Properties

 Modulus $328$ Structure $$C_{40}\times C_{2}\times C_{2}$$ Order $160$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(328)

pari: g = idealstar(,328,2)

Character group

 sage: G.order()  pari: g.no Order = 160 sage: H.invariants()  pari: g.cyc Structure = $$C_{40}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{328}(247,\cdot)$, $\chi_{328}(165,\cdot)$, $\chi_{328}(129,\cdot)$

First 32 of 160 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{328}(1,\cdot)$$ 328.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{328}(3,\cdot)$$ 328.p 8 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$
$$\chi_{328}(5,\cdot)$$ 328.y 20 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{328}(7,\cdot)$$ 328.bc 40 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$i$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{328}(9,\cdot)$$ 328.j 4 no $$1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$-i$$ $$-i$$ $$-i$$ $$-1$$
$$\chi_{328}(11,\cdot)$$ 328.bd 40 yes $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$i$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{328}(13,\cdot)$$ 328.bf 40 yes $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$i$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{328}(15,\cdot)$$ 328.bc 40 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{328}(17,\cdot)$$ 328.be 40 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$-i$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{328}(19,\cdot)$$ 328.bd 40 yes $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$-i$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{328}(21,\cdot)$$ 328.y 20 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{328}(23,\cdot)$$ 328.v 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{328}(25,\cdot)$$ 328.s 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{328}(27,\cdot)$$ 328.p 8 yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$
$$\chi_{328}(29,\cdot)$$ 328.bf 40 yes $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$i$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{328}(31,\cdot)$$ 328.v 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{328}(33,\cdot)$$ 328.ba 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{328}(35,\cdot)$$ 328.bd 40 yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$-i$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{328}(37,\cdot)$$ 328.u 10 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{328}(39,\cdot)$$ 328.bb 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{328}(43,\cdot)$$ 328.z 20 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{328}(45,\cdot)$$ 328.w 10 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{328}(47,\cdot)$$ 328.bc 40 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$-i$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{328}(49,\cdot)$$ 328.ba 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$-1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{328}(51,\cdot)$$ 328.x 10 yes $$-1$$ $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{328}(53,\cdot)$$ 328.bf 40 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$i$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{328}(55,\cdot)$$ 328.q 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$
$$\chi_{328}(57,\cdot)$$ 328.m 5 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{328}(59,\cdot)$$ 328.x 10 yes $$-1$$ $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{328}(61,\cdot)$$ 328.y 20 yes $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{328}(63,\cdot)$$ 328.bc 40 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$-i$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{328}(65,\cdot)$$ 328.be 40 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$-i$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$