Properties

Modulus 4029
Structure \(C_{624}\times C_{2}\times C_{2}\)
Order 2496

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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(4029)
pari: g = idealstar(,4029,2)

Character group

sage: G.order()
pari: g.no
Order = 2496
sage: H.invariants()
pari: g.cyc
Structure = \(C_{624}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4029}(1978,\cdot)$, $\chi_{4029}(1342,\cdot)$, $\chi_{4029}(2687,\cdot)$

First 32 of 2496 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 2 4 5 7 8 10 11 13 14 16
\(\chi_{4029}(1,\cdot)\) 4029.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4029}(2,\cdot)\) 4029.cu 312 Yes \(-1\) \(1\) \(e\left(\frac{149}{156}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{17}{312}\right)\) \(e\left(\frac{107}{312}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{1}{104}\right)\) \(e\left(\frac{35}{312}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{31}{104}\right)\) \(e\left(\frac{32}{39}\right)\)
\(\chi_{4029}(4,\cdot)\) 4029.cn 156 No \(1\) \(1\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{17}{156}\right)\) \(e\left(\frac{107}{156}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{35}{156}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{25}{39}\right)\)
\(\chi_{4029}(5,\cdot)\) 4029.cz 624 Yes \(1\) \(1\) \(e\left(\frac{17}{312}\right)\) \(e\left(\frac{17}{156}\right)\) \(e\left(\frac{215}{624}\right)\) \(e\left(\frac{353}{624}\right)\) \(e\left(\frac{17}{104}\right)\) \(e\left(\frac{83}{208}\right)\) \(e\left(\frac{461}{624}\right)\) \(e\left(\frac{43}{156}\right)\) \(e\left(\frac{129}{208}\right)\) \(e\left(\frac{17}{78}\right)\)
\(\chi_{4029}(7,\cdot)\) 4029.cy 624 No \(1\) \(1\) \(e\left(\frac{107}{312}\right)\) \(e\left(\frac{107}{156}\right)\) \(e\left(\frac{353}{624}\right)\) \(e\left(\frac{359}{624}\right)\) \(e\left(\frac{3}{104}\right)\) \(e\left(\frac{189}{208}\right)\) \(e\left(\frac{11}{624}\right)\) \(e\left(\frac{133}{156}\right)\) \(e\left(\frac{191}{208}\right)\) \(e\left(\frac{29}{78}\right)\)
\(\chi_{4029}(8,\cdot)\) 4029.ck 104 Yes \(-1\) \(1\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{17}{104}\right)\) \(e\left(\frac{3}{104}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{3}{104}\right)\) \(e\left(\frac{35}{104}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{93}{104}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{4029}(10,\cdot)\) 4029.cr 208 No \(-1\) \(1\) \(e\left(\frac{1}{104}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{83}{208}\right)\) \(e\left(\frac{189}{208}\right)\) \(e\left(\frac{3}{104}\right)\) \(e\left(\frac{85}{208}\right)\) \(e\left(\frac{177}{208}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{191}{208}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{4029}(11,\cdot)\) 4029.cz 624 Yes \(1\) \(1\) \(e\left(\frac{35}{312}\right)\) \(e\left(\frac{35}{156}\right)\) \(e\left(\frac{461}{624}\right)\) \(e\left(\frac{11}{624}\right)\) \(e\left(\frac{35}{104}\right)\) \(e\left(\frac{177}{208}\right)\) \(e\left(\frac{527}{624}\right)\) \(e\left(\frac{61}{156}\right)\) \(e\left(\frac{27}{208}\right)\) \(e\left(\frac{35}{78}\right)\)
\(\chi_{4029}(13,\cdot)\) 4029.cn 156 No \(1\) \(1\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{43}{156}\right)\) \(e\left(\frac{133}{156}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{61}{156}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{38}{39}\right)\)
\(\chi_{4029}(14,\cdot)\) 4029.cq 208 Yes \(-1\) \(1\) \(e\left(\frac{31}{104}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{129}{208}\right)\) \(e\left(\frac{191}{208}\right)\) \(e\left(\frac{93}{104}\right)\) \(e\left(\frac{191}{208}\right)\) \(e\left(\frac{27}{208}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{45}{208}\right)\) \(e\left(\frac{5}{26}\right)\)
\(\chi_{4029}(16,\cdot)\) 4029.cf 78 No \(1\) \(1\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{11}{39}\right)\)
\(\chi_{4029}(19,\cdot)\) 4029.cx 312 No \(1\) \(1\) \(e\left(\frac{139}{156}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{253}{312}\right)\) \(e\left(\frac{115}{312}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{73}{104}\right)\) \(e\left(\frac{7}{312}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{27}{104}\right)\) \(e\left(\frac{22}{39}\right)\)
\(\chi_{4029}(20,\cdot)\) 4029.cz 624 Yes \(1\) \(1\) \(e\left(\frac{301}{312}\right)\) \(e\left(\frac{145}{156}\right)\) \(e\left(\frac{283}{624}\right)\) \(e\left(\frac{157}{624}\right)\) \(e\left(\frac{93}{104}\right)\) \(e\left(\frac{87}{208}\right)\) \(e\left(\frac{601}{624}\right)\) \(e\left(\frac{119}{156}\right)\) \(e\left(\frac{45}{208}\right)\) \(e\left(\frac{67}{78}\right)\)
\(\chi_{4029}(22,\cdot)\) 4029.cr 208 No \(-1\) \(1\) \(e\left(\frac{7}{104}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{165}{208}\right)\) \(e\left(\frac{75}{208}\right)\) \(e\left(\frac{21}{104}\right)\) \(e\left(\frac{179}{208}\right)\) \(e\left(\frac{199}{208}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{89}{208}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{4029}(23,\cdot)\) 4029.bv 48 Yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4029}(25,\cdot)\) 4029.cx 312 No \(1\) \(1\) \(e\left(\frac{17}{156}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{215}{312}\right)\) \(e\left(\frac{41}{312}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{83}{104}\right)\) \(e\left(\frac{149}{312}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{25}{104}\right)\) \(e\left(\frac{17}{39}\right)\)
\(\chi_{4029}(26,\cdot)\) 4029.cu 312 Yes \(-1\) \(1\) \(e\left(\frac{31}{156}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{103}{312}\right)\) \(e\left(\frac{61}{312}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{55}{104}\right)\) \(e\left(\frac{157}{312}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{41}{104}\right)\) \(e\left(\frac{31}{39}\right)\)
\(\chi_{4029}(28,\cdot)\) 4029.cy 624 No \(1\) \(1\) \(e\left(\frac{79}{312}\right)\) \(e\left(\frac{79}{156}\right)\) \(e\left(\frac{421}{624}\right)\) \(e\left(\frac{163}{624}\right)\) \(e\left(\frac{79}{104}\right)\) \(e\left(\frac{193}{208}\right)\) \(e\left(\frac{151}{624}\right)\) \(e\left(\frac{53}{156}\right)\) \(e\left(\frac{107}{208}\right)\) \(e\left(\frac{1}{78}\right)\)
\(\chi_{4029}(29,\cdot)\) 4029.db 624 Yes \(-1\) \(1\) \(e\left(\frac{137}{312}\right)\) \(e\left(\frac{137}{156}\right)\) \(e\left(\frac{191}{624}\right)\) \(e\left(\frac{257}{624}\right)\) \(e\left(\frac{33}{104}\right)\) \(e\left(\frac{155}{208}\right)\) \(e\left(\frac{485}{624}\right)\) \(e\left(\frac{7}{156}\right)\) \(e\left(\frac{177}{208}\right)\) \(e\left(\frac{59}{78}\right)\)
\(\chi_{4029}(31,\cdot)\) 4029.da 624 No \(-1\) \(1\) \(e\left(\frac{233}{312}\right)\) \(e\left(\frac{77}{156}\right)\) \(e\left(\frac{203}{624}\right)\) \(e\left(\frac{149}{624}\right)\) \(e\left(\frac{25}{104}\right)\) \(e\left(\frac{15}{208}\right)\) \(e\left(\frac{473}{624}\right)\) \(e\left(\frac{103}{156}\right)\) \(e\left(\frac{205}{208}\right)\) \(e\left(\frac{77}{78}\right)\)
\(\chi_{4029}(32,\cdot)\) 4029.cu 312 Yes \(-1\) \(1\) \(e\left(\frac{121}{156}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{85}{312}\right)\) \(e\left(\frac{223}{312}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{5}{104}\right)\) \(e\left(\frac{175}{312}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{51}{104}\right)\) \(e\left(\frac{4}{39}\right)\)
\(\chi_{4029}(35,\cdot)\) 4029.cb 78 No \(1\) \(1\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{23}{39}\right)\)
\(\chi_{4029}(37,\cdot)\) 4029.cy 624 No \(1\) \(1\) \(e\left(\frac{265}{312}\right)\) \(e\left(\frac{109}{156}\right)\) \(e\left(\frac{259}{624}\right)\) \(e\left(\frac{373}{624}\right)\) \(e\left(\frac{57}{104}\right)\) \(e\left(\frac{55}{208}\right)\) \(e\left(\frac{1}{624}\right)\) \(e\left(\frac{83}{156}\right)\) \(e\left(\frac{93}{208}\right)\) \(e\left(\frac{31}{78}\right)\)
\(\chi_{4029}(38,\cdot)\) 4029.by 52 Yes \(-1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{4029}(40,\cdot)\) 4029.da 624 No \(-1\) \(1\) \(e\left(\frac{287}{312}\right)\) \(e\left(\frac{131}{156}\right)\) \(e\left(\frac{317}{624}\right)\) \(e\left(\frac{371}{624}\right)\) \(e\left(\frac{79}{104}\right)\) \(e\left(\frac{89}{208}\right)\) \(e\left(\frac{47}{624}\right)\) \(e\left(\frac{1}{156}\right)\) \(e\left(\frac{107}{208}\right)\) \(e\left(\frac{53}{78}\right)\)
\(\chi_{4029}(41,\cdot)\) 4029.cq 208 Yes \(-1\) \(1\) \(e\left(\frac{101}{104}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{115}{208}\right)\) \(e\left(\frac{109}{208}\right)\) \(e\left(\frac{95}{104}\right)\) \(e\left(\frac{109}{208}\right)\) \(e\left(\frac{145}{208}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{103}{208}\right)\) \(e\left(\frac{23}{26}\right)\)
\(\chi_{4029}(43,\cdot)\) 4029.cv 312 No \(-1\) \(1\) \(e\left(\frac{41}{156}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{179}{312}\right)\) \(e\left(\frac{209}{312}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{87}{104}\right)\) \(e\left(\frac{185}{312}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{97}{104}\right)\) \(e\left(\frac{2}{39}\right)\)
\(\chi_{4029}(44,\cdot)\) 4029.cz 624 Yes \(1\) \(1\) \(e\left(\frac{7}{312}\right)\) \(e\left(\frac{7}{156}\right)\) \(e\left(\frac{529}{624}\right)\) \(e\left(\frac{439}{624}\right)\) \(e\left(\frac{7}{104}\right)\) \(e\left(\frac{181}{208}\right)\) \(e\left(\frac{43}{624}\right)\) \(e\left(\frac{137}{156}\right)\) \(e\left(\frac{151}{208}\right)\) \(e\left(\frac{7}{78}\right)\)
\(\chi_{4029}(46,\cdot)\) 4029.cr 208 No \(-1\) \(1\) \(e\left(\frac{95}{104}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{189}{208}\right)\) \(e\left(\frac{67}{208}\right)\) \(e\left(\frac{77}{104}\right)\) \(e\left(\frac{171}{208}\right)\) \(e\left(\frac{175}{208}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{49}{208}\right)\) \(e\left(\frac{17}{26}\right)\)
\(\chi_{4029}(47,\cdot)\) 4029.cp 156 Yes \(1\) \(1\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{101}{156}\right)\) \(e\left(\frac{131}{156}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{107}{156}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{4}{39}\right)\)
\(\chi_{4029}(49,\cdot)\) 4029.cx 312 No \(1\) \(1\) \(e\left(\frac{107}{156}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{41}{312}\right)\) \(e\left(\frac{47}{312}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{85}{104}\right)\) \(e\left(\frac{11}{312}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{87}{104}\right)\) \(e\left(\frac{29}{39}\right)\)
\(\chi_{4029}(50,\cdot)\) 4029.cd 78 Yes \(-1\) \(1\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{10}{39}\right)\)