Properties

Conductor 864
Order 72
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6048.jj

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[4523]
 
pari: [g,chi] = znchar(Mod(4523,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 864
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 72
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.jj
Orbit index = 244

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 ]
 

\(\chi_{6048}(155,\cdot)\) \(\chi_{6048}(491,\cdot)\) \(\chi_{6048}(659,\cdot)\) \(\chi_{6048}(995,\cdot)\) \(\chi_{6048}(1163,\cdot)\) \(\chi_{6048}(1499,\cdot)\) \(\chi_{6048}(1667,\cdot)\) \(\chi_{6048}(2003,\cdot)\) \(\chi_{6048}(2171,\cdot)\) \(\chi_{6048}(2507,\cdot)\) \(\chi_{6048}(2675,\cdot)\) \(\chi_{6048}(3011,\cdot)\) \(\chi_{6048}(3179,\cdot)\) \(\chi_{6048}(3515,\cdot)\) \(\chi_{6048}(3683,\cdot)\) \(\chi_{6048}(4019,\cdot)\) \(\chi_{6048}(4187,\cdot)\) \(\chi_{6048}(4523,\cdot)\) \(\chi_{6048}(4691,\cdot)\) \(\chi_{6048}(5027,\cdot)\) \(\chi_{6048}(5195,\cdot)\) \(\chi_{6048}(5531,\cdot)\) \(\chi_{6048}(5699,\cdot)\) \(\chi_{6048}(6035,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{17}{18}\right),1)\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{25}{72}\right)\)\(e\left(\frac{65}{72}\right)\)\(e\left(\frac{67}{72}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{59}{72}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{7}{24}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{72})\)