Properties

Conductor 100
Order 10
Real No
Primitive No
Parity Odd
Orbit Label 4000.bh

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(4000)
sage: chi = H[351]
pari: [g,chi] = znchar(Mod(351,4000))

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 = 4000.bh
Orbit index = 34

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 ]

\(\chi_{4000}(351,\cdot)\) \(\chi_{4000}(1151,\cdot)\) \(\chi_{4000}(1951,\cdot)\) \(\chi_{4000}(3551,\cdot)\)

Inducing primitive character

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

Values on generators

\((2751,2501,1377)\) → \((-1,1,e\left(\frac{3}{5}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{7}{10}\right)\)\(-1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{10}\right)\)
value at  e.g. 2

Related number fields

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