# Properties

 Modulus 800 Structure $$C_{40}\times C_{4}\times C_{2}$$ Order 320

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(800)

pari: g = idealstar(,800,2)

## Character group

 sage: G.order()  pari: g.no Order = 320 sage: H.invariants()  pari: g.cyc Structure = $$C_{40}\times C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{800}(77,\cdot)$, $\chi_{800}(657,\cdot)$, $\chi_{800}(351,\cdot)$

## First 32 of 320 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
$$\chi_{800}(1,\cdot)$$ 800.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{800}(3,\cdot)$$ 800.cd 40 yes $$1$$ $$1$$ $$e\left(\frac{3}{40}\right)$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{800}(7,\cdot)$$ 800.s 4 no $$1$$ $$1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$i$$ $$-i$$ $$1$$
$$\chi_{800}(9,\cdot)$$ 800.bt 20 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{800}(11,\cdot)$$ 800.cb 40 yes $$-1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$-i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{800}(13,\cdot)$$ 800.bw 40 yes $$-1$$ $$1$$ $$e\left(\frac{11}{40}\right)$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{33}{40}\right)$$
$$\chi_{800}(17,\cdot)$$ 800.br 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{800}(19,\cdot)$$ 800.bz 40 yes $$-1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$-i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$
$$\chi_{800}(21,\cdot)$$ 800.ca 40 yes $$1$$ $$1$$ $$e\left(\frac{3}{40}\right)$$ $$i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{800}(23,\cdot)$$ 800.bl 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{800}(27,\cdot)$$ 800.cd 40 yes $$1$$ $$1$$ $$e\left(\frac{9}{40}\right)$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{800}(29,\cdot)$$ 800.by 40 yes $$1$$ $$1$$ $$e\left(\frac{33}{40}\right)$$ $$i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{800}(31,\cdot)$$ 800.bh 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{800}(33,\cdot)$$ 800.bo 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{800}(37,\cdot)$$ 800.bw 40 yes $$-1$$ $$1$$ $$e\left(\frac{21}{40}\right)$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{40}\right)$$
$$\chi_{800}(39,\cdot)$$ 800.bn 20 no $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{800}(41,\cdot)$$ 800.bm 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{800}(43,\cdot)$$ 800.v 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{800}(47,\cdot)$$ 800.bp 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{800}(49,\cdot)$$ 800.f 2 no $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{800}(51,\cdot)$$ 800.x 8 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{800}(53,\cdot)$$ 800.cc 40 yes $$-1$$ $$1$$ $$e\left(\frac{13}{40}\right)$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{39}{40}\right)$$
$$\chi_{800}(57,\cdot)$$ 800.i 4 no $$-1$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$i$$ $$-1$$
$$\chi_{800}(59,\cdot)$$ 800.bz 40 yes $$-1$$ $$1$$ $$e\left(\frac{31}{40}\right)$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$
$$\chi_{800}(61,\cdot)$$ 800.ca 40 yes $$1$$ $$1$$ $$e\left(\frac{29}{40}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{800}(63,\cdot)$$ 800.bq 20 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{800}(67,\cdot)$$ 800.bx 40 yes $$1$$ $$1$$ $$e\left(\frac{7}{40}\right)$$ $$-1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{800}(69,\cdot)$$ 800.by 40 yes $$1$$ $$1$$ $$e\left(\frac{27}{40}\right)$$ $$-i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$
$$\chi_{800}(71,\cdot)$$ 800.bs 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{800}(73,\cdot)$$ 800.bv 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{800}(77,\cdot)$$ 800.cc 40 yes $$-1$$ $$1$$ $$e\left(\frac{39}{40}\right)$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{800}(79,\cdot)$$ 800.bi 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$