LMFDB - Group of Dirichlet characters of modulus 2888

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2888)

pari: g = idealstar(,2888,2)

Character group

sage: G.order() pari: g.no
Order	=	1368
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{342}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2888}(2167,\cdot)$, $\chi_{2888}(1445,\cdot)$, $\chi_{2888}(2529,\cdot)$

First 32 of 1368 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{2888}(1,\cdot)$	2888.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2888}(3,\cdot)$	2888.br	342	yes	$1$	$1$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{287}{342}\right)$
$\chi_{2888}(5,\cdot)$	2888.bt	342	yes	$1$	$1$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{7}{171}\right)$
$\chi_{2888}(7,\cdot)$	2888.bk	114	no	$-1$	$1$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{61}{114}\right)$
$\chi_{2888}(9,\cdot)$	2888.bo	171	no	$1$	$1$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{116}{171}\right)$
$\chi_{2888}(11,\cdot)$	2888.bm	114	yes	$-1$	$1$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{5}{114}\right)$
$\chi_{2888}(13,\cdot)$	2888.bu	342	yes	$-1$	$1$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{77}{171}\right)$
$\chi_{2888}(15,\cdot)$	2888.bq	342	no	$1$	$1$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{301}{342}\right)$
$\chi_{2888}(17,\cdot)$	2888.bo	171	no	$1$	$1$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{82}{171}\right)$
$\chi_{2888}(21,\cdot)$	2888.bu	342	yes	$-1$	$1$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{64}{171}\right)$
$\chi_{2888}(23,\cdot)$	2888.bp	342	no	$-1$	$1$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{283}{342}\right)$
$\chi_{2888}(25,\cdot)$	2888.bo	171	no	$1$	$1$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{14}{171}\right)$
$\chi_{2888}(27,\cdot)$	2888.bi	114	yes	$1$	$1$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{59}{114}\right)$
$\chi_{2888}(29,\cdot)$	2888.bu	342	yes	$-1$	$1$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{44}{171}\right)$
$\chi_{2888}(31,\cdot)$	2888.bn	114	no	$1$	$1$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{97}{114}\right)$
$\chi_{2888}(33,\cdot)$	2888.bv	342	no	$-1$	$1$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{151}{171}\right)$
$\chi_{2888}(35,\cdot)$	2888.bs	342	yes	$-1$	$1$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{217}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{197}{342}\right)$
$\chi_{2888}(37,\cdot)$	2888.ba	38	yes	$-1$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{4}{19}\right)$
$\chi_{2888}(39,\cdot)$	2888.bd	38	no	$-1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{11}{38}\right)$
$\chi_{2888}(41,\cdot)$	2888.bv	342	no	$-1$	$1$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{103}{171}\right)$
$\chi_{2888}(43,\cdot)$	2888.bs	342	yes	$-1$	$1$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{239}{342}\right)$
$\chi_{2888}(45,\cdot)$	2888.bh	114	yes	$1$	$1$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{41}{57}\right)$
$\chi_{2888}(47,\cdot)$	2888.bp	342	no	$-1$	$1$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{205}{342}\right)$
$\chi_{2888}(49,\cdot)$	2888.bg	57	no	$1$	$1$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{4}{57}\right)$
$\chi_{2888}(51,\cdot)$	2888.br	342	yes	$1$	$1$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{109}{342}\right)$
$\chi_{2888}(53,\cdot)$	2888.bu	342	yes	$-1$	$1$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{74}{171}\right)$
$\chi_{2888}(55,\cdot)$	2888.bp	342	no	$-1$	$1$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{29}{342}\right)$
$\chi_{2888}(59,\cdot)$	2888.br	342	yes	$1$	$1$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{263}{342}\right)$
$\chi_{2888}(61,\cdot)$	2888.bt	342	yes	$1$	$1$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{47}{171}\right)$
$\chi_{2888}(63,\cdot)$	2888.bp	342	no	$-1$	$1$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{73}{342}\right)$
$\chi_{2888}(65,\cdot)$	2888.bj	114	no	$-1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{2888}(67,\cdot)$	2888.br	342	yes	$1$	$1$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{115}{342}\right)$

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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	$2888$
Structure	\(C_{2}\times C_{2}\times C_{342}\)
Order	$1368$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{2888}(1,\cdot)\)	2888.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2888}(3,\cdot)\)	2888.br	342	yes	\(1\)	\(1\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{287}{342}\right)\)
\(\chi_{2888}(5,\cdot)\)	2888.bt	342	yes	\(1\)	\(1\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)
\(\chi_{2888}(7,\cdot)\)	2888.bk	114	no	\(-1\)	\(1\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{61}{114}\right)\)
\(\chi_{2888}(9,\cdot)\)	2888.bo	171	no	\(1\)	\(1\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{116}{171}\right)\)
\(\chi_{2888}(11,\cdot)\)	2888.bm	114	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{5}{114}\right)\)
\(\chi_{2888}(13,\cdot)\)	2888.bu	342	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)
\(\chi_{2888}(15,\cdot)\)	2888.bq	342	no	\(1\)	\(1\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{301}{342}\right)\)
\(\chi_{2888}(17,\cdot)\)	2888.bo	171	no	\(1\)	\(1\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)
\(\chi_{2888}(21,\cdot)\)	2888.bu	342	yes	\(-1\)	\(1\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{64}{171}\right)\)
\(\chi_{2888}(23,\cdot)\)	2888.bp	342	no	\(-1\)	\(1\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{283}{342}\right)\)
\(\chi_{2888}(25,\cdot)\)	2888.bo	171	no	\(1\)	\(1\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{14}{171}\right)\)
\(\chi_{2888}(27,\cdot)\)	2888.bi	114	yes	\(1\)	\(1\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{59}{114}\right)\)
\(\chi_{2888}(29,\cdot)\)	2888.bu	342	yes	\(-1\)	\(1\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{44}{171}\right)\)
\(\chi_{2888}(31,\cdot)\)	2888.bn	114	no	\(1\)	\(1\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)
\(\chi_{2888}(33,\cdot)\)	2888.bv	342	no	\(-1\)	\(1\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{151}{171}\right)\)
\(\chi_{2888}(35,\cdot)\)	2888.bs	342	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{217}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{197}{342}\right)\)
\(\chi_{2888}(37,\cdot)\)	2888.ba	38	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)
\(\chi_{2888}(39,\cdot)\)	2888.bd	38	no	\(-1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)
\(\chi_{2888}(41,\cdot)\)	2888.bv	342	no	\(-1\)	\(1\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)
\(\chi_{2888}(43,\cdot)\)	2888.bs	342	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{239}{342}\right)\)
\(\chi_{2888}(45,\cdot)\)	2888.bh	114	yes	\(1\)	\(1\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{41}{57}\right)\)
\(\chi_{2888}(47,\cdot)\)	2888.bp	342	no	\(-1\)	\(1\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{205}{342}\right)\)
\(\chi_{2888}(49,\cdot)\)	2888.bg	57	no	\(1\)	\(1\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)
\(\chi_{2888}(51,\cdot)\)	2888.br	342	yes	\(1\)	\(1\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{109}{342}\right)\)
\(\chi_{2888}(53,\cdot)\)	2888.bu	342	yes	\(-1\)	\(1\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)
\(\chi_{2888}(55,\cdot)\)	2888.bp	342	no	\(-1\)	\(1\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{29}{342}\right)\)
\(\chi_{2888}(59,\cdot)\)	2888.br	342	yes	\(1\)	\(1\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{263}{342}\right)\)
\(\chi_{2888}(61,\cdot)\)	2888.bt	342	yes	\(1\)	\(1\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)
\(\chi_{2888}(63,\cdot)\)	2888.bp	342	no	\(-1\)	\(1\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)
\(\chi_{2888}(65,\cdot)\)	2888.bj	114	no	\(-1\)	\(1\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)
\(\chi_{2888}(67,\cdot)\)	2888.br	342	yes	\(1\)	\(1\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{115}{342}\right)\)

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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.