Properties

 Modulus 110 Structure $$C_{20}\times C_{2}$$ Order 40

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(110)

pari: g = idealstar(,110,2)

Character group

 sage: G.order()  pari: g.no Order = 40 sage: H.invariants()  pari: g.cyc Structure = $$C_{20}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{110}(13,\cdot)$, $\chi_{110}(21,\cdot)$

First 32 of 40 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 13 17 19 21 23 27 29
$$\chi_{110}(1,\cdot)$$ 110.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{110}(3,\cdot)$$ 110.l 20 No $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{110}(7,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{110}(9,\cdot)$$ 110.j 10 No $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{110}(13,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{110}(17,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{110}(19,\cdot)$$ 110.i 10 No $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{110}(21,\cdot)$$ 110.d 2 No $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{110}(23,\cdot)$$ 110.e 4 No $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$
$$\chi_{110}(27,\cdot)$$ 110.l 20 No $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{110}(29,\cdot)$$ 110.i 10 No $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{110}(31,\cdot)$$ 110.g 5 No $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{110}(37,\cdot)$$ 110.l 20 No $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{110}(39,\cdot)$$ 110.i 10 No $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{110}(41,\cdot)$$ 110.h 10 No $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{110}(43,\cdot)$$ 110.f 4 No $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$1$$
$$\chi_{110}(47,\cdot)$$ 110.l 20 No $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{110}(49,\cdot)$$ 110.j 10 No $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{110}(51,\cdot)$$ 110.h 10 No $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{110}(53,\cdot)$$ 110.l 20 No $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{110}(57,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{110}(59,\cdot)$$ 110.j 10 No $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{110}(61,\cdot)$$ 110.h 10 No $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{110}(63,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{110}(67,\cdot)$$ 110.e 4 No $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$
$$\chi_{110}(69,\cdot)$$ 110.j 10 No $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{110}(71,\cdot)$$ 110.g 5 No $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{110}(73,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{110}(79,\cdot)$$ 110.i 10 No $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{110}(81,\cdot)$$ 110.g 5 No $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{110}(83,\cdot)$$ 110.k 20 No $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{110}(87,\cdot)$$ 110.f 4 No $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$i$$ $$1$$