Properties

Conductor 60
Order 4
Real No
Primitive No
Parity Odd
Orbit Label 3600.bk

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(3600)
 
sage: chi = H[143]
 
pari: [g,chi] = znchar(Mod(143,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 60
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 4
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 3600.bk
Orbit index = 37

Galois orbit

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

\(\chi_{3600}(143,\cdot)\) \(\chi_{3600}(1007,\cdot)\)

Inducing primitive character

\(\chi_{60}(23,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,1,-1,-i)\)

Values

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

Related number fields

Field of values \(\Q(i)\)