Properties

Conductor 4003
Order 69
Real No
Primitive Yes
Parity Even
Orbit Label 4003.i

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[129]
pari: [g,chi] = znchar(Mod(129,4003))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 69
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.i
Orbit index = 9

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 ]

\(\chi_{4003}(129,\cdot)\) \(\chi_{4003}(493,\cdot)\) \(\chi_{4003}(534,\cdot)\) \(\chi_{4003}(583,\cdot)\) \(\chi_{4003}(629,\cdot)\) \(\chi_{4003}(651,\cdot)\) \(\chi_{4003}(943,\cdot)\) \(\chi_{4003}(993,\cdot)\) \(\chi_{4003}(1183,\cdot)\) \(\chi_{4003}(1265,\cdot)\) \(\chi_{4003}(1311,\cdot)\) \(\chi_{4003}(1434,\cdot)\) \(\chi_{4003}(1543,\cdot)\) \(\chi_{4003}(1557,\cdot)\) \(\chi_{4003}(1752,\cdot)\) \(\chi_{4003}(1821,\cdot)\) \(\chi_{4003}(1825,\cdot)\) \(\chi_{4003}(1857,\cdot)\) \(\chi_{4003}(1866,\cdot)\) \(\chi_{4003}(1914,\cdot)\) \(\chi_{4003}(2015,\cdot)\) \(\chi_{4003}(2321,\cdot)\) \(\chi_{4003}(2434,\cdot)\) \(\chi_{4003}(2442,\cdot)\) \(\chi_{4003}(2487,\cdot)\) \(\chi_{4003}(2621,\cdot)\) \(\chi_{4003}(2735,\cdot)\) \(\chi_{4003}(2817,\cdot)\) \(\chi_{4003}(2869,\cdot)\) \(\chi_{4003}(2897,\cdot)\) ...

Values on generators

\(2\) → \(e\left(\frac{7}{69}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{69}\right)\)\(e\left(\frac{14}{69}\right)\)\(e\left(\frac{14}{69}\right)\)\(e\left(\frac{16}{69}\right)\)\(e\left(\frac{7}{23}\right)\)\(e\left(\frac{34}{69}\right)\)\(e\left(\frac{7}{23}\right)\)\(e\left(\frac{28}{69}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{23}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{69})\)