LMFDB - Group of Dirichlet characters of modulus 179

Show commands: PariGP / SageMath

sage: H = DirichletGroup(179)

pari: g = idealstar(,179,2)

Character group

sage: G.order() pari: g.no
Order	=	178
sage: H.invariants() pari: g.cyc
Structure	=	$C_{178}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{179}(2,\cdot)$

First 32 of 178 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{179}(1,\cdot)$	179.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{179}(2,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{1}{178}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{109}{178}\right)$	$e\left(\frac{171}{178}\right)$	$e\left(\frac{3}{178}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{139}{178}\right)$	$e\left(\frac{15}{178}\right)$
$\chi_{179}(3,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{12}{89}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{9}{89}\right)$
$\chi_{179}(4,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{15}{89}\right)$
$\chi_{179}(5,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{56}{89}\right)$
$\chi_{179}(6,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{109}{178}\right)$	$e\left(\frac{12}{89}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{149}{178}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{33}{178}\right)$
$\chi_{179}(7,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{171}{178}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{73}{178}\right)$
$\chi_{179}(8,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{3}{178}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{149}{178}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{9}{178}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{45}{178}\right)$
$\chi_{179}(9,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{18}{89}\right)$
$\chi_{179}(10,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{139}{178}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{97}{178}\right)$	$e\left(\frac{127}{178}\right)$
$\chi_{179}(11,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{33}{178}\right)$	$e\left(\frac{73}{178}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{47}{178}\right)$
$\chi_{179}(12,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{66}{89}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{24}{89}\right)$
$\chi_{179}(13,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{54}{89}\right)$
$\chi_{179}(14,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{31}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{44}{89}\right)$
$\chi_{179}(15,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{65}{89}\right)$
$\chi_{179}(16,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{4}{89}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{11}{89}\right)$	$e\left(\frac{30}{89}\right)$
$\chi_{179}(17,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{71}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{88}{89}\right)$
$\chi_{179}(18,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{39}{178}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{83}{178}\right)$	$e\left(\frac{117}{178}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{81}{178}\right)$	$e\left(\frac{51}{178}\right)$
$\chi_{179}(19,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{27}{89}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{78}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{49}{89}\right)$
$\chi_{179}(20,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{48}{89}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{79}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{71}{89}\right)$
$\chi_{179}(21,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{101}{178}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{12}{89}\right)$	$e\left(\frac{27}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{125}{178}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{155}{178}\right)$	$e\left(\frac{91}{178}\right)$
$\chi_{179}(22,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{8}{89}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{71}{89}\right)$	$e\left(\frac{33}{89}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{31}{89}\right)$
$\chi_{179}(23,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{119}{178}\right)$	$e\left(\frac{123}{178}\right)$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{67}{178}\right)$
$\chi_{179}(24,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{31}{89}\right)$	$e\left(\frac{22}{89}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{173}{178}\right)$	$e\left(\frac{113}{178}\right)$	$e\left(\frac{155}{178}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{63}{178}\right)$
$\chi_{179}(25,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{23}{89}\right)$
$\chi_{179}(26,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{115}{178}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{26}{89}\right)$	$e\left(\frac{14}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{167}{178}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{143}{178}\right)$	$e\left(\frac{123}{178}\right)$
$\chi_{179}(27,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{27}{89}\right)$
$\chi_{179}(28,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{173}{178}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{11}{89}\right)$	$e\left(\frac{167}{178}\right)$	$e\left(\frac{35}{178}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{17}{178}\right)$	$e\left(\frac{103}{178}\right)$
$\chi_{179}(29,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{84}{89}\right)$
$\chi_{179}(30,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{69}{178}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{51}{178}\right)$	$e\left(\frac{29}{178}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{145}{178}\right)$
$\chi_{179}(31,\cdot)$	179.c	89	yes	$1$	$1$	$e\left(\frac{31}{89}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{4}{89}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{20}{89}\right)$
$\chi_{179}(32,\cdot)$	179.d	178	yes	$-1$	$1$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{78}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{143}{178}\right)$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{161}{178}\right)$	$e\left(\frac{75}{178}\right)$

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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 $\F_{q}$

Modulus	$179$
Structure	\(C_{178}\)
Order	$178$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{179}(1,\cdot)\)	179.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{179}(2,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{178}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{109}{178}\right)\)	\(e\left(\frac{171}{178}\right)\)	\(e\left(\frac{3}{178}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{139}{178}\right)\)	\(e\left(\frac{15}{178}\right)\)
\(\chi_{179}(3,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{12}{89}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{9}{89}\right)\)
\(\chi_{179}(4,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)
\(\chi_{179}(5,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)
\(\chi_{179}(6,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{178}\right)\)	\(e\left(\frac{12}{89}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{149}{178}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{33}{178}\right)\)
\(\chi_{179}(7,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{171}{178}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{73}{178}\right)\)
\(\chi_{179}(8,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{178}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{149}{178}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{9}{178}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{45}{178}\right)\)
\(\chi_{179}(9,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{18}{89}\right)\)
\(\chi_{179}(10,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{178}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{97}{178}\right)\)	\(e\left(\frac{127}{178}\right)\)
\(\chi_{179}(11,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{33}{178}\right)\)	\(e\left(\frac{73}{178}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{47}{178}\right)\)
\(\chi_{179}(12,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{66}{89}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{24}{89}\right)\)
\(\chi_{179}(13,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{54}{89}\right)\)
\(\chi_{179}(14,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{31}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{44}{89}\right)\)
\(\chi_{179}(15,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{65}{89}\right)\)
\(\chi_{179}(16,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{4}{89}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{11}{89}\right)\)	\(e\left(\frac{30}{89}\right)\)
\(\chi_{179}(17,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{71}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)
\(\chi_{179}(18,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{178}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{83}{178}\right)\)	\(e\left(\frac{117}{178}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{81}{178}\right)\)	\(e\left(\frac{51}{178}\right)\)
\(\chi_{179}(19,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{27}{89}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{78}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{49}{89}\right)\)
\(\chi_{179}(20,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{48}{89}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{79}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{71}{89}\right)\)
\(\chi_{179}(21,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{12}{89}\right)\)	\(e\left(\frac{27}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{125}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{155}{178}\right)\)	\(e\left(\frac{91}{178}\right)\)
\(\chi_{179}(22,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{8}{89}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{71}{89}\right)\)	\(e\left(\frac{33}{89}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{31}{89}\right)\)
\(\chi_{179}(23,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{119}{178}\right)\)	\(e\left(\frac{123}{178}\right)\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{67}{178}\right)\)
\(\chi_{179}(24,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{31}{89}\right)\)	\(e\left(\frac{22}{89}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{173}{178}\right)\)	\(e\left(\frac{113}{178}\right)\)	\(e\left(\frac{155}{178}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{63}{178}\right)\)
\(\chi_{179}(25,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)
\(\chi_{179}(26,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{178}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{26}{89}\right)\)	\(e\left(\frac{14}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{167}{178}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{143}{178}\right)\)	\(e\left(\frac{123}{178}\right)\)
\(\chi_{179}(27,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{27}{89}\right)\)
\(\chi_{179}(28,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{178}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{11}{89}\right)\)	\(e\left(\frac{167}{178}\right)\)	\(e\left(\frac{35}{178}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{17}{178}\right)\)	\(e\left(\frac{103}{178}\right)\)
\(\chi_{179}(29,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)
\(\chi_{179}(30,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{178}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{51}{178}\right)\)	\(e\left(\frac{29}{178}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{145}{178}\right)\)
\(\chi_{179}(31,\cdot)\)	179.c	89	yes	\(1\)	\(1\)	\(e\left(\frac{31}{89}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{4}{89}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{20}{89}\right)\)
\(\chi_{179}(32,\cdot)\)	179.d	178	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{78}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{143}{178}\right)\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{161}{178}\right)\)	\(e\left(\frac{75}{178}\right)\)

Introduction

L-functions

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Character group

First 32 of 178 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.