Properties

 Label 287.t Modulus $287$ Conductor $287$ Order $20$ Real no Primitive yes Minimal yes Parity odd

Related objects

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

H = DirichletGroup(287, base_ring=CyclotomicField(20))

M = H._module

chi = DirichletCharacter(H, M([10,17]))

chi.galois_orbit()

[g,chi] = znchar(Mod(20,287))

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: $$20$$ 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)

Related number fields

 Field of values: $$\Q(\zeta_{20})$$ Fixed field: 20.0.1241291203716901419760482976136252014889.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{287}(20,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{287}(62,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{287}(90,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{287}(118,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{287}(125,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{287}(244,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{287}(251,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{287}(279,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$