Properties

Modulus 8032
Structure \(C_{1000}\times C_{2}\times C_{2}\)
Order 4000

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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(8032)
pari: g = idealstar(,8032,2)

Character group

sage: G.order()
pari: g.no
Order = 4000
sage: H.invariants()
pari: g.cyc
Structure = \(C_{1000}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{8032}(1261,\cdot)$, $\chi_{8032}(5521,\cdot)$, $\chi_{8032}(6527,\cdot)$

First 32 of 4000 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 3 5 7 9 11 13 15 17 19 21
\(\chi_{8032}(1,\cdot)\) 8032.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8032}(3,\cdot)\) 8032.ci 1000 Yes \(-1\) \(1\) \(e\left(\frac{649}{1000}\right)\) \(e\left(\frac{139}{200}\right)\) \(e\left(\frac{61}{500}\right)\) \(e\left(\frac{149}{500}\right)\) \(e\left(\frac{879}{1000}\right)\) \(e\left(\frac{273}{1000}\right)\) \(e\left(\frac{43}{125}\right)\) \(e\left(\frac{59}{250}\right)\) \(e\left(\frac{557}{1000}\right)\) \(e\left(\frac{771}{1000}\right)\)
\(\chi_{8032}(5,\cdot)\) 8032.bv 200 Yes \(1\) \(1\) \(e\left(\frac{139}{200}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{69}{200}\right)\) \(e\left(\frac{103}{200}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{127}{200}\right)\) \(e\left(\frac{181}{200}\right)\)
\(\chi_{8032}(7,\cdot)\) 8032.cf 500 No \(-1\) \(1\) \(e\left(\frac{61}{500}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{2}{125}\right)\) \(e\left(\frac{61}{250}\right)\) \(e\left(\frac{31}{500}\right)\) \(e\left(\frac{147}{500}\right)\) \(e\left(\frac{83}{250}\right)\) \(e\left(\frac{51}{125}\right)\) \(e\left(\frac{473}{500}\right)\) \(e\left(\frac{69}{500}\right)\)
\(\chi_{8032}(9,\cdot)\) 8032.cg 500 No \(1\) \(1\) \(e\left(\frac{149}{500}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{61}{250}\right)\) \(e\left(\frac{149}{250}\right)\) \(e\left(\frac{379}{500}\right)\) \(e\left(\frac{273}{500}\right)\) \(e\left(\frac{86}{125}\right)\) \(e\left(\frac{59}{125}\right)\) \(e\left(\frac{57}{500}\right)\) \(e\left(\frac{271}{500}\right)\)
\(\chi_{8032}(11,\cdot)\) 8032.cj 1000 Yes \(1\) \(1\) \(e\left(\frac{879}{1000}\right)\) \(e\left(\frac{69}{200}\right)\) \(e\left(\frac{31}{500}\right)\) \(e\left(\frac{379}{500}\right)\) \(e\left(\frac{709}{1000}\right)\) \(e\left(\frac{983}{1000}\right)\) \(e\left(\frac{28}{125}\right)\) \(e\left(\frac{239}{250}\right)\) \(e\left(\frac{447}{1000}\right)\) \(e\left(\frac{941}{1000}\right)\)
\(\chi_{8032}(13,\cdot)\) 8032.ck 1000 Yes \(1\) \(1\) \(e\left(\frac{273}{1000}\right)\) \(e\left(\frac{103}{200}\right)\) \(e\left(\frac{147}{500}\right)\) \(e\left(\frac{273}{500}\right)\) \(e\left(\frac{983}{1000}\right)\) \(e\left(\frac{621}{1000}\right)\) \(e\left(\frac{197}{250}\right)\) \(e\left(\frac{93}{250}\right)\) \(e\left(\frac{789}{1000}\right)\) \(e\left(\frac{567}{1000}\right)\)
\(\chi_{8032}(15,\cdot)\) 8032.cb 250 No \(-1\) \(1\) \(e\left(\frac{43}{125}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{83}{250}\right)\) \(e\left(\frac{86}{125}\right)\) \(e\left(\frac{28}{125}\right)\) \(e\left(\frac{197}{250}\right)\) \(e\left(\frac{191}{250}\right)\) \(e\left(\frac{27}{125}\right)\) \(e\left(\frac{24}{125}\right)\) \(e\left(\frac{169}{250}\right)\)
\(\chi_{8032}(17,\cdot)\) 8032.cc 250 No \(1\) \(1\) \(e\left(\frac{59}{250}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{51}{125}\right)\) \(e\left(\frac{59}{125}\right)\) \(e\left(\frac{239}{250}\right)\) \(e\left(\frac{93}{250}\right)\) \(e\left(\frac{27}{125}\right)\) \(e\left(\frac{113}{125}\right)\) \(e\left(\frac{187}{250}\right)\) \(e\left(\frac{161}{250}\right)\)
\(\chi_{8032}(19,\cdot)\) 8032.cj 1000 Yes \(1\) \(1\) \(e\left(\frac{557}{1000}\right)\) \(e\left(\frac{127}{200}\right)\) \(e\left(\frac{473}{500}\right)\) \(e\left(\frac{57}{500}\right)\) \(e\left(\frac{447}{1000}\right)\) \(e\left(\frac{789}{1000}\right)\) \(e\left(\frac{24}{125}\right)\) \(e\left(\frac{187}{250}\right)\) \(e\left(\frac{901}{1000}\right)\) \(e\left(\frac{503}{1000}\right)\)
\(\chi_{8032}(21,\cdot)\) 8032.ck 1000 Yes \(1\) \(1\) \(e\left(\frac{771}{1000}\right)\) \(e\left(\frac{181}{200}\right)\) \(e\left(\frac{69}{500}\right)\) \(e\left(\frac{271}{500}\right)\) \(e\left(\frac{941}{1000}\right)\) \(e\left(\frac{567}{1000}\right)\) \(e\left(\frac{169}{250}\right)\) \(e\left(\frac{161}{250}\right)\) \(e\left(\frac{503}{1000}\right)\) \(e\left(\frac{909}{1000}\right)\)
\(\chi_{8032}(23,\cdot)\) 8032.cf 500 No \(-1\) \(1\) \(e\left(\frac{143}{500}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{101}{125}\right)\) \(e\left(\frac{143}{250}\right)\) \(e\left(\frac{253}{500}\right)\) \(e\left(\frac{361}{500}\right)\) \(e\left(\frac{129}{250}\right)\) \(e\left(\frac{13}{125}\right)\) \(e\left(\frac{199}{500}\right)\) \(e\left(\frac{47}{500}\right)\)
\(\chi_{8032}(25,\cdot)\) 8032.bo 100 No \(1\) \(1\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{81}{100}\right)\)
\(\chi_{8032}(27,\cdot)\) 8032.ci 1000 Yes \(-1\) \(1\) \(e\left(\frac{947}{1000}\right)\) \(e\left(\frac{17}{200}\right)\) \(e\left(\frac{183}{500}\right)\) \(e\left(\frac{447}{500}\right)\) \(e\left(\frac{637}{1000}\right)\) \(e\left(\frac{819}{1000}\right)\) \(e\left(\frac{4}{125}\right)\) \(e\left(\frac{177}{250}\right)\) \(e\left(\frac{671}{1000}\right)\) \(e\left(\frac{313}{1000}\right)\)
\(\chi_{8032}(29,\cdot)\) 8032.cl 1000 Yes \(-1\) \(1\) \(e\left(\frac{437}{1000}\right)\) \(e\left(\frac{107}{200}\right)\) \(e\left(\frac{43}{500}\right)\) \(e\left(\frac{437}{500}\right)\) \(e\left(\frac{927}{1000}\right)\) \(e\left(\frac{49}{1000}\right)\) \(e\left(\frac{243}{250}\right)\) \(e\left(\frac{17}{250}\right)\) \(e\left(\frac{741}{1000}\right)\) \(e\left(\frac{523}{1000}\right)\)
\(\chi_{8032}(31,\cdot)\) 8032.bz 250 No \(-1\) \(1\) \(e\left(\frac{101}{250}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{250}\right)\) \(e\left(\frac{101}{125}\right)\) \(e\left(\frac{121}{250}\right)\) \(e\left(\frac{51}{125}\right)\) \(e\left(\frac{31}{250}\right)\) \(e\left(\frac{7}{125}\right)\) \(e\left(\frac{193}{250}\right)\) \(e\left(\frac{52}{125}\right)\)
\(\chi_{8032}(33,\cdot)\) 8032.bx 250 No \(-1\) \(1\) \(e\left(\frac{66}{125}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{23}{125}\right)\) \(e\left(\frac{7}{125}\right)\) \(e\left(\frac{147}{250}\right)\) \(e\left(\frac{32}{125}\right)\) \(e\left(\frac{71}{125}\right)\) \(e\left(\frac{24}{125}\right)\) \(e\left(\frac{1}{250}\right)\) \(e\left(\frac{89}{125}\right)\)
\(\chi_{8032}(35,\cdot)\) 8032.ci 1000 Yes \(-1\) \(1\) \(e\left(\frac{817}{1000}\right)\) \(e\left(\frac{187}{200}\right)\) \(e\left(\frac{113}{500}\right)\) \(e\left(\frac{317}{500}\right)\) \(e\left(\frac{407}{1000}\right)\) \(e\left(\frac{809}{1000}\right)\) \(e\left(\frac{94}{125}\right)\) \(e\left(\frac{97}{250}\right)\) \(e\left(\frac{581}{1000}\right)\) \(e\left(\frac{43}{1000}\right)\)
\(\chi_{8032}(37,\cdot)\) 8032.cl 1000 Yes \(-1\) \(1\) \(e\left(\frac{623}{1000}\right)\) \(e\left(\frac{153}{200}\right)\) \(e\left(\frac{297}{500}\right)\) \(e\left(\frac{123}{500}\right)\) \(e\left(\frac{333}{1000}\right)\) \(e\left(\frac{571}{1000}\right)\) \(e\left(\frac{97}{250}\right)\) \(e\left(\frac{193}{250}\right)\) \(e\left(\frac{839}{1000}\right)\) \(e\left(\frac{217}{1000}\right)\)
\(\chi_{8032}(39,\cdot)\) 8032.cf 500 No \(-1\) \(1\) \(e\left(\frac{461}{500}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{52}{125}\right)\) \(e\left(\frac{211}{250}\right)\) \(e\left(\frac{431}{500}\right)\) \(e\left(\frac{447}{500}\right)\) \(e\left(\frac{33}{250}\right)\) \(e\left(\frac{76}{125}\right)\) \(e\left(\frac{173}{500}\right)\) \(e\left(\frac{169}{500}\right)\)
\(\chi_{8032}(41,\cdot)\) 8032.cg 500 No \(1\) \(1\) \(e\left(\frac{253}{500}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{117}{250}\right)\) \(e\left(\frac{3}{250}\right)\) \(e\left(\frac{63}{500}\right)\) \(e\left(\frac{81}{500}\right)\) \(e\left(\frac{42}{125}\right)\) \(e\left(\frac{23}{125}\right)\) \(e\left(\frac{429}{500}\right)\) \(e\left(\frac{487}{500}\right)\)
\(\chi_{8032}(43,\cdot)\) 8032.cj 1000 Yes \(1\) \(1\) \(e\left(\frac{183}{1000}\right)\) \(e\left(\frac{13}{200}\right)\) \(e\left(\frac{387}{500}\right)\) \(e\left(\frac{183}{500}\right)\) \(e\left(\frac{93}{1000}\right)\) \(e\left(\frac{191}{1000}\right)\) \(e\left(\frac{31}{125}\right)\) \(e\left(\frac{153}{250}\right)\) \(e\left(\frac{919}{1000}\right)\) \(e\left(\frac{957}{1000}\right)\)
\(\chi_{8032}(45,\cdot)\) 8032.ck 1000 Yes \(1\) \(1\) \(e\left(\frac{993}{1000}\right)\) \(e\left(\frac{23}{200}\right)\) \(e\left(\frac{227}{500}\right)\) \(e\left(\frac{493}{500}\right)\) \(e\left(\frac{103}{1000}\right)\) \(e\left(\frac{61}{1000}\right)\) \(e\left(\frac{27}{250}\right)\) \(e\left(\frac{113}{250}\right)\) \(e\left(\frac{749}{1000}\right)\) \(e\left(\frac{447}{1000}\right)\)
\(\chi_{8032}(47,\cdot)\) 8032.bk 50 No \(1\) \(1\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{43}{50}\right)\)
\(\chi_{8032}(49,\cdot)\) 8032.cc 250 No \(1\) \(1\) \(e\left(\frac{61}{250}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{4}{125}\right)\) \(e\left(\frac{61}{125}\right)\) \(e\left(\frac{31}{250}\right)\) \(e\left(\frac{147}{250}\right)\) \(e\left(\frac{83}{125}\right)\) \(e\left(\frac{102}{125}\right)\) \(e\left(\frac{223}{250}\right)\) \(e\left(\frac{69}{250}\right)\)
\(\chi_{8032}(51,\cdot)\) 8032.bu 200 Yes \(-1\) \(1\) \(e\left(\frac{177}{200}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{167}{200}\right)\) \(e\left(\frac{129}{200}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{61}{200}\right)\) \(e\left(\frac{83}{200}\right)\)
\(\chi_{8032}(53,\cdot)\) 8032.cl 1000 Yes \(-1\) \(1\) \(e\left(\frac{467}{1000}\right)\) \(e\left(\frac{37}{200}\right)\) \(e\left(\frac{213}{500}\right)\) \(e\left(\frac{467}{500}\right)\) \(e\left(\frac{57}{1000}\right)\) \(e\left(\frac{359}{1000}\right)\) \(e\left(\frac{163}{250}\right)\) \(e\left(\frac{247}{250}\right)\) \(e\left(\frac{531}{1000}\right)\) \(e\left(\frac{893}{1000}\right)\)
\(\chi_{8032}(55,\cdot)\) 8032.ch 500 No \(1\) \(1\) \(e\left(\frac{287}{500}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{34}{125}\right)\) \(e\left(\frac{37}{250}\right)\) \(e\left(\frac{27}{500}\right)\) \(e\left(\frac{249}{500}\right)\) \(e\left(\frac{161}{250}\right)\) \(e\left(\frac{117}{125}\right)\) \(e\left(\frac{41}{500}\right)\) \(e\left(\frac{423}{500}\right)\)
\(\chi_{8032}(57,\cdot)\) 8032.ce 500 No \(-1\) \(1\) \(e\left(\frac{103}{500}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{17}{250}\right)\) \(e\left(\frac{103}{250}\right)\) \(e\left(\frac{163}{500}\right)\) \(e\left(\frac{31}{500}\right)\) \(e\left(\frac{67}{125}\right)\) \(e\left(\frac{123}{125}\right)\) \(e\left(\frac{229}{500}\right)\) \(e\left(\frac{137}{500}\right)\)
\(\chi_{8032}(59,\cdot)\) 8032.cj 1000 Yes \(1\) \(1\) \(e\left(\frac{139}{1000}\right)\) \(e\left(\frac{129}{200}\right)\) \(e\left(\frac{171}{500}\right)\) \(e\left(\frac{139}{500}\right)\) \(e\left(\frac{169}{1000}\right)\) \(e\left(\frac{3}{1000}\right)\) \(e\left(\frac{98}{125}\right)\) \(e\left(\frac{149}{250}\right)\) \(e\left(\frac{627}{1000}\right)\) \(e\left(\frac{481}{1000}\right)\)
\(\chi_{8032}(61,\cdot)\) 8032.cl 1000 Yes \(-1\) \(1\) \(e\left(\frac{917}{1000}\right)\) \(e\left(\frac{187}{200}\right)\) \(e\left(\frac{263}{500}\right)\) \(e\left(\frac{417}{500}\right)\) \(e\left(\frac{7}{1000}\right)\) \(e\left(\frac{9}{1000}\right)\) \(e\left(\frac{213}{250}\right)\) \(e\left(\frac{197}{250}\right)\) \(e\left(\frac{381}{1000}\right)\) \(e\left(\frac{443}{1000}\right)\)
\(\chi_{8032}(63,\cdot)\) 8032.bj 50 No \(-1\) \(1\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{17}{25}\right)\)