Properties

Modulus 9900
Structure \(C_{60}\times C_{10}\times C_{2}\times C_{2}\)
Order 2400

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(9900)
pari: g = idealstar(,9900,2)

Character group

sage: G.order()
pari: g.no
Order = 2400
sage: H.invariants()
pari: g.cyc
Structure = \(C_{60}\times C_{10}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{9900}(4577,\cdot)$, $\chi_{9900}(4501,\cdot)$, $\chi_{9900}(4049,\cdot)$, $\chi_{9900}(4951,\cdot)$

First 32 of 2400 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 13 17 19 23 29 31 37 41 43
\(\chi_{9900}(1,\cdot)\) 9900.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{9900}(7,\cdot)\) 9900.mm 60 No \(-1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{9900}(13,\cdot)\) 9900.lx 60 No \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(-i\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(17,\cdot)\) 9900.gk 20 No \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\)
\(\chi_{9900}(19,\cdot)\) 9900.ds 10 No \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(-1\)
\(\chi_{9900}(23,\cdot)\) 9900.lu 60 No \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(29,\cdot)\) 9900.kn 30 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{9900}(31,\cdot)\) 9900.it 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(37,\cdot)\) 9900.hg 20 No \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\)
\(\chi_{9900}(41,\cdot)\) 9900.id 30 No \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(43,\cdot)\) 9900.fh 12 No \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(47,\cdot)\) 9900.lt 60 Yes \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(i\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(49,\cdot)\) 9900.il 30 No \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(53,\cdot)\) 9900.gv 20 No \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{9900}(59,\cdot)\) 9900.kr 30 Yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{9900}(61,\cdot)\) 9900.ic 30 No \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(67,\cdot)\) 9900.lk 60 No \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{9900}(71,\cdot)\) 9900.dx 10 No \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\)
\(\chi_{9900}(73,\cdot)\) 9900.ho 20 No \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(1\) \(e\left(\frac{1}{20}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{9900}(79,\cdot)\) 9900.hx 30 Yes \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(83,\cdot)\) 9900.mc 60 Yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(89,\cdot)\) 9900.by 10 No \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\)
\(\chi_{9900}(91,\cdot)\) 9900.dr 10 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\)
\(\chi_{9900}(97,\cdot)\) 9900.mf 60 No \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{9900}(101,\cdot)\) 9900.ih 30 No \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(103,\cdot)\) 9900.lp 60 Yes \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(107,\cdot)\) 9900.hk 20 No \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\)
\(\chi_{9900}(109,\cdot)\) 9900.ez 10 No \(-1\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\)
\(\chi_{9900}(113,\cdot)\) 9900.ld 60 No \(1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{9900}(119,\cdot)\) 9900.jq 30 Yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{9900}(127,\cdot)\) 9900.ha 20 No \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{9900}(131,\cdot)\) 9900.hq 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\)