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Properties

Modulus 119119
Structure C2×C48C_{2}\times C_{48}
Order 9696

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(119)
 
pari: g = idealstar(,119,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C48C_{2}\times C_{48}
sage: H.gens()
 
pari: g.gen
 
Generators = χ119(52,⋅)\chi_{119}(52,\cdot), χ119(71,⋅)\chi_{119}(71,\cdot)

First 32 of 96 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 33 44 55 66 88 99 1010 1111 1212
χ119(1,⋅)\chi_{119}(1,\cdot) 119.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ119(2,⋅)\chi_{119}(2,\cdot) 119.q 24 yes 11 11 e(1112)e\left(\frac{11}{12}\right) e(524)e\left(\frac{5}{24}\right) e(56)e\left(\frac{5}{6}\right) e(124)e\left(\frac{1}{24}\right) e(18)e\left(\frac{1}{8}\right) −i-i e(512)e\left(\frac{5}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(124)e\left(\frac{1}{24}\right)
χ119(3,⋅)\chi_{119}(3,\cdot) 119.s 48 yes 11 11 e(524)e\left(\frac{5}{24}\right) e(1148)e\left(\frac{11}{48}\right) e(512)e\left(\frac{5}{12}\right) e(748)e\left(\frac{7}{48}\right) e(716)e\left(\frac{7}{16}\right) e(58)e\left(\frac{5}{8}\right) e(1124)e\left(\frac{11}{24}\right) e(1748)e\left(\frac{17}{48}\right) e(548)e\left(\frac{5}{48}\right) e(3148)e\left(\frac{31}{48}\right)
χ119(4,⋅)\chi_{119}(4,\cdot) 119.n 12 yes 11 11 e(56)e\left(\frac{5}{6}\right) e(512)e\left(\frac{5}{12}\right) e(23)e\left(\frac{2}{3}\right) e(112)e\left(\frac{1}{12}\right) ii −1-1 e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right)
χ119(5,⋅)\chi_{119}(5,\cdot) 119.s 48 yes 11 11 e(124)e\left(\frac{1}{24}\right) e(748)e\left(\frac{7}{48}\right) e(112)e\left(\frac{1}{12}\right) e(3548)e\left(\frac{35}{48}\right) e(316)e\left(\frac{3}{16}\right) e(18)e\left(\frac{1}{8}\right) e(724)e\left(\frac{7}{24}\right) e(3748)e\left(\frac{37}{48}\right) e(2548)e\left(\frac{25}{48}\right) e(1148)e\left(\frac{11}{48}\right)
χ119(6,⋅)\chi_{119}(6,\cdot) 119.p 16 yes 11 11 e(18)e\left(\frac{1}{8}\right) e(716)e\left(\frac{7}{16}\right) ii e(316)e\left(\frac{3}{16}\right) e(916)e\left(\frac{9}{16}\right) e(38)e\left(\frac{3}{8}\right) e(78)e\left(\frac{7}{8}\right) e(516)e\left(\frac{5}{16}\right) e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right)
χ119(8,⋅)\chi_{119}(8,\cdot) 119.k 8 no 11 11 −i-i e(58)e\left(\frac{5}{8}\right) −1-1 e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) ii ii e(78)e\left(\frac{7}{8}\right) e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right)
χ119(9,⋅)\chi_{119}(9,\cdot) 119.q 24 yes 11 11 e(512)e\left(\frac{5}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(56)e\left(\frac{5}{6}\right) e(724)e\left(\frac{7}{24}\right) e(78)e\left(\frac{7}{8}\right) ii e(1112)e\left(\frac{11}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(524)e\left(\frac{5}{24}\right) e(724)e\left(\frac{7}{24}\right)
χ119(10,⋅)\chi_{119}(10,\cdot) 119.s 48 yes 11 11 e(2324)e\left(\frac{23}{24}\right) e(1748)e\left(\frac{17}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(3748)e\left(\frac{37}{48}\right) e(516)e\left(\frac{5}{16}\right) e(78)e\left(\frac{7}{8}\right) e(1724)e\left(\frac{17}{24}\right) e(3548)e\left(\frac{35}{48}\right) e(4748)e\left(\frac{47}{48}\right) e(1348)e\left(\frac{13}{48}\right)
χ119(11,⋅)\chi_{119}(11,\cdot) 119.t 48 yes −1-1 11 e(1124)e\left(\frac{11}{24}\right) e(548)e\left(\frac{5}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(2548)e\left(\frac{25}{48}\right) e(916)e\left(\frac{9}{16}\right) e(38)e\left(\frac{3}{8}\right) e(524)e\left(\frac{5}{24}\right) e(4748)e\left(\frac{47}{48}\right) e(3548)e\left(\frac{35}{48}\right) e(148)e\left(\frac{1}{48}\right)
χ119(12,⋅)\chi_{119}(12,\cdot) 119.s 48 yes 11 11 e(124)e\left(\frac{1}{24}\right) e(3148)e\left(\frac{31}{48}\right) e(112)e\left(\frac{1}{12}\right) e(1148)e\left(\frac{11}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(18)e\left(\frac{1}{8}\right) e(724)e\left(\frac{7}{24}\right) e(1348)e\left(\frac{13}{48}\right) e(148)e\left(\frac{1}{48}\right) e(3548)e\left(\frac{35}{48}\right)
χ119(13,⋅)\chi_{119}(13,\cdot) 119.f 4 yes −1-1 11 −1-1 −i-i 11 −i-i ii −1-1 −1-1 ii −i-i −i-i
χ119(15,⋅)\chi_{119}(15,\cdot) 119.k 8 no 11 11 ii e(38)e\left(\frac{3}{8}\right) −1-1 e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) −i-i −i-i e(18)e\left(\frac{1}{8}\right) e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right)
χ119(16,⋅)\chi_{119}(16,\cdot) 119.j 6 yes 11 11 e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right) −1-1 11 e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right)
χ119(18,⋅)\chi_{119}(18,\cdot) 119.e 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)
χ119(19,⋅)\chi_{119}(19,\cdot) 119.r 24 yes −1-1 11 e(1112)e\left(\frac{11}{12}\right) e(1724)e\left(\frac{17}{24}\right) e(56)e\left(\frac{5}{6}\right) e(1324)e\left(\frac{13}{24}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(512)e\left(\frac{5}{12}\right) e(1124)e\left(\frac{11}{24}\right) e(1124)e\left(\frac{11}{24}\right) e(1324)e\left(\frac{13}{24}\right)
χ119(20,⋅)\chi_{119}(20,\cdot) 119.p 16 yes 11 11 e(78)e\left(\frac{7}{8}\right) e(916)e\left(\frac{9}{16}\right) −i-i e(1316)e\left(\frac{13}{16}\right) e(716)e\left(\frac{7}{16}\right) e(58)e\left(\frac{5}{8}\right) e(18)e\left(\frac{1}{8}\right) e(1116)e\left(\frac{11}{16}\right) e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right)
χ119(22,⋅)\chi_{119}(22,\cdot) 119.o 16 no −1-1 11 e(38)e\left(\frac{3}{8}\right) e(516)e\left(\frac{5}{16}\right) −i-i e(916)e\left(\frac{9}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(18)e\left(\frac{1}{8}\right) e(58)e\left(\frac{5}{8}\right) e(1516)e\left(\frac{15}{16}\right) e(316)e\left(\frac{3}{16}\right) e(116)e\left(\frac{1}{16}\right)
χ119(23,⋅)\chi_{119}(23,\cdot) 119.t 48 yes −1-1 11 e(1924)e\left(\frac{19}{24}\right) e(1348)e\left(\frac{13}{48}\right) e(712)e\left(\frac{7}{12}\right) e(1748)e\left(\frac{17}{48}\right) e(116)e\left(\frac{1}{16}\right) e(38)e\left(\frac{3}{8}\right) e(1324)e\left(\frac{13}{24}\right) e(748)e\left(\frac{7}{48}\right) e(4348)e\left(\frac{43}{48}\right) e(4148)e\left(\frac{41}{48}\right)
χ119(24,⋅)\chi_{119}(24,\cdot) 119.s 48 yes 11 11 e(2324)e\left(\frac{23}{24}\right) e(4148)e\left(\frac{41}{48}\right) e(1112)e\left(\frac{11}{12}\right) e(1348)e\left(\frac{13}{48}\right) e(1316)e\left(\frac{13}{16}\right) e(78)e\left(\frac{7}{8}\right) e(1724)e\left(\frac{17}{24}\right) e(1148)e\left(\frac{11}{48}\right) e(2348)e\left(\frac{23}{48}\right) e(3748)e\left(\frac{37}{48}\right)
χ119(25,⋅)\chi_{119}(25,\cdot) 119.q 24 yes 11 11 e(112)e\left(\frac{1}{12}\right) e(724)e\left(\frac{7}{24}\right) e(16)e\left(\frac{1}{6}\right) e(1124)e\left(\frac{11}{24}\right) e(38)e\left(\frac{3}{8}\right) ii e(712)e\left(\frac{7}{12}\right) e(1324)e\left(\frac{13}{24}\right) e(124)e\left(\frac{1}{24}\right) e(1124)e\left(\frac{11}{24}\right)
χ119(26,⋅)\chi_{119}(26,\cdot) 119.r 24 yes −1-1 11 e(512)e\left(\frac{5}{12}\right) e(2324)e\left(\frac{23}{24}\right) e(56)e\left(\frac{5}{6}\right) e(1924)e\left(\frac{19}{24}\right) e(38)e\left(\frac{3}{8}\right) ii e(1112)e\left(\frac{11}{12}\right) e(524)e\left(\frac{5}{24}\right) e(524)e\left(\frac{5}{24}\right) e(1924)e\left(\frac{19}{24}\right)
χ119(27,⋅)\chi_{119}(27,\cdot) 119.p 16 yes 11 11 e(58)e\left(\frac{5}{8}\right) e(1116)e\left(\frac{11}{16}\right) ii e(716)e\left(\frac{7}{16}\right) e(516)e\left(\frac{5}{16}\right) e(78)e\left(\frac{7}{8}\right) e(38)e\left(\frac{3}{8}\right) e(116)e\left(\frac{1}{16}\right) e(516)e\left(\frac{5}{16}\right) e(1516)e\left(\frac{15}{16}\right)
χ119(29,⋅)\chi_{119}(29,\cdot) 119.o 16 no −1-1 11 e(38)e\left(\frac{3}{8}\right) e(1316)e\left(\frac{13}{16}\right) −i-i e(116)e\left(\frac{1}{16}\right) e(316)e\left(\frac{3}{16}\right) e(18)e\left(\frac{1}{8}\right) e(58)e\left(\frac{5}{8}\right) e(716)e\left(\frac{7}{16}\right) e(1116)e\left(\frac{11}{16}\right) e(916)e\left(\frac{9}{16}\right)
χ119(30,⋅)\chi_{119}(30,\cdot) 119.n 12 yes 11 11 e(16)e\left(\frac{1}{6}\right) e(712)e\left(\frac{7}{12}\right) e(13)e\left(\frac{1}{3}\right) e(1112)e\left(\frac{11}{12}\right) −i-i −1-1 e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) e(112)e\left(\frac{1}{12}\right) e(1112)e\left(\frac{11}{12}\right)
χ119(31,⋅)\chi_{119}(31,\cdot) 119.s 48 yes 11 11 e(524)e\left(\frac{5}{24}\right) e(3548)e\left(\frac{35}{48}\right) e(512)e\left(\frac{5}{12}\right) e(3148)e\left(\frac{31}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(58)e\left(\frac{5}{8}\right) e(1124)e\left(\frac{11}{24}\right) e(4148)e\left(\frac{41}{48}\right) e(2948)e\left(\frac{29}{48}\right) e(748)e\left(\frac{7}{48}\right)
χ119(32,⋅)\chi_{119}(32,\cdot) 119.q 24 yes 11 11 e(712)e\left(\frac{7}{12}\right) e(124)e\left(\frac{1}{24}\right) e(16)e\left(\frac{1}{6}\right) e(524)e\left(\frac{5}{24}\right) e(58)e\left(\frac{5}{8}\right) −i-i e(112)e\left(\frac{1}{12}\right) e(1924)e\left(\frac{19}{24}\right) e(724)e\left(\frac{7}{24}\right) e(524)e\left(\frac{5}{24}\right)
χ119(33,⋅)\chi_{119}(33,\cdot) 119.h 6 yes −1-1 11 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) 11 11 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(23)e\left(\frac{2}{3}\right)
χ119(36,⋅)\chi_{119}(36,\cdot) 119.k 8 no 11 11 ii e(78)e\left(\frac{7}{8}\right) −1-1 e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) −i-i −i-i e(58)e\left(\frac{5}{8}\right) e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right)
χ119(37,⋅)\chi_{119}(37,\cdot) 119.t 48 yes −1-1 11 e(1324)e\left(\frac{13}{24}\right) e(1948)e\left(\frac{19}{48}\right) e(112)e\left(\frac{1}{12}\right) e(4748)e\left(\frac{47}{48}\right) e(1516)e\left(\frac{15}{16}\right) e(58)e\left(\frac{5}{8}\right) e(1924)e\left(\frac{19}{24}\right) e(2548)e\left(\frac{25}{48}\right) e(3748)e\left(\frac{37}{48}\right) e(2348)e\left(\frac{23}{48}\right)
χ119(38,⋅)\chi_{119}(38,\cdot) 119.m 12 yes −1-1 11 e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(23)e\left(\frac{2}{3}\right) e(712)e\left(\frac{7}{12}\right) −i-i −1-1 e(56)e\left(\frac{5}{6}\right) e(512)e\left(\frac{5}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(712)e\left(\frac{7}{12}\right)
χ119(39,⋅)\chi_{119}(39,\cdot) 119.t 48 yes −1-1 11 e(1724)e\left(\frac{17}{24}\right) e(4748)e\left(\frac{47}{48}\right) e(512)e\left(\frac{5}{12}\right) e(4348)e\left(\frac{43}{48}\right) e(1116)e\left(\frac{11}{16}\right) e(18)e\left(\frac{1}{8}\right) e(2324)e\left(\frac{23}{24}\right) e(2948)e\left(\frac{29}{48}\right) e(4148)e\left(\frac{41}{48}\right) e(1948)e\left(\frac{19}{48}\right)
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