# Properties

 Label 2300.9 Modulus $2300$ Conductor $575$ Order $110$ 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(2300, base_ring=CyclotomicField(110))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,77,50]))

pari: [g,chi] = znchar(Mod(9,2300))

## Basic properties

 Modulus: $$2300$$ Conductor: $$575$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$110$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{575}(9,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2300.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: $\Q(\zeta_{55})$ Fixed field: Number field defined by a degree 110 polynomial (not computed)

## Values on generators

$$(1151,277,1201)$$ → $$(1,e\left(\frac{7}{10}\right),e\left(\frac{5}{11}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$ $$1$$ $$1$$ $$e\left(\frac{19}{110}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{73}{110}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{57}{110}\right)$$ $$e\left(\frac{32}{55}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2300 }(9,a) \;$$ at $$\;a =$$ e.g. 2