Properties

Label 6003.40
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([308,294,825]))
 
pari: [g,chi] = znchar(Mod(40,6003))
 

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.dp

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

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

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

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\(1\)\(1\)\(e\left(\frac{797}{924}\right)\)\(e\left(\frac{335}{462}\right)\)\(e\left(\frac{145}{231}\right)\)\(e\left(\frac{43}{462}\right)\)\(e\left(\frac{181}{308}\right)\)\(e\left(\frac{151}{308}\right)\)\(e\left(\frac{479}{924}\right)\)\(e\left(\frac{89}{462}\right)\)\(e\left(\frac{883}{924}\right)\)\(e\left(\frac{104}{231}\right)\)
value at e.g. 2

Related number fields

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