LMFDB - Group of Dirichlet characters of modulus 4005

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4005)

pari: g = idealstar(,4005,2)

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	=	$\chi_{4005}(3116,\cdot)$, $\chi_{4005}(802,\cdot)$, $\chi_{4005}(181,\cdot)$

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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{4005}(1,\cdot)$	4005.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4005}(2,\cdot)$	4005.dt	132	yes	$1$	$1$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{4005}(4,\cdot)$	4005.da	66	yes	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{4005}(7,\cdot)$	4005.ed	264	yes	$1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{4005}(8,\cdot)$	4005.ct	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{4005}(11,\cdot)$	4005.cz	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{4005}(13,\cdot)$	4005.ed	264	yes	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{4005}(14,\cdot)$	4005.eh	264	yes	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{23}{264}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{4005}(16,\cdot)$	4005.cm	33	no	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{4005}(17,\cdot)$	4005.cw	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{4005}(19,\cdot)$	4005.dn	88	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{4005}(22,\cdot)$	4005.dv	132	yes	$-1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{4005}(23,\cdot)$	4005.ef	264	yes	$-1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{215}{264}\right)$	$e\left(\frac{131}{264}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{4005}(26,\cdot)$	4005.dm	88	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{4005}(28,\cdot)$	4005.dk	88	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{4005}(29,\cdot)$	4005.eh	264	yes	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{67}{264}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{4005}(31,\cdot)$	4005.eg	264	no	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{4005}(32,\cdot)$	4005.dt	132	yes	$1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{4005}(34,\cdot)$	4005.bv	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-i$
$\chi_{4005}(37,\cdot)$	4005.bf	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{4005}(38,\cdot)$	4005.ee	264	yes	$-1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{95}{264}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{241}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{4005}(41,\cdot)$	4005.eb	264	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{83}{264}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{4005}(43,\cdot)$	4005.ec	264	yes	$1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{43}{264}\right)$	$e\left(\frac{211}{264}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{4005}(44,\cdot)$	4005.bx	22	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{4005}(46,\cdot)$	4005.dh	88	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{4005}(47,\cdot)$	4005.dq	132	yes	$1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{4005}(49,\cdot)$	4005.dp	132	yes	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{4005}(52,\cdot)$	4005.cj	24	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{4005}(53,\cdot)$	4005.cq	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{4005}(56,\cdot)$	4005.eb	264	no	$1$	$1$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{107}{264}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{13}{264}\right)$	$e\left(\frac{7}{264}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{4005}(58,\cdot)$	4005.ed	264	yes	$1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{137}{264}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{4005}(59,\cdot)$	4005.eh	264	yes	$1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{109}{264}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{107}{264}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{88}\right)$

Click here to search among the remaining 2080 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	$4005$
Structure	\(C_{2}\times C_{4}\times C_{264}\)
Order	$2112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{4005}(1,\cdot)\)	4005.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4005}(2,\cdot)\)	4005.dt	132	yes	\(1\)	\(1\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{4005}(4,\cdot)\)	4005.da	66	yes	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{4005}(7,\cdot)\)	4005.ed	264	yes	\(1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{4005}(8,\cdot)\)	4005.ct	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{4005}(11,\cdot)\)	4005.cz	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{4005}(13,\cdot)\)	4005.ed	264	yes	\(1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{4005}(14,\cdot)\)	4005.eh	264	yes	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{23}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{4005}(16,\cdot)\)	4005.cm	33	no	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{4005}(17,\cdot)\)	4005.cw	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{4005}(19,\cdot)\)	4005.dn	88	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{4005}(22,\cdot)\)	4005.dv	132	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{4005}(23,\cdot)\)	4005.ef	264	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{215}{264}\right)\)	\(e\left(\frac{131}{264}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{4005}(26,\cdot)\)	4005.dm	88	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{4005}(28,\cdot)\)	4005.dk	88	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{4005}(29,\cdot)\)	4005.eh	264	yes	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{67}{264}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{4005}(31,\cdot)\)	4005.eg	264	no	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{4005}(32,\cdot)\)	4005.dt	132	yes	\(1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{4005}(34,\cdot)\)	4005.bv	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-i\)
\(\chi_{4005}(37,\cdot)\)	4005.bf	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{4005}(38,\cdot)\)	4005.ee	264	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{95}{264}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{241}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{4005}(41,\cdot)\)	4005.eb	264	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{83}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{4005}(43,\cdot)\)	4005.ec	264	yes	\(1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{43}{264}\right)\)	\(e\left(\frac{211}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{4005}(44,\cdot)\)	4005.bx	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{4005}(46,\cdot)\)	4005.dh	88	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{4005}(47,\cdot)\)	4005.dq	132	yes	\(1\)	\(1\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{4005}(49,\cdot)\)	4005.dp	132	yes	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{4005}(52,\cdot)\)	4005.cj	24	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{4005}(53,\cdot)\)	4005.cq	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{4005}(56,\cdot)\)	4005.eb	264	no	\(1\)	\(1\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{107}{264}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{13}{264}\right)\)	\(e\left(\frac{7}{264}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{4005}(58,\cdot)\)	4005.ed	264	yes	\(1\)	\(1\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{137}{264}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{4005}(59,\cdot)\)	4005.eh	264	yes	\(1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{109}{264}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{107}{264}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

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.