# Properties

 Modulus 287 Structure $$C_{120}\times C_{2}$$ Order 240

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(287)

pari: g = idealstar(,287,2)

## Character group

 sage: G.order()  pari: g.no Order = 240 sage: H.invariants()  pari: g.cyc Structure = $$C_{120}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{287}(47,\cdot)$, $\chi_{287}(286,\cdot)$

## First 32 of 240 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.

orbit label order primitive -1 1 2 3 4 5 6 8 9 10 11 12
$$\chi_{287}(1,\cdot)$$ 287.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{287}(2,\cdot)$$ 287.bc 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{287}(3,\cdot)$$ 287.w 24 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{287}(4,\cdot)$$ 287.z 30 yes $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{287}(5,\cdot)$$ 287.bd 60 yes $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{287}(6,\cdot)$$ 287.bb 40 yes $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{287}(8,\cdot)$$ 287.u 20 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{287}(9,\cdot)$$ 287.r 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{287}(10,\cdot)$$ 287.y 30 yes $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{287}(11,\cdot)$$ 287.bf 120 yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{43}{120}\right)$$
$$\chi_{287}(12,\cdot)$$ 287.be 120 yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{43}{120}\right)$$ $$e\left(\frac{47}{120}\right)$$
$$\chi_{287}(13,\cdot)$$ 287.bb 40 yes $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$
$$\chi_{287}(15,\cdot)$$ 287.ba 40 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$
$$\chi_{287}(16,\cdot)$$ 287.s 15 yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{287}(17,\cdot)$$ 287.be 120 yes $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{13}{120}\right)$$
$$\chi_{287}(18,\cdot)$$ 287.s 15 yes $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{287}(19,\cdot)$$ 287.be 120 yes $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{29}{120}\right)$$
$$\chi_{287}(20,\cdot)$$ 287.t 20 yes $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{287}(22,\cdot)$$ 287.ba 40 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$
$$\chi_{287}(23,\cdot)$$ 287.z 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{287}(24,\cdot)$$ 287.be 120 yes $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{73}{120}\right)$$
$$\chi_{287}(25,\cdot)$$ 287.z 30 yes $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{287}(26,\cdot)$$ 287.be 120 yes $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{73}{120}\right)$$ $$e\left(\frac{77}{120}\right)$$
$$\chi_{287}(27,\cdot)$$ 287.l 8 yes $$1$$ $$1$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{287}(29,\cdot)$$ 287.ba 40 no $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$
$$\chi_{287}(30,\cdot)$$ 287.bf 120 yes $$-1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{23}{120}\right)$$
$$\chi_{287}(31,\cdot)$$ 287.x 30 yes $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{287}(32,\cdot)$$ 287.r 12 yes $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{287}(33,\cdot)$$ 287.bd 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{287}(34,\cdot)$$ 287.bb 40 yes $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$
$$\chi_{287}(36,\cdot)$$ 287.u 20 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{287}(37,\cdot)$$ 287.s 15 yes $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$