# Properties

 Modulus $245$ Structure $$C_{84}\times C_{2}$$ Order $168$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(245)

pari: g = idealstar(,245,2)

## Character group

 sage: G.order()  pari: g.no Order = 168 sage: H.invariants()  pari: g.cyc Structure = $$C_{84}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{245}(197,\cdot)$, $\chi_{245}(101,\cdot)$

## First 32 of 168 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$16$$
$$\chi_{245}(1,\cdot)$$ 245.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{245}(2,\cdot)$$ 245.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{245}(3,\cdot)$$ 245.x 84 yes $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$
$$\chi_{245}(4,\cdot)$$ 245.t 42 yes $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{245}(6,\cdot)$$ 245.n 14 no $$-1$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{245}(8,\cdot)$$ 245.r 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{245}(9,\cdot)$$ 245.t 42 yes $$1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{20}{21}\right)$$
$$\chi_{245}(11,\cdot)$$ 245.q 21 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{245}(12,\cdot)$$ 245.x 84 yes $$1$$ $$1$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{245}(13,\cdot)$$ 245.s 28 yes $$1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{245}(16,\cdot)$$ 245.q 21 no $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{245}(17,\cdot)$$ 245.x 84 yes $$1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{19}{21}\right)$$
$$\chi_{245}(18,\cdot)$$ 245.m 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{245}(19,\cdot)$$ 245.i 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{245}(22,\cdot)$$ 245.r 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{245}(23,\cdot)$$ 245.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{245}(24,\cdot)$$ 245.u 42 yes $$-1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$
$$\chi_{245}(26,\cdot)$$ 245.v 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{245}(27,\cdot)$$ 245.s 28 yes $$1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{245}(29,\cdot)$$ 245.p 14 yes $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{245}(31,\cdot)$$ 245.h 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{245}(32,\cdot)$$ 245.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{21}\right)$$
$$\chi_{245}(33,\cdot)$$ 245.x 84 yes $$1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{245}(34,\cdot)$$ 245.o 14 yes $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{245}(36,\cdot)$$ 245.k 7 no $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{245}(37,\cdot)$$ 245.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{245}(38,\cdot)$$ 245.x 84 yes $$1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{245}(39,\cdot)$$ 245.t 42 yes $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{245}(41,\cdot)$$ 245.n 14 no $$-1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{245}(43,\cdot)$$ 245.r 28 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{245}(44,\cdot)$$ 245.t 42 yes $$1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{245}(46,\cdot)$$ 245.q 21 no $$1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$