Properties

Modulus $5445$
Structure \(C_{660}\times C_{2}\times C_{2}\)
Order $2640$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5445)
 
pari: g = idealstar(,5445,2)
 

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 = $\chi_{5445}(3026,\cdot)$, $\chi_{5445}(4357,\cdot)$, $\chi_{5445}(3511,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(13\) \(14\) \(16\) \(17\) \(19\) \(23\)
\(\chi_{5445}(1,\cdot)\) 5445.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5445}(2,\cdot)\) 5445.dp 660 yes \(-1\) \(1\) \(e\left(\frac{281}{660}\right)\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{647}{660}\right)\) \(e\left(\frac{61}{220}\right)\) \(e\left(\frac{1}{660}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{43}{220}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{29}{132}\right)\)
\(\chi_{5445}(4,\cdot)\) 5445.dn 330 yes \(1\) \(1\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{5445}(7,\cdot)\) 5445.dr 660 yes \(1\) \(1\) \(e\left(\frac{647}{660}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{239}{660}\right)\) \(e\left(\frac{207}{220}\right)\) \(e\left(\frac{337}{660}\right)\) \(e\left(\frac{113}{330}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{71}{132}\right)\)
\(\chi_{5445}(8,\cdot)\) 5445.dg 220 no \(-1\) \(1\) \(e\left(\frac{61}{220}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{207}{220}\right)\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{5445}(13,\cdot)\) 5445.dr 660 yes \(1\) \(1\) \(e\left(\frac{1}{660}\right)\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{337}{660}\right)\) \(e\left(\frac{1}{220}\right)\) \(e\left(\frac{431}{660}\right)\) \(e\left(\frac{169}{330}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{25}{132}\right)\)
\(\chi_{5445}(14,\cdot)\) 5445.dj 330 yes \(-1\) \(1\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{113}{330}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{169}{330}\right)\) \(e\left(\frac{247}{330}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{5445}(16,\cdot)\) 5445.dc 165 no \(1\) \(1\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{5445}(17,\cdot)\) 5445.dg 220 no \(-1\) \(1\) \(e\left(\frac{43}{220}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{129}{220}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{5445}(19,\cdot)\) 5445.cx 110 no \(-1\) \(1\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{5445}(23,\cdot)\) 5445.db 132 yes \(1\) \(1\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{127}{132}\right)\)
\(\chi_{5445}(26,\cdot)\) 5445.cu 110 no \(-1\) \(1\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{5445}(28,\cdot)\) 5445.de 220 no \(1\) \(1\) \(e\left(\frac{183}{220}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{71}{220}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{167}{220}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{5445}(29,\cdot)\) 5445.dk 330 yes \(1\) \(1\) \(e\left(\frac{271}{330}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{5445}(31,\cdot)\) 5445.dc 165 no \(1\) \(1\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{5445}(32,\cdot)\) 5445.da 132 yes \(-1\) \(1\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{132}\right)\)
\(\chi_{5445}(34,\cdot)\) 5445.ck 66 yes \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{5445}(37,\cdot)\) 5445.dd 220 no \(-1\) \(1\) \(e\left(\frac{139}{220}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{211}{220}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{5445}(38,\cdot)\) 5445.do 660 yes \(1\) \(1\) \(e\left(\frac{449}{660}\right)\) \(e\left(\frac{119}{330}\right)\) \(e\left(\frac{503}{660}\right)\) \(e\left(\frac{9}{220}\right)\) \(e\left(\frac{469}{660}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{71}{132}\right)\)
\(\chi_{5445}(41,\cdot)\) 5445.di 330 no \(1\) \(1\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{263}{330}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{259}{330}\right)\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{53}{66}\right)\)
\(\chi_{5445}(43,\cdot)\) 5445.cy 132 yes \(1\) \(1\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{65}{132}\right)\)
\(\chi_{5445}(46,\cdot)\) 5445.cr 110 no \(-1\) \(1\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{5445}(47,\cdot)\) 5445.do 660 yes \(1\) \(1\) \(e\left(\frac{203}{660}\right)\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{101}{660}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{43}{660}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{89}{220}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{125}{132}\right)\)
\(\chi_{5445}(49,\cdot)\) 5445.dn 330 yes \(1\) \(1\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{5445}(52,\cdot)\) 5445.dr 660 yes \(1\) \(1\) \(e\left(\frac{563}{660}\right)\) \(e\left(\frac{233}{330}\right)\) \(e\left(\frac{311}{660}\right)\) \(e\left(\frac{123}{220}\right)\) \(e\left(\frac{433}{660}\right)\) \(e\left(\frac{107}{330}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{29}{220}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{83}{132}\right)\)
\(\chi_{5445}(53,\cdot)\) 5445.df 220 no \(1\) \(1\) \(e\left(\frac{47}{220}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{141}{220}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{5445}(56,\cdot)\) 5445.cm 66 no \(-1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{5445}(58,\cdot)\) 5445.dq 660 yes \(-1\) \(1\) \(e\left(\frac{163}{660}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{151}{660}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{293}{660}\right)\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{169}{220}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{49}{132}\right)\)
\(\chi_{5445}(59,\cdot)\) 5445.dj 330 yes \(-1\) \(1\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{5445}(61,\cdot)\) 5445.dm 330 no \(-1\) \(1\) \(e\left(\frac{217}{330}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{199}{330}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{137}{330}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{5445}(62,\cdot)\) 5445.dg 220 no \(-1\) \(1\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{173}{220}\right)\) \(e\left(\frac{137}{220}\right)\) \(e\left(\frac{139}{220}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{5445}(64,\cdot)\) 5445.cs 110 no \(1\) \(1\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{7}{22}\right)\)