Properties

Modulus 4030
Structure \(C_{60}\times C_{12}\times C_{2}\)
Order 1440

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4030)
 
pari: g = idealstar(,4030,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1440
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{12}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4030}(313,\cdot)$, $\chi_{4030}(1861,\cdot)$, $\chi_{4030}(3719,\cdot)$

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.

orbit label order primitive -1 1 3 7 9 11 17 19 21 23 27 29
\(\chi_{4030}(1,\cdot)\) 4030.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4030}(3,\cdot)\) 4030.gx 60 No \(1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{4030}(7,\cdot)\) 4030.hg 60 No \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{4030}(9,\cdot)\) 4030.fh 30 No \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{4030}(11,\cdot)\) 4030.hq 60 No \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{4030}(17,\cdot)\) 4030.hb 60 No \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{4030}(19,\cdot)\) 4030.hr 60 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{4030}(21,\cdot)\) 4030.gb 60 No \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{4030}(23,\cdot)\) 4030.gu 60 No \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{4030}(27,\cdot)\) 4030.ep 20 No \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{4030}(29,\cdot)\) 4030.fn 30 No \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{4030}(33,\cdot)\) 4030.gh 60 No \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{4030}(37,\cdot)\) 4030.du 12 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(i\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4030}(41,\cdot)\) 4030.fx 60 No \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{4030}(43,\cdot)\) 4030.hb 60 No \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{4030}(47,\cdot)\) 4030.el 20 No \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{4030}(49,\cdot)\) 4030.fu 30 No \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{4030}(51,\cdot)\) 4030.fk 30 No \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{4030}(53,\cdot)\) 4030.go 60 No \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{4030}(57,\cdot)\) 4030.dt 12 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(-i\) \(1\)
\(\chi_{4030}(59,\cdot)\) 4030.hr 60 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{4030}(61,\cdot)\) 4030.bo 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4030}(63,\cdot)\) 4030.ds 12 No \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4030}(67,\cdot)\) 4030.dp 12 No \(1\) \(1\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4030}(69,\cdot)\) 4030.fu 30 No \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{4030}(71,\cdot)\) 4030.hp 60 No \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{4030}(73,\cdot)\) 4030.gg 60 No \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{4030}(77,\cdot)\) 4030.em 20 No \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{4030}(79,\cdot)\) 4030.fm 30 No \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{4030}(81,\cdot)\) 4030.ef 15 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{4030}(83,\cdot)\) 4030.hc 60 No \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{4030}(87,\cdot)\) 4030.cz 12 No \(-1\) \(1\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\)