Properties

Modulus 1800
Structure \(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
Order 480

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(1800)
 
pari: g = idealstar(,1800,2)
 

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 = $\chi_{1800}(977,\cdot)$, $\chi_{1800}(449,\cdot)$, $\chi_{1800}(1351,\cdot)$, $\chi_{1800}(901,\cdot)$

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 7 11 13 17 19 23 29 31 37 41
\(\chi_{1800}(1,\cdot)\) 1800.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1800}(7,\cdot)\) 1800.cl 12 No \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1800}(11,\cdot)\) 1800.dd 30 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1800}(13,\cdot)\) 1800.dl 60 Yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{1800}(17,\cdot)\) 1800.ct 20 No \(1\) \(1\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1800}(19,\cdot)\) 1800.bx 10 No \(-1\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1800}(23,\cdot)\) 1800.dp 60 No \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1800}(29,\cdot)\) 1800.di 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1800}(31,\cdot)\) 1800.de 30 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1800}(37,\cdot)\) 1800.cr 20 No \(-1\) \(1\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(41,\cdot)\) 1800.cy 30 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(43,\cdot)\) 1800.ce 12 No \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1800}(47,\cdot)\) 1800.dp 60 No \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1800}(49,\cdot)\) 1800.bj 6 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1800}(53,\cdot)\) 1800.co 20 No \(1\) \(1\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1800}(59,\cdot)\) 1800.cx 30 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(61,\cdot)\) 1800.cv 30 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1800}(67,\cdot)\) 1800.dr 60 Yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1800}(71,\cdot)\) 1800.bq 10 No \(1\) \(1\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1800}(73,\cdot)\) 1800.cq 20 No \(-1\) \(1\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1800}(77,\cdot)\) 1800.do 60 Yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1800}(79,\cdot)\) 1800.cw 30 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{1800}(83,\cdot)\) 1800.dm 60 Yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1800}(89,\cdot)\) 1800.bv 10 No \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1800}(91,\cdot)\) 1800.br 10 No \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(97,\cdot)\) 1800.dq 60 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{1800}(101,\cdot)\) 1800.bb 6 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1800}(103,\cdot)\) 1800.dk 60 No \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1800}(107,\cdot)\) 1800.r 4 No \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\) \(-i\) \(-1\) \(-1\) \(-i\) \(-1\)
\(\chi_{1800}(109,\cdot)\) 1800.bu 10 No \(1\) \(1\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(113,\cdot)\) 1800.dn 60 No \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(119,\cdot)\) 1800.cz 30 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{30}\right)\)