Properties

Modulus $385$
Structure \(C_{60}\times C_{2}\times C_{2}\)
Order $240$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(385)
 
pari: g = idealstar(,385,2)
 

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 = $\chi_{385}(232,\cdot)$, $\chi_{385}(276,\cdot)$, $\chi_{385}(211,\cdot)$

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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{385}(1,\cdot)\) 385.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{385}(2,\cdot)\) 385.bv 60 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{60}\right)\)
\(\chi_{385}(3,\cdot)\) 385.bu 60 yes \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{385}(4,\cdot)\) 385.bm 30 yes \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{385}(6,\cdot)\) 385.ba 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{385}(8,\cdot)\) 385.bj 20 no \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{385}(9,\cdot)\) 385.bm 30 yes \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{385}(12,\cdot)\) 385.bd 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{385}(13,\cdot)\) 385.bi 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{385}(16,\cdot)\) 385.bg 15 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{385}(17,\cdot)\) 385.bs 60 yes \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{385}(18,\cdot)\) 385.bv 60 yes \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{43}{60}\right)\)
\(\chi_{385}(19,\cdot)\) 385.br 30 yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{385}(23,\cdot)\) 385.be 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{385}(24,\cdot)\) 385.br 30 yes \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{385}(26,\cdot)\) 385.bq 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{385}(27,\cdot)\) 385.bk 20 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{385}(29,\cdot)\) 385.w 10 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{385}(31,\cdot)\) 385.bq 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{385}(32,\cdot)\) 385.bc 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{385}(34,\cdot)\) 385.e 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{385}(36,\cdot)\) 385.n 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{385}(37,\cdot)\) 385.bt 60 yes \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{60}\right)\)
\(\chi_{385}(38,\cdot)\) 385.bu 60 yes \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{385}(39,\cdot)\) 385.bp 30 yes \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{385}(41,\cdot)\) 385.ba 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{385}(43,\cdot)\) 385.k 4 no \(1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\) \(i\)
\(\chi_{385}(46,\cdot)\) 385.bo 30 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{385}(47,\cdot)\) 385.bu 60 yes \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{385}(48,\cdot)\) 385.bk 20 yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{385}(51,\cdot)\) 385.bo 30 no \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{385}(52,\cdot)\) 385.bs 60 yes \(-1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{60}\right)\)