Properties

Conductor 315
Order 12
Real no
Primitive no
Minimal no
Parity even
Orbit label 9450.ch

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(9450)
 
sage: chi = H[5743]
 
pari: [g,chi] = znchar(Mod(5743,9450))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 315
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 12
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 9450.ch
Orbit index = 60

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 ]
 

\(\chi_{9450}(1207,\cdot)\) \(\chi_{9450}(1657,\cdot)\) \(\chi_{9450}(5743,\cdot)\) \(\chi_{9450}(6193,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{1}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(-1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)