Properties

Conductor 147
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.bw

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(3234)
 
sage: chi = H[89]
 
pari: [g,chi] = znchar(Mod(89,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 147
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.bw
Orbit index = 49

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 ]
 

\(\chi_{3234}(89,\cdot)\) \(\chi_{3234}(353,\cdot)\) \(\chi_{3234}(551,\cdot)\) \(\chi_{3234}(1013,\cdot)\) \(\chi_{3234}(1277,\cdot)\) \(\chi_{3234}(1475,\cdot)\) \(\chi_{3234}(1739,\cdot)\) \(\chi_{3234}(1937,\cdot)\) \(\chi_{3234}(2201,\cdot)\) \(\chi_{3234}(2399,\cdot)\) \(\chi_{3234}(2663,\cdot)\) \(\chi_{3234}(3125,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((-1,e\left(\frac{23}{42}\right),1)\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{21}\right)\)\(e\left(\frac{5}{7}\right)\)
value at  e.g. 2

Related number fields

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