# Properties

 Label 2300.243 Modulus $2300$ Conductor $460$ Order $44$ Real no Primitive no Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(2300, base_ring=CyclotomicField(44))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([22,33,28]))

pari: [g,chi] = znchar(Mod(243,2300))

## Basic properties

 Modulus: $$2300$$ Conductor: $$460$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{460}(243,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2300.bi

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

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

## Values

 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$ $$1$$ $$1$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2300 }(243,a) \;$$ at $$\;a =$$ e.g. 2