Properties

Modulus $7056$
Structure \(C_{2}\times C_{2}\times C_{6}\times C_{84}\)
Order $2016$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(7056)
 
pari: g = idealstar(,7056,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2016
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{6}\times C_{84}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{7056}(6175,\cdot)$, $\chi_{7056}(1765,\cdot)$, $\chi_{7056}(785,\cdot)$, $\chi_{7056}(4609,\cdot)$

First 32 of 2016 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{7056}(1,\cdot)\) 7056.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{7056}(5,\cdot)\) 7056.iw 84 yes \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{84}\right)\) \(-1\) \(e\left(\frac{29}{84}\right)\)
\(\chi_{7056}(11,\cdot)\) 7056.ig 84 yes \(1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{84}\right)\) \(-1\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{7056}(13,\cdot)\) 7056.jc 84 yes \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(-i\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{7056}(17,\cdot)\) 7056.hi 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{7056}(19,\cdot)\) 7056.ed 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{7056}(23,\cdot)\) 7056.ha 42 no \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(-1\) \(e\left(\frac{19}{42}\right)\)
\(\chi_{7056}(25,\cdot)\) 7056.gd 42 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(1\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{7056}(29,\cdot)\) 7056.je 84 yes \(-1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{7056}(31,\cdot)\) 7056.bf 6 no \(1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7056}(37,\cdot)\) 7056.it 84 no \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{84}\right)\)
\(\chi_{7056}(41,\cdot)\) 7056.gr 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{7056}(43,\cdot)\) 7056.ic 84 yes \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{7056}(47,\cdot)\) 7056.ft 42 no \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{7056}(53,\cdot)\) 7056.ik 84 no \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{7056}(55,\cdot)\) 7056.er 14 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{7056}(59,\cdot)\) 7056.ja 84 yes \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{84}\right)\)
\(\chi_{7056}(61,\cdot)\) 7056.io 84 yes \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{7056}(65,\cdot)\) 7056.hy 42 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{7056}(67,\cdot)\) 7056.ea 12 no \(-1\) \(1\) \(-i\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{7056}(71,\cdot)\) 7056.ex 14 no \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{7056}(73,\cdot)\) 7056.gx 42 no \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{7056}(79,\cdot)\) 7056.dd 6 no \(-1\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7056}(83,\cdot)\) 7056.ia 84 yes \(-1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{7056}(85,\cdot)\) 7056.ib 84 yes \(1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{7056}(89,\cdot)\) 7056.gm 42 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{7056}(95,\cdot)\) 7056.hu 42 no \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{7056}(97,\cdot)\) 7056.cl 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)
\(\chi_{7056}(101,\cdot)\) 7056.iw 84 yes \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{29}{84}\right)\) \(-1\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{7056}(103,\cdot)\) 7056.ho 42 no \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(1\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{7056}(107,\cdot)\) 7056.ij 84 no \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{7056}(109,\cdot)\) 7056.it 84 no \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{84}\right)\)
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