# Properties

 Modulus $1088$ Structure $$C_{2}\times C_{16}\times C_{16}$$ Order $512$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1088)

pari: g = idealstar(,1088,2)

## Character group

 sage: G.order()  pari: g.no Order = 512 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{16}\times C_{16}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1088}(511,\cdot)$, $\chi_{1088}(69,\cdot)$, $\chi_{1088}(513,\cdot)$

## First 32 of 512 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$19$$ $$21$$ $$23$$
$$\chi_{1088}(1,\cdot)$$ 1088.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1088}(3,\cdot)$$ 1088.bv 16 yes $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{1088}(5,\cdot)$$ 1088.bt 16 yes $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{1088}(7,\cdot)$$ 1088.cg 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{1088}(9,\cdot)$$ 1088.bp 8 no $$1$$ $$1$$ $$i$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1088}(11,\cdot)$$ 1088.bv 16 yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{1088}(13,\cdot)$$ 1088.cs 16 yes $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1088}(15,\cdot)$$ 1088.bf 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$-i$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1088}(19,\cdot)$$ 1088.bw 16 yes $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$
$$\chi_{1088}(21,\cdot)$$ 1088.cs 16 yes $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1088}(23,\cdot)$$ 1088.cr 16 no $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1088}(25,\cdot)$$ 1088.bq 8 no $$1$$ $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1088}(27,\cdot)$$ 1088.bv 16 yes $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{1088}(29,\cdot)$$ 1088.ck 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1088}(31,\cdot)$$ 1088.cy 16 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1088}(33,\cdot)$$ 1088.h 2 no $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{1088}(35,\cdot)$$ 1088.db 16 no $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1088}(37,\cdot)$$ 1088.cb 16 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1088}(39,\cdot)$$ 1088.cx 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1088}(41,\cdot)$$ 1088.cw 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{1088}(43,\cdot)$$ 1088.di 16 yes $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$
$$\chi_{1088}(45,\cdot)$$ 1088.bz 16 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{1088}(47,\cdot)$$ 1088.t 4 no $$-1$$ $$1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$1$$ $$i$$ $$1$$ $$i$$ $$-i$$ $$-i$$
$$\chi_{1088}(49,\cdot)$$ 1088.bg 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{1088}(53,\cdot)$$ 1088.ce 16 yes $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$
$$\chi_{1088}(55,\cdot)$$ 1088.y 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$
$$\chi_{1088}(57,\cdot)$$ 1088.ch 16 no $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{1088}(59,\cdot)$$ 1088.di 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$
$$\chi_{1088}(61,\cdot)$$ 1088.bz 16 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{1088}(63,\cdot)$$ 1088.cp 16 no $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{1088}(65,\cdot)$$ 1088.cz 16 no $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{1088}(67,\cdot)$$ 1088.cm 16 yes $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$