Properties

Modulus 1035
Conductor 1035
Order 6
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1035.r

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([4,3,3]))
 
pari: [g,chi] = znchar(Mod(574,1035))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1035
Conductor = 1035
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 6
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1035.r
Orbit index = 18

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 ]
 

\(\chi_{1035}(229,\cdot)\) \(\chi_{1035}(574,\cdot)\)

Values on generators

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

Values

-112478111314161719
\(-1\)\(1\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(-1\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(1\)\(-1\)
value at  e.g. 2

Related number fields

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