LMFDB - Group of Dirichlet characters of modulus 841

Show commands: PariGP / SageMath

sage: H = DirichletGroup(841)

pari: g = idealstar(,841,2)

Character group

sage: G.order() pari: g.no
Order	=	812
sage: H.invariants() pari: g.cyc
Structure	=	$C_{812}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{841}(2,\cdot)$

First 32 of 812 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{841}(1,\cdot)$	841.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{841}(2,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{1}{812}\right)$	$e\left(\frac{537}{812}\right)$	$e\left(\frac{1}{406}\right)$	$e\left(\frac{151}{406}\right)$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{94}{203}\right)$	$e\left(\frac{3}{812}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{303}{812}\right)$	$e\left(\frac{81}{812}\right)$
$\chi_{841}(3,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{537}{812}\right)$	$e\left(\frac{109}{812}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{293}{406}\right)$	$e\left(\frac{323}{406}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{799}{812}\right)$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{311}{812}\right)$	$e\left(\frac{461}{812}\right)$
$\chi_{841}(4,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{1}{406}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{66}{203}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{303}{406}\right)$	$e\left(\frac{81}{406}\right)$
$\chi_{841}(5,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{151}{406}\right)$	$e\left(\frac{293}{406}\right)$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{19}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{47}{406}\right)$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{281}{406}\right)$	$e\left(\frac{51}{406}\right)$
$\chi_{841}(6,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{323}{406}\right)$	$e\left(\frac{66}{203}\right)$	$e\left(\frac{19}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{401}{406}\right)$	$e\left(\frac{120}{203}\right)$	$e\left(\frac{307}{406}\right)$	$e\left(\frac{271}{406}\right)$
$\chi_{841}(7,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{94}{203}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{79}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{103}{203}\right)$
$\chi_{841}(8,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{3}{812}\right)$	$e\left(\frac{799}{812}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{47}{406}\right)$	$e\left(\frac{401}{406}\right)$	$e\left(\frac{79}{203}\right)$	$e\left(\frac{9}{812}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{97}{812}\right)$	$e\left(\frac{243}{812}\right)$
$\chi_{841}(9,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{120}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{109}{203}\right)$	$e\left(\frac{311}{406}\right)$	$e\left(\frac{55}{406}\right)$
$\chi_{841}(10,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{303}{812}\right)$	$e\left(\frac{311}{812}\right)$	$e\left(\frac{303}{406}\right)$	$e\left(\frac{281}{406}\right)$	$e\left(\frac{307}{406}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{97}{812}\right)$	$e\left(\frac{311}{406}\right)$	$e\left(\frac{53}{812}\right)$	$e\left(\frac{183}{812}\right)$
$\chi_{841}(11,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{81}{812}\right)$	$e\left(\frac{461}{812}\right)$	$e\left(\frac{81}{406}\right)$	$e\left(\frac{51}{406}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{243}{812}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{183}{812}\right)$	$e\left(\frac{65}{812}\right)$
$\chi_{841}(12,\cdot)$	841.i	116	yes	$-1$	$1$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{89}{116}\right)$
$\chi_{841}(13,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{325}{406}\right)$	$e\left(\frac{128}{203}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{11}{406}\right)$	$e\left(\frac{15}{406}\right)$
$\chi_{841}(14,\cdot)$	841.f	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{841}(15,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{27}{812}\right)$	$e\left(\frac{695}{812}\right)$	$e\left(\frac{27}{406}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{361}{406}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{81}{812}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{61}{812}\right)$	$e\left(\frac{563}{812}\right)$
$\chi_{841}(16,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{2}{203}\right)$	$e\left(\frac{99}{203}\right)$	$e\left(\frac{132}{203}\right)$	$e\left(\frac{173}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{81}{203}\right)$
$\chi_{841}(17,\cdot)$	841.i	116	yes	$-1$	$1$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{91}{116}\right)$
$\chi_{841}(18,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{263}{812}\right)$	$e\left(\frac{755}{812}\right)$	$e\left(\frac{263}{406}\right)$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{103}{406}\right)$	$e\left(\frac{159}{203}\right)$	$e\left(\frac{789}{812}\right)$	$e\left(\frac{349}{406}\right)$	$e\left(\frac{113}{812}\right)$	$e\left(\frac{191}{812}\right)$
$\chi_{841}(19,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{625}{812}\right)$	$e\left(\frac{269}{812}\right)$	$e\left(\frac{219}{406}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{41}{406}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{251}{812}\right)$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{179}{812}\right)$	$e\left(\frac{281}{812}\right)$
$\chi_{841}(20,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{76}{203}\right)$	$e\left(\frac{9}{203}\right)$	$e\left(\frac{152}{203}\right)$	$e\left(\frac{13}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{18}{203}\right)$	$e\left(\frac{89}{203}\right)$	$e\left(\frac{66}{203}\right)$
$\chi_{841}(21,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{101}{812}\right)$	$e\left(\frac{645}{812}\right)$	$e\left(\frac{101}{406}\right)$	$e\left(\frac{229}{406}\right)$	$e\left(\frac{373}{406}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{303}{812}\right)$	$e\left(\frac{239}{406}\right)$	$e\left(\frac{559}{812}\right)$	$e\left(\frac{61}{812}\right)$
$\chi_{841}(22,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{41}{406}\right)$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{123}{406}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{243}{406}\right)$	$e\left(\frac{73}{406}\right)$
$\chi_{841}(23,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{201}{203}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{142}{203}\right)$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{41}{203}\right)$
$\chi_{841}(24,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{135}{203}\right)$	$e\left(\frac{24}{203}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{170}{203}\right)$	$e\left(\frac{159}{203}\right)$	$e\left(\frac{10}{203}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{48}{203}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{176}{203}\right)$
$\chi_{841}(25,\cdot)$	841.j	203	yes	$1$	$1$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{99}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{47}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{51}{203}\right)$
$\chi_{841}(26,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{663}{812}\right)$	$e\left(\frac{375}{812}\right)$	$e\left(\frac{257}{406}\right)$	$e\left(\frac{237}{406}\right)$	$e\left(\frac{113}{406}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{365}{812}\right)$	$e\left(\frac{375}{406}\right)$	$e\left(\frac{325}{812}\right)$	$e\left(\frac{111}{812}\right)$
$\chi_{841}(27,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{799}{812}\right)$	$e\left(\frac{327}{812}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{67}{406}\right)$	$e\left(\frac{157}{406}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{773}{812}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{121}{812}\right)$	$e\left(\frac{571}{812}\right)$
$\chi_{841}(28,\cdot)$	841.h	58	yes	$1$	$1$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{841}(30,\cdot)$	841.g	29	yes	$1$	$1$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{23}{29}\right)$
$\chi_{841}(31,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{421}{812}\right)$	$e\left(\frac{341}{812}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{235}{406}\right)$	$e\left(\frac{381}{406}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{451}{812}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{79}{812}\right)$	$e\left(\frac{809}{812}\right)$
$\chi_{841}(32,\cdot)$	841.l	812	yes	$-1$	$1$	$e\left(\frac{5}{812}\right)$	$e\left(\frac{249}{812}\right)$	$e\left(\frac{5}{406}\right)$	$e\left(\frac{349}{406}\right)$	$e\left(\frac{127}{406}\right)$	$e\left(\frac{64}{203}\right)$	$e\left(\frac{15}{812}\right)$	$e\left(\frac{249}{406}\right)$	$e\left(\frac{703}{812}\right)$	$e\left(\frac{405}{812}\right)$
$\chi_{841}(33,\cdot)$	841.k	406	yes	$1$	$1$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{94}{203}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{115}{406}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{247}{406}\right)$	$e\left(\frac{263}{406}\right)$

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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	$841$
Structure	\(C_{812}\)
Order	$812$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{841}(1,\cdot)\)	841.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{841}(2,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{812}\right)\)	\(e\left(\frac{537}{812}\right)\)	\(e\left(\frac{1}{406}\right)\)	\(e\left(\frac{151}{406}\right)\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{94}{203}\right)\)	\(e\left(\frac{3}{812}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{303}{812}\right)\)	\(e\left(\frac{81}{812}\right)\)
\(\chi_{841}(3,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{537}{812}\right)\)	\(e\left(\frac{109}{812}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{293}{406}\right)\)	\(e\left(\frac{323}{406}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{799}{812}\right)\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{311}{812}\right)\)	\(e\left(\frac{461}{812}\right)\)
\(\chi_{841}(4,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{1}{406}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{66}{203}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{303}{406}\right)\)	\(e\left(\frac{81}{406}\right)\)
\(\chi_{841}(5,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{151}{406}\right)\)	\(e\left(\frac{293}{406}\right)\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{19}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{47}{406}\right)\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{281}{406}\right)\)	\(e\left(\frac{51}{406}\right)\)
\(\chi_{841}(6,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{323}{406}\right)\)	\(e\left(\frac{66}{203}\right)\)	\(e\left(\frac{19}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{401}{406}\right)\)	\(e\left(\frac{120}{203}\right)\)	\(e\left(\frac{307}{406}\right)\)	\(e\left(\frac{271}{406}\right)\)
\(\chi_{841}(7,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{94}{203}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{79}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{103}{203}\right)\)
\(\chi_{841}(8,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{812}\right)\)	\(e\left(\frac{799}{812}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{47}{406}\right)\)	\(e\left(\frac{401}{406}\right)\)	\(e\left(\frac{79}{203}\right)\)	\(e\left(\frac{9}{812}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{97}{812}\right)\)	\(e\left(\frac{243}{812}\right)\)
\(\chi_{841}(9,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{120}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{109}{203}\right)\)	\(e\left(\frac{311}{406}\right)\)	\(e\left(\frac{55}{406}\right)\)
\(\chi_{841}(10,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{303}{812}\right)\)	\(e\left(\frac{311}{812}\right)\)	\(e\left(\frac{303}{406}\right)\)	\(e\left(\frac{281}{406}\right)\)	\(e\left(\frac{307}{406}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{97}{812}\right)\)	\(e\left(\frac{311}{406}\right)\)	\(e\left(\frac{53}{812}\right)\)	\(e\left(\frac{183}{812}\right)\)
\(\chi_{841}(11,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{81}{812}\right)\)	\(e\left(\frac{461}{812}\right)\)	\(e\left(\frac{81}{406}\right)\)	\(e\left(\frac{51}{406}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{243}{812}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{183}{812}\right)\)	\(e\left(\frac{65}{812}\right)\)
\(\chi_{841}(12,\cdot)\)	841.i	116	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{89}{116}\right)\)
\(\chi_{841}(13,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{325}{406}\right)\)	\(e\left(\frac{128}{203}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{11}{406}\right)\)	\(e\left(\frac{15}{406}\right)\)
\(\chi_{841}(14,\cdot)\)	841.f	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{841}(15,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{812}\right)\)	\(e\left(\frac{695}{812}\right)\)	\(e\left(\frac{27}{406}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{361}{406}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{81}{812}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{61}{812}\right)\)	\(e\left(\frac{563}{812}\right)\)
\(\chi_{841}(16,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{2}{203}\right)\)	\(e\left(\frac{99}{203}\right)\)	\(e\left(\frac{132}{203}\right)\)	\(e\left(\frac{173}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{81}{203}\right)\)
\(\chi_{841}(17,\cdot)\)	841.i	116	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{91}{116}\right)\)
\(\chi_{841}(18,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{812}\right)\)	\(e\left(\frac{755}{812}\right)\)	\(e\left(\frac{263}{406}\right)\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{103}{406}\right)\)	\(e\left(\frac{159}{203}\right)\)	\(e\left(\frac{789}{812}\right)\)	\(e\left(\frac{349}{406}\right)\)	\(e\left(\frac{113}{812}\right)\)	\(e\left(\frac{191}{812}\right)\)
\(\chi_{841}(19,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{625}{812}\right)\)	\(e\left(\frac{269}{812}\right)\)	\(e\left(\frac{219}{406}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{41}{406}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{251}{812}\right)\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{179}{812}\right)\)	\(e\left(\frac{281}{812}\right)\)
\(\chi_{841}(20,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{76}{203}\right)\)	\(e\left(\frac{9}{203}\right)\)	\(e\left(\frac{152}{203}\right)\)	\(e\left(\frac{13}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{18}{203}\right)\)	\(e\left(\frac{89}{203}\right)\)	\(e\left(\frac{66}{203}\right)\)
\(\chi_{841}(21,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{812}\right)\)	\(e\left(\frac{645}{812}\right)\)	\(e\left(\frac{101}{406}\right)\)	\(e\left(\frac{229}{406}\right)\)	\(e\left(\frac{373}{406}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{303}{812}\right)\)	\(e\left(\frac{239}{406}\right)\)	\(e\left(\frac{559}{812}\right)\)	\(e\left(\frac{61}{812}\right)\)
\(\chi_{841}(22,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{41}{406}\right)\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{123}{406}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{243}{406}\right)\)	\(e\left(\frac{73}{406}\right)\)
\(\chi_{841}(23,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{201}{203}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{142}{203}\right)\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)
\(\chi_{841}(24,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{135}{203}\right)\)	\(e\left(\frac{24}{203}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{170}{203}\right)\)	\(e\left(\frac{159}{203}\right)\)	\(e\left(\frac{10}{203}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{48}{203}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{176}{203}\right)\)
\(\chi_{841}(25,\cdot)\)	841.j	203	yes	\(1\)	\(1\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{99}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{47}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{51}{203}\right)\)
\(\chi_{841}(26,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{663}{812}\right)\)	\(e\left(\frac{375}{812}\right)\)	\(e\left(\frac{257}{406}\right)\)	\(e\left(\frac{237}{406}\right)\)	\(e\left(\frac{113}{406}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{365}{812}\right)\)	\(e\left(\frac{375}{406}\right)\)	\(e\left(\frac{325}{812}\right)\)	\(e\left(\frac{111}{812}\right)\)
\(\chi_{841}(27,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{799}{812}\right)\)	\(e\left(\frac{327}{812}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{67}{406}\right)\)	\(e\left(\frac{157}{406}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{773}{812}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{121}{812}\right)\)	\(e\left(\frac{571}{812}\right)\)
\(\chi_{841}(28,\cdot)\)	841.h	58	yes	\(1\)	\(1\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{841}(30,\cdot)\)	841.g	29	yes	\(1\)	\(1\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)
\(\chi_{841}(31,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{421}{812}\right)\)	\(e\left(\frac{341}{812}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{235}{406}\right)\)	\(e\left(\frac{381}{406}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{451}{812}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{79}{812}\right)\)	\(e\left(\frac{809}{812}\right)\)
\(\chi_{841}(32,\cdot)\)	841.l	812	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{812}\right)\)	\(e\left(\frac{249}{812}\right)\)	\(e\left(\frac{5}{406}\right)\)	\(e\left(\frac{349}{406}\right)\)	\(e\left(\frac{127}{406}\right)\)	\(e\left(\frac{64}{203}\right)\)	\(e\left(\frac{15}{812}\right)\)	\(e\left(\frac{249}{406}\right)\)	\(e\left(\frac{703}{812}\right)\)	\(e\left(\frac{405}{812}\right)\)
\(\chi_{841}(33,\cdot)\)	841.k	406	yes	\(1\)	\(1\)	\(e\left(\frac{309}{406}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{106}{203}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{94}{203}\right)\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{115}{406}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{247}{406}\right)\)	\(e\left(\frac{263}{406}\right)\)

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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.