# Properties

 Modulus $1152$ Structure $$C_{2}\times C_{2}\times C_{96}$$ Order $384$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1152)

pari: g = idealstar(,1152,2)

## Character group

 sage: G.order()  pari: g.no Order = 384 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{96}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1152}(127,\cdot)$, $\chi_{1152}(901,\cdot)$, $\chi_{1152}(641,\cdot)$

## 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{1152}(1,\cdot)$$ 1152.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1152}(5,\cdot)$$ 1152.bt 96 yes $$-1$$ $$1$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1152}(7,\cdot)$$ 1152.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1152}(11,\cdot)$$ 1152.bs 96 yes $$1$$ $$1$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1152}(13,\cdot)$$ 1152.bv 96 yes $$1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1152}(17,\cdot)$$ 1152.x 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$
$$\chi_{1152}(19,\cdot)$$ 1152.bk 32 no $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$i$$
$$\chi_{1152}(23,\cdot)$$ 1152.bp 48 no $$1$$ $$1$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1152}(25,\cdot)$$ 1152.bq 48 no $$1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1152}(29,\cdot)$$ 1152.bt 96 yes $$-1$$ $$1$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1152}(31,\cdot)$$ 1152.z 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1152}(35,\cdot)$$ 1152.bm 32 no $$1$$ $$1$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$i$$
$$\chi_{1152}(37,\cdot)$$ 1152.bl 32 no $$1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$i$$
$$\chi_{1152}(41,\cdot)$$ 1152.br 48 no $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1152}(43,\cdot)$$ 1152.bu 96 yes $$-1$$ $$1$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1152}(47,\cdot)$$ 1152.bj 24 no $$1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1152}(49,\cdot)$$ 1152.bg 24 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1152}(53,\cdot)$$ 1152.bn 32 no $$-1$$ $$1$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$i$$
$$\chi_{1152}(55,\cdot)$$ 1152.bf 16 no $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$1$$
$$\chi_{1152}(59,\cdot)$$ 1152.bs 96 yes $$1$$ $$1$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1152}(61,\cdot)$$ 1152.bv 96 yes $$1$$ $$1$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1152}(65,\cdot)$$ 1152.n 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1152}(67,\cdot)$$ 1152.bu 96 yes $$-1$$ $$1$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1152}(71,\cdot)$$ 1152.be 16 no $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$
$$\chi_{1152}(73,\cdot)$$ 1152.bd 16 no $$1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$
$$\chi_{1152}(77,\cdot)$$ 1152.bt 96 yes $$-1$$ $$1$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1152}(79,\cdot)$$ 1152.bh 24 no $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1152}(83,\cdot)$$ 1152.bs 96 yes $$1$$ $$1$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1152}(85,\cdot)$$ 1152.bv 96 yes $$1$$ $$1$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1152}(89,\cdot)$$ 1152.bc 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$
$$\chi_{1152}(91,\cdot)$$ 1152.bk 32 no $$-1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$-i$$
$$\chi_{1152}(95,\cdot)$$ 1152.y 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$