# Properties

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

# Learn more about

Show commands for: SageMath / Pari/GP

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.

orbit label 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 $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$