# Properties

 Modulus 203 Structure $$C_{84}\times C_{2}$$ Order 168

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(203)

pari: g = idealstar(,203,2)

## 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 = $\chi_{203}(89,\cdot)$, $\chi_{203}(202,\cdot)$

## 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.

orbit label order primitive -1 1 2 3 4 5 6 8 9 10 11 12
$$\chi_{203}(1,\cdot)$$ 203.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{203}(2,\cdot)$$ 203.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{203}(3,\cdot)$$ 203.x 84 yes $$1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{203}(4,\cdot)$$ 203.t 42 yes $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{203}(5,\cdot)$$ 203.u 42 yes $$-1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{203}(6,\cdot)$$ 203.o 14 yes $$-1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$1$$
$$\chi_{203}(8,\cdot)$$ 203.s 28 no $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$-i$$
$$\chi_{203}(9,\cdot)$$ 203.t 42 yes $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{203}(10,\cdot)$$ 203.x 84 yes $$1$$ $$1$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{203}(11,\cdot)$$ 203.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{203}(12,\cdot)$$ 203.l 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{203}(13,\cdot)$$ 203.o 14 yes $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$
$$\chi_{203}(15,\cdot)$$ 203.s 28 no $$-1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$-i$$
$$\chi_{203}(16,\cdot)$$ 203.q 21 yes $$1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{203}(17,\cdot)$$ 203.l 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{203}(18,\cdot)$$ 203.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{203}(19,\cdot)$$ 203.x 84 yes $$1$$ $$1$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{203}(20,\cdot)$$ 203.n 14 yes $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$
$$\chi_{203}(22,\cdot)$$ 203.p 14 no $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$
$$\chi_{203}(23,\cdot)$$ 203.q 21 yes $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{203}(24,\cdot)$$ 203.v 42 yes $$-1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{203}(25,\cdot)$$ 203.q 21 yes $$1$$ $$1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{203}(26,\cdot)$$ 203.x 84 yes $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{203}(27,\cdot)$$ 203.r 28 yes $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$i$$
$$\chi_{203}(30,\cdot)$$ 203.e 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{203}(31,\cdot)$$ 203.x 84 yes $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{203}(32,\cdot)$$ 203.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{203}(33,\cdot)$$ 203.u 42 yes $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{203}(34,\cdot)$$ 203.o 14 yes $$-1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$1$$
$$\chi_{203}(36,\cdot)$$ 203.k 7 no $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$
$$\chi_{203}(37,\cdot)$$ 203.w 84 yes $$-1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{203}(38,\cdot)$$ 203.u 42 yes $$-1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$