.cc

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[244]
 
pari: [g,chi] = znchar(Mod(244,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 667
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 44
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.cc
Orbit index = 55

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 ]
 

\(\chi_{6003}(244,\cdot)\) \(\chi_{6003}(766,\cdot)\) \(\chi_{6003}(1027,\cdot)\) \(\chi_{6003}(1351,\cdot)\) \(\chi_{6003}(1873,\cdot)\) \(\chi_{6003}(2593,\cdot)\) \(\chi_{6003}(2656,\cdot)\) \(\chi_{6003}(2917,\cdot)\) \(\chi_{6003}(3115,\cdot)\) \(\chi_{6003}(3700,\cdot)\) \(\chi_{6003}(3898,\cdot)\) \(\chi_{6003}(3961,\cdot)\) \(\chi_{6003}(4159,\cdot)\) \(\chi_{6003}(4483,\cdot)\) \(\chi_{6003}(4942,\cdot)\) \(\chi_{6003}(5005,\cdot)\) \(\chi_{6003}(5203,\cdot)\) \(\chi_{6003}(5527,\cdot)\) \(\chi_{6003}(5725,\cdot)\) \(\chi_{6003}(5788,\cdot)\)

Inducing primitive character

\(\chi_{667}(244,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((1,e\left(\frac{21}{22}\right),i)\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{7}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)