Properties

Modulus 1849
Conductor 1849
Order 43
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1849.i

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([22]))
 
pari: [g,chi] = znchar(Mod(44,1849))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1849
Conductor = 1849
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 43
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1849.i
Orbit index = 9

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 ]
 

\(\chi_{1849}(44,\cdot)\) \(\chi_{1849}(87,\cdot)\) \(\chi_{1849}(130,\cdot)\) \(\chi_{1849}(173,\cdot)\) \(\chi_{1849}(216,\cdot)\) \(\chi_{1849}(259,\cdot)\) \(\chi_{1849}(302,\cdot)\) \(\chi_{1849}(345,\cdot)\) \(\chi_{1849}(388,\cdot)\) \(\chi_{1849}(431,\cdot)\) \(\chi_{1849}(474,\cdot)\) \(\chi_{1849}(517,\cdot)\) \(\chi_{1849}(560,\cdot)\) \(\chi_{1849}(603,\cdot)\) \(\chi_{1849}(646,\cdot)\) \(\chi_{1849}(689,\cdot)\) \(\chi_{1849}(732,\cdot)\) \(\chi_{1849}(775,\cdot)\) \(\chi_{1849}(818,\cdot)\) \(\chi_{1849}(861,\cdot)\) \(\chi_{1849}(904,\cdot)\) \(\chi_{1849}(947,\cdot)\) \(\chi_{1849}(990,\cdot)\) \(\chi_{1849}(1033,\cdot)\) \(\chi_{1849}(1076,\cdot)\) \(\chi_{1849}(1119,\cdot)\) \(\chi_{1849}(1162,\cdot)\) \(\chi_{1849}(1205,\cdot)\) \(\chi_{1849}(1248,\cdot)\) \(\chi_{1849}(1291,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{22}{43}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{43}\right)\)\(e\left(\frac{22}{43}\right)\)\(e\left(\frac{34}{43}\right)\)\(e\left(\frac{32}{43}\right)\)\(e\left(\frac{39}{43}\right)\)\(e\left(\frac{15}{43}\right)\)\(e\left(\frac{8}{43}\right)\)\(e\left(\frac{1}{43}\right)\)\(e\left(\frac{6}{43}\right)\)\(e\left(\frac{41}{43}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{43})\)