# Properties

 Label 1849.431 Modulus $1849$ Conductor $1849$ Order $43$ Real no Primitive yes Minimal yes Parity even

# Related objects

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([10]))

pari: [g,chi] = znchar(Mod(431,1849))

## 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

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

$$3$$ → $$e\left(\frac{5}{43}\right)$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$e\left(\frac{41}{43}\right)$$ $$e\left(\frac{5}{43}\right)$$ $$e\left(\frac{39}{43}\right)$$ $$e\left(\frac{19}{43}\right)$$ $$e\left(\frac{3}{43}\right)$$ $$e\left(\frac{21}{43}\right)$$ $$e\left(\frac{37}{43}\right)$$ $$e\left(\frac{10}{43}\right)$$ $$e\left(\frac{17}{43}\right)$$ $$e\left(\frac{23}{43}\right)$$
 value at e.g. 2