Properties

 Modulus 229 Structure $$C_{228}$$ Order 228

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(229)

pari: g = idealstar(,229,2)

Character group

 sage: G.order()  pari: g.no Order = 228 sage: H.invariants()  pari: g.cyc Structure = $$C_{228}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{229}(6,\cdot)$

First 32 of 228 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 7 8 9 10 11
$$\chi_{229}(1,\cdot)$$ 229.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{229}(2,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{71}{76}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{65}{76}\right)$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{73}{76}\right)$$ $$e\left(\frac{35}{38}\right)$$
$$\chi_{229}(3,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{229}(4,\cdot)$$ 229.h 38 yes $$1$$ $$1$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{229}(5,\cdot)$$ 229.k 114 yes $$1$$ $$1$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{17}{114}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{229}(6,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{49}{114}\right)$$ $$e\left(\frac{1}{228}\right)$$ $$e\left(\frac{107}{228}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{119}{228}\right)$$ $$e\left(\frac{27}{38}\right)$$
$$\chi_{229}(7,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{65}{76}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{107}{228}\right)$$ $$e\left(\frac{49}{228}\right)$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{193}{228}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{229}(8,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{31}{76}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{29}{38}\right)$$
$$\chi_{229}(9,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{229}(10,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{73}{76}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{17}{114}\right)$$ $$e\left(\frac{119}{228}\right)$$ $$e\left(\frac{193}{228}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{25}{228}\right)$$ $$e\left(\frac{21}{38}\right)$$
$$\chi_{229}(11,\cdot)$$ 229.h 38 yes $$1$$ $$1$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{229}(12,\cdot)$$ 229.k 114 yes $$1$$ $$1$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{11}{114}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{8}{57}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{229}(13,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{59}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{11}{38}\right)$$ $$e\left(\frac{39}{76}\right)$$ $$e\left(\frac{69}{76}\right)$$ $$e\left(\frac{25}{76}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{5}{76}\right)$$ $$e\left(\frac{5}{38}\right)$$
$$\chi_{229}(14,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{229}(15,\cdot)$$ 229.h 38 yes $$1$$ $$1$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$
$$\chi_{229}(16,\cdot)$$ 229.g 19 yes $$1$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$
$$\chi_{229}(17,\cdot)$$ 229.g 19 yes $$1$$ $$1$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$
$$\chi_{229}(18,\cdot)$$ 229.f 12 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$
$$\chi_{229}(19,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{229}(20,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{41}{57}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{10}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{229}(21,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{63}{76}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{31}{76}\right)$$ $$e\left(\frac{31}{38}\right)$$
$$\chi_{229}(22,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{65}{76}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{39}{76}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{229}(23,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{25}{57}\right)$$ $$e\left(\frac{3}{38}\right)$$ $$e\left(\frac{97}{114}\right)$$ $$e\left(\frac{109}{228}\right)$$ $$e\left(\frac{35}{228}\right)$$ $$e\left(\frac{9}{76}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{203}{228}\right)$$ $$e\left(\frac{17}{38}\right)$$
$$\chi_{229}(24,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{73}{76}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{43}{228}\right)$$ $$e\left(\frac{41}{228}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{101}{228}\right)$$ $$e\left(\frac{21}{38}\right)$$
$$\chi_{229}(25,\cdot)$$ 229.i 57 yes $$1$$ $$1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{229}(26,\cdot)$$ 229.h 38 yes $$1$$ $$1$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{23}{38}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{229}(27,\cdot)$$ 229.g 19 yes $$1$$ $$1$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{229}(28,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{55}{76}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{211}{228}\right)$$ $$e\left(\frac{13}{76}\right)$$ $$e\left(\frac{49}{57}\right)$$ $$e\left(\frac{175}{228}\right)$$ $$e\left(\frac{33}{38}\right)$$
$$\chi_{229}(29,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{27}{76}\right)$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{145}{228}\right)$$ $$e\left(\frac{11}{228}\right)$$ $$e\left(\frac{5}{76}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{155}{228}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{229}(30,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{9}{76}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{33}{76}\right)$$ $$e\left(\frac{35}{76}\right)$$ $$e\left(\frac{27}{76}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{51}{76}\right)$$ $$e\left(\frac{13}{38}\right)$$
$$\chi_{229}(31,\cdot)$$ 229.l 228 yes $$-1$$ $$1$$ $$e\left(\frac{51}{76}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{53}{114}\right)$$ $$e\left(\frac{29}{228}\right)$$ $$e\left(\frac{139}{228}\right)$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{31}{228}\right)$$ $$e\left(\frac{23}{38}\right)$$
$$\chi_{229}(32,\cdot)$$ 229.j 76 yes $$-1$$ $$1$$ $$e\left(\frac{51}{76}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{35}{76}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{23}{38}\right)$$