Properties

Modulus 133
Structure \(C_{18}\times C_{6}\)
Order 108

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(133)
 
pari: g = idealstar(,133,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 108
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{18}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{133}(78,\cdot)$, $\chi_{133}(115,\cdot)$

First 32 of 108 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.

orbit label order primitive -1 1 2 3 4 5 6 8 9 10 11 12
\(\chi_{133}(1,\cdot)\) 133.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{133}(2,\cdot)\) 133.be 18 Yes \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(1\) \(-1\)
\(\chi_{133}(3,\cdot)\) 133.bb 18 Yes \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{133}(4,\cdot)\) 133.w 9 Yes \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(1\)
\(\chi_{133}(5,\cdot)\) 133.z 18 Yes \(-1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(1\) \(-1\)
\(\chi_{133}(6,\cdot)\) 133.y 18 Yes \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(8,\cdot)\) 133.q 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)
\(\chi_{133}(9,\cdot)\) 133.u 9 Yes \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{133}(10,\cdot)\) 133.bf 18 Yes \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)
\(\chi_{133}(11,\cdot)\) 133.h 3 Yes \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{133}(12,\cdot)\) 133.i 6 Yes \(1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{133}(13,\cdot)\) 133.ba 18 Yes \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{133}(15,\cdot)\) 133.bc 18 No \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(16,\cdot)\) 133.w 9 Yes \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(1\)
\(\chi_{133}(17,\cdot)\) 133.x 18 Yes \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(18,\cdot)\) 133.r 6 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{133}(20,\cdot)\) 133.d 2 No \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{133}(22,\cdot)\) 133.bc 18 No \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{133}(23,\cdot)\) 133.u 9 Yes \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{133}(24,\cdot)\) 133.x 18 Yes \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(25,\cdot)\) 133.w 9 Yes \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(1\)
\(\chi_{133}(26,\cdot)\) 133.t 6 Yes \(-1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(27,\cdot)\) 133.p 6 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)
\(\chi_{133}(29,\cdot)\) 133.bc 18 No \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(30,\cdot)\) 133.g 3 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{133}(31,\cdot)\) 133.s 6 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{133}(32,\cdot)\) 133.be 18 Yes \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(1\) \(-1\)
\(\chi_{133}(33,\cdot)\) 133.bf 18 Yes \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(1\) \(1\)
\(\chi_{133}(34,\cdot)\) 133.ba 18 Yes \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{133}(36,\cdot)\) 133.v 9 No \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{133}(37,\cdot)\) 133.r 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{133}(39,\cdot)\) 133.f 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)