Properties

Conductor 4003
Order 29
Real No
Primitive Yes
Parity Even
Orbit Label 4003.f

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[102]
pari: [g,chi] = znchar(Mod(102,4003))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 29
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.f
Orbit index = 6

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 ]

\(\chi_{4003}(102,\cdot)\) \(\chi_{4003}(168,\cdot)\) \(\chi_{4003}(203,\cdot)\) \(\chi_{4003}(413,\cdot)\) \(\chi_{4003}(691,\cdot)\) \(\chi_{4003}(1000,\cdot)\) \(\chi_{4003}(1124,\cdot)\) \(\chi_{4003}(1170,\cdot)\) \(\chi_{4003}(1179,\cdot)\) \(\chi_{4003}(1333,\cdot)\) \(\chi_{4003}(1633,\cdot)\) \(\chi_{4003}(1925,\cdot)\) \(\chi_{4003}(2080,\cdot)\) \(\chi_{4003}(2096,\cdot)\) \(\chi_{4003}(2118,\cdot)\) \(\chi_{4003}(2140,\cdot)\) \(\chi_{4003}(2398,\cdot)\) \(\chi_{4003}(2431,\cdot)\) \(\chi_{4003}(2443,\cdot)\) \(\chi_{4003}(2484,\cdot)\) \(\chi_{4003}(2564,\cdot)\) \(\chi_{4003}(2850,\cdot)\) \(\chi_{4003}(3160,\cdot)\) \(\chi_{4003}(3253,\cdot)\) \(\chi_{4003}(3560,\cdot)\) \(\chi_{4003}(3779,\cdot)\) \(\chi_{4003}(3867,\cdot)\) \(\chi_{4003}(3877,\cdot)\)

Values on generators

\(2\) → \(e\left(\frac{17}{29}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{29}\right)\)\(e\left(\frac{25}{29}\right)\)\(e\left(\frac{5}{29}\right)\)\(e\left(\frac{9}{29}\right)\)\(e\left(\frac{13}{29}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{22}{29}\right)\)\(e\left(\frac{21}{29}\right)\)\(e\left(\frac{26}{29}\right)\)\(e\left(\frac{10}{29}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{29})\)