Properties

Conductor 1001
Order 6
Real No
Primitive Yes
Parity Odd
Orbit Label 1001.bo

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(1001)
sage: chi = H[373]
pari: [g,chi] = znchar(Mod(373,1001))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1001
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 = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 1001.bo
Orbit index = 41

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 ]

\(\chi_{1001}(263,\cdot)\) \(\chi_{1001}(373,\cdot)\)

Values on generators

\((430,365,925)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{2}{3}\right))\)

Values

-112345689101215
\(-1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(1\)\(-1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)
value at  e.g. 2

Related number fields

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