# Properties

 Modulus 4033 Structure $$C_{108}\times C_{36}$$ Order 3888

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4033)

pari: g = idealstar(,4033,2)

## Character group

 sage: G.order()  pari: g.no Order = 3888 sage: H.invariants()  pari: g.cyc Structure = $$C_{108}\times C_{36}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4033}(2295,\cdot)$, $\chi_{4033}(1963,\cdot)$

## First 32 of 3888 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 2 3 4 5 6 7 8 9 10 11
$$\chi_{4033}(1,\cdot)$$ 4033.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4033}(2,\cdot)$$ 4033.go 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$-i$$ $$e\left(\frac{5}{18}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{4033}(3,\cdot)$$ 4033.hw 54 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$-1$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{17}{27}\right)$$
$$\chi_{4033}(4,\cdot)$$ 4033.co 18 yes $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{9}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{4033}(5,\cdot)$$ 4033.ic 108 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{54}\right)$$ $$-1$$ $$e\left(\frac{19}{108}\right)$$ $$e\left(\frac{103}{108}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$i$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{31}{54}\right)$$
$$\chi_{4033}(6,\cdot)$$ 4033.jl 108 yes $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{103}{108}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{25}{108}\right)$$ $$e\left(\frac{29}{108}\right)$$
$$\chi_{4033}(7,\cdot)$$ 4033.ec 27 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{10}{27}\right)$$ $$1$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$1$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{11}{27}\right)$$
$$\chi_{4033}(8,\cdot)$$ 4033.bn 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4033}(9,\cdot)$$ 4033.du 27 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$1$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$
$$\chi_{4033}(10,\cdot)$$ 4033.ir 108 yes $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{25}{108}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{85}{108}\right)$$ $$e\left(\frac{23}{108}\right)$$
$$\chi_{4033}(11,\cdot)$$ 4033.ja 108 yes $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{29}{108}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{23}{108}\right)$$ $$e\left(\frac{85}{108}\right)$$
$$\chi_{4033}(12,\cdot)$$ 4033.hi 54 yes $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{49}{54}\right)$$
$$\chi_{4033}(13,\cdot)$$ 4033.ia 108 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{108}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$1$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{91}{108}\right)$$ $$e\left(\frac{71}{108}\right)$$
$$\chi_{4033}(14,\cdot)$$ 4033.ih 108 yes $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{37}{108}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{49}{108}\right)$$ $$e\left(\frac{5}{108}\right)$$
$$\chi_{4033}(15,\cdot)$$ 4033.js 108 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{41}{108}\right)$$ $$e\left(\frac{101}{108}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$-i$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{11}{54}\right)$$
$$\chi_{4033}(16,\cdot)$$ 4033.bd 9 yes $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{4033}(17,\cdot)$$ 4033.gn 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$
$$\chi_{4033}(18,\cdot)$$ 4033.ig 108 yes $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{17}{108}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{65}{108}\right)$$ $$e\left(\frac{97}{108}\right)$$
$$\chi_{4033}(19,\cdot)$$ 4033.ev 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{4033}(20,\cdot)$$ 4033.iu 108 yes $$-1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{73}{108}\right)$$ $$e\left(\frac{55}{108}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{23}{27}\right)$$
$$\chi_{4033}(21,\cdot)$$ 4033.hu 54 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$-1$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{1}{27}\right)$$
$$\chi_{4033}(22,\cdot)$$ 4033.ic 108 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{43}{54}\right)$$ $$-1$$ $$e\left(\frac{35}{108}\right)$$ $$e\left(\frac{59}{108}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$i$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{23}{54}\right)$$
$$\chi_{4033}(23,\cdot)$$ 4033.gu 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{4033}(24,\cdot)$$ 4033.hy 108 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{17}{54}\right)$$ $$1$$ $$e\left(\frac{49}{108}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$-1$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{103}{108}\right)$$ $$e\left(\frac{59}{108}\right)$$
$$\chi_{4033}(25,\cdot)$$ 4033.gy 54 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{11}{27}\right)$$ $$1$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$-1$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$
$$\chi_{4033}(26,\cdot)$$ 4033.dy 27 yes $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{8}{27}\right)$$
$$\chi_{4033}(27,\cdot)$$ 4033.ck 18 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{4033}(28,\cdot)$$ 4033.hg 54 yes $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{37}{54}\right)$$
$$\chi_{4033}(29,\cdot)$$ 4033.jg 108 yes $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{37}{108}\right)$$ $$e\left(\frac{7}{108}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{17}{27}\right)$$
$$\chi_{4033}(30,\cdot)$$ 4033.io 108 yes $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{23}{108}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{17}{108}\right)$$ $$e\left(\frac{91}{108}\right)$$
$$\chi_{4033}(31,\cdot)$$ 4033.il 108 yes $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{65}{108}\right)$$ $$e\left(\frac{95}{108}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{7}{27}\right)$$
$$\chi_{4033}(32,\cdot)$$ 4033.go 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-i$$ $$e\left(\frac{7}{18}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$