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Properties

Modulus 483483
Structure C2×C2×C66C_{2}\times C_{2}\times C_{66}
Order 264264

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(483)
 
pari: g = idealstar(,483,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 264
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C66C_{2}\times C_{2}\times C_{66}
sage: H.gens()
 
pari: g.gen
 
Generators = χ483(323,⋅)\chi_{483}(323,\cdot), χ483(346,⋅)\chi_{483}(346,\cdot), χ483(442,⋅)\chi_{483}(442,\cdot)

First 32 of 264 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 22 44 55 88 1010 1111 1313 1616 1717 1919
χ483(1,⋅)\chi_{483}(1,\cdot) 483.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ483(2,⋅)\chi_{483}(2,\cdot) 483.z 66 yes −1-1 11 e(2366)e\left(\frac{23}{66}\right) e(2333)e\left(\frac{23}{33}\right) e(1766)e\left(\frac{17}{66}\right) e(122)e\left(\frac{1}{22}\right) e(2033)e\left(\frac{20}{33}\right) e(4366)e\left(\frac{43}{66}\right) e(311)e\left(\frac{3}{11}\right) e(1333)e\left(\frac{13}{33}\right) e(3166)e\left(\frac{31}{66}\right) e(133)e\left(\frac{1}{33}\right)
χ483(4,⋅)\chi_{483}(4,\cdot) 483.y 33 no 11 11 e(2333)e\left(\frac{23}{33}\right) e(1333)e\left(\frac{13}{33}\right) e(1733)e\left(\frac{17}{33}\right) e(111)e\left(\frac{1}{11}\right) e(733)e\left(\frac{7}{33}\right) e(1033)e\left(\frac{10}{33}\right) e(611)e\left(\frac{6}{11}\right) e(2633)e\left(\frac{26}{33}\right) e(3133)e\left(\frac{31}{33}\right) e(233)e\left(\frac{2}{33}\right)
χ483(5,⋅)\chi_{483}(5,\cdot) 483.ba 66 yes −1-1 11 e(1766)e\left(\frac{17}{66}\right) e(1733)e\left(\frac{17}{33}\right) e(4766)e\left(\frac{47}{66}\right) e(1722)e\left(\frac{17}{22}\right) e(3233)e\left(\frac{32}{33}\right) e(833)e\left(\frac{8}{33}\right) e(322)e\left(\frac{3}{22}\right) e(133)e\left(\frac{1}{33}\right) e(4366)e\left(\frac{43}{66}\right) e(2833)e\left(\frac{28}{33}\right)
χ483(8,⋅)\chi_{483}(8,\cdot) 483.x 22 no −1-1 11 e(122)e\left(\frac{1}{22}\right) e(111)e\left(\frac{1}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(322)e\left(\frac{3}{22}\right) e(911)e\left(\frac{9}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(911)e\left(\frac{9}{11}\right) e(211)e\left(\frac{2}{11}\right) e(922)e\left(\frac{9}{22}\right) e(111)e\left(\frac{1}{11}\right)
χ483(10,⋅)\chi_{483}(10,\cdot) 483.bf 66 no 11 11 e(2033)e\left(\frac{20}{33}\right) e(733)e\left(\frac{7}{33}\right) e(3233)e\left(\frac{32}{33}\right) e(911)e\left(\frac{9}{11}\right) e(1933)e\left(\frac{19}{33}\right) e(5966)e\left(\frac{59}{66}\right) e(922)e\left(\frac{9}{22}\right) e(1433)e\left(\frac{14}{33}\right) e(433)e\left(\frac{4}{33}\right) e(2933)e\left(\frac{29}{33}\right)
χ483(11,⋅)\chi_{483}(11,\cdot) 483.bc 66 yes 11 11 e(4366)e\left(\frac{43}{66}\right) e(1033)e\left(\frac{10}{33}\right) e(833)e\left(\frac{8}{33}\right) e(2122)e\left(\frac{21}{22}\right) e(5966)e\left(\frac{59}{66}\right) e(2833)e\left(\frac{28}{33}\right) e(811)e\left(\frac{8}{11}\right) e(2033)e\left(\frac{20}{33}\right) e(133)e\left(\frac{1}{33}\right) e(3166)e\left(\frac{31}{66}\right)
χ483(13,⋅)\chi_{483}(13,\cdot) 483.s 22 no −1-1 11 e(311)e\left(\frac{3}{11}\right) e(611)e\left(\frac{6}{11}\right) e(322)e\left(\frac{3}{22}\right) e(911)e\left(\frac{9}{11}\right) e(922)e\left(\frac{9}{22}\right) e(811)e\left(\frac{8}{11}\right) e(922)e\left(\frac{9}{22}\right) e(111)e\left(\frac{1}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(122)e\left(\frac{1}{22}\right)
χ483(16,⋅)\chi_{483}(16,\cdot) 483.y 33 no 11 11 e(1333)e\left(\frac{13}{33}\right) e(2633)e\left(\frac{26}{33}\right) e(133)e\left(\frac{1}{33}\right) e(211)e\left(\frac{2}{11}\right) e(1433)e\left(\frac{14}{33}\right) e(2033)e\left(\frac{20}{33}\right) e(111)e\left(\frac{1}{11}\right) e(1933)e\left(\frac{19}{33}\right) e(2933)e\left(\frac{29}{33}\right) e(433)e\left(\frac{4}{33}\right)
χ483(17,⋅)\chi_{483}(17,\cdot) 483.ba 66 yes −1-1 11 e(3166)e\left(\frac{31}{66}\right) e(3133)e\left(\frac{31}{33}\right) e(4366)e\left(\frac{43}{66}\right) e(922)e\left(\frac{9}{22}\right) e(433)e\left(\frac{4}{33}\right) e(133)e\left(\frac{1}{33}\right) e(2122)e\left(\frac{21}{22}\right) e(2933)e\left(\frac{29}{33}\right) e(5966)e\left(\frac{59}{66}\right) e(2033)e\left(\frac{20}{33}\right)
χ483(19,⋅)\chi_{483}(19,\cdot) 483.bf 66 no 11 11 e(133)e\left(\frac{1}{33}\right) e(233)e\left(\frac{2}{33}\right) e(2833)e\left(\frac{28}{33}\right) e(111)e\left(\frac{1}{11}\right) e(2933)e\left(\frac{29}{33}\right) e(3166)e\left(\frac{31}{66}\right) e(122)e\left(\frac{1}{22}\right) e(433)e\left(\frac{4}{33}\right) e(2033)e\left(\frac{20}{33}\right) e(1333)e\left(\frac{13}{33}\right)
χ483(20,⋅)\chi_{483}(20,\cdot) 483.w 22 yes −1-1 11 e(2122)e\left(\frac{21}{22}\right) e(1011)e\left(\frac{10}{11}\right) e(522)e\left(\frac{5}{22}\right) e(1922)e\left(\frac{19}{22}\right) e(211)e\left(\frac{2}{11}\right) e(611)e\left(\frac{6}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(911)e\left(\frac{9}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(1011)e\left(\frac{10}{11}\right)
χ483(22,⋅)\chi_{483}(22,\cdot) 483.f 2 no −1-1 11 11 11 −1-1 11 −1-1 −1-1 11 11 −1-1 −1-1
χ483(25,⋅)\chi_{483}(25,\cdot) 483.y 33 no 11 11 e(1733)e\left(\frac{17}{33}\right) e(133)e\left(\frac{1}{33}\right) e(1433)e\left(\frac{14}{33}\right) e(611)e\left(\frac{6}{11}\right) e(3133)e\left(\frac{31}{33}\right) e(1633)e\left(\frac{16}{33}\right) e(311)e\left(\frac{3}{11}\right) e(233)e\left(\frac{2}{33}\right) e(1033)e\left(\frac{10}{33}\right) e(2333)e\left(\frac{23}{33}\right)
χ483(26,⋅)\chi_{483}(26,\cdot) 483.bb 66 yes 11 11 e(4166)e\left(\frac{41}{66}\right) e(833)e\left(\frac{8}{33}\right) e(1333)e\left(\frac{13}{33}\right) e(1922)e\left(\frac{19}{22}\right) e(166)e\left(\frac{1}{66}\right) e(2566)e\left(\frac{25}{66}\right) e(1522)e\left(\frac{15}{22}\right) e(1633)e\left(\frac{16}{33}\right) e(1433)e\left(\frac{14}{33}\right) e(566)e\left(\frac{5}{66}\right)
χ483(29,⋅)\chi_{483}(29,\cdot) 483.x 22 no −1-1 11 e(322)e\left(\frac{3}{22}\right) e(311)e\left(\frac{3}{11}\right) e(722)e\left(\frac{7}{22}\right) e(922)e\left(\frac{9}{22}\right) e(511)e\left(\frac{5}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(511)e\left(\frac{5}{11}\right) e(611)e\left(\frac{6}{11}\right) e(522)e\left(\frac{5}{22}\right) e(311)e\left(\frac{3}{11}\right)
χ483(31,⋅)\chi_{483}(31,\cdot) 483.be 66 no −1-1 11 e(2933)e\left(\frac{29}{33}\right) e(2533)e\left(\frac{25}{33}\right) e(766)e\left(\frac{7}{66}\right) e(711)e\left(\frac{7}{11}\right) e(6566)e\left(\frac{65}{66}\right) e(433)e\left(\frac{4}{33}\right) e(722)e\left(\frac{7}{22}\right) e(1733)e\left(\frac{17}{33}\right) e(566)e\left(\frac{5}{66}\right) e(6166)e\left(\frac{61}{66}\right)
χ483(32,⋅)\chi_{483}(32,\cdot) 483.z 66 yes −1-1 11 e(4966)e\left(\frac{49}{66}\right) e(1633)e\left(\frac{16}{33}\right) e(1966)e\left(\frac{19}{66}\right) e(522)e\left(\frac{5}{22}\right) e(133)e\left(\frac{1}{33}\right) e(1766)e\left(\frac{17}{66}\right) e(411)e\left(\frac{4}{11}\right) e(3233)e\left(\frac{32}{33}\right) e(2366)e\left(\frac{23}{66}\right) e(533)e\left(\frac{5}{33}\right)
χ483(34,⋅)\chi_{483}(34,\cdot) 483.r 22 no 11 11 e(911)e\left(\frac{9}{11}\right) e(711)e\left(\frac{7}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(511)e\left(\frac{5}{11}\right) e(811)e\left(\frac{8}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(522)e\left(\frac{5}{22}\right) e(311)e\left(\frac{3}{11}\right) e(411)e\left(\frac{4}{11}\right) e(711)e\left(\frac{7}{11}\right)
χ483(37,⋅)\chi_{483}(37,\cdot) 483.bd 66 no −1-1 11 e(1933)e\left(\frac{19}{33}\right) e(533)e\left(\frac{5}{33}\right) e(4166)e\left(\frac{41}{66}\right) e(811)e\left(\frac{8}{11}\right) e(1366)e\left(\frac{13}{66}\right) e(6166)e\left(\frac{61}{66}\right) e(411)e\left(\frac{4}{11}\right) e(1033)e\left(\frac{10}{33}\right) e(166)e\left(\frac{1}{66}\right) e(6566)e\left(\frac{65}{66}\right)
χ483(38,⋅)\chi_{483}(38,\cdot) 483.ba 66 yes −1-1 11 e(2566)e\left(\frac{25}{66}\right) e(2533)e\left(\frac{25}{33}\right) e(766)e\left(\frac{7}{66}\right) e(322)e\left(\frac{3}{22}\right) e(1633)e\left(\frac{16}{33}\right) e(433)e\left(\frac{4}{33}\right) e(722)e\left(\frac{7}{22}\right) e(1733)e\left(\frac{17}{33}\right) e(566)e\left(\frac{5}{66}\right) e(1433)e\left(\frac{14}{33}\right)
χ483(40,⋅)\chi_{483}(40,\cdot) 483.bf 66 no 11 11 e(1033)e\left(\frac{10}{33}\right) e(2033)e\left(\frac{20}{33}\right) e(1633)e\left(\frac{16}{33}\right) e(1011)e\left(\frac{10}{11}\right) e(2633)e\left(\frac{26}{33}\right) e(1366)e\left(\frac{13}{66}\right) e(2122)e\left(\frac{21}{22}\right) e(733)e\left(\frac{7}{33}\right) e(233)e\left(\frac{2}{33}\right) e(3133)e\left(\frac{31}{33}\right)
χ483(41,⋅)\chi_{483}(41,\cdot) 483.v 22 yes 11 11 e(1322)e\left(\frac{13}{22}\right) e(211)e\left(\frac{2}{11}\right) e(611)e\left(\frac{6}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(322)e\left(\frac{3}{22}\right) e(922)e\left(\frac{9}{22}\right) e(322)e\left(\frac{3}{22}\right) e(411)e\left(\frac{4}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1522)e\left(\frac{15}{22}\right)
χ483(43,⋅)\chi_{483}(43,\cdot) 483.t 22 no −1-1 11 e(511)e\left(\frac{5}{11}\right) e(1011)e\left(\frac{10}{11}\right) e(522)e\left(\frac{5}{22}\right) e(411)e\left(\frac{4}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(122)e\left(\frac{1}{22}\right) e(211)e\left(\frac{2}{11}\right) e(911)e\left(\frac{9}{11}\right) e(1322)e\left(\frac{13}{22}\right) e(922)e\left(\frac{9}{22}\right)
χ483(44,⋅)\chi_{483}(44,\cdot) 483.bc 66 yes 11 11 e(2366)e\left(\frac{23}{66}\right) e(2333)e\left(\frac{23}{33}\right) e(2533)e\left(\frac{25}{33}\right) e(122)e\left(\frac{1}{22}\right) e(766)e\left(\frac{7}{66}\right) e(533)e\left(\frac{5}{33}\right) e(311)e\left(\frac{3}{11}\right) e(1333)e\left(\frac{13}{33}\right) e(3233)e\left(\frac{32}{33}\right) e(3566)e\left(\frac{35}{66}\right)
χ483(47,⋅)\chi_{483}(47,\cdot) 483.n 6 no 11 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right)
χ483(50,⋅)\chi_{483}(50,\cdot) 483.x 22 no −1-1 11 e(1922)e\left(\frac{19}{22}\right) e(811)e\left(\frac{8}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(1322)e\left(\frac{13}{22}\right) e(611)e\left(\frac{6}{11}\right) e(322)e\left(\frac{3}{22}\right) e(611)e\left(\frac{6}{11}\right) e(511)e\left(\frac{5}{11}\right) e(1722)e\left(\frac{17}{22}\right) e(811)e\left(\frac{8}{11}\right)
χ483(52,⋅)\chi_{483}(52,\cdot) 483.be 66 no −1-1 11 e(3233)e\left(\frac{32}{33}\right) e(3133)e\left(\frac{31}{33}\right) e(4366)e\left(\frac{43}{66}\right) e(1011)e\left(\frac{10}{11}\right) e(4166)e\left(\frac{41}{66}\right) e(133)e\left(\frac{1}{33}\right) e(2122)e\left(\frac{21}{22}\right) e(2933)e\left(\frac{29}{33}\right) e(5966)e\left(\frac{59}{66}\right) e(766)e\left(\frac{7}{66}\right)
χ483(53,⋅)\chi_{483}(53,\cdot) 483.bc 66 yes 11 11 e(3766)e\left(\frac{37}{66}\right) e(433)e\left(\frac{4}{33}\right) e(2333)e\left(\frac{23}{33}\right) e(1522)e\left(\frac{15}{22}\right) e(1766)e\left(\frac{17}{66}\right) e(3133)e\left(\frac{31}{33}\right) e(111)e\left(\frac{1}{11}\right) e(833)e\left(\frac{8}{33}\right) e(733)e\left(\frac{7}{33}\right) e(1966)e\left(\frac{19}{66}\right)
χ483(55,⋅)\chi_{483}(55,\cdot) 483.s 22 no −1-1 11 e(1011)e\left(\frac{10}{11}\right) e(911)e\left(\frac{9}{11}\right) e(2122)e\left(\frac{21}{22}\right) e(811)e\left(\frac{8}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(111)e\left(\frac{1}{11}\right) e(1922)e\left(\frac{19}{22}\right) e(711)e\left(\frac{7}{11}\right) e(1522)e\left(\frac{15}{22}\right) e(722)e\left(\frac{7}{22}\right)
χ483(58,⋅)\chi_{483}(58,\cdot) 483.y 33 no 11 11 e(1633)e\left(\frac{16}{33}\right) e(3233)e\left(\frac{32}{33}\right) e(1933)e\left(\frac{19}{33}\right) e(511)e\left(\frac{5}{11}\right) e(233)e\left(\frac{2}{33}\right) e(1733)e\left(\frac{17}{33}\right) e(811)e\left(\frac{8}{11}\right) e(3133)e\left(\frac{31}{33}\right) e(2333)e\left(\frac{23}{33}\right) e(1033)e\left(\frac{10}{33}\right)
χ483(59,⋅)\chi_{483}(59,\cdot) 483.bb 66 yes 11 11 e(766)e\left(\frac{7}{66}\right) e(733)e\left(\frac{7}{33}\right) e(3233)e\left(\frac{32}{33}\right) e(722)e\left(\frac{7}{22}\right) e(566)e\left(\frac{5}{66}\right) e(5966)e\left(\frac{59}{66}\right) e(922)e\left(\frac{9}{22}\right) e(1433)e\left(\frac{14}{33}\right) e(433)e\left(\frac{4}{33}\right) e(2566)e\left(\frac{25}{66}\right)
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