Properties

Modulus 4002
Structure \(C_{308}\times C_{2}\times C_{2}\)
Order 1232

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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(4002)
pari: g = idealstar(,4002,2)

Character group

sage: G.order()
pari: g.no
Order = 1232
sage: H.invariants()
pari: g.cyc
Structure = \(C_{308}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4002}(727,\cdot)$, $\chi_{4002}(2437,\cdot)$, $\chi_{4002}(2669,\cdot)$

First 32 of 1232 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 5 7 11 13 17 19 25 31 35 37
\(\chi_{4002}(1,\cdot)\) 4002.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4002}(5,\cdot)\) 4002.bp 154 No \(1\) \(1\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{19}{154}\right)\) \(e\left(\frac{24}{77}\right)\)
\(\chi_{4002}(7,\cdot)\) 4002.bl 154 No \(-1\) \(1\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{62}{77}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{65}{154}\right)\)
\(\chi_{4002}(11,\cdot)\) 4002.bs 308 No \(-1\) \(1\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{155}{308}\right)\) \(e\left(\frac{123}{154}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{53}{308}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{107}{308}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{83}{308}\right)\)
\(\chi_{4002}(13,\cdot)\) 4002.br 154 No \(1\) \(1\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{62}{77}\right)\) \(e\left(\frac{123}{154}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{71}{154}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{45}{154}\right)\)
\(\chi_{4002}(17,\cdot)\) 4002.bj 44 No \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{4002}(19,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{53}{308}\right)\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{37}{308}\right)\) \(e\left(\frac{39}{77}\right)\) \(e\left(\frac{127}{308}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{87}{308}\right)\)
\(\chi_{4002}(25,\cdot)\) 4002.bk 77 No \(1\) \(1\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{39}{77}\right)\) \(e\left(\frac{25}{77}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{19}{77}\right)\) \(e\left(\frac{48}{77}\right)\)
\(\chi_{4002}(31,\cdot)\) 4002.bt 308 No \(-1\) \(1\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{107}{308}\right)\) \(e\left(\frac{71}{154}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{127}{308}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{207}{308}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{257}{308}\right)\)
\(\chi_{4002}(35,\cdot)\) 4002.bo 154 No \(-1\) \(1\) \(e\left(\frac{19}{154}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{19}{77}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{149}{154}\right)\) \(e\left(\frac{113}{154}\right)\)
\(\chi_{4002}(37,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{24}{77}\right)\) \(e\left(\frac{65}{154}\right)\) \(e\left(\frac{83}{308}\right)\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{87}{308}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{257}{308}\right)\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{113}{308}\right)\)
\(\chi_{4002}(41,\cdot)\) 4002.bg 44 No \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{4002}(43,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{34}{77}\right)\) \(e\left(\frac{137}{154}\right)\) \(e\left(\frac{201}{308}\right)\) \(e\left(\frac{83}{154}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{181}{308}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{255}{308}\right)\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{51}{308}\right)\)
\(\chi_{4002}(47,\cdot)\) 4002.bc 28 No \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(-i\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{4002}(49,\cdot)\) 4002.bk 77 No \(1\) \(1\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{75}{77}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{65}{77}\right)\)
\(\chi_{4002}(53,\cdot)\) 4002.bq 154 No \(1\) \(1\) \(e\left(\frac{50}{77}\right)\) \(e\left(\frac{129}{154}\right)\) \(e\left(\frac{32}{77}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{81}{154}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{153}{154}\right)\)
\(\chi_{4002}(55,\cdot)\) 4002.bt 308 No \(-1\) \(1\) \(e\left(\frac{59}{154}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{17}{308}\right)\) \(e\left(\frac{89}{154}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{285}{308}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{25}{154}\right)\) \(e\left(\frac{179}{308}\right)\)
\(\chi_{4002}(59,\cdot)\) 4002.z 22 No \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{4002}(61,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{127}{154}\right)\) \(e\left(\frac{129}{308}\right)\) \(e\left(\frac{5}{154}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{61}{308}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{251}{308}\right)\) \(e\left(\frac{81}{154}\right)\) \(e\left(\frac{235}{308}\right)\)
\(\chi_{4002}(65,\cdot)\) 4002.bq 154 No \(1\) \(1\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{15}{154}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{20}{77}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{154}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{40}{77}\right)\) \(e\left(\frac{109}{154}\right)\) \(e\left(\frac{93}{154}\right)\)
\(\chi_{4002}(67,\cdot)\) 4002.bm 154 No \(-1\) \(1\) \(e\left(\frac{69}{154}\right)\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{19}{77}\right)\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{37}{77}\right)\)
\(\chi_{4002}(71,\cdot)\) 4002.bo 154 No \(-1\) \(1\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{34}{77}\right)\) \(e\left(\frac{30}{77}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{23}{154}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{29}{154}\right)\) \(e\left(\frac{27}{154}\right)\) \(e\left(\frac{129}{154}\right)\)
\(\chi_{4002}(73,\cdot)\) 4002.bt 308 No \(-1\) \(1\) \(e\left(\frac{61}{154}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{229}{308}\right)\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{17}{308}\right)\) \(e\left(\frac{65}{154}\right)\) \(e\left(\frac{219}{308}\right)\)
\(\chi_{4002}(77,\cdot)\) 4002.bv 308 No \(1\) \(1\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{305}{308}\right)\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{303}{308}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{295}{308}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{213}{308}\right)\)
\(\chi_{4002}(79,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{38}{77}\right)\) \(e\left(\frac{135}{154}\right)\) \(e\left(\frac{125}{308}\right)\) \(e\left(\frac{129}{154}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{157}{308}\right)\) \(e\left(\frac{76}{77}\right)\) \(e\left(\frac{131}{308}\right)\) \(e\left(\frac{57}{154}\right)\) \(e\left(\frac{211}{308}\right)\)
\(\chi_{4002}(83,\cdot)\) 4002.bq 154 No \(1\) \(1\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{153}{154}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{50}{77}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{71}{154}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{3}{154}\right)\) \(e\left(\frac{117}{154}\right)\)
\(\chi_{4002}(85,\cdot)\) 4002.bt 308 No \(-1\) \(1\) \(e\left(\frac{23}{154}\right)\) \(e\left(\frac{26}{77}\right)\) \(e\left(\frac{205}{308}\right)\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{85}{308}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{221}{308}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{75}{308}\right)\)
\(\chi_{4002}(89,\cdot)\) 4002.bs 308 No \(-1\) \(1\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{135}{308}\right)\) \(e\left(\frac{127}{154}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{225}{308}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{123}{308}\right)\) \(e\left(\frac{20}{77}\right)\) \(e\left(\frac{271}{308}\right)\)
\(\chi_{4002}(91,\cdot)\) 4002.t 14 No \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{4002}(95,\cdot)\) 4002.bv 308 No \(1\) \(1\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{223}{308}\right)\) \(e\left(\frac{17}{154}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{269}{308}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{145}{308}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{183}{308}\right)\)
\(\chi_{4002}(97,\cdot)\) 4002.bu 308 No \(1\) \(1\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{291}{308}\right)\) \(e\left(\frac{65}{154}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{23}{308}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{29}{308}\right)\) \(e\left(\frac{129}{154}\right)\) \(e\left(\frac{129}{308}\right)\)
\(\chi_{4002}(101,\cdot)\) 4002.bv 308 No \(1\) \(1\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{61}{308}\right)\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{307}{308}\right)\) \(e\left(\frac{26}{77}\right)\) \(e\left(\frac{59}{308}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{289}{308}\right)\)