Properties

Conductor 4003
Order 667
Real No
Primitive Yes
Parity Even
Orbit Label 4003.m

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(4003)
sage: chi = H[6]
pari: [g,chi] = znchar(Mod(6,4003))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 667
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 = Even
Orbit label = 4003.m
Orbit index = 13

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 ]

\(\chi_{4003}(6,\cdot)\) \(\chi_{4003}(11,\cdot)\) \(\chi_{4003}(13,\cdot)\) \(\chi_{4003}(15,\cdot)\) \(\chi_{4003}(17,\cdot)\) \(\chi_{4003}(28,\cdot)\) \(\chi_{4003}(36,\cdot)\) \(\chi_{4003}(64,\cdot)\) \(\chi_{4003}(66,\cdot)\) \(\chi_{4003}(69,\cdot)\) \(\chi_{4003}(70,\cdot)\) \(\chi_{4003}(73,\cdot)\) \(\chi_{4003}(76,\cdot)\) \(\chi_{4003}(78,\cdot)\) \(\chi_{4003}(86,\cdot)\) \(\chi_{4003}(90,\cdot)\) \(\chi_{4003}(93,\cdot)\) \(\chi_{4003}(94,\cdot)\) \(\chi_{4003}(103,\cdot)\) \(\chi_{4003}(121,\cdot)\) \(\chi_{4003}(142,\cdot)\) \(\chi_{4003}(143,\cdot)\) \(\chi_{4003}(149,\cdot)\) \(\chi_{4003}(151,\cdot)\) \(\chi_{4003}(160,\cdot)\) \(\chi_{4003}(165,\cdot)\) \(\chi_{4003}(169,\cdot)\) \(\chi_{4003}(175,\cdot)\) \(\chi_{4003}(183,\cdot)\) \(\chi_{4003}(187,\cdot)\) ...

Values on generators

\(2\) → \(e\left(\frac{403}{667}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{403}{667}\right)\)\(e\left(\frac{231}{667}\right)\)\(e\left(\frac{139}{667}\right)\)\(e\left(\frac{517}{667}\right)\)\(e\left(\frac{634}{667}\right)\)\(e\left(\frac{239}{667}\right)\)\(e\left(\frac{542}{667}\right)\)\(e\left(\frac{462}{667}\right)\)\(e\left(\frac{11}{29}\right)\)\(e\left(\frac{452}{667}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{667})\)