Properties

Modulus 1849
Conductor 1849
Order 301
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1849.m

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([212]))
 
pari: [g,chi] = znchar(Mod(4,1849))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1849
Conductor = 1849
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 301
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.m
Orbit index = 13

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 ]
 

\(\chi_{1849}(4,\cdot)\) \(\chi_{1849}(11,\cdot)\) \(\chi_{1849}(16,\cdot)\) \(\chi_{1849}(21,\cdot)\) \(\chi_{1849}(35,\cdot)\) \(\chi_{1849}(41,\cdot)\) \(\chi_{1849}(47,\cdot)\) \(\chi_{1849}(54,\cdot)\) \(\chi_{1849}(59,\cdot)\) \(\chi_{1849}(64,\cdot)\) \(\chi_{1849}(84,\cdot)\) \(\chi_{1849}(90,\cdot)\) \(\chi_{1849}(97,\cdot)\) \(\chi_{1849}(102,\cdot)\) \(\chi_{1849}(107,\cdot)\) \(\chi_{1849}(121,\cdot)\) \(\chi_{1849}(127,\cdot)\) \(\chi_{1849}(133,\cdot)\) \(\chi_{1849}(140,\cdot)\) \(\chi_{1849}(145,\cdot)\) \(\chi_{1849}(150,\cdot)\) \(\chi_{1849}(164,\cdot)\) \(\chi_{1849}(170,\cdot)\) \(\chi_{1849}(176,\cdot)\) \(\chi_{1849}(183,\cdot)\) \(\chi_{1849}(188,\cdot)\) \(\chi_{1849}(193,\cdot)\) \(\chi_{1849}(207,\cdot)\) \(\chi_{1849}(213,\cdot)\) \(\chi_{1849}(219,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{212}{301}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{285}{301}\right)\)\(e\left(\frac{212}{301}\right)\)\(e\left(\frac{269}{301}\right)\)\(e\left(\frac{281}{301}\right)\)\(e\left(\frac{28}{43}\right)\)\(e\left(\frac{24}{43}\right)\)\(e\left(\frac{253}{301}\right)\)\(e\left(\frac{123}{301}\right)\)\(e\left(\frac{265}{301}\right)\)\(e\left(\frac{270}{301}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{301})\)