Properties

Conductor 21
Order 6
Real No
Primitive No
Parity Even
Orbit Label 9450.bf

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(9450)
sage: chi = H[4751]
pari: [g,chi] = znchar(Mod(4751,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 21
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 6
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 = 9450.bf
Orbit index = 32

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 ]

\(\chi_{9450}(4751,\cdot)\) \(\chi_{9450}(7451,\cdot)\)

Inducing primitive character

\(\chi_{21}(5,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((-1,1,e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{6}\right)\)\(-1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3})\)