# Properties

 Modulus 3150 Conductor 175 Order 60 Real no Primitive no Minimal yes Parity even Orbit label 3150.em

# Learn more about

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

sage: H = DirichletGroup(3150)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,51,50]))

pari: [g,chi] = znchar(Mod(397,3150))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 3150 Conductor = 175 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 60 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 3150.em Orbit index = 117

## Galois orbit

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

$$(2801,127,451)$$ → $$(1,e\left(\frac{17}{20}\right),e\left(\frac{5}{6}\right))$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{60})$$