Properties

Label 6003.2
Modulus $6003$
Conductor $6003$
Order $924$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6003)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([154,84,33]))
 
pari: [g,chi] = znchar(Mod(2,6003))
 

Basic properties

Modulus: \(6003\)
Conductor: \(6003\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(924\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6003.do

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

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

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

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{355}{924}\right)\)\(e\left(\frac{355}{462}\right)\)\(e\left(\frac{164}{231}\right)\)\(e\left(\frac{190}{231}\right)\)\(e\left(\frac{47}{308}\right)\)\(e\left(\frac{29}{308}\right)\)\(e\left(\frac{811}{924}\right)\)\(e\left(\frac{115}{462}\right)\)\(e\left(\frac{191}{924}\right)\)\(e\left(\frac{124}{231}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{924})$
Fixed field: Number field defined by a degree 924 polynomial