# Properties

 Modulus $1792$ Structure $$C_{192}\times C_{2}\times C_{2}$$ Order $768$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1792)

pari: g = idealstar(,1792,2)

## Character group

 sage: G.order()  pari: g.no Order = 768 sage: H.invariants()  pari: g.cyc Structure = $$C_{192}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1792}(1023,\cdot)$, $\chi_{1792}(1541,\cdot)$, $\chi_{1792}(1025,\cdot)$

## First 32 of 768 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1792}(1,\cdot)$$ 1792.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1792}(3,\cdot)$$ 1792.cc 192 yes $$1$$ $$1$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{73}{192}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$
$$\chi_{1792}(5,\cdot)$$ 1792.ca 192 yes $$-1$$ $$1$$ $$e\left(\frac{73}{192}\right)$$ $$e\left(\frac{35}{192}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$
$$\chi_{1792}(9,\cdot)$$ 1792.by 96 no $$1$$ $$1$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$
$$\chi_{1792}(11,\cdot)$$ 1792.cd 192 yes $$-1$$ $$1$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{127}{192}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{73}{192}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{31}{96}\right)$$
$$\chi_{1792}(13,\cdot)$$ 1792.bt 64 yes $$-1$$ $$1$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$
$$\chi_{1792}(15,\cdot)$$ 1792.be 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1792}(17,\cdot)$$ 1792.bo 48 no $$-1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{1792}(19,\cdot)$$ 1792.cc 192 yes $$1$$ $$1$$ $$e\left(\frac{175}{192}\right)$$ $$e\left(\frac{101}{192}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{73}{192}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{179}{192}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{5}{96}\right)$$
$$\chi_{1792}(23,\cdot)$$ 1792.bw 96 no $$-1$$ $$1$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$
$$\chi_{1792}(25,\cdot)$$ 1792.by 96 no $$1$$ $$1$$ $$e\left(\frac{73}{96}\right)$$ $$e\left(\frac{35}{96}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{31}{96}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{1792}(27,\cdot)$$ 1792.bv 64 yes $$1$$ $$1$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{1792}(29,\cdot)$$ 1792.bs 64 no $$1$$ $$1$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$
$$\chi_{1792}(31,\cdot)$$ 1792.bi 24 no $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1792}(33,\cdot)$$ 1792.bg 24 no $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1792}(37,\cdot)$$ 1792.cb 192 yes $$1$$ $$1$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{11}{96}\right)$$
$$\chi_{1792}(39,\cdot)$$ 1792.bw 96 no $$-1$$ $$1$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{1792}(41,\cdot)$$ 1792.bm 32 no $$-1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1792}(43,\cdot)$$ 1792.bu 64 no $$-1$$ $$1$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$
$$\chi_{1792}(45,\cdot)$$ 1792.ca 192 yes $$-1$$ $$1$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{181}{192}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{67}{192}\right)$$ $$e\left(\frac{83}{96}\right)$$ $$e\left(\frac{85}{96}\right)$$
$$\chi_{1792}(47,\cdot)$$ 1792.bq 48 no $$1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{1792}(51,\cdot)$$ 1792.cd 192 yes $$-1$$ $$1$$ $$e\left(\frac{55}{192}\right)$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{55}{96}\right)$$ $$e\left(\frac{97}{192}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{155}{192}\right)$$ $$e\left(\frac{91}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$
$$\chi_{1792}(53,\cdot)$$ 1792.cb 192 yes $$1$$ $$1$$ $$e\left(\frac{77}{192}\right)$$ $$e\left(\frac{79}{192}\right)$$ $$e\left(\frac{77}{96}\right)$$ $$e\left(\frac{59}{192}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{41}{96}\right)$$ $$e\left(\frac{79}{96}\right)$$
$$\chi_{1792}(55,\cdot)$$ 1792.bk 32 no $$1$$ $$1$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{1792}(57,\cdot)$$ 1792.bn 32 no $$1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1792}(59,\cdot)$$ 1792.cc 192 yes $$1$$ $$1$$ $$e\left(\frac{185}{192}\right)$$ $$e\left(\frac{19}{192}\right)$$ $$e\left(\frac{89}{96}\right)$$ $$e\left(\frac{143}{192}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{85}{192}\right)$$ $$e\left(\frac{53}{96}\right)$$ $$e\left(\frac{19}{96}\right)$$
$$\chi_{1792}(61,\cdot)$$ 1792.ca 192 yes $$-1$$ $$1$$ $$e\left(\frac{43}{192}\right)$$ $$e\left(\frac{89}{192}\right)$$ $$e\left(\frac{43}{96}\right)$$ $$e\left(\frac{109}{192}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{191}{192}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{89}{96}\right)$$
$$\chi_{1792}(65,\cdot)$$ 1792.ba 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1792}(67,\cdot)$$ 1792.cd 192 yes $$-1$$ $$1$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{25}{192}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{173}{192}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{31}{192}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{25}{96}\right)$$
$$\chi_{1792}(69,\cdot)$$ 1792.bt 64 yes $$-1$$ $$1$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{1792}(71,\cdot)$$ 1792.bl 32 no $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1792}(73,\cdot)$$ 1792.bz 96 no $$-1$$ $$1$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{37}{96}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$