Properties

Modulus 861
Structure \(C_{120}\times C_{2}\times C_{2}\)
Order 480

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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(861)
 
pari: g = idealstar(,861,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{120}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{861}(334,\cdot)$, $\chi_{861}(286,\cdot)$, $\chi_{861}(575,\cdot)$

First 32 of 480 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 2 4 5 8 10 11 13 16 17 19
\(\chi_{861}(1,\cdot)\) 861.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{861}(2,\cdot)\) 861.ch 60 yes \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{861}(4,\cdot)\) 861.bz 30 no \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{861}(5,\cdot)\) 861.cg 60 yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{861}(8,\cdot)\) 861.bl 20 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{861}(10,\cdot)\) 861.by 30 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{861}(11,\cdot)\) 861.cl 120 yes \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{1}{120}\right)\)
\(\chi_{861}(13,\cdot)\) 861.cd 40 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{861}(16,\cdot)\) 861.bk 15 no \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{861}(17,\cdot)\) 861.cj 120 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{31}{120}\right)\)
\(\chi_{861}(19,\cdot)\) 861.ci 120 no \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{23}{120}\right)\)
\(\chi_{861}(20,\cdot)\) 861.bm 20 yes \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{861}(22,\cdot)\) 861.cb 40 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{861}(23,\cdot)\) 861.bu 30 yes \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{861}(25,\cdot)\) 861.bz 30 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{861}(26,\cdot)\) 861.cj 120 yes \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{119}{120}\right)\)
\(\chi_{861}(29,\cdot)\) 861.ca 40 no \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{861}(31,\cdot)\) 861.bx 30 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{861}(32,\cdot)\) 861.bg 12 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{861}(34,\cdot)\) 861.cd 40 no \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{31}{40}\right)\)
\(\chi_{861}(37,\cdot)\) 861.bk 15 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{861}(38,\cdot)\) 861.br 24 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{861}(40,\cdot)\) 861.q 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{861}(43,\cdot)\) 861.bo 20 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{861}(44,\cdot)\) 861.bp 24 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{861}(46,\cdot)\) 861.ce 60 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{861}(47,\cdot)\) 861.cj 120 yes \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{47}{120}\right)\)
\(\chi_{861}(50,\cdot)\) 861.m 4 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-i\) \(i\) \(1\) \(i\) \(-i\)
\(\chi_{861}(52,\cdot)\) 861.ci 120 no \(1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{61}{120}\right)\)
\(\chi_{861}(53,\cdot)\) 861.cl 120 yes \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{49}{120}\right)\)
\(\chi_{861}(55,\cdot)\) 861.v 8 no \(1\) \(1\) \(i\) \(-1\) \(i\) \(-i\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{861}(58,\cdot)\) 861.ck 120 no \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{97}{120}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{11}{120}\right)\)