↑

Properties

Modulus 7676
Structure C2×C18C_{2}\times C_{18}
Order 3636

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(76)
 
pari: g = idealstar(,76,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 36
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C18C_{2}\times C_{18}
sage: H.gens()
 
pari: g.gen
 
Generators = χ76(39,⋅)\chi_{76}(39,\cdot), χ76(21,⋅)\chi_{76}(21,\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.

Character Orbit Order Primitive −1-1 11 33 55 77 99 1111 1313 1515 1717 2121 2323
χ76(1,⋅)\chi_{76}(1,\cdot) 76.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ76(3,⋅)\chi_{76}(3,\cdot) 76.k 18 yes 11 11 e(89)e\left(\frac{8}{9}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) e(1118)e\left(\frac{11}{18}\right) e(49)e\left(\frac{4}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(1718)e\left(\frac{17}{18}\right)
χ76(5,⋅)\chi_{76}(5,\cdot) 76.i 9 no 11 11 e(59)e\left(\frac{5}{9}\right) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(49)e\left(\frac{4}{9}\right) e(79)e\left(\frac{7}{9}\right) e(89)e\left(\frac{8}{9}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right)
χ76(7,⋅)\chi_{76}(7,\cdot) 76.g 6 yes −1-1 11 e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right)
χ76(9,⋅)\chi_{76}(9,\cdot) 76.i 9 no 11 11 e(79)e\left(\frac{7}{9}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(29)e\left(\frac{2}{9}\right) e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(49)e\left(\frac{4}{9}\right) e(89)e\left(\frac{8}{9}\right)
χ76(11,⋅)\chi_{76}(11,\cdot) 76.g 6 yes −1-1 11 e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right)
χ76(13,⋅)\chi_{76}(13,\cdot) 76.j 18 no −1-1 11 e(1118)e\left(\frac{11}{18}\right) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(718)e\left(\frac{7}{18}\right) e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(518)e\left(\frac{5}{18}\right) e(59)e\left(\frac{5}{9}\right)
χ76(15,⋅)\chi_{76}(15,\cdot) 76.k 18 yes 11 11 e(49)e\left(\frac{4}{9}\right) e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) e(118)e\left(\frac{1}{18}\right) e(29)e\left(\frac{2}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(1318)e\left(\frac{13}{18}\right)
χ76(17,⋅)\chi_{76}(17,\cdot) 76.i 9 no 11 11 e(29)e\left(\frac{2}{9}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(79)e\left(\frac{7}{9}\right) e(19)e\left(\frac{1}{9}\right) e(59)e\left(\frac{5}{9}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right)
χ76(21,⋅)\chi_{76}(21,\cdot) 76.j 18 no −1-1 11 e(1318)e\left(\frac{13}{18}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(518)e\left(\frac{5}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(118)e\left(\frac{1}{18}\right) e(19)e\left(\frac{1}{9}\right)
χ76(23,⋅)\chi_{76}(23,\cdot) 76.l 18 yes −1-1 11 e(1718)e\left(\frac{17}{18}\right) e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) e(59)e\left(\frac{5}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1318)e\left(\frac{13}{18}\right)
χ76(25,⋅)\chi_{76}(25,\cdot) 76.i 9 no 11 11 e(19)e\left(\frac{1}{9}\right) e(49)e\left(\frac{4}{9}\right) e(23)e\left(\frac{2}{3}\right) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(89)e\left(\frac{8}{9}\right) e(59)e\left(\frac{5}{9}\right) e(79)e\left(\frac{7}{9}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right)
χ76(27,⋅)\chi_{76}(27,\cdot) 76.f 6 yes 11 11 e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right) −1-1 e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right)
χ76(29,⋅)\chi_{76}(29,\cdot) 76.j 18 no −1-1 11 e(518)e\left(\frac{5}{18}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(1318)e\left(\frac{13}{18}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(89)e\left(\frac{8}{9}\right)
χ76(31,⋅)\chi_{76}(31,\cdot) 76.f 6 yes 11 11 e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) −1-1 e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right)
χ76(33,⋅)\chi_{76}(33,\cdot) 76.j 18 no −1-1 11 e(118)e\left(\frac{1}{18}\right) e(29)e\left(\frac{2}{9}\right) e(13)e\left(\frac{1}{3}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(1718)e\left(\frac{17}{18}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(718)e\left(\frac{7}{18}\right) e(79)e\left(\frac{7}{9}\right)
χ76(35,⋅)\chi_{76}(35,\cdot) 76.l 18 yes −1-1 11 e(718)e\left(\frac{7}{18}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(79)e\left(\frac{7}{9}\right) e(16)e\left(\frac{1}{6}\right) e(19)e\left(\frac{1}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1718)e\left(\frac{17}{18}\right)
χ76(37,⋅)\chi_{76}(37,\cdot) 76.c 2 no −1-1 11 −1-1 11 11 11 11 −1-1 −1-1 11 −1-1 11
χ76(39,⋅)\chi_{76}(39,\cdot) 76.b 2 no −1-1 11 −1-1 11 −1-1 11 −1-1 11 −1-1 11 11 −1-1
χ76(41,⋅)\chi_{76}(41,\cdot) 76.j 18 no −1-1 11 e(718)e\left(\frac{7}{18}\right) e(59)e\left(\frac{5}{9}\right) e(13)e\left(\frac{1}{3}\right) e(79)e\left(\frac{7}{9}\right) e(23)e\left(\frac{2}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(49)e\left(\frac{4}{9}\right)
χ76(43,⋅)\chi_{76}(43,\cdot) 76.l 18 yes −1-1 11 e(118)e\left(\frac{1}{18}\right) e(29)e\left(\frac{2}{9}\right) e(56)e\left(\frac{5}{6}\right) e(19)e\left(\frac{1}{9}\right) e(16)e\left(\frac{1}{6}\right) e(49)e\left(\frac{4}{9}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(89)e\left(\frac{8}{9}\right) e(518)e\left(\frac{5}{18}\right)
χ76(45,⋅)\chi_{76}(45,\cdot) 76.e 3 no 11 11 e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) 11 e(23)e\left(\frac{2}{3}\right) 11 e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right)
χ76(47,⋅)\chi_{76}(47,\cdot) 76.l 18 yes −1-1 11 e(518)e\left(\frac{5}{18}\right) e(19)e\left(\frac{1}{9}\right) e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(29)e\left(\frac{2}{9}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(49)e\left(\frac{4}{9}\right) e(718)e\left(\frac{7}{18}\right)
χ76(49,⋅)\chi_{76}(49,\cdot) 76.e 3 no 11 11 e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) 11 e(13)e\left(\frac{1}{3}\right) 11 e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)
χ76(51,⋅)\chi_{76}(51,\cdot) 76.k 18 yes 11 11 e(19)e\left(\frac{1}{9}\right) e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) e(29)e\left(\frac{2}{9}\right) e(56)e\left(\frac{5}{6}\right) e(718)e\left(\frac{7}{18}\right) e(59)e\left(\frac{5}{9}\right) e(79)e\left(\frac{7}{9}\right) e(518)e\left(\frac{5}{18}\right) e(118)e\left(\frac{1}{18}\right)
χ76(53,⋅)\chi_{76}(53,\cdot) 76.j 18 no −1-1 11 e(1718)e\left(\frac{17}{18}\right) e(79)e\left(\frac{7}{9}\right) e(23)e\left(\frac{2}{3}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(118)e\left(\frac{1}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(29)e\left(\frac{2}{9}\right)
χ76(55,⋅)\chi_{76}(55,\cdot) 76.l 18 yes −1-1 11 e(1318)e\left(\frac{13}{18}\right) e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) e(79)e\left(\frac{7}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1118)e\left(\frac{11}{18}\right)
χ76(59,⋅)\chi_{76}(59,\cdot) 76.k 18 yes 11 11 e(29)e\left(\frac{2}{9}\right) e(89)e\left(\frac{8}{9}\right) e(56)e\left(\frac{5}{6}\right) e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) e(518)e\left(\frac{5}{18}\right) e(19)e\left(\frac{1}{9}\right) e(59)e\left(\frac{5}{9}\right) e(118)e\left(\frac{1}{18}\right) e(1118)e\left(\frac{11}{18}\right)
χ76(61,⋅)\chi_{76}(61,\cdot) 76.i 9 no 11 11 e(49)e\left(\frac{4}{9}\right) e(79)e\left(\frac{7}{9}\right) e(23)e\left(\frac{2}{3}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(59)e\left(\frac{5}{9}\right) e(29)e\left(\frac{2}{9}\right) e(19)e\left(\frac{1}{9}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right)
χ76(63,⋅)\chi_{76}(63,\cdot) 76.l 18 yes −1-1 11 e(1118)e\left(\frac{11}{18}\right) e(49)e\left(\frac{4}{9}\right) e(16)e\left(\frac{1}{6}\right) e(29)e\left(\frac{2}{9}\right) e(56)e\left(\frac{5}{6}\right) e(89)e\left(\frac{8}{9}\right) e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(79)e\left(\frac{7}{9}\right) e(118)e\left(\frac{1}{18}\right)
χ76(65,⋅)\chi_{76}(65,\cdot) 76.h 6 no −1-1 11 e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) 11 e(13)e\left(\frac{1}{3}\right) 11 e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right)
χ76(67,⋅)\chi_{76}(67,\cdot) 76.k 18 yes 11 11 e(79)e\left(\frac{7}{9}\right) e(19)e\left(\frac{1}{9}\right) e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(1318)e\left(\frac{13}{18}\right) e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(718)e\left(\frac{7}{18}\right)
Click here to search among the remaining 4 characters.