LMFDB - Group of Dirichlet characters of modulus 226576

Show commands: PariGP / SageMath

sage: H = DirichletGroup(226576)

pari: g = idealstar(,226576,2)

Character group

sage: G.order() pari: g.no
Order	=	91392
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{5712}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{226576}(198255,\cdot)$, $\chi_{226576}(56645,\cdot)$, $\chi_{226576}(50865,\cdot)$, $\chi_{226576}(147393,\cdot)$

First 32 of 91392 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{226576}(1,\cdot)$	226576.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{226576}(3,\cdot)$	226576.wb	5712	yes	$-1$	$1$	$e\left(\frac{4441}{5712}\right)$	$e\left(\frac{1613}{5712}\right)$	$e\left(\frac{1585}{2856}\right)$	$e\left(\frac{1639}{5712}\right)$	$e\left(\frac{90}{119}\right)$	$e\left(\frac{57}{952}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{4139}{5712}\right)$	$e\left(\frac{1613}{2856}\right)$	$e\left(\frac{633}{1904}\right)$
$\chi_{226576}(5,\cdot)$	226576.vo	5712	yes	$1$	$1$	$e\left(\frac{1613}{5712}\right)$	$e\left(\frac{409}{5712}\right)$	$e\left(\frac{1613}{2856}\right)$	$e\left(\frac{1331}{5712}\right)$	$e\left(\frac{131}{238}\right)$	$e\left(\frac{337}{952}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{2767}{5712}\right)$	$e\left(\frac{409}{2856}\right)$	$e\left(\frac{1613}{1904}\right)$
$\chi_{226576}(9,\cdot)$	226576.vl	2856	no	$1$	$1$	$e\left(\frac{1585}{2856}\right)$	$e\left(\frac{1613}{2856}\right)$	$e\left(\frac{157}{1428}\right)$	$e\left(\frac{1639}{2856}\right)$	$e\left(\frac{61}{119}\right)$	$e\left(\frac{57}{476}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{1283}{2856}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{633}{952}\right)$
$\chi_{226576}(11,\cdot)$	226576.vq	5712	yes	$1$	$1$	$e\left(\frac{1639}{5712}\right)$	$e\left(\frac{1331}{5712}\right)$	$e\left(\frac{1639}{2856}\right)$	$e\left(\frac{4513}{5712}\right)$	$e\left(\frac{179}{238}\right)$	$e\left(\frac{495}{952}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{269}{5712}\right)$	$e\left(\frac{1331}{2856}\right)$	$e\left(\frac{1639}{1904}\right)$
$\chi_{226576}(13,\cdot)$	226576.rl	476	yes	$-1$	$1$	$e\left(\frac{90}{119}\right)$	$e\left(\frac{131}{238}\right)$	$e\left(\frac{61}{119}\right)$	$e\left(\frac{179}{238}\right)$	$e\left(\frac{197}{476}\right)$	$e\left(\frac{73}{238}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{23}{476}\right)$	$e\left(\frac{12}{119}\right)$	$e\left(\frac{32}{119}\right)$
$\chi_{226576}(15,\cdot)$	226576.sx	952	no	$-1$	$1$	$e\left(\frac{57}{952}\right)$	$e\left(\frac{337}{952}\right)$	$e\left(\frac{57}{476}\right)$	$e\left(\frac{495}{952}\right)$	$e\left(\frac{73}{238}\right)$	$e\left(\frac{197}{476}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{199}{952}\right)$	$e\left(\frac{337}{476}\right)$	$e\left(\frac{171}{952}\right)$
$\chi_{226576}(19,\cdot)$	226576.qf	408	no	$1$	$1$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{55}{204}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{123}{136}\right)$
$\chi_{226576}(23,\cdot)$	226576.vw	5712	no	$1$	$1$	$e\left(\frac{4139}{5712}\right)$	$e\left(\frac{2767}{5712}\right)$	$e\left(\frac{1283}{2856}\right)$	$e\left(\frac{269}{5712}\right)$	$e\left(\frac{23}{476}\right)$	$e\left(\frac{199}{952}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{4045}{5712}\right)$	$e\left(\frac{2767}{2856}\right)$	$e\left(\frac{331}{1904}\right)$
$\chi_{226576}(25,\cdot)$	226576.vl	2856	no	$1$	$1$	$e\left(\frac{1613}{2856}\right)$	$e\left(\frac{409}{2856}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{1331}{2856}\right)$	$e\left(\frac{12}{119}\right)$	$e\left(\frac{337}{476}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{2767}{2856}\right)$	$e\left(\frac{409}{1428}\right)$	$e\left(\frac{661}{952}\right)$
$\chi_{226576}(27,\cdot)$	226576.uw	1904	yes	$-1$	$1$	$e\left(\frac{633}{1904}\right)$	$e\left(\frac{1613}{1904}\right)$	$e\left(\frac{633}{952}\right)$	$e\left(\frac{1639}{1904}\right)$	$e\left(\frac{32}{119}\right)$	$e\left(\frac{171}{952}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{331}{1904}\right)$	$e\left(\frac{661}{952}\right)$	$e\left(\frac{1899}{1904}\right)$
$\chi_{226576}(29,\cdot)$	226576.ui	1904	yes	$-1$	$1$	$e\left(\frac{263}{1904}\right)$	$e\left(\frac{795}{1904}\right)$	$e\left(\frac{263}{952}\right)$	$e\left(\frac{881}{1904}\right)$	$e\left(\frac{111}{238}\right)$	$e\left(\frac{529}{952}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{509}{1904}\right)$	$e\left(\frac{795}{952}\right)$	$e\left(\frac{789}{1904}\right)$
$\chi_{226576}(31,\cdot)$	226576.sp	816	no	$-1$	$1$	$e\left(\frac{571}{816}\right)$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{757}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{173}{816}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{27}{272}\right)$
$\chi_{226576}(33,\cdot)$	226576.rq	714	no	$-1$	$1$	$e\left(\frac{23}{357}\right)$	$e\left(\frac{184}{357}\right)$	$e\left(\frac{46}{357}\right)$	$e\left(\frac{55}{714}\right)$	$e\left(\frac{121}{238}\right)$	$e\left(\frac{69}{119}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{551}{714}\right)$	$e\left(\frac{11}{357}\right)$	$e\left(\frac{23}{119}\right)$
$\chi_{226576}(37,\cdot)$	226576.wd	5712	yes	$-1$	$1$	$e\left(\frac{5633}{5712}\right)$	$e\left(\frac{5437}{5712}\right)$	$e\left(\frac{2777}{2856}\right)$	$e\left(\frac{3623}{5712}\right)$	$e\left(\frac{101}{119}\right)$	$e\left(\frac{893}{952}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{1219}{5712}\right)$	$e\left(\frac{2581}{2856}\right)$	$e\left(\frac{1825}{1904}\right)$
$\chi_{226576}(39,\cdot)$	226576.vw	5712	no	$1$	$1$	$e\left(\frac{3049}{5712}\right)$	$e\left(\frac{4757}{5712}\right)$	$e\left(\frac{193}{2856}\right)$	$e\left(\frac{223}{5712}\right)$	$e\left(\frac{81}{476}\right)$	$e\left(\frac{349}{952}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{4415}{5712}\right)$	$e\left(\frac{1901}{2856}\right)$	$e\left(\frac{1145}{1904}\right)$
$\chi_{226576}(41,\cdot)$	226576.ur	1904	no	$1$	$1$	$e\left(\frac{925}{1904}\right)$	$e\left(\frac{1569}{1904}\right)$	$e\left(\frac{925}{952}\right)$	$e\left(\frac{467}{1904}\right)$	$e\left(\frac{241}{476}\right)$	$e\left(\frac{295}{952}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{1459}{1904}\right)$	$e\left(\frac{617}{952}\right)$	$e\left(\frac{871}{1904}\right)$
$\chi_{226576}(43,\cdot)$	226576.tb	952	yes	$-1$	$1$	$e\left(\frac{213}{952}\right)$	$e\left(\frac{633}{952}\right)$	$e\left(\frac{213}{476}\right)$	$e\left(\frac{547}{952}\right)$	$e\left(\frac{151}{476}\right)$	$e\left(\frac{423}{476}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{681}{952}\right)$	$e\left(\frac{157}{476}\right)$	$e\left(\frac{639}{952}\right)$
$\chi_{226576}(45,\cdot)$	226576.vo	5712	yes	$1$	$1$	$e\left(\frac{4783}{5712}\right)$	$e\left(\frac{3635}{5712}\right)$	$e\left(\frac{1927}{2856}\right)$	$e\left(\frac{4609}{5712}\right)$	$e\left(\frac{15}{238}\right)$	$e\left(\frac{451}{952}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{5333}{5712}\right)$	$e\left(\frac{779}{2856}\right)$	$e\left(\frac{975}{1904}\right)$
$\chi_{226576}(47,\cdot)$	226576.tr	1428	no	$1$	$1$	$e\left(\frac{1409}{1428}\right)$	$e\left(\frac{919}{1428}\right)$	$e\left(\frac{695}{714}\right)$	$e\left(\frac{1025}{1428}\right)$	$e\left(\frac{235}{238}\right)$	$e\left(\frac{75}{119}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{13}{1428}\right)$	$e\left(\frac{205}{714}\right)$	$e\left(\frac{457}{476}\right)$
$\chi_{226576}(53,\cdot)$	226576.vh	2856	yes	$1$	$1$	$e\left(\frac{2129}{2856}\right)$	$e\left(\frac{1681}{2856}\right)$	$e\left(\frac{701}{1428}\right)$	$e\left(\frac{551}{2856}\right)$	$e\left(\frac{23}{476}\right)$	$e\left(\frac{159}{476}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{1249}{2856}\right)$	$e\left(\frac{253}{1428}\right)$	$e\left(\frac{225}{952}\right)$
$\chi_{226576}(55,\cdot)$	226576.rj	476	no	$1$	$1$	$e\left(\frac{271}{476}\right)$	$e\left(\frac{145}{476}\right)$	$e\left(\frac{33}{238}\right)$	$e\left(\frac{11}{476}\right)$	$e\left(\frac{36}{119}\right)$	$e\left(\frac{104}{119}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{253}{476}\right)$	$e\left(\frac{145}{238}\right)$	$e\left(\frac{337}{476}\right)$
$\chi_{226576}(57,\cdot)$	226576.um	1904	no	$-1$	$1$	$e\left(\frac{785}{1904}\right)$	$e\left(\frac{1877}{1904}\right)$	$e\left(\frac{785}{952}\right)$	$e\left(\frac{103}{1904}\right)$	$e\left(\frac{283}{476}\right)$	$e\left(\frac{379}{952}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{1655}{1904}\right)$	$e\left(\frac{925}{952}\right)$	$e\left(\frac{451}{1904}\right)$
$\chi_{226576}(59,\cdot)$	226576.vf	2856	yes	$1$	$1$	$e\left(\frac{1199}{2856}\right)$	$e\left(\frac{667}{2856}\right)$	$e\left(\frac{1199}{1428}\right)$	$e\left(\frac{2621}{2856}\right)$	$e\left(\frac{277}{476}\right)$	$e\left(\frac{311}{476}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{1735}{2856}\right)$	$e\left(\frac{667}{1428}\right)$	$e\left(\frac{247}{952}\right)$
$\chi_{226576}(61,\cdot)$	226576.vo	5712	yes	$1$	$1$	$e\left(\frac{2651}{5712}\right)$	$e\left(\frac{2287}{5712}\right)$	$e\left(\frac{2651}{2856}\right)$	$e\left(\frac{725}{5712}\right)$	$e\left(\frac{125}{238}\right)$	$e\left(\frac{823}{952}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{4537}{5712}\right)$	$e\left(\frac{2287}{2856}\right)$	$e\left(\frac{747}{1904}\right)$
$\chi_{226576}(65,\cdot)$	226576.pq	336	no	$-1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{226576}(67,\cdot)$	226576.nu	204	no	$-1$	$1$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{203}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{226576}(69,\cdot)$	226576.re	476	yes	$-1$	$1$	$e\left(\frac{239}{476}\right)$	$e\left(\frac{365}{476}\right)$	$e\left(\frac{1}{238}\right)$	$e\left(\frac{159}{476}\right)$	$e\left(\frac{383}{476}\right)$	$e\left(\frac{32}{119}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{103}{238}\right)$	$e\left(\frac{127}{238}\right)$	$e\left(\frac{241}{476}\right)$
$\chi_{226576}(71,\cdot)$	226576.uo	1904	no	$1$	$1$	$e\left(\frac{983}{1904}\right)$	$e\left(\frac{843}{1904}\right)$	$e\left(\frac{31}{952}\right)$	$e\left(\frac{1121}{1904}\right)$	$e\left(\frac{261}{476}\right)$	$e\left(\frac{913}{952}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{1745}{1904}\right)$	$e\left(\frac{843}{952}\right)$	$e\left(\frac{1045}{1904}\right)$
$\chi_{226576}(73,\cdot)$	226576.vv	5712	no	$1$	$1$	$e\left(\frac{5641}{5712}\right)$	$e\left(\frac{5501}{5712}\right)$	$e\left(\frac{2785}{2856}\right)$	$e\left(\frac{3943}{5712}\right)$	$e\left(\frac{223}{476}\right)$	$e\left(\frac{905}{952}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{4295}{5712}\right)$	$e\left(\frac{2645}{2856}\right)$	$e\left(\frac{1833}{1904}\right)$
$\chi_{226576}(75,\cdot)$	226576.pm	336	no	$-1$	$1$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{226576}(79,\cdot)$	226576.sk	816	no	$1$	$1$	$e\left(\frac{365}{816}\right)$	$e\left(\frac{217}{816}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{67}{816}\right)$	$e\left(\frac{217}{408}\right)$	$e\left(\frac{93}{272}\right)$

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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	$226576$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{5712}\)
Order	$91392$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{226576}(1,\cdot)\)	226576.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{226576}(3,\cdot)\)	226576.wb	5712	yes	\(-1\)	\(1\)	\(e\left(\frac{4441}{5712}\right)\)	\(e\left(\frac{1613}{5712}\right)\)	\(e\left(\frac{1585}{2856}\right)\)	\(e\left(\frac{1639}{5712}\right)\)	\(e\left(\frac{90}{119}\right)\)	\(e\left(\frac{57}{952}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{4139}{5712}\right)\)	\(e\left(\frac{1613}{2856}\right)\)	\(e\left(\frac{633}{1904}\right)\)
\(\chi_{226576}(5,\cdot)\)	226576.vo	5712	yes	\(1\)	\(1\)	\(e\left(\frac{1613}{5712}\right)\)	\(e\left(\frac{409}{5712}\right)\)	\(e\left(\frac{1613}{2856}\right)\)	\(e\left(\frac{1331}{5712}\right)\)	\(e\left(\frac{131}{238}\right)\)	\(e\left(\frac{337}{952}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{2767}{5712}\right)\)	\(e\left(\frac{409}{2856}\right)\)	\(e\left(\frac{1613}{1904}\right)\)
\(\chi_{226576}(9,\cdot)\)	226576.vl	2856	no	\(1\)	\(1\)	\(e\left(\frac{1585}{2856}\right)\)	\(e\left(\frac{1613}{2856}\right)\)	\(e\left(\frac{157}{1428}\right)\)	\(e\left(\frac{1639}{2856}\right)\)	\(e\left(\frac{61}{119}\right)\)	\(e\left(\frac{57}{476}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{1283}{2856}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{633}{952}\right)\)
\(\chi_{226576}(11,\cdot)\)	226576.vq	5712	yes	\(1\)	\(1\)	\(e\left(\frac{1639}{5712}\right)\)	\(e\left(\frac{1331}{5712}\right)\)	\(e\left(\frac{1639}{2856}\right)\)	\(e\left(\frac{4513}{5712}\right)\)	\(e\left(\frac{179}{238}\right)\)	\(e\left(\frac{495}{952}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{269}{5712}\right)\)	\(e\left(\frac{1331}{2856}\right)\)	\(e\left(\frac{1639}{1904}\right)\)
\(\chi_{226576}(13,\cdot)\)	226576.rl	476	yes	\(-1\)	\(1\)	\(e\left(\frac{90}{119}\right)\)	\(e\left(\frac{131}{238}\right)\)	\(e\left(\frac{61}{119}\right)\)	\(e\left(\frac{179}{238}\right)\)	\(e\left(\frac{197}{476}\right)\)	\(e\left(\frac{73}{238}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{23}{476}\right)\)	\(e\left(\frac{12}{119}\right)\)	\(e\left(\frac{32}{119}\right)\)
\(\chi_{226576}(15,\cdot)\)	226576.sx	952	no	\(-1\)	\(1\)	\(e\left(\frac{57}{952}\right)\)	\(e\left(\frac{337}{952}\right)\)	\(e\left(\frac{57}{476}\right)\)	\(e\left(\frac{495}{952}\right)\)	\(e\left(\frac{73}{238}\right)\)	\(e\left(\frac{197}{476}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{199}{952}\right)\)	\(e\left(\frac{337}{476}\right)\)	\(e\left(\frac{171}{952}\right)\)
\(\chi_{226576}(19,\cdot)\)	226576.qf	408	no	\(1\)	\(1\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{55}{204}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{123}{136}\right)\)
\(\chi_{226576}(23,\cdot)\)	226576.vw	5712	no	\(1\)	\(1\)	\(e\left(\frac{4139}{5712}\right)\)	\(e\left(\frac{2767}{5712}\right)\)	\(e\left(\frac{1283}{2856}\right)\)	\(e\left(\frac{269}{5712}\right)\)	\(e\left(\frac{23}{476}\right)\)	\(e\left(\frac{199}{952}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{4045}{5712}\right)\)	\(e\left(\frac{2767}{2856}\right)\)	\(e\left(\frac{331}{1904}\right)\)
\(\chi_{226576}(25,\cdot)\)	226576.vl	2856	no	\(1\)	\(1\)	\(e\left(\frac{1613}{2856}\right)\)	\(e\left(\frac{409}{2856}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{1331}{2856}\right)\)	\(e\left(\frac{12}{119}\right)\)	\(e\left(\frac{337}{476}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{2767}{2856}\right)\)	\(e\left(\frac{409}{1428}\right)\)	\(e\left(\frac{661}{952}\right)\)
\(\chi_{226576}(27,\cdot)\)	226576.uw	1904	yes	\(-1\)	\(1\)	\(e\left(\frac{633}{1904}\right)\)	\(e\left(\frac{1613}{1904}\right)\)	\(e\left(\frac{633}{952}\right)\)	\(e\left(\frac{1639}{1904}\right)\)	\(e\left(\frac{32}{119}\right)\)	\(e\left(\frac{171}{952}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{331}{1904}\right)\)	\(e\left(\frac{661}{952}\right)\)	\(e\left(\frac{1899}{1904}\right)\)
\(\chi_{226576}(29,\cdot)\)	226576.ui	1904	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{1904}\right)\)	\(e\left(\frac{795}{1904}\right)\)	\(e\left(\frac{263}{952}\right)\)	\(e\left(\frac{881}{1904}\right)\)	\(e\left(\frac{111}{238}\right)\)	\(e\left(\frac{529}{952}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{509}{1904}\right)\)	\(e\left(\frac{795}{952}\right)\)	\(e\left(\frac{789}{1904}\right)\)
\(\chi_{226576}(31,\cdot)\)	226576.sp	816	no	\(-1\)	\(1\)	\(e\left(\frac{571}{816}\right)\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{757}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{173}{816}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{27}{272}\right)\)
\(\chi_{226576}(33,\cdot)\)	226576.rq	714	no	\(-1\)	\(1\)	\(e\left(\frac{23}{357}\right)\)	\(e\left(\frac{184}{357}\right)\)	\(e\left(\frac{46}{357}\right)\)	\(e\left(\frac{55}{714}\right)\)	\(e\left(\frac{121}{238}\right)\)	\(e\left(\frac{69}{119}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{551}{714}\right)\)	\(e\left(\frac{11}{357}\right)\)	\(e\left(\frac{23}{119}\right)\)
\(\chi_{226576}(37,\cdot)\)	226576.wd	5712	yes	\(-1\)	\(1\)	\(e\left(\frac{5633}{5712}\right)\)	\(e\left(\frac{5437}{5712}\right)\)	\(e\left(\frac{2777}{2856}\right)\)	\(e\left(\frac{3623}{5712}\right)\)	\(e\left(\frac{101}{119}\right)\)	\(e\left(\frac{893}{952}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{1219}{5712}\right)\)	\(e\left(\frac{2581}{2856}\right)\)	\(e\left(\frac{1825}{1904}\right)\)
\(\chi_{226576}(39,\cdot)\)	226576.vw	5712	no	\(1\)	\(1\)	\(e\left(\frac{3049}{5712}\right)\)	\(e\left(\frac{4757}{5712}\right)\)	\(e\left(\frac{193}{2856}\right)\)	\(e\left(\frac{223}{5712}\right)\)	\(e\left(\frac{81}{476}\right)\)	\(e\left(\frac{349}{952}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{4415}{5712}\right)\)	\(e\left(\frac{1901}{2856}\right)\)	\(e\left(\frac{1145}{1904}\right)\)
\(\chi_{226576}(41,\cdot)\)	226576.ur	1904	no	\(1\)	\(1\)	\(e\left(\frac{925}{1904}\right)\)	\(e\left(\frac{1569}{1904}\right)\)	\(e\left(\frac{925}{952}\right)\)	\(e\left(\frac{467}{1904}\right)\)	\(e\left(\frac{241}{476}\right)\)	\(e\left(\frac{295}{952}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{1459}{1904}\right)\)	\(e\left(\frac{617}{952}\right)\)	\(e\left(\frac{871}{1904}\right)\)
\(\chi_{226576}(43,\cdot)\)	226576.tb	952	yes	\(-1\)	\(1\)	\(e\left(\frac{213}{952}\right)\)	\(e\left(\frac{633}{952}\right)\)	\(e\left(\frac{213}{476}\right)\)	\(e\left(\frac{547}{952}\right)\)	\(e\left(\frac{151}{476}\right)\)	\(e\left(\frac{423}{476}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{681}{952}\right)\)	\(e\left(\frac{157}{476}\right)\)	\(e\left(\frac{639}{952}\right)\)
\(\chi_{226576}(45,\cdot)\)	226576.vo	5712	yes	\(1\)	\(1\)	\(e\left(\frac{4783}{5712}\right)\)	\(e\left(\frac{3635}{5712}\right)\)	\(e\left(\frac{1927}{2856}\right)\)	\(e\left(\frac{4609}{5712}\right)\)	\(e\left(\frac{15}{238}\right)\)	\(e\left(\frac{451}{952}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{5333}{5712}\right)\)	\(e\left(\frac{779}{2856}\right)\)	\(e\left(\frac{975}{1904}\right)\)
\(\chi_{226576}(47,\cdot)\)	226576.tr	1428	no	\(1\)	\(1\)	\(e\left(\frac{1409}{1428}\right)\)	\(e\left(\frac{919}{1428}\right)\)	\(e\left(\frac{695}{714}\right)\)	\(e\left(\frac{1025}{1428}\right)\)	\(e\left(\frac{235}{238}\right)\)	\(e\left(\frac{75}{119}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{13}{1428}\right)\)	\(e\left(\frac{205}{714}\right)\)	\(e\left(\frac{457}{476}\right)\)
\(\chi_{226576}(53,\cdot)\)	226576.vh	2856	yes	\(1\)	\(1\)	\(e\left(\frac{2129}{2856}\right)\)	\(e\left(\frac{1681}{2856}\right)\)	\(e\left(\frac{701}{1428}\right)\)	\(e\left(\frac{551}{2856}\right)\)	\(e\left(\frac{23}{476}\right)\)	\(e\left(\frac{159}{476}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{1249}{2856}\right)\)	\(e\left(\frac{253}{1428}\right)\)	\(e\left(\frac{225}{952}\right)\)
\(\chi_{226576}(55,\cdot)\)	226576.rj	476	no	\(1\)	\(1\)	\(e\left(\frac{271}{476}\right)\)	\(e\left(\frac{145}{476}\right)\)	\(e\left(\frac{33}{238}\right)\)	\(e\left(\frac{11}{476}\right)\)	\(e\left(\frac{36}{119}\right)\)	\(e\left(\frac{104}{119}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{253}{476}\right)\)	\(e\left(\frac{145}{238}\right)\)	\(e\left(\frac{337}{476}\right)\)
\(\chi_{226576}(57,\cdot)\)	226576.um	1904	no	\(-1\)	\(1\)	\(e\left(\frac{785}{1904}\right)\)	\(e\left(\frac{1877}{1904}\right)\)	\(e\left(\frac{785}{952}\right)\)	\(e\left(\frac{103}{1904}\right)\)	\(e\left(\frac{283}{476}\right)\)	\(e\left(\frac{379}{952}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{1655}{1904}\right)\)	\(e\left(\frac{925}{952}\right)\)	\(e\left(\frac{451}{1904}\right)\)
\(\chi_{226576}(59,\cdot)\)	226576.vf	2856	yes	\(1\)	\(1\)	\(e\left(\frac{1199}{2856}\right)\)	\(e\left(\frac{667}{2856}\right)\)	\(e\left(\frac{1199}{1428}\right)\)	\(e\left(\frac{2621}{2856}\right)\)	\(e\left(\frac{277}{476}\right)\)	\(e\left(\frac{311}{476}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{1735}{2856}\right)\)	\(e\left(\frac{667}{1428}\right)\)	\(e\left(\frac{247}{952}\right)\)
\(\chi_{226576}(61,\cdot)\)	226576.vo	5712	yes	\(1\)	\(1\)	\(e\left(\frac{2651}{5712}\right)\)	\(e\left(\frac{2287}{5712}\right)\)	\(e\left(\frac{2651}{2856}\right)\)	\(e\left(\frac{725}{5712}\right)\)	\(e\left(\frac{125}{238}\right)\)	\(e\left(\frac{823}{952}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{4537}{5712}\right)\)	\(e\left(\frac{2287}{2856}\right)\)	\(e\left(\frac{747}{1904}\right)\)
\(\chi_{226576}(65,\cdot)\)	226576.pq	336	no	\(-1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{226576}(67,\cdot)\)	226576.nu	204	no	\(-1\)	\(1\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{203}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{19}{102}\right)\)	\(e\left(\frac{101}{102}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{226576}(69,\cdot)\)	226576.re	476	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{476}\right)\)	\(e\left(\frac{365}{476}\right)\)	\(e\left(\frac{1}{238}\right)\)	\(e\left(\frac{159}{476}\right)\)	\(e\left(\frac{383}{476}\right)\)	\(e\left(\frac{32}{119}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{103}{238}\right)\)	\(e\left(\frac{127}{238}\right)\)	\(e\left(\frac{241}{476}\right)\)
\(\chi_{226576}(71,\cdot)\)	226576.uo	1904	no	\(1\)	\(1\)	\(e\left(\frac{983}{1904}\right)\)	\(e\left(\frac{843}{1904}\right)\)	\(e\left(\frac{31}{952}\right)\)	\(e\left(\frac{1121}{1904}\right)\)	\(e\left(\frac{261}{476}\right)\)	\(e\left(\frac{913}{952}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{1745}{1904}\right)\)	\(e\left(\frac{843}{952}\right)\)	\(e\left(\frac{1045}{1904}\right)\)
\(\chi_{226576}(73,\cdot)\)	226576.vv	5712	no	\(1\)	\(1\)	\(e\left(\frac{5641}{5712}\right)\)	\(e\left(\frac{5501}{5712}\right)\)	\(e\left(\frac{2785}{2856}\right)\)	\(e\left(\frac{3943}{5712}\right)\)	\(e\left(\frac{223}{476}\right)\)	\(e\left(\frac{905}{952}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{4295}{5712}\right)\)	\(e\left(\frac{2645}{2856}\right)\)	\(e\left(\frac{1833}{1904}\right)\)
\(\chi_{226576}(75,\cdot)\)	226576.pm	336	no	\(-1\)	\(1\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{226576}(79,\cdot)\)	226576.sk	816	no	\(1\)	\(1\)	\(e\left(\frac{365}{816}\right)\)	\(e\left(\frac{217}{816}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{67}{816}\right)\)	\(e\left(\frac{217}{408}\right)\)	\(e\left(\frac{93}{272}\right)\)

Introduction

L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.