Properties

 Label 2300.1841 Modulus $2300$ Conductor $25$ Order $5$ 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(10))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,2,0]))

pari: [g,chi] = znchar(Mod(1841,2300))

Basic properties

 Modulus: $$2300$$ Conductor: $$25$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$5$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{25}(16,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 2300.m

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: $$\Q(\zeta_{5})$$ Fixed field: 5.5.390625.1

Values on generators

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

Values

 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$27$$ $$29$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2300 }(1841,a) \;$$ at $$\;a =$$ e.g. 2