Properties

Conductor 731
Order 48
Real No
Primitive No
Parity Even
Orbit Label 8041.dg

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(8041)
 
sage: chi = H[265]
 
pari: [g,chi] = znchar(Mod(265,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 731
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 48
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.dg
Orbit index = 85

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 ]
 

\(\chi_{8041}(265,\cdot)\) \(\chi_{8041}(639,\cdot)\) \(\chi_{8041}(738,\cdot)\) \(\chi_{8041}(1112,\cdot)\) \(\chi_{8041}(2630,\cdot)\) \(\chi_{8041}(3004,\cdot)\) \(\chi_{8041}(3576,\cdot)\) \(\chi_{8041}(3950,\cdot)\) \(\chi_{8041}(4049,\cdot)\) \(\chi_{8041}(4423,\cdot)\) \(\chi_{8041}(4995,\cdot)\) \(\chi_{8041}(5369,\cdot)\) \(\chi_{8041}(5468,\cdot)\) \(\chi_{8041}(5842,\cdot)\) \(\chi_{8041}(6414,\cdot)\) \(\chi_{8041}(6788,\cdot)\)

Inducing primitive character

\(\chi_{731}(265,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((1,e\left(\frac{3}{16}\right),e\left(\frac{5}{6}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{48}\right)\)\(i\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{13}{48}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{48})\)