Properties

Conductor 77
Order 15
Real no
Primitive no
Minimal no
Parity even
Orbit label 3234.bg

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[361]
 
pari: [g,chi] = znchar(Mod(361,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 77
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 15
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 = 3234.bg
Orbit index = 33

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 ]
 

\(\chi_{3234}(361,\cdot)\) \(\chi_{3234}(949,\cdot)\) \(\chi_{3234}(961,\cdot)\) \(\chi_{3234}(1549,\cdot)\) \(\chi_{3234}(1831,\cdot)\) \(\chi_{3234}(2137,\cdot)\) \(\chi_{3234}(3007,\cdot)\) \(\chi_{3234}(3019,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{3}{5}\right))\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{4}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)