# Properties

 Label 287.bb Modulus $287$ Conductor $287$ Order $40$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

H = DirichletGroup(287, base_ring=CyclotomicField(40))

M = H._module

chi = DirichletCharacter(H, M([20,1]))

chi.galois_orbit()

[g,chi] = znchar(Mod(6,287))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$287$$ Conductor: $$287$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$40$$ 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{287}(6,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{287}(13,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$
$$\chi_{287}(34,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$
$$\chi_{287}(48,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$
$$\chi_{287}(69,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{287}(76,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{287}(97,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{287}(104,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{287}(111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{287}(153,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$
$$\chi_{287}(181,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$
$$\chi_{287}(188,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$
$$\chi_{287}(216,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{287}(258,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$
$$\chi_{287}(265,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$
$$\chi_{287}(272,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$