Properties

Modulus 287
Structure \(C_{120}\times C_{2}\)
Order 240

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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(287)
 
pari: g = idealstar(,287,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 240
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{120}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{287}(47,\cdot)$, $\chi_{287}(286,\cdot)$

First 32 of 240 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 3 4 5 6 8 9 10 11 12
\(\chi_{287}(1,\cdot)\) 287.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{287}(2,\cdot)\) 287.bc 60 yes \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{60}\right)\)
\(\chi_{287}(3,\cdot)\) 287.w 24 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{287}(4,\cdot)\) 287.z 30 yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{287}(5,\cdot)\) 287.bd 60 yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{287}(6,\cdot)\) 287.bb 40 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{287}(8,\cdot)\) 287.u 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{287}(9,\cdot)\) 287.r 12 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{287}(10,\cdot)\) 287.y 30 yes \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{287}(11,\cdot)\) 287.bf 120 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{43}{120}\right)\)
\(\chi_{287}(12,\cdot)\) 287.be 120 yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{47}{120}\right)\)
\(\chi_{287}(13,\cdot)\) 287.bb 40 yes \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{40}\right)\)
\(\chi_{287}(15,\cdot)\) 287.ba 40 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{287}(16,\cdot)\) 287.s 15 yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{287}(17,\cdot)\) 287.be 120 yes \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{13}{120}\right)\)
\(\chi_{287}(18,\cdot)\) 287.s 15 yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{287}(19,\cdot)\) 287.be 120 yes \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{29}{120}\right)\)
\(\chi_{287}(20,\cdot)\) 287.t 20 yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{287}(22,\cdot)\) 287.ba 40 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{287}(23,\cdot)\) 287.z 30 yes \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{287}(24,\cdot)\) 287.be 120 yes \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{73}{120}\right)\)
\(\chi_{287}(25,\cdot)\) 287.z 30 yes \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{287}(26,\cdot)\) 287.be 120 yes \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{77}{120}\right)\)
\(\chi_{287}(27,\cdot)\) 287.l 8 yes \(1\) \(1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{287}(29,\cdot)\) 287.ba 40 no \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{287}(30,\cdot)\) 287.bf 120 yes \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{23}{120}\right)\)
\(\chi_{287}(31,\cdot)\) 287.x 30 yes \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{287}(32,\cdot)\) 287.r 12 yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{287}(33,\cdot)\) 287.bd 60 yes \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{287}(34,\cdot)\) 287.bb 40 yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{287}(36,\cdot)\) 287.u 20 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{287}(37,\cdot)\) 287.s 15 yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\)