Properties

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

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[1699]
 
pari: [g,chi] = znchar(Mod(1699,6048))
 

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.jh
Orbit index = 242

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 ]
 

\(\chi_{6048}(187,\cdot)\) \(\chi_{6048}(283,\cdot)\) \(\chi_{6048}(691,\cdot)\) \(\chi_{6048}(787,\cdot)\) \(\chi_{6048}(1195,\cdot)\) \(\chi_{6048}(1291,\cdot)\) \(\chi_{6048}(1699,\cdot)\) \(\chi_{6048}(1795,\cdot)\) \(\chi_{6048}(2203,\cdot)\) \(\chi_{6048}(2299,\cdot)\) \(\chi_{6048}(2707,\cdot)\) \(\chi_{6048}(2803,\cdot)\) \(\chi_{6048}(3211,\cdot)\) \(\chi_{6048}(3307,\cdot)\) \(\chi_{6048}(3715,\cdot)\) \(\chi_{6048}(3811,\cdot)\) \(\chi_{6048}(4219,\cdot)\) \(\chi_{6048}(4315,\cdot)\) \(\chi_{6048}(4723,\cdot)\) \(\chi_{6048}(4819,\cdot)\) \(\chi_{6048}(5227,\cdot)\) \(\chi_{6048}(5323,\cdot)\) \(\chi_{6048}(5731,\cdot)\) \(\chi_{6048}(5827,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{5}{9}\right),e\left(\frac{5}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{23}{72}\right)\)\(e\left(\frac{67}{72}\right)\)\(e\left(\frac{41}{72}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{49}{72}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{3}{8}\right)\)
value at  e.g. 2

Related number fields

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