# Properties

 Modulus 291 Structure $$C_{96}\times C_{2}$$ Order 192

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(291)

pari: g = idealstar(,291,2)

## Character group

 sage: G.order()  pari: g.no Order = 192 sage: H.invariants()  pari: g.cyc Structure = $$C_{96}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{291}(199,\cdot)$, $\chi_{291}(98,\cdot)$

## First 32 of 192 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 4 5 7 8 10 11 13 14 16
$$\chi_{291}(1,\cdot)$$ 291.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{291}(2,\cdot)$$ 291.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{291}(4,\cdot)$$ 291.q 24 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$i$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{291}(5,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{291}(7,\cdot)$$ 291.w 96 no $$-1$$ $$1$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{291}(8,\cdot)$$ 291.o 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$
$$\chi_{291}(10,\cdot)$$ 291.w 96 no $$-1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{291}(11,\cdot)$$ 291.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{291}(13,\cdot)$$ 291.w 96 no $$-1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{291}(14,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{291}(16,\cdot)$$ 291.n 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{291}(17,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{291}(19,\cdot)$$ 291.t 32 no $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$-i$$
$$\chi_{291}(20,\cdot)$$ 291.s 32 yes $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$-i$$
$$\chi_{291}(22,\cdot)$$ 291.f 4 no $$1$$ $$1$$ $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$1$$
$$\chi_{291}(23,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{291}(25,\cdot)$$ 291.u 48 no $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{291}(26,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{291}(28,\cdot)$$ 291.t 32 no $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$i$$
$$\chi_{291}(29,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{291}(31,\cdot)$$ 291.u 48 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{291}(32,\cdot)$$ 291.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{291}(34,\cdot)$$ 291.t 32 no $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$i$$
$$\chi_{291}(35,\cdot)$$ 291.j 6 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{291}(37,\cdot)$$ 291.w 96 no $$-1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{291}(38,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{291}(40,\cdot)$$ 291.w 96 no $$-1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{291}(41,\cdot)$$ 291.x 96 yes $$1$$ $$1$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{291}(43,\cdot)$$ 291.q 24 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$i$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{291}(44,\cdot)$$ 291.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{291}(46,\cdot)$$ 291.t 32 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$i$$
$$\chi_{291}(47,\cdot)$$ 291.k 8 yes $$-1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$