LMFDB - Group of Dirichlet characters of modulus 4029

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4029)

pari: g = idealstar(,4029,2)

Character group

sage: G.order() pari: g.no
Order	=	2496
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{624}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4029}(2687,\cdot)$, $\chi_{4029}(3556,\cdot)$, $\chi_{4029}(3163,\cdot)$

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.

Character	Orbit	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	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{10}{39}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

Character	Orbit	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	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)

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Character group

First 32 of 2496 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.