Properties

 Label 517.i Modulus $517$ Conductor $47$ Order $23$ Real no Primitive no Minimal yes Parity even

Related objects

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

sage: H = DirichletGroup(517, base_ring=CyclotomicField(46))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,10]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(12,517))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$517$$ Conductor: $$47$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$23$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 47.c 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: $$\Q(\zeta_{23})$$ Fixed field: $$\Q(\zeta_{47})^+$$

Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{517}(12,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$
$$\chi_{517}(34,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{517}(56,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$
$$\chi_{517}(89,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$
$$\chi_{517}(100,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$
$$\chi_{517}(111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$
$$\chi_{517}(122,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$
$$\chi_{517}(144,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$
$$\chi_{517}(155,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$
$$\chi_{517}(166,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$
$$\chi_{517}(177,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{517}(243,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$
$$\chi_{517}(298,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$
$$\chi_{517}(309,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$
$$\chi_{517}(331,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$
$$\chi_{517}(353,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$
$$\chi_{517}(397,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$
$$\chi_{517}(408,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$
$$\chi_{517}(430,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$
$$\chi_{517}(441,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$
$$\chi_{517}(474,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$
$$\chi_{517}(507,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$