# Properties

 Modulus 320 Structure $$C_{16}\times C_{4}\times C_{2}$$ Order 128

# 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(320)

pari: g = idealstar(,320,2)

## Character group

 sage: G.order()  pari: g.no Order = 128 sage: H.invariants()  pari: g.cyc Structure = $$C_{16}\times C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{320}(261,\cdot)$, $\chi_{320}(257,\cdot)$, $\chi_{320}(191,\cdot)$

## First 32 of 128 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
$$\chi_{320}(1,\cdot)$$ 320.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{320}(3,\cdot)$$ 320.bj 16 yes $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{320}(7,\cdot)$$ 320.ba 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{320}(9,\cdot)$$ 320.z 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{320}(11,\cdot)$$ 320.bg 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{320}(13,\cdot)$$ 320.bi 16 yes $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{320}(17,\cdot)$$ 320.t 4 no $$-1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-i$$ $$-i$$ $$i$$ $$1$$
$$\chi_{320}(19,\cdot)$$ 320.bh 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{320}(21,\cdot)$$ 320.be 16 no $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{320}(23,\cdot)$$ 320.ba 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{320}(27,\cdot)$$ 320.bj 16 yes $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{320}(29,\cdot)$$ 320.bf 16 yes $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{320}(31,\cdot)$$ 320.g 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{320}(33,\cdot)$$ 320.m 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$i$$
$$\chi_{320}(37,\cdot)$$ 320.bi 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{320}(39,\cdot)$$ 320.y 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{320}(41,\cdot)$$ 320.x 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{320}(43,\cdot)$$ 320.bd 16 yes $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{320}(47,\cdot)$$ 320.j 4 no $$1$$ $$1$$ $$-1$$ $$i$$ $$1$$ $$i$$ $$1$$ $$i$$ $$i$$ $$-i$$ $$-i$$ $$-1$$
$$\chi_{320}(49,\cdot)$$ 320.q 4 no $$1$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$-i$$
$$\chi_{320}(51,\cdot)$$ 320.bg 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{320}(53,\cdot)$$ 320.bc 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{320}(57,\cdot)$$ 320.v 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{320}(59,\cdot)$$ 320.bh 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{320}(61,\cdot)$$ 320.be 16 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{320}(63,\cdot)$$ 320.n 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$1$$ $$-i$$ $$i$$
$$\chi_{320}(67,\cdot)$$ 320.bd 16 yes $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{320}(69,\cdot)$$ 320.bf 16 yes $$1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{320}(71,\cdot)$$ 320.w 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{320}(73,\cdot)$$ 320.v 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{320}(77,\cdot)$$ 320.bc 16 yes $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{320}(79,\cdot)$$ 320.k 4 no $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$i$$