Properties

Modulus 3234
Conductor 539
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.br

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3234)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,29,21]))
 
pari: [g,chi] = znchar(Mod(2749,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 3234
Conductor = 539
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 42
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 = 3234.br
Orbit index = 44

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 ]
 

\(\chi_{3234}(241,\cdot)\) \(\chi_{3234}(439,\cdot)\) \(\chi_{3234}(703,\cdot)\) \(\chi_{3234}(1165,\cdot)\) \(\chi_{3234}(1363,\cdot)\) \(\chi_{3234}(1627,\cdot)\) \(\chi_{3234}(1825,\cdot)\) \(\chi_{3234}(2287,\cdot)\) \(\chi_{3234}(2551,\cdot)\) \(\chi_{3234}(2749,\cdot)\) \(\chi_{3234}(3013,\cdot)\) \(\chi_{3234}(3211,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{29}{42}\right),-1)\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{6}{7}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)