Properties

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

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[2]
 
pari: [g,chi] = znchar(Mod(2,6003))
 

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.do
Orbit index = 93

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 ]
 

\(\chi_{6003}(2,\cdot)\) \(\chi_{6003}(32,\cdot)\) \(\chi_{6003}(50,\cdot)\) \(\chi_{6003}(77,\cdot)\) \(\chi_{6003}(95,\cdot)\) \(\chi_{6003}(101,\cdot)\) \(\chi_{6003}(119,\cdot)\) \(\chi_{6003}(131,\cdot)\) \(\chi_{6003}(164,\cdot)\) \(\chi_{6003}(200,\cdot)\) \(\chi_{6003}(308,\cdot)\) \(\chi_{6003}(311,\cdot)\) \(\chi_{6003}(317,\cdot)\) \(\chi_{6003}(338,\cdot)\) \(\chi_{6003}(374,\cdot)\) \(\chi_{6003}(380,\cdot)\) \(\chi_{6003}(416,\cdot)\) \(\chi_{6003}(443,\cdot)\) \(\chi_{6003}(446,\cdot)\) \(\chi_{6003}(491,\cdot)\) \(\chi_{6003}(524,\cdot)\) \(\chi_{6003}(533,\cdot)\) \(\chi_{6003}(554,\cdot)\) \(\chi_{6003}(578,\cdot)\) \(\chi_{6003}(623,\cdot)\) \(\chi_{6003}(653,\cdot)\) \(\chi_{6003}(698,\cdot)\) \(\chi_{6003}(722,\cdot)\) \(\chi_{6003}(740,\cdot)\) \(\chi_{6003}(752,\cdot)\) ...

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{11}\right),e\left(\frac{1}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{355}{924}\right)\)\(e\left(\frac{355}{462}\right)\)\(e\left(\frac{164}{231}\right)\)\(e\left(\frac{190}{231}\right)\)\(e\left(\frac{47}{308}\right)\)\(e\left(\frac{29}{308}\right)\)\(e\left(\frac{811}{924}\right)\)\(e\left(\frac{115}{462}\right)\)\(e\left(\frac{191}{924}\right)\)\(e\left(\frac{124}{231}\right)\)
value at  e.g. 2

Related number fields

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