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Properties

Modulus 156156
Structure C2×C2×C12C_{2}\times C_{2}\times C_{12}
Order 4848

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(156)
 
pari: g = idealstar(,156,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 48
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C2×C12C_{2}\times C_{2}\times C_{12}
sage: H.gens()
 
pari: g.gen
 
Generators = χ156(79,⋅)\chi_{156}(79,\cdot), χ156(53,⋅)\chi_{156}(53,\cdot), χ156(145,⋅)\chi_{156}(145,\cdot)

First 32 of 48 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 1717 1919 2323 2525 2929 3131 3535
χ156(1,⋅)\chi_{156}(1,\cdot) 156.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ156(5,⋅)\chi_{156}(5,\cdot) 156.m 4 no 11 11 ii ii −i-i 11 −i-i 11 −1-1 −1-1 −i-i −1-1
χ156(7,⋅)\chi_{156}(7,\cdot) 156.w 12 no 11 11 ii e(712)e\left(\frac{7}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) −i-i e(56)e\left(\frac{5}{6}\right)
χ156(11,⋅)\chi_{156}(11,\cdot) 156.v 12 yes −1-1 11 −i-i e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(56)e\left(\frac{5}{6}\right) −i-i e(23)e\left(\frac{2}{3}\right)
χ156(17,⋅)\chi_{156}(17,\cdot) 156.s 6 no −1-1 11 11 e(56)e\left(\frac{5}{6}\right) 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) 11 e(16)e\left(\frac{1}{6}\right) −1-1 e(56)e\left(\frac{5}{6}\right)
χ156(19,⋅)\chi_{156}(19,\cdot) 156.w 12 no 11 11 −i-i e(112)e\left(\frac{1}{12}\right) e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) ii e(56)e\left(\frac{5}{6}\right)
χ156(23,⋅)\chi_{156}(23,\cdot) 156.r 6 yes 11 11 11 e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) 11 e(56)e\left(\frac{5}{6}\right) 11 e(23)e\left(\frac{2}{3}\right)
χ156(25,⋅)\chi_{156}(25,\cdot) 156.b 2 no 11 11 −1-1 −1-1 −1-1 11 −1-1 11 11 11 −1-1 11
χ156(29,⋅)\chi_{156}(29,\cdot) 156.o 6 no −1-1 11 −1-1 e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) 11 e(16)e\left(\frac{1}{6}\right)
χ156(31,⋅)\chi_{156}(31,\cdot) 156.k 4 no 11 11 −i-i −i-i −i-i −1-1 ii 11 −1-1 11 ii −1-1
χ156(35,⋅)\chi_{156}(35,\cdot) 156.p 6 yes 11 11 −1-1 e(56)e\left(\frac{5}{6}\right) 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(23)e\left(\frac{2}{3}\right) 11 e(16)e\left(\frac{1}{6}\right) −1-1 e(13)e\left(\frac{1}{3}\right)
χ156(37,⋅)\chi_{156}(37,\cdot) 156.x 12 no −1-1 11 ii e(512)e\left(\frac{5}{12}\right) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) −1-1 e(13)e\left(\frac{1}{3}\right) ii e(23)e\left(\frac{2}{3}\right)
χ156(41,⋅)\chi_{156}(41,\cdot) 156.u 12 no 11 11 ii e(1112)e\left(\frac{11}{12}\right) e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(56)e\left(\frac{5}{6}\right) −i-i e(16)e\left(\frac{1}{6}\right)
χ156(43,⋅)\chi_{156}(43,\cdot) 156.n 6 no −1-1 11 −1-1 e(13)e\left(\frac{1}{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(16)e\left(\frac{1}{6}\right) 11 e(23)e\left(\frac{2}{3}\right) 11 e(56)e\left(\frac{5}{6}\right)
χ156(47,⋅)\chi_{156}(47,\cdot) 156.l 4 yes −1-1 11 −i-i ii −i-i 11 −i-i −1-1 −1-1 −1-1 −i-i 11
χ156(49,⋅)\chi_{156}(49,\cdot) 156.q 6 no 11 11 −1-1 e(16)e\left(\frac{1}{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) 11 e(13)e\left(\frac{1}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right)
χ156(53,⋅)\chi_{156}(53,\cdot) 156.d 2 no −1-1 11 −1-1 11 −1-1 −1-1 11 −1-1 11 −1-1 11 −1-1
χ156(55,⋅)\chi_{156}(55,\cdot) 156.t 6 no −1-1 11 11 e(16)e\left(\frac{1}{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(56)e\left(\frac{5}{6}\right) 11 e(13)e\left(\frac{1}{3}\right) −1-1 e(16)e\left(\frac{1}{6}\right)
χ156(59,⋅)\chi_{156}(59,\cdot) 156.v 12 yes −1-1 11 −i-i e(712)e\left(\frac{7}{12}\right) e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(16)e\left(\frac{1}{6}\right) −i-i e(13)e\left(\frac{1}{3}\right)
χ156(61,⋅)\chi_{156}(61,\cdot) 156.i 3 no 11 11 11 e(13)e\left(\frac{1}{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) 11 e(23)e\left(\frac{2}{3}\right) 11 e(13)e\left(\frac{1}{3}\right)
χ156(67,⋅)\chi_{156}(67,\cdot) 156.w 12 no 11 11 −i-i e(512)e\left(\frac{5}{12}\right) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right) ii e(16)e\left(\frac{1}{6}\right)
χ156(71,⋅)\chi_{156}(71,\cdot) 156.v 12 yes −1-1 11 ii e(112)e\left(\frac{1}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(16)e\left(\frac{1}{6}\right) ii e(13)e\left(\frac{1}{3}\right)
χ156(73,⋅)\chi_{156}(73,\cdot) 156.j 4 no −1-1 11 ii −i-i −i-i −1-1 ii −1-1 −1-1 11 ii 11
χ156(77,⋅)\chi_{156}(77,\cdot) 156.g 2 no −1-1 11 11 −1-1 11 −1-1 −1-1 −1-1 11 −1-1 −1-1 −1-1
χ156(79,⋅)\chi_{156}(79,\cdot) 156.f 2 no −1-1 11 11 −1-1 −1-1 11 −1-1 −1-1 11 11 −1-1 −1-1
χ156(83,⋅)\chi_{156}(83,\cdot) 156.l 4 yes −1-1 11 ii −i-i ii 11 ii −1-1 −1-1 −1-1 ii 11
χ156(85,⋅)\chi_{156}(85,\cdot) 156.x 12 no −1-1 11 ii e(112)e\left(\frac{1}{12}\right) e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right) e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(23)e\left(\frac{2}{3}\right) ii e(13)e\left(\frac{1}{3}\right)
χ156(89,⋅)\chi_{156}(89,\cdot) 156.u 12 no 11 11 −i-i e(512)e\left(\frac{5}{12}\right) e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right) e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(56)e\left(\frac{5}{6}\right) ii e(16)e\left(\frac{1}{6}\right)
χ156(95,⋅)\chi_{156}(95,\cdot) 156.r 6 yes 11 11 11 e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) 11 e(16)e\left(\frac{1}{6}\right) 11 e(13)e\left(\frac{1}{3}\right)
χ156(97,⋅)\chi_{156}(97,\cdot) 156.x 12 no −1-1 11 −i-i e(712)e\left(\frac{7}{12}\right) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right) e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) −1-1 e(23)e\left(\frac{2}{3}\right) −i-i e(13)e\left(\frac{1}{3}\right)
χ156(101,⋅)\chi_{156}(101,\cdot) 156.s 6 no −1-1 11 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) −1-1 e(16)e\left(\frac{1}{6}\right)
χ156(103,⋅)\chi_{156}(103,\cdot) 156.e 2 no −1-1 11 −1-1 11 11 11 11 −1-1 11 11 11 −1-1
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