# Properties

 Label 1805.q Modulus $1805$ Conductor $361$ Order $19$ Real no Primitive no Minimal yes Parity even

# Related objects

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

H = DirichletGroup(1805, base_ring=CyclotomicField(38))

M = H._module

chi = DirichletCharacter(H, M([0,16]))

chi.galois_orbit()

[g,chi] = znchar(Mod(96,1805))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1805$$ Conductor: $$361$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$19$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 361.g sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\zeta_{19})$$ Fixed field: 19.19.10842505080063916320800450434338728415281531281.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{1805}(96,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$
$$\chi_{1805}(191,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{1805}(286,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{1805}(381,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{1805}(476,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{1805}(571,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$
$$\chi_{1805}(666,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$
$$\chi_{1805}(761,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$
$$\chi_{1805}(856,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{1805}(951,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{1805}(1046,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{1805}(1141,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$
$$\chi_{1805}(1236,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{1805}(1331,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{1805}(1426,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$
$$\chi_{1805}(1521,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$
$$\chi_{1805}(1616,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{1805}(1711,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$