# Properties

 Modulus 640 Structure $$C_{32}\times C_{4}\times C_{2}$$ Order 256

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(640)

pari: g = idealstar(,640,2)

## Character group

 sage: G.order()  pari: g.no Order = 256 sage: H.invariants()  pari: g.cyc Structure = $$C_{32}\times C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{640}(261,\cdot)$, $\chi_{640}(257,\cdot)$, $\chi_{640}(511,\cdot)$

## First 32 of 256 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
$$\chi_{640}(1,\cdot)$$ 640.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{640}(3,\cdot)$$ 640.bl 32 yes $$1$$ $$1$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$
$$\chi_{640}(7,\cdot)$$ 640.bj 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{640}(9,\cdot)$$ 640.bf 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{640}(11,\cdot)$$ 640.bp 32 no $$-1$$ $$1$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{640}(13,\cdot)$$ 640.bk 32 yes $$-1$$ $$1$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$
$$\chi_{640}(17,\cdot)$$ 640.bb 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{640}(19,\cdot)$$ 640.bn 32 yes $$-1$$ $$1$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$
$$\chi_{640}(21,\cdot)$$ 640.bm 32 no $$1$$ $$1$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$
$$\chi_{640}(23,\cdot)$$ 640.bj 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{640}(27,\cdot)$$ 640.bl 32 yes $$1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{640}(29,\cdot)$$ 640.bo 32 yes $$1$$ $$1$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$
$$\chi_{640}(31,\cdot)$$ 640.r 4 no $$-1$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-i$$
$$\chi_{640}(33,\cdot)$$ 640.i 4 no $$-1$$ $$1$$ $$-1$$ $$i$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$-i$$ $$-i$$ $$-i$$ $$-1$$
$$\chi_{640}(37,\cdot)$$ 640.bk 32 yes $$-1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{640}(39,\cdot)$$ 640.bh 16 no $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{640}(41,\cdot)$$ 640.be 16 no $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{640}(43,\cdot)$$ 640.br 32 yes $$1$$ $$1$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{640}(47,\cdot)$$ 640.u 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{640}(49,\cdot)$$ 640.z 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{640}(51,\cdot)$$ 640.bp 32 no $$-1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{640}(53,\cdot)$$ 640.bq 32 yes $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$
$$\chi_{640}(57,\cdot)$$ 640.bi 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{640}(59,\cdot)$$ 640.bn 32 yes $$-1$$ $$1$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$
$$\chi_{640}(61,\cdot)$$ 640.bm 32 no $$1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{640}(63,\cdot)$$ 640.o 4 no $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$-i$$
$$\chi_{640}(67,\cdot)$$ 640.br 32 yes $$1$$ $$1$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$
$$\chi_{640}(69,\cdot)$$ 640.bo 32 yes $$1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{640}(71,\cdot)$$ 640.bg 16 no $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{640}(73,\cdot)$$ 640.bi 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{640}(77,\cdot)$$ 640.bq 32 yes $$-1$$ $$1$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$
$$\chi_{640}(79,\cdot)$$ 640.y 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$