Properties

Modulus 3600
Conductor 180
Order 12
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 3600.da

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3600)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6,0,2,9]))
 
pari: [g,chi] = znchar(Mod(1343,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 3600
Conductor = 180
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 12
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 3600.da
Orbit index = 79

Galois orbit

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

\(\chi_{3600}(1343,\cdot)\) \(\chi_{3600}(2207,\cdot)\) \(\chi_{3600}(2543,\cdot)\) \(\chi_{3600}(3407,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,1,e\left(\frac{1}{6}\right),-i)\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{12}\right)\)\(i\)\(1\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(-i\)\(e\left(\frac{5}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)