# Properties

 Modulus $143$ Structure $$C_{2}\times C_{60}$$ Order $120$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(143)

pari: g = idealstar(,143,2)

## Character group

 sage: G.order()  pari: g.no Order = 120 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{143}(79,\cdot)$, $\chi_{143}(67,\cdot)$

## First 32 of 120 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$12$$
$$\chi_{143}(1,\cdot)$$ 143.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{143}(2,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{143}(3,\cdot)$$ 143.q 15 yes $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{143}(4,\cdot)$$ 143.u 30 yes $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{143}(5,\cdot)$$ 143.r 20 yes $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$-1$$
$$\chi_{143}(6,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{143}(7,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{143}(8,\cdot)$$ 143.s 20 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$-1$$
$$\chi_{143}(9,\cdot)$$ 143.q 15 yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{143}(10,\cdot)$$ 143.i 6 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{143}(12,\cdot)$$ 143.b 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$
$$\chi_{143}(14,\cdot)$$ 143.h 5 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$1$$
$$\chi_{143}(15,\cdot)$$ 143.x 60 yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{143}(16,\cdot)$$ 143.q 15 yes $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{143}(17,\cdot)$$ 143.v 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{143}(18,\cdot)$$ 143.s 20 yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$-1$$
$$\chi_{143}(19,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{143}(20,\cdot)$$ 143.x 60 yes $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$
$$\chi_{143}(21,\cdot)$$ 143.g 4 yes $$1$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$i$$ $$i$$ $$1$$ $$1$$ $$-1$$
$$\chi_{143}(23,\cdot)$$ 143.j 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{143}(24,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{143}(25,\cdot)$$ 143.n 10 yes $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$1$$
$$\chi_{143}(27,\cdot)$$ 143.h 5 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$1$$
$$\chi_{143}(28,\cdot)$$ 143.w 60 yes $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{143}(29,\cdot)$$ 143.t 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{143}(30,\cdot)$$ 143.v 30 yes $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{143}(31,\cdot)$$ 143.r 20 yes $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$-1$$
$$\chi_{143}(32,\cdot)$$ 143.o 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{143}(34,\cdot)$$ 143.f 4 no $$-1$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{143}(35,\cdot)$$ 143.t 30 yes $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{143}(36,\cdot)$$ 143.u 30 yes $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{143}(37,\cdot)$$ 143.x 60 yes $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$