LMFDB - Group of Dirichlet characters of modulus 555579

Show commands: PariGP / SageMath

sage: H = DirichletGroup(555579)

pari: g = idealstar(,555579,2)

Character group

sage: G.order() pari: g.no
Order	=	350892
sage: H.invariants() pari: g.cyc
Structure	=	$C_{18}\times C_{19494}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{555579}(192053,\cdot)$, $\chi_{555579}(363529,\cdot)$

First 32 of 350892 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{555579}(1,\cdot)$	555579.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{555579}(2,\cdot)$	555579.lp	19494	yes	$1$	$1$	$e\left(\frac{182}{9747}\right)$	$e\left(\frac{364}{9747}\right)$	$e\left(\frac{3869}{19494}\right)$	$e\left(\frac{3626}{9747}\right)$	$e\left(\frac{182}{3249}\right)$	$e\left(\frac{1411}{6498}\right)$	$e\left(\frac{2947}{19494}\right)$	$e\left(\frac{19265}{19494}\right)$	$e\left(\frac{3808}{9747}\right)$	$e\left(\frac{728}{9747}\right)$
$\chi_{555579}(4,\cdot)$	555579.ks	9747	yes	$1$	$1$	$e\left(\frac{364}{9747}\right)$	$e\left(\frac{728}{9747}\right)$	$e\left(\frac{3869}{9747}\right)$	$e\left(\frac{7252}{9747}\right)$	$e\left(\frac{364}{3249}\right)$	$e\left(\frac{1411}{3249}\right)$	$e\left(\frac{2947}{9747}\right)$	$e\left(\frac{9518}{9747}\right)$	$e\left(\frac{7616}{9747}\right)$	$e\left(\frac{1456}{9747}\right)$
$\chi_{555579}(5,\cdot)$	555579.lg	19494	yes	$-1$	$1$	$e\left(\frac{3869}{19494}\right)$	$e\left(\frac{3869}{9747}\right)$	$e\left(\frac{18991}{19494}\right)$	$e\left(\frac{8842}{9747}\right)$	$e\left(\frac{3869}{6498}\right)$	$e\left(\frac{187}{1083}\right)$	$e\left(\frac{17849}{19494}\right)$	$e\left(\frac{7142}{9747}\right)$	$e\left(\frac{2059}{19494}\right)$	$e\left(\frac{7738}{9747}\right)$
$\chi_{555579}(7,\cdot)$	555579.kq	9747	yes	$1$	$1$	$e\left(\frac{3626}{9747}\right)$	$e\left(\frac{7252}{9747}\right)$	$e\left(\frac{8842}{9747}\right)$	$e\left(\frac{9677}{9747}\right)$	$e\left(\frac{377}{3249}\right)$	$e\left(\frac{907}{3249}\right)$	$e\left(\frac{7655}{9747}\right)$	$e\left(\frac{6841}{9747}\right)$	$e\left(\frac{3556}{9747}\right)$	$e\left(\frac{4757}{9747}\right)$
$\chi_{555579}(8,\cdot)$	555579.km	6498	no	$1$	$1$	$e\left(\frac{182}{3249}\right)$	$e\left(\frac{364}{3249}\right)$	$e\left(\frac{3869}{6498}\right)$	$e\left(\frac{377}{3249}\right)$	$e\left(\frac{182}{1083}\right)$	$e\left(\frac{1411}{2166}\right)$	$e\left(\frac{2947}{6498}\right)$	$e\left(\frac{6269}{6498}\right)$	$e\left(\frac{559}{3249}\right)$	$e\left(\frac{728}{3249}\right)$
$\chi_{555579}(10,\cdot)$	555579.jy	6498	no	$-1$	$1$	$e\left(\frac{1411}{6498}\right)$	$e\left(\frac{1411}{3249}\right)$	$e\left(\frac{187}{1083}\right)$	$e\left(\frac{907}{3249}\right)$	$e\left(\frac{1411}{2166}\right)$	$e\left(\frac{2533}{6498}\right)$	$e\left(\frac{217}{3249}\right)$	$e\left(\frac{4685}{6498}\right)$	$e\left(\frac{1075}{2166}\right)$	$e\left(\frac{2822}{3249}\right)$
$\chi_{555579}(11,\cdot)$	555579.lu	19494	yes	$-1$	$1$	$e\left(\frac{2947}{19494}\right)$	$e\left(\frac{2947}{9747}\right)$	$e\left(\frac{17849}{19494}\right)$	$e\left(\frac{7655}{9747}\right)$	$e\left(\frac{2947}{6498}\right)$	$e\left(\frac{217}{3249}\right)$	$e\left(\frac{5011}{19494}\right)$	$e\left(\frac{9601}{9747}\right)$	$e\left(\frac{18257}{19494}\right)$	$e\left(\frac{5894}{9747}\right)$
$\chi_{555579}(13,\cdot)$	555579.lk	19494	yes	$-1$	$1$	$e\left(\frac{19265}{19494}\right)$	$e\left(\frac{9518}{9747}\right)$	$e\left(\frac{7142}{9747}\right)$	$e\left(\frac{6841}{9747}\right)$	$e\left(\frac{6269}{6498}\right)$	$e\left(\frac{4685}{6498}\right)$	$e\left(\frac{9601}{9747}\right)$	$e\left(\frac{6169}{19494}\right)$	$e\left(\frac{13453}{19494}\right)$	$e\left(\frac{9289}{9747}\right)$
$\chi_{555579}(14,\cdot)$	555579.lf	19494	yes	$1$	$1$	$e\left(\frac{3808}{9747}\right)$	$e\left(\frac{7616}{9747}\right)$	$e\left(\frac{2059}{19494}\right)$	$e\left(\frac{3556}{9747}\right)$	$e\left(\frac{559}{3249}\right)$	$e\left(\frac{1075}{2166}\right)$	$e\left(\frac{18257}{19494}\right)$	$e\left(\frac{13453}{19494}\right)$	$e\left(\frac{7364}{9747}\right)$	$e\left(\frac{5485}{9747}\right)$
$\chi_{555579}(16,\cdot)$	555579.ks	9747	yes	$1$	$1$	$e\left(\frac{728}{9747}\right)$	$e\left(\frac{1456}{9747}\right)$	$e\left(\frac{7738}{9747}\right)$	$e\left(\frac{4757}{9747}\right)$	$e\left(\frac{728}{3249}\right)$	$e\left(\frac{2822}{3249}\right)$	$e\left(\frac{5894}{9747}\right)$	$e\left(\frac{9289}{9747}\right)$	$e\left(\frac{5485}{9747}\right)$	$e\left(\frac{2912}{9747}\right)$
$\chi_{555579}(17,\cdot)$	555579.js	6498	no	$-1$	$1$	$e\left(\frac{1285}{2166}\right)$	$e\left(\frac{202}{1083}\right)$	$e\left(\frac{2861}{6498}\right)$	$e\left(\frac{3232}{3249}\right)$	$e\left(\frac{563}{722}\right)$	$e\left(\frac{109}{3249}\right)$	$e\left(\frac{2171}{6498}\right)$	$e\left(\frac{473}{1083}\right)$	$e\left(\frac{3821}{6498}\right)$	$e\left(\frac{404}{1083}\right)$
$\chi_{555579}(20,\cdot)$	555579.lz	19494	yes	$-1$	$1$	$e\left(\frac{4597}{19494}\right)$	$e\left(\frac{4597}{9747}\right)$	$e\left(\frac{7235}{19494}\right)$	$e\left(\frac{6347}{9747}\right)$	$e\left(\frac{4597}{6498}\right)$	$e\left(\frac{1972}{3249}\right)$	$e\left(\frac{4249}{19494}\right)$	$e\left(\frac{6913}{9747}\right)$	$e\left(\frac{17291}{19494}\right)$	$e\left(\frac{9194}{9747}\right)$
$\chi_{555579}(22,\cdot)$	555579.lc	19494	yes	$-1$	$1$	$e\left(\frac{3311}{19494}\right)$	$e\left(\frac{3311}{9747}\right)$	$e\left(\frac{1112}{9747}\right)$	$e\left(\frac{1534}{9747}\right)$	$e\left(\frac{3311}{6498}\right)$	$e\left(\frac{205}{722}\right)$	$e\left(\frac{3979}{9747}\right)$	$e\left(\frac{18973}{19494}\right)$	$e\left(\frac{6379}{19494}\right)$	$e\left(\frac{6622}{9747}\right)$
$\chi_{555579}(23,\cdot)$	555579.lh	19494	yes	$-1$	$1$	$e\left(\frac{15695}{19494}\right)$	$e\left(\frac{5948}{9747}\right)$	$e\left(\frac{15451}{19494}\right)$	$e\left(\frac{1519}{9747}\right)$	$e\left(\frac{2699}{6498}\right)$	$e\left(\frac{1942}{3249}\right)$	$e\left(\frac{12167}{19494}\right)$	$e\left(\frac{7394}{9747}\right)$	$e\left(\frac{18733}{19494}\right)$	$e\left(\frac{2149}{9747}\right)$
$\chi_{555579}(25,\cdot)$	555579.kv	9747	yes	$1$	$1$	$e\left(\frac{3869}{9747}\right)$	$e\left(\frac{7738}{9747}\right)$	$e\left(\frac{9244}{9747}\right)$	$e\left(\frac{7937}{9747}\right)$	$e\left(\frac{620}{3249}\right)$	$e\left(\frac{374}{1083}\right)$	$e\left(\frac{8102}{9747}\right)$	$e\left(\frac{4537}{9747}\right)$	$e\left(\frac{2059}{9747}\right)$	$e\left(\frac{5729}{9747}\right)$
$\chi_{555579}(26,\cdot)$	555579.im	2166	no	$-1$	$1$	$e\left(\frac{5}{722}\right)$	$e\left(\frac{5}{361}\right)$	$e\left(\frac{2017}{2166}\right)$	$e\left(\frac{80}{1083}\right)$	$e\left(\frac{15}{722}\right)$	$e\left(\frac{1016}{1083}\right)$	$e\left(\frac{295}{2166}\right)$	$e\left(\frac{110}{361}\right)$	$e\left(\frac{175}{2166}\right)$	$e\left(\frac{10}{361}\right)$
$\chi_{555579}(28,\cdot)$	555579.ew	171	no	$1$	$1$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{109}{171}\right)$
$\chi_{555579}(29,\cdot)$	555579.lt	19494	yes	$1$	$1$	$e\left(\frac{9269}{9747}\right)$	$e\left(\frac{8791}{9747}\right)$	$e\left(\frac{18425}{19494}\right)$	$e\left(\frac{7055}{9747}\right)$	$e\left(\frac{2771}{3249}\right)$	$e\left(\frac{647}{722}\right)$	$e\left(\frac{4423}{19494}\right)$	$e\left(\frac{6671}{19494}\right)$	$e\left(\frac{6577}{9747}\right)$	$e\left(\frac{7835}{9747}\right)$
$\chi_{555579}(31,\cdot)$	555579.lw	19494	yes	$-1$	$1$	$e\left(\frac{947}{19494}\right)$	$e\left(\frac{947}{9747}\right)$	$e\left(\frac{1229}{9747}\right)$	$e\left(\frac{5893}{9747}\right)$	$e\left(\frac{947}{6498}\right)$	$e\left(\frac{1135}{6498}\right)$	$e\left(\frac{949}{9747}\right)$	$e\left(\frac{5929}{19494}\right)$	$e\left(\frac{12733}{19494}\right)$	$e\left(\frac{1894}{9747}\right)$
$\chi_{555579}(32,\cdot)$	555579.lp	19494	yes	$1$	$1$	$e\left(\frac{910}{9747}\right)$	$e\left(\frac{1820}{9747}\right)$	$e\left(\frac{19345}{19494}\right)$	$e\left(\frac{8383}{9747}\right)$	$e\left(\frac{910}{3249}\right)$	$e\left(\frac{557}{6498}\right)$	$e\left(\frac{14735}{19494}\right)$	$e\left(\frac{18349}{19494}\right)$	$e\left(\frac{9293}{9747}\right)$	$e\left(\frac{3640}{9747}\right)$
$\chi_{555579}(34,\cdot)$	555579.lc	19494	yes	$-1$	$1$	$e\left(\frac{11929}{19494}\right)$	$e\left(\frac{2182}{9747}\right)$	$e\left(\frac{6226}{9747}\right)$	$e\left(\frac{3575}{9747}\right)$	$e\left(\frac{5431}{6498}\right)$	$e\left(\frac{181}{722}\right)$	$e\left(\frac{4730}{9747}\right)$	$e\left(\frac{8285}{19494}\right)$	$e\left(\frac{19079}{19494}\right)$	$e\left(\frac{4364}{9747}\right)$
$\chi_{555579}(35,\cdot)$	555579.jv	6498	no	$-1$	$1$	$e\left(\frac{3707}{6498}\right)$	$e\left(\frac{458}{3249}\right)$	$e\left(\frac{1909}{2166}\right)$	$e\left(\frac{2924}{3249}\right)$	$e\left(\frac{1541}{2166}\right)$	$e\left(\frac{1468}{3249}\right)$	$e\left(\frac{4555}{6498}\right)$	$e\left(\frac{1412}{3249}\right)$	$e\left(\frac{1019}{2166}\right)$	$e\left(\frac{916}{3249}\right)$
$\chi_{555579}(37,\cdot)$	555579.ji	6498	no	$-1$	$1$	$e\left(\frac{4415}{6498}\right)$	$e\left(\frac{1166}{3249}\right)$	$e\left(\frac{755}{3249}\right)$	$e\left(\frac{202}{3249}\right)$	$e\left(\frac{83}{2166}\right)$	$e\left(\frac{1975}{2166}\right)$	$e\left(\frac{1117}{3249}\right)$	$e\left(\frac{2569}{6498}\right)$	$e\left(\frac{4819}{6498}\right)$	$e\left(\frac{2332}{3249}\right)$
$\chi_{555579}(40,\cdot)$	555579.lc	19494	yes	$-1$	$1$	$e\left(\frac{4961}{19494}\right)$	$e\left(\frac{4961}{9747}\right)$	$e\left(\frac{5552}{9747}\right)$	$e\left(\frac{226}{9747}\right)$	$e\left(\frac{4961}{6498}\right)$	$e\left(\frac{595}{722}\right)$	$e\left(\frac{3598}{9747}\right)$	$e\left(\frac{13597}{19494}\right)$	$e\left(\frac{5413}{19494}\right)$	$e\left(\frac{175}{9747}\right)$
$\chi_{555579}(41,\cdot)$	555579.ld	19494	yes	$1$	$1$	$e\left(\frac{1459}{9747}\right)$	$e\left(\frac{2918}{9747}\right)$	$e\left(\frac{18835}{19494}\right)$	$e\left(\frac{4492}{9747}\right)$	$e\left(\frac{1459}{3249}\right)$	$e\left(\frac{251}{2166}\right)$	$e\left(\frac{16835}{19494}\right)$	$e\left(\frac{1681}{19494}\right)$	$e\left(\frac{5951}{9747}\right)$	$e\left(\frac{5836}{9747}\right)$
$\chi_{555579}(43,\cdot)$	555579.kt	9747	yes	$1$	$1$	$e\left(\frac{7127}{9747}\right)$	$e\left(\frac{4507}{9747}\right)$	$e\left(\frac{7855}{9747}\right)$	$e\left(\frac{8033}{9747}\right)$	$e\left(\frac{629}{3249}\right)$	$e\left(\frac{1745}{3249}\right)$	$e\left(\frac{8279}{9747}\right)$	$e\left(\frac{8182}{9747}\right)$	$e\left(\frac{5413}{9747}\right)$	$e\left(\frac{9014}{9747}\right)$
$\chi_{555579}(44,\cdot)$	555579.jv	6498	no	$-1$	$1$	$e\left(\frac{1225}{6498}\right)$	$e\left(\frac{1225}{3249}\right)$	$e\left(\frac{677}{2166}\right)$	$e\left(\frac{1720}{3249}\right)$	$e\left(\frac{1225}{2166}\right)$	$e\left(\frac{1628}{3249}\right)$	$e\left(\frac{3635}{6498}\right)$	$e\left(\frac{3124}{3249}\right)$	$e\left(\frac{1555}{2166}\right)$	$e\left(\frac{2450}{3249}\right)$
$\chi_{555579}(46,\cdot)$	555579.kn	6498	no	$-1$	$1$	$e\left(\frac{5353}{6498}\right)$	$e\left(\frac{2104}{3249}\right)$	$e\left(\frac{3220}{3249}\right)$	$e\left(\frac{1715}{3249}\right)$	$e\left(\frac{1021}{2166}\right)$	$e\left(\frac{1765}{2166}\right)$	$e\left(\frac{2519}{3249}\right)$	$e\left(\frac{4853}{6498}\right)$	$e\left(\frac{2285}{6498}\right)$	$e\left(\frac{959}{3249}\right)$
$\chi_{555579}(47,\cdot)$	555579.lg	19494	yes	$-1$	$1$	$e\left(\frac{9787}{19494}\right)$	$e\left(\frac{40}{9747}\right)$	$e\left(\frac{10553}{19494}\right)$	$e\left(\frac{2981}{9747}\right)$	$e\left(\frac{3289}{6498}\right)$	$e\left(\frac{47}{1083}\right)$	$e\left(\frac{18235}{19494}\right)$	$e\left(\frac{880}{9747}\right)$	$e\left(\frac{15749}{19494}\right)$	$e\left(\frac{80}{9747}\right)$
$\chi_{555579}(49,\cdot)$	555579.kq	9747	yes	$1$	$1$	$e\left(\frac{7252}{9747}\right)$	$e\left(\frac{4757}{9747}\right)$	$e\left(\frac{7937}{9747}\right)$	$e\left(\frac{9607}{9747}\right)$	$e\left(\frac{754}{3249}\right)$	$e\left(\frac{1814}{3249}\right)$	$e\left(\frac{5563}{9747}\right)$	$e\left(\frac{3935}{9747}\right)$	$e\left(\frac{7112}{9747}\right)$	$e\left(\frac{9514}{9747}\right)$
$\chi_{555579}(50,\cdot)$	555579.lv	19494	yes	$1$	$1$	$e\left(\frac{4051}{9747}\right)$	$e\left(\frac{8102}{9747}\right)$	$e\left(\frac{2863}{19494}\right)$	$e\left(\frac{1816}{9747}\right)$	$e\left(\frac{802}{3249}\right)$	$e\left(\frac{3655}{6498}\right)$	$e\left(\frac{19151}{19494}\right)$	$e\left(\frac{8845}{19494}\right)$	$e\left(\frac{5867}{9747}\right)$	$e\left(\frac{6457}{9747}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$555579$
Structure	\(C_{18}\times C_{19494}\)
Order	$350892$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{555579}(1,\cdot)\)	555579.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{555579}(2,\cdot)\)	555579.lp	19494	yes	\(1\)	\(1\)	\(e\left(\frac{182}{9747}\right)\)	\(e\left(\frac{364}{9747}\right)\)	\(e\left(\frac{3869}{19494}\right)\)	\(e\left(\frac{3626}{9747}\right)\)	\(e\left(\frac{182}{3249}\right)\)	\(e\left(\frac{1411}{6498}\right)\)	\(e\left(\frac{2947}{19494}\right)\)	\(e\left(\frac{19265}{19494}\right)\)	\(e\left(\frac{3808}{9747}\right)\)	\(e\left(\frac{728}{9747}\right)\)
\(\chi_{555579}(4,\cdot)\)	555579.ks	9747	yes	\(1\)	\(1\)	\(e\left(\frac{364}{9747}\right)\)	\(e\left(\frac{728}{9747}\right)\)	\(e\left(\frac{3869}{9747}\right)\)	\(e\left(\frac{7252}{9747}\right)\)	\(e\left(\frac{364}{3249}\right)\)	\(e\left(\frac{1411}{3249}\right)\)	\(e\left(\frac{2947}{9747}\right)\)	\(e\left(\frac{9518}{9747}\right)\)	\(e\left(\frac{7616}{9747}\right)\)	\(e\left(\frac{1456}{9747}\right)\)
\(\chi_{555579}(5,\cdot)\)	555579.lg	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{3869}{19494}\right)\)	\(e\left(\frac{3869}{9747}\right)\)	\(e\left(\frac{18991}{19494}\right)\)	\(e\left(\frac{8842}{9747}\right)\)	\(e\left(\frac{3869}{6498}\right)\)	\(e\left(\frac{187}{1083}\right)\)	\(e\left(\frac{17849}{19494}\right)\)	\(e\left(\frac{7142}{9747}\right)\)	\(e\left(\frac{2059}{19494}\right)\)	\(e\left(\frac{7738}{9747}\right)\)
\(\chi_{555579}(7,\cdot)\)	555579.kq	9747	yes	\(1\)	\(1\)	\(e\left(\frac{3626}{9747}\right)\)	\(e\left(\frac{7252}{9747}\right)\)	\(e\left(\frac{8842}{9747}\right)\)	\(e\left(\frac{9677}{9747}\right)\)	\(e\left(\frac{377}{3249}\right)\)	\(e\left(\frac{907}{3249}\right)\)	\(e\left(\frac{7655}{9747}\right)\)	\(e\left(\frac{6841}{9747}\right)\)	\(e\left(\frac{3556}{9747}\right)\)	\(e\left(\frac{4757}{9747}\right)\)
\(\chi_{555579}(8,\cdot)\)	555579.km	6498	no	\(1\)	\(1\)	\(e\left(\frac{182}{3249}\right)\)	\(e\left(\frac{364}{3249}\right)\)	\(e\left(\frac{3869}{6498}\right)\)	\(e\left(\frac{377}{3249}\right)\)	\(e\left(\frac{182}{1083}\right)\)	\(e\left(\frac{1411}{2166}\right)\)	\(e\left(\frac{2947}{6498}\right)\)	\(e\left(\frac{6269}{6498}\right)\)	\(e\left(\frac{559}{3249}\right)\)	\(e\left(\frac{728}{3249}\right)\)
\(\chi_{555579}(10,\cdot)\)	555579.jy	6498	no	\(-1\)	\(1\)	\(e\left(\frac{1411}{6498}\right)\)	\(e\left(\frac{1411}{3249}\right)\)	\(e\left(\frac{187}{1083}\right)\)	\(e\left(\frac{907}{3249}\right)\)	\(e\left(\frac{1411}{2166}\right)\)	\(e\left(\frac{2533}{6498}\right)\)	\(e\left(\frac{217}{3249}\right)\)	\(e\left(\frac{4685}{6498}\right)\)	\(e\left(\frac{1075}{2166}\right)\)	\(e\left(\frac{2822}{3249}\right)\)
\(\chi_{555579}(11,\cdot)\)	555579.lu	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{2947}{19494}\right)\)	\(e\left(\frac{2947}{9747}\right)\)	\(e\left(\frac{17849}{19494}\right)\)	\(e\left(\frac{7655}{9747}\right)\)	\(e\left(\frac{2947}{6498}\right)\)	\(e\left(\frac{217}{3249}\right)\)	\(e\left(\frac{5011}{19494}\right)\)	\(e\left(\frac{9601}{9747}\right)\)	\(e\left(\frac{18257}{19494}\right)\)	\(e\left(\frac{5894}{9747}\right)\)
\(\chi_{555579}(13,\cdot)\)	555579.lk	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{19265}{19494}\right)\)	\(e\left(\frac{9518}{9747}\right)\)	\(e\left(\frac{7142}{9747}\right)\)	\(e\left(\frac{6841}{9747}\right)\)	\(e\left(\frac{6269}{6498}\right)\)	\(e\left(\frac{4685}{6498}\right)\)	\(e\left(\frac{9601}{9747}\right)\)	\(e\left(\frac{6169}{19494}\right)\)	\(e\left(\frac{13453}{19494}\right)\)	\(e\left(\frac{9289}{9747}\right)\)
\(\chi_{555579}(14,\cdot)\)	555579.lf	19494	yes	\(1\)	\(1\)	\(e\left(\frac{3808}{9747}\right)\)	\(e\left(\frac{7616}{9747}\right)\)	\(e\left(\frac{2059}{19494}\right)\)	\(e\left(\frac{3556}{9747}\right)\)	\(e\left(\frac{559}{3249}\right)\)	\(e\left(\frac{1075}{2166}\right)\)	\(e\left(\frac{18257}{19494}\right)\)	\(e\left(\frac{13453}{19494}\right)\)	\(e\left(\frac{7364}{9747}\right)\)	\(e\left(\frac{5485}{9747}\right)\)
\(\chi_{555579}(16,\cdot)\)	555579.ks	9747	yes	\(1\)	\(1\)	\(e\left(\frac{728}{9747}\right)\)	\(e\left(\frac{1456}{9747}\right)\)	\(e\left(\frac{7738}{9747}\right)\)	\(e\left(\frac{4757}{9747}\right)\)	\(e\left(\frac{728}{3249}\right)\)	\(e\left(\frac{2822}{3249}\right)\)	\(e\left(\frac{5894}{9747}\right)\)	\(e\left(\frac{9289}{9747}\right)\)	\(e\left(\frac{5485}{9747}\right)\)	\(e\left(\frac{2912}{9747}\right)\)
\(\chi_{555579}(17,\cdot)\)	555579.js	6498	no	\(-1\)	\(1\)	\(e\left(\frac{1285}{2166}\right)\)	\(e\left(\frac{202}{1083}\right)\)	\(e\left(\frac{2861}{6498}\right)\)	\(e\left(\frac{3232}{3249}\right)\)	\(e\left(\frac{563}{722}\right)\)	\(e\left(\frac{109}{3249}\right)\)	\(e\left(\frac{2171}{6498}\right)\)	\(e\left(\frac{473}{1083}\right)\)	\(e\left(\frac{3821}{6498}\right)\)	\(e\left(\frac{404}{1083}\right)\)
\(\chi_{555579}(20,\cdot)\)	555579.lz	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{4597}{19494}\right)\)	\(e\left(\frac{4597}{9747}\right)\)	\(e\left(\frac{7235}{19494}\right)\)	\(e\left(\frac{6347}{9747}\right)\)	\(e\left(\frac{4597}{6498}\right)\)	\(e\left(\frac{1972}{3249}\right)\)	\(e\left(\frac{4249}{19494}\right)\)	\(e\left(\frac{6913}{9747}\right)\)	\(e\left(\frac{17291}{19494}\right)\)	\(e\left(\frac{9194}{9747}\right)\)
\(\chi_{555579}(22,\cdot)\)	555579.lc	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{3311}{19494}\right)\)	\(e\left(\frac{3311}{9747}\right)\)	\(e\left(\frac{1112}{9747}\right)\)	\(e\left(\frac{1534}{9747}\right)\)	\(e\left(\frac{3311}{6498}\right)\)	\(e\left(\frac{205}{722}\right)\)	\(e\left(\frac{3979}{9747}\right)\)	\(e\left(\frac{18973}{19494}\right)\)	\(e\left(\frac{6379}{19494}\right)\)	\(e\left(\frac{6622}{9747}\right)\)
\(\chi_{555579}(23,\cdot)\)	555579.lh	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{15695}{19494}\right)\)	\(e\left(\frac{5948}{9747}\right)\)	\(e\left(\frac{15451}{19494}\right)\)	\(e\left(\frac{1519}{9747}\right)\)	\(e\left(\frac{2699}{6498}\right)\)	\(e\left(\frac{1942}{3249}\right)\)	\(e\left(\frac{12167}{19494}\right)\)	\(e\left(\frac{7394}{9747}\right)\)	\(e\left(\frac{18733}{19494}\right)\)	\(e\left(\frac{2149}{9747}\right)\)
\(\chi_{555579}(25,\cdot)\)	555579.kv	9747	yes	\(1\)	\(1\)	\(e\left(\frac{3869}{9747}\right)\)	\(e\left(\frac{7738}{9747}\right)\)	\(e\left(\frac{9244}{9747}\right)\)	\(e\left(\frac{7937}{9747}\right)\)	\(e\left(\frac{620}{3249}\right)\)	\(e\left(\frac{374}{1083}\right)\)	\(e\left(\frac{8102}{9747}\right)\)	\(e\left(\frac{4537}{9747}\right)\)	\(e\left(\frac{2059}{9747}\right)\)	\(e\left(\frac{5729}{9747}\right)\)
\(\chi_{555579}(26,\cdot)\)	555579.im	2166	no	\(-1\)	\(1\)	\(e\left(\frac{5}{722}\right)\)	\(e\left(\frac{5}{361}\right)\)	\(e\left(\frac{2017}{2166}\right)\)	\(e\left(\frac{80}{1083}\right)\)	\(e\left(\frac{15}{722}\right)\)	\(e\left(\frac{1016}{1083}\right)\)	\(e\left(\frac{295}{2166}\right)\)	\(e\left(\frac{110}{361}\right)\)	\(e\left(\frac{175}{2166}\right)\)	\(e\left(\frac{10}{361}\right)\)
\(\chi_{555579}(28,\cdot)\)	555579.ew	171	no	\(1\)	\(1\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)
\(\chi_{555579}(29,\cdot)\)	555579.lt	19494	yes	\(1\)	\(1\)	\(e\left(\frac{9269}{9747}\right)\)	\(e\left(\frac{8791}{9747}\right)\)	\(e\left(\frac{18425}{19494}\right)\)	\(e\left(\frac{7055}{9747}\right)\)	\(e\left(\frac{2771}{3249}\right)\)	\(e\left(\frac{647}{722}\right)\)	\(e\left(\frac{4423}{19494}\right)\)	\(e\left(\frac{6671}{19494}\right)\)	\(e\left(\frac{6577}{9747}\right)\)	\(e\left(\frac{7835}{9747}\right)\)
\(\chi_{555579}(31,\cdot)\)	555579.lw	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{947}{19494}\right)\)	\(e\left(\frac{947}{9747}\right)\)	\(e\left(\frac{1229}{9747}\right)\)	\(e\left(\frac{5893}{9747}\right)\)	\(e\left(\frac{947}{6498}\right)\)	\(e\left(\frac{1135}{6498}\right)\)	\(e\left(\frac{949}{9747}\right)\)	\(e\left(\frac{5929}{19494}\right)\)	\(e\left(\frac{12733}{19494}\right)\)	\(e\left(\frac{1894}{9747}\right)\)
\(\chi_{555579}(32,\cdot)\)	555579.lp	19494	yes	\(1\)	\(1\)	\(e\left(\frac{910}{9747}\right)\)	\(e\left(\frac{1820}{9747}\right)\)	\(e\left(\frac{19345}{19494}\right)\)	\(e\left(\frac{8383}{9747}\right)\)	\(e\left(\frac{910}{3249}\right)\)	\(e\left(\frac{557}{6498}\right)\)	\(e\left(\frac{14735}{19494}\right)\)	\(e\left(\frac{18349}{19494}\right)\)	\(e\left(\frac{9293}{9747}\right)\)	\(e\left(\frac{3640}{9747}\right)\)
\(\chi_{555579}(34,\cdot)\)	555579.lc	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{11929}{19494}\right)\)	\(e\left(\frac{2182}{9747}\right)\)	\(e\left(\frac{6226}{9747}\right)\)	\(e\left(\frac{3575}{9747}\right)\)	\(e\left(\frac{5431}{6498}\right)\)	\(e\left(\frac{181}{722}\right)\)	\(e\left(\frac{4730}{9747}\right)\)	\(e\left(\frac{8285}{19494}\right)\)	\(e\left(\frac{19079}{19494}\right)\)	\(e\left(\frac{4364}{9747}\right)\)
\(\chi_{555579}(35,\cdot)\)	555579.jv	6498	no	\(-1\)	\(1\)	\(e\left(\frac{3707}{6498}\right)\)	\(e\left(\frac{458}{3249}\right)\)	\(e\left(\frac{1909}{2166}\right)\)	\(e\left(\frac{2924}{3249}\right)\)	\(e\left(\frac{1541}{2166}\right)\)	\(e\left(\frac{1468}{3249}\right)\)	\(e\left(\frac{4555}{6498}\right)\)	\(e\left(\frac{1412}{3249}\right)\)	\(e\left(\frac{1019}{2166}\right)\)	\(e\left(\frac{916}{3249}\right)\)
\(\chi_{555579}(37,\cdot)\)	555579.ji	6498	no	\(-1\)	\(1\)	\(e\left(\frac{4415}{6498}\right)\)	\(e\left(\frac{1166}{3249}\right)\)	\(e\left(\frac{755}{3249}\right)\)	\(e\left(\frac{202}{3249}\right)\)	\(e\left(\frac{83}{2166}\right)\)	\(e\left(\frac{1975}{2166}\right)\)	\(e\left(\frac{1117}{3249}\right)\)	\(e\left(\frac{2569}{6498}\right)\)	\(e\left(\frac{4819}{6498}\right)\)	\(e\left(\frac{2332}{3249}\right)\)
\(\chi_{555579}(40,\cdot)\)	555579.lc	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{4961}{19494}\right)\)	\(e\left(\frac{4961}{9747}\right)\)	\(e\left(\frac{5552}{9747}\right)\)	\(e\left(\frac{226}{9747}\right)\)	\(e\left(\frac{4961}{6498}\right)\)	\(e\left(\frac{595}{722}\right)\)	\(e\left(\frac{3598}{9747}\right)\)	\(e\left(\frac{13597}{19494}\right)\)	\(e\left(\frac{5413}{19494}\right)\)	\(e\left(\frac{175}{9747}\right)\)
\(\chi_{555579}(41,\cdot)\)	555579.ld	19494	yes	\(1\)	\(1\)	\(e\left(\frac{1459}{9747}\right)\)	\(e\left(\frac{2918}{9747}\right)\)	\(e\left(\frac{18835}{19494}\right)\)	\(e\left(\frac{4492}{9747}\right)\)	\(e\left(\frac{1459}{3249}\right)\)	\(e\left(\frac{251}{2166}\right)\)	\(e\left(\frac{16835}{19494}\right)\)	\(e\left(\frac{1681}{19494}\right)\)	\(e\left(\frac{5951}{9747}\right)\)	\(e\left(\frac{5836}{9747}\right)\)
\(\chi_{555579}(43,\cdot)\)	555579.kt	9747	yes	\(1\)	\(1\)	\(e\left(\frac{7127}{9747}\right)\)	\(e\left(\frac{4507}{9747}\right)\)	\(e\left(\frac{7855}{9747}\right)\)	\(e\left(\frac{8033}{9747}\right)\)	\(e\left(\frac{629}{3249}\right)\)	\(e\left(\frac{1745}{3249}\right)\)	\(e\left(\frac{8279}{9747}\right)\)	\(e\left(\frac{8182}{9747}\right)\)	\(e\left(\frac{5413}{9747}\right)\)	\(e\left(\frac{9014}{9747}\right)\)
\(\chi_{555579}(44,\cdot)\)	555579.jv	6498	no	\(-1\)	\(1\)	\(e\left(\frac{1225}{6498}\right)\)	\(e\left(\frac{1225}{3249}\right)\)	\(e\left(\frac{677}{2166}\right)\)	\(e\left(\frac{1720}{3249}\right)\)	\(e\left(\frac{1225}{2166}\right)\)	\(e\left(\frac{1628}{3249}\right)\)	\(e\left(\frac{3635}{6498}\right)\)	\(e\left(\frac{3124}{3249}\right)\)	\(e\left(\frac{1555}{2166}\right)\)	\(e\left(\frac{2450}{3249}\right)\)
\(\chi_{555579}(46,\cdot)\)	555579.kn	6498	no	\(-1\)	\(1\)	\(e\left(\frac{5353}{6498}\right)\)	\(e\left(\frac{2104}{3249}\right)\)	\(e\left(\frac{3220}{3249}\right)\)	\(e\left(\frac{1715}{3249}\right)\)	\(e\left(\frac{1021}{2166}\right)\)	\(e\left(\frac{1765}{2166}\right)\)	\(e\left(\frac{2519}{3249}\right)\)	\(e\left(\frac{4853}{6498}\right)\)	\(e\left(\frac{2285}{6498}\right)\)	\(e\left(\frac{959}{3249}\right)\)
\(\chi_{555579}(47,\cdot)\)	555579.lg	19494	yes	\(-1\)	\(1\)	\(e\left(\frac{9787}{19494}\right)\)	\(e\left(\frac{40}{9747}\right)\)	\(e\left(\frac{10553}{19494}\right)\)	\(e\left(\frac{2981}{9747}\right)\)	\(e\left(\frac{3289}{6498}\right)\)	\(e\left(\frac{47}{1083}\right)\)	\(e\left(\frac{18235}{19494}\right)\)	\(e\left(\frac{880}{9747}\right)\)	\(e\left(\frac{15749}{19494}\right)\)	\(e\left(\frac{80}{9747}\right)\)
\(\chi_{555579}(49,\cdot)\)	555579.kq	9747	yes	\(1\)	\(1\)	\(e\left(\frac{7252}{9747}\right)\)	\(e\left(\frac{4757}{9747}\right)\)	\(e\left(\frac{7937}{9747}\right)\)	\(e\left(\frac{9607}{9747}\right)\)	\(e\left(\frac{754}{3249}\right)\)	\(e\left(\frac{1814}{3249}\right)\)	\(e\left(\frac{5563}{9747}\right)\)	\(e\left(\frac{3935}{9747}\right)\)	\(e\left(\frac{7112}{9747}\right)\)	\(e\left(\frac{9514}{9747}\right)\)
\(\chi_{555579}(50,\cdot)\)	555579.lv	19494	yes	\(1\)	\(1\)	\(e\left(\frac{4051}{9747}\right)\)	\(e\left(\frac{8102}{9747}\right)\)	\(e\left(\frac{2863}{19494}\right)\)	\(e\left(\frac{1816}{9747}\right)\)	\(e\left(\frac{802}{3249}\right)\)	\(e\left(\frac{3655}{6498}\right)\)	\(e\left(\frac{19151}{19494}\right)\)	\(e\left(\frac{8845}{19494}\right)\)	\(e\left(\frac{5867}{9747}\right)\)	\(e\left(\frac{6457}{9747}\right)\)

Introduction

L-functions

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Character group

First 32 of 350892 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.