Properties

Modulus 6030
Conductor 1
Order 1
Real yes
Primitive no
Minimal yes
Parity even
Orbit label 6030.a

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6030)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,0]))
 
pari: [g,chi] = znchar(Mod(1,6030))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6030
Conductor = 1
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1
Real = yes
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 = even
Orbit label = 6030.a
Orbit index = 1

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 ]
 

\(\chi_{6030}(1,\cdot)\)

Values on generators

\((4691,1207,3151)\) → \((1,1,1)\)

Values

-117111317192329313741
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)