Properties

Modulus 1035
Conductor 9
Order 3
Real no
Primitive no
Minimal yes
Parity even
Orbit label 1035.i

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1035)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,0,0]))
 
pari: [g,chi] = znchar(Mod(691,1035))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1035
Conductor = 9
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 3
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 = even
Orbit label = 1035.i
Orbit index = 9

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 ]
 

\(\chi_{1035}(346,\cdot)\) \(\chi_{1035}(691,\cdot)\)

Values on generators

\((461,622,856)\) → \((e\left(\frac{2}{3}\right),1,1)\)

Values

-112478111314161719
\(1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3})\)