Properties

Conductor 189
Order 9
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6048.dt

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[961]
 
pari: [g,chi] = znchar(Mod(961,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 189
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 9
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.dt
Orbit index = 98

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 ]
 

\(\chi_{6048}(193,\cdot)\) \(\chi_{6048}(961,\cdot)\) \(\chi_{6048}(2209,\cdot)\) \(\chi_{6048}(2977,\cdot)\) \(\chi_{6048}(4225,\cdot)\) \(\chi_{6048}(4993,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,1,e\left(\frac{2}{9}\right),e\left(\frac{1}{3}\right))\)

Values

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

Related number fields

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