Properties

Modulus 6039
Structure \(C_{60}\times C_{30}\times C_{2}\)
Order 3600

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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(6039)
pari: g = idealstar(,6039,2)

Character group

sage: G.order()
pari: g.no
Order = 3600
sage: H.invariants()
pari: g.cyc
Structure = \(C_{60}\times C_{30}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{6039}(5248,\cdot)$, $\chi_{6039}(4820,\cdot)$, $\chi_{6039}(1099,\cdot)$

First 32 of 3600 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 4 5 7 8 10 13 14 16 17
\(\chi_{6039}(1,\cdot)\) 6039.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6039}(2,\cdot)\) 6039.nc 60 Yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{6039}(4,\cdot)\) 6039.hj 30 Yes \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{6039}(5,\cdot)\) 6039.hb 30 Yes \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6039}(7,\cdot)\) 6039.oo 60 Yes \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{41}{60}\right)\)
\(\chi_{6039}(8,\cdot)\) 6039.fm 20 No \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{6039}(10,\cdot)\) 6039.nt 60 No \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{6039}(13,\cdot)\) 6039.lt 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{6039}(14,\cdot)\) 6039.ku 30 Yes \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{6039}(16,\cdot)\) 6039.eq 15 Yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{6039}(17,\cdot)\) 6039.mt 60 No \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{6039}(19,\cdot)\) 6039.kj 30 No \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{6039}(20,\cdot)\) 6039.ma 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{6039}(23,\cdot)\) 6039.nv 60 No \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{6039}(25,\cdot)\) 6039.eh 15 Yes \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{6039}(26,\cdot)\) 6039.mu 60 No \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{6039}(28,\cdot)\) 6039.ff 20 No \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{6039}(29,\cdot)\) 6039.pk 60 Yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{60}\right)\)
\(\chi_{6039}(31,\cdot)\) 6039.qc 60 Yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{43}{60}\right)\) \(-i\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{37}{60}\right)\)
\(\chi_{6039}(32,\cdot)\) 6039.ec 12 Yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{6039}(34,\cdot)\) 6039.ev 15 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{6039}(35,\cdot)\) 6039.nz 60 No \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{6039}(37,\cdot)\) 6039.fr 20 No \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{6039}(38,\cdot)\) 6039.mv 60 Yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(i\)
\(\chi_{6039}(40,\cdot)\) 6039.pd 60 Yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{53}{60}\right)\)
\(\chi_{6039}(41,\cdot)\) 6039.je 30 Yes \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(-1\)
\(\chi_{6039}(43,\cdot)\) 6039.ok 60 Yes \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{6039}(46,\cdot)\) 6039.jn 30 No \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6039}(47,\cdot)\) 6039.lg 30 Yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{6039}(49,\cdot)\) 6039.ho 30 Yes \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{6039}(50,\cdot)\) 6039.nx 60 Yes \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{6039}(52,\cdot)\) 6039.gj 30 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)