LMFDB - Group of Dirichlet characters of modulus 4034

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4034)

pari: g = idealstar(,4034,2)

Character group

sage: G.order() pari: g.no
Order	=	2016
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2016}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4034}(5,\cdot)$

First 32 of 2016 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4034}(1,\cdot)$	4034.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4034}(3,\cdot)$	4034.bi	1008	no	$1$	$1$	$e\left(\frac{121}{504}\right)$	$e\left(\frac{515}{1008}\right)$	$e\left(\frac{445}{504}\right)$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{757}{1008}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{19}{1008}\right)$	$e\left(\frac{31}{252}\right)$
$\chi_{4034}(5,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{515}{1008}\right)$	$e\left(\frac{1}{2016}\right)$	$e\left(\frac{407}{1008}\right)$	$e\left(\frac{11}{504}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{101}{288}\right)$	$e\left(\frac{1031}{2016}\right)$	$e\left(\frac{377}{672}\right)$	$e\left(\frac{1697}{2016}\right)$	$e\left(\frac{461}{504}\right)$
$\chi_{4034}(7,\cdot)$	4034.bi	1008	no	$1$	$1$	$e\left(\frac{445}{504}\right)$	$e\left(\frac{407}{1008}\right)$	$e\left(\frac{337}{504}\right)$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{289}{1008}\right)$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{199}{1008}\right)$	$e\left(\frac{139}{252}\right)$
$\chi_{4034}(9,\cdot)$	4034.bg	504	no	$1$	$1$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{11}{504}\right)$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{253}{504}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{19}{504}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{4034}(11,\cdot)$	4034.bd	252	no	$1$	$1$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{4034}(13,\cdot)$	4034.be	288	no	$-1$	$1$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{101}{288}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{271}{288}\right)$	$e\left(\frac{163}{288}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{4034}(15,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{757}{1008}\right)$	$e\left(\frac{1031}{2016}\right)$	$e\left(\frac{289}{1008}\right)$	$e\left(\frac{253}{504}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{163}{288}\right)$	$e\left(\frac{529}{2016}\right)$	$e\left(\frac{271}{672}\right)$	$e\left(\frac{1735}{2016}\right)$	$e\left(\frac{19}{504}\right)$
$\chi_{4034}(17,\cdot)$	4034.bh	672	no	$-1$	$1$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{377}{672}\right)$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{271}{672}\right)$	$e\left(\frac{113}{224}\right)$	$e\left(\frac{25}{672}\right)$	$e\left(\frac{85}{168}\right)$
$\chi_{4034}(19,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{19}{1008}\right)$	$e\left(\frac{1697}{2016}\right)$	$e\left(\frac{199}{1008}\right)$	$e\left(\frac{19}{504}\right)$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{1735}{2016}\right)$	$e\left(\frac{25}{672}\right)$	$e\left(\frac{961}{2016}\right)$	$e\left(\frac{109}{504}\right)$
$\chi_{4034}(21,\cdot)$	4034.bg	504	no	$1$	$1$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{461}{504}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{19}{504}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{109}{504}\right)$	$e\left(\frac{85}{126}\right)$
$\chi_{4034}(23,\cdot)$	4034.bg	504	no	$1$	$1$	$e\left(\frac{145}{252}\right)$	$e\left(\frac{59}{504}\right)$	$e\left(\frac{73}{252}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{349}{504}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{331}{504}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{4034}(25,\cdot)$	4034.bi	1008	no	$1$	$1$	$e\left(\frac{11}{504}\right)$	$e\left(\frac{1}{1008}\right)$	$e\left(\frac{407}{504}\right)$	$e\left(\frac{11}{252}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{23}{1008}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{689}{1008}\right)$	$e\left(\frac{209}{252}\right)$
$\chi_{4034}(27,\cdot)$	4034.bf	336	no	$1$	$1$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{4034}(29,\cdot)$	4034.bf	336	no	$1$	$1$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{4034}(31,\cdot)$	4034.bf	336	no	$1$	$1$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{263}{336}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{4034}(33,\cdot)$	4034.bf	336	no	$1$	$1$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{4034}(35,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{397}{1008}\right)$	$e\left(\frac{815}{2016}\right)$	$e\left(\frac{73}{1008}\right)$	$e\left(\frac{397}{504}\right)$	$e\left(\frac{71}{252}\right)$	$e\left(\frac{235}{288}\right)$	$e\left(\frac{1609}{2016}\right)$	$e\left(\frac{151}{672}\right)$	$e\left(\frac{79}{2016}\right)$	$e\left(\frac{235}{504}\right)$
$\chi_{4034}(37,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{979}{1008}\right)$	$e\left(\frac{1601}{2016}\right)$	$e\left(\frac{439}{1008}\right)$	$e\left(\frac{475}{504}\right)$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{133}{288}\right)$	$e\left(\frac{1543}{2016}\right)$	$e\left(\frac{121}{672}\right)$	$e\left(\frac{1345}{2016}\right)$	$e\left(\frac{205}{504}\right)$
$\chi_{4034}(39,\cdot)$	4034.bc	224	no	$-1$	$1$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{71}{224}\right)$	$e\left(\frac{107}{224}\right)$	$e\left(\frac{33}{224}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{4034}(41,\cdot)$	4034.bi	1008	no	$1$	$1$	$e\left(\frac{109}{504}\right)$	$e\left(\frac{743}{1008}\right)$	$e\left(\frac{1}{504}\right)$	$e\left(\frac{109}{252}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{961}{1008}\right)$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{871}{1008}\right)$	$e\left(\frac{55}{252}\right)$
$\chi_{4034}(43,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{557}{1008}\right)$	$e\left(\frac{463}{2016}\right)$	$e\left(\frac{953}{1008}\right)$	$e\left(\frac{53}{504}\right)$	$e\left(\frac{19}{252}\right)$	$e\left(\frac{107}{288}\right)$	$e\left(\frac{1577}{2016}\right)$	$e\left(\frac{503}{672}\right)$	$e\left(\frac{1487}{2016}\right)$	$e\left(\frac{251}{504}\right)$
$\chi_{4034}(45,\cdot)$	4034.bc	224	no	$-1$	$1$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{5}{224}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{224}\right)$	$e\left(\frac{55}{224}\right)$	$e\left(\frac{197}{224}\right)$	$e\left(\frac{9}{56}\right)$
$\chi_{4034}(47,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{103}{1008}\right)$	$e\left(\frac{1613}{2016}\right)$	$e\left(\frac{283}{1008}\right)$	$e\left(\frac{103}{504}\right)$	$e\left(\frac{113}{252}\right)$	$e\left(\frac{193}{288}\right)$	$e\left(\frac{1819}{2016}\right)$	$e\left(\frac{613}{672}\right)$	$e\left(\frac{1549}{2016}\right)$	$e\left(\frac{193}{504}\right)$
$\chi_{4034}(49,\cdot)$	4034.bg	504	no	$1$	$1$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{407}{504}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{289}{504}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{199}{504}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{4034}(51,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{83}{1008}\right)$	$e\left(\frac{145}{2016}\right)$	$e\left(\frac{551}{1008}\right)$	$e\left(\frac{83}{504}\right)$	$e\left(\frac{25}{252}\right)$	$e\left(\frac{245}{288}\right)$	$e\left(\frac{311}{2016}\right)$	$e\left(\frac{233}{672}\right)$	$e\left(\frac{113}{2016}\right)$	$e\left(\frac{317}{504}\right)$
$\chi_{4034}(53,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{901}{1008}\right)$	$e\left(\frac{311}{2016}\right)$	$e\left(\frac{577}{1008}\right)$	$e\left(\frac{397}{504}\right)$	$e\left(\frac{71}{252}\right)$	$e\left(\frac{19}{288}\right)$	$e\left(\frac{97}{2016}\right)$	$e\left(\frac{319}{672}\right)$	$e\left(\frac{1591}{2016}\right)$	$e\left(\frac{235}{504}\right)$
$\chi_{4034}(55,\cdot)$	4034.bh	672	no	$-1$	$1$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{163}{672}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{53}{672}\right)$	$e\left(\frac{75}{224}\right)$	$e\left(\frac{419}{672}\right)$	$e\left(\frac{47}{168}\right)$
$\chi_{4034}(57,\cdot)$	4034.bc	224	no	$-1$	$1$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{79}{224}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{197}{224}\right)$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{4034}(59,\cdot)$	4034.bj	2016	no	$-1$	$1$	$e\left(\frac{157}{1008}\right)$	$e\left(\frac{335}{2016}\right)$	$e\left(\frac{265}{1008}\right)$	$e\left(\frac{157}{504}\right)$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{139}{288}\right)$	$e\left(\frac{649}{2016}\right)$	$e\left(\frac{631}{672}\right)$	$e\left(\frac{1999}{2016}\right)$	$e\left(\frac{211}{504}\right)$
$\chi_{4034}(61,\cdot)$	4034.y	112	no	$1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{4034}(63,\cdot)$	4034.bf	336	no	$1$	$1$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{67}{84}\right)$

Click here to search among the remaining 1984 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	$4034$
Structure	\(C_{2016}\)
Order	$2016$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4034}(1,\cdot)\)	4034.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4034}(3,\cdot)\)	4034.bi	1008	no	\(1\)	\(1\)	\(e\left(\frac{121}{504}\right)\)	\(e\left(\frac{515}{1008}\right)\)	\(e\left(\frac{445}{504}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{757}{1008}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{19}{1008}\right)\)	\(e\left(\frac{31}{252}\right)\)
\(\chi_{4034}(5,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{515}{1008}\right)\)	\(e\left(\frac{1}{2016}\right)\)	\(e\left(\frac{407}{1008}\right)\)	\(e\left(\frac{11}{504}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{101}{288}\right)\)	\(e\left(\frac{1031}{2016}\right)\)	\(e\left(\frac{377}{672}\right)\)	\(e\left(\frac{1697}{2016}\right)\)	\(e\left(\frac{461}{504}\right)\)
\(\chi_{4034}(7,\cdot)\)	4034.bi	1008	no	\(1\)	\(1\)	\(e\left(\frac{445}{504}\right)\)	\(e\left(\frac{407}{1008}\right)\)	\(e\left(\frac{337}{504}\right)\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{289}{1008}\right)\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{199}{1008}\right)\)	\(e\left(\frac{139}{252}\right)\)
\(\chi_{4034}(9,\cdot)\)	4034.bg	504	no	\(1\)	\(1\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{11}{504}\right)\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{253}{504}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{19}{504}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{4034}(11,\cdot)\)	4034.bd	252	no	\(1\)	\(1\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{4034}(13,\cdot)\)	4034.be	288	no	\(-1\)	\(1\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{101}{288}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{271}{288}\right)\)	\(e\left(\frac{163}{288}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{4034}(15,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{757}{1008}\right)\)	\(e\left(\frac{1031}{2016}\right)\)	\(e\left(\frac{289}{1008}\right)\)	\(e\left(\frac{253}{504}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{163}{288}\right)\)	\(e\left(\frac{529}{2016}\right)\)	\(e\left(\frac{271}{672}\right)\)	\(e\left(\frac{1735}{2016}\right)\)	\(e\left(\frac{19}{504}\right)\)
\(\chi_{4034}(17,\cdot)\)	4034.bh	672	no	\(-1\)	\(1\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{377}{672}\right)\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{271}{672}\right)\)	\(e\left(\frac{113}{224}\right)\)	\(e\left(\frac{25}{672}\right)\)	\(e\left(\frac{85}{168}\right)\)
\(\chi_{4034}(19,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{19}{1008}\right)\)	\(e\left(\frac{1697}{2016}\right)\)	\(e\left(\frac{199}{1008}\right)\)	\(e\left(\frac{19}{504}\right)\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{1735}{2016}\right)\)	\(e\left(\frac{25}{672}\right)\)	\(e\left(\frac{961}{2016}\right)\)	\(e\left(\frac{109}{504}\right)\)
\(\chi_{4034}(21,\cdot)\)	4034.bg	504	no	\(1\)	\(1\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{461}{504}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{19}{504}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{109}{504}\right)\)	\(e\left(\frac{85}{126}\right)\)
\(\chi_{4034}(23,\cdot)\)	4034.bg	504	no	\(1\)	\(1\)	\(e\left(\frac{145}{252}\right)\)	\(e\left(\frac{59}{504}\right)\)	\(e\left(\frac{73}{252}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{349}{504}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{331}{504}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{4034}(25,\cdot)\)	4034.bi	1008	no	\(1\)	\(1\)	\(e\left(\frac{11}{504}\right)\)	\(e\left(\frac{1}{1008}\right)\)	\(e\left(\frac{407}{504}\right)\)	\(e\left(\frac{11}{252}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{23}{1008}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{689}{1008}\right)\)	\(e\left(\frac{209}{252}\right)\)
\(\chi_{4034}(27,\cdot)\)	4034.bf	336	no	\(1\)	\(1\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{4034}(29,\cdot)\)	4034.bf	336	no	\(1\)	\(1\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{4034}(31,\cdot)\)	4034.bf	336	no	\(1\)	\(1\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{263}{336}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{4034}(33,\cdot)\)	4034.bf	336	no	\(1\)	\(1\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{4034}(35,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{397}{1008}\right)\)	\(e\left(\frac{815}{2016}\right)\)	\(e\left(\frac{73}{1008}\right)\)	\(e\left(\frac{397}{504}\right)\)	\(e\left(\frac{71}{252}\right)\)	\(e\left(\frac{235}{288}\right)\)	\(e\left(\frac{1609}{2016}\right)\)	\(e\left(\frac{151}{672}\right)\)	\(e\left(\frac{79}{2016}\right)\)	\(e\left(\frac{235}{504}\right)\)
\(\chi_{4034}(37,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{979}{1008}\right)\)	\(e\left(\frac{1601}{2016}\right)\)	\(e\left(\frac{439}{1008}\right)\)	\(e\left(\frac{475}{504}\right)\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{133}{288}\right)\)	\(e\left(\frac{1543}{2016}\right)\)	\(e\left(\frac{121}{672}\right)\)	\(e\left(\frac{1345}{2016}\right)\)	\(e\left(\frac{205}{504}\right)\)
\(\chi_{4034}(39,\cdot)\)	4034.bc	224	no	\(-1\)	\(1\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{71}{224}\right)\)	\(e\left(\frac{107}{224}\right)\)	\(e\left(\frac{33}{224}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{4034}(41,\cdot)\)	4034.bi	1008	no	\(1\)	\(1\)	\(e\left(\frac{109}{504}\right)\)	\(e\left(\frac{743}{1008}\right)\)	\(e\left(\frac{1}{504}\right)\)	\(e\left(\frac{109}{252}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{961}{1008}\right)\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{871}{1008}\right)\)	\(e\left(\frac{55}{252}\right)\)
\(\chi_{4034}(43,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{557}{1008}\right)\)	\(e\left(\frac{463}{2016}\right)\)	\(e\left(\frac{953}{1008}\right)\)	\(e\left(\frac{53}{504}\right)\)	\(e\left(\frac{19}{252}\right)\)	\(e\left(\frac{107}{288}\right)\)	\(e\left(\frac{1577}{2016}\right)\)	\(e\left(\frac{503}{672}\right)\)	\(e\left(\frac{1487}{2016}\right)\)	\(e\left(\frac{251}{504}\right)\)
\(\chi_{4034}(45,\cdot)\)	4034.bc	224	no	\(-1\)	\(1\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{224}\right)\)	\(e\left(\frac{55}{224}\right)\)	\(e\left(\frac{197}{224}\right)\)	\(e\left(\frac{9}{56}\right)\)
\(\chi_{4034}(47,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{103}{1008}\right)\)	\(e\left(\frac{1613}{2016}\right)\)	\(e\left(\frac{283}{1008}\right)\)	\(e\left(\frac{103}{504}\right)\)	\(e\left(\frac{113}{252}\right)\)	\(e\left(\frac{193}{288}\right)\)	\(e\left(\frac{1819}{2016}\right)\)	\(e\left(\frac{613}{672}\right)\)	\(e\left(\frac{1549}{2016}\right)\)	\(e\left(\frac{193}{504}\right)\)
\(\chi_{4034}(49,\cdot)\)	4034.bg	504	no	\(1\)	\(1\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{407}{504}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{289}{504}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{199}{504}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{4034}(51,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{83}{1008}\right)\)	\(e\left(\frac{145}{2016}\right)\)	\(e\left(\frac{551}{1008}\right)\)	\(e\left(\frac{83}{504}\right)\)	\(e\left(\frac{25}{252}\right)\)	\(e\left(\frac{245}{288}\right)\)	\(e\left(\frac{311}{2016}\right)\)	\(e\left(\frac{233}{672}\right)\)	\(e\left(\frac{113}{2016}\right)\)	\(e\left(\frac{317}{504}\right)\)
\(\chi_{4034}(53,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{901}{1008}\right)\)	\(e\left(\frac{311}{2016}\right)\)	\(e\left(\frac{577}{1008}\right)\)	\(e\left(\frac{397}{504}\right)\)	\(e\left(\frac{71}{252}\right)\)	\(e\left(\frac{19}{288}\right)\)	\(e\left(\frac{97}{2016}\right)\)	\(e\left(\frac{319}{672}\right)\)	\(e\left(\frac{1591}{2016}\right)\)	\(e\left(\frac{235}{504}\right)\)
\(\chi_{4034}(55,\cdot)\)	4034.bh	672	no	\(-1\)	\(1\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{163}{672}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{53}{672}\right)\)	\(e\left(\frac{75}{224}\right)\)	\(e\left(\frac{419}{672}\right)\)	\(e\left(\frac{47}{168}\right)\)
\(\chi_{4034}(57,\cdot)\)	4034.bc	224	no	\(-1\)	\(1\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{79}{224}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{197}{224}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{4034}(59,\cdot)\)	4034.bj	2016	no	\(-1\)	\(1\)	\(e\left(\frac{157}{1008}\right)\)	\(e\left(\frac{335}{2016}\right)\)	\(e\left(\frac{265}{1008}\right)\)	\(e\left(\frac{157}{504}\right)\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{139}{288}\right)\)	\(e\left(\frac{649}{2016}\right)\)	\(e\left(\frac{631}{672}\right)\)	\(e\left(\frac{1999}{2016}\right)\)	\(e\left(\frac{211}{504}\right)\)
\(\chi_{4034}(61,\cdot)\)	4034.y	112	no	\(1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{4034}(63,\cdot)\)	4034.bf	336	no	\(1\)	\(1\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{67}{84}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 2016 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.