# Properties

 Modulus $95$ Structure $$C_{2}\times C_{36}$$ Order $72$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(95)

pari: g = idealstar(,95,2)

## Character group

 sage: G.order()  pari: g.no Order = 72 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{36}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{95}(77,\cdot)$, $\chi_{95}(21,\cdot)$

## First 32 of 72 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{95}(1,\cdot)$$ 95.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{95}(2,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{95}(3,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{95}(4,\cdot)$$ 95.p 18 yes $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{95}(6,\cdot)$$ 95.k 9 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{95}(7,\cdot)$$ 95.m 12 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{95}(8,\cdot)$$ 95.l 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{95}(9,\cdot)$$ 95.p 18 yes $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{95}(11,\cdot)$$ 95.e 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{95}(12,\cdot)$$ 95.l 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{95}(13,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{95}(14,\cdot)$$ 95.o 18 yes $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{95}(16,\cdot)$$ 95.k 9 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{95}(17,\cdot)$$ 95.q 36 yes $$-1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{95}(18,\cdot)$$ 95.g 4 yes $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$-i$$
$$\chi_{95}(21,\cdot)$$ 95.n 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{95}(22,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{36}\right)$$
$$\chi_{95}(23,\cdot)$$ 95.q 36 yes $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{95}(24,\cdot)$$ 95.p 18 yes $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{95}(26,\cdot)$$ 95.e 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{95}(27,\cdot)$$ 95.l 12 yes $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{95}(28,\cdot)$$ 95.q 36 yes $$-1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$
$$\chi_{95}(29,\cdot)$$ 95.o 18 yes $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{95}(31,\cdot)$$ 95.j 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{95}(32,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{95}(33,\cdot)$$ 95.r 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{36}\right)$$
$$\chi_{95}(34,\cdot)$$ 95.o 18 yes $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{95}(36,\cdot)$$ 95.k 9 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{95}(37,\cdot)$$ 95.g 4 yes $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$i$$
$$\chi_{95}(39,\cdot)$$ 95.b 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{95}(41,\cdot)$$ 95.n 18 no $$-1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{95}(42,\cdot)$$ 95.q 36 yes $$-1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{36}\right)$$