Properties

Modulus 76
Structure \(C_{18}\times C_{2}\)
Order 36

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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(76)
pari: g = idealstar(,76,2)

Character group

sage: G.order()
pari: g.no
Order = 36
sage: H.invariants()
pari: g.cyc
Structure = \(C_{18}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{76}(21,\cdot)$, $\chi_{76}(39,\cdot)$

First 32 of 36 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 3 5 7 9 11 13 15 17 21 23
\(\chi_{76}(1,\cdot)\) 76.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{76}(3,\cdot)\) 76.k 18 Yes \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{76}(5,\cdot)\) 76.i 9 No \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{76}(7,\cdot)\) 76.g 6 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{76}(9,\cdot)\) 76.i 9 No \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{76}(11,\cdot)\) 76.g 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{76}(13,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{76}(15,\cdot)\) 76.k 18 Yes \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{76}(17,\cdot)\) 76.i 9 No \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{76}(21,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{76}(23,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{76}(25,\cdot)\) 76.i 9 No \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{76}(27,\cdot)\) 76.f 6 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{76}(29,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{76}(31,\cdot)\) 76.f 6 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{76}(33,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{76}(35,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{76}(37,\cdot)\) 76.c 2 No \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{76}(39,\cdot)\) 76.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{76}(41,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{76}(43,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{76}(45,\cdot)\) 76.e 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{76}(47,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{76}(49,\cdot)\) 76.e 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{76}(51,\cdot)\) 76.k 18 Yes \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{76}(53,\cdot)\) 76.j 18 No \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{76}(55,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{76}(59,\cdot)\) 76.k 18 Yes \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{76}(61,\cdot)\) 76.i 9 No \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{76}(63,\cdot)\) 76.l 18 Yes \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{76}(65,\cdot)\) 76.h 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{76}(67,\cdot)\) 76.k 18 Yes \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\)