# Properties

 Modulus 200 Structure $$C_{20}\times C_{2}\times C_{2}$$ Order 80

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(200)

pari: g = idealstar(,200,2)

## Character group

 sage: G.order()  pari: g.no Order = 80 sage: H.invariants()  pari: g.cyc Structure = $$C_{20}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{200}(177,\cdot)$, $\chi_{200}(151,\cdot)$, $\chi_{200}(101,\cdot)$

## First 32 of 80 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
$$\chi_{200}(1,\cdot)$$ 200.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{200}(3,\cdot)$$ 200.v 20 yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{200}(7,\cdot)$$ 200.j 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$i$$ $$-i$$
$$\chi_{200}(9,\cdot)$$ 200.q 10 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{200}(11,\cdot)$$ 200.n 10 yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{200}(13,\cdot)$$ 200.x 20 yes $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{200}(17,\cdot)$$ 200.u 20 no $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{200}(19,\cdot)$$ 200.s 10 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{200}(21,\cdot)$$ 200.t 10 yes $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{200}(23,\cdot)$$ 200.w 20 no $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{200}(27,\cdot)$$ 200.v 20 yes $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{200}(29,\cdot)$$ 200.o 10 yes $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{200}(31,\cdot)$$ 200.r 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{200}(33,\cdot)$$ 200.u 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{200}(37,\cdot)$$ 200.x 20 yes $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{200}(39,\cdot)$$ 200.p 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{200}(41,\cdot)$$ 200.m 5 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{200}(43,\cdot)$$ 200.k 4 no $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$-i$$
$$\chi_{200}(47,\cdot)$$ 200.w 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{200}(49,\cdot)$$ 200.c 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{200}(51,\cdot)$$ 200.g 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{200}(53,\cdot)$$ 200.x 20 yes $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{200}(57,\cdot)$$ 200.l 4 no $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$i$$
$$\chi_{200}(59,\cdot)$$ 200.s 10 yes $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{200}(61,\cdot)$$ 200.t 10 yes $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{200}(63,\cdot)$$ 200.w 20 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{200}(67,\cdot)$$ 200.v 20 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{200}(69,\cdot)$$ 200.o 10 yes $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{200}(71,\cdot)$$ 200.r 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{200}(73,\cdot)$$ 200.u 20 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{200}(77,\cdot)$$ 200.x 20 yes $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{200}(79,\cdot)$$ 200.p 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$