LMFDB - Group of Dirichlet characters of modulus 3971

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3971)

pari: g = idealstar(,3971,2)

Character group

sage: G.order() pari: g.no
Order	=	3420
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1710}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3971}(1806,\cdot)$, $\chi_{3971}(2168,\cdot)$

First 32 of 3420 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{3971}(1,\cdot)$	3971.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3971}(2,\cdot)$	3971.bu	1710	yes	$1$	$1$	$e\left(\frac{88}{855}\right)$	$e\left(\frac{353}{1710}\right)$	$e\left(\frac{176}{855}\right)$	$e\left(\frac{67}{855}\right)$	$e\left(\frac{529}{1710}\right)$	$e\left(\frac{79}{570}\right)$	$e\left(\frac{88}{285}\right)$	$e\left(\frac{353}{855}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{47}{114}\right)$
$\chi_{3971}(3,\cdot)$	3971.bt	1710	yes	$-1$	$1$	$e\left(\frac{353}{1710}\right)$	$e\left(\frac{1529}{1710}\right)$	$e\left(\frac{353}{855}\right)$	$e\left(\frac{421}{855}\right)$	$e\left(\frac{86}{855}\right)$	$e\left(\frac{161}{285}\right)$	$e\left(\frac{353}{570}\right)$	$e\left(\frac{674}{855}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{35}{114}\right)$
$\chi_{3971}(4,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{176}{855}\right)$	$e\left(\frac{353}{855}\right)$	$e\left(\frac{352}{855}\right)$	$e\left(\frac{134}{855}\right)$	$e\left(\frac{529}{855}\right)$	$e\left(\frac{79}{285}\right)$	$e\left(\frac{176}{285}\right)$	$e\left(\frac{706}{855}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{47}{57}\right)$
$\chi_{3971}(5,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{67}{855}\right)$	$e\left(\frac{421}{855}\right)$	$e\left(\frac{134}{855}\right)$	$e\left(\frac{838}{855}\right)$	$e\left(\frac{488}{855}\right)$	$e\left(\frac{158}{285}\right)$	$e\left(\frac{67}{285}\right)$	$e\left(\frac{842}{855}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{37}{57}\right)$
$\chi_{3971}(6,\cdot)$	3971.bv	1710	yes	$-1$	$1$	$e\left(\frac{529}{1710}\right)$	$e\left(\frac{86}{855}\right)$	$e\left(\frac{529}{855}\right)$	$e\left(\frac{488}{855}\right)$	$e\left(\frac{701}{1710}\right)$	$e\left(\frac{401}{570}\right)$	$e\left(\frac{529}{570}\right)$	$e\left(\frac{172}{855}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{41}{57}\right)$
$\chi_{3971}(7,\cdot)$	3971.bq	570	yes	$-1$	$1$	$e\left(\frac{79}{570}\right)$	$e\left(\frac{161}{285}\right)$	$e\left(\frac{79}{285}\right)$	$e\left(\frac{158}{285}\right)$	$e\left(\frac{401}{570}\right)$	$e\left(\frac{131}{190}\right)$	$e\left(\frac{79}{190}\right)$	$e\left(\frac{37}{285}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{3971}(8,\cdot)$	3971.bp	570	yes	$1$	$1$	$e\left(\frac{88}{285}\right)$	$e\left(\frac{353}{570}\right)$	$e\left(\frac{176}{285}\right)$	$e\left(\frac{67}{285}\right)$	$e\left(\frac{529}{570}\right)$	$e\left(\frac{79}{190}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{9}{38}\right)$
$\chi_{3971}(9,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{353}{855}\right)$	$e\left(\frac{674}{855}\right)$	$e\left(\frac{706}{855}\right)$	$e\left(\frac{842}{855}\right)$	$e\left(\frac{172}{855}\right)$	$e\left(\frac{37}{285}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{493}{855}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{35}{57}\right)$
$\chi_{3971}(10,\cdot)$	3971.bn	342	yes	$1$	$1$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{3971}(12,\cdot)$	3971.be	114	no	$-1$	$1$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{5}{38}\right)$
$\chi_{3971}(13,\cdot)$	3971.bu	1710	yes	$1$	$1$	$e\left(\frac{53}{855}\right)$	$e\left(\frac{883}{1710}\right)$	$e\left(\frac{106}{855}\right)$	$e\left(\frac{497}{855}\right)$	$e\left(\frac{989}{1710}\right)$	$e\left(\frac{569}{570}\right)$	$e\left(\frac{53}{285}\right)$	$e\left(\frac{28}{855}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{3971}(14,\cdot)$	3971.bt	1710	yes	$-1$	$1$	$e\left(\frac{413}{1710}\right)$	$e\left(\frac{1319}{1710}\right)$	$e\left(\frac{413}{855}\right)$	$e\left(\frac{541}{855}\right)$	$e\left(\frac{11}{855}\right)$	$e\left(\frac{236}{285}\right)$	$e\left(\frac{413}{570}\right)$	$e\left(\frac{464}{855}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{29}{114}\right)$
$\chi_{3971}(15,\cdot)$	3971.bt	1710	yes	$-1$	$1$	$e\left(\frac{487}{1710}\right)$	$e\left(\frac{661}{1710}\right)$	$e\left(\frac{487}{855}\right)$	$e\left(\frac{404}{855}\right)$	$e\left(\frac{574}{855}\right)$	$e\left(\frac{34}{285}\right)$	$e\left(\frac{487}{570}\right)$	$e\left(\frac{661}{855}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{109}{114}\right)$
$\chi_{3971}(16,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{352}{855}\right)$	$e\left(\frac{706}{855}\right)$	$e\left(\frac{704}{855}\right)$	$e\left(\frac{268}{855}\right)$	$e\left(\frac{203}{855}\right)$	$e\left(\frac{158}{285}\right)$	$e\left(\frac{67}{285}\right)$	$e\left(\frac{557}{855}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{37}{57}\right)$
$\chi_{3971}(17,\cdot)$	3971.bv	1710	yes	$-1$	$1$	$e\left(\frac{959}{1710}\right)$	$e\left(\frac{46}{855}\right)$	$e\left(\frac{104}{855}\right)$	$e\left(\frac{778}{855}\right)$	$e\left(\frac{1051}{1710}\right)$	$e\left(\frac{241}{570}\right)$	$e\left(\frac{389}{570}\right)$	$e\left(\frac{92}{855}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{10}{57}\right)$
$\chi_{3971}(18,\cdot)$	3971.bk	190	yes	$1$	$1$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{189}{190}\right)$	$e\left(\frac{3}{95}\right)$	$e\left(\frac{6}{95}\right)$	$e\left(\frac{97}{190}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{1}{38}\right)$
$\chi_{3971}(20,\cdot)$	3971.bd	95	yes	$1$	$1$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{18}{95}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{3971}(21,\cdot)$	3971.bn	342	yes	$1$	$1$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{17}{114}\right)$
$\chi_{3971}(23,\cdot)$	3971.bh	171	no	$1$	$1$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{3971}(24,\cdot)$	3971.bv	1710	yes	$-1$	$1$	$e\left(\frac{881}{1710}\right)$	$e\left(\frac{439}{855}\right)$	$e\left(\frac{26}{855}\right)$	$e\left(\frac{622}{855}\right)$	$e\left(\frac{49}{1710}\right)$	$e\left(\frac{559}{570}\right)$	$e\left(\frac{311}{570}\right)$	$e\left(\frac{23}{855}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{31}{57}\right)$
$\chi_{3971}(25,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{134}{855}\right)$	$e\left(\frac{842}{855}\right)$	$e\left(\frac{268}{855}\right)$	$e\left(\frac{821}{855}\right)$	$e\left(\frac{121}{855}\right)$	$e\left(\frac{31}{285}\right)$	$e\left(\frac{134}{285}\right)$	$e\left(\frac{829}{855}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{17}{57}\right)$
$\chi_{3971}(26,\cdot)$	3971.bl	285	yes	$1$	$1$	$e\left(\frac{47}{285}\right)$	$e\left(\frac{206}{285}\right)$	$e\left(\frac{94}{285}\right)$	$e\left(\frac{188}{285}\right)$	$e\left(\frac{253}{285}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{127}{285}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{3971}(27,\cdot)$	3971.br	570	yes	$-1$	$1$	$e\left(\frac{353}{570}\right)$	$e\left(\frac{389}{570}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{136}{285}\right)$	$e\left(\frac{86}{285}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{163}{190}\right)$	$e\left(\frac{104}{285}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{35}{38}\right)$
$\chi_{3971}(28,\cdot)$	3971.ba	90	no	$-1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3971}(29,\cdot)$	3971.bu	1710	yes	$1$	$1$	$e\left(\frac{641}{855}\right)$	$e\left(\frac{871}{1710}\right)$	$e\left(\frac{427}{855}\right)$	$e\left(\frac{284}{855}\right)$	$e\left(\frac{443}{1710}\right)$	$e\left(\frac{203}{570}\right)$	$e\left(\frac{71}{285}\right)$	$e\left(\frac{16}{855}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{3971}(30,\cdot)$	3971.bq	570	yes	$-1$	$1$	$e\left(\frac{221}{570}\right)$	$e\left(\frac{169}{285}\right)$	$e\left(\frac{221}{285}\right)$	$e\left(\frac{157}{285}\right)$	$e\left(\frac{559}{570}\right)$	$e\left(\frac{49}{190}\right)$	$e\left(\frac{31}{190}\right)$	$e\left(\frac{53}{285}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{3971}(31,\cdot)$	3971.br	570	yes	$-1$	$1$	$e\left(\frac{277}{570}\right)$	$e\left(\frac{541}{570}\right)$	$e\left(\frac{277}{285}\right)$	$e\left(\frac{269}{285}\right)$	$e\left(\frac{124}{285}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{87}{190}\right)$	$e\left(\frac{256}{285}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{35}{38}\right)$
$\chi_{3971}(32,\cdot)$	3971.bn	342	yes	$1$	$1$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{3971}(34,\cdot)$	3971.bo	342	no	$-1$	$1$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{67}{114}\right)$
$\chi_{3971}(35,\cdot)$	3971.bv	1710	yes	$-1$	$1$	$e\left(\frac{371}{1710}\right)$	$e\left(\frac{49}{855}\right)$	$e\left(\frac{371}{855}\right)$	$e\left(\frac{457}{855}\right)$	$e\left(\frac{469}{1710}\right)$	$e\left(\frac{139}{570}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{98}{855}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{3971}(36,\cdot)$	3971.bs	855	yes	$1$	$1$	$e\left(\frac{529}{855}\right)$	$e\left(\frac{172}{855}\right)$	$e\left(\frac{203}{855}\right)$	$e\left(\frac{121}{855}\right)$	$e\left(\frac{701}{855}\right)$	$e\left(\frac{116}{285}\right)$	$e\left(\frac{244}{285}\right)$	$e\left(\frac{344}{855}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{25}{57}\right)$

Click here to search among the remaining 3388 characters.

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	$3971$
Structure	\(C_{2}\times C_{1710}\)
Order	$3420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{3971}(1,\cdot)\)	3971.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3971}(2,\cdot)\)	3971.bu	1710	yes	\(1\)	\(1\)	\(e\left(\frac{88}{855}\right)\)	\(e\left(\frac{353}{1710}\right)\)	\(e\left(\frac{176}{855}\right)\)	\(e\left(\frac{67}{855}\right)\)	\(e\left(\frac{529}{1710}\right)\)	\(e\left(\frac{79}{570}\right)\)	\(e\left(\frac{88}{285}\right)\)	\(e\left(\frac{353}{855}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)
\(\chi_{3971}(3,\cdot)\)	3971.bt	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{353}{1710}\right)\)	\(e\left(\frac{1529}{1710}\right)\)	\(e\left(\frac{353}{855}\right)\)	\(e\left(\frac{421}{855}\right)\)	\(e\left(\frac{86}{855}\right)\)	\(e\left(\frac{161}{285}\right)\)	\(e\left(\frac{353}{570}\right)\)	\(e\left(\frac{674}{855}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)
\(\chi_{3971}(4,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{176}{855}\right)\)	\(e\left(\frac{353}{855}\right)\)	\(e\left(\frac{352}{855}\right)\)	\(e\left(\frac{134}{855}\right)\)	\(e\left(\frac{529}{855}\right)\)	\(e\left(\frac{79}{285}\right)\)	\(e\left(\frac{176}{285}\right)\)	\(e\left(\frac{706}{855}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{47}{57}\right)\)
\(\chi_{3971}(5,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{67}{855}\right)\)	\(e\left(\frac{421}{855}\right)\)	\(e\left(\frac{134}{855}\right)\)	\(e\left(\frac{838}{855}\right)\)	\(e\left(\frac{488}{855}\right)\)	\(e\left(\frac{158}{285}\right)\)	\(e\left(\frac{67}{285}\right)\)	\(e\left(\frac{842}{855}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)
\(\chi_{3971}(6,\cdot)\)	3971.bv	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{529}{1710}\right)\)	\(e\left(\frac{86}{855}\right)\)	\(e\left(\frac{529}{855}\right)\)	\(e\left(\frac{488}{855}\right)\)	\(e\left(\frac{701}{1710}\right)\)	\(e\left(\frac{401}{570}\right)\)	\(e\left(\frac{529}{570}\right)\)	\(e\left(\frac{172}{855}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{41}{57}\right)\)
\(\chi_{3971}(7,\cdot)\)	3971.bq	570	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{570}\right)\)	\(e\left(\frac{161}{285}\right)\)	\(e\left(\frac{79}{285}\right)\)	\(e\left(\frac{158}{285}\right)\)	\(e\left(\frac{401}{570}\right)\)	\(e\left(\frac{131}{190}\right)\)	\(e\left(\frac{79}{190}\right)\)	\(e\left(\frac{37}{285}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{3971}(8,\cdot)\)	3971.bp	570	yes	\(1\)	\(1\)	\(e\left(\frac{88}{285}\right)\)	\(e\left(\frac{353}{570}\right)\)	\(e\left(\frac{176}{285}\right)\)	\(e\left(\frac{67}{285}\right)\)	\(e\left(\frac{529}{570}\right)\)	\(e\left(\frac{79}{190}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{9}{38}\right)\)
\(\chi_{3971}(9,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{353}{855}\right)\)	\(e\left(\frac{674}{855}\right)\)	\(e\left(\frac{706}{855}\right)\)	\(e\left(\frac{842}{855}\right)\)	\(e\left(\frac{172}{855}\right)\)	\(e\left(\frac{37}{285}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{493}{855}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{35}{57}\right)\)
\(\chi_{3971}(10,\cdot)\)	3971.bn	342	yes	\(1\)	\(1\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{3971}(12,\cdot)\)	3971.be	114	no	\(-1\)	\(1\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{5}{38}\right)\)
\(\chi_{3971}(13,\cdot)\)	3971.bu	1710	yes	\(1\)	\(1\)	\(e\left(\frac{53}{855}\right)\)	\(e\left(\frac{883}{1710}\right)\)	\(e\left(\frac{106}{855}\right)\)	\(e\left(\frac{497}{855}\right)\)	\(e\left(\frac{989}{1710}\right)\)	\(e\left(\frac{569}{570}\right)\)	\(e\left(\frac{53}{285}\right)\)	\(e\left(\frac{28}{855}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{3971}(14,\cdot)\)	3971.bt	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{413}{1710}\right)\)	\(e\left(\frac{1319}{1710}\right)\)	\(e\left(\frac{413}{855}\right)\)	\(e\left(\frac{541}{855}\right)\)	\(e\left(\frac{11}{855}\right)\)	\(e\left(\frac{236}{285}\right)\)	\(e\left(\frac{413}{570}\right)\)	\(e\left(\frac{464}{855}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)
\(\chi_{3971}(15,\cdot)\)	3971.bt	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{487}{1710}\right)\)	\(e\left(\frac{661}{1710}\right)\)	\(e\left(\frac{487}{855}\right)\)	\(e\left(\frac{404}{855}\right)\)	\(e\left(\frac{574}{855}\right)\)	\(e\left(\frac{34}{285}\right)\)	\(e\left(\frac{487}{570}\right)\)	\(e\left(\frac{661}{855}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{109}{114}\right)\)
\(\chi_{3971}(16,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{352}{855}\right)\)	\(e\left(\frac{706}{855}\right)\)	\(e\left(\frac{704}{855}\right)\)	\(e\left(\frac{268}{855}\right)\)	\(e\left(\frac{203}{855}\right)\)	\(e\left(\frac{158}{285}\right)\)	\(e\left(\frac{67}{285}\right)\)	\(e\left(\frac{557}{855}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)
\(\chi_{3971}(17,\cdot)\)	3971.bv	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{959}{1710}\right)\)	\(e\left(\frac{46}{855}\right)\)	\(e\left(\frac{104}{855}\right)\)	\(e\left(\frac{778}{855}\right)\)	\(e\left(\frac{1051}{1710}\right)\)	\(e\left(\frac{241}{570}\right)\)	\(e\left(\frac{389}{570}\right)\)	\(e\left(\frac{92}{855}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{10}{57}\right)\)
\(\chi_{3971}(18,\cdot)\)	3971.bk	190	yes	\(1\)	\(1\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{189}{190}\right)\)	\(e\left(\frac{3}{95}\right)\)	\(e\left(\frac{6}{95}\right)\)	\(e\left(\frac{97}{190}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)
\(\chi_{3971}(20,\cdot)\)	3971.bd	95	yes	\(1\)	\(1\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{18}{95}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{3971}(21,\cdot)\)	3971.bn	342	yes	\(1\)	\(1\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)
\(\chi_{3971}(23,\cdot)\)	3971.bh	171	no	\(1\)	\(1\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{11}{57}\right)\)
\(\chi_{3971}(24,\cdot)\)	3971.bv	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{881}{1710}\right)\)	\(e\left(\frac{439}{855}\right)\)	\(e\left(\frac{26}{855}\right)\)	\(e\left(\frac{622}{855}\right)\)	\(e\left(\frac{49}{1710}\right)\)	\(e\left(\frac{559}{570}\right)\)	\(e\left(\frac{311}{570}\right)\)	\(e\left(\frac{23}{855}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{31}{57}\right)\)
\(\chi_{3971}(25,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{134}{855}\right)\)	\(e\left(\frac{842}{855}\right)\)	\(e\left(\frac{268}{855}\right)\)	\(e\left(\frac{821}{855}\right)\)	\(e\left(\frac{121}{855}\right)\)	\(e\left(\frac{31}{285}\right)\)	\(e\left(\frac{134}{285}\right)\)	\(e\left(\frac{829}{855}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{17}{57}\right)\)
\(\chi_{3971}(26,\cdot)\)	3971.bl	285	yes	\(1\)	\(1\)	\(e\left(\frac{47}{285}\right)\)	\(e\left(\frac{206}{285}\right)\)	\(e\left(\frac{94}{285}\right)\)	\(e\left(\frac{188}{285}\right)\)	\(e\left(\frac{253}{285}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{127}{285}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{3971}(27,\cdot)\)	3971.br	570	yes	\(-1\)	\(1\)	\(e\left(\frac{353}{570}\right)\)	\(e\left(\frac{389}{570}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{136}{285}\right)\)	\(e\left(\frac{86}{285}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{163}{190}\right)\)	\(e\left(\frac{104}{285}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{35}{38}\right)\)
\(\chi_{3971}(28,\cdot)\)	3971.ba	90	no	\(-1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3971}(29,\cdot)\)	3971.bu	1710	yes	\(1\)	\(1\)	\(e\left(\frac{641}{855}\right)\)	\(e\left(\frac{871}{1710}\right)\)	\(e\left(\frac{427}{855}\right)\)	\(e\left(\frac{284}{855}\right)\)	\(e\left(\frac{443}{1710}\right)\)	\(e\left(\frac{203}{570}\right)\)	\(e\left(\frac{71}{285}\right)\)	\(e\left(\frac{16}{855}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{3971}(30,\cdot)\)	3971.bq	570	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{570}\right)\)	\(e\left(\frac{169}{285}\right)\)	\(e\left(\frac{221}{285}\right)\)	\(e\left(\frac{157}{285}\right)\)	\(e\left(\frac{559}{570}\right)\)	\(e\left(\frac{49}{190}\right)\)	\(e\left(\frac{31}{190}\right)\)	\(e\left(\frac{53}{285}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{3971}(31,\cdot)\)	3971.br	570	yes	\(-1\)	\(1\)	\(e\left(\frac{277}{570}\right)\)	\(e\left(\frac{541}{570}\right)\)	\(e\left(\frac{277}{285}\right)\)	\(e\left(\frac{269}{285}\right)\)	\(e\left(\frac{124}{285}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{87}{190}\right)\)	\(e\left(\frac{256}{285}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{35}{38}\right)\)
\(\chi_{3971}(32,\cdot)\)	3971.bn	342	yes	\(1\)	\(1\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{3971}(34,\cdot)\)	3971.bo	342	no	\(-1\)	\(1\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)
\(\chi_{3971}(35,\cdot)\)	3971.bv	1710	yes	\(-1\)	\(1\)	\(e\left(\frac{371}{1710}\right)\)	\(e\left(\frac{49}{855}\right)\)	\(e\left(\frac{371}{855}\right)\)	\(e\left(\frac{457}{855}\right)\)	\(e\left(\frac{469}{1710}\right)\)	\(e\left(\frac{139}{570}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{98}{855}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{28}{57}\right)\)
\(\chi_{3971}(36,\cdot)\)	3971.bs	855	yes	\(1\)	\(1\)	\(e\left(\frac{529}{855}\right)\)	\(e\left(\frac{172}{855}\right)\)	\(e\left(\frac{203}{855}\right)\)	\(e\left(\frac{121}{855}\right)\)	\(e\left(\frac{701}{855}\right)\)	\(e\left(\frac{116}{285}\right)\)	\(e\left(\frac{244}{285}\right)\)	\(e\left(\frac{344}{855}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{25}{57}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 3420 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.