# Properties

 Modulus $960$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{16}$$ Order $256$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(960)

pari: g = idealstar(,960,2)

## Character group

 sage: G.order()  pari: g.no Order = 256 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{16}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{960}(511,\cdot)$, $\chi_{960}(901,\cdot)$, $\chi_{960}(641,\cdot)$, $\chi_{960}(577,\cdot)$

## 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{960}(1,\cdot)$$ 960.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{960}(7,\cdot)$$ 960.cc 8 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$
$$\chi_{960}(11,\cdot)$$ 960.cn 16 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{960}(13,\cdot)$$ 960.cq 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{960}(17,\cdot)$$ 960.bf 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$1$$
$$\chi_{960}(19,\cdot)$$ 960.co 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{960}(23,\cdot)$$ 960.ca 8 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$
$$\chi_{960}(29,\cdot)$$ 960.cl 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{960}(31,\cdot)$$ 960.g 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{960}(37,\cdot)$$ 960.cq 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{960}(41,\cdot)$$ 960.bz 8 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$
$$\chi_{960}(43,\cdot)$$ 960.cg 16 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{960}(47,\cdot)$$ 960.bd 4 no $$-1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$i$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$1$$
$$\chi_{960}(49,\cdot)$$ 960.bl 4 no $$1$$ $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{960}(53,\cdot)$$ 960.cr 16 yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{960}(59,\cdot)$$ 960.cp 16 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{960}(61,\cdot)$$ 960.ci 16 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{960}(67,\cdot)$$ 960.cg 16 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{960}(71,\cdot)$$ 960.bx 8 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$
$$\chi_{960}(73,\cdot)$$ 960.bp 8 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$
$$\chi_{960}(77,\cdot)$$ 960.cr 16 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{960}(79,\cdot)$$ 960.q 4 no $$-1$$ $$1$$ $$-1$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$-i$$ $$-1$$
$$\chi_{960}(83,\cdot)$$ 960.ch 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{960}(89,\cdot)$$ 960.bu 8 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$
$$\chi_{960}(91,\cdot)$$ 960.cm 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{960}(97,\cdot)$$ 960.x 4 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$1$$ $$1$$ $$-i$$ $$1$$
$$\chi_{960}(101,\cdot)$$ 960.cj 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{960}(103,\cdot)$$ 960.bo 8 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$
$$\chi_{960}(107,\cdot)$$ 960.ch 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{960}(109,\cdot)$$ 960.ck 16 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{960}(113,\cdot)$$ 960.bf 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$i$$ $$-i$$ $$1$$ $$1$$ $$1$$
$$\chi_{960}(119,\cdot)$$ 960.bs 8 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$