LMFDB - Group of Dirichlet characters of modulus 8024

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8024)

pari: g = idealstar(,8024,2)

Character group

sage: G.order() pari: g.no
Order	=	3712
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{464}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8024}(2007,\cdot)$, $\chi_{8024}(4013,\cdot)$, $\chi_{8024}(3777,\cdot)$, $\chi_{8024}(3129,\cdot)$

First 32 of 3712 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$23$
$\chi_{8024}(1,\cdot)$	8024.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8024}(3,\cdot)$	8024.cz	464	yes	$1$	$1$	$e\left(\frac{77}{464}\right)$	$e\left(\frac{457}{464}\right)$	$e\left(\frac{327}{464}\right)$	$e\left(\frac{77}{232}\right)$	$e\left(\frac{459}{464}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{35}{232}\right)$	$e\left(\frac{147}{232}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{171}{464}\right)$
$\chi_{8024}(5,\cdot)$	8024.db	464	yes	$-1$	$1$	$e\left(\frac{457}{464}\right)$	$e\left(\frac{317}{464}\right)$	$e\left(\frac{139}{464}\right)$	$e\left(\frac{225}{232}\right)$	$e\left(\frac{127}{464}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{155}{232}\right)$	$e\left(\frac{187}{232}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{111}{464}\right)$
$\chi_{8024}(7,\cdot)$	8024.da	464	no	$1$	$1$	$e\left(\frac{327}{464}\right)$	$e\left(\frac{139}{464}\right)$	$e\left(\frac{301}{464}\right)$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{33}{464}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{1}{232}\right)$	$e\left(\frac{213}{232}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{217}{464}\right)$
$\chi_{8024}(9,\cdot)$	8024.cs	232	no	$1$	$1$	$e\left(\frac{77}{232}\right)$	$e\left(\frac{225}{232}\right)$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{227}{232}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{171}{232}\right)$
$\chi_{8024}(11,\cdot)$	8024.cu	464	yes	$-1$	$1$	$e\left(\frac{459}{464}\right)$	$e\left(\frac{127}{464}\right)$	$e\left(\frac{33}{464}\right)$	$e\left(\frac{227}{232}\right)$	$e\left(\frac{389}{464}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{61}{232}\right)$	$e\left(\frac{117}{232}\right)$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{245}{464}\right)$
$\chi_{8024}(13,\cdot)$	8024.cg	116	yes	$-1$	$1$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{45}{116}\right)$
$\chi_{8024}(15,\cdot)$	8024.ct	232	no	$-1$	$1$	$e\left(\frac{35}{232}\right)$	$e\left(\frac{155}{232}\right)$	$e\left(\frac{1}{232}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{61}{232}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{141}{232}\right)$
$\chi_{8024}(19,\cdot)$	8024.cm	232	yes	$-1$	$1$	$e\left(\frac{147}{232}\right)$	$e\left(\frac{187}{232}\right)$	$e\left(\frac{213}{232}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{117}{232}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{105}{232}\right)$
$\chi_{8024}(21,\cdot)$	8024.ck	116	yes	$1$	$1$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{97}{116}\right)$
$\chi_{8024}(23,\cdot)$	8024.cx	464	no	$-1$	$1$	$e\left(\frac{171}{464}\right)$	$e\left(\frac{111}{464}\right)$	$e\left(\frac{217}{464}\right)$	$e\left(\frac{171}{232}\right)$	$e\left(\frac{245}{464}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{141}{232}\right)$	$e\left(\frac{105}{232}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{205}{464}\right)$
$\chi_{8024}(25,\cdot)$	8024.cs	232	no	$1$	$1$	$e\left(\frac{225}{232}\right)$	$e\left(\frac{85}{232}\right)$	$e\left(\frac{139}{232}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{127}{232}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{111}{232}\right)$
$\chi_{8024}(27,\cdot)$	8024.cz	464	yes	$1$	$1$	$e\left(\frac{231}{464}\right)$	$e\left(\frac{443}{464}\right)$	$e\left(\frac{53}{464}\right)$	$e\left(\frac{231}{232}\right)$	$e\left(\frac{449}{464}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{105}{232}\right)$	$e\left(\frac{209}{232}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{49}{464}\right)$
$\chi_{8024}(29,\cdot)$	8024.db	464	yes	$-1$	$1$	$e\left(\frac{209}{464}\right)$	$e\left(\frac{213}{464}\right)$	$e\left(\frac{291}{464}\right)$	$e\left(\frac{209}{232}\right)$	$e\left(\frac{119}{464}\right)$	$e\left(\frac{55}{116}\right)$	$e\left(\frac{211}{232}\right)$	$e\left(\frac{51}{232}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{199}{464}\right)$
$\chi_{8024}(31,\cdot)$	8024.cx	464	no	$-1$	$1$	$e\left(\frac{141}{464}\right)$	$e\left(\frac{409}{464}\right)$	$e\left(\frac{415}{464}\right)$	$e\left(\frac{141}{232}\right)$	$e\left(\frac{259}{464}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{43}{232}\right)$	$e\left(\frac{111}{232}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{283}{464}\right)$
$\chi_{8024}(33,\cdot)$	8024.cc	58	no	$-1$	$1$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{26}{29}\right)$
$\chi_{8024}(35,\cdot)$	8024.bu	58	no	$-1$	$1$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{8024}(37,\cdot)$	8024.cw	464	yes	$1$	$1$	$e\left(\frac{453}{464}\right)$	$e\left(\frac{233}{464}\right)$	$e\left(\frac{351}{464}\right)$	$e\left(\frac{221}{232}\right)$	$e\left(\frac{299}{464}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{111}{232}\right)$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{75}{464}\right)$
$\chi_{8024}(39,\cdot)$	8024.cx	464	no	$-1$	$1$	$e\left(\frac{329}{464}\right)$	$e\left(\frac{181}{464}\right)$	$e\left(\frac{195}{464}\right)$	$e\left(\frac{97}{232}\right)$	$e\left(\frac{295}{464}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{23}{232}\right)$	$e\left(\frac{27}{232}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{351}{464}\right)$
$\chi_{8024}(41,\cdot)$	8024.cy	464	no	$-1$	$1$	$e\left(\frac{351}{464}\right)$	$e\left(\frac{411}{464}\right)$	$e\left(\frac{421}{464}\right)$	$e\left(\frac{119}{232}\right)$	$e\left(\frac{393}{464}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{149}{232}\right)$	$e\left(\frac{185}{232}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{433}{464}\right)$
$\chi_{8024}(43,\cdot)$	8024.cq	232	yes	$1$	$1$	$e\left(\frac{133}{232}\right)$	$e\left(\frac{125}{232}\right)$	$e\left(\frac{27}{232}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{23}{232}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{211}{232}\right)$
$\chi_{8024}(45,\cdot)$	8024.db	464	yes	$-1$	$1$	$e\left(\frac{147}{464}\right)$	$e\left(\frac{303}{464}\right)$	$e\left(\frac{329}{464}\right)$	$e\left(\frac{147}{232}\right)$	$e\left(\frac{117}{464}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{225}{232}\right)$	$e\left(\frac{17}{232}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{453}{464}\right)$
$\chi_{8024}(47,\cdot)$	8024.ci	116	no	$1$	$1$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{23}{116}\right)$
$\chi_{8024}(49,\cdot)$	8024.cs	232	no	$1$	$1$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{139}{232}\right)$	$e\left(\frac{69}{232}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{33}{232}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{217}{232}\right)$
$\chi_{8024}(53,\cdot)$	8024.cn	232	yes	$1$	$1$	$e\left(\frac{79}{232}\right)$	$e\left(\frac{35}{232}\right)$	$e\left(\frac{105}{232}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{25}{232}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{189}{232}\right)$
$\chi_{8024}(55,\cdot)$	8024.ci	116	no	$1$	$1$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{89}{116}\right)$
$\chi_{8024}(57,\cdot)$	8024.cy	464	no	$-1$	$1$	$e\left(\frac{371}{464}\right)$	$e\left(\frac{367}{464}\right)$	$e\left(\frac{289}{464}\right)$	$e\left(\frac{139}{232}\right)$	$e\left(\frac{229}{464}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{137}{232}\right)$	$e\left(\frac{181}{232}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{381}{464}\right)$
$\chi_{8024}(61,\cdot)$	8024.cw	464	yes	$1$	$1$	$e\left(\frac{255}{464}\right)$	$e\left(\frac{251}{464}\right)$	$e\left(\frac{173}{464}\right)$	$e\left(\frac{23}{232}\right)$	$e\left(\frac{113}{464}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{21}{232}\right)$	$e\left(\frac{181}{232}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{33}{464}\right)$
$\chi_{8024}(63,\cdot)$	8024.da	464	no	$1$	$1$	$e\left(\frac{17}{464}\right)$	$e\left(\frac{125}{464}\right)$	$e\left(\frac{27}{464}\right)$	$e\left(\frac{17}{232}\right)$	$e\left(\frac{23}{464}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{71}{232}\right)$	$e\left(\frac{43}{232}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{95}{464}\right)$
$\chi_{8024}(65,\cdot)$	8024.cv	464	no	$1$	$1$	$e\left(\frac{245}{464}\right)$	$e\left(\frac{41}{464}\right)$	$e\left(\frac{7}{464}\right)$	$e\left(\frac{13}{232}\right)$	$e\left(\frac{427}{464}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{143}{232}\right)$	$e\left(\frac{67}{232}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{291}{464}\right)$
$\chi_{8024}(67,\cdot)$	8024.bw	58	yes	$1$	$1$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{8024}(69,\cdot)$	8024.ca	58	no	$-1$	$1$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{47}{58}\right)$

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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	$8024$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{464}\)
Order	$3712$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\(\chi_{8024}(1,\cdot)\)	8024.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8024}(3,\cdot)\)	8024.cz	464	yes	\(1\)	\(1\)	\(e\left(\frac{77}{464}\right)\)	\(e\left(\frac{457}{464}\right)\)	\(e\left(\frac{327}{464}\right)\)	\(e\left(\frac{77}{232}\right)\)	\(e\left(\frac{459}{464}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{35}{232}\right)\)	\(e\left(\frac{147}{232}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{171}{464}\right)\)
\(\chi_{8024}(5,\cdot)\)	8024.db	464	yes	\(-1\)	\(1\)	\(e\left(\frac{457}{464}\right)\)	\(e\left(\frac{317}{464}\right)\)	\(e\left(\frac{139}{464}\right)\)	\(e\left(\frac{225}{232}\right)\)	\(e\left(\frac{127}{464}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{155}{232}\right)\)	\(e\left(\frac{187}{232}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{111}{464}\right)\)
\(\chi_{8024}(7,\cdot)\)	8024.da	464	no	\(1\)	\(1\)	\(e\left(\frac{327}{464}\right)\)	\(e\left(\frac{139}{464}\right)\)	\(e\left(\frac{301}{464}\right)\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{33}{464}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{1}{232}\right)\)	\(e\left(\frac{213}{232}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{217}{464}\right)\)
\(\chi_{8024}(9,\cdot)\)	8024.cs	232	no	\(1\)	\(1\)	\(e\left(\frac{77}{232}\right)\)	\(e\left(\frac{225}{232}\right)\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{227}{232}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{171}{232}\right)\)
\(\chi_{8024}(11,\cdot)\)	8024.cu	464	yes	\(-1\)	\(1\)	\(e\left(\frac{459}{464}\right)\)	\(e\left(\frac{127}{464}\right)\)	\(e\left(\frac{33}{464}\right)\)	\(e\left(\frac{227}{232}\right)\)	\(e\left(\frac{389}{464}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{61}{232}\right)\)	\(e\left(\frac{117}{232}\right)\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{245}{464}\right)\)
\(\chi_{8024}(13,\cdot)\)	8024.cg	116	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{45}{116}\right)\)
\(\chi_{8024}(15,\cdot)\)	8024.ct	232	no	\(-1\)	\(1\)	\(e\left(\frac{35}{232}\right)\)	\(e\left(\frac{155}{232}\right)\)	\(e\left(\frac{1}{232}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{61}{232}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{141}{232}\right)\)
\(\chi_{8024}(19,\cdot)\)	8024.cm	232	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{232}\right)\)	\(e\left(\frac{187}{232}\right)\)	\(e\left(\frac{213}{232}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{117}{232}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{105}{232}\right)\)
\(\chi_{8024}(21,\cdot)\)	8024.ck	116	yes	\(1\)	\(1\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{97}{116}\right)\)
\(\chi_{8024}(23,\cdot)\)	8024.cx	464	no	\(-1\)	\(1\)	\(e\left(\frac{171}{464}\right)\)	\(e\left(\frac{111}{464}\right)\)	\(e\left(\frac{217}{464}\right)\)	\(e\left(\frac{171}{232}\right)\)	\(e\left(\frac{245}{464}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{141}{232}\right)\)	\(e\left(\frac{105}{232}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{205}{464}\right)\)
\(\chi_{8024}(25,\cdot)\)	8024.cs	232	no	\(1\)	\(1\)	\(e\left(\frac{225}{232}\right)\)	\(e\left(\frac{85}{232}\right)\)	\(e\left(\frac{139}{232}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{127}{232}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{111}{232}\right)\)
\(\chi_{8024}(27,\cdot)\)	8024.cz	464	yes	\(1\)	\(1\)	\(e\left(\frac{231}{464}\right)\)	\(e\left(\frac{443}{464}\right)\)	\(e\left(\frac{53}{464}\right)\)	\(e\left(\frac{231}{232}\right)\)	\(e\left(\frac{449}{464}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{105}{232}\right)\)	\(e\left(\frac{209}{232}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{49}{464}\right)\)
\(\chi_{8024}(29,\cdot)\)	8024.db	464	yes	\(-1\)	\(1\)	\(e\left(\frac{209}{464}\right)\)	\(e\left(\frac{213}{464}\right)\)	\(e\left(\frac{291}{464}\right)\)	\(e\left(\frac{209}{232}\right)\)	\(e\left(\frac{119}{464}\right)\)	\(e\left(\frac{55}{116}\right)\)	\(e\left(\frac{211}{232}\right)\)	\(e\left(\frac{51}{232}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{199}{464}\right)\)
\(\chi_{8024}(31,\cdot)\)	8024.cx	464	no	\(-1\)	\(1\)	\(e\left(\frac{141}{464}\right)\)	\(e\left(\frac{409}{464}\right)\)	\(e\left(\frac{415}{464}\right)\)	\(e\left(\frac{141}{232}\right)\)	\(e\left(\frac{259}{464}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{43}{232}\right)\)	\(e\left(\frac{111}{232}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{283}{464}\right)\)
\(\chi_{8024}(33,\cdot)\)	8024.cc	58	no	\(-1\)	\(1\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)
\(\chi_{8024}(35,\cdot)\)	8024.bu	58	no	\(-1\)	\(1\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{8024}(37,\cdot)\)	8024.cw	464	yes	\(1\)	\(1\)	\(e\left(\frac{453}{464}\right)\)	\(e\left(\frac{233}{464}\right)\)	\(e\left(\frac{351}{464}\right)\)	\(e\left(\frac{221}{232}\right)\)	\(e\left(\frac{299}{464}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{111}{232}\right)\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{75}{464}\right)\)
\(\chi_{8024}(39,\cdot)\)	8024.cx	464	no	\(-1\)	\(1\)	\(e\left(\frac{329}{464}\right)\)	\(e\left(\frac{181}{464}\right)\)	\(e\left(\frac{195}{464}\right)\)	\(e\left(\frac{97}{232}\right)\)	\(e\left(\frac{295}{464}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{23}{232}\right)\)	\(e\left(\frac{27}{232}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{351}{464}\right)\)
\(\chi_{8024}(41,\cdot)\)	8024.cy	464	no	\(-1\)	\(1\)	\(e\left(\frac{351}{464}\right)\)	\(e\left(\frac{411}{464}\right)\)	\(e\left(\frac{421}{464}\right)\)	\(e\left(\frac{119}{232}\right)\)	\(e\left(\frac{393}{464}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{149}{232}\right)\)	\(e\left(\frac{185}{232}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{433}{464}\right)\)
\(\chi_{8024}(43,\cdot)\)	8024.cq	232	yes	\(1\)	\(1\)	\(e\left(\frac{133}{232}\right)\)	\(e\left(\frac{125}{232}\right)\)	\(e\left(\frac{27}{232}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{23}{232}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{211}{232}\right)\)
\(\chi_{8024}(45,\cdot)\)	8024.db	464	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{464}\right)\)	\(e\left(\frac{303}{464}\right)\)	\(e\left(\frac{329}{464}\right)\)	\(e\left(\frac{147}{232}\right)\)	\(e\left(\frac{117}{464}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{225}{232}\right)\)	\(e\left(\frac{17}{232}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{453}{464}\right)\)
\(\chi_{8024}(47,\cdot)\)	8024.ci	116	no	\(1\)	\(1\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{23}{116}\right)\)
\(\chi_{8024}(49,\cdot)\)	8024.cs	232	no	\(1\)	\(1\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{139}{232}\right)\)	\(e\left(\frac{69}{232}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{33}{232}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{217}{232}\right)\)
\(\chi_{8024}(53,\cdot)\)	8024.cn	232	yes	\(1\)	\(1\)	\(e\left(\frac{79}{232}\right)\)	\(e\left(\frac{35}{232}\right)\)	\(e\left(\frac{105}{232}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{25}{232}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{189}{232}\right)\)
\(\chi_{8024}(55,\cdot)\)	8024.ci	116	no	\(1\)	\(1\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{89}{116}\right)\)
\(\chi_{8024}(57,\cdot)\)	8024.cy	464	no	\(-1\)	\(1\)	\(e\left(\frac{371}{464}\right)\)	\(e\left(\frac{367}{464}\right)\)	\(e\left(\frac{289}{464}\right)\)	\(e\left(\frac{139}{232}\right)\)	\(e\left(\frac{229}{464}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{137}{232}\right)\)	\(e\left(\frac{181}{232}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{381}{464}\right)\)
\(\chi_{8024}(61,\cdot)\)	8024.cw	464	yes	\(1\)	\(1\)	\(e\left(\frac{255}{464}\right)\)	\(e\left(\frac{251}{464}\right)\)	\(e\left(\frac{173}{464}\right)\)	\(e\left(\frac{23}{232}\right)\)	\(e\left(\frac{113}{464}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{21}{232}\right)\)	\(e\left(\frac{181}{232}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{33}{464}\right)\)
\(\chi_{8024}(63,\cdot)\)	8024.da	464	no	\(1\)	\(1\)	\(e\left(\frac{17}{464}\right)\)	\(e\left(\frac{125}{464}\right)\)	\(e\left(\frac{27}{464}\right)\)	\(e\left(\frac{17}{232}\right)\)	\(e\left(\frac{23}{464}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{71}{232}\right)\)	\(e\left(\frac{43}{232}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{95}{464}\right)\)
\(\chi_{8024}(65,\cdot)\)	8024.cv	464	no	\(1\)	\(1\)	\(e\left(\frac{245}{464}\right)\)	\(e\left(\frac{41}{464}\right)\)	\(e\left(\frac{7}{464}\right)\)	\(e\left(\frac{13}{232}\right)\)	\(e\left(\frac{427}{464}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{143}{232}\right)\)	\(e\left(\frac{67}{232}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{291}{464}\right)\)
\(\chi_{8024}(67,\cdot)\)	8024.bw	58	yes	\(1\)	\(1\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{8024}(69,\cdot)\)	8024.ca	58	no	\(-1\)	\(1\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)

Introduction

L-functions

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