Properties

 Modulus 388 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(388)

pari: g = idealstar(,388,2)

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 = $\chi_{388}(5,\cdot)$, $\chi_{388}(195,\cdot)$

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 3 5 7 9 11 13 15 17 19 21
$$\chi_{388}(1,\cdot)$$ 388.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{388}(3,\cdot)$$ 388.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{31}{48}\right)$$
$$\chi_{388}(5,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{5}{96}\right)$$
$$\chi_{388}(7,\cdot)$$ 388.x 96 yes $$1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{59}{96}\right)$$
$$\chi_{388}(9,\cdot)$$ 388.q 24 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{388}(11,\cdot)$$ 388.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{48}\right)$$
$$\chi_{388}(13,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{29}{96}\right)$$
$$\chi_{388}(15,\cdot)$$ 388.x 96 yes $$1$$ $$1$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{67}{96}\right)$$
$$\chi_{388}(17,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{49}{96}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{61}{96}\right)$$
$$\chi_{388}(19,\cdot)$$ 388.s 32 yes $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{388}(21,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{25}{96}\right)$$
$$\chi_{388}(23,\cdot)$$ 388.x 96 yes $$1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{96}\right)$$
$$\chi_{388}(25,\cdot)$$ 388.u 48 no $$1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{388}(27,\cdot)$$ 388.o 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{388}(29,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{65}{96}\right)$$
$$\chi_{388}(31,\cdot)$$ 388.v 48 yes $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{388}(33,\cdot)$$ 388.l 8 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{388}(35,\cdot)$$ 388.i 6 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{388}(37,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{71}{96}\right)$$
$$\chi_{388}(39,\cdot)$$ 388.x 96 yes $$1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{91}{96}\right)$$
$$\chi_{388}(41,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{41}{96}\right)$$
$$\chi_{388}(43,\cdot)$$ 388.r 24 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{388}(45,\cdot)$$ 388.t 32 no $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{388}(47,\cdot)$$ 388.k 8 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{388}(49,\cdot)$$ 388.u 48 no $$1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{388}(51,\cdot)$$ 388.s 32 yes $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{388}(53,\cdot)$$ 388.u 48 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{388}(55,\cdot)$$ 388.s 32 yes $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{388}(57,\cdot)$$ 388.w 96 no $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{83}{96}\right)$$
$$\chi_{388}(59,\cdot)$$ 388.x 96 yes $$1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{47}{96}\right)$$
$$\chi_{388}(61,\cdot)$$ 388.e 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{388}(63,\cdot)$$ 388.s 32 yes $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$