Properties

Modulus $5148$
Structure \(C_{60}\times C_{6}\times C_{2}\times C_{2}\)
Order $1440$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5148)
 
pari: g = idealstar(,5148,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{5148}(2575,\cdot)$, $\chi_{5148}(1145,\cdot)$, $\chi_{5148}(937,\cdot)$, $\chi_{5148}(4357,\cdot)$

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 \(-1\) \(1\) \(5\) \(7\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\) \(37\)
\(\chi_{5148}(1,\cdot)\) 5148.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5148}(5,\cdot)\) 5148.ib 60 no \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{5148}(7,\cdot)\) 5148.jb 60 yes \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\)
\(\chi_{5148}(17,\cdot)\) 5148.fy 30 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{5148}(19,\cdot)\) 5148.iv 60 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{5148}(23,\cdot)\) 5148.cf 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5148}(25,\cdot)\) 5148.gd 30 no \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{5148}(29,\cdot)\) 5148.gi 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{5148}(31,\cdot)\) 5148.jd 60 yes \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{5148}(35,\cdot)\) 5148.hy 30 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{5148}(37,\cdot)\) 5148.in 60 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{60}\right)\)
\(\chi_{5148}(41,\cdot)\) 5148.ip 60 no \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{60}\right)\)
\(\chi_{5148}(43,\cdot)\) 5148.ci 6 yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5148}(47,\cdot)\) 5148.ic 60 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{5148}(49,\cdot)\) 5148.gw 30 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{5148}(53,\cdot)\) 5148.du 10 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{5148}(59,\cdot)\) 5148.ix 60 yes \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\)
\(\chi_{5148}(61,\cdot)\) 5148.hp 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{5148}(67,\cdot)\) 5148.fb 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{5148}(71,\cdot)\) 5148.iz 60 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\)
\(\chi_{5148}(73,\cdot)\) 5148.fl 20 no \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{5148}(79,\cdot)\) 5148.hn 30 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{5148}(83,\cdot)\) 5148.jf 60 yes \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{5148}(85,\cdot)\) 5148.iw 60 no \(1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{5148}(89,\cdot)\) 5148.eh 12 no \(1\) \(1\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{5148}(95,\cdot)\) 5148.he 30 yes \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{5148}(97,\cdot)\) 5148.if 60 no \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(-1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{5148}(101,\cdot)\) 5148.hl 30 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{5148}(103,\cdot)\) 5148.gm 30 yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{5148}(107,\cdot)\) 5148.hy 30 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{5148}(109,\cdot)\) 5148.y 4 no \(1\) \(1\) \(-i\) \(-i\) \(1\) \(i\) \(-1\) \(-1\) \(-1\) \(-i\) \(-1\) \(i\)
\(\chi_{5148}(113,\cdot)\) 5148.go 30 no \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\)