# Properties

 Modulus 6017 Conductor 6017 Order 910 Real no Primitive yes Minimal yes Parity even Orbit label 6017.cf

# Learn more about

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

sage: H = DirichletGroup(6017)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([91,515]))

pari: [g,chi] = znchar(Mod(343,6017))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 6017 Conductor = 6017 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 910 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 6017.cf Orbit index = 58

## 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

$$(3830,2190)$$ → $$(e\left(\frac{1}{10}\right),e\left(\frac{103}{182}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 12 $$1$$ $$1$$ $$e\left(\frac{303}{455}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{151}{455}\right)$$ $$e\left(\frac{639}{910}\right)$$ $$e\left(\frac{229}{910}\right)$$ $$e\left(\frac{451}{455}\right)$$ $$e\left(\frac{454}{455}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{67}{182}\right)$$ $$e\left(\frac{167}{182}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{455})$$