Properties

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

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[4957]
 
pari: [g,chi] = znchar(Mod(4957,6048))
 

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.jn
Orbit index = 248

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 ]
 

\(\chi_{6048}(85,\cdot)\) \(\chi_{6048}(421,\cdot)\) \(\chi_{6048}(589,\cdot)\) \(\chi_{6048}(925,\cdot)\) \(\chi_{6048}(1093,\cdot)\) \(\chi_{6048}(1429,\cdot)\) \(\chi_{6048}(1597,\cdot)\) \(\chi_{6048}(1933,\cdot)\) \(\chi_{6048}(2101,\cdot)\) \(\chi_{6048}(2437,\cdot)\) \(\chi_{6048}(2605,\cdot)\) \(\chi_{6048}(2941,\cdot)\) \(\chi_{6048}(3109,\cdot)\) \(\chi_{6048}(3445,\cdot)\) \(\chi_{6048}(3613,\cdot)\) \(\chi_{6048}(3949,\cdot)\) \(\chi_{6048}(4117,\cdot)\) \(\chi_{6048}(4453,\cdot)\) \(\chi_{6048}(4621,\cdot)\) \(\chi_{6048}(4957,\cdot)\) \(\chi_{6048}(5125,\cdot)\) \(\chi_{6048}(5461,\cdot)\) \(\chi_{6048}(5629,\cdot)\) \(\chi_{6048}(5965,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{2}{9}\right),1)\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{35}{72}\right)\)\(e\left(\frac{55}{72}\right)\)\(e\left(\frac{29}{72}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{35}{36}\right)\)\(e\left(\frac{25}{72}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{17}{24}\right)\)
value at  e.g. 2

Related number fields

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