Properties

Modulus $2015$
Structure \(C_{60}\times C_{12}\times C_{2}\)
Order $1440$

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2015)
 
pari: g = idealstar(,2015,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{12}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2015}(313,\cdot)$, $\chi_{2015}(1861,\cdot)$, $\chi_{2015}(1704,\cdot)$

First 32 of 1440 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.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(14\)
\(\chi_{2015}(1,\cdot)\) 2015.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2015}(2,\cdot)\) 2015.hk 60 yes \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2015}(3,\cdot)\) 2015.gn 60 yes \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{2015}(4,\cdot)\) 2015.fm 30 yes \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2015}(6,\cdot)\) 2015.cr 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2015}(7,\cdot)\) 2015.gc 60 yes \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{2015}(8,\cdot)\) 2015.ej 20 yes \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{2015}(9,\cdot)\) 2015.fb 30 yes \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{2015}(11,\cdot)\) 2015.hi 60 no \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{2015}(12,\cdot)\) 2015.gz 60 yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{2015}(14,\cdot)\) 2015.ft 30 no \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{2015}(16,\cdot)\) 2015.eg 15 no \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2015}(17,\cdot)\) 2015.gr 60 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{2015}(18,\cdot)\) 2015.hr 60 yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{2015}(19,\cdot)\) 2015.hj 60 yes \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{2015}(21,\cdot)\) 2015.gl 60 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{2015}(22,\cdot)\) 2015.gn 60 yes \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{2015}(23,\cdot)\) 2015.gp 60 yes \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{2015}(24,\cdot)\) 2015.hc 60 yes \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{2015}(27,\cdot)\) 2015.en 20 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{2015}(28,\cdot)\) 2015.fy 60 yes \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{2015}(29,\cdot)\) 2015.fg 30 yes \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{2015}(32,\cdot)\) 2015.cp 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-1\)
\(\chi_{2015}(33,\cdot)\) 2015.hk 60 yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2015}(34,\cdot)\) 2015.hh 60 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{2015}(36,\cdot)\) 2015.bx 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2015}(37,\cdot)\) 2015.ea 12 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2015}(38,\cdot)\) 2015.hb 60 yes \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{2015}(41,\cdot)\) 2015.gf 60 no \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{2015}(42,\cdot)\) 2015.gu 60 yes \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{2015}(43,\cdot)\) 2015.gr 60 yes \(1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{2015}(44,\cdot)\) 2015.hh 60 yes \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{15}\right)\)