Properties

Modulus $2100$
Structure \(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
Order $480$

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(2100)
 
pari: g = idealstar(,2100,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2100}(2077,\cdot)$, $\chi_{2100}(349,\cdot)$, $\chi_{2100}(701,\cdot)$, $\chi_{2100}(1051,\cdot)$

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.

Character Orbit Order Primitive \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{2100}(1,\cdot)\) 2100.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2100}(11,\cdot)\) 2100.dd 30 yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\)
\(\chi_{2100}(13,\cdot)\) 2100.co 20 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{2100}(17,\cdot)\) 2100.dm 60 no \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{2100}(19,\cdot)\) 2100.cy 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\)
\(\chi_{2100}(23,\cdot)\) 2100.dq 60 yes \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\)
\(\chi_{2100}(29,\cdot)\) 2100.ca 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\)
\(\chi_{2100}(31,\cdot)\) 2100.da 30 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\)
\(\chi_{2100}(37,\cdot)\) 2100.dp 60 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\)
\(\chi_{2100}(41,\cdot)\) 2100.cb 10 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{2100}(43,\cdot)\) 2100.t 4 no \(1\) \(1\) \(-1\) \(i\) \(-i\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(1\) \(-i\)
\(\chi_{2100}(47,\cdot)\) 2100.do 60 yes \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\)
\(\chi_{2100}(53,\cdot)\) 2100.dk 60 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{2100}(59,\cdot)\) 2100.de 30 yes \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{2100}(61,\cdot)\) 2100.dg 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)
\(\chi_{2100}(67,\cdot)\) 2100.dn 60 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\)
\(\chi_{2100}(71,\cdot)\) 2100.br 10 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\)
\(\chi_{2100}(73,\cdot)\) 2100.dr 60 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{2100}(79,\cdot)\) 2100.cz 30 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{2100}(83,\cdot)\) 2100.cp 20 yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{2100}(89,\cdot)\) 2100.cv 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\)
\(\chi_{2100}(97,\cdot)\) 2100.co 20 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{2100}(101,\cdot)\) 2100.bi 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)
\(\chi_{2100}(103,\cdot)\) 2100.dl 60 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{2100}(107,\cdot)\) 2100.cf 12 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(i\)
\(\chi_{2100}(109,\cdot)\) 2100.dh 30 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\)
\(\chi_{2100}(113,\cdot)\) 2100.ct 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{2100}(121,\cdot)\) 2100.cm 15 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{2100}(127,\cdot)\) 2100.cs 20 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{2100}(131,\cdot)\) 2100.dj 30 yes \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\)
\(\chi_{2100}(137,\cdot)\) 2100.dk 60 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{2100}(139,\cdot)\) 2100.bw 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)