Properties

Modulus 1849
Conductor 43
Order 21
Real no
Primitive no
Minimal no
Parity even
Orbit label 1849.g

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1849)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2]))
 
pari: [g,chi] = znchar(Mod(210,1849))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1849
Conductor = 43
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 21
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1849.g
Orbit index = 7

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1849}(210,\cdot)\) \(\chi_{1849}(361,\cdot)\) \(\chi_{1849}(367,\cdot)\) \(\chi_{1849}(660,\cdot)\) \(\chi_{1849}(891,\cdot)\) \(\chi_{1849}(1085,\cdot)\) \(\chi_{1849}(1261,\cdot)\) \(\chi_{1849}(1557,\cdot)\) \(\chi_{1849}(1561,\cdot)\) \(\chi_{1849}(1573,\cdot)\) \(\chi_{1849}(1588,\cdot)\) \(\chi_{1849}(1830,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{2}{21}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{6}{7}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)