Properties

Label 1849.474
Modulus $1849$
Conductor $1849$
Order $43$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1849, base_ring=CyclotomicField(86))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([54]))
 
pari: [g,chi] = znchar(Mod(474,1849))
 

Basic properties

Modulus: \(1849\)
Conductor: \(1849\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(43\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1849.i

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

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

Related number fields

Field of values: $\Q(\zeta_{43})$
Fixed field: 43.43.162686032778208990102858628859785420567496242104134005559503199497609643882923419981647276367075859293620549051195773051892887390454194801.1

Values on generators

\(3\) → \(e\left(\frac{27}{43}\right)\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{15}{43}\right)\)\(e\left(\frac{27}{43}\right)\)\(e\left(\frac{30}{43}\right)\)\(e\left(\frac{8}{43}\right)\)\(e\left(\frac{42}{43}\right)\)\(e\left(\frac{36}{43}\right)\)\(e\left(\frac{2}{43}\right)\)\(e\left(\frac{11}{43}\right)\)\(e\left(\frac{23}{43}\right)\)\(e\left(\frac{21}{43}\right)\)
value at e.g. 2