Properties

Modulus $930$
Structure \(C_{60}\times C_{2}\times C_{2}\)
Order $240$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(930)
 
pari: g = idealstar(,930,2)
 

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 = $\chi_{930}(311,\cdot)$, $\chi_{930}(187,\cdot)$, $\chi_{930}(871,\cdot)$

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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(37\) \(41\) \(43\)
\(\chi_{930}(1,\cdot)\) 930.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{930}(7,\cdot)\) 930.bv 60 no \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{60}\right)\)
\(\chi_{930}(11,\cdot)\) 930.br 30 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{930}(13,\cdot)\) 930.bt 60 no \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{60}\right)\)
\(\chi_{930}(17,\cdot)\) 930.bu 60 no \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{930}(19,\cdot)\) 930.bn 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{930}(23,\cdot)\) 930.bi 20 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{930}(29,\cdot)\) 930.y 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{930}(37,\cdot)\) 930.be 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{930}(41,\cdot)\) 930.bq 30 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{930}(43,\cdot)\) 930.bt 60 no \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{930}(47,\cdot)\) 930.bk 20 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{930}(49,\cdot)\) 930.bn 30 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{930}(53,\cdot)\) 930.bu 60 no \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{930}(59,\cdot)\) 930.bl 30 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{930}(61,\cdot)\) 930.f 2 no \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\)
\(\chi_{930}(67,\cdot)\) 930.bc 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{930}(71,\cdot)\) 930.bq 30 no \(-1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{930}(73,\cdot)\) 930.bt 60 no \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{49}{60}\right)\)
\(\chi_{930}(77,\cdot)\) 930.bi 20 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{930}(79,\cdot)\) 930.bm 30 no \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{930}(83,\cdot)\) 930.bu 60 no \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{37}{60}\right)\)
\(\chi_{930}(89,\cdot)\) 930.y 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{930}(91,\cdot)\) 930.x 10 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{930}(97,\cdot)\) 930.bh 20 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{930}(101,\cdot)\) 930.w 10 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{930}(103,\cdot)\) 930.bv 60 no \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{930}(107,\cdot)\) 930.bs 60 no \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{60}\right)\)
\(\chi_{930}(109,\cdot)\) 930.z 10 no \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{930}(113,\cdot)\) 930.bs 60 no \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{930}(119,\cdot)\) 930.r 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{930}(121,\cdot)\) 930.bg 15 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\)