Properties

Modulus $4410$
Structure \(C_{84}\times C_{6}\times C_{2}\)
Order $1008$

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4410)
 
pari: g = idealstar(,4410,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1008
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4410}(1963,\cdot)$, $\chi_{4410}(3431,\cdot)$, $\chi_{4410}(3331,\cdot)$

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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4410}(1,\cdot)\) 4410.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4410}(11,\cdot)\) 4410.dh 42 no \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{4410}(13,\cdot)\) 4410.en 84 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{25}{84}\right)\)
\(\chi_{4410}(17,\cdot)\) 4410.ed 84 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{4410}(19,\cdot)\) 4410.bc 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)
\(\chi_{4410}(23,\cdot)\) 4410.eg 84 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{13}{21}\right)\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{4410}(29,\cdot)\) 4410.de 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{4410}(31,\cdot)\) 4410.br 6 no \(-1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4410}(37,\cdot)\) 4410.em 84 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{4410}(41,\cdot)\) 4410.dd 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{4410}(43,\cdot)\) 4410.ei 84 no \(-1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{4410}(47,\cdot)\) 4410.eo 84 no \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{4410}(53,\cdot)\) 4410.ef 84 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{4410}(59,\cdot)\) 4410.dz 42 no \(1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{4410}(61,\cdot)\) 4410.cz 42 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{4410}(67,\cdot)\) 4410.ci 12 no \(-1\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4410}(71,\cdot)\) 4410.cn 14 no \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{4410}(73,\cdot)\) 4410.ek 84 no \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{4410}(79,\cdot)\) 4410.bq 6 no \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4410}(83,\cdot)\) 4410.eh 84 no \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{84}\right)\)
\(\chi_{4410}(89,\cdot)\) 4410.dc 42 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{4410}(97,\cdot)\) 4410.ca 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4410}(101,\cdot)\) 4410.dg 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(-1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{4410}(103,\cdot)\) 4410.ej 84 no \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(-1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{4410}(107,\cdot)\) 4410.ef 84 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{4410}(109,\cdot)\) 4410.du 42 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{4410}(113,\cdot)\) 4410.ec 84 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{4410}(121,\cdot)\) 4410.ct 21 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{4410}(127,\cdot)\) 4410.cu 28 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(-1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{4410}(131,\cdot)\) 4410.dg 42 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(-1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{4410}(137,\cdot)\) 4410.eg 84 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{21}\right)\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{4410}(139,\cdot)\) 4410.ds 42 no \(-1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\)