Properties

Conductor 2003
Order 286
Real No
Primitive Yes
Parity Odd
Orbit Label 2003.n

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(2003)
 
sage: chi = H[2]
 
pari: [g,chi] = znchar(Mod(2,2003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 286
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 = 2003.n
Orbit index = 14

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 ]
 

\(\chi_{2003}(2,\cdot)\) \(\chi_{2003}(8,\cdot)\) \(\chi_{2003}(11,\cdot)\) \(\chi_{2003}(21,\cdot)\) \(\chi_{2003}(23,\cdot)\) \(\chi_{2003}(32,\cdot)\) \(\chi_{2003}(44,\cdot)\) \(\chi_{2003}(67,\cdot)\) \(\chi_{2003}(71,\cdot)\) \(\chi_{2003}(84,\cdot)\) \(\chi_{2003}(92,\cdot)\) \(\chi_{2003}(128,\cdot)\) \(\chi_{2003}(149,\cdot)\) \(\chi_{2003}(176,\cdot)\) \(\chi_{2003}(178,\cdot)\) \(\chi_{2003}(195,\cdot)\) \(\chi_{2003}(226,\cdot)\) \(\chi_{2003}(239,\cdot)\) \(\chi_{2003}(242,\cdot)\) \(\chi_{2003}(249,\cdot)\) \(\chi_{2003}(268,\cdot)\) \(\chi_{2003}(284,\cdot)\) \(\chi_{2003}(310,\cdot)\) \(\chi_{2003}(313,\cdot)\) \(\chi_{2003}(336,\cdot)\) \(\chi_{2003}(348,\cdot)\) \(\chi_{2003}(364,\cdot)\) \(\chi_{2003}(368,\cdot)\) \(\chi_{2003}(370,\cdot)\) \(\chi_{2003}(377,\cdot)\) ...

Values on generators

\(5\) → \(e\left(\frac{191}{286}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{255}{286}\right)\)\(e\left(\frac{10}{143}\right)\)\(e\left(\frac{112}{143}\right)\)\(e\left(\frac{191}{286}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{41}{286}\right)\)\(e\left(\frac{193}{286}\right)\)\(e\left(\frac{20}{143}\right)\)\(e\left(\frac{80}{143}\right)\)\(e\left(\frac{207}{286}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{143})\)