# Properties

 Label 4017.2105 Modulus $4017$ Conductor $4017$ Order $102$ Real no Primitive yes Minimal yes Parity even

# Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(4017, base_ring=CyclotomicField(102))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([51,51,79]))

pari: [g,chi] = znchar(Mod(2105,4017))

## Basic properties

 Modulus: $$4017$$ Conductor: $$4017$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$102$$ 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 4017.dp

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: $\Q(\zeta_{51})$ Fixed field: Number field defined by a degree 102 polynomial (not computed)

## Values on generators

$$(1340,1237,1756)$$ → $$(-1,-1,e\left(\frac{79}{102}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$14$$ $$16$$ $$17$$ $$1$$ $$1$$ $$e\left(\frac{4}{51}\right)$$ $$e\left(\frac{8}{51}\right)$$ $$e\left(\frac{79}{102}\right)$$ $$e\left(\frac{61}{102}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{25}{102}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{16}{51}\right)$$ $$e\left(\frac{73}{102}\right)$$
 value at e.g. 2