Properties

 Modulus 485 Structure $$C_{96}\times C_{4}$$ Order 384

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(485)

pari: g = idealstar(,485,2)

Character group

 sage: G.order()  pari: g.no Order = 384 sage: H.invariants()  pari: g.cyc Structure = $$C_{96}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{485}(296,\cdot)$, $\chi_{485}(292,\cdot)$

First 32 of 384 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 6 7 8 9 11 12 13
$$\chi_{485}(1,\cdot)$$ 485.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{485}(2,\cdot)$$ 485.bm 48 yes $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{485}(3,\cdot)$$ 485.bm 48 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{48}\right)$$
$$\chi_{485}(4,\cdot)$$ 485.bd 24 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{485}(6,\cdot)$$ 485.x 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{485}(7,\cdot)$$ 485.br 96 yes $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{25}{96}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{79}{96}\right)$$
$$\chi_{485}(8,\cdot)$$ 485.ba 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{485}(9,\cdot)$$ 485.bd 24 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{485}(11,\cdot)$$ 485.bk 48 no $$1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{485}(12,\cdot)$$ 485.ba 16 yes $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{485}(13,\cdot)$$ 485.br 96 yes $$1$$ $$1$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{79}{96}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{73}{96}\right)$$
$$\chi_{485}(14,\cdot)$$ 485.bp 96 yes $$-1$$ $$1$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{41}{96}\right)$$
$$\chi_{485}(16,\cdot)$$ 485.x 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{485}(17,\cdot)$$ 485.bo 96 yes $$1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{95}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{89}{96}\right)$$
$$\chi_{485}(18,\cdot)$$ 485.ba 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{485}(19,\cdot)$$ 485.bi 32 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$
$$\chi_{485}(21,\cdot)$$ 485.bq 96 no $$-1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{29}{96}\right)$$
$$\chi_{485}(22,\cdot)$$ 485.j 4 yes $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{485}(23,\cdot)$$ 485.br 96 yes $$1$$ $$1$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{29}{96}\right)$$
$$\chi_{485}(24,\cdot)$$ 485.bd 24 yes $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{485}(26,\cdot)$$ 485.bq 96 no $$-1$$ $$1$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{96}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{35}{96}\right)$$
$$\chi_{485}(27,\cdot)$$ 485.ba 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{485}(28,\cdot)$$ 485.bg 32 yes $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$
$$\chi_{485}(29,\cdot)$$ 485.bp 96 yes $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{67}{96}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{85}{96}\right)$$
$$\chi_{485}(31,\cdot)$$ 485.bk 48 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{485}(32,\cdot)$$ 485.bm 48 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{485}(33,\cdot)$$ 485.r 8 yes $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{485}(34,\cdot)$$ 485.bi 32 yes $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{485}(36,\cdot)$$ 485.l 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{485}(37,\cdot)$$ 485.br 96 yes $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{61}{96}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{43}{96}\right)$$
$$\chi_{485}(38,\cdot)$$ 485.bo 96 yes $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{85}{96}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{19}{96}\right)$$
$$\chi_{485}(39,\cdot)$$ 485.bp 96 yes $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{96}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{96}\right)$$