# Properties

 Modulus 4032 Structure $$C_{48}\times C_{6}\times C_{2}\times C_{2}$$ Order 1152

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(4032)

pari: g = idealstar(,4032,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{48}\times C_{6}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4032}(901,\cdot)$, $\chi_{4032}(1793,\cdot)$, $\chi_{4032}(1441,\cdot)$, $\chi_{4032}(127,\cdot)$

## First 32 of 1152 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 5 11 13 17 19 23 25 29 31 37
$$\chi_{4032}(1,\cdot)$$ 4032.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4032}(5,\cdot)$$ 4032.hp 48 yes $$1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$1$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{4032}(11,\cdot)$$ 4032.ho 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$1$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{4032}(13,\cdot)$$ 4032.gu 48 yes $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{4032}(17,\cdot)$$ 4032.ea 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4032}(19,\cdot)$$ 4032.he 48 no $$1$$ $$1$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{4032}(23,\cdot)$$ 4032.fk 24 no $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$-1$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{4032}(25,\cdot)$$ 4032.gg 24 no $$1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$1$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{4032}(29,\cdot)$$ 4032.hk 48 no $$-1$$ $$1$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{4032}(31,\cdot)$$ 4032.dh 6 no $$1$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4032}(37,\cdot)$$ 4032.hf 48 no $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{4032}(41,\cdot)$$ 4032.fj 24 no $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{4032}(43,\cdot)$$ 4032.gr 48 no $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{4032}(47,\cdot)$$ 4032.dx 12 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4032}(53,\cdot)$$ 4032.hi 48 no $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{4032}(55,\cdot)$$ 4032.dq 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{4032}(59,\cdot)$$ 4032.hm 48 yes $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{43}{48}\right)$$
$$\chi_{4032}(61,\cdot)$$ 4032.gt 48 yes $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{48}\right)$$
$$\chi_{4032}(65,\cdot)$$ 4032.bd 6 no $$-1$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4032}(67,\cdot)$$ 4032.gs 48 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{4032}(71,\cdot)$$ 4032.do 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{4032}(73,\cdot)$$ 4032.fq 24 no $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{4032}(79,\cdot)$$ 4032.eh 12 no $$-1$$ $$1$$ $$i$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4032}(83,\cdot)$$ 4032.hl 48 yes $$-1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{4032}(85,\cdot)$$ 4032.hg 48 no $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{4032}(89,\cdot)$$ 4032.ge 24 no $$1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{4032}(95,\cdot)$$ 4032.dg 6 no $$1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4032}(97,\cdot)$$ 4032.bv 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{4032}(101,\cdot)$$ 4032.hp 48 yes $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$1$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{4032}(103,\cdot)$$ 4032.fu 24 no $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$1$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{4032}(107,\cdot)$$ 4032.gz 48 no $$1$$ $$1$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{4032}(109,\cdot)$$ 4032.hf 48 no $$1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{48}\right)$$