LMFDB - Group of Dirichlet characters of modulus 355008

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(355008)

gp:g = idealstar(,355008,2)

magma:G = FullDirichletGroup(355008);

Character group

Order	=	115584	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{14448}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{355008}(321727,\cdot)$, $\chi_{355008}(66565,\cdot)$, $\chi_{355008}(118337,\cdot)$, $\chi_{355008}(85057,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 115584 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{355008}(1,\cdot)$	355008.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{355008}(5,\cdot)$	355008.mg	14448	yes	$1$	$1$	$e\left(\frac{2711}{14448}\right)$	$e\left(\frac{833}{1032}\right)$	$e\left(\frac{3001}{4816}\right)$	$e\left(\frac{1129}{14448}\right)$	$e\left(\frac{2299}{3612}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{4309}{7224}\right)$	$e\left(\frac{2711}{7224}\right)$	$e\left(\frac{8221}{14448}\right)$	$e\left(\frac{1165}{1806}\right)$
$\chi_{355008}(7,\cdot)$	355008.ji	1032	no	$1$	$1$	$e\left(\frac{833}{1032}\right)$	$e\left(\frac{509}{516}\right)$	$e\left(\frac{143}{344}\right)$	$e\left(\frac{475}{1032}\right)$	$e\left(\frac{31}{258}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{373}{516}\right)$	$e\left(\frac{317}{516}\right)$	$e\left(\frac{451}{1032}\right)$	$e\left(\frac{107}{258}\right)$
$\chi_{355008}(11,\cdot)$	355008.lo	4816	yes	$1$	$1$	$e\left(\frac{3001}{4816}\right)$	$e\left(\frac{143}{344}\right)$	$e\left(\frac{2981}{4816}\right)$	$e\left(\frac{1391}{4816}\right)$	$e\left(\frac{641}{1204}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{927}{2408}\right)$	$e\left(\frac{593}{2408}\right)$	$e\left(\frac{179}{4816}\right)$	$e\left(\frac{163}{301}\right)$
$\chi_{355008}(13,\cdot)$	355008.mh	14448	no	$1$	$1$	$e\left(\frac{1129}{14448}\right)$	$e\left(\frac{475}{1032}\right)$	$e\left(\frac{1391}{4816}\right)$	$e\left(\frac{13799}{14448}\right)$	$e\left(\frac{3335}{3612}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{1103}{7224}\right)$	$e\left(\frac{1129}{7224}\right)$	$e\left(\frac{13331}{14448}\right)$	$e\left(\frac{1613}{1806}\right)$
$\chi_{355008}(17,\cdot)$	355008.le	3612	no	$-1$	$1$	$e\left(\frac{2299}{3612}\right)$	$e\left(\frac{31}{258}\right)$	$e\left(\frac{641}{1204}\right)$	$e\left(\frac{3335}{3612}\right)$	$e\left(\frac{1045}{1806}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{346}{903}\right)$	$e\left(\frac{493}{1806}\right)$	$e\left(\frac{3305}{3612}\right)$	$e\left(\frac{37}{903}\right)$
$\chi_{355008}(19,\cdot)$	355008.hs	336	no	$1$	$1$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{121}{336}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{355008}(23,\cdot)$	355008.lu	7224	no	$1$	$1$	$e\left(\frac{4309}{7224}\right)$	$e\left(\frac{373}{516}\right)$	$e\left(\frac{927}{2408}\right)$	$e\left(\frac{1103}{7224}\right)$	$e\left(\frac{346}{903}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{2255}{3612}\right)$	$e\left(\frac{697}{3612}\right)$	$e\left(\frac{3863}{7224}\right)$	$e\left(\frac{1111}{1806}\right)$
$\chi_{355008}(25,\cdot)$	355008.lx	7224	no	$1$	$1$	$e\left(\frac{2711}{7224}\right)$	$e\left(\frac{317}{516}\right)$	$e\left(\frac{593}{2408}\right)$	$e\left(\frac{1129}{7224}\right)$	$e\left(\frac{493}{1806}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{697}{3612}\right)$	$e\left(\frac{2711}{3612}\right)$	$e\left(\frac{997}{7224}\right)$	$e\left(\frac{262}{903}\right)$
$\chi_{355008}(29,\cdot)$	355008.mg	14448	yes	$1$	$1$	$e\left(\frac{8221}{14448}\right)$	$e\left(\frac{451}{1032}\right)$	$e\left(\frac{179}{4816}\right)$	$e\left(\frac{13331}{14448}\right)$	$e\left(\frac{3305}{3612}\right)$	$e\left(\frac{121}{336}\right)$	$e\left(\frac{3863}{7224}\right)$	$e\left(\frac{997}{7224}\right)$	$e\left(\frac{14351}{14448}\right)$	$e\left(\frac{575}{1806}\right)$
$\chi_{355008}(31,\cdot)$	355008.kg	1806	no	$-1$	$1$	$e\left(\frac{1165}{1806}\right)$	$e\left(\frac{107}{258}\right)$	$e\left(\frac{163}{301}\right)$	$e\left(\frac{1613}{1806}\right)$	$e\left(\frac{37}{903}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1111}{1806}\right)$	$e\left(\frac{262}{903}\right)$	$e\left(\frac{575}{1806}\right)$	$e\left(\frac{967}{1806}\right)$
$\chi_{355008}(35,\cdot)$	355008.lo	4816	yes	$1$	$1$	$e\left(\frac{4791}{4816}\right)$	$e\left(\frac{273}{344}\right)$	$e\left(\frac{187}{4816}\right)$	$e\left(\frac{2593}{4816}\right)$	$e\left(\frac{911}{1204}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{769}{2408}\right)$	$e\left(\frac{2383}{2408}\right)$	$e\left(\frac{29}{4816}\right)$	$e\left(\frac{18}{301}\right)$
$\chi_{355008}(37,\cdot)$	355008.ko	2064	no	$-1$	$1$	$e\left(\frac{1745}{2064}\right)$	$e\left(\frac{497}{1032}\right)$	$e\left(\frac{511}{688}\right)$	$e\left(\frac{1879}{2064}\right)$	$e\left(\frac{379}{516}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{607}{1032}\right)$	$e\left(\frac{713}{1032}\right)$	$e\left(\frac{1003}{2064}\right)$	$e\left(\frac{7}{258}\right)$
$\chi_{355008}(41,\cdot)$	355008.la	2408	no	$-1$	$1$	$e\left(\frac{2335}{2408}\right)$	$e\left(\frac{61}{172}\right)$	$e\left(\frac{835}{2408}\right)$	$e\left(\frac{781}{2408}\right)$	$e\left(\frac{108}{301}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{295}{1204}\right)$	$e\left(\frac{1131}{1204}\right)$	$e\left(\frac{181}{2408}\right)$	$e\left(\frac{69}{301}\right)$
$\chi_{355008}(47,\cdot)$	355008.jp	1204	no	$1$	$1$	$e\left(\frac{445}{1204}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{163}{1204}\right)$	$e\left(\frac{921}{1204}\right)$	$e\left(\frac{257}{602}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{519}{602}\right)$	$e\left(\frac{445}{602}\right)$	$e\left(\frac{447}{1204}\right)$	$e\left(\frac{507}{602}\right)$
$\chi_{355008}(49,\cdot)$	355008.id	516	no	$1$	$1$	$e\left(\frac{317}{516}\right)$	$e\left(\frac{251}{258}\right)$	$e\left(\frac{143}{172}\right)$	$e\left(\frac{475}{516}\right)$	$e\left(\frac{31}{129}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{115}{258}\right)$	$e\left(\frac{59}{258}\right)$	$e\left(\frac{451}{516}\right)$	$e\left(\frac{107}{129}\right)$
$\chi_{355008}(53,\cdot)$	355008.me	14448	yes	$-1$	$1$	$e\left(\frac{8363}{14448}\right)$	$e\left(\frac{641}{1032}\right)$	$e\left(\frac{3453}{4816}\right)$	$e\left(\frac{4093}{14448}\right)$	$e\left(\frac{3091}{3612}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{73}{7224}\right)$	$e\left(\frac{1139}{7224}\right)$	$e\left(\frac{13801}{14448}\right)$	$e\left(\frac{1117}{1806}\right)$
$\chi_{355008}(55,\cdot)$	355008.ly	7224	no	$1$	$1$	$e\left(\frac{5857}{7224}\right)$	$e\left(\frac{115}{516}\right)$	$e\left(\frac{583}{2408}\right)$	$e\left(\frac{2651}{7224}\right)$	$e\left(\frac{305}{1806}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{3545}{3612}\right)$	$e\left(\frac{2245}{3612}\right)$	$e\left(\frac{4379}{7224}\right)$	$e\left(\frac{337}{1806}\right)$
$\chi_{355008}(59,\cdot)$	355008.lo	4816	yes	$1$	$1$	$e\left(\frac{2293}{4816}\right)$	$e\left(\frac{155}{344}\right)$	$e\left(\frac{2305}{4816}\right)$	$e\left(\frac{851}{4816}\right)$	$e\left(\frac{97}{1204}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{1611}{2408}\right)$	$e\left(\frac{2293}{2408}\right)$	$e\left(\frac{615}{4816}\right)$	$e\left(\frac{143}{301}\right)$
$\chi_{355008}(61,\cdot)$	355008.mf	14448	no	$-1$	$1$	$e\left(\frac{11533}{14448}\right)$	$e\left(\frac{115}{1032}\right)$	$e\left(\frac{2131}{4816}\right)$	$e\left(\frac{4715}{14448}\right)$	$e\left(\frac{1595}{3612}\right)$	$e\left(\frac{145}{336}\right)$	$e\left(\frac{5867}{7224}\right)$	$e\left(\frac{4309}{7224}\right)$	$e\left(\frac{11087}{14448}\right)$	$e\left(\frac{1007}{1806}\right)$
$\chi_{355008}(65,\cdot)$	355008.iw	602	no	$1$	$1$	$e\left(\frac{80}{301}\right)$	$e\left(\frac{23}{86}\right)$	$e\left(\frac{549}{602}\right)$	$e\left(\frac{10}{301}\right)$	$e\left(\frac{337}{602}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{451}{602}\right)$	$e\left(\frac{160}{301}\right)$	$e\left(\frac{148}{301}\right)$	$e\left(\frac{162}{301}\right)$
$\chi_{355008}(67,\cdot)$	355008.mc	14448	no	$-1$	$1$	$e\left(\frac{5669}{14448}\right)$	$e\left(\frac{1019}{1032}\right)$	$e\left(\frac{827}{4816}\right)$	$e\left(\frac{13915}{14448}\right)$	$e\left(\frac{919}{3612}\right)$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{6655}{7224}\right)$	$e\left(\frac{5669}{7224}\right)$	$e\left(\frac{9991}{14448}\right)$	$e\left(\frac{638}{903}\right)$
$\chi_{355008}(71,\cdot)$	355008.lv	7224	no	$-1$	$1$	$e\left(\frac{899}{7224}\right)$	$e\left(\frac{269}{516}\right)$	$e\left(\frac{2125}{2408}\right)$	$e\left(\frac{5869}{7224}\right)$	$e\left(\frac{410}{903}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{3121}{3612}\right)$	$e\left(\frac{899}{3612}\right)$	$e\left(\frac{2521}{7224}\right)$	$e\left(\frac{1661}{1806}\right)$
$\chi_{355008}(73,\cdot)$	355008.lw	7224	no	$-1$	$1$	$e\left(\frac{953}{7224}\right)$	$e\left(\frac{185}{516}\right)$	$e\left(\frac{979}{2408}\right)$	$e\left(\frac{4747}{7224}\right)$	$e\left(\frac{1489}{1806}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{1171}{3612}\right)$	$e\left(\frac{953}{3612}\right)$	$e\left(\frac{5059}{7224}\right)$	$e\left(\frac{229}{903}\right)$
$\chi_{355008}(77,\cdot)$	355008.mg	14448	yes	$1$	$1$	$e\left(\frac{6217}{14448}\right)$	$e\left(\frac{415}{1032}\right)$	$e\left(\frac{167}{4816}\right)$	$e\left(\frac{10823}{14448}\right)$	$e\left(\frac{2357}{3612}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{779}{7224}\right)$	$e\left(\frac{6217}{7224}\right)$	$e\left(\frac{6851}{14448}\right)$	$e\left(\frac{1727}{1806}\right)$
$\chi_{355008}(79,\cdot)$	355008.ii	516	no	$-1$	$1$	$e\left(\frac{445}{516}\right)$	$e\left(\frac{119}{129}\right)$	$e\left(\frac{169}{172}\right)$	$e\left(\frac{491}{516}\right)$	$e\left(\frac{107}{129}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{109}{129}\right)$	$e\left(\frac{187}{258}\right)$	$e\left(\frac{275}{516}\right)$	$e\left(\frac{77}{258}\right)$
$\chi_{355008}(83,\cdot)$	355008.mb	14448	yes	$1$	$1$	$e\left(\frac{5513}{14448}\right)$	$e\left(\frac{287}{1032}\right)$	$e\left(\frac{3335}{4816}\right)$	$e\left(\frac{10735}{14448}\right)$	$e\left(\frac{2197}{3612}\right)$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{4663}{7224}\right)$	$e\left(\frac{5513}{7224}\right)$	$e\left(\frac{2659}{14448}\right)$	$e\left(\frac{353}{903}\right)$
$\chi_{355008}(85,\cdot)$	355008.jf	688	no	$-1$	$1$	$e\left(\frac{567}{688}\right)$	$e\left(\frac{319}{344}\right)$	$e\left(\frac{107}{688}\right)$	$e\left(\frac{1}{688}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{337}{344}\right)$	$e\left(\frac{223}{344}\right)$	$e\left(\frac{333}{688}\right)$	$e\left(\frac{59}{86}\right)$
$\chi_{355008}(89,\cdot)$	355008.lt	7224	no	$1$	$1$	$e\left(\frac{6463}{7224}\right)$	$e\left(\frac{319}{516}\right)$	$e\left(\frac{565}{2408}\right)$	$e\left(\frac{6113}{7224}\right)$	$e\left(\frac{796}{903}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{2531}{3612}\right)$	$e\left(\frac{2851}{3612}\right)$	$e\left(\frac{3965}{7224}\right)$	$e\left(\frac{542}{903}\right)$
$\chi_{355008}(91,\cdot)$	355008.ma	14448	no	$1$	$1$	$e\left(\frac{12791}{14448}\right)$	$e\left(\frac{461}{1032}\right)$	$e\left(\frac{3393}{4816}\right)$	$e\left(\frac{6001}{14448}\right)$	$e\left(\frac{157}{3612}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{6325}{7224}\right)$	$e\left(\frac{5567}{7224}\right)$	$e\left(\frac{5197}{14448}\right)$	$e\left(\frac{278}{903}\right)$
$\chi_{355008}(95,\cdot)$	355008.ka	1806	no	$1$	$1$	$e\left(\frac{844}{903}\right)$	$e\left(\frac{133}{258}\right)$	$e\left(\frac{531}{602}\right)$	$e\left(\frac{211}{1806}\right)$	$e\left(\frac{139}{1806}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{415}{903}\right)$	$e\left(\frac{785}{903}\right)$	$e\left(\frac{839}{903}\right)$	$e\left(\frac{47}{1806}\right)$
$\chi_{355008}(97,\cdot)$	355008.ik	602	no	$1$	$1$	$e\left(\frac{159}{602}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{111}{602}\right)$	$e\left(\frac{509}{602}\right)$	$e\left(\frac{127}{301}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{178}{301}\right)$	$e\left(\frac{159}{301}\right)$	$e\left(\frac{249}{602}\right)$	$e\left(\frac{240}{301}\right)$

Click here to search among the remaining 115552 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 $\F_{q}$
Belyi maps

Modulus	$355008$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{14448}\)
Order	$115584$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{355008}(1,\cdot)\)	355008.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{355008}(5,\cdot)\)	355008.mg	14448	yes	\(1\)	\(1\)	\(e\left(\frac{2711}{14448}\right)\)	\(e\left(\frac{833}{1032}\right)\)	\(e\left(\frac{3001}{4816}\right)\)	\(e\left(\frac{1129}{14448}\right)\)	\(e\left(\frac{2299}{3612}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{4309}{7224}\right)\)	\(e\left(\frac{2711}{7224}\right)\)	\(e\left(\frac{8221}{14448}\right)\)	\(e\left(\frac{1165}{1806}\right)\)
\(\chi_{355008}(7,\cdot)\)	355008.ji	1032	no	\(1\)	\(1\)	\(e\left(\frac{833}{1032}\right)\)	\(e\left(\frac{509}{516}\right)\)	\(e\left(\frac{143}{344}\right)\)	\(e\left(\frac{475}{1032}\right)\)	\(e\left(\frac{31}{258}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{373}{516}\right)\)	\(e\left(\frac{317}{516}\right)\)	\(e\left(\frac{451}{1032}\right)\)	\(e\left(\frac{107}{258}\right)\)
\(\chi_{355008}(11,\cdot)\)	355008.lo	4816	yes	\(1\)	\(1\)	\(e\left(\frac{3001}{4816}\right)\)	\(e\left(\frac{143}{344}\right)\)	\(e\left(\frac{2981}{4816}\right)\)	\(e\left(\frac{1391}{4816}\right)\)	\(e\left(\frac{641}{1204}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{927}{2408}\right)\)	\(e\left(\frac{593}{2408}\right)\)	\(e\left(\frac{179}{4816}\right)\)	\(e\left(\frac{163}{301}\right)\)
\(\chi_{355008}(13,\cdot)\)	355008.mh	14448	no	\(1\)	\(1\)	\(e\left(\frac{1129}{14448}\right)\)	\(e\left(\frac{475}{1032}\right)\)	\(e\left(\frac{1391}{4816}\right)\)	\(e\left(\frac{13799}{14448}\right)\)	\(e\left(\frac{3335}{3612}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{1103}{7224}\right)\)	\(e\left(\frac{1129}{7224}\right)\)	\(e\left(\frac{13331}{14448}\right)\)	\(e\left(\frac{1613}{1806}\right)\)
\(\chi_{355008}(17,\cdot)\)	355008.le	3612	no	\(-1\)	\(1\)	\(e\left(\frac{2299}{3612}\right)\)	\(e\left(\frac{31}{258}\right)\)	\(e\left(\frac{641}{1204}\right)\)	\(e\left(\frac{3335}{3612}\right)\)	\(e\left(\frac{1045}{1806}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{346}{903}\right)\)	\(e\left(\frac{493}{1806}\right)\)	\(e\left(\frac{3305}{3612}\right)\)	\(e\left(\frac{37}{903}\right)\)
\(\chi_{355008}(19,\cdot)\)	355008.hs	336	no	\(1\)	\(1\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{121}{336}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{355008}(23,\cdot)\)	355008.lu	7224	no	\(1\)	\(1\)	\(e\left(\frac{4309}{7224}\right)\)	\(e\left(\frac{373}{516}\right)\)	\(e\left(\frac{927}{2408}\right)\)	\(e\left(\frac{1103}{7224}\right)\)	\(e\left(\frac{346}{903}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{2255}{3612}\right)\)	\(e\left(\frac{697}{3612}\right)\)	\(e\left(\frac{3863}{7224}\right)\)	\(e\left(\frac{1111}{1806}\right)\)
\(\chi_{355008}(25,\cdot)\)	355008.lx	7224	no	\(1\)	\(1\)	\(e\left(\frac{2711}{7224}\right)\)	\(e\left(\frac{317}{516}\right)\)	\(e\left(\frac{593}{2408}\right)\)	\(e\left(\frac{1129}{7224}\right)\)	\(e\left(\frac{493}{1806}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{697}{3612}\right)\)	\(e\left(\frac{2711}{3612}\right)\)	\(e\left(\frac{997}{7224}\right)\)	\(e\left(\frac{262}{903}\right)\)
\(\chi_{355008}(29,\cdot)\)	355008.mg	14448	yes	\(1\)	\(1\)	\(e\left(\frac{8221}{14448}\right)\)	\(e\left(\frac{451}{1032}\right)\)	\(e\left(\frac{179}{4816}\right)\)	\(e\left(\frac{13331}{14448}\right)\)	\(e\left(\frac{3305}{3612}\right)\)	\(e\left(\frac{121}{336}\right)\)	\(e\left(\frac{3863}{7224}\right)\)	\(e\left(\frac{997}{7224}\right)\)	\(e\left(\frac{14351}{14448}\right)\)	\(e\left(\frac{575}{1806}\right)\)
\(\chi_{355008}(31,\cdot)\)	355008.kg	1806	no	\(-1\)	\(1\)	\(e\left(\frac{1165}{1806}\right)\)	\(e\left(\frac{107}{258}\right)\)	\(e\left(\frac{163}{301}\right)\)	\(e\left(\frac{1613}{1806}\right)\)	\(e\left(\frac{37}{903}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1111}{1806}\right)\)	\(e\left(\frac{262}{903}\right)\)	\(e\left(\frac{575}{1806}\right)\)	\(e\left(\frac{967}{1806}\right)\)
\(\chi_{355008}(35,\cdot)\)	355008.lo	4816	yes	\(1\)	\(1\)	\(e\left(\frac{4791}{4816}\right)\)	\(e\left(\frac{273}{344}\right)\)	\(e\left(\frac{187}{4816}\right)\)	\(e\left(\frac{2593}{4816}\right)\)	\(e\left(\frac{911}{1204}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{769}{2408}\right)\)	\(e\left(\frac{2383}{2408}\right)\)	\(e\left(\frac{29}{4816}\right)\)	\(e\left(\frac{18}{301}\right)\)
\(\chi_{355008}(37,\cdot)\)	355008.ko	2064	no	\(-1\)	\(1\)	\(e\left(\frac{1745}{2064}\right)\)	\(e\left(\frac{497}{1032}\right)\)	\(e\left(\frac{511}{688}\right)\)	\(e\left(\frac{1879}{2064}\right)\)	\(e\left(\frac{379}{516}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{607}{1032}\right)\)	\(e\left(\frac{713}{1032}\right)\)	\(e\left(\frac{1003}{2064}\right)\)	\(e\left(\frac{7}{258}\right)\)
\(\chi_{355008}(41,\cdot)\)	355008.la	2408	no	\(-1\)	\(1\)	\(e\left(\frac{2335}{2408}\right)\)	\(e\left(\frac{61}{172}\right)\)	\(e\left(\frac{835}{2408}\right)\)	\(e\left(\frac{781}{2408}\right)\)	\(e\left(\frac{108}{301}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{295}{1204}\right)\)	\(e\left(\frac{1131}{1204}\right)\)	\(e\left(\frac{181}{2408}\right)\)	\(e\left(\frac{69}{301}\right)\)
\(\chi_{355008}(47,\cdot)\)	355008.jp	1204	no	\(1\)	\(1\)	\(e\left(\frac{445}{1204}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{163}{1204}\right)\)	\(e\left(\frac{921}{1204}\right)\)	\(e\left(\frac{257}{602}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{519}{602}\right)\)	\(e\left(\frac{445}{602}\right)\)	\(e\left(\frac{447}{1204}\right)\)	\(e\left(\frac{507}{602}\right)\)
\(\chi_{355008}(49,\cdot)\)	355008.id	516	no	\(1\)	\(1\)	\(e\left(\frac{317}{516}\right)\)	\(e\left(\frac{251}{258}\right)\)	\(e\left(\frac{143}{172}\right)\)	\(e\left(\frac{475}{516}\right)\)	\(e\left(\frac{31}{129}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{115}{258}\right)\)	\(e\left(\frac{59}{258}\right)\)	\(e\left(\frac{451}{516}\right)\)	\(e\left(\frac{107}{129}\right)\)
\(\chi_{355008}(53,\cdot)\)	355008.me	14448	yes	\(-1\)	\(1\)	\(e\left(\frac{8363}{14448}\right)\)	\(e\left(\frac{641}{1032}\right)\)	\(e\left(\frac{3453}{4816}\right)\)	\(e\left(\frac{4093}{14448}\right)\)	\(e\left(\frac{3091}{3612}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{73}{7224}\right)\)	\(e\left(\frac{1139}{7224}\right)\)	\(e\left(\frac{13801}{14448}\right)\)	\(e\left(\frac{1117}{1806}\right)\)
\(\chi_{355008}(55,\cdot)\)	355008.ly	7224	no	\(1\)	\(1\)	\(e\left(\frac{5857}{7224}\right)\)	\(e\left(\frac{115}{516}\right)\)	\(e\left(\frac{583}{2408}\right)\)	\(e\left(\frac{2651}{7224}\right)\)	\(e\left(\frac{305}{1806}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{3545}{3612}\right)\)	\(e\left(\frac{2245}{3612}\right)\)	\(e\left(\frac{4379}{7224}\right)\)	\(e\left(\frac{337}{1806}\right)\)
\(\chi_{355008}(59,\cdot)\)	355008.lo	4816	yes	\(1\)	\(1\)	\(e\left(\frac{2293}{4816}\right)\)	\(e\left(\frac{155}{344}\right)\)	\(e\left(\frac{2305}{4816}\right)\)	\(e\left(\frac{851}{4816}\right)\)	\(e\left(\frac{97}{1204}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{1611}{2408}\right)\)	\(e\left(\frac{2293}{2408}\right)\)	\(e\left(\frac{615}{4816}\right)\)	\(e\left(\frac{143}{301}\right)\)
\(\chi_{355008}(61,\cdot)\)	355008.mf	14448	no	\(-1\)	\(1\)	\(e\left(\frac{11533}{14448}\right)\)	\(e\left(\frac{115}{1032}\right)\)	\(e\left(\frac{2131}{4816}\right)\)	\(e\left(\frac{4715}{14448}\right)\)	\(e\left(\frac{1595}{3612}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{5867}{7224}\right)\)	\(e\left(\frac{4309}{7224}\right)\)	\(e\left(\frac{11087}{14448}\right)\)	\(e\left(\frac{1007}{1806}\right)\)
\(\chi_{355008}(65,\cdot)\)	355008.iw	602	no	\(1\)	\(1\)	\(e\left(\frac{80}{301}\right)\)	\(e\left(\frac{23}{86}\right)\)	\(e\left(\frac{549}{602}\right)\)	\(e\left(\frac{10}{301}\right)\)	\(e\left(\frac{337}{602}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{451}{602}\right)\)	\(e\left(\frac{160}{301}\right)\)	\(e\left(\frac{148}{301}\right)\)	\(e\left(\frac{162}{301}\right)\)
\(\chi_{355008}(67,\cdot)\)	355008.mc	14448	no	\(-1\)	\(1\)	\(e\left(\frac{5669}{14448}\right)\)	\(e\left(\frac{1019}{1032}\right)\)	\(e\left(\frac{827}{4816}\right)\)	\(e\left(\frac{13915}{14448}\right)\)	\(e\left(\frac{919}{3612}\right)\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{6655}{7224}\right)\)	\(e\left(\frac{5669}{7224}\right)\)	\(e\left(\frac{9991}{14448}\right)\)	\(e\left(\frac{638}{903}\right)\)
\(\chi_{355008}(71,\cdot)\)	355008.lv	7224	no	\(-1\)	\(1\)	\(e\left(\frac{899}{7224}\right)\)	\(e\left(\frac{269}{516}\right)\)	\(e\left(\frac{2125}{2408}\right)\)	\(e\left(\frac{5869}{7224}\right)\)	\(e\left(\frac{410}{903}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{3121}{3612}\right)\)	\(e\left(\frac{899}{3612}\right)\)	\(e\left(\frac{2521}{7224}\right)\)	\(e\left(\frac{1661}{1806}\right)\)
\(\chi_{355008}(73,\cdot)\)	355008.lw	7224	no	\(-1\)	\(1\)	\(e\left(\frac{953}{7224}\right)\)	\(e\left(\frac{185}{516}\right)\)	\(e\left(\frac{979}{2408}\right)\)	\(e\left(\frac{4747}{7224}\right)\)	\(e\left(\frac{1489}{1806}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{1171}{3612}\right)\)	\(e\left(\frac{953}{3612}\right)\)	\(e\left(\frac{5059}{7224}\right)\)	\(e\left(\frac{229}{903}\right)\)
\(\chi_{355008}(77,\cdot)\)	355008.mg	14448	yes	\(1\)	\(1\)	\(e\left(\frac{6217}{14448}\right)\)	\(e\left(\frac{415}{1032}\right)\)	\(e\left(\frac{167}{4816}\right)\)	\(e\left(\frac{10823}{14448}\right)\)	\(e\left(\frac{2357}{3612}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{779}{7224}\right)\)	\(e\left(\frac{6217}{7224}\right)\)	\(e\left(\frac{6851}{14448}\right)\)	\(e\left(\frac{1727}{1806}\right)\)
\(\chi_{355008}(79,\cdot)\)	355008.ii	516	no	\(-1\)	\(1\)	\(e\left(\frac{445}{516}\right)\)	\(e\left(\frac{119}{129}\right)\)	\(e\left(\frac{169}{172}\right)\)	\(e\left(\frac{491}{516}\right)\)	\(e\left(\frac{107}{129}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{109}{129}\right)\)	\(e\left(\frac{187}{258}\right)\)	\(e\left(\frac{275}{516}\right)\)	\(e\left(\frac{77}{258}\right)\)
\(\chi_{355008}(83,\cdot)\)	355008.mb	14448	yes	\(1\)	\(1\)	\(e\left(\frac{5513}{14448}\right)\)	\(e\left(\frac{287}{1032}\right)\)	\(e\left(\frac{3335}{4816}\right)\)	\(e\left(\frac{10735}{14448}\right)\)	\(e\left(\frac{2197}{3612}\right)\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{4663}{7224}\right)\)	\(e\left(\frac{5513}{7224}\right)\)	\(e\left(\frac{2659}{14448}\right)\)	\(e\left(\frac{353}{903}\right)\)
\(\chi_{355008}(85,\cdot)\)	355008.jf	688	no	\(-1\)	\(1\)	\(e\left(\frac{567}{688}\right)\)	\(e\left(\frac{319}{344}\right)\)	\(e\left(\frac{107}{688}\right)\)	\(e\left(\frac{1}{688}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{337}{344}\right)\)	\(e\left(\frac{223}{344}\right)\)	\(e\left(\frac{333}{688}\right)\)	\(e\left(\frac{59}{86}\right)\)
\(\chi_{355008}(89,\cdot)\)	355008.lt	7224	no	\(1\)	\(1\)	\(e\left(\frac{6463}{7224}\right)\)	\(e\left(\frac{319}{516}\right)\)	\(e\left(\frac{565}{2408}\right)\)	\(e\left(\frac{6113}{7224}\right)\)	\(e\left(\frac{796}{903}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{2531}{3612}\right)\)	\(e\left(\frac{2851}{3612}\right)\)	\(e\left(\frac{3965}{7224}\right)\)	\(e\left(\frac{542}{903}\right)\)
\(\chi_{355008}(91,\cdot)\)	355008.ma	14448	no	\(1\)	\(1\)	\(e\left(\frac{12791}{14448}\right)\)	\(e\left(\frac{461}{1032}\right)\)	\(e\left(\frac{3393}{4816}\right)\)	\(e\left(\frac{6001}{14448}\right)\)	\(e\left(\frac{157}{3612}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{6325}{7224}\right)\)	\(e\left(\frac{5567}{7224}\right)\)	\(e\left(\frac{5197}{14448}\right)\)	\(e\left(\frac{278}{903}\right)\)
\(\chi_{355008}(95,\cdot)\)	355008.ka	1806	no	\(1\)	\(1\)	\(e\left(\frac{844}{903}\right)\)	\(e\left(\frac{133}{258}\right)\)	\(e\left(\frac{531}{602}\right)\)	\(e\left(\frac{211}{1806}\right)\)	\(e\left(\frac{139}{1806}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{415}{903}\right)\)	\(e\left(\frac{785}{903}\right)\)	\(e\left(\frac{839}{903}\right)\)	\(e\left(\frac{47}{1806}\right)\)
\(\chi_{355008}(97,\cdot)\)	355008.ik	602	no	\(1\)	\(1\)	\(e\left(\frac{159}{602}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{111}{602}\right)\)	\(e\left(\frac{509}{602}\right)\)	\(e\left(\frac{127}{301}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{178}{301}\right)\)	\(e\left(\frac{159}{301}\right)\)	\(e\left(\frac{249}{602}\right)\)	\(e\left(\frac{240}{301}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 115584 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.