# Properties

 Label 9652.35 Modulus $9652$ Conductor $9652$ Order $126$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(9652, base_ring=CyclotomicField(126))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([63,28,76]))

pari: [g,chi] = znchar(Mod(35,9652))

## Basic properties

 Modulus: $$9652$$ Conductor: $$9652$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$126$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 9652.iz

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: $\Q(\zeta_{63})$ Fixed field: Number field defined by a degree 126 polynomial (not computed)

## Values on generators

$$(4827,7621,8893)$$ → $$(-1,e\left(\frac{2}{9}\right),e\left(\frac{38}{63}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$21$$ $$23$$ $$-1$$ $$1$$ $$e\left(\frac{125}{126}\right)$$ $$e\left(\frac{2}{63}\right)$$ $$e\left(\frac{25}{126}\right)$$ $$e\left(\frac{62}{63}\right)$$ $$e\left(\frac{23}{126}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 9652 }(35,a) \;$$ at $$\;a =$$ e.g. 2