Properties

Modulus 4024
Structure \(C_{502}\times C_{2}\times C_{2}\)
Order 2008

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4024)
pari: g = idealstar(,4024,2)

Character group

sage: G.order()
pari: g.no
Order = 2008
sage: H.invariants()
pari: g.cyc
Structure = \(C_{502}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4024}(2017,\cdot)$, $\chi_{4024}(1007,\cdot)$, $\chi_{4024}(2013,\cdot)$

First 32 of 2008 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
\(\chi_{4024}(1,\cdot)\) 4024.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4024}(3,\cdot)\) 4024.l 502 Yes \(-1\) \(1\) \(e\left(\frac{120}{251}\right)\) \(e\left(\frac{407}{502}\right)\) \(e\left(\frac{113}{502}\right)\) \(e\left(\frac{240}{251}\right)\) \(e\left(\frac{13}{251}\right)\) \(e\left(\frac{17}{502}\right)\) \(e\left(\frac{145}{502}\right)\) \(e\left(\frac{41}{251}\right)\) \(e\left(\frac{163}{251}\right)\) \(e\left(\frac{353}{502}\right)\)
\(\chi_{4024}(5,\cdot)\) 4024.m 502 Yes \(-1\) \(1\) \(e\left(\frac{407}{502}\right)\) \(e\left(\frac{126}{251}\right)\) \(e\left(\frac{43}{251}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{293}{502}\right)\) \(e\left(\frac{375}{502}\right)\) \(e\left(\frac{157}{502}\right)\) \(e\left(\frac{229}{502}\right)\) \(e\left(\frac{244}{251}\right)\) \(e\left(\frac{493}{502}\right)\)
\(\chi_{4024}(7,\cdot)\) 4024.n 502 No \(-1\) \(1\) \(e\left(\frac{113}{502}\right)\) \(e\left(\frac{43}{251}\right)\) \(e\left(\frac{117}{502}\right)\) \(e\left(\frac{113}{251}\right)\) \(e\left(\frac{349}{502}\right)\) \(e\left(\frac{61}{251}\right)\) \(e\left(\frac{199}{502}\right)\) \(e\left(\frac{58}{251}\right)\) \(e\left(\frac{51}{502}\right)\) \(e\left(\frac{115}{251}\right)\)
\(\chi_{4024}(9,\cdot)\) 4024.i 251 No \(1\) \(1\) \(e\left(\frac{240}{251}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{113}{251}\right)\) \(e\left(\frac{229}{251}\right)\) \(e\left(\frac{26}{251}\right)\) \(e\left(\frac{17}{251}\right)\) \(e\left(\frac{145}{251}\right)\) \(e\left(\frac{82}{251}\right)\) \(e\left(\frac{75}{251}\right)\) \(e\left(\frac{102}{251}\right)\)
\(\chi_{4024}(11,\cdot)\) 4024.l 502 Yes \(-1\) \(1\) \(e\left(\frac{13}{251}\right)\) \(e\left(\frac{293}{502}\right)\) \(e\left(\frac{349}{502}\right)\) \(e\left(\frac{26}{251}\right)\) \(e\left(\frac{129}{251}\right)\) \(e\left(\frac{439}{502}\right)\) \(e\left(\frac{319}{502}\right)\) \(e\left(\frac{40}{251}\right)\) \(e\left(\frac{208}{251}\right)\) \(e\left(\frac{375}{502}\right)\)
\(\chi_{4024}(13,\cdot)\) 4024.o 502 Yes \(1\) \(1\) \(e\left(\frac{17}{502}\right)\) \(e\left(\frac{375}{502}\right)\) \(e\left(\frac{61}{251}\right)\) \(e\left(\frac{17}{251}\right)\) \(e\left(\frac{439}{502}\right)\) \(e\left(\frac{65}{502}\right)\) \(e\left(\frac{196}{251}\right)\) \(e\left(\frac{142}{251}\right)\) \(e\left(\frac{21}{502}\right)\) \(e\left(\frac{139}{502}\right)\)
\(\chi_{4024}(15,\cdot)\) 4024.p 502 No \(1\) \(1\) \(e\left(\frac{145}{502}\right)\) \(e\left(\frac{157}{502}\right)\) \(e\left(\frac{199}{502}\right)\) \(e\left(\frac{145}{251}\right)\) \(e\left(\frac{319}{502}\right)\) \(e\left(\frac{196}{251}\right)\) \(e\left(\frac{151}{251}\right)\) \(e\left(\frac{311}{502}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{172}{251}\right)\)
\(\chi_{4024}(17,\cdot)\) 4024.k 502 No \(-1\) \(1\) \(e\left(\frac{41}{251}\right)\) \(e\left(\frac{229}{502}\right)\) \(e\left(\frac{58}{251}\right)\) \(e\left(\frac{82}{251}\right)\) \(e\left(\frac{40}{251}\right)\) \(e\left(\frac{142}{251}\right)\) \(e\left(\frac{311}{502}\right)\) \(e\left(\frac{233}{502}\right)\) \(e\left(\frac{57}{502}\right)\) \(e\left(\frac{99}{251}\right)\)
\(\chi_{4024}(19,\cdot)\) 4024.j 502 Yes \(1\) \(1\) \(e\left(\frac{163}{251}\right)\) \(e\left(\frac{244}{251}\right)\) \(e\left(\frac{51}{502}\right)\) \(e\left(\frac{75}{251}\right)\) \(e\left(\frac{208}{251}\right)\) \(e\left(\frac{21}{502}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{57}{502}\right)\) \(e\left(\frac{447}{502}\right)\) \(e\left(\frac{377}{502}\right)\)
\(\chi_{4024}(21,\cdot)\) 4024.o 502 Yes \(1\) \(1\) \(e\left(\frac{353}{502}\right)\) \(e\left(\frac{493}{502}\right)\) \(e\left(\frac{115}{251}\right)\) \(e\left(\frac{102}{251}\right)\) \(e\left(\frac{375}{502}\right)\) \(e\left(\frac{139}{502}\right)\) \(e\left(\frac{172}{251}\right)\) \(e\left(\frac{99}{251}\right)\) \(e\left(\frac{377}{502}\right)\) \(e\left(\frac{81}{502}\right)\)
\(\chi_{4024}(23,\cdot)\) 4024.n 502 No \(-1\) \(1\) \(e\left(\frac{77}{502}\right)\) \(e\left(\frac{207}{251}\right)\) \(e\left(\frac{213}{502}\right)\) \(e\left(\frac{77}{251}\right)\) \(e\left(\frac{69}{502}\right)\) \(e\left(\frac{66}{251}\right)\) \(e\left(\frac{491}{502}\right)\) \(e\left(\frac{215}{251}\right)\) \(e\left(\frac{479}{502}\right)\) \(e\left(\frac{145}{251}\right)\)
\(\chi_{4024}(25,\cdot)\) 4024.i 251 No \(1\) \(1\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{1}{251}\right)\) \(e\left(\frac{86}{251}\right)\) \(e\left(\frac{61}{251}\right)\) \(e\left(\frac{42}{251}\right)\) \(e\left(\frac{124}{251}\right)\) \(e\left(\frac{157}{251}\right)\) \(e\left(\frac{229}{251}\right)\) \(e\left(\frac{237}{251}\right)\) \(e\left(\frac{242}{251}\right)\)
\(\chi_{4024}(27,\cdot)\) 4024.l 502 Yes \(-1\) \(1\) \(e\left(\frac{109}{251}\right)\) \(e\left(\frac{217}{502}\right)\) \(e\left(\frac{339}{502}\right)\) \(e\left(\frac{218}{251}\right)\) \(e\left(\frac{39}{251}\right)\) \(e\left(\frac{51}{502}\right)\) \(e\left(\frac{435}{502}\right)\) \(e\left(\frac{123}{251}\right)\) \(e\left(\frac{238}{251}\right)\) \(e\left(\frac{55}{502}\right)\)
\(\chi_{4024}(29,\cdot)\) 4024.m 502 Yes \(-1\) \(1\) \(e\left(\frac{211}{502}\right)\) \(e\left(\frac{238}{251}\right)\) \(e\left(\frac{137}{251}\right)\) \(e\left(\frac{211}{251}\right)\) \(e\left(\frac{163}{502}\right)\) \(e\left(\frac{39}{502}\right)\) \(e\left(\frac{185}{502}\right)\) \(e\left(\frac{321}{502}\right)\) \(e\left(\frac{182}{251}\right)\) \(e\left(\frac{485}{502}\right)\)
\(\chi_{4024}(31,\cdot)\) 4024.p 502 No \(1\) \(1\) \(e\left(\frac{67}{502}\right)\) \(e\left(\frac{31}{502}\right)\) \(e\left(\frac{407}{502}\right)\) \(e\left(\frac{67}{251}\right)\) \(e\left(\frac{47}{502}\right)\) \(e\left(\frac{165}{251}\right)\) \(e\left(\frac{49}{251}\right)\) \(e\left(\frac{71}{502}\right)\) \(e\left(\frac{34}{251}\right)\) \(e\left(\frac{237}{251}\right)\)
\(\chi_{4024}(33,\cdot)\) 4024.i 251 No \(1\) \(1\) \(e\left(\frac{133}{251}\right)\) \(e\left(\frac{99}{251}\right)\) \(e\left(\frac{231}{251}\right)\) \(e\left(\frac{15}{251}\right)\) \(e\left(\frac{142}{251}\right)\) \(e\left(\frac{228}{251}\right)\) \(e\left(\frac{232}{251}\right)\) \(e\left(\frac{81}{251}\right)\) \(e\left(\frac{120}{251}\right)\) \(e\left(\frac{113}{251}\right)\)
\(\chi_{4024}(35,\cdot)\) 4024.j 502 Yes \(1\) \(1\) \(e\left(\frac{9}{251}\right)\) \(e\left(\frac{169}{251}\right)\) \(e\left(\frac{203}{502}\right)\) \(e\left(\frac{18}{251}\right)\) \(e\left(\frac{70}{251}\right)\) \(e\left(\frac{497}{502}\right)\) \(e\left(\frac{178}{251}\right)\) \(e\left(\frac{345}{502}\right)\) \(e\left(\frac{37}{502}\right)\) \(e\left(\frac{221}{502}\right)\)
\(\chi_{4024}(37,\cdot)\) 4024.m 502 Yes \(-1\) \(1\) \(e\left(\frac{397}{502}\right)\) \(e\left(\frac{60}{251}\right)\) \(e\left(\frac{140}{251}\right)\) \(e\left(\frac{146}{251}\right)\) \(e\left(\frac{271}{502}\right)\) \(e\left(\frac{71}{502}\right)\) \(e\left(\frac{15}{502}\right)\) \(e\left(\frac{121}{502}\right)\) \(e\left(\frac{164}{251}\right)\) \(e\left(\frac{175}{502}\right)\)
\(\chi_{4024}(39,\cdot)\) 4024.n 502 No \(-1\) \(1\) \(e\left(\frac{257}{502}\right)\) \(e\left(\frac{140}{251}\right)\) \(e\left(\frac{235}{502}\right)\) \(e\left(\frac{6}{251}\right)\) \(e\left(\frac{465}{502}\right)\) \(e\left(\frac{41}{251}\right)\) \(e\left(\frac{35}{502}\right)\) \(e\left(\frac{183}{251}\right)\) \(e\left(\frac{347}{502}\right)\) \(e\left(\frac{246}{251}\right)\)
\(\chi_{4024}(41,\cdot)\) 4024.k 502 No \(-1\) \(1\) \(e\left(\frac{7}{251}\right)\) \(e\left(\frac{235}{502}\right)\) \(e\left(\frac{65}{251}\right)\) \(e\left(\frac{14}{251}\right)\) \(e\left(\frac{166}{251}\right)\) \(e\left(\frac{12}{251}\right)\) \(e\left(\frac{249}{502}\right)\) \(e\left(\frac{101}{502}\right)\) \(e\left(\frac{475}{502}\right)\) \(e\left(\frac{72}{251}\right)\)
\(\chi_{4024}(43,\cdot)\) 4024.l 502 Yes \(-1\) \(1\) \(e\left(\frac{128}{251}\right)\) \(e\left(\frac{317}{502}\right)\) \(e\left(\frac{405}{502}\right)\) \(e\left(\frac{5}{251}\right)\) \(e\left(\frac{131}{251}\right)\) \(e\left(\frac{403}{502}\right)\) \(e\left(\frac{71}{502}\right)\) \(e\left(\frac{27}{251}\right)\) \(e\left(\frac{40}{251}\right)\) \(e\left(\frac{159}{502}\right)\)
\(\chi_{4024}(45,\cdot)\) 4024.m 502 Yes \(-1\) \(1\) \(e\left(\frac{385}{502}\right)\) \(e\left(\frac{31}{251}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{134}{251}\right)\) \(e\left(\frac{345}{502}\right)\) \(e\left(\frac{409}{502}\right)\) \(e\left(\frac{447}{502}\right)\) \(e\left(\frac{393}{502}\right)\) \(e\left(\frac{68}{251}\right)\) \(e\left(\frac{195}{502}\right)\)
\(\chi_{4024}(47,\cdot)\) 4024.n 502 No \(-1\) \(1\) \(e\left(\frac{475}{502}\right)\) \(e\left(\frac{123}{251}\right)\) \(e\left(\frac{323}{502}\right)\) \(e\left(\frac{224}{251}\right)\) \(e\left(\frac{41}{502}\right)\) \(e\left(\frac{192}{251}\right)\) \(e\left(\frac{219}{502}\right)\) \(e\left(\frac{55}{251}\right)\) \(e\left(\frac{321}{502}\right)\) \(e\left(\frac{148}{251}\right)\)
\(\chi_{4024}(49,\cdot)\) 4024.i 251 No \(1\) \(1\) \(e\left(\frac{113}{251}\right)\) \(e\left(\frac{86}{251}\right)\) \(e\left(\frac{117}{251}\right)\) \(e\left(\frac{226}{251}\right)\) \(e\left(\frac{98}{251}\right)\) \(e\left(\frac{122}{251}\right)\) \(e\left(\frac{199}{251}\right)\) \(e\left(\frac{116}{251}\right)\) \(e\left(\frac{51}{251}\right)\) \(e\left(\frac{230}{251}\right)\)
\(\chi_{4024}(51,\cdot)\) 4024.j 502 Yes \(1\) \(1\) \(e\left(\frac{161}{251}\right)\) \(e\left(\frac{67}{251}\right)\) \(e\left(\frac{229}{502}\right)\) \(e\left(\frac{71}{251}\right)\) \(e\left(\frac{53}{251}\right)\) \(e\left(\frac{301}{502}\right)\) \(e\left(\frac{228}{251}\right)\) \(e\left(\frac{315}{502}\right)\) \(e\left(\frac{383}{502}\right)\) \(e\left(\frac{49}{502}\right)\)
\(\chi_{4024}(53,\cdot)\) 4024.m 502 Yes \(-1\) \(1\) \(e\left(\frac{427}{502}\right)\) \(e\left(\frac{7}{251}\right)\) \(e\left(\frac{100}{251}\right)\) \(e\left(\frac{176}{251}\right)\) \(e\left(\frac{337}{502}\right)\) \(e\left(\frac{481}{502}\right)\) \(e\left(\frac{441}{502}\right)\) \(e\left(\frac{445}{502}\right)\) \(e\left(\frac{153}{251}\right)\) \(e\left(\frac{125}{502}\right)\)
\(\chi_{4024}(55,\cdot)\) 4024.p 502 No \(1\) \(1\) \(e\left(\frac{433}{502}\right)\) \(e\left(\frac{43}{502}\right)\) \(e\left(\frac{435}{502}\right)\) \(e\left(\frac{182}{251}\right)\) \(e\left(\frac{49}{502}\right)\) \(e\left(\frac{156}{251}\right)\) \(e\left(\frac{238}{251}\right)\) \(e\left(\frac{309}{502}\right)\) \(e\left(\frac{201}{251}\right)\) \(e\left(\frac{183}{251}\right)\)
\(\chi_{4024}(57,\cdot)\) 4024.k 502 No \(-1\) \(1\) \(e\left(\frac{32}{251}\right)\) \(e\left(\frac{393}{502}\right)\) \(e\left(\frac{82}{251}\right)\) \(e\left(\frac{64}{251}\right)\) \(e\left(\frac{221}{251}\right)\) \(e\left(\frac{19}{251}\right)\) \(e\left(\frac{457}{502}\right)\) \(e\left(\frac{139}{502}\right)\) \(e\left(\frac{271}{502}\right)\) \(e\left(\frac{114}{251}\right)\)
\(\chi_{4024}(59,\cdot)\) 4024.l 502 Yes \(-1\) \(1\) \(e\left(\frac{79}{251}\right)\) \(e\left(\frac{429}{502}\right)\) \(e\left(\frac{499}{502}\right)\) \(e\left(\frac{158}{251}\right)\) \(e\left(\frac{224}{251}\right)\) \(e\left(\frac{235}{502}\right)\) \(e\left(\frac{85}{502}\right)\) \(e\left(\frac{50}{251}\right)\) \(e\left(\frac{9}{251}\right)\) \(e\left(\frac{155}{502}\right)\)
\(\chi_{4024}(61,\cdot)\) 4024.o 502 Yes \(1\) \(1\) \(e\left(\frac{487}{502}\right)\) \(e\left(\frac{53}{502}\right)\) \(e\left(\frac{20}{251}\right)\) \(e\left(\frac{236}{251}\right)\) \(e\left(\frac{469}{502}\right)\) \(e\left(\frac{297}{502}\right)\) \(e\left(\frac{19}{251}\right)\) \(e\left(\frac{170}{251}\right)\) \(e\left(\frac{11}{502}\right)\) \(e\left(\frac{25}{502}\right)\)
\(\chi_{4024}(63,\cdot)\) 4024.n 502 No \(-1\) \(1\) \(e\left(\frac{91}{502}\right)\) \(e\left(\frac{199}{251}\right)\) \(e\left(\frac{343}{502}\right)\) \(e\left(\frac{91}{251}\right)\) \(e\left(\frac{401}{502}\right)\) \(e\left(\frac{78}{251}\right)\) \(e\left(\frac{489}{502}\right)\) \(e\left(\frac{140}{251}\right)\) \(e\left(\frac{201}{502}\right)\) \(e\left(\frac{217}{251}\right)\)