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Properties

Modulus 162162
Structure C54C_{54}
Order 5454

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Show commands: Pari/GP / SageMath

Copy content sage:H = DirichletGroup(162)
 
Copy content pari:g = idealstar(,162,2)
 

Character group

Copy content sage:G.order()
 
Copy content pari:g.no
 
Order = 54
Copy content sage:H.invariants()
 
Copy content pari:g.cyc
 
Structure = C54C_{54}
Copy content sage:H.gens()
 
Copy content pari:g.gen
 
Generators = χ162(83,⋅)\chi_{162}(83,\cdot)

First 32 of 54 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 55 77 1111 1313 1717 1919 2323 2525 2929 3131
χ162(1,⋅)\chi_{162}(1,\cdot) 162.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ162(5,⋅)\chi_{162}(5,\cdot) 162.h 54 no −1-1 11 e(4354)e\left(\frac{43}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right) e(3754)e\left(\frac{37}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(4154)e\left(\frac{41}{54}\right) e(1427)e\left(\frac{14}{27}\right)
χ162(7,⋅)\chi_{162}(7,\cdot) 162.g 27 no 11 11 e(2227)e\left(\frac{22}{27}\right) e(2027)e\left(\frac{20}{27}\right) e(2327)e\left(\frac{23}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(727)e\left(\frac{7}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(2627)e\left(\frac{26}{27}\right) e(2527)e\left(\frac{25}{27}\right)
χ162(11,⋅)\chi_{162}(11,\cdot) 162.h 54 no −1-1 11 e(2954)e\left(\frac{29}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(754)e\left(\frac{7}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right) e(3554)e\left(\frac{35}{54}\right) e(227)e\left(\frac{2}{27}\right) e(4954)e\left(\frac{49}{54}\right) e(2227)e\left(\frac{22}{27}\right)
χ162(13,⋅)\chi_{162}(13,\cdot) 162.g 27 no 11 11 e(1127)e\left(\frac{11}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(2527)e\left(\frac{25}{27}\right) e(527)e\left(\frac{5}{27}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(1727)e\left(\frac{17}{27}\right) e(2227)e\left(\frac{22}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(2627)e\left(\frac{26}{27}\right)
χ162(17,⋅)\chi_{162}(17,\cdot) 162.f 18 no −1-1 11 e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\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)
χ162(19,⋅)\chi_{162}(19,\cdot) 162.e 9 no 11 11 e(49)e\left(\frac{4}{9}\right) e(29)e\left(\frac{2}{9}\right) e(59)e\left(\frac{5}{9}\right) e(19)e\left(\frac{1}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\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)
χ162(23,⋅)\chi_{162}(23,\cdot) 162.h 54 no −1-1 11 e(3754)e\left(\frac{37}{54}\right) e(727)e\left(\frac{7}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1354)e\left(\frac{13}{54}\right) e(1027)e\left(\frac{10}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(227)e\left(\frac{2}{27}\right)
χ162(25,⋅)\chi_{162}(25,\cdot) 162.g 27 no 11 11 e(1627)e\left(\frac{16}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(227)e\left(\frac{2}{27}\right) e(2227)e\left(\frac{22}{27}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1027)e\left(\frac{10}{27}\right) e(527)e\left(\frac{5}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(127)e\left(\frac{1}{27}\right)
χ162(29,⋅)\chi_{162}(29,\cdot) 162.h 54 no −1-1 11 e(4154)e\left(\frac{41}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(4954)e\left(\frac{49}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right) e(2954)e\left(\frac{29}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(1954)e\left(\frac{19}{54}\right) e(1927)e\left(\frac{19}{27}\right)
χ162(31,⋅)\chi_{162}(31,\cdot) 162.g 27 no 11 11 e(1427)e\left(\frac{14}{27}\right) e(2527)e\left(\frac{25}{27}\right) e(2227)e\left(\frac{22}{27}\right) e(2627)e\left(\frac{26}{27}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(227)e\left(\frac{2}{27}\right) e(127)e\left(\frac{1}{27}\right) e(1927)e\left(\frac{19}{27}\right) e(1127)e\left(\frac{11}{27}\right)
χ162(35,⋅)\chi_{162}(35,\cdot) 162.f 18 no −1-1 11 e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(718)e\left(\frac{7}{18}\right) e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\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)
χ162(37,⋅)\chi_{162}(37,\cdot) 162.e 9 no 11 11 e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(19)e\left(\frac{1}{9}\right) e(29)e\left(\frac{2}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\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)
χ162(41,⋅)\chi_{162}(41,\cdot) 162.h 54 no −1-1 11 e(3154)e\left(\frac{31}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(4154)e\left(\frac{41}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(4354)e\left(\frac{43}{54}\right) e(427)e\left(\frac{4}{27}\right) e(1754)e\left(\frac{17}{54}\right) e(1727)e\left(\frac{17}{27}\right)
χ162(43,⋅)\chi_{162}(43,\cdot) 162.g 27 no 11 11 e(1027)e\left(\frac{10}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(827)e\left(\frac{8}{27}\right) e(727)e\left(\frac{7}{27}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1327)e\left(\frac{13}{27}\right) e(2027)e\left(\frac{20}{27}\right) e(227)e\left(\frac{2}{27}\right) e(427)e\left(\frac{4}{27}\right)
χ162(47,⋅)\chi_{162}(47,\cdot) 162.h 54 no −1-1 11 e(5354)e\left(\frac{53}{54}\right) e(227)e\left(\frac{2}{27}\right) e(3754)e\left(\frac{37}{54}\right) e(127)e\left(\frac{1}{27}\right) e(518)e\left(\frac{5}{18}\right) e(29)e\left(\frac{2}{9}\right) e(2354)e\left(\frac{23}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(1627)e\left(\frac{16}{27}\right)
χ162(49,⋅)\chi_{162}(49,\cdot) 162.g 27 no 11 11 e(1727)e\left(\frac{17}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(1927)e\left(\frac{19}{27}\right) e(2027)e\left(\frac{20}{27}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right) e(1427)e\left(\frac{14}{27}\right) e(727)e\left(\frac{7}{27}\right) e(2527)e\left(\frac{25}{27}\right) e(2327)e\left(\frac{23}{27}\right)
χ162(53,⋅)\chi_{162}(53,\cdot) 162.d 6 no −1-1 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right) −1-1 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right)
χ162(55,⋅)\chi_{162}(55,\cdot) 162.c 3 no 11 11 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) 11 11 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)
χ162(59,⋅)\chi_{162}(59,\cdot) 162.h 54 no −1-1 11 e(2554)e\left(\frac{25}{54}\right) e(427)e\left(\frac{4}{27}\right) e(4754)e\left(\frac{47}{54}\right) e(227)e\left(\frac{2}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right) e(1954)e\left(\frac{19}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(554)e\left(\frac{5}{54}\right) e(527)e\left(\frac{5}{27}\right)
χ162(61,⋅)\chi_{162}(61,\cdot) 162.g 27 no 11 11 e(427)e\left(\frac{4}{27}\right) e(1127)e\left(\frac{11}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(1927)e\left(\frac{19}{27}\right) e(79)e\left(\frac{7}{9}\right) e(29)e\left(\frac{2}{9}\right) e(1627)e\left(\frac{16}{27}\right) e(827)e\left(\frac{8}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(727)e\left(\frac{7}{27}\right)
χ162(65,⋅)\chi_{162}(65,\cdot) 162.h 54 no −1-1 11 e(1154)e\left(\frac{11}{54}\right) e(527)e\left(\frac{5}{27}\right) e(2554)e\left(\frac{25}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right) e(1754)e\left(\frac{17}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(1354)e\left(\frac{13}{54}\right) e(1327)e\left(\frac{13}{27}\right)
χ162(67,⋅)\chi_{162}(67,\cdot) 162.g 27 no 11 11 e(2027)e\left(\frac{20}{27}\right) e(127)e\left(\frac{1}{27}\right) e(1627)e\left(\frac{16}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right) e(2627)e\left(\frac{26}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(427)e\left(\frac{4}{27}\right) e(827)e\left(\frac{8}{27}\right)
χ162(71,⋅)\chi_{162}(71,\cdot) 162.f 18 no −1-1 11 e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(518)e\left(\frac{5}{18}\right) e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\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)
χ162(73,⋅)\chi_{162}(73,\cdot) 162.e 9 no 11 11 e(79)e\left(\frac{7}{9}\right) e(89)e\left(\frac{8}{9}\right) e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\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)
χ162(77,⋅)\chi_{162}(77,\cdot) 162.h 54 no −1-1 11 e(1954)e\left(\frac{19}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(827)e\left(\frac{8}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right) e(4954)e\left(\frac{49}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(4754)e\left(\frac{47}{54}\right) e(2027)e\left(\frac{20}{27}\right)
χ162(79,⋅)\chi_{162}(79,\cdot) 162.g 27 no 11 11 e(2527)e\left(\frac{25}{27}\right) e(827)e\left(\frac{8}{27}\right) e(2027)e\left(\frac{20}{27}\right) e(427)e\left(\frac{4}{27}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right) e(1927)e\left(\frac{19}{27}\right) e(2327)e\left(\frac{23}{27}\right) e(527)e\left(\frac{5}{27}\right) e(1027)e\left(\frac{10}{27}\right)
χ162(83,⋅)\chi_{162}(83,\cdot) 162.h 54 no −1-1 11 e(2354)e\left(\frac{23}{54}\right) e(827)e\left(\frac{8}{27}\right) e(1354)e\left(\frac{13}{54}\right) e(427)e\left(\frac{4}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right) e(1154)e\left(\frac{11}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(3754)e\left(\frac{37}{54}\right) e(1027)e\left(\frac{10}{27}\right)
χ162(85,⋅)\chi_{162}(85,\cdot) 162.g 27 no 11 11 e(2327)e\left(\frac{23}{27}\right) e(1627)e\left(\frac{16}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(827)e\left(\frac{8}{27}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right) e(1127)e\left(\frac{11}{27}\right) e(1927)e\left(\frac{19}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(2027)e\left(\frac{20}{27}\right)
χ162(89,⋅)\chi_{162}(89,\cdot) 162.f 18 no −1-1 11 e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\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)
χ162(91,⋅)\chi_{162}(91,\cdot) 162.e 9 no 11 11 e(29)e\left(\frac{2}{9}\right) e(19)e\left(\frac{1}{9}\right) e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\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)
χ162(95,⋅)\chi_{162}(95,\cdot) 162.h 54 no −1-1 11 e(1354)e\left(\frac{13}{54}\right) e(127)e\left(\frac{1}{27}\right) e(554)e\left(\frac{5}{54}\right) e(1427)e\left(\frac{14}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right) e(2554)e\left(\frac{25}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(827)e\left(\frac{8}{27}\right)
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