Properties

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

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[4475]
 
pari: [g,chi] = znchar(Mod(4475,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6048
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6048.jg
Orbit index = 241

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 ]
 

\(\chi_{6048}(347,\cdot)\) \(\chi_{6048}(443,\cdot)\) \(\chi_{6048}(851,\cdot)\) \(\chi_{6048}(947,\cdot)\) \(\chi_{6048}(1355,\cdot)\) \(\chi_{6048}(1451,\cdot)\) \(\chi_{6048}(1859,\cdot)\) \(\chi_{6048}(1955,\cdot)\) \(\chi_{6048}(2363,\cdot)\) \(\chi_{6048}(2459,\cdot)\) \(\chi_{6048}(2867,\cdot)\) \(\chi_{6048}(2963,\cdot)\) \(\chi_{6048}(3371,\cdot)\) \(\chi_{6048}(3467,\cdot)\) \(\chi_{6048}(3875,\cdot)\) \(\chi_{6048}(3971,\cdot)\) \(\chi_{6048}(4379,\cdot)\) \(\chi_{6048}(4475,\cdot)\) \(\chi_{6048}(4883,\cdot)\) \(\chi_{6048}(4979,\cdot)\) \(\chi_{6048}(5387,\cdot)\) \(\chi_{6048}(5483,\cdot)\) \(\chi_{6048}(5891,\cdot)\) \(\chi_{6048}(5987,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{7}{18}\right),e\left(\frac{1}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{53}{72}\right)\)\(e\left(\frac{37}{72}\right)\)\(e\left(\frac{71}{72}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{7}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{55}{72}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{8}\right)\)
value at  e.g. 2

Related number fields

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