Properties

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

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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 \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(-i\) \(e\left(\frac{7}{18}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\)