LMFDB - Group of Dirichlet characters of modulus 8042

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8042)

pari: g = idealstar(,8042,2)

Character group

sage: G.order() pari: g.no
Order	=	4020
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4020}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8042}(4023,\cdot)$

First 32 of 4020 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8042}(1,\cdot)$	8042.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8042}(3,\cdot)$	8042.u	1005	no	$1$	$1$	$e\left(\frac{994}{1005}\right)$	$e\left(\frac{964}{1005}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{983}{1005}\right)$	$e\left(\frac{32}{1005}\right)$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{953}{1005}\right)$	$e\left(\frac{264}{335}\right)$	$e\left(\frac{316}{1005}\right)$	$e\left(\frac{592}{1005}\right)$
$\chi_{8042}(5,\cdot)$	8042.u	1005	no	$1$	$1$	$e\left(\frac{964}{1005}\right)$	$e\left(\frac{304}{1005}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{923}{1005}\right)$	$e\left(\frac{302}{1005}\right)$	$e\left(\frac{52}{67}\right)$	$e\left(\frac{263}{1005}\right)$	$e\left(\frac{314}{335}\right)$	$e\left(\frac{721}{1005}\right)$	$e\left(\frac{562}{1005}\right)$
$\chi_{8042}(7,\cdot)$	8042.j	20	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{8042}(9,\cdot)$	8042.u	1005	no	$1$	$1$	$e\left(\frac{983}{1005}\right)$	$e\left(\frac{923}{1005}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{961}{1005}\right)$	$e\left(\frac{64}{1005}\right)$	$e\left(\frac{23}{67}\right)$	$e\left(\frac{901}{1005}\right)$	$e\left(\frac{193}{335}\right)$	$e\left(\frac{632}{1005}\right)$	$e\left(\frac{179}{1005}\right)$
$\chi_{8042}(11,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{32}{1005}\right)$	$e\left(\frac{302}{1005}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{64}{1005}\right)$	$e\left(\frac{1729}{4020}\right)$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{334}{1005}\right)$	$e\left(\frac{139}{670}\right)$	$e\left(\frac{2627}{4020}\right)$	$e\left(\frac{2339}{4020}\right)$
$\chi_{8042}(13,\cdot)$	8042.n	134	no	$1$	$1$	$e\left(\frac{45}{67}\right)$	$e\left(\frac{52}{67}\right)$	$-1$	$e\left(\frac{23}{67}\right)$	$e\left(\frac{61}{134}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{30}{67}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{125}{134}\right)$	$e\left(\frac{23}{134}\right)$
$\chi_{8042}(15,\cdot)$	8042.u	1005	no	$1$	$1$	$e\left(\frac{953}{1005}\right)$	$e\left(\frac{263}{1005}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{901}{1005}\right)$	$e\left(\frac{334}{1005}\right)$	$e\left(\frac{30}{67}\right)$	$e\left(\frac{211}{1005}\right)$	$e\left(\frac{243}{335}\right)$	$e\left(\frac{32}{1005}\right)$	$e\left(\frac{149}{1005}\right)$
$\chi_{8042}(17,\cdot)$	8042.s	670	no	$1$	$1$	$e\left(\frac{264}{335}\right)$	$e\left(\frac{314}{335}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{193}{335}\right)$	$e\left(\frac{139}{670}\right)$	$e\left(\frac{43}{67}\right)$	$e\left(\frac{243}{335}\right)$	$e\left(\frac{87}{335}\right)$	$e\left(\frac{577}{670}\right)$	$e\left(\frac{59}{670}\right)$
$\chi_{8042}(19,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{316}{1005}\right)$	$e\left(\frac{721}{1005}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{632}{1005}\right)$	$e\left(\frac{2627}{4020}\right)$	$e\left(\frac{125}{134}\right)$	$e\left(\frac{32}{1005}\right)$	$e\left(\frac{577}{670}\right)$	$e\left(\frac{2701}{4020}\right)$	$e\left(\frac{3877}{4020}\right)$
$\chi_{8042}(21,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{592}{1005}\right)$	$e\left(\frac{562}{1005}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{179}{1005}\right)$	$e\left(\frac{2339}{4020}\right)$	$e\left(\frac{23}{134}\right)$	$e\left(\frac{149}{1005}\right)$	$e\left(\frac{59}{670}\right)$	$e\left(\frac{3877}{4020}\right)$	$e\left(\frac{2569}{4020}\right)$
$\chi_{8042}(23,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{971}{1005}\right)$	$e\left(\frac{56}{1005}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{937}{1005}\right)$	$e\left(\frac{487}{4020}\right)$	$e\left(\frac{65}{134}\right)$	$e\left(\frac{22}{1005}\right)$	$e\left(\frac{627}{670}\right)$	$e\left(\frac{161}{4020}\right)$	$e\left(\frac{2477}{4020}\right)$
$\chi_{8042}(25,\cdot)$	8042.u	1005	no	$1$	$1$	$e\left(\frac{923}{1005}\right)$	$e\left(\frac{608}{1005}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{841}{1005}\right)$	$e\left(\frac{604}{1005}\right)$	$e\left(\frac{37}{67}\right)$	$e\left(\frac{526}{1005}\right)$	$e\left(\frac{293}{335}\right)$	$e\left(\frac{437}{1005}\right)$	$e\left(\frac{119}{1005}\right)$
$\chi_{8042}(27,\cdot)$	8042.q	335	no	$1$	$1$	$e\left(\frac{324}{335}\right)$	$e\left(\frac{294}{335}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{313}{335}\right)$	$e\left(\frac{32}{335}\right)$	$e\left(\frac{1}{67}\right)$	$e\left(\frac{283}{335}\right)$	$e\left(\frac{122}{335}\right)$	$e\left(\frac{316}{335}\right)$	$e\left(\frac{257}{335}\right)$
$\chi_{8042}(29,\cdot)$	8042.t	804	no	$-1$	$1$	$e\left(\frac{124}{201}\right)$	$e\left(\frac{115}{201}\right)$	$-i$	$e\left(\frac{47}{201}\right)$	$e\left(\frac{293}{804}\right)$	$e\left(\frac{1}{134}\right)$	$e\left(\frac{38}{201}\right)$	$e\left(\frac{11}{134}\right)$	$e\left(\frac{607}{804}\right)$	$e\left(\frac{295}{804}\right)$
$\chi_{8042}(31,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{608}{1005}\right)$	$e\left(\frac{713}{1005}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{211}{1005}\right)$	$e\left(\frac{2701}{4020}\right)$	$e\left(\frac{87}{134}\right)$	$e\left(\frac{316}{1005}\right)$	$e\left(\frac{631}{670}\right)$	$e\left(\frac{3683}{4020}\right)$	$e\left(\frac{2231}{4020}\right)$
$\chi_{8042}(33,\cdot)$	8042.v	1340	no	$-1$	$1$	$e\left(\frac{7}{335}\right)$	$e\left(\frac{87}{335}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{14}{335}\right)$	$e\left(\frac{619}{1340}\right)$	$e\left(\frac{17}{134}\right)$	$e\left(\frac{94}{335}\right)$	$e\left(\frac{667}{670}\right)$	$e\left(\frac{1297}{1340}\right)$	$e\left(\frac{229}{1340}\right)$
$\chi_{8042}(35,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{562}{1005}\right)$	$e\left(\frac{907}{1005}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{119}{1005}\right)$	$e\left(\frac{3419}{4020}\right)$	$e\left(\frac{37}{134}\right)$	$e\left(\frac{464}{1005}\right)$	$e\left(\frac{159}{670}\right)$	$e\left(\frac{1477}{4020}\right)$	$e\left(\frac{2449}{4020}\right)$
$\chi_{8042}(37,\cdot)$	8042.i	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{8042}(39,\cdot)$	8042.w	2010	no	$1$	$1$	$e\left(\frac{664}{1005}\right)$	$e\left(\frac{739}{1005}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{323}{1005}\right)$	$e\left(\frac{979}{2010}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{398}{1005}\right)$	$e\left(\frac{144}{335}\right)$	$e\left(\frac{497}{2010}\right)$	$e\left(\frac{1529}{2010}\right)$
$\chi_{8042}(41,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{47}{1005}\right)$	$e\left(\frac{632}{1005}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{94}{1005}\right)$	$e\left(\frac{3199}{4020}\right)$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{679}{1005}\right)$	$e\left(\frac{89}{670}\right)$	$e\left(\frac{1817}{4020}\right)$	$e\left(\frac{389}{4020}\right)$
$\chi_{8042}(43,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{181}{1005}\right)$	$e\left(\frac{766}{1005}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{362}{1005}\right)$	$e\left(\frac{3467}{4020}\right)$	$e\left(\frac{121}{134}\right)$	$e\left(\frac{947}{1005}\right)$	$e\left(\frac{357}{670}\right)$	$e\left(\frac{3961}{4020}\right)$	$e\left(\frac{3337}{4020}\right)$
$\chi_{8042}(45,\cdot)$	8042.q	335	no	$1$	$1$	$e\left(\frac{314}{335}\right)$	$e\left(\frac{74}{335}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{293}{335}\right)$	$e\left(\frac{122}{335}\right)$	$e\left(\frac{8}{67}\right)$	$e\left(\frac{53}{335}\right)$	$e\left(\frac{172}{335}\right)$	$e\left(\frac{116}{335}\right)$	$e\left(\frac{247}{335}\right)$
$\chi_{8042}(47,\cdot)$	8042.h	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8042}(49,\cdot)$	8042.g	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{8042}(51,\cdot)$	8042.w	2010	no	$1$	$1$	$e\left(\frac{781}{1005}\right)$	$e\left(\frac{901}{1005}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{557}{1005}\right)$	$e\left(\frac{481}{2010}\right)$	$e\left(\frac{21}{67}\right)$	$e\left(\frac{677}{1005}\right)$	$e\left(\frac{16}{335}\right)$	$e\left(\frac{353}{2010}\right)$	$e\left(\frac{1361}{2010}\right)$
$\chi_{8042}(53,\cdot)$	8042.r	402	no	$1$	$1$	$e\left(\frac{161}{201}\right)$	$e\left(\frac{125}{201}\right)$	$-1$	$e\left(\frac{121}{201}\right)$	$e\left(\frac{251}{402}\right)$	$e\left(\frac{2}{67}\right)$	$e\left(\frac{85}{201}\right)$	$e\left(\frac{22}{67}\right)$	$e\left(\frac{343}{402}\right)$	$e\left(\frac{121}{402}\right)$
$\chi_{8042}(55,\cdot)$	8042.v	1340	no	$-1$	$1$	$e\left(\frac{332}{335}\right)$	$e\left(\frac{202}{335}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{329}{335}\right)$	$e\left(\frac{979}{1340}\right)$	$e\left(\frac{31}{134}\right)$	$e\left(\frac{199}{335}\right)$	$e\left(\frac{97}{670}\right)$	$e\left(\frac{497}{1340}\right)$	$e\left(\frac{189}{1340}\right)$
$\chi_{8042}(57,\cdot)$	8042.t	804	no	$-1$	$1$	$e\left(\frac{61}{201}\right)$	$e\left(\frac{136}{201}\right)$	$i$	$e\left(\frac{122}{201}\right)$	$e\left(\frac{551}{804}\right)$	$e\left(\frac{81}{134}\right)$	$e\left(\frac{197}{201}\right)$	$e\left(\frac{87}{134}\right)$	$e\left(\frac{793}{804}\right)$	$e\left(\frac{445}{804}\right)$
$\chi_{8042}(59,\cdot)$	8042.w	2010	no	$1$	$1$	$e\left(\frac{709}{1005}\right)$	$e\left(\frac{724}{1005}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{413}{1005}\right)$	$e\left(\frac{169}{2010}\right)$	$e\left(\frac{11}{67}\right)$	$e\left(\frac{428}{1005}\right)$	$e\left(\frac{69}{335}\right)$	$e\left(\frac{287}{2010}\right)$	$e\left(\frac{1619}{2010}\right)$
$\chi_{8042}(61,\cdot)$	8042.w	2010	no	$1$	$1$	$e\left(\frac{197}{1005}\right)$	$e\left(\frac{917}{1005}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{394}{1005}\right)$	$e\left(\frac{407}{2010}\right)$	$e\left(\frac{59}{67}\right)$	$e\left(\frac{109}{1005}\right)$	$e\left(\frac{297}{335}\right)$	$e\left(\frac{1381}{2010}\right)$	$e\left(\frac{997}{2010}\right)$
$\chi_{8042}(63,\cdot)$	8042.x	4020	no	$-1$	$1$	$e\left(\frac{581}{1005}\right)$	$e\left(\frac{521}{1005}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{157}{1005}\right)$	$e\left(\frac{2467}{4020}\right)$	$e\left(\frac{113}{134}\right)$	$e\left(\frac{97}{1005}\right)$	$e\left(\frac{587}{670}\right)$	$e\left(\frac{1121}{4020}\right)$	$e\left(\frac{917}{4020}\right)$

Click here to search among the remaining 3988 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	$8042$
Structure	\(C_{4020}\)
Order	$4020$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8042}(1,\cdot)\)	8042.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8042}(3,\cdot)\)	8042.u	1005	no	\(1\)	\(1\)	\(e\left(\frac{994}{1005}\right)\)	\(e\left(\frac{964}{1005}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{983}{1005}\right)\)	\(e\left(\frac{32}{1005}\right)\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{953}{1005}\right)\)	\(e\left(\frac{264}{335}\right)\)	\(e\left(\frac{316}{1005}\right)\)	\(e\left(\frac{592}{1005}\right)\)
\(\chi_{8042}(5,\cdot)\)	8042.u	1005	no	\(1\)	\(1\)	\(e\left(\frac{964}{1005}\right)\)	\(e\left(\frac{304}{1005}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{923}{1005}\right)\)	\(e\left(\frac{302}{1005}\right)\)	\(e\left(\frac{52}{67}\right)\)	\(e\left(\frac{263}{1005}\right)\)	\(e\left(\frac{314}{335}\right)\)	\(e\left(\frac{721}{1005}\right)\)	\(e\left(\frac{562}{1005}\right)\)
\(\chi_{8042}(7,\cdot)\)	8042.j	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{8042}(9,\cdot)\)	8042.u	1005	no	\(1\)	\(1\)	\(e\left(\frac{983}{1005}\right)\)	\(e\left(\frac{923}{1005}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{961}{1005}\right)\)	\(e\left(\frac{64}{1005}\right)\)	\(e\left(\frac{23}{67}\right)\)	\(e\left(\frac{901}{1005}\right)\)	\(e\left(\frac{193}{335}\right)\)	\(e\left(\frac{632}{1005}\right)\)	\(e\left(\frac{179}{1005}\right)\)
\(\chi_{8042}(11,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{32}{1005}\right)\)	\(e\left(\frac{302}{1005}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{64}{1005}\right)\)	\(e\left(\frac{1729}{4020}\right)\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{334}{1005}\right)\)	\(e\left(\frac{139}{670}\right)\)	\(e\left(\frac{2627}{4020}\right)\)	\(e\left(\frac{2339}{4020}\right)\)
\(\chi_{8042}(13,\cdot)\)	8042.n	134	no	\(1\)	\(1\)	\(e\left(\frac{45}{67}\right)\)	\(e\left(\frac{52}{67}\right)\)	\(-1\)	\(e\left(\frac{23}{67}\right)\)	\(e\left(\frac{61}{134}\right)\)	\(e\left(\frac{10}{67}\right)\)	\(e\left(\frac{30}{67}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{125}{134}\right)\)	\(e\left(\frac{23}{134}\right)\)
\(\chi_{8042}(15,\cdot)\)	8042.u	1005	no	\(1\)	\(1\)	\(e\left(\frac{953}{1005}\right)\)	\(e\left(\frac{263}{1005}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{901}{1005}\right)\)	\(e\left(\frac{334}{1005}\right)\)	\(e\left(\frac{30}{67}\right)\)	\(e\left(\frac{211}{1005}\right)\)	\(e\left(\frac{243}{335}\right)\)	\(e\left(\frac{32}{1005}\right)\)	\(e\left(\frac{149}{1005}\right)\)
\(\chi_{8042}(17,\cdot)\)	8042.s	670	no	\(1\)	\(1\)	\(e\left(\frac{264}{335}\right)\)	\(e\left(\frac{314}{335}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{193}{335}\right)\)	\(e\left(\frac{139}{670}\right)\)	\(e\left(\frac{43}{67}\right)\)	\(e\left(\frac{243}{335}\right)\)	\(e\left(\frac{87}{335}\right)\)	\(e\left(\frac{577}{670}\right)\)	\(e\left(\frac{59}{670}\right)\)
\(\chi_{8042}(19,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{316}{1005}\right)\)	\(e\left(\frac{721}{1005}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{632}{1005}\right)\)	\(e\left(\frac{2627}{4020}\right)\)	\(e\left(\frac{125}{134}\right)\)	\(e\left(\frac{32}{1005}\right)\)	\(e\left(\frac{577}{670}\right)\)	\(e\left(\frac{2701}{4020}\right)\)	\(e\left(\frac{3877}{4020}\right)\)
\(\chi_{8042}(21,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{592}{1005}\right)\)	\(e\left(\frac{562}{1005}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{179}{1005}\right)\)	\(e\left(\frac{2339}{4020}\right)\)	\(e\left(\frac{23}{134}\right)\)	\(e\left(\frac{149}{1005}\right)\)	\(e\left(\frac{59}{670}\right)\)	\(e\left(\frac{3877}{4020}\right)\)	\(e\left(\frac{2569}{4020}\right)\)
\(\chi_{8042}(23,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{971}{1005}\right)\)	\(e\left(\frac{56}{1005}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{937}{1005}\right)\)	\(e\left(\frac{487}{4020}\right)\)	\(e\left(\frac{65}{134}\right)\)	\(e\left(\frac{22}{1005}\right)\)	\(e\left(\frac{627}{670}\right)\)	\(e\left(\frac{161}{4020}\right)\)	\(e\left(\frac{2477}{4020}\right)\)
\(\chi_{8042}(25,\cdot)\)	8042.u	1005	no	\(1\)	\(1\)	\(e\left(\frac{923}{1005}\right)\)	\(e\left(\frac{608}{1005}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{841}{1005}\right)\)	\(e\left(\frac{604}{1005}\right)\)	\(e\left(\frac{37}{67}\right)\)	\(e\left(\frac{526}{1005}\right)\)	\(e\left(\frac{293}{335}\right)\)	\(e\left(\frac{437}{1005}\right)\)	\(e\left(\frac{119}{1005}\right)\)
\(\chi_{8042}(27,\cdot)\)	8042.q	335	no	\(1\)	\(1\)	\(e\left(\frac{324}{335}\right)\)	\(e\left(\frac{294}{335}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{313}{335}\right)\)	\(e\left(\frac{32}{335}\right)\)	\(e\left(\frac{1}{67}\right)\)	\(e\left(\frac{283}{335}\right)\)	\(e\left(\frac{122}{335}\right)\)	\(e\left(\frac{316}{335}\right)\)	\(e\left(\frac{257}{335}\right)\)
\(\chi_{8042}(29,\cdot)\)	8042.t	804	no	\(-1\)	\(1\)	\(e\left(\frac{124}{201}\right)\)	\(e\left(\frac{115}{201}\right)\)	\(-i\)	\(e\left(\frac{47}{201}\right)\)	\(e\left(\frac{293}{804}\right)\)	\(e\left(\frac{1}{134}\right)\)	\(e\left(\frac{38}{201}\right)\)	\(e\left(\frac{11}{134}\right)\)	\(e\left(\frac{607}{804}\right)\)	\(e\left(\frac{295}{804}\right)\)
\(\chi_{8042}(31,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{608}{1005}\right)\)	\(e\left(\frac{713}{1005}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{211}{1005}\right)\)	\(e\left(\frac{2701}{4020}\right)\)	\(e\left(\frac{87}{134}\right)\)	\(e\left(\frac{316}{1005}\right)\)	\(e\left(\frac{631}{670}\right)\)	\(e\left(\frac{3683}{4020}\right)\)	\(e\left(\frac{2231}{4020}\right)\)
\(\chi_{8042}(33,\cdot)\)	8042.v	1340	no	\(-1\)	\(1\)	\(e\left(\frac{7}{335}\right)\)	\(e\left(\frac{87}{335}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{14}{335}\right)\)	\(e\left(\frac{619}{1340}\right)\)	\(e\left(\frac{17}{134}\right)\)	\(e\left(\frac{94}{335}\right)\)	\(e\left(\frac{667}{670}\right)\)	\(e\left(\frac{1297}{1340}\right)\)	\(e\left(\frac{229}{1340}\right)\)
\(\chi_{8042}(35,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{562}{1005}\right)\)	\(e\left(\frac{907}{1005}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{119}{1005}\right)\)	\(e\left(\frac{3419}{4020}\right)\)	\(e\left(\frac{37}{134}\right)\)	\(e\left(\frac{464}{1005}\right)\)	\(e\left(\frac{159}{670}\right)\)	\(e\left(\frac{1477}{4020}\right)\)	\(e\left(\frac{2449}{4020}\right)\)
\(\chi_{8042}(37,\cdot)\)	8042.i	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{8042}(39,\cdot)\)	8042.w	2010	no	\(1\)	\(1\)	\(e\left(\frac{664}{1005}\right)\)	\(e\left(\frac{739}{1005}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{323}{1005}\right)\)	\(e\left(\frac{979}{2010}\right)\)	\(e\left(\frac{55}{67}\right)\)	\(e\left(\frac{398}{1005}\right)\)	\(e\left(\frac{144}{335}\right)\)	\(e\left(\frac{497}{2010}\right)\)	\(e\left(\frac{1529}{2010}\right)\)
\(\chi_{8042}(41,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{47}{1005}\right)\)	\(e\left(\frac{632}{1005}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{94}{1005}\right)\)	\(e\left(\frac{3199}{4020}\right)\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{679}{1005}\right)\)	\(e\left(\frac{89}{670}\right)\)	\(e\left(\frac{1817}{4020}\right)\)	\(e\left(\frac{389}{4020}\right)\)
\(\chi_{8042}(43,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{181}{1005}\right)\)	\(e\left(\frac{766}{1005}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{362}{1005}\right)\)	\(e\left(\frac{3467}{4020}\right)\)	\(e\left(\frac{121}{134}\right)\)	\(e\left(\frac{947}{1005}\right)\)	\(e\left(\frac{357}{670}\right)\)	\(e\left(\frac{3961}{4020}\right)\)	\(e\left(\frac{3337}{4020}\right)\)
\(\chi_{8042}(45,\cdot)\)	8042.q	335	no	\(1\)	\(1\)	\(e\left(\frac{314}{335}\right)\)	\(e\left(\frac{74}{335}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{293}{335}\right)\)	\(e\left(\frac{122}{335}\right)\)	\(e\left(\frac{8}{67}\right)\)	\(e\left(\frac{53}{335}\right)\)	\(e\left(\frac{172}{335}\right)\)	\(e\left(\frac{116}{335}\right)\)	\(e\left(\frac{247}{335}\right)\)
\(\chi_{8042}(47,\cdot)\)	8042.h	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8042}(49,\cdot)\)	8042.g	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{8042}(51,\cdot)\)	8042.w	2010	no	\(1\)	\(1\)	\(e\left(\frac{781}{1005}\right)\)	\(e\left(\frac{901}{1005}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{557}{1005}\right)\)	\(e\left(\frac{481}{2010}\right)\)	\(e\left(\frac{21}{67}\right)\)	\(e\left(\frac{677}{1005}\right)\)	\(e\left(\frac{16}{335}\right)\)	\(e\left(\frac{353}{2010}\right)\)	\(e\left(\frac{1361}{2010}\right)\)
\(\chi_{8042}(53,\cdot)\)	8042.r	402	no	\(1\)	\(1\)	\(e\left(\frac{161}{201}\right)\)	\(e\left(\frac{125}{201}\right)\)	\(-1\)	\(e\left(\frac{121}{201}\right)\)	\(e\left(\frac{251}{402}\right)\)	\(e\left(\frac{2}{67}\right)\)	\(e\left(\frac{85}{201}\right)\)	\(e\left(\frac{22}{67}\right)\)	\(e\left(\frac{343}{402}\right)\)	\(e\left(\frac{121}{402}\right)\)
\(\chi_{8042}(55,\cdot)\)	8042.v	1340	no	\(-1\)	\(1\)	\(e\left(\frac{332}{335}\right)\)	\(e\left(\frac{202}{335}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{329}{335}\right)\)	\(e\left(\frac{979}{1340}\right)\)	\(e\left(\frac{31}{134}\right)\)	\(e\left(\frac{199}{335}\right)\)	\(e\left(\frac{97}{670}\right)\)	\(e\left(\frac{497}{1340}\right)\)	\(e\left(\frac{189}{1340}\right)\)
\(\chi_{8042}(57,\cdot)\)	8042.t	804	no	\(-1\)	\(1\)	\(e\left(\frac{61}{201}\right)\)	\(e\left(\frac{136}{201}\right)\)	\(i\)	\(e\left(\frac{122}{201}\right)\)	\(e\left(\frac{551}{804}\right)\)	\(e\left(\frac{81}{134}\right)\)	\(e\left(\frac{197}{201}\right)\)	\(e\left(\frac{87}{134}\right)\)	\(e\left(\frac{793}{804}\right)\)	\(e\left(\frac{445}{804}\right)\)
\(\chi_{8042}(59,\cdot)\)	8042.w	2010	no	\(1\)	\(1\)	\(e\left(\frac{709}{1005}\right)\)	\(e\left(\frac{724}{1005}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{413}{1005}\right)\)	\(e\left(\frac{169}{2010}\right)\)	\(e\left(\frac{11}{67}\right)\)	\(e\left(\frac{428}{1005}\right)\)	\(e\left(\frac{69}{335}\right)\)	\(e\left(\frac{287}{2010}\right)\)	\(e\left(\frac{1619}{2010}\right)\)
\(\chi_{8042}(61,\cdot)\)	8042.w	2010	no	\(1\)	\(1\)	\(e\left(\frac{197}{1005}\right)\)	\(e\left(\frac{917}{1005}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{394}{1005}\right)\)	\(e\left(\frac{407}{2010}\right)\)	\(e\left(\frac{59}{67}\right)\)	\(e\left(\frac{109}{1005}\right)\)	\(e\left(\frac{297}{335}\right)\)	\(e\left(\frac{1381}{2010}\right)\)	\(e\left(\frac{997}{2010}\right)\)
\(\chi_{8042}(63,\cdot)\)	8042.x	4020	no	\(-1\)	\(1\)	\(e\left(\frac{581}{1005}\right)\)	\(e\left(\frac{521}{1005}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{157}{1005}\right)\)	\(e\left(\frac{2467}{4020}\right)\)	\(e\left(\frac{113}{134}\right)\)	\(e\left(\frac{97}{1005}\right)\)	\(e\left(\frac{587}{670}\right)\)	\(e\left(\frac{1121}{4020}\right)\)	\(e\left(\frac{917}{4020}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 4020 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.