Properties

Label 6012.43
Modulus $6012$
Conductor $6012$
Order $498$
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(6012)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([249,332,261]))
 
pari: [g,chi] = znchar(Mod(43,6012))
 

Basic properties

Modulus: \(6012\)
Conductor: \(6012\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(498\)
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 6012.z

\(\chi_{6012}(43,\cdot)\) \(\chi_{6012}(67,\cdot)\) \(\chi_{6012}(79,\cdot)\) \(\chi_{6012}(103,\cdot)\) \(\chi_{6012}(139,\cdot)\) \(\chi_{6012}(151,\cdot)\) \(\chi_{6012}(187,\cdot)\) \(\chi_{6012}(247,\cdot)\) \(\chi_{6012}(259,\cdot)\) \(\chi_{6012}(331,\cdot)\) \(\chi_{6012}(403,\cdot)\) \(\chi_{6012}(439,\cdot)\) \(\chi_{6012}(463,\cdot)\) \(\chi_{6012}(499,\cdot)\) \(\chi_{6012}(511,\cdot)\) \(\chi_{6012}(535,\cdot)\) \(\chi_{6012}(547,\cdot)\) \(\chi_{6012}(571,\cdot)\) \(\chi_{6012}(583,\cdot)\) \(\chi_{6012}(607,\cdot)\) \(\chi_{6012}(619,\cdot)\) \(\chi_{6012}(643,\cdot)\) \(\chi_{6012}(691,\cdot)\) \(\chi_{6012}(727,\cdot)\) \(\chi_{6012}(751,\cdot)\) \(\chi_{6012}(763,\cdot)\) \(\chi_{6012}(787,\cdot)\) \(\chi_{6012}(799,\cdot)\) \(\chi_{6012}(823,\cdot)\) \(\chi_{6012}(895,\cdot)\) ...

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

\((3007,3341,4681)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{87}{166}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{427}{498}\right)\)\(e\left(\frac{5}{498}\right)\)\(e\left(\frac{419}{498}\right)\)\(e\left(\frac{157}{498}\right)\)\(e\left(\frac{129}{166}\right)\)\(e\left(\frac{149}{166}\right)\)\(e\left(\frac{179}{249}\right)\)\(e\left(\frac{178}{249}\right)\)\(e\left(\frac{70}{249}\right)\)\(e\left(\frac{1}{498}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{249})$
Fixed field: Number field defined by a degree 498 polynomial