Properties

Modulus $900$
Structure \(C_{60}\times C_{2}\times C_{2}\)
Order $240$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(900)
 
pari: g = idealstar(,900,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 240
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{900}(451,\cdot)$, $\chi_{900}(101,\cdot)$, $\chi_{900}(577,\cdot)$

First 32 of 240 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{900}(1,\cdot)\) 900.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{900}(7,\cdot)\) 900.bf 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{900}(11,\cdot)\) 900.br 30 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{900}(13,\cdot)\) 900.bv 60 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{900}(17,\cdot)\) 900.bk 20 no \(1\) \(1\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{900}(19,\cdot)\) 900.bb 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{900}(23,\cdot)\) 900.bu 60 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{900}(29,\cdot)\) 900.bo 30 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{900}(31,\cdot)\) 900.bp 30 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{900}(37,\cdot)\) 900.bi 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(41,\cdot)\) 900.bm 30 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(43,\cdot)\) 900.bf 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{900}(47,\cdot)\) 900.bu 60 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{900}(49,\cdot)\) 900.s 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{900}(53,\cdot)\) 900.bk 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{900}(59,\cdot)\) 900.bn 30 yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(61,\cdot)\) 900.bg 15 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{900}(67,\cdot)\) 900.bs 60 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{900}(71,\cdot)\) 900.v 10 no \(1\) \(1\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{900}(73,\cdot)\) 900.bi 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{900}(77,\cdot)\) 900.bt 60 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{900}(79,\cdot)\) 900.bl 30 yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{900}(83,\cdot)\) 900.bu 60 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{900}(89,\cdot)\) 900.y 10 no \(-1\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{900}(91,\cdot)\) 900.x 10 no \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(97,\cdot)\) 900.bv 60 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{900}(101,\cdot)\) 900.p 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{900}(103,\cdot)\) 900.bs 60 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{900}(107,\cdot)\) 900.m 4 no \(-1\) \(1\) \(-i\) \(1\) \(-i\) \(-i\) \(1\) \(-i\) \(1\) \(-1\) \(i\) \(-1\)
\(\chi_{900}(109,\cdot)\) 900.w 10 no \(1\) \(1\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(113,\cdot)\) 900.bt 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(119,\cdot)\) 900.bn 30 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{30}\right)\)