Properties

Modulus 1032
Structure \(C_{42}\times C_{2}\times C_{2}\times C_{2}\)
Order 336

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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(1032)
 
pari: g = idealstar(,1032,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 336
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{42}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1032}(433,\cdot)$, $\chi_{1032}(689,\cdot)$, $\chi_{1032}(775,\cdot)$, $\chi_{1032}(517,\cdot)$

First 32 of 336 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 5 7 11 13 17 19 23 25 29 31
\(\chi_{1032}(1,\cdot)\) 1032.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1032}(5,\cdot)\) 1032.cb 42 Yes \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{1032}(7,\cdot)\) 1032.y 6 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1032}(11,\cdot)\) 1032.bk 14 Yes \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{1032}(13,\cdot)\) 1032.by 42 No \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1032}(17,\cdot)\) 1032.bz 42 No \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{1032}(19,\cdot)\) 1032.cg 42 No \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{1032}(23,\cdot)\) 1032.cd 42 No \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\)
\(\chi_{1032}(25,\cdot)\) 1032.bw 21 No \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{1032}(29,\cdot)\) 1032.cb 42 Yes \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{1032}(31,\cdot)\) 1032.cl 42 No \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{1032}(35,\cdot)\) 1032.bk 14 Yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(-1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{1032}(37,\cdot)\) 1032.w 6 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1032}(41,\cdot)\) 1032.bt 14 No \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{1032}(47,\cdot)\) 1032.bp 14 No \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{1032}(49,\cdot)\) 1032.q 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1032}(53,\cdot)\) 1032.cf 42 Yes \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{1032}(55,\cdot)\) 1032.ca 42 No \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{1032}(59,\cdot)\) 1032.bk 14 Yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{1032}(61,\cdot)\) 1032.cj 42 No \(-1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{1032}(65,\cdot)\) 1032.bi 14 No \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{1032}(67,\cdot)\) 1032.cc 42 No \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{1032}(71,\cdot)\) 1032.ch 42 No \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{1032}(73,\cdot)\) 1032.ce 42 No \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{1032}(77,\cdot)\) 1032.cb 42 Yes \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{1032}(79,\cdot)\) 1032.u 6 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1032}(83,\cdot)\) 1032.ci 42 Yes \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{13}{42}\right)\)
\(\chi_{1032}(85,\cdot)\) 1032.k 2 No \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1032}(89,\cdot)\) 1032.ck 42 No \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{1032}(91,\cdot)\) 1032.cg 42 No \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{1032}(95,\cdot)\) 1032.cd 42 No \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{42}\right)\)
\(\chi_{1032}(97,\cdot)\) 1032.bg 7 No \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\)