LMFDB - Group of Dirichlet characters of modulus 1291

sage:H = DirichletGroup(1291)

pari:g = idealstar(,1291,2)

Character group

sage:G.order() pari:g.no
Order	=	1290
sage:H.invariants() pari:g.cyc
Structure	=	$C_{1290}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1291}(2,\cdot)$

First 32 of 1290 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1291}(1,\cdot)$	1291.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1291}(2,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{1}{1290}\right)$	$e\left(\frac{77}{1290}\right)$	$e\left(\frac{1}{645}\right)$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{13}{215}\right)$	$e\left(\frac{266}{645}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{77}{645}\right)$	$e\left(\frac{313}{1290}\right)$	$e\left(\frac{193}{258}\right)$
$\chi_{1291}(3,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{77}{1290}\right)$	$e\left(\frac{769}{1290}\right)$	$e\left(\frac{77}{645}\right)$	$e\left(\frac{134}{215}\right)$	$e\left(\frac{141}{215}\right)$	$e\left(\frac{487}{645}\right)$	$e\left(\frac{77}{430}\right)$	$e\left(\frac{124}{645}\right)$	$e\left(\frac{881}{1290}\right)$	$e\left(\frac{155}{258}\right)$
$\chi_{1291}(4,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{1}{645}\right)$	$e\left(\frac{77}{645}\right)$	$e\left(\frac{2}{645}\right)$	$e\left(\frac{104}{215}\right)$	$e\left(\frac{26}{215}\right)$	$e\left(\frac{532}{645}\right)$	$e\left(\frac{1}{215}\right)$	$e\left(\frac{154}{645}\right)$	$e\left(\frac{313}{645}\right)$	$e\left(\frac{64}{129}\right)$
$\chi_{1291}(5,\cdot)$	1291.l	215	yes	$1$	$1$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{134}{215}\right)$	$e\left(\frac{104}{215}\right)$	$e\left(\frac{99}{215}\right)$	$e\left(\frac{186}{215}\right)$	$e\left(\frac{144}{215}\right)$	$e\left(\frac{156}{215}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{151}{215}\right)$	$e\left(\frac{17}{43}\right)$
$\chi_{1291}(6,\cdot)$	1291.l	215	yes	$1$	$1$	$e\left(\frac{13}{215}\right)$	$e\left(\frac{141}{215}\right)$	$e\left(\frac{26}{215}\right)$	$e\left(\frac{186}{215}\right)$	$e\left(\frac{154}{215}\right)$	$e\left(\frac{36}{215}\right)$	$e\left(\frac{39}{215}\right)$	$e\left(\frac{67}{215}\right)$	$e\left(\frac{199}{215}\right)$	$e\left(\frac{15}{43}\right)$
$\chi_{1291}(7,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{266}{645}\right)$	$e\left(\frac{487}{645}\right)$	$e\left(\frac{532}{645}\right)$	$e\left(\frac{144}{215}\right)$	$e\left(\frac{36}{215}\right)$	$e\left(\frac{257}{645}\right)$	$e\left(\frac{51}{215}\right)$	$e\left(\frac{329}{645}\right)$	$e\left(\frac{53}{645}\right)$	$e\left(\frac{125}{129}\right)$
$\chi_{1291}(8,\cdot)$	1291.n	430	yes	$-1$	$1$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{77}{430}\right)$	$e\left(\frac{1}{215}\right)$	$e\left(\frac{156}{215}\right)$	$e\left(\frac{39}{215}\right)$	$e\left(\frac{51}{215}\right)$	$e\left(\frac{3}{430}\right)$	$e\left(\frac{77}{215}\right)$	$e\left(\frac{313}{430}\right)$	$e\left(\frac{21}{86}\right)$
$\chi_{1291}(9,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{77}{645}\right)$	$e\left(\frac{124}{645}\right)$	$e\left(\frac{154}{645}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{67}{215}\right)$	$e\left(\frac{329}{645}\right)$	$e\left(\frac{77}{215}\right)$	$e\left(\frac{248}{645}\right)$	$e\left(\frac{236}{645}\right)$	$e\left(\frac{26}{129}\right)$
$\chi_{1291}(10,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{313}{1290}\right)$	$e\left(\frac{881}{1290}\right)$	$e\left(\frac{313}{645}\right)$	$e\left(\frac{151}{215}\right)$	$e\left(\frac{199}{215}\right)$	$e\left(\frac{53}{645}\right)$	$e\left(\frac{313}{430}\right)$	$e\left(\frac{236}{645}\right)$	$e\left(\frac{1219}{1290}\right)$	$e\left(\frac{37}{258}\right)$
$\chi_{1291}(11,\cdot)$	1291.m	258	yes	$-1$	$1$	$e\left(\frac{193}{258}\right)$	$e\left(\frac{155}{258}\right)$	$e\left(\frac{64}{129}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{125}{129}\right)$	$e\left(\frac{21}{86}\right)$	$e\left(\frac{26}{129}\right)$	$e\left(\frac{37}{258}\right)$	$e\left(\frac{227}{258}\right)$
$\chi_{1291}(12,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{79}{1290}\right)$	$e\left(\frac{923}{1290}\right)$	$e\left(\frac{79}{645}\right)$	$e\left(\frac{23}{215}\right)$	$e\left(\frac{167}{215}\right)$	$e\left(\frac{374}{645}\right)$	$e\left(\frac{79}{430}\right)$	$e\left(\frac{278}{645}\right)$	$e\left(\frac{217}{1290}\right)$	$e\left(\frac{25}{258}\right)$
$\chi_{1291}(13,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{409}{645}\right)$	$e\left(\frac{533}{645}\right)$	$e\left(\frac{173}{645}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{99}{215}\right)$	$e\left(\frac{223}{645}\right)$	$e\left(\frac{194}{215}\right)$	$e\left(\frac{421}{645}\right)$	$e\left(\frac{307}{645}\right)$	$e\left(\frac{118}{129}\right)$
$\chi_{1291}(14,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{533}{1290}\right)$	$e\left(\frac{1051}{1290}\right)$	$e\left(\frac{533}{645}\right)$	$e\left(\frac{196}{215}\right)$	$e\left(\frac{49}{215}\right)$	$e\left(\frac{523}{645}\right)$	$e\left(\frac{103}{430}\right)$	$e\left(\frac{406}{645}\right)$	$e\left(\frac{419}{1290}\right)$	$e\left(\frac{185}{258}\right)$
$\chi_{1291}(15,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{389}{1290}\right)$	$e\left(\frac{283}{1290}\right)$	$e\left(\frac{389}{645}\right)$	$e\left(\frac{18}{215}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{274}{645}\right)$	$e\left(\frac{389}{430}\right)$	$e\left(\frac{283}{645}\right)$	$e\left(\frac{497}{1290}\right)$	$e\left(\frac{257}{258}\right)$
$\chi_{1291}(16,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{2}{645}\right)$	$e\left(\frac{154}{645}\right)$	$e\left(\frac{4}{645}\right)$	$e\left(\frac{208}{215}\right)$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{419}{645}\right)$	$e\left(\frac{2}{215}\right)$	$e\left(\frac{308}{645}\right)$	$e\left(\frac{626}{645}\right)$	$e\left(\frac{128}{129}\right)$
$\chi_{1291}(17,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{619}{645}\right)$	$e\left(\frac{578}{645}\right)$	$e\left(\frac{593}{645}\right)$	$e\left(\frac{91}{215}\right)$	$e\left(\frac{184}{215}\right)$	$e\left(\frac{358}{645}\right)$	$e\left(\frac{189}{215}\right)$	$e\left(\frac{511}{645}\right)$	$e\left(\frac{247}{645}\right)$	$e\left(\frac{13}{129}\right)$
$\chi_{1291}(18,\cdot)$	1291.m	258	yes	$-1$	$1$	$e\left(\frac{31}{258}\right)$	$e\left(\frac{65}{258}\right)$	$e\left(\frac{31}{129}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{119}{129}\right)$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{65}{129}\right)$	$e\left(\frac{157}{258}\right)$	$e\left(\frac{245}{258}\right)$
$\chi_{1291}(19,\cdot)$	1291.k	129	yes	$1$	$1$	$e\left(\frac{5}{129}\right)$	$e\left(\frac{127}{129}\right)$	$e\left(\frac{10}{129}\right)$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{80}{129}\right)$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{125}{129}\right)$	$e\left(\frac{17}{129}\right)$	$e\left(\frac{52}{129}\right)$
$\chi_{1291}(20,\cdot)$	1291.o	645	yes	$1$	$1$	$e\left(\frac{157}{645}\right)$	$e\left(\frac{479}{645}\right)$	$e\left(\frac{314}{645}\right)$	$e\left(\frac{203}{215}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{319}{645}\right)$	$e\left(\frac{157}{215}\right)$	$e\left(\frac{313}{645}\right)$	$e\left(\frac{121}{645}\right)$	$e\left(\frac{115}{129}\right)$
$\chi_{1291}(21,\cdot)$	1291.n	430	yes	$-1$	$1$	$e\left(\frac{203}{430}\right)$	$e\left(\frac{151}{430}\right)$	$e\left(\frac{203}{215}\right)$	$e\left(\frac{63}{215}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{33}{215}\right)$	$e\left(\frac{179}{430}\right)$	$e\left(\frac{151}{215}\right)$	$e\left(\frac{329}{430}\right)$	$e\left(\frac{49}{86}\right)$
$\chi_{1291}(22,\cdot)$	1291.l	215	yes	$1$	$1$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{142}{215}\right)$	$e\left(\frac{107}{215}\right)$	$e\left(\frac{137}{215}\right)$	$e\left(\frac{88}{215}\right)$	$e\left(\frac{82}{215}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{69}{215}\right)$	$e\left(\frac{83}{215}\right)$	$e\left(\frac{27}{43}\right)$
$\chi_{1291}(23,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{187}{1290}\right)$	$e\left(\frac{209}{1290}\right)$	$e\left(\frac{187}{645}\right)$	$e\left(\frac{49}{215}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{77}{645}\right)$	$e\left(\frac{187}{430}\right)$	$e\left(\frac{209}{645}\right)$	$e\left(\frac{481}{1290}\right)$	$e\left(\frac{229}{258}\right)$
$\chi_{1291}(24,\cdot)$	1291.k	129	yes	$1$	$1$	$e\left(\frac{8}{129}\right)$	$e\left(\frac{100}{129}\right)$	$e\left(\frac{16}{129}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{128}{129}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{71}{129}\right)$	$e\left(\frac{53}{129}\right)$	$e\left(\frac{109}{129}\right)$
$\chi_{1291}(25,\cdot)$	1291.l	215	yes	$1$	$1$	$e\left(\frac{104}{215}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{208}{215}\right)$	$e\left(\frac{198}{215}\right)$	$e\left(\frac{157}{215}\right)$	$e\left(\frac{73}{215}\right)$	$e\left(\frac{97}{215}\right)$	$e\left(\frac{106}{215}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{34}{43}\right)$
$\chi_{1291}(26,\cdot)$	1291.n	430	yes	$-1$	$1$	$e\left(\frac{273}{430}\right)$	$e\left(\frac{381}{430}\right)$	$e\left(\frac{58}{215}\right)$	$e\left(\frac{18}{215}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{163}{215}\right)$	$e\left(\frac{389}{430}\right)$	$e\left(\frac{166}{215}\right)$	$e\left(\frac{309}{430}\right)$	$e\left(\frac{57}{86}\right)$
$\chi_{1291}(27,\cdot)$	1291.n	430	yes	$-1$	$1$	$e\left(\frac{77}{430}\right)$	$e\left(\frac{339}{430}\right)$	$e\left(\frac{77}{215}\right)$	$e\left(\frac{187}{215}\right)$	$e\left(\frac{208}{215}\right)$	$e\left(\frac{57}{215}\right)$	$e\left(\frac{231}{430}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{21}{430}\right)$	$e\left(\frac{69}{86}\right)$
$\chi_{1291}(28,\cdot)$	1291.l	215	yes	$1$	$1$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{188}{215}\right)$	$e\left(\frac{178}{215}\right)$	$e\left(\frac{33}{215}\right)$	$e\left(\frac{62}{215}\right)$	$e\left(\frac{48}{215}\right)$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{122}{215}\right)$	$e\left(\frac{20}{43}\right)$
$\chi_{1291}(29,\cdot)$	1291.p	1290	yes	$-1$	$1$	$e\left(\frac{67}{1290}\right)$	$e\left(\frac{1289}{1290}\right)$	$e\left(\frac{67}{645}\right)$	$e\left(\frac{44}{215}\right)$	$e\left(\frac{11}{215}\right)$	$e\left(\frac{407}{645}\right)$	$e\left(\frac{67}{430}\right)$	$e\left(\frac{644}{645}\right)$	$e\left(\frac{331}{1290}\right)$	$e\left(\frac{31}{258}\right)$
$\chi_{1291}(30,\cdot)$	1291.i	43	yes	$1$	$1$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{32}{43}\right)$
$\chi_{1291}(31,\cdot)$	1291.m	258	yes	$-1$	$1$	$e\left(\frac{71}{258}\right)$	$e\left(\frac{49}{258}\right)$	$e\left(\frac{71}{129}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{52}{129}\right)$	$e\left(\frac{71}{86}\right)$	$e\left(\frac{49}{129}\right)$	$e\left(\frac{35}{258}\right)$	$e\left(\frac{145}{258}\right)$
$\chi_{1291}(32,\cdot)$	1291.m	258	yes	$-1$	$1$	$e\left(\frac{1}{258}\right)$	$e\left(\frac{77}{258}\right)$	$e\left(\frac{1}{129}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{8}{129}\right)$	$e\left(\frac{1}{86}\right)$	$e\left(\frac{77}{129}\right)$	$e\left(\frac{55}{258}\right)$	$e\left(\frac{191}{258}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1291$
Structure	\(C_{1290}\)
Order	$1290$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1291}(1,\cdot)\)	1291.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1291}(2,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{1290}\right)\)	\(e\left(\frac{77}{1290}\right)\)	\(e\left(\frac{1}{645}\right)\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{13}{215}\right)\)	\(e\left(\frac{266}{645}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{77}{645}\right)\)	\(e\left(\frac{313}{1290}\right)\)	\(e\left(\frac{193}{258}\right)\)
\(\chi_{1291}(3,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{1290}\right)\)	\(e\left(\frac{769}{1290}\right)\)	\(e\left(\frac{77}{645}\right)\)	\(e\left(\frac{134}{215}\right)\)	\(e\left(\frac{141}{215}\right)\)	\(e\left(\frac{487}{645}\right)\)	\(e\left(\frac{77}{430}\right)\)	\(e\left(\frac{124}{645}\right)\)	\(e\left(\frac{881}{1290}\right)\)	\(e\left(\frac{155}{258}\right)\)
\(\chi_{1291}(4,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{1}{645}\right)\)	\(e\left(\frac{77}{645}\right)\)	\(e\left(\frac{2}{645}\right)\)	\(e\left(\frac{104}{215}\right)\)	\(e\left(\frac{26}{215}\right)\)	\(e\left(\frac{532}{645}\right)\)	\(e\left(\frac{1}{215}\right)\)	\(e\left(\frac{154}{645}\right)\)	\(e\left(\frac{313}{645}\right)\)	\(e\left(\frac{64}{129}\right)\)
\(\chi_{1291}(5,\cdot)\)	1291.l	215	yes	\(1\)	\(1\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{134}{215}\right)\)	\(e\left(\frac{104}{215}\right)\)	\(e\left(\frac{99}{215}\right)\)	\(e\left(\frac{186}{215}\right)\)	\(e\left(\frac{144}{215}\right)\)	\(e\left(\frac{156}{215}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{151}{215}\right)\)	\(e\left(\frac{17}{43}\right)\)
\(\chi_{1291}(6,\cdot)\)	1291.l	215	yes	\(1\)	\(1\)	\(e\left(\frac{13}{215}\right)\)	\(e\left(\frac{141}{215}\right)\)	\(e\left(\frac{26}{215}\right)\)	\(e\left(\frac{186}{215}\right)\)	\(e\left(\frac{154}{215}\right)\)	\(e\left(\frac{36}{215}\right)\)	\(e\left(\frac{39}{215}\right)\)	\(e\left(\frac{67}{215}\right)\)	\(e\left(\frac{199}{215}\right)\)	\(e\left(\frac{15}{43}\right)\)
\(\chi_{1291}(7,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{266}{645}\right)\)	\(e\left(\frac{487}{645}\right)\)	\(e\left(\frac{532}{645}\right)\)	\(e\left(\frac{144}{215}\right)\)	\(e\left(\frac{36}{215}\right)\)	\(e\left(\frac{257}{645}\right)\)	\(e\left(\frac{51}{215}\right)\)	\(e\left(\frac{329}{645}\right)\)	\(e\left(\frac{53}{645}\right)\)	\(e\left(\frac{125}{129}\right)\)
\(\chi_{1291}(8,\cdot)\)	1291.n	430	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{77}{430}\right)\)	\(e\left(\frac{1}{215}\right)\)	\(e\left(\frac{156}{215}\right)\)	\(e\left(\frac{39}{215}\right)\)	\(e\left(\frac{51}{215}\right)\)	\(e\left(\frac{3}{430}\right)\)	\(e\left(\frac{77}{215}\right)\)	\(e\left(\frac{313}{430}\right)\)	\(e\left(\frac{21}{86}\right)\)
\(\chi_{1291}(9,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{77}{645}\right)\)	\(e\left(\frac{124}{645}\right)\)	\(e\left(\frac{154}{645}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{67}{215}\right)\)	\(e\left(\frac{329}{645}\right)\)	\(e\left(\frac{77}{215}\right)\)	\(e\left(\frac{248}{645}\right)\)	\(e\left(\frac{236}{645}\right)\)	\(e\left(\frac{26}{129}\right)\)
\(\chi_{1291}(10,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{1290}\right)\)	\(e\left(\frac{881}{1290}\right)\)	\(e\left(\frac{313}{645}\right)\)	\(e\left(\frac{151}{215}\right)\)	\(e\left(\frac{199}{215}\right)\)	\(e\left(\frac{53}{645}\right)\)	\(e\left(\frac{313}{430}\right)\)	\(e\left(\frac{236}{645}\right)\)	\(e\left(\frac{1219}{1290}\right)\)	\(e\left(\frac{37}{258}\right)\)
\(\chi_{1291}(11,\cdot)\)	1291.m	258	yes	\(-1\)	\(1\)	\(e\left(\frac{193}{258}\right)\)	\(e\left(\frac{155}{258}\right)\)	\(e\left(\frac{64}{129}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{125}{129}\right)\)	\(e\left(\frac{21}{86}\right)\)	\(e\left(\frac{26}{129}\right)\)	\(e\left(\frac{37}{258}\right)\)	\(e\left(\frac{227}{258}\right)\)
\(\chi_{1291}(12,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{1290}\right)\)	\(e\left(\frac{923}{1290}\right)\)	\(e\left(\frac{79}{645}\right)\)	\(e\left(\frac{23}{215}\right)\)	\(e\left(\frac{167}{215}\right)\)	\(e\left(\frac{374}{645}\right)\)	\(e\left(\frac{79}{430}\right)\)	\(e\left(\frac{278}{645}\right)\)	\(e\left(\frac{217}{1290}\right)\)	\(e\left(\frac{25}{258}\right)\)
\(\chi_{1291}(13,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{409}{645}\right)\)	\(e\left(\frac{533}{645}\right)\)	\(e\left(\frac{173}{645}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{99}{215}\right)\)	\(e\left(\frac{223}{645}\right)\)	\(e\left(\frac{194}{215}\right)\)	\(e\left(\frac{421}{645}\right)\)	\(e\left(\frac{307}{645}\right)\)	\(e\left(\frac{118}{129}\right)\)
\(\chi_{1291}(14,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{533}{1290}\right)\)	\(e\left(\frac{1051}{1290}\right)\)	\(e\left(\frac{533}{645}\right)\)	\(e\left(\frac{196}{215}\right)\)	\(e\left(\frac{49}{215}\right)\)	\(e\left(\frac{523}{645}\right)\)	\(e\left(\frac{103}{430}\right)\)	\(e\left(\frac{406}{645}\right)\)	\(e\left(\frac{419}{1290}\right)\)	\(e\left(\frac{185}{258}\right)\)
\(\chi_{1291}(15,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{1290}\right)\)	\(e\left(\frac{283}{1290}\right)\)	\(e\left(\frac{389}{645}\right)\)	\(e\left(\frac{18}{215}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{274}{645}\right)\)	\(e\left(\frac{389}{430}\right)\)	\(e\left(\frac{283}{645}\right)\)	\(e\left(\frac{497}{1290}\right)\)	\(e\left(\frac{257}{258}\right)\)
\(\chi_{1291}(16,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{2}{645}\right)\)	\(e\left(\frac{154}{645}\right)\)	\(e\left(\frac{4}{645}\right)\)	\(e\left(\frac{208}{215}\right)\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{419}{645}\right)\)	\(e\left(\frac{2}{215}\right)\)	\(e\left(\frac{308}{645}\right)\)	\(e\left(\frac{626}{645}\right)\)	\(e\left(\frac{128}{129}\right)\)
\(\chi_{1291}(17,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{619}{645}\right)\)	\(e\left(\frac{578}{645}\right)\)	\(e\left(\frac{593}{645}\right)\)	\(e\left(\frac{91}{215}\right)\)	\(e\left(\frac{184}{215}\right)\)	\(e\left(\frac{358}{645}\right)\)	\(e\left(\frac{189}{215}\right)\)	\(e\left(\frac{511}{645}\right)\)	\(e\left(\frac{247}{645}\right)\)	\(e\left(\frac{13}{129}\right)\)
\(\chi_{1291}(18,\cdot)\)	1291.m	258	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{258}\right)\)	\(e\left(\frac{65}{258}\right)\)	\(e\left(\frac{31}{129}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{119}{129}\right)\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{65}{129}\right)\)	\(e\left(\frac{157}{258}\right)\)	\(e\left(\frac{245}{258}\right)\)
\(\chi_{1291}(19,\cdot)\)	1291.k	129	yes	\(1\)	\(1\)	\(e\left(\frac{5}{129}\right)\)	\(e\left(\frac{127}{129}\right)\)	\(e\left(\frac{10}{129}\right)\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{80}{129}\right)\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{125}{129}\right)\)	\(e\left(\frac{17}{129}\right)\)	\(e\left(\frac{52}{129}\right)\)
\(\chi_{1291}(20,\cdot)\)	1291.o	645	yes	\(1\)	\(1\)	\(e\left(\frac{157}{645}\right)\)	\(e\left(\frac{479}{645}\right)\)	\(e\left(\frac{314}{645}\right)\)	\(e\left(\frac{203}{215}\right)\)	\(e\left(\frac{212}{215}\right)\)	\(e\left(\frac{319}{645}\right)\)	\(e\left(\frac{157}{215}\right)\)	\(e\left(\frac{313}{645}\right)\)	\(e\left(\frac{121}{645}\right)\)	\(e\left(\frac{115}{129}\right)\)
\(\chi_{1291}(21,\cdot)\)	1291.n	430	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{430}\right)\)	\(e\left(\frac{151}{430}\right)\)	\(e\left(\frac{203}{215}\right)\)	\(e\left(\frac{63}{215}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{33}{215}\right)\)	\(e\left(\frac{179}{430}\right)\)	\(e\left(\frac{151}{215}\right)\)	\(e\left(\frac{329}{430}\right)\)	\(e\left(\frac{49}{86}\right)\)
\(\chi_{1291}(22,\cdot)\)	1291.l	215	yes	\(1\)	\(1\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{142}{215}\right)\)	\(e\left(\frac{107}{215}\right)\)	\(e\left(\frac{137}{215}\right)\)	\(e\left(\frac{88}{215}\right)\)	\(e\left(\frac{82}{215}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{69}{215}\right)\)	\(e\left(\frac{83}{215}\right)\)	\(e\left(\frac{27}{43}\right)\)
\(\chi_{1291}(23,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{1290}\right)\)	\(e\left(\frac{209}{1290}\right)\)	\(e\left(\frac{187}{645}\right)\)	\(e\left(\frac{49}{215}\right)\)	\(e\left(\frac{66}{215}\right)\)	\(e\left(\frac{77}{645}\right)\)	\(e\left(\frac{187}{430}\right)\)	\(e\left(\frac{209}{645}\right)\)	\(e\left(\frac{481}{1290}\right)\)	\(e\left(\frac{229}{258}\right)\)
\(\chi_{1291}(24,\cdot)\)	1291.k	129	yes	\(1\)	\(1\)	\(e\left(\frac{8}{129}\right)\)	\(e\left(\frac{100}{129}\right)\)	\(e\left(\frac{16}{129}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{128}{129}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{71}{129}\right)\)	\(e\left(\frac{53}{129}\right)\)	\(e\left(\frac{109}{129}\right)\)
\(\chi_{1291}(25,\cdot)\)	1291.l	215	yes	\(1\)	\(1\)	\(e\left(\frac{104}{215}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{208}{215}\right)\)	\(e\left(\frac{198}{215}\right)\)	\(e\left(\frac{157}{215}\right)\)	\(e\left(\frac{73}{215}\right)\)	\(e\left(\frac{97}{215}\right)\)	\(e\left(\frac{106}{215}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{34}{43}\right)\)
\(\chi_{1291}(26,\cdot)\)	1291.n	430	yes	\(-1\)	\(1\)	\(e\left(\frac{273}{430}\right)\)	\(e\left(\frac{381}{430}\right)\)	\(e\left(\frac{58}{215}\right)\)	\(e\left(\frac{18}{215}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{163}{215}\right)\)	\(e\left(\frac{389}{430}\right)\)	\(e\left(\frac{166}{215}\right)\)	\(e\left(\frac{309}{430}\right)\)	\(e\left(\frac{57}{86}\right)\)
\(\chi_{1291}(27,\cdot)\)	1291.n	430	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{430}\right)\)	\(e\left(\frac{339}{430}\right)\)	\(e\left(\frac{77}{215}\right)\)	\(e\left(\frac{187}{215}\right)\)	\(e\left(\frac{208}{215}\right)\)	\(e\left(\frac{57}{215}\right)\)	\(e\left(\frac{231}{430}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{21}{430}\right)\)	\(e\left(\frac{69}{86}\right)\)
\(\chi_{1291}(28,\cdot)\)	1291.l	215	yes	\(1\)	\(1\)	\(e\left(\frac{89}{215}\right)\)	\(e\left(\frac{188}{215}\right)\)	\(e\left(\frac{178}{215}\right)\)	\(e\left(\frac{33}{215}\right)\)	\(e\left(\frac{62}{215}\right)\)	\(e\left(\frac{48}{215}\right)\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{122}{215}\right)\)	\(e\left(\frac{20}{43}\right)\)
\(\chi_{1291}(29,\cdot)\)	1291.p	1290	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{1290}\right)\)	\(e\left(\frac{1289}{1290}\right)\)	\(e\left(\frac{67}{645}\right)\)	\(e\left(\frac{44}{215}\right)\)	\(e\left(\frac{11}{215}\right)\)	\(e\left(\frac{407}{645}\right)\)	\(e\left(\frac{67}{430}\right)\)	\(e\left(\frac{644}{645}\right)\)	\(e\left(\frac{331}{1290}\right)\)	\(e\left(\frac{31}{258}\right)\)
\(\chi_{1291}(30,\cdot)\)	1291.i	43	yes	\(1\)	\(1\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{32}{43}\right)\)
\(\chi_{1291}(31,\cdot)\)	1291.m	258	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{258}\right)\)	\(e\left(\frac{49}{258}\right)\)	\(e\left(\frac{71}{129}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{52}{129}\right)\)	\(e\left(\frac{71}{86}\right)\)	\(e\left(\frac{49}{129}\right)\)	\(e\left(\frac{35}{258}\right)\)	\(e\left(\frac{145}{258}\right)\)
\(\chi_{1291}(32,\cdot)\)	1291.m	258	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{258}\right)\)	\(e\left(\frac{77}{258}\right)\)	\(e\left(\frac{1}{129}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{8}{129}\right)\)	\(e\left(\frac{1}{86}\right)\)	\(e\left(\frac{77}{129}\right)\)	\(e\left(\frac{55}{258}\right)\)	\(e\left(\frac{191}{258}\right)\)

Introduction

L-functions

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Character group

First 32 of 1290 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.