# Properties

 Label 2850.401 Modulus $2850$ Conductor $57$ Order $18$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(2850, base_ring=CyclotomicField(18))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([9,0,1]))

pari: [g,chi] = znchar(Mod(401,2850))

## Basic properties

 Modulus: $$2850$$ Conductor: $$57$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$18$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{57}(2,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2850.bk

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: $$\Q(\zeta_{9})$$ Fixed field: $$\Q(\zeta_{57})^+$$

## Values on generators

$$(1901,1027,1351)$$ → $$(-1,1,e\left(\frac{1}{18}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$
 value at e.g. 2