# Properties

 Label 1476.5 Modulus $1476$ Conductor $369$ Order $60$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1476, base_ring=CyclotomicField(60))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,50,33]))

pari: [g,chi] = znchar(Mod(5,1476))

## Basic properties

 Modulus: $$1476$$ Conductor: $$369$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$60$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{369}(5,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1476.cg

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: $$\Q(\zeta_{60})$$ Fixed field: Number field defined by a degree 60 polynomial

## Values on generators

$$(739,821,1441)$$ → $$(1,e\left(\frac{5}{6}\right),e\left(\frac{11}{20}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$\chi_{ 1476 }(5, a)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1476 }(5,a) \;$$ at $$\;a =$$ e.g. 2