Properties

Conductor 6003
Order 462
Real No
Primitive Yes
Parity Even
Orbit Label 6003.dk

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[4]
 
pari: [g,chi] = znchar(Mod(4,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 462
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6003.dk
Orbit index = 89

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 ]
 

\(\chi_{6003}(4,\cdot)\) \(\chi_{6003}(13,\cdot)\) \(\chi_{6003}(121,\cdot)\) \(\chi_{6003}(151,\cdot)\) \(\chi_{6003}(187,\cdot)\) \(\chi_{6003}(196,\cdot)\) \(\chi_{6003}(238,\cdot)\) \(\chi_{6003}(265,\cdot)\) \(\chi_{6003}(328,\cdot)\) \(\chi_{6003}(439,\cdot)\) \(\chi_{6003}(499,\cdot)\) \(\chi_{6003}(535,\cdot)\) \(\chi_{6003}(556,\cdot)\) \(\chi_{6003}(673,\cdot)\) \(\chi_{6003}(763,\cdot)\) \(\chi_{6003}(817,\cdot)\) \(\chi_{6003}(961,\cdot)\) \(\chi_{6003}(970,\cdot)\) \(\chi_{6003}(979,\cdot)\) \(\chi_{6003}(1021,\cdot)\) \(\chi_{6003}(1024,\cdot)\) \(\chi_{6003}(1048,\cdot)\) \(\chi_{6003}(1066,\cdot)\) \(\chi_{6003}(1222,\cdot)\) \(\chi_{6003}(1231,\cdot)\) \(\chi_{6003}(1327,\cdot)\) \(\chi_{6003}(1501,\cdot)\) \(\chi_{6003}(1543,\cdot)\) \(\chi_{6003}(1570,\cdot)\) \(\chi_{6003}(1600,\cdot)\) ...

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{11}\right),e\left(\frac{1}{14}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{355}{462}\right)\)\(e\left(\frac{124}{231}\right)\)\(e\left(\frac{97}{231}\right)\)\(e\left(\frac{149}{231}\right)\)\(e\left(\frac{47}{154}\right)\)\(e\left(\frac{29}{154}\right)\)\(e\left(\frac{349}{462}\right)\)\(e\left(\frac{115}{231}\right)\)\(e\left(\frac{191}{462}\right)\)\(e\left(\frac{17}{231}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{231})\)