Properties

Modulus $4235$
Structure \(C_{660}\times C_{2}\times C_{2}\)
Order $2640$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4235)
 
pari: g = idealstar(,4235,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2640
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{660}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4235}(2542,\cdot)$, $\chi_{4235}(1816,\cdot)$, $\chi_{4235}(2906,\cdot)$

First 32 of 2640 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(1,\cdot)\) 4235.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4235}(2,\cdot)\) 4235.do 660 yes \(1\) \(1\) \(e\left(\frac{611}{660}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{171}{220}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{19}{660}\right)\)
\(\chi_{4235}(3,\cdot)\) 4235.ci 60 no \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{4235}(4,\cdot)\) 4235.dk 330 yes \(1\) \(1\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{19}{330}\right)\)
\(\chi_{4235}(6,\cdot)\) 4235.cu 110 no \(1\) \(1\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{8}{55}\right)\)
\(\chi_{4235}(8,\cdot)\) 4235.de 220 no \(1\) \(1\) \(e\left(\frac{171}{220}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{73}{220}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{19}{220}\right)\)
\(\chi_{4235}(9,\cdot)\) 4235.bu 30 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{4235}(12,\cdot)\) 4235.da 132 yes \(1\) \(1\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{23}{132}\right)\)
\(\chi_{4235}(13,\cdot)\) 4235.df 220 yes \(-1\) \(1\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{107}{220}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{53}{220}\right)\)
\(\chi_{4235}(16,\cdot)\) 4235.dc 165 no \(1\) \(1\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{19}{165}\right)\)
\(\chi_{4235}(17,\cdot)\) 4235.dr 660 yes \(-1\) \(1\) \(e\left(\frac{19}{660}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{19}{330}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{19}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{53}{220}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{161}{660}\right)\)
\(\chi_{4235}(18,\cdot)\) 4235.do 660 yes \(1\) \(1\) \(e\left(\frac{457}{660}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{127}{330}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{17}{220}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{169}{220}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{173}{660}\right)\)
\(\chi_{4235}(19,\cdot)\) 4235.dj 330 yes \(1\) \(1\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{101}{330}\right)\)
\(\chi_{4235}(23,\cdot)\) 4235.cz 132 yes \(-1\) \(1\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{35}{132}\right)\)
\(\chi_{4235}(24,\cdot)\) 4235.dj 330 yes \(1\) \(1\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{67}{330}\right)\)
\(\chi_{4235}(26,\cdot)\) 4235.dh 330 no \(-1\) \(1\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{89}{330}\right)\)
\(\chi_{4235}(27,\cdot)\) 4235.bl 20 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{4235}(29,\cdot)\) 4235.cx 110 no \(-1\) \(1\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{4}{55}\right)\)
\(\chi_{4235}(31,\cdot)\) 4235.dh 330 no \(-1\) \(1\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{157}{330}\right)\)
\(\chi_{4235}(32,\cdot)\) 4235.db 132 yes \(1\) \(1\) \(e\left(\frac{83}{132}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{19}{132}\right)\)
\(\chi_{4235}(34,\cdot)\) 4235.br 22 yes \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{4235}(36,\cdot)\) 4235.cf 55 no \(1\) \(1\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{16}{55}\right)\)
\(\chi_{4235}(37,\cdot)\) 4235.dq 660 yes \(-1\) \(1\) \(e\left(\frac{197}{660}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{32}{165}\right)\) \(e\left(\frac{193}{660}\right)\)
\(\chi_{4235}(38,\cdot)\) 4235.dp 660 yes \(1\) \(1\) \(e\left(\frac{559}{660}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{193}{220}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{221}{660}\right)\)
\(\chi_{4235}(39,\cdot)\) 4235.di 330 yes \(-1\) \(1\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{59}{165}\right)\)
\(\chi_{4235}(41,\cdot)\) 4235.cu 110 no \(1\) \(1\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{41}{55}\right)\)
\(\chi_{4235}(43,\cdot)\) 4235.cd 44 no \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(i\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(-1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{4235}(46,\cdot)\) 4235.dm 330 no \(-1\) \(1\) \(e\left(\frac{323}{330}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{97}{330}\right)\)
\(\chi_{4235}(47,\cdot)\) 4235.dp 660 yes \(1\) \(1\) \(e\left(\frac{533}{660}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{93}{220}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{487}{660}\right)\)
\(\chi_{4235}(48,\cdot)\) 4235.dd 220 yes \(1\) \(1\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{49}{220}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{51}{220}\right)\)
\(\chi_{4235}(51,\cdot)\) 4235.dm 330 no \(-1\) \(1\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{119}{330}\right)\)
\(\chi_{4235}(52,\cdot)\) 4235.dr 660 yes \(-1\) \(1\) \(e\left(\frac{343}{660}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{330}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{123}{220}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{181}{220}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{197}{660}\right)\)