# Properties

 Modulus $265$ Structure $$C_{52}\times C_{4}$$ Order $208$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(265)

pari: g = idealstar(,265,2)

## Character group

 sage: G.order()  pari: g.no Order = 208 sage: H.invariants()  pari: g.cyc Structure = $$C_{52}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{265}(107,\cdot)$, $\chi_{265}(161,\cdot)$

## First 32 of 208 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$
$$\chi_{265}(1,\cdot)$$ 265.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{265}(2,\cdot)$$ 265.t 52 yes $$1$$ $$1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{11}{52}\right)$$
$$\chi_{265}(3,\cdot)$$ 265.o 52 yes $$1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{5}{52}\right)$$
$$\chi_{265}(4,\cdot)$$ 265.l 26 yes $$1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{265}(6,\cdot)$$ 265.m 26 no $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{265}(7,\cdot)$$ 265.p 52 yes $$-1$$ $$1$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$
$$\chi_{265}(8,\cdot)$$ 265.t 52 yes $$1$$ $$1$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{33}{52}\right)$$
$$\chi_{265}(9,\cdot)$$ 265.l 26 yes $$1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$
$$\chi_{265}(11,\cdot)$$ 265.m 26 no $$1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$
$$\chi_{265}(12,\cdot)$$ 265.o 52 yes $$1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{27}{52}\right)$$
$$\chi_{265}(13,\cdot)$$ 265.q 52 yes $$-1$$ $$1$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{17}{52}\right)$$
$$\chi_{265}(14,\cdot)$$ 265.r 52 yes $$-1$$ $$1$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{265}(16,\cdot)$$ 265.k 13 no $$1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{265}(17,\cdot)$$ 265.p 52 yes $$-1$$ $$1$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{19}{52}\right)$$
$$\chi_{265}(18,\cdot)$$ 265.t 52 yes $$1$$ $$1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{21}{52}\right)$$
$$\chi_{265}(19,\cdot)$$ 265.r 52 yes $$-1$$ $$1$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{265}(21,\cdot)$$ 265.s 52 no $$-1$$ $$1$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{265}(22,\cdot)$$ 265.o 52 yes $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$
$$\chi_{265}(23,\cdot)$$ 265.e 4 yes $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$i$$
$$\chi_{265}(24,\cdot)$$ 265.n 26 yes $$1$$ $$1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{265}(26,\cdot)$$ 265.s 52 no $$-1$$ $$1$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{7}{13}\right)$$
$$\chi_{265}(27,\cdot)$$ 265.o 52 yes $$1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{15}{52}\right)$$
$$\chi_{265}(28,\cdot)$$ 265.q 52 yes $$-1$$ $$1$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{33}{52}\right)$$
$$\chi_{265}(29,\cdot)$$ 265.l 26 yes $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{265}(31,\cdot)$$ 265.s 52 no $$-1$$ $$1$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{265}(32,\cdot)$$ 265.t 52 yes $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{3}{52}\right)$$
$$\chi_{265}(33,\cdot)$$ 265.t 52 yes $$1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{45}{52}\right)$$
$$\chi_{265}(34,\cdot)$$ 265.r 52 yes $$-1$$ $$1$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$
$$\chi_{265}(36,\cdot)$$ 265.k 13 no $$1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{265}(37,\cdot)$$ 265.p 52 yes $$-1$$ $$1$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{31}{52}\right)$$
$$\chi_{265}(38,\cdot)$$ 265.p 52 yes $$-1$$ $$1$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{41}{52}\right)$$
$$\chi_{265}(39,\cdot)$$ 265.r 52 yes $$-1$$ $$1$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$