Properties

Conductor 600
Order 10
Real No
Primitive No
Parity Odd
Orbit Label 1800.bp

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(1800)
 
sage: chi = H[269]
 
pari: [g,chi] = znchar(Mod(269,1800))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 600
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 10
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 = Odd
Orbit label = 1800.bp
Orbit index = 42

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 ]
 

\(\chi_{1800}(269,\cdot)\) \(\chi_{1800}(629,\cdot)\) \(\chi_{1800}(989,\cdot)\) \(\chi_{1800}(1709,\cdot)\)

Inducing primitive character

\(\chi_{600}(269,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((1,-1,-1,e\left(\frac{9}{10}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(-1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{1}{10}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{5})\)