Properties

Modulus 915
Structure \(C_{60}\times C_{4}\times C_{2}\)
Order 480

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(915)
pari: g = idealstar(,915,2)

Character group

sage: G.order()
pari: g.no
Order = 480
sage: H.invariants()
pari: g.cyc
Structure = \(C_{60}\times C_{4}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{915}(856,\cdot)$, $\chi_{915}(367,\cdot)$, $\chi_{915}(611,\cdot)$

First 32 of 480 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 7 8 11 13 14 16 17 19
\(\chi_{915}(1,\cdot)\) 915.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{915}(2,\cdot)\) 915.cr 60 Yes \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{915}(4,\cdot)\) 915.cp 30 No \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{915}(7,\cdot)\) 915.db 60 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{915}(8,\cdot)\) 915.ch 20 Yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(i\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{915}(11,\cdot)\) 915.q 4 No \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(i\) \(1\) \(1\) \(1\) \(i\) \(-1\)
\(\chi_{915}(13,\cdot)\) 915.bt 12 No \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{915}(14,\cdot)\) 915.ba 6 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{915}(16,\cdot)\) 915.bw 15 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{915}(17,\cdot)\) 915.da 60 Yes \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{915}(19,\cdot)\) 915.cp 30 No \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{915}(22,\cdot)\) 915.cz 60 No \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{915}(23,\cdot)\) 915.by 20 Yes \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(i\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{915}(26,\cdot)\) 915.cu 60 No \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{915}(28,\cdot)\) 915.bx 20 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(i\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{915}(29,\cdot)\) 915.bq 12 Yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{915}(31,\cdot)\) 915.cv 60 No \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{915}(32,\cdot)\) 915.bu 12 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{915}(34,\cdot)\) 915.bj 10 No \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{915}(37,\cdot)\) 915.ci 20 No \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(-i\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{915}(38,\cdot)\) 915.ch 20 Yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(i\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{915}(41,\cdot)\) 915.bf 10 No \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{915}(43,\cdot)\) 915.db 60 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{915}(44,\cdot)\) 915.cw 60 Yes \(1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{915}(46,\cdot)\) 915.cj 30 No \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{915}(47,\cdot)\) 915.bm 12 Yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{915}(49,\cdot)\) 915.cp 30 No \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{915}(52,\cdot)\) 915.bz 20 No \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(-1\) \(-i\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{915}(53,\cdot)\) 915.by 20 Yes \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\) \(i\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{915}(56,\cdot)\) 915.cl 30 No \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{915}(58,\cdot)\) 915.cf 20 No \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(1\) \(i\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{915}(59,\cdot)\) 915.cw 60 Yes \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{30}\right)\)