# Properties

 Label 7098.5203 Modulus $7098$ Conductor $1183$ Order $39$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(7098, base_ring=CyclotomicField(78))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,26,8]))

pari: [g,chi] = znchar(Mod(5203,7098))

## Basic properties

 Modulus: $$7098$$ Conductor: $$1183$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$39$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1183}(471,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 7098.cs

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: $\Q(\zeta_{39})$ Fixed field: 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2

## Values on generators

$$(4733,5071,6931)$$ → $$(1,e\left(\frac{1}{3}\right),e\left(\frac{4}{39}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 7098 }(5203,a) \;$$ at $$\;a =$$ e.g. 2