Properties

Conductor 189
Order 18
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6048.go

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6048)
 
sage: chi = H[353]
 
pari: [g,chi] = znchar(Mod(353,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 189
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 18
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 = 6048.go
Orbit index = 171

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 ]
 

\(\chi_{6048}(257,\cdot)\) \(\chi_{6048}(353,\cdot)\) \(\chi_{6048}(2273,\cdot)\) \(\chi_{6048}(2369,\cdot)\) \(\chi_{6048}(4289,\cdot)\) \(\chi_{6048}(4385,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,1,e\left(\frac{1}{18}\right),e\left(\frac{1}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{17}{18}\right)\)\(1\)\(-1\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{2}{3}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{9})\)