Properties

Modulus 74
Structure \(C_{36}\)
Order 36

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(74)
pari: g = idealstar(,74,2)

Character group

sage: G.order()
pari: g.no
Order = 36
sage: H.invariants()
pari: g.cyc
Structure = \(C_{36}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{74}(39,\cdot)$

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 19 21
\(\chi_{74}(1,\cdot)\) 74.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{74}(3,\cdot)\) 74.h 18 No \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{74}(5,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{74}(7,\cdot)\) 74.f 9 No \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{74}(9,\cdot)\) 74.f 9 No \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{74}(11,\cdot)\) 74.e 6 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{74}(13,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{74}(15,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{74}(17,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{74}(19,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{74}(21,\cdot)\) 74.h 18 No \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{74}(23,\cdot)\) 74.g 12 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{74}(25,\cdot)\) 74.h 18 No \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{74}(27,\cdot)\) 74.e 6 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{74}(29,\cdot)\) 74.g 12 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{74}(31,\cdot)\) 74.d 4 No \(-1\) \(1\) \(-1\) \(-i\) \(1\) \(1\) \(-1\) \(-i\) \(i\) \(-i\) \(-i\) \(-1\)
\(\chi_{74}(33,\cdot)\) 74.f 9 No \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{74}(35,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{74}(39,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{74}(41,\cdot)\) 74.h 18 No \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{74}(43,\cdot)\) 74.d 4 No \(-1\) \(1\) \(-1\) \(i\) \(1\) \(1\) \(-1\) \(i\) \(-i\) \(i\) \(i\) \(-1\)
\(\chi_{74}(45,\cdot)\) 74.g 12 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{74}(47,\cdot)\) 74.c 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{74}(49,\cdot)\) 74.f 9 No \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{74}(51,\cdot)\) 74.g 12 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{74}(53,\cdot)\) 74.f 9 No \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{74}(55,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{74}(57,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{74}(59,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{74}(61,\cdot)\) 74.i 36 No \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{74}(63,\cdot)\) 74.c 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{74}(65,\cdot)\) 74.h 18 No \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\)