Properties

Modulus 1849
Conductor 1849
Order 903
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1849.o

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([1]))
 
pari: [g,chi] = znchar(Mod(9,1849))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1849
Conductor = 1849
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 903
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.o
Orbit index = 15

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 ]
 

\(\chi_{1849}(9,\cdot)\) \(\chi_{1849}(10,\cdot)\) \(\chi_{1849}(13,\cdot)\) \(\chi_{1849}(14,\cdot)\) \(\chi_{1849}(15,\cdot)\) \(\chi_{1849}(17,\cdot)\) \(\chi_{1849}(23,\cdot)\) \(\chi_{1849}(24,\cdot)\) \(\chi_{1849}(25,\cdot)\) \(\chi_{1849}(31,\cdot)\) \(\chi_{1849}(38,\cdot)\) \(\chi_{1849}(40,\cdot)\) \(\chi_{1849}(52,\cdot)\) \(\chi_{1849}(53,\cdot)\) \(\chi_{1849}(56,\cdot)\) \(\chi_{1849}(57,\cdot)\) \(\chi_{1849}(58,\cdot)\) \(\chi_{1849}(60,\cdot)\) \(\chi_{1849}(66,\cdot)\) \(\chi_{1849}(67,\cdot)\) \(\chi_{1849}(68,\cdot)\) \(\chi_{1849}(74,\cdot)\) \(\chi_{1849}(81,\cdot)\) \(\chi_{1849}(83,\cdot)\) \(\chi_{1849}(95,\cdot)\) \(\chi_{1849}(96,\cdot)\) \(\chi_{1849}(99,\cdot)\) \(\chi_{1849}(100,\cdot)\) \(\chi_{1849}(101,\cdot)\) \(\chi_{1849}(103,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{1}{903}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{212}{301}\right)\)\(e\left(\frac{1}{903}\right)\)\(e\left(\frac{123}{301}\right)\)\(e\left(\frac{193}{903}\right)\)\(e\left(\frac{91}{129}\right)\)\(e\left(\frac{35}{129}\right)\)\(e\left(\frac{34}{301}\right)\)\(e\left(\frac{2}{903}\right)\)\(e\left(\frac{829}{903}\right)\)\(e\left(\frac{185}{301}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{903})\)