Properties

Modulus 3600
Structure \(C_{60}\times C_{4}\times C_{2}\times C_{2}\)
Order 960

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(3600)
pari: g = idealstar(,3600,2)

Character group

sage: G.order()
pari: g.no
Order = 960
sage: H.invariants()
pari: g.cyc
Structure = \(C_{60}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{3600}(1877,\cdot)$, $\chi_{3600}(793,\cdot)$, $\chi_{3600}(3401,\cdot)$, $\chi_{3600}(3151,\cdot)$

First 32 of 960 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 7 11 13 17 19 23 29 31 37 41
\(\chi_{3600}(1,\cdot)\) 3600.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3600}(7,\cdot)\) 3600.cy 12 No \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3600}(11,\cdot)\) 3600.fi 60 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{3600}(13,\cdot)\) 3600.fq 60 Yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{3600}(17,\cdot)\) 3600.el 20 No \(1\) \(1\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{3600}(19,\cdot)\) 3600.dw 20 No \(-1\) \(1\) \(-1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{3600}(23,\cdot)\) 3600.fm 60 No \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{3600}(29,\cdot)\) 3600.fg 60 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{3600}(31,\cdot)\) 3600.fa 30 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{3600}(37,\cdot)\) 3600.eg 20 No \(-1\) \(1\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{3600}(41,\cdot)\) 3600.ew 30 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{3600}(43,\cdot)\) 3600.df 12 No \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3600}(47,\cdot)\) 3600.fx 60 No \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{3600}(49,\cdot)\) 3600.bz 6 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3600}(53,\cdot)\) 3600.eb 20 No \(1\) \(1\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{3600}(59,\cdot)\) 3600.gb 60 Yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{3600}(61,\cdot)\) 3600.ga 60 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{3600}(67,\cdot)\) 3600.fs 60 Yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{3600}(71,\cdot)\) 3600.cm 10 No \(1\) \(1\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{3600}(73,\cdot)\) 3600.ej 20 No \(-1\) \(1\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{3600}(77,\cdot)\) 3600.fv 60 Yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{3600}(79,\cdot)\) 3600.es 30 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{3600}(83,\cdot)\) 3600.fp 60 Yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{3600}(89,\cdot)\) 3600.cf 10 No \(-1\) \(1\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{3600}(91,\cdot)\) 3600.en 20 No \(-1\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{3600}(97,\cdot)\) 3600.fy 60 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{3600}(101,\cdot)\) 3600.do 12 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3600}(103,\cdot)\) 3600.fz 60 No \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{3600}(107,\cdot)\) 3600.ba 4 No \(-1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(-i\) \(i\) \(-i\) \(-1\) \(-1\) \(1\)
\(\chi_{3600}(109,\cdot)\) 3600.ep 20 No \(1\) \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{3600}(113,\cdot)\) 3600.fn 60 No \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{3600}(119,\cdot)\) 3600.et 30 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{30}\right)\)