# Properties

 Label 1110.ce Modulus $1110$ Conductor $37$ 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([0,0,29]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(61,1110))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1110$$ Conductor: $$37$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 37.i sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{36})$$ Fixed field: $$\Q(\zeta_{37})$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$41$$ $$43$$
$$\chi_{1110}(61,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{11}{18}\right)$$ $$-i$$
$$\chi_{1110}(91,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{18}\right)$$ $$i$$
$$\chi_{1110}(241,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{17}{18}\right)$$ $$i$$
$$\chi_{1110}(301,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{18}\right)$$ $$i$$
$$\chi_{1110}(331,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{18}\right)$$ $$i$$
$$\chi_{1110}(631,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{1}{18}\right)$$ $$-i$$
$$\chi_{1110}(661,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{5}{18}\right)$$ $$-i$$
$$\chi_{1110}(721,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{17}{18}\right)$$ $$-i$$
$$\chi_{1110}(871,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{7}{18}\right)$$ $$-i$$
$$\chi_{1110}(901,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{11}{18}\right)$$ $$i$$
$$\chi_{1110}(1021,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{13}{18}\right)$$ $$i$$
$$\chi_{1110}(1051,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{13}{18}\right)$$ $$-i$$