Properties

Modulus $6930$
Structure \(C_{2}\times C_{2}\times C_{6}\times C_{60}\)
Order $1440$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(6930)
 
pari: g = idealstar(,6930,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{6}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6930}(1541,\cdot)$, $\chi_{6930}(1387,\cdot)$, $\chi_{6930}(2971,\cdot)$, $\chi_{6930}(2521,\cdot)$

First 32 of 1440 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 \(-1\) \(1\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{6930}(1,\cdot)\) 6930.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6930}(13,\cdot)\) 6930.je 60 no \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{60}\right)\)
\(\chi_{6930}(17,\cdot)\) 6930.io 60 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{47}{60}\right)\)
\(\chi_{6930}(19,\cdot)\) 6930.hv 30 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{6930}(23,\cdot)\) 6930.ev 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\)
\(\chi_{6930}(29,\cdot)\) 6930.hr 30 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{6930}(31,\cdot)\) 6930.gg 30 no \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{6930}(37,\cdot)\) 6930.ip 60 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{6930}(41,\cdot)\) 6930.hp 30 no \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{6930}(43,\cdot)\) 6930.fc 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{6930}(47,\cdot)\) 6930.ix 60 no \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(i\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{59}{60}\right)\)
\(\chi_{6930}(53,\cdot)\) 6930.if 60 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\) \(e\left(\frac{23}{60}\right)\)
\(\chi_{6930}(59,\cdot)\) 6930.hc 30 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{6930}(61,\cdot)\) 6930.hn 30 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{6930}(67,\cdot)\) 6930.ex 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{6930}(71,\cdot)\) 6930.dp 10 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{6930}(73,\cdot)\) 6930.ie 60 no \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{6930}(79,\cdot)\) 6930.hi 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(-1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{6930}(83,\cdot)\) 6930.jc 60 no \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{60}\right)\)
\(\chi_{6930}(89,\cdot)\) 6930.dj 6 no \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{6930}(97,\cdot)\) 6930.ia 60 no \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{60}\right)\)
\(\chi_{6930}(101,\cdot)\) 6930.hh 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{6930}(103,\cdot)\) 6930.iv 60 no \(1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{6930}(107,\cdot)\) 6930.jb 60 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\) \(e\left(\frac{49}{60}\right)\)
\(\chi_{6930}(109,\cdot)\) 6930.df 6 no \(-1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{6930}(113,\cdot)\) 6930.jf 60 no \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{59}{60}\right)\)
\(\chi_{6930}(127,\cdot)\) 6930.fk 20 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{6930}(131,\cdot)\) 6930.bx 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{6930}(137,\cdot)\) 6930.ik 60 no \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{6930}(139,\cdot)\) 6930.gt 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{6930}(149,\cdot)\) 6930.hb 30 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{6930}(151,\cdot)\) 6930.gd 30 no \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{5}\right)\)
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