LMFDB - Group of Dirichlet characters of modulus 8010

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8010)

pari: g = idealstar(,8010,2)

Character group

sage: G.order() pari: g.no
Order	=	2112
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{264}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8010}(7121,\cdot)$, $\chi_{8010}(4807,\cdot)$, $\chi_{8010}(181,\cdot)$

First 32 of 2112 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8010}(1,\cdot)$	8010.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8010}(7,\cdot)$	8010.ed	264	no	$1$	$1$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{175}{264}\right)$
$\chi_{8010}(11,\cdot)$	8010.da	66	no	$-1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{61}{66}\right)$	$-1$	$e\left(\frac{29}{33}\right)$
$\chi_{8010}(13,\cdot)$	8010.ed	264	no	$1$	$1$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{264}\right)$
$\chi_{8010}(17,\cdot)$	8010.cy	44	no	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{44}\right)$	$1$	$e\left(\frac{41}{44}\right)$
$\chi_{8010}(19,\cdot)$	8010.dm	88	no	$-1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{8010}(23,\cdot)$	8010.eh	264	no	$-1$	$1$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{197}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{203}{264}\right)$
$\chi_{8010}(29,\cdot)$	8010.ef	264	no	$1$	$1$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{241}{264}\right)$
$\chi_{8010}(31,\cdot)$	8010.ec	264	no	$-1$	$1$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{197}{264}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{155}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{264}\right)$
$\chi_{8010}(37,\cdot)$	8010.bf	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8010}(41,\cdot)$	8010.eg	264	no	$1$	$1$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{241}{264}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{47}{264}\right)$
$\chi_{8010}(43,\cdot)$	8010.ea	264	no	$1$	$1$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{43}{264}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{97}{264}\right)$	$e\left(\frac{161}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{67}{264}\right)$
$\chi_{8010}(47,\cdot)$	8010.do	132	no	$1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{47}{132}\right)$	$1$	$e\left(\frac{95}{132}\right)$
$\chi_{8010}(49,\cdot)$	8010.du	132	no	$1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{97}{132}\right)$	$-i$	$e\left(\frac{43}{132}\right)$
$\chi_{8010}(53,\cdot)$	8010.co	44	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{44}\right)$	$-1$	$e\left(\frac{5}{44}\right)$
$\chi_{8010}(59,\cdot)$	8010.ef	264	no	$1$	$1$	$e\left(\frac{109}{264}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{107}{264}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{113}{264}\right)$
$\chi_{8010}(61,\cdot)$	8010.ec	264	no	$-1$	$1$	$e\left(\frac{47}{264}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{97}{264}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{7}{264}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{169}{264}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{211}{264}\right)$
$\chi_{8010}(67,\cdot)$	8010.dw	132	no	$-1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{33}\right)$	$i$	$e\left(\frac{1}{33}\right)$
$\chi_{8010}(71,\cdot)$	8010.ct	44	no	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{37}{44}\right)$	$-i$	$e\left(\frac{13}{44}\right)$
$\chi_{8010}(73,\cdot)$	8010.cq	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{22}\right)$	$i$	$e\left(\frac{17}{22}\right)$
$\chi_{8010}(77,\cdot)$	8010.ch	24	no	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8010}(79,\cdot)$	8010.du	132	no	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{17}{132}\right)$	$-i$	$e\left(\frac{47}{132}\right)$
$\chi_{8010}(83,\cdot)$	8010.eh	264	no	$-1$	$1$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{217}{264}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{103}{264}\right)$
$\chi_{8010}(91,\cdot)$	8010.bk	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{11}\right)$	$1$	$e\left(\frac{9}{11}\right)$
$\chi_{8010}(97,\cdot)$	8010.dw	132	no	$-1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{8}{33}\right)$	$i$	$e\left(\frac{26}{33}\right)$
$\chi_{8010}(101,\cdot)$	8010.cf	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{24}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8010}(103,\cdot)$	8010.ea	264	no	$1$	$1$	$e\left(\frac{97}{264}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{71}{264}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{197}{264}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{215}{264}\right)$
$\chi_{8010}(107,\cdot)$	8010.co	44	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{44}\right)$	$-1$	$e\left(\frac{35}{44}\right)$
$\chi_{8010}(109,\cdot)$	8010.cp	44	no	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{41}{44}\right)$	$i$	$e\left(\frac{15}{44}\right)$
$\chi_{8010}(113,\cdot)$	8010.eh	264	no	$-1$	$1$	$e\left(\frac{49}{264}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{49}{264}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{227}{264}\right)$
$\chi_{8010}(119,\cdot)$	8010.ef	264	no	$1$	$1$	$e\left(\frac{65}{264}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{151}{264}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{259}{264}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{157}{264}\right)$
$\chi_{8010}(121,\cdot)$	8010.cm	33	no	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{28}{33}\right)$	$1$	$e\left(\frac{25}{33}\right)$

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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	$8010$
Structure	\(C_{2}\times C_{4}\times C_{264}\)
Order	$2112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8010}(1,\cdot)\)	8010.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8010}(7,\cdot)\)	8010.ed	264	no	\(1\)	\(1\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{175}{264}\right)\)
\(\chi_{8010}(11,\cdot)\)	8010.da	66	no	\(-1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(-1\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{8010}(13,\cdot)\)	8010.ed	264	no	\(1\)	\(1\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{264}\right)\)
\(\chi_{8010}(17,\cdot)\)	8010.cy	44	no	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(1\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{8010}(19,\cdot)\)	8010.dm	88	no	\(-1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{8010}(23,\cdot)\)	8010.eh	264	no	\(-1\)	\(1\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{197}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{203}{264}\right)\)
\(\chi_{8010}(29,\cdot)\)	8010.ef	264	no	\(1\)	\(1\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{241}{264}\right)\)
\(\chi_{8010}(31,\cdot)\)	8010.ec	264	no	\(-1\)	\(1\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{197}{264}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{155}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{264}\right)\)
\(\chi_{8010}(37,\cdot)\)	8010.bf	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8010}(41,\cdot)\)	8010.eg	264	no	\(1\)	\(1\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{241}{264}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{47}{264}\right)\)
\(\chi_{8010}(43,\cdot)\)	8010.ea	264	no	\(1\)	\(1\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{43}{264}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{97}{264}\right)\)	\(e\left(\frac{161}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{67}{264}\right)\)
\(\chi_{8010}(47,\cdot)\)	8010.do	132	no	\(1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(1\)	\(e\left(\frac{95}{132}\right)\)
\(\chi_{8010}(49,\cdot)\)	8010.du	132	no	\(1\)	\(1\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(-i\)	\(e\left(\frac{43}{132}\right)\)
\(\chi_{8010}(53,\cdot)\)	8010.co	44	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(-1\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{8010}(59,\cdot)\)	8010.ef	264	no	\(1\)	\(1\)	\(e\left(\frac{109}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{107}{264}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{113}{264}\right)\)
\(\chi_{8010}(61,\cdot)\)	8010.ec	264	no	\(-1\)	\(1\)	\(e\left(\frac{47}{264}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{97}{264}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{7}{264}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{169}{264}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{211}{264}\right)\)
\(\chi_{8010}(67,\cdot)\)	8010.dw	132	no	\(-1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(i\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{8010}(71,\cdot)\)	8010.ct	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(-i\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{8010}(73,\cdot)\)	8010.cq	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(i\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{8010}(77,\cdot)\)	8010.ch	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8010}(79,\cdot)\)	8010.du	132	no	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(-i\)	\(e\left(\frac{47}{132}\right)\)
\(\chi_{8010}(83,\cdot)\)	8010.eh	264	no	\(-1\)	\(1\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{217}{264}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{103}{264}\right)\)
\(\chi_{8010}(91,\cdot)\)	8010.bk	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(1\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{8010}(97,\cdot)\)	8010.dw	132	no	\(-1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(i\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{8010}(101,\cdot)\)	8010.cf	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8010}(103,\cdot)\)	8010.ea	264	no	\(1\)	\(1\)	\(e\left(\frac{97}{264}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{71}{264}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{197}{264}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{215}{264}\right)\)
\(\chi_{8010}(107,\cdot)\)	8010.co	44	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(-1\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{8010}(109,\cdot)\)	8010.cp	44	no	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(i\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{8010}(113,\cdot)\)	8010.eh	264	no	\(-1\)	\(1\)	\(e\left(\frac{49}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{49}{264}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{227}{264}\right)\)
\(\chi_{8010}(119,\cdot)\)	8010.ef	264	no	\(1\)	\(1\)	\(e\left(\frac{65}{264}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{151}{264}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{259}{264}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{157}{264}\right)\)
\(\chi_{8010}(121,\cdot)\)	8010.cm	33	no	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(1\)	\(e\left(\frac{25}{33}\right)\)

Introduction

L-functions

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Character group

First 32 of 2112 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.