# Properties

 Label 1110.109 Modulus $1110$ Conductor $185$ Order $36$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1110, base_ring=CyclotomicField(36))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,18,19]))

pari: [g,chi] = znchar(Mod(109,1110))

## Basic properties

 Modulus: $$1110$$ Conductor: $$185$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{185}(109,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1110.cf

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: $$\Q(\zeta_{36})$$ Fixed field: 36.0.29411719834995153896864925426307140281034671856927417346954345703125.1

## Values on generators

$$(371,667,631)$$ → $$(1,-1,e\left(\frac{19}{36}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$ $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{18}\right)$$ $$-i$$
 value at e.g. 2