Properties

Conductor 7
Order 3
Real No
Primitive No
Parity Even
Orbit Label 1169.e

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(1169)
sage: chi = H[669]
pari: [g,chi] = znchar(Mod(669,1169))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 7
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 3
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 = 1169.e
Orbit index = 5

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 ]

\(\chi_{1169}(669,\cdot)\) \(\chi_{1169}(1003,\cdot)\)

Inducing primitive character

\(\chi_{7}(4,\cdot)\)

Values on generators

\((836,673)\) → \((e\left(\frac{2}{3}\right),1)\)

Values

-112345689101112
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

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