Properties

Conductor 100
Order 10
Real No
Primitive No
Parity Odd
Orbit Label 1800.bt

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[271]
 
pari: [g,chi] = znchar(Mod(271,1800))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 100
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.bt
Orbit index = 46

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 ]
 

\(\chi_{1800}(271,\cdot)\) \(\chi_{1800}(631,\cdot)\) \(\chi_{1800}(991,\cdot)\) \(\chi_{1800}(1711,\cdot)\)

Inducing primitive character

\(\chi_{100}(71,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((-1,1,1,e\left(\frac{3}{5}\right))\)

Values

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

Related number fields

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