Properties

Modulus 1015
Structure \(C_{84}\times C_{4}\times C_{2}\)
Order 672

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1015)
pari: g = idealstar(,1015,2)

Character group

sage: G.order()
pari: g.no
Order = 672
sage: H.invariants()
pari: g.cyc
Structure = \(C_{84}\times C_{4}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{1015}(292,\cdot)$, $\chi_{1015}(99,\cdot)$, $\chi_{1015}(349,\cdot)$

First 32 of 672 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 8 9 11 12 13 16
\(\chi_{1015}(1,\cdot)\) 1015.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1015}(2,\cdot)\) 1015.da 84 Yes \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{1015}(3,\cdot)\) 1015.cq 84 Yes \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{1015}(4,\cdot)\) 1015.cp 42 Yes \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{1015}(6,\cdot)\) 1015.bt 14 No \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1015}(8,\cdot)\) 1015.by 28 No \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1015}(9,\cdot)\) 1015.cp 42 Yes \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{1015}(11,\cdot)\) 1015.cy 84 No \(-1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1015}(12,\cdot)\) 1015.bo 12 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1015}(13,\cdot)\) 1015.cg 28 Yes \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(-i\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{1015}(16,\cdot)\) 1015.bw 21 No \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{1015}(17,\cdot)\) 1015.bd 12 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1015}(18,\cdot)\) 1015.da 84 Yes \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1015}(19,\cdot)\) 1015.cu 84 Yes \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{1015}(22,\cdot)\) 1015.cc 28 No \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1015}(23,\cdot)\) 1015.cv 84 Yes \(-1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{1015}(24,\cdot)\) 1015.cm 42 Yes \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{1015}(26,\cdot)\) 1015.ct 84 No \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{1015}(27,\cdot)\) 1015.ci 28 Yes \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(-1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1015}(31,\cdot)\) 1015.ct 84 No \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{1015}(32,\cdot)\) 1015.da 84 Yes \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{1015}(33,\cdot)\) 1015.cw 84 Yes \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{1015}(34,\cdot)\) 1015.br 14 Yes \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1015}(36,\cdot)\) 1015.bc 7 No \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1015}(37,\cdot)\) 1015.cr 84 Yes \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{1015}(38,\cdot)\) 1015.cw 84 Yes \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{1015}(39,\cdot)\) 1015.cx 84 Yes \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{1015}(41,\cdot)\) 1015.r 4 No \(1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(1\)
\(\chi_{1015}(43,\cdot)\) 1015.ch 28 No \(1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1015}(44,\cdot)\) 1015.cx 84 Yes \(-1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{1015}(46,\cdot)\) 1015.bg 12 No \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1015}(47,\cdot)\) 1015.cq 84 Yes \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{21}\right)\)