Properties

Modulus $7440$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}\)
Order $1920$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(7440)
 
pari: g = idealstar(,7440,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1920
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{7440}(6511,\cdot)$, $\chi_{7440}(1861,\cdot)$, $\chi_{7440}(4961,\cdot)$, $\chi_{7440}(2977,\cdot)$, $\chi_{7440}(5521,\cdot)$

First 32 of 1920 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(37\) \(41\) \(43\)
\(\chi_{7440}(1,\cdot)\) 7440.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{7440}(7,\cdot)\) 7440.lt 60 no \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{60}\right)\)
\(\chi_{7440}(11,\cdot)\) 7440.mf 60 no \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{7440}(13,\cdot)\) 7440.lk 60 no \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{7440}(17,\cdot)\) 7440.lu 60 no \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{7440}(19,\cdot)\) 7440.ko 60 no \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{7440}(23,\cdot)\) 7440.hy 20 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{7440}(29,\cdot)\) 7440.hp 20 yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{7440}(37,\cdot)\) 7440.gk 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{7440}(41,\cdot)\) 7440.kf 30 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{7440}(43,\cdot)\) 7440.lc 60 no \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{7440}(47,\cdot)\) 7440.hu 20 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{7440}(49,\cdot)\) 7440.jq 30 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{7440}(53,\cdot)\) 7440.lj 60 yes \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{7440}(59,\cdot)\) 7440.kr 60 yes \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{60}\right)\)
\(\chi_{7440}(61,\cdot)\) 7440.bj 4 no \(-1\) \(1\) \(-1\) \(i\) \(-i\) \(-1\) \(i\) \(1\) \(-i\) \(i\) \(-1\) \(i\)
\(\chi_{7440}(67,\cdot)\) 7440.gi 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7440}(71,\cdot)\) 7440.ji 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{7440}(73,\cdot)\) 7440.lz 60 no \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{7440}(77,\cdot)\) 7440.ij 20 yes \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{7440}(79,\cdot)\) 7440.kl 30 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{7440}(83,\cdot)\) 7440.lr 60 yes \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{7440}(89,\cdot)\) 7440.fn 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{7440}(91,\cdot)\) 7440.hs 20 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{7440}(97,\cdot)\) 7440.hz 20 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{7440}(101,\cdot)\) 7440.jd 20 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{7440}(103,\cdot)\) 7440.lt 60 no \(1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{7440}(107,\cdot)\) 7440.lh 60 yes \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{7440}(109,\cdot)\) 7440.hq 20 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{7440}(113,\cdot)\) 7440.ku 60 no \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{7440}(119,\cdot)\) 7440.dj 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7440}(121,\cdot)\) 7440.jz 30 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
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