# Properties

 Label 916.p Modulus $916$ Conductor $916$ Order $38$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(916, base_ring=CyclotomicField(38))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([19,28]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(27,916))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$916$$ Conductor: $$916$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$38$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{916}(27,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{916}(43,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{916}(203,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$
$$\chi_{916}(271,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$
$$\chi_{916}(443,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{916}(447,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$
$$\chi_{916}(475,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$
$$\chi_{916}(511,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{916}(515,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{916}(519,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{916}(579,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{916}(619,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$
$$\chi_{916}(623,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{916}(683,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$
$$\chi_{916}(703,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{916}(731,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{916}(747,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{916}(791,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$