Properties

Conductor 165
Order 2
Real Yes
Primitive No
Parity Even
Orbit Label 5610.o

Related objects

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Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(5610)
 
sage: chi = H[3299]
 
pari: [g,chi] = znchar(Mod(3299,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 165
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2
Real = Yes
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 = Even
Orbit label = 5610.o
Orbit index = 15

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 ]
 

\(\chi_{5610}(3299,\cdot)\)

Inducing primitive character

\(\chi_{165}(164,\cdot)\) = \(\displaystyle\left(\frac{165}{\bullet}\right)\)

Values on generators

\((1871,3367,1531,3301)\) → \((-1,-1,-1,1)\)

Values

-117131923293137414347
\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)