Properties

Modulus 96
Structure \(C_{8}\times C_{2}\times C_{2}\)
Order 32

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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(96)
 
pari: g = idealstar(,96,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 32
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{8}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{96}(37,\cdot)$, $\chi_{96}(65,\cdot)$, $\chi_{96}(31,\cdot)$

First 32 of 32 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 5 7 11 13 17 19 23 25 29 31
\(\chi_{96}(1,\cdot)\) 96.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{96}(5,\cdot)\) 96.p 8 Yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{96}(7,\cdot)\) 96.l 4 No \(-1\) \(1\) \(i\) \(1\) \(-i\) \(-i\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-1\)
\(\chi_{96}(11,\cdot)\) 96.o 8 Yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\)
\(\chi_{96}(13,\cdot)\) 96.n 8 No \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(1\)
\(\chi_{96}(17,\cdot)\) 96.h 2 No \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{96}(19,\cdot)\) 96.m 8 No \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\)
\(\chi_{96}(23,\cdot)\) 96.k 4 No \(1\) \(1\) \(i\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(-1\) \(-1\) \(-i\) \(-1\)
\(\chi_{96}(25,\cdot)\) 96.j 4 No \(1\) \(1\) \(i\) \(-1\) \(i\) \(-i\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(1\)
\(\chi_{96}(29,\cdot)\) 96.p 8 Yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(1\)
\(\chi_{96}(31,\cdot)\) 96.g 2 No \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{96}(35,\cdot)\) 96.o 8 Yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\)
\(\chi_{96}(37,\cdot)\) 96.n 8 No \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{96}(41,\cdot)\) 96.i 4 No \(-1\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(-1\) \(i\) \(1\) \(-1\) \(-i\) \(1\)
\(\chi_{96}(43,\cdot)\) 96.m 8 No \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\)
\(\chi_{96}(47,\cdot)\) 96.f 2 No \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\)
\(\chi_{96}(49,\cdot)\) 96.d 2 No \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{96}(53,\cdot)\) 96.p 8 Yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{96}(55,\cdot)\) 96.l 4 No \(-1\) \(1\) \(-i\) \(1\) \(i\) \(i\) \(1\) \(-i\) \(1\) \(-1\) \(i\) \(-1\)
\(\chi_{96}(59,\cdot)\) 96.o 8 Yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\)
\(\chi_{96}(61,\cdot)\) 96.n 8 No \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{96}(65,\cdot)\) 96.e 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{96}(67,\cdot)\) 96.m 8 No \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\)
\(\chi_{96}(71,\cdot)\) 96.k 4 No \(1\) \(1\) \(-i\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-1\) \(-1\) \(i\) \(-1\)
\(\chi_{96}(73,\cdot)\) 96.j 4 No \(1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(1\) \(i\) \(-1\) \(-1\) \(i\) \(1\)
\(\chi_{96}(77,\cdot)\) 96.p 8 Yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{96}(79,\cdot)\) 96.b 2 No \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\)
\(\chi_{96}(83,\cdot)\) 96.o 8 Yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\)
\(\chi_{96}(85,\cdot)\) 96.n 8 No \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{96}(89,\cdot)\) 96.i 4 No \(-1\) \(1\) \(-i\) \(-1\) \(-i\) \(-i\) \(-1\) \(-i\) \(1\) \(-1\) \(i\) \(1\)
\(\chi_{96}(91,\cdot)\) 96.m 8 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\)
\(\chi_{96}(95,\cdot)\) 96.c 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)