Properties

Conductor 2805
Order 20
Real No
Primitive No
Parity Even
Orbit Label 5610.ee

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[863]
 
pari: [g,chi] = znchar(Mod(863,5610))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2805
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 20
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.ee
Orbit index = 109

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 ]
 

\(\chi_{5610}(863,\cdot)\) \(\chi_{5610}(1373,\cdot)\) \(\chi_{5610}(2027,\cdot)\) \(\chi_{5610}(3413,\cdot)\) \(\chi_{5610}(3557,\cdot)\) \(\chi_{5610}(4943,\cdot)\) \(\chi_{5610}(5087,\cdot)\) \(\chi_{5610}(5597,\cdot)\)

Inducing primitive character

\(\chi_{2805}(863,\cdot)\)

Values on generators

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

Values

-117131923293137414347
\(1\)\(1\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{1}{5}\right)\)\(-1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{9}{20}\right)\)\(-i\)\(e\left(\frac{9}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)