# Properties

 Label 185.bc Modulus $185$ Conductor $185$ Order $36$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(185, base_ring=CyclotomicField(36))

sage: M = H._module

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

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(2,185))

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Basic properties

 Modulus: $$185$$ Conductor: $$185$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{185}(2,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$-i$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{185}(13,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$i$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{185}(32,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$-i$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{185}(52,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$-i$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{185}(57,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$-i$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{185}(92,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$-i$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{185}(93,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$i$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{185}(128,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$i$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{185}(133,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$i$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{185}(153,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$i$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{185}(172,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-i$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{185}(183,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$i$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$