Properties

Modulus $4010$
Structure \(C_{4}\times C_{400}\)
Order $1600$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(4010)
 
pari: g = idealstar(,4010,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1600
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{4}\times C_{400}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4010}(2407,\cdot)$, $\chi_{4010}(3211,\cdot)$

First 32 of 1600 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{4010}(1,\cdot)\) 4010.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4010}(3,\cdot)\) 4010.by 400 no \(1\) \(1\) \(e\left(\frac{101}{400}\right)\) \(e\left(\frac{181}{200}\right)\) \(e\left(\frac{101}{200}\right)\) \(e\left(\frac{97}{200}\right)\) \(e\left(\frac{19}{400}\right)\) \(e\left(\frac{283}{400}\right)\) \(e\left(\frac{363}{400}\right)\) \(e\left(\frac{63}{400}\right)\) \(e\left(\frac{391}{400}\right)\) \(e\left(\frac{303}{400}\right)\)
\(\chi_{4010}(7,\cdot)\) 4010.bw 200 no \(-1\) \(1\) \(e\left(\frac{181}{200}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{39}{200}\right)\) \(e\left(\frac{123}{200}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{171}{200}\right)\) \(e\left(\frac{143}{200}\right)\)
\(\chi_{4010}(9,\cdot)\) 4010.bv 200 no \(1\) \(1\) \(e\left(\frac{101}{200}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{19}{200}\right)\) \(e\left(\frac{83}{200}\right)\) \(e\left(\frac{163}{200}\right)\) \(e\left(\frac{63}{200}\right)\) \(e\left(\frac{191}{200}\right)\) \(e\left(\frac{103}{200}\right)\)
\(\chi_{4010}(11,\cdot)\) 4010.bu 200 no \(1\) \(1\) \(e\left(\frac{97}{200}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{143}{200}\right)\) \(e\left(\frac{151}{200}\right)\) \(e\left(\frac{11}{200}\right)\) \(e\left(\frac{111}{200}\right)\) \(e\left(\frac{27}{200}\right)\) \(e\left(\frac{91}{200}\right)\)
\(\chi_{4010}(13,\cdot)\) 4010.bz 400 no \(1\) \(1\) \(e\left(\frac{19}{400}\right)\) \(e\left(\frac{39}{200}\right)\) \(e\left(\frac{19}{200}\right)\) \(e\left(\frac{143}{200}\right)\) \(e\left(\frac{261}{400}\right)\) \(e\left(\frac{77}{400}\right)\) \(e\left(\frac{197}{400}\right)\) \(e\left(\frac{97}{400}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{57}{400}\right)\)
\(\chi_{4010}(17,\cdot)\) 4010.by 400 no \(1\) \(1\) \(e\left(\frac{283}{400}\right)\) \(e\left(\frac{123}{200}\right)\) \(e\left(\frac{83}{200}\right)\) \(e\left(\frac{151}{200}\right)\) \(e\left(\frac{77}{400}\right)\) \(e\left(\frac{389}{400}\right)\) \(e\left(\frac{229}{400}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{153}{400}\right)\) \(e\left(\frac{49}{400}\right)\)
\(\chi_{4010}(19,\cdot)\) 4010.ca 400 no \(-1\) \(1\) \(e\left(\frac{363}{400}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{163}{200}\right)\) \(e\left(\frac{11}{200}\right)\) \(e\left(\frac{197}{400}\right)\) \(e\left(\frac{229}{400}\right)\) \(e\left(\frac{169}{400}\right)\) \(e\left(\frac{269}{400}\right)\) \(e\left(\frac{33}{400}\right)\) \(e\left(\frac{289}{400}\right)\)
\(\chi_{4010}(21,\cdot)\) 4010.cb 400 no \(-1\) \(1\) \(e\left(\frac{63}{400}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{63}{200}\right)\) \(e\left(\frac{111}{200}\right)\) \(e\left(\frac{97}{400}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{269}{400}\right)\) \(e\left(\frac{369}{400}\right)\) \(e\left(\frac{333}{400}\right)\) \(e\left(\frac{189}{400}\right)\)
\(\chi_{4010}(23,\cdot)\) 4010.bz 400 no \(1\) \(1\) \(e\left(\frac{391}{400}\right)\) \(e\left(\frac{171}{200}\right)\) \(e\left(\frac{191}{200}\right)\) \(e\left(\frac{27}{200}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{153}{400}\right)\) \(e\left(\frac{33}{400}\right)\) \(e\left(\frac{333}{400}\right)\) \(e\left(\frac{381}{400}\right)\) \(e\left(\frac{373}{400}\right)\)
\(\chi_{4010}(27,\cdot)\) 4010.by 400 no \(1\) \(1\) \(e\left(\frac{303}{400}\right)\) \(e\left(\frac{143}{200}\right)\) \(e\left(\frac{103}{200}\right)\) \(e\left(\frac{91}{200}\right)\) \(e\left(\frac{57}{400}\right)\) \(e\left(\frac{49}{400}\right)\) \(e\left(\frac{289}{400}\right)\) \(e\left(\frac{189}{400}\right)\) \(e\left(\frac{373}{400}\right)\) \(e\left(\frac{109}{400}\right)\)
\(\chi_{4010}(29,\cdot)\) 4010.p 10 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{4010}(31,\cdot)\) 4010.cb 400 no \(-1\) \(1\) \(e\left(\frac{107}{400}\right)\) \(e\left(\frac{117}{200}\right)\) \(e\left(\frac{107}{200}\right)\) \(e\left(\frac{179}{200}\right)\) \(e\left(\frac{133}{400}\right)\) \(e\left(\frac{181}{400}\right)\) \(e\left(\frac{241}{400}\right)\) \(e\left(\frac{341}{400}\right)\) \(e\left(\frac{337}{400}\right)\) \(e\left(\frac{321}{400}\right)\)
\(\chi_{4010}(33,\cdot)\) 4010.bn 80 no \(1\) \(1\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{17}{80}\right)\)
\(\chi_{4010}(37,\cdot)\) 4010.bz 400 no \(1\) \(1\) \(e\left(\frac{133}{400}\right)\) \(e\left(\frac{73}{200}\right)\) \(e\left(\frac{133}{200}\right)\) \(e\left(\frac{1}{200}\right)\) \(e\left(\frac{227}{400}\right)\) \(e\left(\frac{139}{400}\right)\) \(e\left(\frac{179}{400}\right)\) \(e\left(\frac{279}{400}\right)\) \(e\left(\frac{103}{400}\right)\) \(e\left(\frac{399}{400}\right)\)
\(\chi_{4010}(39,\cdot)\) 4010.r 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{4010}(41,\cdot)\) 4010.bi 50 no \(1\) \(1\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{4010}(43,\cdot)\) 4010.bx 200 no \(-1\) \(1\) \(e\left(\frac{193}{200}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{67}{200}\right)\) \(e\left(\frac{119}{200}\right)\) \(e\left(\frac{9}{200}\right)\) \(e\left(\frac{9}{200}\right)\) \(e\left(\frac{63}{200}\right)\) \(e\left(\frac{179}{200}\right)\)
\(\chi_{4010}(47,\cdot)\) 4010.bx 200 no \(-1\) \(1\) \(e\left(\frac{59}{200}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{121}{200}\right)\) \(e\left(\frac{197}{200}\right)\) \(e\left(\frac{67}{200}\right)\) \(e\left(\frac{67}{200}\right)\) \(e\left(\frac{69}{200}\right)\) \(e\left(\frac{177}{200}\right)\)
\(\chi_{4010}(49,\cdot)\) 4010.bp 100 no \(1\) \(1\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{43}{100}\right)\)
\(\chi_{4010}(51,\cdot)\) 4010.bc 25 no \(1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{4010}(53,\cdot)\) 4010.by 400 no \(1\) \(1\) \(e\left(\frac{313}{400}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{113}{200}\right)\) \(e\left(\frac{61}{200}\right)\) \(e\left(\frac{47}{400}\right)\) \(e\left(\frac{279}{400}\right)\) \(e\left(\frac{119}{400}\right)\) \(e\left(\frac{219}{400}\right)\) \(e\left(\frac{83}{400}\right)\) \(e\left(\frac{139}{400}\right)\)
\(\chi_{4010}(57,\cdot)\) 4010.bt 100 no \(-1\) \(1\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{4010}(59,\cdot)\) 4010.ca 400 no \(-1\) \(1\) \(e\left(\frac{191}{400}\right)\) \(e\left(\frac{21}{200}\right)\) \(e\left(\frac{191}{200}\right)\) \(e\left(\frac{127}{200}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{353}{400}\right)\) \(e\left(\frac{133}{400}\right)\) \(e\left(\frac{233}{400}\right)\) \(e\left(\frac{381}{400}\right)\) \(e\left(\frac{173}{400}\right)\)
\(\chi_{4010}(61,\cdot)\) 4010.cb 400 no \(-1\) \(1\) \(e\left(\frac{283}{400}\right)\) \(e\left(\frac{173}{200}\right)\) \(e\left(\frac{83}{200}\right)\) \(e\left(\frac{51}{200}\right)\) \(e\left(\frac{277}{400}\right)\) \(e\left(\frac{389}{400}\right)\) \(e\left(\frac{129}{400}\right)\) \(e\left(\frac{229}{400}\right)\) \(e\left(\frac{353}{400}\right)\) \(e\left(\frac{49}{400}\right)\)
\(\chi_{4010}(63,\cdot)\) 4010.bs 100 no \(-1\) \(1\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{23}{100}\right)\)
\(\chi_{4010}(67,\cdot)\) 4010.bz 400 no \(1\) \(1\) \(e\left(\frac{273}{400}\right)\) \(e\left(\frac{13}{200}\right)\) \(e\left(\frac{73}{200}\right)\) \(e\left(\frac{181}{200}\right)\) \(e\left(\frac{87}{400}\right)\) \(e\left(\frac{159}{400}\right)\) \(e\left(\frac{199}{400}\right)\) \(e\left(\frac{299}{400}\right)\) \(e\left(\frac{43}{400}\right)\) \(e\left(\frac{19}{400}\right)\)
\(\chi_{4010}(69,\cdot)\) 4010.bp 100 no \(1\) \(1\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{69}{100}\right)\)
\(\chi_{4010}(71,\cdot)\) 4010.cb 400 no \(-1\) \(1\) \(e\left(\frac{69}{400}\right)\) \(e\left(\frac{139}{200}\right)\) \(e\left(\frac{69}{200}\right)\) \(e\left(\frac{93}{200}\right)\) \(e\left(\frac{11}{400}\right)\) \(e\left(\frac{27}{400}\right)\) \(e\left(\frac{47}{400}\right)\) \(e\left(\frac{347}{400}\right)\) \(e\left(\frac{79}{400}\right)\) \(e\left(\frac{207}{400}\right)\)
\(\chi_{4010}(73,\cdot)\) 4010.bx 200 no \(-1\) \(1\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{107}{200}\right)\) \(e\left(\frac{199}{200}\right)\) \(e\left(\frac{89}{200}\right)\) \(e\left(\frac{89}{200}\right)\) \(e\left(\frac{23}{200}\right)\) \(e\left(\frac{59}{200}\right)\)
\(\chi_{4010}(77,\cdot)\) 4010.bs 100 no \(-1\) \(1\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{17}{100}\right)\)
\(\chi_{4010}(79,\cdot)\) 4010.ca 400 no \(-1\) \(1\) \(e\left(\frac{379}{400}\right)\) \(e\left(\frac{49}{200}\right)\) \(e\left(\frac{179}{200}\right)\) \(e\left(\frac{163}{200}\right)\) \(e\left(\frac{101}{400}\right)\) \(e\left(\frac{357}{400}\right)\) \(e\left(\frac{377}{400}\right)\) \(e\left(\frac{77}{400}\right)\) \(e\left(\frac{289}{400}\right)\) \(e\left(\frac{337}{400}\right)\)
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