Properties

Modulus 104
Structure \(C_{12}\times C_{2}\times C_{2}\)
Order 48

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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(104)
 
pari: g = idealstar(,104,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 48
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{104}(41,\cdot)$, $\chi_{104}(79,\cdot)$, $\chi_{104}(53,\cdot)$

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.

orbit label order primitive -1 1 3 5 7 9 11 15 17 19 21 23
\(\chi_{104}(1,\cdot)\) 104.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{104}(3,\cdot)\) 104.n 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(5,\cdot)\) 104.j 4 Yes \(-1\) \(1\) \(-1\) \(i\) \(i\) \(1\) \(-i\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\)
\(\chi_{104}(7,\cdot)\) 104.w 12 No \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(9,\cdot)\) 104.i 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(11,\cdot)\) 104.u 12 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(15,\cdot)\) 104.w 12 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(17,\cdot)\) 104.o 6 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(19,\cdot)\) 104.u 12 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(21,\cdot)\) 104.j 4 Yes \(-1\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(i\) \(-1\)
\(\chi_{104}(23,\cdot)\) 104.q 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(25,\cdot)\) 104.f 2 No \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{104}(27,\cdot)\) 104.g 2 No \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{104}(29,\cdot)\) 104.r 6 Yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(31,\cdot)\) 104.k 4 No \(1\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(1\)
\(\chi_{104}(33,\cdot)\) 104.v 12 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(35,\cdot)\) 104.n 6 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(37,\cdot)\) 104.x 12 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(41,\cdot)\) 104.v 12 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(43,\cdot)\) 104.p 6 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(45,\cdot)\) 104.x 12 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{104}(47,\cdot)\) 104.k 4 No \(1\) \(1\) \(-1\) \(i\) \(i\) \(1\) \(i\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\)
\(\chi_{104}(49,\cdot)\) 104.o 6 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(51,\cdot)\) 104.h 2 Yes \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{104}(53,\cdot)\) 104.b 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{104}(55,\cdot)\) 104.t 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{104}(57,\cdot)\) 104.l 4 No \(-1\) \(1\) \(1\) \(-i\) \(i\) \(1\) \(i\) \(-i\) \(-1\) \(-i\) \(i\) \(-1\)
\(\chi_{104}(59,\cdot)\) 104.u 12 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(61,\cdot)\) 104.r 6 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{104}(63,\cdot)\) 104.w 12 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(67,\cdot)\) 104.u 12 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{104}(69,\cdot)\) 104.s 6 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)