Properties

Modulus 8030
Structure \(C_{360}\times C_{4}\times C_{2}\)
Order 2880

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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(8030)
 
pari: g = idealstar(,8030,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2880
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{360}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{8030}(5407,\cdot)$, $\chi_{8030}(6423,\cdot)$, $\chi_{8030}(3651,\cdot)$

First 32 of 2880 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 13 17 19 21 23 27 29
\(\chi_{8030}(1,\cdot)\) 8030.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8030}(3,\cdot)\) 8030.es 60 No \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{8030}(7,\cdot)\) 8030.fr 120 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{53}{120}\right)\)
\(\chi_{8030}(9,\cdot)\) 8030.dl 30 No \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{8030}(13,\cdot)\) 8030.gf 360 No \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{251}{360}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{317}{360}\right)\)
\(\chi_{8030}(17,\cdot)\) 8030.fr 120 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{120}\right)\)
\(\chi_{8030}(19,\cdot)\) 8030.gd 180 No \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{43}{180}\right)\)
\(\chi_{8030}(21,\cdot)\) 8030.db 24 No \(1\) \(1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{8030}(23,\cdot)\) 8030.dx 36 No \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(i\) \(e\left(\frac{31}{36}\right)\)
\(\chi_{8030}(27,\cdot)\) 8030.cv 20 No \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{8030}(29,\cdot)\) 8030.gh 360 No \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{317}{360}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{329}{360}\right)\)
\(\chi_{8030}(31,\cdot)\) 8030.gi 360 No \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{221}{360}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{197}{360}\right)\)
\(\chi_{8030}(37,\cdot)\) 8030.fw 180 No \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{90}\right)\)
\(\chi_{8030}(39,\cdot)\) 8030.gh 360 No \(1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{239}{360}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{121}{180}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{323}{360}\right)\)
\(\chi_{8030}(41,\cdot)\) 8030.fj 90 No \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{45}\right)\)
\(\chi_{8030}(43,\cdot)\) 8030.cz 24 No \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{8030}(47,\cdot)\) 8030.gl 360 No \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{343}{360}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{107}{180}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{61}{360}\right)\)
\(\chi_{8030}(49,\cdot)\) 8030.ej 60 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{30}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{53}{60}\right)\)
\(\chi_{8030}(51,\cdot)\) 8030.ec 40 No \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{8030}(53,\cdot)\) 8030.gl 360 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{101}{360}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{169}{180}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{167}{360}\right)\)
\(\chi_{8030}(57,\cdot)\) 8030.fx 180 No \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{103}{180}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{90}\right)\)
\(\chi_{8030}(59,\cdot)\) 8030.gg 360 No \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{287}{360}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{299}{360}\right)\)
\(\chi_{8030}(61,\cdot)\) 8030.ft 180 No \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{89}{180}\right)\)
\(\chi_{8030}(63,\cdot)\) 8030.ea 40 No \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{8030}(67,\cdot)\) 8030.dx 36 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(-i\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{8030}(69,\cdot)\) 8030.fg 90 No \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{79}{90}\right)\)
\(\chi_{8030}(71,\cdot)\) 8030.fh 90 No \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{90}\right)\)
\(\chi_{8030}(79,\cdot)\) 8030.gd 180 No \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{91}{180}\right)\)
\(\chi_{8030}(81,\cdot)\) 8030.cf 15 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{8030}(83,\cdot)\) 8030.ea 40 No \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{8030}(87,\cdot)\) 8030.fb 72 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{17}{18}\right)\) \(-1\) \(e\left(\frac{67}{72}\right)\)
\(\chi_{8030}(89,\cdot)\) 8030.cm 18 No \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(-1\) \(e\left(\frac{5}{9}\right)\)