Properties

Conductor 6003
Order 924
Real No
Primitive Yes
Parity Even
Orbit Label 6003.dp

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[40]
 
pari: [g,chi] = znchar(Mod(40,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 924
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.dp
Orbit index = 94

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 ]
 

\(\chi_{6003}(40,\cdot)\) \(\chi_{6003}(43,\cdot)\) \(\chi_{6003}(61,\cdot)\) \(\chi_{6003}(76,\cdot)\) \(\chi_{6003}(79,\cdot)\) \(\chi_{6003}(97,\cdot)\) \(\chi_{6003}(106,\cdot)\) \(\chi_{6003}(130,\cdot)\) \(\chi_{6003}(148,\cdot)\) \(\chi_{6003}(166,\cdot)\) \(\chi_{6003}(205,\cdot)\) \(\chi_{6003}(214,\cdot)\) \(\chi_{6003}(247,\cdot)\) \(\chi_{6003}(250,\cdot)\) \(\chi_{6003}(304,\cdot)\) \(\chi_{6003}(337,\cdot)\) \(\chi_{6003}(385,\cdot)\) \(\chi_{6003}(421,\cdot)\) \(\chi_{6003}(454,\cdot)\) \(\chi_{6003}(475,\cdot)\) \(\chi_{6003}(490,\cdot)\) \(\chi_{6003}(511,\cdot)\) \(\chi_{6003}(520,\cdot)\) \(\chi_{6003}(562,\cdot)\) \(\chi_{6003}(619,\cdot)\) \(\chi_{6003}(628,\cdot)\) \(\chi_{6003}(664,\cdot)\) \(\chi_{6003}(682,\cdot)\) \(\chi_{6003}(688,\cdot)\) \(\chi_{6003}(727,\cdot)\) ...

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{7}{22}\right),e\left(\frac{25}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{797}{924}\right)\)\(e\left(\frac{335}{462}\right)\)\(e\left(\frac{145}{231}\right)\)\(e\left(\frac{43}{462}\right)\)\(e\left(\frac{181}{308}\right)\)\(e\left(\frac{151}{308}\right)\)\(e\left(\frac{479}{924}\right)\)\(e\left(\frac{89}{462}\right)\)\(e\left(\frac{883}{924}\right)\)\(e\left(\frac{104}{231}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{924})\)