Properties

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

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[3125]
 
pari: [g,chi] = znchar(Mod(3125,6048))
 

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.iy
Orbit index = 233

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 ]
 

\(\chi_{6048}(5,\cdot)\) \(\chi_{6048}(101,\cdot)\) \(\chi_{6048}(509,\cdot)\) \(\chi_{6048}(605,\cdot)\) \(\chi_{6048}(1013,\cdot)\) \(\chi_{6048}(1109,\cdot)\) \(\chi_{6048}(1517,\cdot)\) \(\chi_{6048}(1613,\cdot)\) \(\chi_{6048}(2021,\cdot)\) \(\chi_{6048}(2117,\cdot)\) \(\chi_{6048}(2525,\cdot)\) \(\chi_{6048}(2621,\cdot)\) \(\chi_{6048}(3029,\cdot)\) \(\chi_{6048}(3125,\cdot)\) \(\chi_{6048}(3533,\cdot)\) \(\chi_{6048}(3629,\cdot)\) \(\chi_{6048}(4037,\cdot)\) \(\chi_{6048}(4133,\cdot)\) \(\chi_{6048}(4541,\cdot)\) \(\chi_{6048}(4637,\cdot)\) \(\chi_{6048}(5045,\cdot)\) \(\chi_{6048}(5141,\cdot)\) \(\chi_{6048}(5549,\cdot)\) \(\chi_{6048}(5645,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{7}{18}\right),e\left(\frac{1}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{29}{72}\right)\)\(e\left(\frac{61}{72}\right)\)\(e\left(\frac{71}{72}\right)\)\(-1\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{13}{36}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{19}{72}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{7}{24}\right)\)
value at  e.g. 2

Related number fields

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