# Properties

 Modulus $896$ Structure $$C_{96}\times C_{2}\times C_{2}$$ Order $384$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(896)

pari: g = idealstar(,896,2)

## Character group

 sage: G.order()  pari: g.no Order = 384 sage: H.invariants()  pari: g.cyc Structure = $$C_{96}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{896}(127,\cdot)$, $\chi_{896}(645,\cdot)$, $\chi_{896}(129,\cdot)$

## First 32 of 384 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{896}(1,\cdot)$$ 896.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{896}(3,\cdot)$$ 896.bt 96 yes $$1$$ $$1$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$
$$\chi_{896}(5,\cdot)$$ 896.bv 96 yes $$-1$$ $$1$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{896}(9,\cdot)$$ 896.br 48 no $$1$$ $$1$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{896}(11,\cdot)$$ 896.bs 96 yes $$-1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{896}(13,\cdot)$$ 896.bm 32 yes $$-1$$ $$1$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{896}(15,\cdot)$$ 896.w 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$i$$
$$\chi_{896}(17,\cdot)$$ 896.bg 24 no $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{896}(19,\cdot)$$ 896.bt 96 yes $$1$$ $$1$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{896}(23,\cdot)$$ 896.bp 48 no $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{896}(25,\cdot)$$ 896.br 48 no $$1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{896}(27,\cdot)$$ 896.bk 32 yes $$1$$ $$1$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{896}(29,\cdot)$$ 896.bn 32 no $$1$$ $$1$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{896}(31,\cdot)$$ 896.z 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{896}(33,\cdot)$$ 896.bb 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{896}(37,\cdot)$$ 896.bu 96 yes $$1$$ $$1$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$
$$\chi_{896}(39,\cdot)$$ 896.bp 48 no $$-1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{896}(41,\cdot)$$ 896.bf 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{896}(43,\cdot)$$ 896.bl 32 no $$-1$$ $$1$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{896}(45,\cdot)$$ 896.bv 96 yes $$-1$$ $$1$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{896}(47,\cdot)$$ 896.bi 24 no $$1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{896}(51,\cdot)$$ 896.bs 96 yes $$-1$$ $$1$$ $$e\left(\frac{71}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$
$$\chi_{896}(53,\cdot)$$ 896.bu 96 yes $$1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{896}(55,\cdot)$$ 896.bd 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{896}(57,\cdot)$$ 896.bc 16 no $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{896}(59,\cdot)$$ 896.bt 96 yes $$1$$ $$1$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{896}(61,\cdot)$$ 896.bv 96 yes $$-1$$ $$1$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{896}(65,\cdot)$$ 896.t 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{896}(67,\cdot)$$ 896.bs 96 yes $$-1$$ $$1$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$
$$\chi_{896}(69,\cdot)$$ 896.bm 32 yes $$-1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{896}(71,\cdot)$$ 896.be 16 no $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{896}(73,\cdot)$$ 896.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$