Properties

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

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[3469]
 
pari: [g,chi] = znchar(Mod(3469,6048))
 

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.jk
Orbit index = 245

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 ]
 

\(\chi_{6048}(205,\cdot)\) \(\chi_{6048}(445,\cdot)\) \(\chi_{6048}(709,\cdot)\) \(\chi_{6048}(949,\cdot)\) \(\chi_{6048}(1213,\cdot)\) \(\chi_{6048}(1453,\cdot)\) \(\chi_{6048}(1717,\cdot)\) \(\chi_{6048}(1957,\cdot)\) \(\chi_{6048}(2221,\cdot)\) \(\chi_{6048}(2461,\cdot)\) \(\chi_{6048}(2725,\cdot)\) \(\chi_{6048}(2965,\cdot)\) \(\chi_{6048}(3229,\cdot)\) \(\chi_{6048}(3469,\cdot)\) \(\chi_{6048}(3733,\cdot)\) \(\chi_{6048}(3973,\cdot)\) \(\chi_{6048}(4237,\cdot)\) \(\chi_{6048}(4477,\cdot)\) \(\chi_{6048}(4741,\cdot)\) \(\chi_{6048}(4981,\cdot)\) \(\chi_{6048}(5245,\cdot)\) \(\chi_{6048}(5485,\cdot)\) \(\chi_{6048}(5749,\cdot)\) \(\chi_{6048}(5989,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{4}{9}\right),e\left(\frac{2}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{31}{72}\right)\)\(e\left(\frac{59}{72}\right)\)\(e\left(\frac{49}{72}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{5}{72}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{7}{8}\right)\)
value at  e.g. 2

Related number fields

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