Properties

Modulus $160$
Structure \(C_{8}\times C_{4}\times C_{2}\)
Order $64$

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(160)
 
pari: g = idealstar(,160,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 64
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{8}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{160}(101,\cdot)$, $\chi_{160}(97,\cdot)$, $\chi_{160}(31,\cdot)$

First 32 of 64 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{160}(1,\cdot)\) 160.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{160}(3,\cdot)\) 160.ba 8 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{160}(7,\cdot)\) 160.s 4 no \(1\) \(1\) \(1\) \(i\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(i\) \(-i\) \(1\)
\(\chi_{160}(9,\cdot)\) 160.q 4 no \(1\) \(1\) \(-i\) \(1\) \(-1\) \(-i\) \(-i\) \(-1\) \(i\) \(-i\) \(1\) \(i\)
\(\chi_{160}(11,\cdot)\) 160.w 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{160}(13,\cdot)\) 160.v 8 yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{160}(17,\cdot)\) 160.m 4 no \(-1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(i\) \(i\) \(1\) \(-1\) \(-i\) \(-i\)
\(\chi_{160}(19,\cdot)\) 160.y 8 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{160}(21,\cdot)\) 160.x 8 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{160}(23,\cdot)\) 160.s 4 no \(1\) \(1\) \(1\) \(-i\) \(1\) \(i\) \(-1\) \(-i\) \(i\) \(-i\) \(i\) \(1\)
\(\chi_{160}(27,\cdot)\) 160.ba 8 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{160}(29,\cdot)\) 160.z 8 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{160}(31,\cdot)\) 160.b 2 no \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\)
\(\chi_{160}(33,\cdot)\) 160.p 4 no \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\)
\(\chi_{160}(37,\cdot)\) 160.v 8 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{160}(39,\cdot)\) 160.k 4 no \(-1\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(-1\) \(i\)
\(\chi_{160}(41,\cdot)\) 160.l 4 no \(1\) \(1\) \(i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(i\) \(-i\) \(-1\) \(-i\)
\(\chi_{160}(43,\cdot)\) 160.u 8 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{160}(47,\cdot)\) 160.o 4 no \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(i\) \(i\)
\(\chi_{160}(49,\cdot)\) 160.f 2 no \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{160}(51,\cdot)\) 160.w 8 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{160}(53,\cdot)\) 160.bb 8 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{160}(57,\cdot)\) 160.i 4 no \(-1\) \(1\) \(-1\) \(-i\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(i\) \(i\) \(-1\)
\(\chi_{160}(59,\cdot)\) 160.y 8 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{160}(61,\cdot)\) 160.x 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{160}(63,\cdot)\) 160.n 4 no \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(1\) \(1\) \(-i\) \(i\)
\(\chi_{160}(67,\cdot)\) 160.u 8 yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{160}(69,\cdot)\) 160.z 8 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{160}(71,\cdot)\) 160.r 4 no \(-1\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(i\) \(i\) \(1\) \(-i\)
\(\chi_{160}(73,\cdot)\) 160.i 4 no \(-1\) \(1\) \(-1\) \(i\) \(1\) \(-i\) \(-1\) \(-i\) \(-i\) \(-i\) \(-i\) \(-1\)
\(\chi_{160}(77,\cdot)\) 160.bb 8 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{160}(79,\cdot)\) 160.e 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\)