Properties

Modulus $3822$
Structure \(C_{2}\times C_{6}\times C_{84}\)
Order $1008$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3822)
 
pari: g = idealstar(,3822,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1008
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{6}\times C_{84}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3822}(2549,\cdot)$, $\chi_{3822}(3433,\cdot)$, $\chi_{3822}(1471,\cdot)$

First 32 of 1008 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.

Character Orbit Order Primitive \(-1\) \(1\) \(5\) \(11\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{3822}(1,\cdot)\) 3822.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3822}(5,\cdot)\) 3822.eg 84 no \(-1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{3822}(11,\cdot)\) 3822.el 84 no \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(i\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{31}{84}\right)\)
\(\chi_{3822}(17,\cdot)\) 3822.dh 42 no \(1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{3822}(19,\cdot)\) 3822.bz 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{3822}(23,\cdot)\) 3822.dt 42 no \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{3822}(25,\cdot)\) 3822.df 42 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{3822}(29,\cdot)\) 3822.dw 42 no \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{42}\right)\)
\(\chi_{3822}(31,\cdot)\) 3822.ca 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\)
\(\chi_{3822}(37,\cdot)\) 3822.ep 84 no \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{3822}(41,\cdot)\) 3822.eh 84 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(i\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{79}{84}\right)\)
\(\chi_{3822}(43,\cdot)\) 3822.dx 42 no \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{13}{42}\right)\)
\(\chi_{3822}(47,\cdot)\) 3822.eg 84 no \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{3822}(53,\cdot)\) 3822.de 42 no \(-1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{3822}(55,\cdot)\) 3822.dy 42 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(-1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{41}{42}\right)\)
\(\chi_{3822}(59,\cdot)\) 3822.eo 84 no \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{84}\right)\)
\(\chi_{3822}(61,\cdot)\) 3822.db 42 no \(-1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(-1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{3822}(67,\cdot)\) 3822.cf 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{3822}(71,\cdot)\) 3822.en 84 no \(1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(-i\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{41}{84}\right)\)
\(\chi_{3822}(73,\cdot)\) 3822.ei 84 no \(1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{3822}(79,\cdot)\) 3822.i 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{3822}(83,\cdot)\) 3822.cw 28 no \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(i\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{3822}(85,\cdot)\) 3822.ee 84 no \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(i\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{17}{84}\right)\)
\(\chi_{3822}(89,\cdot)\) 3822.eo 84 no \(-1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{25}{84}\right)\)
\(\chi_{3822}(95,\cdot)\) 3822.dt 42 no \(-1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{3822}(97,\cdot)\) 3822.by 12 no \(1\) \(1\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{3822}(101,\cdot)\) 3822.dc 42 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{3822}(103,\cdot)\) 3822.dp 42 no \(-1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{3822}(107,\cdot)\) 3822.dg 42 no \(-1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{3822}(109,\cdot)\) 3822.ec 84 no \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{3822}(113,\cdot)\) 3822.dw 42 no \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{3822}(115,\cdot)\) 3822.ej 84 no \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(-i\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{43}{84}\right)\)
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