# Properties

 Label 1375.868 Modulus $1375$ Conductor $275$ Order $20$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(1375, base_ring=CyclotomicField(20))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([7,10]))

pari: [g,chi] = znchar(Mod(868,1375))

## Basic properties

 Modulus: $$1375$$ Conductor: $$275$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$20$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{275}(153,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1375.bo

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: $$\Q(\zeta_{20})$$ Fixed field: 20.20.75487840807181783020496368408203125.1

## Values on generators

$$(1002,376)$$ → $$(e\left(\frac{7}{20}\right),-1)$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$12$$ $$13$$ $$14$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1375 }(868,a) \;$$ at $$\;a =$$ e.g. 2