LMFDB - Group of Dirichlet characters of modulus 716

sage:H = DirichletGroup(716)

pari:g = idealstar(,716,2)

Character group

sage:G.order() pari:g.no
Order	=	356
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{178}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{716}(359,\cdot)$, $\chi_{716}(181,\cdot)$

First 32 of 356 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{716}(1,\cdot)$	716.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{716}(3,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{107}{178}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{47}{178}\right)$	$e\left(\frac{25}{89}\right)$
$\chi_{716}(5,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{27}{89}\right)$
$\chi_{716}(7,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{147}{178}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{5}{178}\right)$
$\chi_{716}(9,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{50}{89}\right)$
$\chi_{716}(11,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{107}{178}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{41}{178}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{9}{178}\right)$	$e\left(\frac{91}{178}\right)$
$\chi_{716}(13,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{61}{89}\right)$
$\chi_{716}(15,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{147}{178}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{41}{178}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{52}{89}\right)$
$\chi_{716}(17,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{17}{89}\right)$
$\chi_{716}(19,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{47}{178}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{9}{178}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{57}{89}\right)$
$\chi_{716}(21,\cdot)$	716.f	178	no	$-1$	$1$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{27}{89}\right)$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{91}{178}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{55}{178}\right)$
$\chi_{716}(23,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{73}{178}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{78}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{13}{178}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{81}{178}\right)$	$e\left(\frac{107}{178}\right)$
$\chi_{716}(25,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{54}{89}\right)$
$\chi_{716}(27,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{143}{178}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{14}{89}\right)$	$e\left(\frac{141}{178}\right)$	$e\left(\frac{75}{89}\right)$
$\chi_{716}(29,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{4}{89}\right)$	$e\left(\frac{71}{89}\right)$	$e\left(\frac{85}{89}\right)$
$\chi_{716}(31,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{129}{178}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{33}{178}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{16}{89}\right)$
$\chi_{716}(33,\cdot)$	716.f	178	no	$-1$	$1$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{29}{178}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{65}{178}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{141}{178}\right)$
$\chi_{716}(35,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{175}{178}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{31}{89}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{48}{89}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{97}{178}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{59}{178}\right)$
$\chi_{716}(37,\cdot)$	716.f	178	no	$-1$	$1$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{25}{178}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{99}{178}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{97}{178}\right)$
$\chi_{716}(39,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{35}{178}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{137}{178}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{37}{178}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{86}{89}\right)$
$\chi_{716}(41,\cdot)$	716.f	178	no	$-1$	$1$	$e\left(\frac{4}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{161}{178}\right)$	$e\left(\frac{8}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{169}{178}\right)$
$\chi_{716}(43,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{7}{178}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{63}{178}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{137}{178}\right)$	$e\left(\frac{35}{89}\right)$
$\chi_{716}(45,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{12}{89}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{77}{89}\right)$
$\chi_{716}(47,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{38}{89}\right)$
$\chi_{716}(49,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{5}{89}\right)$
$\chi_{716}(51,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{129}{178}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{105}{178}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{31}{178}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{42}{89}\right)$
$\chi_{716}(53,\cdot)$	716.f	178	no	$-1$	$1$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{35}{178}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{117}{178}\right)$
$\chi_{716}(55,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{59}{178}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{169}{178}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{145}{178}\right)$
$\chi_{716}(57,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{26}{89}\right)$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{79}{89}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{82}{89}\right)$
$\chi_{716}(59,\cdot)$	716.h	178	yes	$-1$	$1$	$e\left(\frac{103}{178}\right)$	$e\left(\frac{4}{89}\right)$	$e\left(\frac{37}{178}\right)$	$e\left(\frac{14}{89}\right)$	$e\left(\frac{175}{178}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{7}{178}\right)$	$e\left(\frac{70}{89}\right)$
$\chi_{716}(61,\cdot)$	716.e	89	no	$1$	$1$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{33}{89}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{76}{89}\right)$
$\chi_{716}(63,\cdot)$	716.g	178	yes	$1$	$1$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{161}{178}\right)$	$e\left(\frac{105}{178}\right)$

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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	$716$
Structure	\(C_{2}\times C_{178}\)
Order	$356$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{716}(1,\cdot)\)	716.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{716}(3,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{107}{178}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)
\(\chi_{716}(5,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{27}{89}\right)\)
\(\chi_{716}(7,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{147}{178}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{5}{178}\right)\)
\(\chi_{716}(9,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{50}{89}\right)\)
\(\chi_{716}(11,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{107}{178}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{41}{178}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{9}{178}\right)\)	\(e\left(\frac{91}{178}\right)\)
\(\chi_{716}(13,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{61}{89}\right)\)
\(\chi_{716}(15,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{147}{178}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{41}{178}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)
\(\chi_{716}(17,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)
\(\chi_{716}(19,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{9}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{57}{89}\right)\)
\(\chi_{716}(21,\cdot)\)	716.f	178	no	\(-1\)	\(1\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{27}{89}\right)\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{91}{178}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)
\(\chi_{716}(23,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{73}{178}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{78}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{13}{178}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{81}{178}\right)\)	\(e\left(\frac{107}{178}\right)\)
\(\chi_{716}(25,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{54}{89}\right)\)
\(\chi_{716}(27,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{143}{178}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{14}{89}\right)\)	\(e\left(\frac{141}{178}\right)\)	\(e\left(\frac{75}{89}\right)\)
\(\chi_{716}(29,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{4}{89}\right)\)	\(e\left(\frac{71}{89}\right)\)	\(e\left(\frac{85}{89}\right)\)
\(\chi_{716}(31,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{129}{178}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{33}{178}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{16}{89}\right)\)
\(\chi_{716}(33,\cdot)\)	716.f	178	no	\(-1\)	\(1\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{29}{178}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{65}{178}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{141}{178}\right)\)
\(\chi_{716}(35,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{175}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{31}{89}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{48}{89}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{97}{178}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{59}{178}\right)\)
\(\chi_{716}(37,\cdot)\)	716.f	178	no	\(-1\)	\(1\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{25}{178}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{99}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{97}{178}\right)\)
\(\chi_{716}(39,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{178}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{137}{178}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{37}{178}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{86}{89}\right)\)
\(\chi_{716}(41,\cdot)\)	716.f	178	no	\(-1\)	\(1\)	\(e\left(\frac{4}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{161}{178}\right)\)	\(e\left(\frac{8}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{169}{178}\right)\)
\(\chi_{716}(43,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{178}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{63}{178}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{137}{178}\right)\)	\(e\left(\frac{35}{89}\right)\)
\(\chi_{716}(45,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{12}{89}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{77}{89}\right)\)
\(\chi_{716}(47,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)
\(\chi_{716}(49,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{5}{89}\right)\)
\(\chi_{716}(51,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{129}{178}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{105}{178}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{31}{178}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{42}{89}\right)\)
\(\chi_{716}(53,\cdot)\)	716.f	178	no	\(-1\)	\(1\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{35}{178}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{117}{178}\right)\)
\(\chi_{716}(55,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{59}{178}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{169}{178}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{145}{178}\right)\)
\(\chi_{716}(57,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{26}{89}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{79}{89}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)
\(\chi_{716}(59,\cdot)\)	716.h	178	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{178}\right)\)	\(e\left(\frac{4}{89}\right)\)	\(e\left(\frac{37}{178}\right)\)	\(e\left(\frac{14}{89}\right)\)	\(e\left(\frac{175}{178}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{7}{178}\right)\)	\(e\left(\frac{70}{89}\right)\)
\(\chi_{716}(61,\cdot)\)	716.e	89	no	\(1\)	\(1\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{33}{89}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{76}{89}\right)\)
\(\chi_{716}(63,\cdot)\)	716.g	178	yes	\(1\)	\(1\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{161}{178}\right)\)	\(e\left(\frac{105}{178}\right)\)

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L-functions

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First 32 of 356 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.