Properties

Modulus 804
Structure \(C_{66}\times C_{2}\times C_{2}\)
Order 264

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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(804)
 
pari: g = idealstar(,804,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 264
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{804}(337,\cdot)$, $\chi_{804}(269,\cdot)$, $\chi_{804}(403,\cdot)$

First 32 of 264 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
\(\chi_{804}(1,\cdot)\) 804.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{804}(5,\cdot)\) 804.s 22 no \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(-1\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{804}(7,\cdot)\) 804.bf 66 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{804}(11,\cdot)\) 804.bb 66 yes \(-1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{804}(13,\cdot)\) 804.bc 66 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{35}{66}\right)\)
\(\chi_{804}(17,\cdot)\) 804.be 66 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{804}(19,\cdot)\) 804.z 66 no \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{804}(23,\cdot)\) 804.bd 66 yes \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{804}(25,\cdot)\) 804.q 11 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{804}(29,\cdot)\) 804.k 6 no \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{804}(31,\cdot)\) 804.bf 66 no \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{804}(35,\cdot)\) 804.bd 66 yes \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{804}(37,\cdot)\) 804.i 3 no \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{804}(41,\cdot)\) 804.ba 66 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{804}(43,\cdot)\) 804.u 22 no \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{804}(47,\cdot)\) 804.bd 66 yes \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{804}(49,\cdot)\) 804.y 33 no \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{804}(53,\cdot)\) 804.s 22 no \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(-1\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{804}(55,\cdot)\) 804.z 66 no \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{804}(59,\cdot)\) 804.w 22 yes \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(-1\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{804}(61,\cdot)\) 804.bc 66 no \(-1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{804}(65,\cdot)\) 804.be 66 no \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{804}(71,\cdot)\) 804.bd 66 yes \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{804}(73,\cdot)\) 804.y 33 no \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{804}(77,\cdot)\) 804.be 66 no \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{804}(79,\cdot)\) 804.bf 66 no \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{804}(83,\cdot)\) 804.bd 66 yes \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{804}(85,\cdot)\) 804.bc 66 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{66}\right)\)
\(\chi_{804}(89,\cdot)\) 804.v 22 no \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(-1\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{804}(91,\cdot)\) 804.t 22 no \(-1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(1\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{804}(95,\cdot)\) 804.bb 66 yes \(-1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{804}(97,\cdot)\) 804.m 6 no \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)