Properties

Modulus $3630$
Structure \(C_{220}\times C_{2}\times C_{2}\)
Order $880$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3630)
 
pari: g = idealstar(,3630,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 880
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{220}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3630}(1211,\cdot)$, $\chi_{3630}(727,\cdot)$, $\chi_{3630}(3511,\cdot)$

First 32 of 880 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 \(-1\) \(1\) \(7\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{3630}(1,\cdot)\) 3630.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3630}(7,\cdot)\) 3630.bv 220 no \(1\) \(1\) \(e\left(\frac{153}{220}\right)\) \(e\left(\frac{39}{220}\right)\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{3630}(13,\cdot)\) 3630.bv 220 no \(1\) \(1\) \(e\left(\frac{39}{220}\right)\) \(e\left(\frac{217}{220}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{3630}(17,\cdot)\) 3630.bu 220 no \(-1\) \(1\) \(e\left(\frac{81}{220}\right)\) \(e\left(\frac{163}{220}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{211}{220}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{3630}(19,\cdot)\) 3630.br 110 no \(-1\) \(1\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3630}(23,\cdot)\) 3630.bi 44 no \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{3630}(29,\cdot)\) 3630.bp 110 no \(1\) \(1\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3630}(31,\cdot)\) 3630.bk 55 no \(1\) \(1\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{3630}(37,\cdot)\) 3630.bs 220 no \(-1\) \(1\) \(e\left(\frac{203}{220}\right)\) \(e\left(\frac{69}{220}\right)\) \(e\left(\frac{211}{220}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{63}{220}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{3630}(41,\cdot)\) 3630.bn 110 no \(1\) \(1\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3630}(43,\cdot)\) 3630.bg 44 no \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{3630}(47,\cdot)\) 3630.bt 220 no \(1\) \(1\) \(e\left(\frac{107}{220}\right)\) \(e\left(\frac{161}{220}\right)\) \(e\left(\frac{89}{220}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{147}{220}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{3630}(49,\cdot)\) 3630.bm 110 no \(1\) \(1\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{3630}(53,\cdot)\) 3630.bt 220 no \(1\) \(1\) \(e\left(\frac{109}{220}\right)\) \(e\left(\frac{127}{220}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{49}{220}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{3630}(59,\cdot)\) 3630.bo 110 no \(-1\) \(1\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3630}(61,\cdot)\) 3630.bl 110 no \(-1\) \(1\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3630}(67,\cdot)\) 3630.bj 44 no \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{3630}(71,\cdot)\) 3630.bq 110 no \(-1\) \(1\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{3630}(73,\cdot)\) 3630.bv 220 no \(1\) \(1\) \(e\left(\frac{23}{220}\right)\) \(e\left(\frac{49}{220}\right)\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{193}{220}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{3630}(79,\cdot)\) 3630.br 110 no \(-1\) \(1\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{3630}(83,\cdot)\) 3630.bu 220 no \(-1\) \(1\) \(e\left(\frac{131}{220}\right)\) \(e\left(\frac{193}{220}\right)\) \(e\left(\frac{37}{220}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{181}{220}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{3630}(89,\cdot)\) 3630.bc 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{3630}(91,\cdot)\) 3630.bk 55 no \(1\) \(1\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{3630}(97,\cdot)\) 3630.bs 220 no \(-1\) \(1\) \(e\left(\frac{119}{220}\right)\) \(e\left(\frac{177}{220}\right)\) \(e\left(\frac{63}{220}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{219}{220}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{3630}(101,\cdot)\) 3630.bn 110 no \(1\) \(1\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3630}(103,\cdot)\) 3630.bs 220 no \(-1\) \(1\) \(e\left(\frac{113}{220}\right)\) \(e\left(\frac{59}{220}\right)\) \(e\left(\frac{21}{220}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{73}{220}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{3630}(107,\cdot)\) 3630.bu 220 no \(-1\) \(1\) \(e\left(\frac{57}{220}\right)\) \(e\left(\frac{131}{220}\right)\) \(e\left(\frac{179}{220}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{67}{220}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{3630}(109,\cdot)\) 3630.z 22 no \(-1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{3630}(113,\cdot)\) 3630.bt 220 no \(1\) \(1\) \(e\left(\frac{97}{220}\right)\) \(e\left(\frac{111}{220}\right)\) \(e\left(\frac{19}{220}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{3630}(119,\cdot)\) 3630.bo 110 no \(-1\) \(1\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3630}(127,\cdot)\) 3630.bv 220 no \(1\) \(1\) \(e\left(\frac{201}{220}\right)\) \(e\left(\frac{103}{220}\right)\) \(e\left(\frac{197}{220}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{51}{220}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{3630}(131,\cdot)\) 3630.bd 22 no \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\)