Properties

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

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[461]
 
pari: [g,chi] = znchar(Mod(461,6048))
 

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.jm
Orbit index = 247

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 ]
 

\(\chi_{6048}(293,\cdot)\) \(\chi_{6048}(461,\cdot)\) \(\chi_{6048}(797,\cdot)\) \(\chi_{6048}(965,\cdot)\) \(\chi_{6048}(1301,\cdot)\) \(\chi_{6048}(1469,\cdot)\) \(\chi_{6048}(1805,\cdot)\) \(\chi_{6048}(1973,\cdot)\) \(\chi_{6048}(2309,\cdot)\) \(\chi_{6048}(2477,\cdot)\) \(\chi_{6048}(2813,\cdot)\) \(\chi_{6048}(2981,\cdot)\) \(\chi_{6048}(3317,\cdot)\) \(\chi_{6048}(3485,\cdot)\) \(\chi_{6048}(3821,\cdot)\) \(\chi_{6048}(3989,\cdot)\) \(\chi_{6048}(4325,\cdot)\) \(\chi_{6048}(4493,\cdot)\) \(\chi_{6048}(4829,\cdot)\) \(\chi_{6048}(4997,\cdot)\) \(\chi_{6048}(5333,\cdot)\) \(\chi_{6048}(5501,\cdot)\) \(\chi_{6048}(5837,\cdot)\) \(\chi_{6048}(6005,\cdot)\)

Values on generators

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

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{47}{72}\right)\)\(e\left(\frac{7}{72}\right)\)\(e\left(\frac{5}{72}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{11}{36}\right)\)\(e\left(\frac{49}{72}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{24}\right)\)
value at  e.g. 2

Related number fields

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