Properties

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

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[4307]
 
pari: [g,chi] = znchar(Mod(4307,6048))
 

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.jv
Orbit index = 256

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 ]
 

\(\chi_{6048}(11,\cdot)\) \(\chi_{6048}(275,\cdot)\) \(\chi_{6048}(515,\cdot)\) \(\chi_{6048}(779,\cdot)\) \(\chi_{6048}(1019,\cdot)\) \(\chi_{6048}(1283,\cdot)\) \(\chi_{6048}(1523,\cdot)\) \(\chi_{6048}(1787,\cdot)\) \(\chi_{6048}(2027,\cdot)\) \(\chi_{6048}(2291,\cdot)\) \(\chi_{6048}(2531,\cdot)\) \(\chi_{6048}(2795,\cdot)\) \(\chi_{6048}(3035,\cdot)\) \(\chi_{6048}(3299,\cdot)\) \(\chi_{6048}(3539,\cdot)\) \(\chi_{6048}(3803,\cdot)\) \(\chi_{6048}(4043,\cdot)\) \(\chi_{6048}(4307,\cdot)\) \(\chi_{6048}(4547,\cdot)\) \(\chi_{6048}(4811,\cdot)\) \(\chi_{6048}(5051,\cdot)\) \(\chi_{6048}(5315,\cdot)\) \(\chi_{6048}(5555,\cdot)\) \(\chi_{6048}(5819,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{17}{18}\right),e\left(\frac{1}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{19}{72}\right)\)\(e\left(\frac{35}{72}\right)\)\(e\left(\frac{49}{72}\right)\)\(1\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{41}{72}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{5}{24}\right)\)
value at  e.g. 2

Related number fields

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