LMFDB - Group of Dirichlet characters of modulus 862

Show commands: PariGP / SageMath

sage: H = DirichletGroup(862)

pari: g = idealstar(,862,2)

Character group

sage: G.order() pari: g.no
Order	=	430
sage: H.invariants() pari: g.cyc
Structure	=	$C_{430}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{862}(7,\cdot)$

First 32 of 430 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{862}(1,\cdot)$	862.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{862}(3,\cdot)$	862.e	43	no	$1$	$1$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{42}{43}\right)$
$\chi_{862}(5,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{2}{215}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{98}{215}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{152}{215}\right)$	$e\left(\frac{141}{215}\right)$	$e\left(\frac{84}{215}\right)$	$e\left(\frac{106}{215}\right)$
$\chi_{862}(7,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{167}{430}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{31}{430}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{281}{430}\right)$
$\chi_{862}(9,\cdot)$	862.e	43	no	$1$	$1$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{41}{43}\right)$
$\chi_{862}(11,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{98}{215}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{72}{215}\right)$	$e\left(\frac{73}{215}\right)$	$e\left(\frac{138}{215}\right)$	$e\left(\frac{29}{215}\right)$	$e\left(\frac{31}{215}\right)$	$e\left(\frac{34}{215}\right)$
$\chi_{862}(13,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{32}{43}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{167}{430}\right)$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{73}{215}\right)$	$e\left(\frac{369}{430}\right)$	$e\left(\frac{122}{215}\right)$	$e\left(\frac{17}{430}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{57}{430}\right)$
$\chi_{862}(15,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{152}{215}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{138}{215}\right)$	$e\left(\frac{122}{215}\right)$	$e\left(\frac{157}{215}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{149}{215}\right)$	$e\left(\frac{101}{215}\right)$
$\chi_{862}(17,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{141}{215}\right)$	$e\left(\frac{31}{430}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{29}{215}\right)$	$e\left(\frac{17}{430}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{101}{430}\right)$	$e\left(\frac{117}{215}\right)$	$e\left(\frac{111}{430}\right)$
$\chi_{862}(19,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{84}{215}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{31}{215}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{149}{215}\right)$	$e\left(\frac{117}{215}\right)$	$e\left(\frac{88}{215}\right)$	$e\left(\frac{152}{215}\right)$
$\chi_{862}(21,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{106}{215}\right)$	$e\left(\frac{281}{430}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{34}{215}\right)$	$e\left(\frac{57}{430}\right)$	$e\left(\frac{101}{215}\right)$	$e\left(\frac{111}{430}\right)$	$e\left(\frac{152}{215}\right)$	$e\left(\frac{271}{430}\right)$
$\chi_{862}(23,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{61}{215}\right)$	$e\left(\frac{163}{215}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{194}{215}\right)$	$e\left(\frac{131}{215}\right)$	$e\left(\frac{121}{215}\right)$	$e\left(\frac{108}{215}\right)$	$e\left(\frac{197}{215}\right)$	$e\left(\frac{8}{215}\right)$
$\chi_{862}(25,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{4}{215}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{196}{215}\right)$	$e\left(\frac{139}{215}\right)$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{67}{215}\right)$	$e\left(\frac{168}{215}\right)$	$e\left(\frac{212}{215}\right)$
$\chi_{862}(27,\cdot)$	862.e	43	no	$1$	$1$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{40}{43}\right)$
$\chi_{862}(29,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{21}{43}\right)$	$e\left(\frac{53}{215}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{17}{215}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{158}{215}\right)$	$e\left(\frac{189}{215}\right)$	$e\left(\frac{76}{215}\right)$	$e\left(\frac{14}{215}\right)$
$\chi_{862}(31,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{199}{215}\right)$	$e\left(\frac{59}{430}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{76}{215}\right)$	$e\left(\frac{393}{430}\right)$	$e\left(\frac{74}{215}\right)$	$e\left(\frac{109}{430}\right)$	$e\left(\frac{188}{215}\right)$	$e\left(\frac{239}{430}\right)$
$\chi_{862}(33,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{33}{215}\right)$	$e\left(\frac{134}{215}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{18}{215}\right)$	$e\left(\frac{143}{215}\right)$	$e\left(\frac{69}{215}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{29}{215}\right)$
$\chi_{862}(35,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{173}{215}\right)$	$e\left(\frac{343}{430}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{92}{215}\right)$	$e\left(\frac{91}{430}\right)$	$e\left(\frac{33}{215}\right)$	$e\left(\frac{313}{430}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{63}{430}\right)$
$\chi_{862}(37,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{37}{215}\right)$	$e\left(\frac{307}{430}\right)$	$e\left(\frac{35}{43}\right)$	$e\left(\frac{93}{215}\right)$	$e\left(\frac{99}{430}\right)$	$e\left(\frac{17}{215}\right)$	$e\left(\frac{57}{430}\right)$	$e\left(\frac{49}{215}\right)$	$e\left(\frac{267}{430}\right)$
$\chi_{862}(39,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{17}{430}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{113}{215}\right)$	$e\left(\frac{259}{430}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{97}{430}\right)$	$e\left(\frac{189}{215}\right)$	$e\left(\frac{47}{430}\right)$
$\chi_{862}(41,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{109}{215}\right)$	$e\left(\frac{182}{215}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{79}{215}\right)$	$e\left(\frac{114}{215}\right)$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{63}{215}\right)$	$e\left(\frac{187}{215}\right)$
$\chi_{862}(43,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{3}{215}\right)$	$e\left(\frac{83}{430}\right)$	$e\left(\frac{4}{43}\right)$	$e\left(\frac{147}{215}\right)$	$e\left(\frac{101}{430}\right)$	$e\left(\frac{13}{215}\right)$	$e\left(\frac{423}{430}\right)$	$e\left(\frac{126}{215}\right)$	$e\left(\frac{103}{430}\right)$
$\chi_{862}(45,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{21}{215}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{178}{215}\right)$	$e\left(\frac{67}{215}\right)$	$e\left(\frac{162}{215}\right)$	$e\left(\frac{6}{215}\right)$	$e\left(\frac{214}{215}\right)$	$e\left(\frac{96}{215}\right)$
$\chi_{862}(47,\cdot)$	862.f	86	no	$-1$	$1$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{29}{86}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{73}{86}\right)$
$\chi_{862}(49,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{1}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{203}{215}\right)$	$e\left(\frac{167}{215}\right)$	$e\left(\frac{192}{215}\right)$	$e\left(\frac{31}{215}\right)$	$e\left(\frac{174}{215}\right)$	$e\left(\frac{66}{215}\right)$
$\chi_{862}(51,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{76}{215}\right)$	$e\left(\frac{311}{430}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{69}{215}\right)$	$e\left(\frac{337}{430}\right)$	$e\left(\frac{186}{215}\right)$	$e\left(\frac{181}{430}\right)$	$e\left(\frac{182}{215}\right)$	$e\left(\frac{101}{430}\right)$
$\chi_{862}(53,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{186}{215}\right)$	$e\left(\frac{208}{215}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{84}{215}\right)$	$e\left(\frac{121}{215}\right)$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{213}{215}\right)$	$e\left(\frac{72}{215}\right)$	$e\left(\frac{183}{215}\right)$
$\chi_{862}(55,\cdot)$	862.e	43	no	$1$	$1$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{34}{43}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{28}{43}\right)$
$\chi_{862}(57,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{19}{215}\right)$	$e\left(\frac{12}{215}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{71}{215}\right)$	$e\left(\frac{69}{215}\right)$	$e\left(\frac{154}{215}\right)$	$e\left(\frac{157}{215}\right)$	$e\left(\frac{153}{215}\right)$	$e\left(\frac{147}{215}\right)$
$\chi_{862}(59,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{67}{215}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{56}{215}\right)$	$e\left(\frac{9}{215}\right)$	$e\left(\frac{179}{215}\right)$	$e\left(\frac{142}{215}\right)$	$e\left(\frac{48}{215}\right)$	$e\left(\frac{122}{215}\right)$
$\chi_{862}(61,\cdot)$	862.g	215	no	$1$	$1$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{34}{215}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{214}{215}\right)$	$e\left(\frac{4}{215}\right)$	$e\left(\frac{32}{215}\right)$	$e\left(\frac{138}{215}\right)$	$e\left(\frac{82}{215}\right)$
$\chi_{862}(63,\cdot)$	862.h	430	no	$-1$	$1$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{41}{215}\right)$	$e\left(\frac{131}{430}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{74}{215}\right)$	$e\left(\frac{377}{430}\right)$	$e\left(\frac{106}{215}\right)$	$e\left(\frac{191}{430}\right)$	$e\left(\frac{2}{215}\right)$	$e\left(\frac{261}{430}\right)$

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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	$862$
Structure	\(C_{430}\)
Order	$430$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{862}(1,\cdot)\)	862.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{862}(3,\cdot)\)	862.e	43	no	\(1\)	\(1\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{42}{43}\right)\)
\(\chi_{862}(5,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{2}{215}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{98}{215}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{152}{215}\right)\)	\(e\left(\frac{141}{215}\right)\)	\(e\left(\frac{84}{215}\right)\)	\(e\left(\frac{106}{215}\right)\)
\(\chi_{862}(7,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{167}{430}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{31}{430}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{281}{430}\right)\)
\(\chi_{862}(9,\cdot)\)	862.e	43	no	\(1\)	\(1\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)
\(\chi_{862}(11,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{98}{215}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{72}{215}\right)\)	\(e\left(\frac{73}{215}\right)\)	\(e\left(\frac{138}{215}\right)\)	\(e\left(\frac{29}{215}\right)\)	\(e\left(\frac{31}{215}\right)\)	\(e\left(\frac{34}{215}\right)\)
\(\chi_{862}(13,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{32}{43}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{167}{430}\right)\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{73}{215}\right)\)	\(e\left(\frac{369}{430}\right)\)	\(e\left(\frac{122}{215}\right)\)	\(e\left(\frac{17}{430}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{57}{430}\right)\)
\(\chi_{862}(15,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{152}{215}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{138}{215}\right)\)	\(e\left(\frac{122}{215}\right)\)	\(e\left(\frac{157}{215}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{149}{215}\right)\)	\(e\left(\frac{101}{215}\right)\)
\(\chi_{862}(17,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{141}{215}\right)\)	\(e\left(\frac{31}{430}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{29}{215}\right)\)	\(e\left(\frac{17}{430}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{101}{430}\right)\)	\(e\left(\frac{117}{215}\right)\)	\(e\left(\frac{111}{430}\right)\)
\(\chi_{862}(19,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{84}{215}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{31}{215}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{149}{215}\right)\)	\(e\left(\frac{117}{215}\right)\)	\(e\left(\frac{88}{215}\right)\)	\(e\left(\frac{152}{215}\right)\)
\(\chi_{862}(21,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{106}{215}\right)\)	\(e\left(\frac{281}{430}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{34}{215}\right)\)	\(e\left(\frac{57}{430}\right)\)	\(e\left(\frac{101}{215}\right)\)	\(e\left(\frac{111}{430}\right)\)	\(e\left(\frac{152}{215}\right)\)	\(e\left(\frac{271}{430}\right)\)
\(\chi_{862}(23,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{61}{215}\right)\)	\(e\left(\frac{163}{215}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{194}{215}\right)\)	\(e\left(\frac{131}{215}\right)\)	\(e\left(\frac{121}{215}\right)\)	\(e\left(\frac{108}{215}\right)\)	\(e\left(\frac{197}{215}\right)\)	\(e\left(\frac{8}{215}\right)\)
\(\chi_{862}(25,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{4}{215}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{196}{215}\right)\)	\(e\left(\frac{139}{215}\right)\)	\(e\left(\frac{89}{215}\right)\)	\(e\left(\frac{67}{215}\right)\)	\(e\left(\frac{168}{215}\right)\)	\(e\left(\frac{212}{215}\right)\)
\(\chi_{862}(27,\cdot)\)	862.e	43	no	\(1\)	\(1\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{40}{43}\right)\)
\(\chi_{862}(29,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{21}{43}\right)\)	\(e\left(\frac{53}{215}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{17}{215}\right)\)	\(e\left(\frac{68}{215}\right)\)	\(e\left(\frac{158}{215}\right)\)	\(e\left(\frac{189}{215}\right)\)	\(e\left(\frac{76}{215}\right)\)	\(e\left(\frac{14}{215}\right)\)
\(\chi_{862}(31,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{199}{215}\right)\)	\(e\left(\frac{59}{430}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{76}{215}\right)\)	\(e\left(\frac{393}{430}\right)\)	\(e\left(\frac{74}{215}\right)\)	\(e\left(\frac{109}{430}\right)\)	\(e\left(\frac{188}{215}\right)\)	\(e\left(\frac{239}{430}\right)\)
\(\chi_{862}(33,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{33}{215}\right)\)	\(e\left(\frac{134}{215}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{18}{215}\right)\)	\(e\left(\frac{143}{215}\right)\)	\(e\left(\frac{69}{215}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{29}{215}\right)\)
\(\chi_{862}(35,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{173}{215}\right)\)	\(e\left(\frac{343}{430}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{92}{215}\right)\)	\(e\left(\frac{91}{430}\right)\)	\(e\left(\frac{33}{215}\right)\)	\(e\left(\frac{313}{430}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{63}{430}\right)\)
\(\chi_{862}(37,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{37}{215}\right)\)	\(e\left(\frac{307}{430}\right)\)	\(e\left(\frac{35}{43}\right)\)	\(e\left(\frac{93}{215}\right)\)	\(e\left(\frac{99}{430}\right)\)	\(e\left(\frac{17}{215}\right)\)	\(e\left(\frac{57}{430}\right)\)	\(e\left(\frac{49}{215}\right)\)	\(e\left(\frac{267}{430}\right)\)
\(\chi_{862}(39,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{17}{430}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{113}{215}\right)\)	\(e\left(\frac{259}{430}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{97}{430}\right)\)	\(e\left(\frac{189}{215}\right)\)	\(e\left(\frac{47}{430}\right)\)
\(\chi_{862}(41,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{109}{215}\right)\)	\(e\left(\frac{182}{215}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{79}{215}\right)\)	\(e\left(\frac{114}{215}\right)\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{63}{215}\right)\)	\(e\left(\frac{187}{215}\right)\)
\(\chi_{862}(43,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{3}{215}\right)\)	\(e\left(\frac{83}{430}\right)\)	\(e\left(\frac{4}{43}\right)\)	\(e\left(\frac{147}{215}\right)\)	\(e\left(\frac{101}{430}\right)\)	\(e\left(\frac{13}{215}\right)\)	\(e\left(\frac{423}{430}\right)\)	\(e\left(\frac{126}{215}\right)\)	\(e\left(\frac{103}{430}\right)\)
\(\chi_{862}(45,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{21}{215}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{178}{215}\right)\)	\(e\left(\frac{67}{215}\right)\)	\(e\left(\frac{162}{215}\right)\)	\(e\left(\frac{6}{215}\right)\)	\(e\left(\frac{214}{215}\right)\)	\(e\left(\frac{96}{215}\right)\)
\(\chi_{862}(47,\cdot)\)	862.f	86	no	\(-1\)	\(1\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{29}{86}\right)\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{73}{86}\right)\)
\(\chi_{862}(49,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{1}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{203}{215}\right)\)	\(e\left(\frac{167}{215}\right)\)	\(e\left(\frac{192}{215}\right)\)	\(e\left(\frac{31}{215}\right)\)	\(e\left(\frac{174}{215}\right)\)	\(e\left(\frac{66}{215}\right)\)
\(\chi_{862}(51,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{76}{215}\right)\)	\(e\left(\frac{311}{430}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{69}{215}\right)\)	\(e\left(\frac{337}{430}\right)\)	\(e\left(\frac{186}{215}\right)\)	\(e\left(\frac{181}{430}\right)\)	\(e\left(\frac{182}{215}\right)\)	\(e\left(\frac{101}{430}\right)\)
\(\chi_{862}(53,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{186}{215}\right)\)	\(e\left(\frac{208}{215}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{84}{215}\right)\)	\(e\left(\frac{121}{215}\right)\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{213}{215}\right)\)	\(e\left(\frac{72}{215}\right)\)	\(e\left(\frac{183}{215}\right)\)
\(\chi_{862}(55,\cdot)\)	862.e	43	no	\(1\)	\(1\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{34}{43}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)
\(\chi_{862}(57,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{19}{215}\right)\)	\(e\left(\frac{12}{215}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{71}{215}\right)\)	\(e\left(\frac{69}{215}\right)\)	\(e\left(\frac{154}{215}\right)\)	\(e\left(\frac{157}{215}\right)\)	\(e\left(\frac{153}{215}\right)\)	\(e\left(\frac{147}{215}\right)\)
\(\chi_{862}(59,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{67}{215}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{56}{215}\right)\)	\(e\left(\frac{9}{215}\right)\)	\(e\left(\frac{179}{215}\right)\)	\(e\left(\frac{142}{215}\right)\)	\(e\left(\frac{48}{215}\right)\)	\(e\left(\frac{122}{215}\right)\)
\(\chi_{862}(61,\cdot)\)	862.g	215	no	\(1\)	\(1\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{34}{215}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{214}{215}\right)\)	\(e\left(\frac{4}{215}\right)\)	\(e\left(\frac{32}{215}\right)\)	\(e\left(\frac{138}{215}\right)\)	\(e\left(\frac{82}{215}\right)\)
\(\chi_{862}(63,\cdot)\)	862.h	430	no	\(-1\)	\(1\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{41}{215}\right)\)	\(e\left(\frac{131}{430}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{74}{215}\right)\)	\(e\left(\frac{377}{430}\right)\)	\(e\left(\frac{106}{215}\right)\)	\(e\left(\frac{191}{430}\right)\)	\(e\left(\frac{2}{215}\right)\)	\(e\left(\frac{261}{430}\right)\)

Introduction

L-functions

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Character group

First 32 of 430 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.