LMFDB - Group of Dirichlet characters of modulus 508032

Show commands: PariGP / SageMath

sage: H = DirichletGroup(508032)

pari: g = idealstar(,508032,2)

Character group

sage: G.order() pari: g.no
Order	=	145152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{6048}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{508032}(500095,\cdot)$, $\chi_{508032}(15877,\cdot)$, $\chi_{508032}(275969,\cdot)$, $\chi_{508032}(456193,\cdot)$

First 32 of 145152 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{508032}(1,\cdot)$	508032.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{508032}(5,\cdot)$	508032.bof	6048	yes	$1$	$1$	$e\left(\frac{5149}{6048}\right)$	$e\left(\frac{4913}{6048}\right)$	$e\left(\frac{4003}{6048}\right)$	$e\left(\frac{97}{504}\right)$	$e\left(\frac{95}{288}\right)$	$e\left(\frac{1091}{3024}\right)$	$e\left(\frac{2125}{3024}\right)$	$e\left(\frac{191}{6048}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{1543}{2016}\right)$
$\chi_{508032}(11,\cdot)$	508032.bol	6048	yes	$1$	$1$	$e\left(\frac{4913}{6048}\right)$	$e\left(\frac{3061}{6048}\right)$	$e\left(\frac{1199}{6048}\right)$	$e\left(\frac{65}{504}\right)$	$e\left(\frac{139}{288}\right)$	$e\left(\frac{1591}{3024}\right)$	$e\left(\frac{1889}{3024}\right)$	$e\left(\frac{4651}{6048}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{2003}{2016}\right)$
$\chi_{508032}(13,\cdot)$	508032.boh	6048	yes	$-1$	$1$	$e\left(\frac{4003}{6048}\right)$	$e\left(\frac{1199}{6048}\right)$	$e\left(\frac{877}{6048}\right)$	$e\left(\frac{331}{504}\right)$	$e\left(\frac{113}{288}\right)$	$e\left(\frac{149}{3024}\right)$	$e\left(\frac{979}{3024}\right)$	$e\left(\frac{1697}{6048}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{169}{2016}\right)$
$\chi_{508032}(17,\cdot)$	508032.bgk	504	no	$1$	$1$	$e\left(\frac{97}{504}\right)$	$e\left(\frac{65}{504}\right)$	$e\left(\frac{331}{504}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{149}{252}\right)$	$e\left(\frac{97}{252}\right)$	$e\left(\frac{479}{504}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{508032}(19,\cdot)$	508032.bbz	288	no	$1$	$1$	$e\left(\frac{95}{288}\right)$	$e\left(\frac{139}{288}\right)$	$e\left(\frac{113}{288}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{85}{288}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{508032}(23,\cdot)$	508032.bne	3024	no	$1$	$1$	$e\left(\frac{1091}{3024}\right)$	$e\left(\frac{1591}{3024}\right)$	$e\left(\frac{149}{3024}\right)$	$e\left(\frac{149}{252}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{373}{1512}\right)$	$e\left(\frac{1091}{1512}\right)$	$e\left(\frac{1921}{3024}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{449}{1008}\right)$
$\chi_{508032}(25,\cdot)$	508032.bnk	3024	no	$1$	$1$	$e\left(\frac{2125}{3024}\right)$	$e\left(\frac{1889}{3024}\right)$	$e\left(\frac{979}{3024}\right)$	$e\left(\frac{97}{252}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{1091}{1512}\right)$	$e\left(\frac{613}{1512}\right)$	$e\left(\frac{191}{3024}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{535}{1008}\right)$
$\chi_{508032}(29,\cdot)$	508032.bnz	6048	yes	$-1$	$1$	$e\left(\frac{191}{6048}\right)$	$e\left(\frac{4651}{6048}\right)$	$e\left(\frac{1697}{6048}\right)$	$e\left(\frac{479}{504}\right)$	$e\left(\frac{85}{288}\right)$	$e\left(\frac{1921}{3024}\right)$	$e\left(\frac{191}{3024}\right)$	$e\left(\frac{5125}{6048}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{1181}{2016}\right)$
$\chi_{508032}(31,\cdot)$	508032.uh	108	no	$1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{508032}(37,\cdot)$	508032.bmn	2016	no	$1$	$1$	$e\left(\frac{1543}{2016}\right)$	$e\left(\frac{2003}{2016}\right)$	$e\left(\frac{169}{2016}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{449}{1008}\right)$	$e\left(\frac{535}{1008}\right)$	$e\left(\frac{1181}{2016}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{389}{672}\right)$
$\chi_{508032}(41,\cdot)$	508032.bnb	3024	no	$1$	$1$	$e\left(\frac{2627}{3024}\right)$	$e\left(\frac{2215}{3024}\right)$	$e\left(\frac{2117}{3024}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{745}{1512}\right)$	$e\left(\frac{1115}{1512}\right)$	$e\left(\frac{169}{3024}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{89}{1008}\right)$
$\chi_{508032}(43,\cdot)$	508032.boj	6048	yes	$-1$	$1$	$e\left(\frac{2537}{6048}\right)$	$e\left(\frac{3277}{6048}\right)$	$e\left(\frac{3431}{6048}\right)$	$e\left(\frac{197}{504}\right)$	$e\left(\frac{259}{288}\right)$	$e\left(\frac{295}{3024}\right)$	$e\left(\frac{2537}{3024}\right)$	$e\left(\frac{691}{6048}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{683}{2016}\right)$
$\chi_{508032}(47,\cdot)$	508032.blv	1512	no	$-1$	$1$	$e\left(\frac{1223}{1512}\right)$	$e\left(\frac{1243}{1512}\right)$	$e\left(\frac{893}{1512}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{529}{756}\right)$	$e\left(\frac{467}{756}\right)$	$e\left(\frac{97}{1512}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{317}{504}\right)$
$\chi_{508032}(53,\cdot)$	508032.bht	672	no	$-1$	$1$	$e\left(\frac{51}{224}\right)$	$e\left(\frac{143}{224}\right)$	$e\left(\frac{583}{672}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{227}{672}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{353}{672}\right)$
$\chi_{508032}(55,\cdot)$	508032.bdc	336	no	$1$	$1$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{85}{112}\right)$
$\chi_{508032}(59,\cdot)$	508032.bop	6048	yes	$-1$	$1$	$e\left(\frac{5869}{6048}\right)$	$e\left(\frac{5489}{6048}\right)$	$e\left(\frac{1555}{6048}\right)$	$e\left(\frac{337}{504}\right)$	$e\left(\frac{287}{288}\right)$	$e\left(\frac{155}{3024}\right)$	$e\left(\frac{2845}{3024}\right)$	$e\left(\frac{47}{6048}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{151}{2016}\right)$
$\chi_{508032}(61,\cdot)$	508032.bnt	6048	yes	$-1$	$1$	$e\left(\frac{2039}{6048}\right)$	$e\left(\frac{2803}{6048}\right)$	$e\left(\frac{1529}{6048}\right)$	$e\left(\frac{479}{504}\right)$	$e\left(\frac{13}{288}\right)$	$e\left(\frac{2593}{3024}\right)$	$e\left(\frac{2039}{3024}\right)$	$e\left(\frac{2269}{6048}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{1349}{2016}\right)$
$\chi_{508032}(65,\cdot)$	508032.bes	378	no	$-1$	$1$	$e\left(\frac{97}{189}\right)$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{305}{378}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{155}{378}\right)$	$e\left(\frac{5}{189}\right)$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{107}{126}\right)$
$\chi_{508032}(67,\cdot)$	508032.bjw	864	no	$-1$	$1$	$e\left(\frac{577}{864}\right)$	$e\left(\frac{197}{864}\right)$	$e\left(\frac{367}{864}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{47}{432}\right)$	$e\left(\frac{145}{432}\right)$	$e\left(\frac{155}{864}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{115}{288}\right)$
$\chi_{508032}(71,\cdot)$	508032.bkf	1008	no	$1$	$1$	$e\left(\frac{107}{1008}\right)$	$e\left(\frac{703}{1008}\right)$	$e\left(\frac{605}{1008}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{493}{504}\right)$	$e\left(\frac{107}{504}\right)$	$e\left(\frac{169}{1008}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{89}{336}\right)$
$\chi_{508032}(73,\cdot)$	508032.bkx	1008	no	$-1$	$1$	$e\left(\frac{13}{1008}\right)$	$e\left(\frac{905}{1008}\right)$	$e\left(\frac{835}{1008}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{107}{504}\right)$	$e\left(\frac{13}{504}\right)$	$e\left(\frac{983}{1008}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{239}{336}\right)$
$\chi_{508032}(79,\cdot)$	508032.zy	216	no	$-1$	$1$	$e\left(\frac{47}{216}\right)$	$e\left(\frac{151}{216}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{13}{216}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{72}\right)$
$\chi_{508032}(83,\cdot)$	508032.bob	6048	yes	$-1$	$1$	$e\left(\frac{5195}{6048}\right)$	$e\left(\frac{5479}{6048}\right)$	$e\left(\frac{3029}{6048}\right)$	$e\left(\frac{47}{504}\right)$	$e\left(\frac{265}{288}\right)$	$e\left(\frac{2749}{3024}\right)$	$e\left(\frac{2171}{3024}\right)$	$e\left(\frac{2713}{6048}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{209}{2016}\right)$
$\chi_{508032}(85,\cdot)$	508032.boa	6048	yes	$1$	$1$	$e\left(\frac{265}{6048}\right)$	$e\left(\frac{5693}{6048}\right)$	$e\left(\frac{1927}{6048}\right)$	$e\left(\frac{373}{504}\right)$	$e\left(\frac{179}{288}\right)$	$e\left(\frac{2879}{3024}\right)$	$e\left(\frac{265}{3024}\right)$	$e\left(\frac{5939}{6048}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{715}{2016}\right)$
$\chi_{508032}(89,\cdot)$	508032.bkq	1008	no	$1$	$1$	$e\left(\frac{727}{1008}\right)$	$e\left(\frac{443}{1008}\right)$	$e\left(\frac{961}{1008}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{149}{504}\right)$	$e\left(\frac{223}{504}\right)$	$e\left(\frac{101}{1008}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{103}{112}\right)$
$\chi_{508032}(95,\cdot)$	508032.bir	756	no	$1$	$1$	$e\left(\frac{137}{756}\right)$	$e\left(\frac{223}{756}\right)$	$e\left(\frac{41}{756}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{139}{378}\right)$	$e\left(\frac{137}{378}\right)$	$e\left(\frac{247}{756}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{185}{252}\right)$
$\chi_{508032}(97,\cdot)$	508032.tx	108	no	$-1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{508032}(101,\cdot)$	508032.bof	6048	yes	$1$	$1$	$e\left(\frac{3749}{6048}\right)$	$e\left(\frac{5305}{6048}\right)$	$e\left(\frac{4283}{6048}\right)$	$e\left(\frac{377}{504}\right)$	$e\left(\frac{151}{288}\right)$	$e\left(\frac{2827}{3024}\right)$	$e\left(\frac{725}{3024}\right)$	$e\left(\frac{919}{6048}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{479}{2016}\right)$
$\chi_{508032}(103,\cdot)$	508032.bni	3024	no	$1$	$1$	$e\left(\frac{149}{3024}\right)$	$e\left(\frac{2425}{3024}\right)$	$e\left(\frac{2411}{3024}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{703}{1512}\right)$	$e\left(\frac{149}{1512}\right)$	$e\left(\frac{2143}{3024}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{551}{1008}\right)$
$\chi_{508032}(107,\cdot)$	508032.bhz	672	no	$1$	$1$	$e\left(\frac{139}{224}\right)$	$e\left(\frac{23}{224}\right)$	$e\left(\frac{671}{672}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{667}{672}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{457}{672}\right)$
$\chi_{508032}(109,\cdot)$	508032.bhc	672	no	$1$	$1$	$e\left(\frac{1}{224}\right)$	$e\left(\frac{117}{224}\right)$	$e\left(\frac{589}{672}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{593}{672}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{299}{672}\right)$

Click here to search among the remaining 145120 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	$508032$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{6048}\)
Order	$145152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{508032}(1,\cdot)\)	508032.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{508032}(5,\cdot)\)	508032.bof	6048	yes	\(1\)	\(1\)	\(e\left(\frac{5149}{6048}\right)\)	\(e\left(\frac{4913}{6048}\right)\)	\(e\left(\frac{4003}{6048}\right)\)	\(e\left(\frac{97}{504}\right)\)	\(e\left(\frac{95}{288}\right)\)	\(e\left(\frac{1091}{3024}\right)\)	\(e\left(\frac{2125}{3024}\right)\)	\(e\left(\frac{191}{6048}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{1543}{2016}\right)\)
\(\chi_{508032}(11,\cdot)\)	508032.bol	6048	yes	\(1\)	\(1\)	\(e\left(\frac{4913}{6048}\right)\)	\(e\left(\frac{3061}{6048}\right)\)	\(e\left(\frac{1199}{6048}\right)\)	\(e\left(\frac{65}{504}\right)\)	\(e\left(\frac{139}{288}\right)\)	\(e\left(\frac{1591}{3024}\right)\)	\(e\left(\frac{1889}{3024}\right)\)	\(e\left(\frac{4651}{6048}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{2003}{2016}\right)\)
\(\chi_{508032}(13,\cdot)\)	508032.boh	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{4003}{6048}\right)\)	\(e\left(\frac{1199}{6048}\right)\)	\(e\left(\frac{877}{6048}\right)\)	\(e\left(\frac{331}{504}\right)\)	\(e\left(\frac{113}{288}\right)\)	\(e\left(\frac{149}{3024}\right)\)	\(e\left(\frac{979}{3024}\right)\)	\(e\left(\frac{1697}{6048}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{169}{2016}\right)\)
\(\chi_{508032}(17,\cdot)\)	508032.bgk	504	no	\(1\)	\(1\)	\(e\left(\frac{97}{504}\right)\)	\(e\left(\frac{65}{504}\right)\)	\(e\left(\frac{331}{504}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{149}{252}\right)\)	\(e\left(\frac{97}{252}\right)\)	\(e\left(\frac{479}{504}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{508032}(19,\cdot)\)	508032.bbz	288	no	\(1\)	\(1\)	\(e\left(\frac{95}{288}\right)\)	\(e\left(\frac{139}{288}\right)\)	\(e\left(\frac{113}{288}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{85}{288}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{508032}(23,\cdot)\)	508032.bne	3024	no	\(1\)	\(1\)	\(e\left(\frac{1091}{3024}\right)\)	\(e\left(\frac{1591}{3024}\right)\)	\(e\left(\frac{149}{3024}\right)\)	\(e\left(\frac{149}{252}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{373}{1512}\right)\)	\(e\left(\frac{1091}{1512}\right)\)	\(e\left(\frac{1921}{3024}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{449}{1008}\right)\)
\(\chi_{508032}(25,\cdot)\)	508032.bnk	3024	no	\(1\)	\(1\)	\(e\left(\frac{2125}{3024}\right)\)	\(e\left(\frac{1889}{3024}\right)\)	\(e\left(\frac{979}{3024}\right)\)	\(e\left(\frac{97}{252}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{1091}{1512}\right)\)	\(e\left(\frac{613}{1512}\right)\)	\(e\left(\frac{191}{3024}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{535}{1008}\right)\)
\(\chi_{508032}(29,\cdot)\)	508032.bnz	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{6048}\right)\)	\(e\left(\frac{4651}{6048}\right)\)	\(e\left(\frac{1697}{6048}\right)\)	\(e\left(\frac{479}{504}\right)\)	\(e\left(\frac{85}{288}\right)\)	\(e\left(\frac{1921}{3024}\right)\)	\(e\left(\frac{191}{3024}\right)\)	\(e\left(\frac{5125}{6048}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{1181}{2016}\right)\)
\(\chi_{508032}(31,\cdot)\)	508032.uh	108	no	\(1\)	\(1\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{508032}(37,\cdot)\)	508032.bmn	2016	no	\(1\)	\(1\)	\(e\left(\frac{1543}{2016}\right)\)	\(e\left(\frac{2003}{2016}\right)\)	\(e\left(\frac{169}{2016}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{449}{1008}\right)\)	\(e\left(\frac{535}{1008}\right)\)	\(e\left(\frac{1181}{2016}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{389}{672}\right)\)
\(\chi_{508032}(41,\cdot)\)	508032.bnb	3024	no	\(1\)	\(1\)	\(e\left(\frac{2627}{3024}\right)\)	\(e\left(\frac{2215}{3024}\right)\)	\(e\left(\frac{2117}{3024}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{745}{1512}\right)\)	\(e\left(\frac{1115}{1512}\right)\)	\(e\left(\frac{169}{3024}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{89}{1008}\right)\)
\(\chi_{508032}(43,\cdot)\)	508032.boj	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{2537}{6048}\right)\)	\(e\left(\frac{3277}{6048}\right)\)	\(e\left(\frac{3431}{6048}\right)\)	\(e\left(\frac{197}{504}\right)\)	\(e\left(\frac{259}{288}\right)\)	\(e\left(\frac{295}{3024}\right)\)	\(e\left(\frac{2537}{3024}\right)\)	\(e\left(\frac{691}{6048}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{683}{2016}\right)\)
\(\chi_{508032}(47,\cdot)\)	508032.blv	1512	no	\(-1\)	\(1\)	\(e\left(\frac{1223}{1512}\right)\)	\(e\left(\frac{1243}{1512}\right)\)	\(e\left(\frac{893}{1512}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{529}{756}\right)\)	\(e\left(\frac{467}{756}\right)\)	\(e\left(\frac{97}{1512}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{317}{504}\right)\)
\(\chi_{508032}(53,\cdot)\)	508032.bht	672	no	\(-1\)	\(1\)	\(e\left(\frac{51}{224}\right)\)	\(e\left(\frac{143}{224}\right)\)	\(e\left(\frac{583}{672}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{227}{672}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{353}{672}\right)\)
\(\chi_{508032}(55,\cdot)\)	508032.bdc	336	no	\(1\)	\(1\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{85}{112}\right)\)
\(\chi_{508032}(59,\cdot)\)	508032.bop	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{5869}{6048}\right)\)	\(e\left(\frac{5489}{6048}\right)\)	\(e\left(\frac{1555}{6048}\right)\)	\(e\left(\frac{337}{504}\right)\)	\(e\left(\frac{287}{288}\right)\)	\(e\left(\frac{155}{3024}\right)\)	\(e\left(\frac{2845}{3024}\right)\)	\(e\left(\frac{47}{6048}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{151}{2016}\right)\)
\(\chi_{508032}(61,\cdot)\)	508032.bnt	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{2039}{6048}\right)\)	\(e\left(\frac{2803}{6048}\right)\)	\(e\left(\frac{1529}{6048}\right)\)	\(e\left(\frac{479}{504}\right)\)	\(e\left(\frac{13}{288}\right)\)	\(e\left(\frac{2593}{3024}\right)\)	\(e\left(\frac{2039}{3024}\right)\)	\(e\left(\frac{2269}{6048}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{1349}{2016}\right)\)
\(\chi_{508032}(65,\cdot)\)	508032.bes	378	no	\(-1\)	\(1\)	\(e\left(\frac{97}{189}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{305}{378}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{155}{378}\right)\)	\(e\left(\frac{5}{189}\right)\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{107}{126}\right)\)
\(\chi_{508032}(67,\cdot)\)	508032.bjw	864	no	\(-1\)	\(1\)	\(e\left(\frac{577}{864}\right)\)	\(e\left(\frac{197}{864}\right)\)	\(e\left(\frac{367}{864}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{47}{432}\right)\)	\(e\left(\frac{145}{432}\right)\)	\(e\left(\frac{155}{864}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{115}{288}\right)\)
\(\chi_{508032}(71,\cdot)\)	508032.bkf	1008	no	\(1\)	\(1\)	\(e\left(\frac{107}{1008}\right)\)	\(e\left(\frac{703}{1008}\right)\)	\(e\left(\frac{605}{1008}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{493}{504}\right)\)	\(e\left(\frac{107}{504}\right)\)	\(e\left(\frac{169}{1008}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{89}{336}\right)\)
\(\chi_{508032}(73,\cdot)\)	508032.bkx	1008	no	\(-1\)	\(1\)	\(e\left(\frac{13}{1008}\right)\)	\(e\left(\frac{905}{1008}\right)\)	\(e\left(\frac{835}{1008}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{107}{504}\right)\)	\(e\left(\frac{13}{504}\right)\)	\(e\left(\frac{983}{1008}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{239}{336}\right)\)
\(\chi_{508032}(79,\cdot)\)	508032.zy	216	no	\(-1\)	\(1\)	\(e\left(\frac{47}{216}\right)\)	\(e\left(\frac{151}{216}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{13}{216}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{72}\right)\)
\(\chi_{508032}(83,\cdot)\)	508032.bob	6048	yes	\(-1\)	\(1\)	\(e\left(\frac{5195}{6048}\right)\)	\(e\left(\frac{5479}{6048}\right)\)	\(e\left(\frac{3029}{6048}\right)\)	\(e\left(\frac{47}{504}\right)\)	\(e\left(\frac{265}{288}\right)\)	\(e\left(\frac{2749}{3024}\right)\)	\(e\left(\frac{2171}{3024}\right)\)	\(e\left(\frac{2713}{6048}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{209}{2016}\right)\)
\(\chi_{508032}(85,\cdot)\)	508032.boa	6048	yes	\(1\)	\(1\)	\(e\left(\frac{265}{6048}\right)\)	\(e\left(\frac{5693}{6048}\right)\)	\(e\left(\frac{1927}{6048}\right)\)	\(e\left(\frac{373}{504}\right)\)	\(e\left(\frac{179}{288}\right)\)	\(e\left(\frac{2879}{3024}\right)\)	\(e\left(\frac{265}{3024}\right)\)	\(e\left(\frac{5939}{6048}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{715}{2016}\right)\)
\(\chi_{508032}(89,\cdot)\)	508032.bkq	1008	no	\(1\)	\(1\)	\(e\left(\frac{727}{1008}\right)\)	\(e\left(\frac{443}{1008}\right)\)	\(e\left(\frac{961}{1008}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{149}{504}\right)\)	\(e\left(\frac{223}{504}\right)\)	\(e\left(\frac{101}{1008}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{103}{112}\right)\)
\(\chi_{508032}(95,\cdot)\)	508032.bir	756	no	\(1\)	\(1\)	\(e\left(\frac{137}{756}\right)\)	\(e\left(\frac{223}{756}\right)\)	\(e\left(\frac{41}{756}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{139}{378}\right)\)	\(e\left(\frac{137}{378}\right)\)	\(e\left(\frac{247}{756}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{185}{252}\right)\)
\(\chi_{508032}(97,\cdot)\)	508032.tx	108	no	\(-1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{508032}(101,\cdot)\)	508032.bof	6048	yes	\(1\)	\(1\)	\(e\left(\frac{3749}{6048}\right)\)	\(e\left(\frac{5305}{6048}\right)\)	\(e\left(\frac{4283}{6048}\right)\)	\(e\left(\frac{377}{504}\right)\)	\(e\left(\frac{151}{288}\right)\)	\(e\left(\frac{2827}{3024}\right)\)	\(e\left(\frac{725}{3024}\right)\)	\(e\left(\frac{919}{6048}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{479}{2016}\right)\)
\(\chi_{508032}(103,\cdot)\)	508032.bni	3024	no	\(1\)	\(1\)	\(e\left(\frac{149}{3024}\right)\)	\(e\left(\frac{2425}{3024}\right)\)	\(e\left(\frac{2411}{3024}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{703}{1512}\right)\)	\(e\left(\frac{149}{1512}\right)\)	\(e\left(\frac{2143}{3024}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{551}{1008}\right)\)
\(\chi_{508032}(107,\cdot)\)	508032.bhz	672	no	\(1\)	\(1\)	\(e\left(\frac{139}{224}\right)\)	\(e\left(\frac{23}{224}\right)\)	\(e\left(\frac{671}{672}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{667}{672}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{457}{672}\right)\)
\(\chi_{508032}(109,\cdot)\)	508032.bhc	672	no	\(1\)	\(1\)	\(e\left(\frac{1}{224}\right)\)	\(e\left(\frac{117}{224}\right)\)	\(e\left(\frac{589}{672}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{593}{672}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{299}{672}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 145152 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.