Properties

Conductor 4003
Order 23
Real No
Primitive Yes
Parity Even
Orbit Label 4003.e

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[551]
 
pari: [g,chi] = znchar(Mod(551,4003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 23
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.e
Orbit index = 5

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 ]
 

\(\chi_{4003}(551,\cdot)\) \(\chi_{4003}(703,\cdot)\) \(\chi_{4003}(835,\cdot)\) \(\chi_{4003}(848,\cdot)\) \(\chi_{4003}(1081,\cdot)\) \(\chi_{4003}(1173,\cdot)\) \(\chi_{4003}(1358,\cdot)\) \(\chi_{4003}(1840,\cdot)\) \(\chi_{4003}(1960,\cdot)\) \(\chi_{4003}(2567,\cdot)\) \(\chi_{4003}(2723,\cdot)\) \(\chi_{4003}(2784,\cdot)\) \(\chi_{4003}(2900,\cdot)\) \(\chi_{4003}(3065,\cdot)\) \(\chi_{4003}(3153,\cdot)\) \(\chi_{4003}(3187,\cdot)\) \(\chi_{4003}(3251,\cdot)\) \(\chi_{4003}(3376,\cdot)\) \(\chi_{4003}(3552,\cdot)\) \(\chi_{4003}(3688,\cdot)\) \(\chi_{4003}(3700,\cdot)\) \(\chi_{4003}(3743,\cdot)\)

Values on generators

\(2\) → \(e\left(\frac{18}{23}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{18}{23}\right)\)\(e\left(\frac{13}{23}\right)\)\(e\left(\frac{13}{23}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{8}{23}\right)\)\(e\left(\frac{2}{23}\right)\)\(e\left(\frac{8}{23}\right)\)\(e\left(\frac{3}{23}\right)\)\(1\)\(e\left(\frac{11}{23}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{23})\)