LMFDB - Group of Dirichlet characters of modulus 2527

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2527)

pari: g = idealstar(,2527,2)

Character group

sage: G.order() pari: g.no
Order	=	2052
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{342}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2527}(1445,\cdot)$, $\chi_{2527}(1807,\cdot)$

First 32 of 2052 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{2527}(1,\cdot)$	2527.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2527}(2,\cdot)$	2527.ce	342	yes	$-1$	$1$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{3}{38}\right)$
$\chi_{2527}(3,\cdot)$	2527.ch	342	yes	$1$	$1$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{8}{57}\right)$
$\chi_{2527}(4,\cdot)$	2527.ca	171	yes	$1$	$1$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{2527}(5,\cdot)$	2527.cj	342	yes	$-1$	$1$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{31}{38}\right)$
$\chi_{2527}(6,\cdot)$	2527.ck	342	yes	$-1$	$1$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{2527}(8,\cdot)$	2527.br	114	no	$-1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{9}{38}\right)$
$\chi_{2527}(9,\cdot)$	2527.cc	171	yes	$1$	$1$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{16}{57}\right)$
$\chi_{2527}(10,\cdot)$	2527.cd	342	yes	$1$	$1$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{17}{19}\right)$
$\chi_{2527}(11,\cdot)$	2527.bk	57	yes	$1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{22}{57}\right)$
$\chi_{2527}(12,\cdot)$	2527.bz	114	yes	$1$	$1$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{17}{57}\right)$
$\chi_{2527}(13,\cdot)$	2527.ci	342	yes	$1$	$1$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{8}{57}\right)$
$\chi_{2527}(15,\cdot)$	2527.cg	342	no	$-1$	$1$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{109}{114}\right)$
$\chi_{2527}(16,\cdot)$	2527.ca	171	yes	$1$	$1$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{2527}(17,\cdot)$	2527.cl	342	yes	$-1$	$1$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{2527}(18,\cdot)$	2527.bq	114	yes	$-1$	$1$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{41}{114}\right)$
$\chi_{2527}(20,\cdot)$	2527.bh	38	yes	$-1$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{37}{38}\right)$
$\chi_{2527}(22,\cdot)$	2527.cg	342	no	$-1$	$1$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{295}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{53}{114}\right)$
$\chi_{2527}(23,\cdot)$	2527.cc	171	yes	$1$	$1$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{49}{57}\right)$
$\chi_{2527}(24,\cdot)$	2527.cl	342	yes	$-1$	$1$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{43}{114}\right)$
$\chi_{2527}(25,\cdot)$	2527.ca	171	yes	$1$	$1$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{2527}(26,\cdot)$	2527.bo	114	yes	$-1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{2527}(27,\cdot)$	2527.bs	114	yes	$1$	$1$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{8}{19}\right)$
$\chi_{2527}(29,\cdot)$	2527.cg	342	no	$-1$	$1$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{2527}(30,\cdot)$	2527.bl	57	yes	$1$	$1$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{2}{57}\right)$
$\chi_{2527}(31,\cdot)$	2527.bp	114	yes	$1$	$1$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{43}{57}\right)$
$\chi_{2527}(32,\cdot)$	2527.ce	342	yes	$-1$	$1$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{15}{38}\right)$
$\chi_{2527}(33,\cdot)$	2527.cd	342	yes	$1$	$1$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{2527}(34,\cdot)$	2527.ci	342	yes	$1$	$1$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{5}{57}\right)$
$\chi_{2527}(36,\cdot)$	2527.cb	171	no	$1$	$1$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{25}{57}\right)$
$\chi_{2527}(37,\cdot)$	2527.bq	114	yes	$-1$	$1$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{2527}(39,\cdot)$	2527.bm	57	yes	$1$	$1$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{16}{57}\right)$

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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	$2527$
Structure	\(C_{6}\times C_{342}\)
Order	$2052$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{2527}(1,\cdot)\)	2527.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2527}(2,\cdot)\)	2527.ce	342	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)
\(\chi_{2527}(3,\cdot)\)	2527.ch	342	yes	\(1\)	\(1\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)
\(\chi_{2527}(4,\cdot)\)	2527.ca	171	yes	\(1\)	\(1\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{2527}(5,\cdot)\)	2527.cj	342	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)
\(\chi_{2527}(6,\cdot)\)	2527.ck	342	yes	\(-1\)	\(1\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{2527}(8,\cdot)\)	2527.br	114	no	\(-1\)	\(1\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)
\(\chi_{2527}(9,\cdot)\)	2527.cc	171	yes	\(1\)	\(1\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)
\(\chi_{2527}(10,\cdot)\)	2527.cd	342	yes	\(1\)	\(1\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)
\(\chi_{2527}(11,\cdot)\)	2527.bk	57	yes	\(1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)
\(\chi_{2527}(12,\cdot)\)	2527.bz	114	yes	\(1\)	\(1\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)
\(\chi_{2527}(13,\cdot)\)	2527.ci	342	yes	\(1\)	\(1\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)
\(\chi_{2527}(15,\cdot)\)	2527.cg	342	no	\(-1\)	\(1\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{109}{114}\right)\)
\(\chi_{2527}(16,\cdot)\)	2527.ca	171	yes	\(1\)	\(1\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{2527}(17,\cdot)\)	2527.cl	342	yes	\(-1\)	\(1\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{2527}(18,\cdot)\)	2527.bq	114	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{41}{114}\right)\)
\(\chi_{2527}(20,\cdot)\)	2527.bh	38	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)
\(\chi_{2527}(22,\cdot)\)	2527.cg	342	no	\(-1\)	\(1\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{295}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{53}{114}\right)\)
\(\chi_{2527}(23,\cdot)\)	2527.cc	171	yes	\(1\)	\(1\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)
\(\chi_{2527}(24,\cdot)\)	2527.cl	342	yes	\(-1\)	\(1\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)
\(\chi_{2527}(25,\cdot)\)	2527.ca	171	yes	\(1\)	\(1\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{2527}(26,\cdot)\)	2527.bo	114	yes	\(-1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{2527}(27,\cdot)\)	2527.bs	114	yes	\(1\)	\(1\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)
\(\chi_{2527}(29,\cdot)\)	2527.cg	342	no	\(-1\)	\(1\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{2527}(30,\cdot)\)	2527.bl	57	yes	\(1\)	\(1\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)
\(\chi_{2527}(31,\cdot)\)	2527.bp	114	yes	\(1\)	\(1\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)
\(\chi_{2527}(32,\cdot)\)	2527.ce	342	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)
\(\chi_{2527}(33,\cdot)\)	2527.cd	342	yes	\(1\)	\(1\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{2527}(34,\cdot)\)	2527.ci	342	yes	\(1\)	\(1\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)
\(\chi_{2527}(36,\cdot)\)	2527.cb	171	no	\(1\)	\(1\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)
\(\chi_{2527}(37,\cdot)\)	2527.bq	114	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{2527}(39,\cdot)\)	2527.bm	57	yes	\(1\)	\(1\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)

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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.