Properties

Conductor 561
Order 80
Real No
Primitive No
Parity Even
Orbit Label 5610.fd

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(5610)
 
sage: chi = H[71]
 
pari: [g,chi] = znchar(Mod(71,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 561
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 80
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 = 5610.fd
Orbit index = 134

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 ]
 

\(\chi_{5610}(71,\cdot)\) \(\chi_{5610}(311,\cdot)\) \(\chi_{5610}(401,\cdot)\) \(\chi_{5610}(521,\cdot)\) \(\chi_{5610}(581,\cdot)\) \(\chi_{5610}(641,\cdot)\) \(\chi_{5610}(911,\cdot)\) \(\chi_{5610}(1061,\cdot)\) \(\chi_{5610}(1391,\cdot)\) \(\chi_{5610}(1571,\cdot)\) \(\chi_{5610}(1841,\cdot)\) \(\chi_{5610}(1901,\cdot)\) \(\chi_{5610}(1961,\cdot)\) \(\chi_{5610}(2051,\cdot)\) \(\chi_{5610}(2171,\cdot)\) \(\chi_{5610}(2561,\cdot)\) \(\chi_{5610}(2621,\cdot)\) \(\chi_{5610}(2951,\cdot)\) \(\chi_{5610}(3371,\cdot)\) \(\chi_{5610}(3491,\cdot)\) \(\chi_{5610}(3611,\cdot)\) \(\chi_{5610}(3701,\cdot)\) \(\chi_{5610}(3881,\cdot)\) \(\chi_{5610}(3941,\cdot)\) \(\chi_{5610}(4151,\cdot)\) \(\chi_{5610}(4211,\cdot)\) \(\chi_{5610}(4481,\cdot)\) \(\chi_{5610}(4601,\cdot)\) \(\chi_{5610}(5021,\cdot)\) \(\chi_{5610}(5141,\cdot)\) ...

Inducing primitive character

\(\chi_{561}(71,\cdot)\)

Values on generators

\((1871,3367,1531,3301)\) → \((-1,1,e\left(\frac{2}{5}\right),e\left(\frac{1}{16}\right))\)

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{39}{80}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{9}{80}\right)\)\(e\left(\frac{77}{80}\right)\)\(e\left(\frac{69}{80}\right)\)\(e\left(\frac{31}{80}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{19}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{80})\)