LMFDB - Group of Dirichlet characters of modulus 382347

Show commands: PariGP / SageMath

sage: H = DirichletGroup(382347)

pari: g = idealstar(,382347,2)

Character group

sage: G.order() pari: g.no
Order	=	205632
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{17136}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{382347}(354026,\cdot)$, $\chi_{382347}(319924,\cdot)$, $\chi_{382347}(119071,\cdot)$

First 32 of 205632 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{382347}(1,\cdot)$	382347.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{382347}(2,\cdot)$	382347.xt	8568	yes	$-1$	$1$	$e\left(\frac{3733}{4284}\right)$	$e\left(\frac{1591}{2142}\right)$	$e\left(\frac{1657}{8568}\right)$	$e\left(\frac{877}{1428}\right)$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{4715}{8568}\right)$	$e\left(\frac{1681}{2142}\right)$	$e\left(\frac{520}{1071}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{8021}{8568}\right)$
$\chi_{382347}(4,\cdot)$	382347.wy	4284	yes	$1$	$1$	$e\left(\frac{1591}{2142}\right)$	$e\left(\frac{520}{1071}\right)$	$e\left(\frac{1657}{4284}\right)$	$e\left(\frac{163}{714}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{431}{4284}\right)$	$e\left(\frac{610}{1071}\right)$	$e\left(\frac{1040}{1071}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{3737}{4284}\right)$
$\chi_{382347}(5,\cdot)$	382347.yh	17136	yes	$-1$	$1$	$e\left(\frac{1657}{8568}\right)$	$e\left(\frac{1657}{4284}\right)$	$e\left(\frac{3607}{17136}\right)$	$e\left(\frac{1657}{2856}\right)$	$e\left(\frac{769}{1904}\right)$	$e\left(\frac{10181}{17136}\right)$	$e\left(\frac{97}{4284}\right)$	$e\left(\frac{1657}{2142}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{10235}{17136}\right)$
$\chi_{382347}(8,\cdot)$	382347.wm	2856	no	$-1$	$1$	$e\left(\frac{877}{1428}\right)$	$e\left(\frac{163}{714}\right)$	$e\left(\frac{1657}{2856}\right)$	$e\left(\frac{401}{476}\right)$	$e\left(\frac{185}{952}\right)$	$e\left(\frac{1859}{2856}\right)$	$e\left(\frac{253}{714}\right)$	$e\left(\frac{163}{357}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{2309}{2856}\right)$
$\chi_{382347}(10,\cdot)$	382347.xi	5712	no	$1$	$1$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{769}{1904}\right)$	$e\left(\frac{185}{952}\right)$	$e\left(\frac{2677}{5712}\right)$	$e\left(\frac{275}{1904}\right)$	$e\left(\frac{1153}{1428}\right)$	$e\left(\frac{185}{714}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{3047}{5712}\right)$
$\chi_{382347}(11,\cdot)$	382347.ym	17136	yes	$1$	$1$	$e\left(\frac{4715}{8568}\right)$	$e\left(\frac{431}{4284}\right)$	$e\left(\frac{10181}{17136}\right)$	$e\left(\frac{1859}{2856}\right)$	$e\left(\frac{275}{1904}\right)$	$e\left(\frac{7351}{17136}\right)$	$e\left(\frac{3341}{4284}\right)$	$e\left(\frac{431}{2142}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{11905}{17136}\right)$
$\chi_{382347}(13,\cdot)$	382347.xa	4284	yes	$-1$	$1$	$e\left(\frac{1681}{2142}\right)$	$e\left(\frac{610}{1071}\right)$	$e\left(\frac{97}{4284}\right)$	$e\left(\frac{253}{714}\right)$	$e\left(\frac{1153}{1428}\right)$	$e\left(\frac{3341}{4284}\right)$	$e\left(\frac{1541}{2142}\right)$	$e\left(\frac{149}{1071}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{2537}{4284}\right)$
$\chi_{382347}(16,\cdot)$	382347.uz	2142	yes	$1$	$1$	$e\left(\frac{520}{1071}\right)$	$e\left(\frac{1040}{1071}\right)$	$e\left(\frac{1657}{2142}\right)$	$e\left(\frac{163}{357}\right)$	$e\left(\frac{185}{714}\right)$	$e\left(\frac{431}{2142}\right)$	$e\left(\frac{149}{1071}\right)$	$e\left(\frac{1009}{1071}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{1595}{2142}\right)$
$\chi_{382347}(19,\cdot)$	382347.pt	408	no	$-1$	$1$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{39}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{209}{408}\right)$
$\chi_{382347}(20,\cdot)$	382347.yi	17136	yes	$-1$	$1$	$e\left(\frac{8021}{8568}\right)$	$e\left(\frac{3737}{4284}\right)$	$e\left(\frac{10235}{17136}\right)$	$e\left(\frac{2309}{2856}\right)$	$e\left(\frac{3047}{5712}\right)$	$e\left(\frac{11905}{17136}\right)$	$e\left(\frac{2537}{4284}\right)$	$e\left(\frac{1595}{2142}\right)$	$e\left(\frac{209}{408}\right)$	$e\left(\frac{8047}{17136}\right)$
$\chi_{382347}(22,\cdot)$	382347.yn	17136	yes	$-1$	$1$	$e\left(\frac{3613}{8568}\right)$	$e\left(\frac{3613}{4284}\right)$	$e\left(\frac{13495}{17136}\right)$	$e\left(\frac{757}{2856}\right)$	$e\left(\frac{1195}{5712}\right)$	$e\left(\frac{16781}{17136}\right)$	$e\left(\frac{2419}{4284}\right)$	$e\left(\frac{1471}{2142}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{10811}{17136}\right)$
$\chi_{382347}(23,\cdot)$	382347.ym	17136	yes	$1$	$1$	$e\left(\frac{7771}{8568}\right)$	$e\left(\frac{3487}{4284}\right)$	$e\left(\frac{685}{17136}\right)$	$e\left(\frac{2059}{2856}\right)$	$e\left(\frac{1803}{1904}\right)$	$e\left(\frac{16991}{17136}\right)$	$e\left(\frac{1873}{4284}\right)$	$e\left(\frac{1345}{2142}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{14633}{17136}\right)$
$\chi_{382347}(25,\cdot)$	382347.xs	8568	yes	$1$	$1$	$e\left(\frac{1657}{4284}\right)$	$e\left(\frac{1657}{2142}\right)$	$e\left(\frac{3607}{8568}\right)$	$e\left(\frac{229}{1428}\right)$	$e\left(\frac{769}{952}\right)$	$e\left(\frac{1613}{8568}\right)$	$e\left(\frac{97}{2142}\right)$	$e\left(\frac{586}{1071}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{1667}{8568}\right)$
$\chi_{382347}(26,\cdot)$	382347.wo	2856	no	$1$	$1$	$e\left(\frac{937}{1428}\right)$	$e\left(\frac{223}{714}\right)$	$e\left(\frac{617}{2856}\right)$	$e\left(\frac{461}{476}\right)$	$e\left(\frac{2491}{2856}\right)$	$e\left(\frac{943}{2856}\right)$	$e\left(\frac{60}{119}\right)$	$e\left(\frac{223}{357}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{503}{952}\right)$
$\chi_{382347}(29,\cdot)$	382347.yl	17136	yes	$1$	$1$	$e\left(\frac{4409}{8568}\right)$	$e\left(\frac{125}{4284}\right)$	$e\left(\frac{16199}{17136}\right)$	$e\left(\frac{1553}{2856}\right)$	$e\left(\frac{2627}{5712}\right)$	$e\left(\frac{7453}{17136}\right)$	$e\left(\frac{2831}{4284}\right)$	$e\left(\frac{125}{2142}\right)$	$e\left(\frac{41}{408}\right)$	$e\left(\frac{16699}{17136}\right)$
$\chi_{382347}(31,\cdot)$	382347.vu	2448	no	$1$	$1$	$e\left(\frac{895}{1224}\right)$	$e\left(\frac{283}{612}\right)$	$e\left(\frac{2365}{2448}\right)$	$e\left(\frac{79}{408}\right)$	$e\left(\frac{569}{816}\right)$	$e\left(\frac{2135}{2448}\right)$	$e\left(\frac{535}{612}\right)$	$e\left(\frac{283}{306}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{1049}{2448}\right)$
$\chi_{382347}(32,\cdot)$	382347.xt	8568	yes	$-1$	$1$	$e\left(\frac{1529}{4284}\right)$	$e\left(\frac{1529}{2142}\right)$	$e\left(\frac{8285}{8568}\right)$	$e\left(\frac{101}{1428}\right)$	$e\left(\frac{925}{2856}\right)$	$e\left(\frac{6439}{8568}\right)$	$e\left(\frac{1979}{2142}\right)$	$e\left(\frac{458}{1071}\right)$	$e\left(\frac{115}{204}\right)$	$e\left(\frac{5833}{8568}\right)$
$\chi_{382347}(37,\cdot)$	382347.xc	5712	no	$-1$	$1$	$e\left(\frac{241}{952}\right)$	$e\left(\frac{241}{476}\right)$	$e\left(\frac{2105}{5712}\right)$	$e\left(\frac{723}{952}\right)$	$e\left(\frac{3551}{5712}\right)$	$e\left(\frac{4099}{5712}\right)$	$e\left(\frac{1093}{1428}\right)$	$e\left(\frac{3}{238}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{4997}{5712}\right)$
$\chi_{382347}(38,\cdot)$	382347.nq	252	no	$1$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{185}{252}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{59}{63}\right)$	$1$	$e\left(\frac{113}{252}\right)$
$\chi_{382347}(40,\cdot)$	382347.ti	1008	no	$1$	$1$	$e\left(\frac{407}{504}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{797}{1008}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{247}{1008}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{409}{1008}\right)$
$\chi_{382347}(41,\cdot)$	382347.yi	17136	yes	$-1$	$1$	$e\left(\frac{5815}{8568}\right)$	$e\left(\frac{1531}{4284}\right)$	$e\left(\frac{793}{17136}\right)$	$e\left(\frac{103}{2856}\right)$	$e\left(\frac{4141}{5712}\right)$	$e\left(\frac{395}{17136}\right)$	$e\left(\frac{2407}{4284}\right)$	$e\left(\frac{1531}{2142}\right)$	$e\left(\frac{259}{408}\right)$	$e\left(\frac{6917}{17136}\right)$
$\chi_{382347}(43,\cdot)$	382347.xv	8568	yes	$1$	$1$	$e\left(\frac{3445}{4284}\right)$	$e\left(\frac{1303}{2142}\right)$	$e\left(\frac{4507}{8568}\right)$	$e\left(\frac{589}{1428}\right)$	$e\left(\frac{943}{2856}\right)$	$e\left(\frac{6113}{8568}\right)$	$e\left(\frac{739}{2142}\right)$	$e\left(\frac{232}{1071}\right)$	$e\left(\frac{61}{204}\right)$	$e\left(\frac{1151}{8568}\right)$
$\chi_{382347}(44,\cdot)$	382347.xe	5712	no	$1$	$1$	$e\left(\frac{279}{952}\right)$	$e\left(\frac{279}{476}\right)$	$e\left(\frac{5603}{5712}\right)$	$e\left(\frac{837}{952}\right)$	$e\left(\frac{1565}{5712}\right)$	$e\left(\frac{3025}{5712}\right)$	$e\left(\frac{499}{1428}\right)$	$e\left(\frac{41}{238}\right)$	$e\left(\frac{167}{408}\right)$	$e\left(\frac{3239}{5712}\right)$
$\chi_{382347}(46,\cdot)$	382347.xc	5712	no	$-1$	$1$	$e\left(\frac{741}{952}\right)$	$e\left(\frac{265}{476}\right)$	$e\left(\frac{1333}{5712}\right)$	$e\left(\frac{319}{952}\right)$	$e\left(\frac{67}{5712}\right)$	$e\left(\frac{3095}{5712}\right)$	$e\left(\frac{317}{1428}\right)$	$e\left(\frac{27}{238}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{4513}{5712}\right)$
$\chi_{382347}(47,\cdot)$	382347.wu	4284	yes	$1$	$1$	$e\left(\frac{361}{1071}\right)$	$e\left(\frac{722}{1071}\right)$	$e\left(\frac{2519}{4284}\right)$	$e\left(\frac{4}{357}\right)$	$e\left(\frac{1321}{1428}\right)$	$e\left(\frac{1171}{4284}\right)$	$e\left(\frac{211}{2142}\right)$	$e\left(\frac{373}{1071}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{1123}{4284}\right)$
$\chi_{382347}(50,\cdot)$	382347.oa	306	no	$-1$	$1$	$e\left(\frac{79}{306}\right)$	$e\left(\frac{79}{153}\right)$	$e\left(\frac{94}{153}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{113}{153}\right)$	$e\left(\frac{127}{153}\right)$	$e\left(\frac{5}{153}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{20}{153}\right)$
$\chi_{382347}(52,\cdot)$	382347.uu	2142	yes	$-1$	$1$	$e\left(\frac{565}{1071}\right)$	$e\left(\frac{59}{1071}\right)$	$e\left(\frac{877}{2142}\right)$	$e\left(\frac{208}{357}\right)$	$e\left(\frac{223}{238}\right)$	$e\left(\frac{943}{1071}\right)$	$e\left(\frac{619}{2142}\right)$	$e\left(\frac{118}{1071}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{995}{2142}\right)$
$\chi_{382347}(53,\cdot)$	382347.wf	2856	no	$-1$	$1$	$e\left(\frac{839}{1428}\right)$	$e\left(\frac{125}{714}\right)$	$e\left(\frac{2395}{2856}\right)$	$e\left(\frac{363}{476}\right)$	$e\left(\frac{1217}{2856}\right)$	$e\left(\frac{1265}{2856}\right)$	$e\left(\frac{71}{238}\right)$	$e\left(\frac{125}{357}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{13}{952}\right)$
$\chi_{382347}(55,\cdot)$	382347.qa	476	no	$-1$	$1$	$e\left(\frac{177}{238}\right)$	$e\left(\frac{58}{119}\right)$	$e\left(\frac{383}{476}\right)$	$e\left(\frac{55}{238}\right)$	$e\left(\frac{261}{476}\right)$	$e\left(\frac{11}{476}\right)$	$e\left(\frac{191}{238}\right)$	$e\left(\frac{116}{119}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{139}{476}\right)$
$\chi_{382347}(58,\cdot)$	382347.yo	17136	yes	$-1$	$1$	$e\left(\frac{3307}{8568}\right)$	$e\left(\frac{3307}{4284}\right)$	$e\left(\frac{2377}{17136}\right)$	$e\left(\frac{451}{2856}\right)$	$e\left(\frac{999}{1904}\right)$	$e\left(\frac{16883}{17136}\right)$	$e\left(\frac{1909}{4284}\right)$	$e\left(\frac{1165}{2142}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{15605}{17136}\right)$
$\chi_{382347}(59,\cdot)$	382347.yc	8568	yes	$1$	$1$	$e\left(\frac{3347}{4284}\right)$	$e\left(\frac{1205}{2142}\right)$	$e\left(\frac{3191}{8568}\right)$	$e\left(\frac{491}{1428}\right)$	$e\left(\frac{439}{2856}\right)$	$e\left(\frac{6673}{8568}\right)$	$e\left(\frac{58}{1071}\right)$	$e\left(\frac{134}{1071}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{8011}{8568}\right)$

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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	$382347$
Structure	\(C_{2}\times C_{6}\times C_{17136}\)
Order	$205632$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(19\)	\(20\)
\(\chi_{382347}(1,\cdot)\)	382347.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{382347}(2,\cdot)\)	382347.xt	8568	yes	\(-1\)	\(1\)	\(e\left(\frac{3733}{4284}\right)\)	\(e\left(\frac{1591}{2142}\right)\)	\(e\left(\frac{1657}{8568}\right)\)	\(e\left(\frac{877}{1428}\right)\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{4715}{8568}\right)\)	\(e\left(\frac{1681}{2142}\right)\)	\(e\left(\frac{520}{1071}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{8021}{8568}\right)\)
\(\chi_{382347}(4,\cdot)\)	382347.wy	4284	yes	\(1\)	\(1\)	\(e\left(\frac{1591}{2142}\right)\)	\(e\left(\frac{520}{1071}\right)\)	\(e\left(\frac{1657}{4284}\right)\)	\(e\left(\frac{163}{714}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{431}{4284}\right)\)	\(e\left(\frac{610}{1071}\right)\)	\(e\left(\frac{1040}{1071}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{3737}{4284}\right)\)
\(\chi_{382347}(5,\cdot)\)	382347.yh	17136	yes	\(-1\)	\(1\)	\(e\left(\frac{1657}{8568}\right)\)	\(e\left(\frac{1657}{4284}\right)\)	\(e\left(\frac{3607}{17136}\right)\)	\(e\left(\frac{1657}{2856}\right)\)	\(e\left(\frac{769}{1904}\right)\)	\(e\left(\frac{10181}{17136}\right)\)	\(e\left(\frac{97}{4284}\right)\)	\(e\left(\frac{1657}{2142}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{10235}{17136}\right)\)
\(\chi_{382347}(8,\cdot)\)	382347.wm	2856	no	\(-1\)	\(1\)	\(e\left(\frac{877}{1428}\right)\)	\(e\left(\frac{163}{714}\right)\)	\(e\left(\frac{1657}{2856}\right)\)	\(e\left(\frac{401}{476}\right)\)	\(e\left(\frac{185}{952}\right)\)	\(e\left(\frac{1859}{2856}\right)\)	\(e\left(\frac{253}{714}\right)\)	\(e\left(\frac{163}{357}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{2309}{2856}\right)\)
\(\chi_{382347}(10,\cdot)\)	382347.xi	5712	no	\(1\)	\(1\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{769}{1904}\right)\)	\(e\left(\frac{185}{952}\right)\)	\(e\left(\frac{2677}{5712}\right)\)	\(e\left(\frac{275}{1904}\right)\)	\(e\left(\frac{1153}{1428}\right)\)	\(e\left(\frac{185}{714}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{3047}{5712}\right)\)
\(\chi_{382347}(11,\cdot)\)	382347.ym	17136	yes	\(1\)	\(1\)	\(e\left(\frac{4715}{8568}\right)\)	\(e\left(\frac{431}{4284}\right)\)	\(e\left(\frac{10181}{17136}\right)\)	\(e\left(\frac{1859}{2856}\right)\)	\(e\left(\frac{275}{1904}\right)\)	\(e\left(\frac{7351}{17136}\right)\)	\(e\left(\frac{3341}{4284}\right)\)	\(e\left(\frac{431}{2142}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{11905}{17136}\right)\)
\(\chi_{382347}(13,\cdot)\)	382347.xa	4284	yes	\(-1\)	\(1\)	\(e\left(\frac{1681}{2142}\right)\)	\(e\left(\frac{610}{1071}\right)\)	\(e\left(\frac{97}{4284}\right)\)	\(e\left(\frac{253}{714}\right)\)	\(e\left(\frac{1153}{1428}\right)\)	\(e\left(\frac{3341}{4284}\right)\)	\(e\left(\frac{1541}{2142}\right)\)	\(e\left(\frac{149}{1071}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{2537}{4284}\right)\)
\(\chi_{382347}(16,\cdot)\)	382347.uz	2142	yes	\(1\)	\(1\)	\(e\left(\frac{520}{1071}\right)\)	\(e\left(\frac{1040}{1071}\right)\)	\(e\left(\frac{1657}{2142}\right)\)	\(e\left(\frac{163}{357}\right)\)	\(e\left(\frac{185}{714}\right)\)	\(e\left(\frac{431}{2142}\right)\)	\(e\left(\frac{149}{1071}\right)\)	\(e\left(\frac{1009}{1071}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{1595}{2142}\right)\)
\(\chi_{382347}(19,\cdot)\)	382347.pt	408	no	\(-1\)	\(1\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{23}{102}\right)\)	\(e\left(\frac{39}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{209}{408}\right)\)
\(\chi_{382347}(20,\cdot)\)	382347.yi	17136	yes	\(-1\)	\(1\)	\(e\left(\frac{8021}{8568}\right)\)	\(e\left(\frac{3737}{4284}\right)\)	\(e\left(\frac{10235}{17136}\right)\)	\(e\left(\frac{2309}{2856}\right)\)	\(e\left(\frac{3047}{5712}\right)\)	\(e\left(\frac{11905}{17136}\right)\)	\(e\left(\frac{2537}{4284}\right)\)	\(e\left(\frac{1595}{2142}\right)\)	\(e\left(\frac{209}{408}\right)\)	\(e\left(\frac{8047}{17136}\right)\)
\(\chi_{382347}(22,\cdot)\)	382347.yn	17136	yes	\(-1\)	\(1\)	\(e\left(\frac{3613}{8568}\right)\)	\(e\left(\frac{3613}{4284}\right)\)	\(e\left(\frac{13495}{17136}\right)\)	\(e\left(\frac{757}{2856}\right)\)	\(e\left(\frac{1195}{5712}\right)\)	\(e\left(\frac{16781}{17136}\right)\)	\(e\left(\frac{2419}{4284}\right)\)	\(e\left(\frac{1471}{2142}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{10811}{17136}\right)\)
\(\chi_{382347}(23,\cdot)\)	382347.ym	17136	yes	\(1\)	\(1\)	\(e\left(\frac{7771}{8568}\right)\)	\(e\left(\frac{3487}{4284}\right)\)	\(e\left(\frac{685}{17136}\right)\)	\(e\left(\frac{2059}{2856}\right)\)	\(e\left(\frac{1803}{1904}\right)\)	\(e\left(\frac{16991}{17136}\right)\)	\(e\left(\frac{1873}{4284}\right)\)	\(e\left(\frac{1345}{2142}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{14633}{17136}\right)\)
\(\chi_{382347}(25,\cdot)\)	382347.xs	8568	yes	\(1\)	\(1\)	\(e\left(\frac{1657}{4284}\right)\)	\(e\left(\frac{1657}{2142}\right)\)	\(e\left(\frac{3607}{8568}\right)\)	\(e\left(\frac{229}{1428}\right)\)	\(e\left(\frac{769}{952}\right)\)	\(e\left(\frac{1613}{8568}\right)\)	\(e\left(\frac{97}{2142}\right)\)	\(e\left(\frac{586}{1071}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{1667}{8568}\right)\)
\(\chi_{382347}(26,\cdot)\)	382347.wo	2856	no	\(1\)	\(1\)	\(e\left(\frac{937}{1428}\right)\)	\(e\left(\frac{223}{714}\right)\)	\(e\left(\frac{617}{2856}\right)\)	\(e\left(\frac{461}{476}\right)\)	\(e\left(\frac{2491}{2856}\right)\)	\(e\left(\frac{943}{2856}\right)\)	\(e\left(\frac{60}{119}\right)\)	\(e\left(\frac{223}{357}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{503}{952}\right)\)
\(\chi_{382347}(29,\cdot)\)	382347.yl	17136	yes	\(1\)	\(1\)	\(e\left(\frac{4409}{8568}\right)\)	\(e\left(\frac{125}{4284}\right)\)	\(e\left(\frac{16199}{17136}\right)\)	\(e\left(\frac{1553}{2856}\right)\)	\(e\left(\frac{2627}{5712}\right)\)	\(e\left(\frac{7453}{17136}\right)\)	\(e\left(\frac{2831}{4284}\right)\)	\(e\left(\frac{125}{2142}\right)\)	\(e\left(\frac{41}{408}\right)\)	\(e\left(\frac{16699}{17136}\right)\)
\(\chi_{382347}(31,\cdot)\)	382347.vu	2448	no	\(1\)	\(1\)	\(e\left(\frac{895}{1224}\right)\)	\(e\left(\frac{283}{612}\right)\)	\(e\left(\frac{2365}{2448}\right)\)	\(e\left(\frac{79}{408}\right)\)	\(e\left(\frac{569}{816}\right)\)	\(e\left(\frac{2135}{2448}\right)\)	\(e\left(\frac{535}{612}\right)\)	\(e\left(\frac{283}{306}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{1049}{2448}\right)\)
\(\chi_{382347}(32,\cdot)\)	382347.xt	8568	yes	\(-1\)	\(1\)	\(e\left(\frac{1529}{4284}\right)\)	\(e\left(\frac{1529}{2142}\right)\)	\(e\left(\frac{8285}{8568}\right)\)	\(e\left(\frac{101}{1428}\right)\)	\(e\left(\frac{925}{2856}\right)\)	\(e\left(\frac{6439}{8568}\right)\)	\(e\left(\frac{1979}{2142}\right)\)	\(e\left(\frac{458}{1071}\right)\)	\(e\left(\frac{115}{204}\right)\)	\(e\left(\frac{5833}{8568}\right)\)
\(\chi_{382347}(37,\cdot)\)	382347.xc	5712	no	\(-1\)	\(1\)	\(e\left(\frac{241}{952}\right)\)	\(e\left(\frac{241}{476}\right)\)	\(e\left(\frac{2105}{5712}\right)\)	\(e\left(\frac{723}{952}\right)\)	\(e\left(\frac{3551}{5712}\right)\)	\(e\left(\frac{4099}{5712}\right)\)	\(e\left(\frac{1093}{1428}\right)\)	\(e\left(\frac{3}{238}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{4997}{5712}\right)\)
\(\chi_{382347}(38,\cdot)\)	382347.nq	252	no	\(1\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{185}{252}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(1\)	\(e\left(\frac{113}{252}\right)\)
\(\chi_{382347}(40,\cdot)\)	382347.ti	1008	no	\(1\)	\(1\)	\(e\left(\frac{407}{504}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{797}{1008}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{247}{1008}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{409}{1008}\right)\)
\(\chi_{382347}(41,\cdot)\)	382347.yi	17136	yes	\(-1\)	\(1\)	\(e\left(\frac{5815}{8568}\right)\)	\(e\left(\frac{1531}{4284}\right)\)	\(e\left(\frac{793}{17136}\right)\)	\(e\left(\frac{103}{2856}\right)\)	\(e\left(\frac{4141}{5712}\right)\)	\(e\left(\frac{395}{17136}\right)\)	\(e\left(\frac{2407}{4284}\right)\)	\(e\left(\frac{1531}{2142}\right)\)	\(e\left(\frac{259}{408}\right)\)	\(e\left(\frac{6917}{17136}\right)\)
\(\chi_{382347}(43,\cdot)\)	382347.xv	8568	yes	\(1\)	\(1\)	\(e\left(\frac{3445}{4284}\right)\)	\(e\left(\frac{1303}{2142}\right)\)	\(e\left(\frac{4507}{8568}\right)\)	\(e\left(\frac{589}{1428}\right)\)	\(e\left(\frac{943}{2856}\right)\)	\(e\left(\frac{6113}{8568}\right)\)	\(e\left(\frac{739}{2142}\right)\)	\(e\left(\frac{232}{1071}\right)\)	\(e\left(\frac{61}{204}\right)\)	\(e\left(\frac{1151}{8568}\right)\)
\(\chi_{382347}(44,\cdot)\)	382347.xe	5712	no	\(1\)	\(1\)	\(e\left(\frac{279}{952}\right)\)	\(e\left(\frac{279}{476}\right)\)	\(e\left(\frac{5603}{5712}\right)\)	\(e\left(\frac{837}{952}\right)\)	\(e\left(\frac{1565}{5712}\right)\)	\(e\left(\frac{3025}{5712}\right)\)	\(e\left(\frac{499}{1428}\right)\)	\(e\left(\frac{41}{238}\right)\)	\(e\left(\frac{167}{408}\right)\)	\(e\left(\frac{3239}{5712}\right)\)
\(\chi_{382347}(46,\cdot)\)	382347.xc	5712	no	\(-1\)	\(1\)	\(e\left(\frac{741}{952}\right)\)	\(e\left(\frac{265}{476}\right)\)	\(e\left(\frac{1333}{5712}\right)\)	\(e\left(\frac{319}{952}\right)\)	\(e\left(\frac{67}{5712}\right)\)	\(e\left(\frac{3095}{5712}\right)\)	\(e\left(\frac{317}{1428}\right)\)	\(e\left(\frac{27}{238}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{4513}{5712}\right)\)
\(\chi_{382347}(47,\cdot)\)	382347.wu	4284	yes	\(1\)	\(1\)	\(e\left(\frac{361}{1071}\right)\)	\(e\left(\frac{722}{1071}\right)\)	\(e\left(\frac{2519}{4284}\right)\)	\(e\left(\frac{4}{357}\right)\)	\(e\left(\frac{1321}{1428}\right)\)	\(e\left(\frac{1171}{4284}\right)\)	\(e\left(\frac{211}{2142}\right)\)	\(e\left(\frac{373}{1071}\right)\)	\(e\left(\frac{50}{51}\right)\)	\(e\left(\frac{1123}{4284}\right)\)
\(\chi_{382347}(50,\cdot)\)	382347.oa	306	no	\(-1\)	\(1\)	\(e\left(\frac{79}{306}\right)\)	\(e\left(\frac{79}{153}\right)\)	\(e\left(\frac{94}{153}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{113}{153}\right)\)	\(e\left(\frac{127}{153}\right)\)	\(e\left(\frac{5}{153}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{20}{153}\right)\)
\(\chi_{382347}(52,\cdot)\)	382347.uu	2142	yes	\(-1\)	\(1\)	\(e\left(\frac{565}{1071}\right)\)	\(e\left(\frac{59}{1071}\right)\)	\(e\left(\frac{877}{2142}\right)\)	\(e\left(\frac{208}{357}\right)\)	\(e\left(\frac{223}{238}\right)\)	\(e\left(\frac{943}{1071}\right)\)	\(e\left(\frac{619}{2142}\right)\)	\(e\left(\frac{118}{1071}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{995}{2142}\right)\)
\(\chi_{382347}(53,\cdot)\)	382347.wf	2856	no	\(-1\)	\(1\)	\(e\left(\frac{839}{1428}\right)\)	\(e\left(\frac{125}{714}\right)\)	\(e\left(\frac{2395}{2856}\right)\)	\(e\left(\frac{363}{476}\right)\)	\(e\left(\frac{1217}{2856}\right)\)	\(e\left(\frac{1265}{2856}\right)\)	\(e\left(\frac{71}{238}\right)\)	\(e\left(\frac{125}{357}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{13}{952}\right)\)
\(\chi_{382347}(55,\cdot)\)	382347.qa	476	no	\(-1\)	\(1\)	\(e\left(\frac{177}{238}\right)\)	\(e\left(\frac{58}{119}\right)\)	\(e\left(\frac{383}{476}\right)\)	\(e\left(\frac{55}{238}\right)\)	\(e\left(\frac{261}{476}\right)\)	\(e\left(\frac{11}{476}\right)\)	\(e\left(\frac{191}{238}\right)\)	\(e\left(\frac{116}{119}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{139}{476}\right)\)
\(\chi_{382347}(58,\cdot)\)	382347.yo	17136	yes	\(-1\)	\(1\)	\(e\left(\frac{3307}{8568}\right)\)	\(e\left(\frac{3307}{4284}\right)\)	\(e\left(\frac{2377}{17136}\right)\)	\(e\left(\frac{451}{2856}\right)\)	\(e\left(\frac{999}{1904}\right)\)	\(e\left(\frac{16883}{17136}\right)\)	\(e\left(\frac{1909}{4284}\right)\)	\(e\left(\frac{1165}{2142}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{15605}{17136}\right)\)
\(\chi_{382347}(59,\cdot)\)	382347.yc	8568	yes	\(1\)	\(1\)	\(e\left(\frac{3347}{4284}\right)\)	\(e\left(\frac{1205}{2142}\right)\)	\(e\left(\frac{3191}{8568}\right)\)	\(e\left(\frac{491}{1428}\right)\)	\(e\left(\frac{439}{2856}\right)\)	\(e\left(\frac{6673}{8568}\right)\)	\(e\left(\frac{58}{1071}\right)\)	\(e\left(\frac{134}{1071}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{8011}{8568}\right)\)

Introduction

L-functions

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Character group

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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.