# Properties

 Label 3630.323 Modulus $3630$ Conductor $165$ Order $20$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(3630)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([10,15,4]))

pari: [g,chi] = znchar(Mod(323,3630))

## Basic properties

 Modulus: $$3630$$ Conductor: $$165$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$20$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{165}(158,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3630.x

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

$$(1211,727,3511)$$ → $$(-1,-i,e\left(\frac{1}{5}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{20})$$ Fixed field: 20.20.82802905234194108120391845703125.1