LMFDB - Group of Dirichlet characters of modulus 1129

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1129)

pari: g = idealstar(,1129,2)

Character group

sage: G.order() pari: g.no
Order	=	1128
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1128}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1129}(11,\cdot)$

First 32 of 1128 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1129}(1,\cdot)$	1129.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1129}(2,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{205}{282}\right)$	$e\left(\frac{85}{282}\right)$	$e\left(\frac{64}{141}\right)$	$e\left(\frac{134}{141}\right)$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{5}{282}\right)$	$e\left(\frac{17}{94}\right)$	$e\left(\frac{85}{141}\right)$	$e\left(\frac{191}{282}\right)$	$e\left(\frac{149}{564}\right)$
$\chi_{1129}(3,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{85}{282}\right)$	$e\left(\frac{49}{282}\right)$	$e\left(\frac{85}{141}\right)$	$e\left(\frac{59}{141}\right)$	$e\left(\frac{67}{141}\right)$	$e\left(\frac{119}{282}\right)$	$e\left(\frac{85}{94}\right)$	$e\left(\frac{49}{141}\right)$	$e\left(\frac{203}{282}\right)$	$e\left(\frac{557}{564}\right)$
$\chi_{1129}(4,\cdot)$	1129.m	282	yes	$1$	$1$	$e\left(\frac{64}{141}\right)$	$e\left(\frac{85}{141}\right)$	$e\left(\frac{128}{141}\right)$	$e\left(\frac{127}{141}\right)$	$e\left(\frac{8}{141}\right)$	$e\left(\frac{5}{141}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{29}{141}\right)$	$e\left(\frac{50}{141}\right)$	$e\left(\frac{149}{282}\right)$
$\chi_{1129}(5,\cdot)$	1129.m	282	yes	$1$	$1$	$e\left(\frac{134}{141}\right)$	$e\left(\frac{59}{141}\right)$	$e\left(\frac{127}{141}\right)$	$e\left(\frac{50}{141}\right)$	$e\left(\frac{52}{141}\right)$	$e\left(\frac{103}{141}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{118}{141}\right)$	$e\left(\frac{43}{141}\right)$	$e\left(\frac{193}{282}\right)$
$\chi_{1129}(6,\cdot)$	1129.m	282	yes	$1$	$1$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{67}{141}\right)$	$e\left(\frac{8}{141}\right)$	$e\left(\frac{52}{141}\right)$	$e\left(\frac{71}{141}\right)$	$e\left(\frac{62}{141}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{134}{141}\right)$	$e\left(\frac{56}{141}\right)$	$e\left(\frac{71}{282}\right)$
$\chi_{1129}(7,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{5}{282}\right)$	$e\left(\frac{119}{282}\right)$	$e\left(\frac{5}{141}\right)$	$e\left(\frac{103}{141}\right)$	$e\left(\frac{62}{141}\right)$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{5}{94}\right)$	$e\left(\frac{119}{141}\right)$	$e\left(\frac{211}{282}\right)$	$e\left(\frac{265}{564}\right)$
$\chi_{1129}(8,\cdot)$	1129.l	188	yes	$1$	$1$	$e\left(\frac{17}{94}\right)$	$e\left(\frac{85}{94}\right)$	$e\left(\frac{17}{47}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{4}{47}\right)$	$e\left(\frac{5}{94}\right)$	$e\left(\frac{51}{94}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{3}{94}\right)$	$e\left(\frac{149}{188}\right)$
$\chi_{1129}(9,\cdot)$	1129.m	282	yes	$1$	$1$	$e\left(\frac{85}{141}\right)$	$e\left(\frac{49}{141}\right)$	$e\left(\frac{29}{141}\right)$	$e\left(\frac{118}{141}\right)$	$e\left(\frac{134}{141}\right)$	$e\left(\frac{119}{141}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{98}{141}\right)$	$e\left(\frac{62}{141}\right)$	$e\left(\frac{275}{282}\right)$
$\chi_{1129}(10,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{191}{282}\right)$	$e\left(\frac{203}{282}\right)$	$e\left(\frac{50}{141}\right)$	$e\left(\frac{43}{141}\right)$	$e\left(\frac{56}{141}\right)$	$e\left(\frac{211}{282}\right)$	$e\left(\frac{3}{94}\right)$	$e\left(\frac{62}{141}\right)$	$e\left(\frac{277}{282}\right)$	$e\left(\frac{535}{564}\right)$
$\chi_{1129}(11,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{149}{564}\right)$	$e\left(\frac{557}{564}\right)$	$e\left(\frac{149}{282}\right)$	$e\left(\frac{193}{282}\right)$	$e\left(\frac{71}{282}\right)$	$e\left(\frac{265}{564}\right)$	$e\left(\frac{149}{188}\right)$	$e\left(\frac{275}{282}\right)$	$e\left(\frac{535}{564}\right)$	$e\left(\frac{1}{1128}\right)$
$\chi_{1129}(12,\cdot)$	1129.l	188	yes	$1$	$1$	$e\left(\frac{71}{94}\right)$	$e\left(\frac{73}{94}\right)$	$e\left(\frac{24}{47}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{43}{94}\right)$	$e\left(\frac{25}{94}\right)$	$e\left(\frac{26}{47}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{97}{188}\right)$
$\chi_{1129}(13,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{455}{564}\right)$	$e\left(\frac{395}{564}\right)$	$e\left(\frac{173}{282}\right)$	$e\left(\frac{67}{282}\right)$	$e\left(\frac{143}{282}\right)$	$e\left(\frac{355}{564}\right)$	$e\left(\frac{79}{188}\right)$	$e\left(\frac{113}{282}\right)$	$e\left(\frac{25}{564}\right)$	$e\left(\frac{991}{1128}\right)$
$\chi_{1129}(14,\cdot)$	1129.j	94	yes	$1$	$1$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{32}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{69}{94}\right)$
$\chi_{1129}(15,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{71}{282}\right)$	$e\left(\frac{167}{282}\right)$	$e\left(\frac{71}{141}\right)$	$e\left(\frac{109}{141}\right)$	$e\left(\frac{119}{141}\right)$	$e\left(\frac{43}{282}\right)$	$e\left(\frac{71}{94}\right)$	$e\left(\frac{26}{141}\right)$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{379}{564}\right)$
$\chi_{1129}(16,\cdot)$	1129.k	141	yes	$1$	$1$	$e\left(\frac{128}{141}\right)$	$e\left(\frac{29}{141}\right)$	$e\left(\frac{115}{141}\right)$	$e\left(\frac{113}{141}\right)$	$e\left(\frac{16}{141}\right)$	$e\left(\frac{10}{141}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{58}{141}\right)$	$e\left(\frac{100}{141}\right)$	$e\left(\frac{8}{141}\right)$
$\chi_{1129}(17,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{409}{564}\right)$	$e\left(\frac{541}{564}\right)$	$e\left(\frac{127}{282}\right)$	$e\left(\frac{191}{282}\right)$	$e\left(\frac{193}{282}\right)$	$e\left(\frac{65}{564}\right)$	$e\left(\frac{33}{188}\right)$	$e\left(\frac{259}{282}\right)$	$e\left(\frac{227}{564}\right)$	$e\left(\frac{809}{1128}\right)$
$\chi_{1129}(18,\cdot)$	1129.l	188	yes	$1$	$1$	$e\left(\frac{31}{94}\right)$	$e\left(\frac{61}{94}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{81}{94}\right)$	$e\left(\frac{93}{94}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{11}{94}\right)$	$e\left(\frac{45}{188}\right)$
$\chi_{1129}(19,\cdot)$	1129.n	376	yes	$-1$	$1$	$e\left(\frac{105}{188}\right)$	$e\left(\frac{149}{188}\right)$	$e\left(\frac{11}{94}\right)$	$e\left(\frac{1}{94}\right)$	$e\left(\frac{33}{94}\right)$	$e\left(\frac{53}{188}\right)$	$e\left(\frac{127}{188}\right)$	$e\left(\frac{55}{94}\right)$	$e\left(\frac{107}{188}\right)$	$e\left(\frac{301}{376}\right)$
$\chi_{1129}(20,\cdot)$	1129.i	47	yes	$1$	$1$	$e\left(\frac{19}{47}\right)$	$e\left(\frac{1}{47}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{10}{47}\right)$
$\chi_{1129}(21,\cdot)$	1129.j	94	yes	$1$	$1$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{28}{47}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{22}{47}\right)$	$e\left(\frac{43}{94}\right)$
$\chi_{1129}(22,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{559}{564}\right)$	$e\left(\frac{163}{564}\right)$	$e\left(\frac{277}{282}\right)$	$e\left(\frac{179}{282}\right)$	$e\left(\frac{79}{282}\right)$	$e\left(\frac{275}{564}\right)$	$e\left(\frac{183}{188}\right)$	$e\left(\frac{163}{282}\right)$	$e\left(\frac{353}{564}\right)$	$e\left(\frac{299}{1128}\right)$
$\chi_{1129}(23,\cdot)$	1129.l	188	yes	$1$	$1$	$e\left(\frac{65}{94}\right)$	$e\left(\frac{43}{94}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{91}{94}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{17}{94}\right)$	$e\left(\frac{155}{188}\right)$
$\chi_{1129}(24,\cdot)$	1129.k	141	yes	$1$	$1$	$e\left(\frac{68}{141}\right)$	$e\left(\frac{11}{141}\right)$	$e\left(\frac{136}{141}\right)$	$e\left(\frac{38}{141}\right)$	$e\left(\frac{79}{141}\right)$	$e\left(\frac{67}{141}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{22}{141}\right)$	$e\left(\frac{106}{141}\right)$	$e\left(\frac{110}{141}\right)$
$\chi_{1129}(25,\cdot)$	1129.k	141	yes	$1$	$1$	$e\left(\frac{127}{141}\right)$	$e\left(\frac{118}{141}\right)$	$e\left(\frac{113}{141}\right)$	$e\left(\frac{100}{141}\right)$	$e\left(\frac{104}{141}\right)$	$e\left(\frac{65}{141}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{95}{141}\right)$	$e\left(\frac{86}{141}\right)$	$e\left(\frac{52}{141}\right)$
$\chi_{1129}(26,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{301}{564}\right)$	$e\left(\frac{1}{564}\right)$	$e\left(\frac{19}{282}\right)$	$e\left(\frac{53}{282}\right)$	$e\left(\frac{151}{282}\right)$	$e\left(\frac{365}{564}\right)$	$e\left(\frac{113}{188}\right)$	$e\left(\frac{1}{282}\right)$	$e\left(\frac{407}{564}\right)$	$e\left(\frac{161}{1128}\right)$
$\chi_{1129}(27,\cdot)$	1129.l	188	yes	$1$	$1$	$e\left(\frac{85}{94}\right)$	$e\left(\frac{49}{94}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{25}{94}\right)$	$e\left(\frac{67}{94}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{15}{94}\right)$	$e\left(\frac{181}{188}\right)$
$\chi_{1129}(28,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{133}{282}\right)$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{133}{141}\right)$	$e\left(\frac{89}{141}\right)$	$e\left(\frac{70}{141}\right)$	$e\left(\frac{17}{282}\right)$	$e\left(\frac{39}{94}\right)$	$e\left(\frac{7}{141}\right)$	$e\left(\frac{29}{282}\right)$	$e\left(\frac{563}{564}\right)$
$\chi_{1129}(29,\cdot)$	1129.p	1128	yes	$-1$	$1$	$e\left(\frac{349}{564}\right)$	$e\left(\frac{241}{564}\right)$	$e\left(\frac{67}{282}\right)$	$e\left(\frac{83}{282}\right)$	$e\left(\frac{13}{282}\right)$	$e\left(\frac{545}{564}\right)$	$e\left(\frac{161}{188}\right)$	$e\left(\frac{241}{282}\right)$	$e\left(\frac{515}{564}\right)$	$e\left(\frac{449}{1128}\right)$
$\chi_{1129}(30,\cdot)$	1129.i	47	yes	$1$	$1$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{42}{47}\right)$	$e\left(\frac{45}{47}\right)$	$e\left(\frac{34}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{33}{47}\right)$	$e\left(\frac{44}{47}\right)$
$\chi_{1129}(31,\cdot)$	1129.f	8	yes	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-1$	$-i$	$i$	$-1$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{1129}(32,\cdot)$	1129.o	564	yes	$1$	$1$	$e\left(\frac{179}{282}\right)$	$e\left(\frac{143}{282}\right)$	$e\left(\frac{38}{141}\right)$	$e\left(\frac{106}{141}\right)$	$e\left(\frac{20}{141}\right)$	$e\left(\frac{25}{282}\right)$	$e\left(\frac{85}{94}\right)$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{109}{282}\right)$	$e\left(\frac{181}{564}\right)$

Click here to search among the remaining 1096 characters.

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	$1129$
Structure	\(C_{1128}\)
Order	$1128$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1129}(1,\cdot)\)	1129.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1129}(2,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{205}{282}\right)\)	\(e\left(\frac{85}{282}\right)\)	\(e\left(\frac{64}{141}\right)\)	\(e\left(\frac{134}{141}\right)\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{5}{282}\right)\)	\(e\left(\frac{17}{94}\right)\)	\(e\left(\frac{85}{141}\right)\)	\(e\left(\frac{191}{282}\right)\)	\(e\left(\frac{149}{564}\right)\)
\(\chi_{1129}(3,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{85}{282}\right)\)	\(e\left(\frac{49}{282}\right)\)	\(e\left(\frac{85}{141}\right)\)	\(e\left(\frac{59}{141}\right)\)	\(e\left(\frac{67}{141}\right)\)	\(e\left(\frac{119}{282}\right)\)	\(e\left(\frac{85}{94}\right)\)	\(e\left(\frac{49}{141}\right)\)	\(e\left(\frac{203}{282}\right)\)	\(e\left(\frac{557}{564}\right)\)
\(\chi_{1129}(4,\cdot)\)	1129.m	282	yes	\(1\)	\(1\)	\(e\left(\frac{64}{141}\right)\)	\(e\left(\frac{85}{141}\right)\)	\(e\left(\frac{128}{141}\right)\)	\(e\left(\frac{127}{141}\right)\)	\(e\left(\frac{8}{141}\right)\)	\(e\left(\frac{5}{141}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{29}{141}\right)\)	\(e\left(\frac{50}{141}\right)\)	\(e\left(\frac{149}{282}\right)\)
\(\chi_{1129}(5,\cdot)\)	1129.m	282	yes	\(1\)	\(1\)	\(e\left(\frac{134}{141}\right)\)	\(e\left(\frac{59}{141}\right)\)	\(e\left(\frac{127}{141}\right)\)	\(e\left(\frac{50}{141}\right)\)	\(e\left(\frac{52}{141}\right)\)	\(e\left(\frac{103}{141}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{118}{141}\right)\)	\(e\left(\frac{43}{141}\right)\)	\(e\left(\frac{193}{282}\right)\)
\(\chi_{1129}(6,\cdot)\)	1129.m	282	yes	\(1\)	\(1\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{67}{141}\right)\)	\(e\left(\frac{8}{141}\right)\)	\(e\left(\frac{52}{141}\right)\)	\(e\left(\frac{71}{141}\right)\)	\(e\left(\frac{62}{141}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{134}{141}\right)\)	\(e\left(\frac{56}{141}\right)\)	\(e\left(\frac{71}{282}\right)\)
\(\chi_{1129}(7,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{5}{282}\right)\)	\(e\left(\frac{119}{282}\right)\)	\(e\left(\frac{5}{141}\right)\)	\(e\left(\frac{103}{141}\right)\)	\(e\left(\frac{62}{141}\right)\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{5}{94}\right)\)	\(e\left(\frac{119}{141}\right)\)	\(e\left(\frac{211}{282}\right)\)	\(e\left(\frac{265}{564}\right)\)
\(\chi_{1129}(8,\cdot)\)	1129.l	188	yes	\(1\)	\(1\)	\(e\left(\frac{17}{94}\right)\)	\(e\left(\frac{85}{94}\right)\)	\(e\left(\frac{17}{47}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{4}{47}\right)\)	\(e\left(\frac{5}{94}\right)\)	\(e\left(\frac{51}{94}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{3}{94}\right)\)	\(e\left(\frac{149}{188}\right)\)
\(\chi_{1129}(9,\cdot)\)	1129.m	282	yes	\(1\)	\(1\)	\(e\left(\frac{85}{141}\right)\)	\(e\left(\frac{49}{141}\right)\)	\(e\left(\frac{29}{141}\right)\)	\(e\left(\frac{118}{141}\right)\)	\(e\left(\frac{134}{141}\right)\)	\(e\left(\frac{119}{141}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{98}{141}\right)\)	\(e\left(\frac{62}{141}\right)\)	\(e\left(\frac{275}{282}\right)\)
\(\chi_{1129}(10,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{191}{282}\right)\)	\(e\left(\frac{203}{282}\right)\)	\(e\left(\frac{50}{141}\right)\)	\(e\left(\frac{43}{141}\right)\)	\(e\left(\frac{56}{141}\right)\)	\(e\left(\frac{211}{282}\right)\)	\(e\left(\frac{3}{94}\right)\)	\(e\left(\frac{62}{141}\right)\)	\(e\left(\frac{277}{282}\right)\)	\(e\left(\frac{535}{564}\right)\)
\(\chi_{1129}(11,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{564}\right)\)	\(e\left(\frac{557}{564}\right)\)	\(e\left(\frac{149}{282}\right)\)	\(e\left(\frac{193}{282}\right)\)	\(e\left(\frac{71}{282}\right)\)	\(e\left(\frac{265}{564}\right)\)	\(e\left(\frac{149}{188}\right)\)	\(e\left(\frac{275}{282}\right)\)	\(e\left(\frac{535}{564}\right)\)	\(e\left(\frac{1}{1128}\right)\)
\(\chi_{1129}(12,\cdot)\)	1129.l	188	yes	\(1\)	\(1\)	\(e\left(\frac{71}{94}\right)\)	\(e\left(\frac{73}{94}\right)\)	\(e\left(\frac{24}{47}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{43}{94}\right)\)	\(e\left(\frac{25}{94}\right)\)	\(e\left(\frac{26}{47}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{97}{188}\right)\)
\(\chi_{1129}(13,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{455}{564}\right)\)	\(e\left(\frac{395}{564}\right)\)	\(e\left(\frac{173}{282}\right)\)	\(e\left(\frac{67}{282}\right)\)	\(e\left(\frac{143}{282}\right)\)	\(e\left(\frac{355}{564}\right)\)	\(e\left(\frac{79}{188}\right)\)	\(e\left(\frac{113}{282}\right)\)	\(e\left(\frac{25}{564}\right)\)	\(e\left(\frac{991}{1128}\right)\)
\(\chi_{1129}(14,\cdot)\)	1129.j	94	yes	\(1\)	\(1\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{32}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{69}{94}\right)\)
\(\chi_{1129}(15,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{71}{282}\right)\)	\(e\left(\frac{167}{282}\right)\)	\(e\left(\frac{71}{141}\right)\)	\(e\left(\frac{109}{141}\right)\)	\(e\left(\frac{119}{141}\right)\)	\(e\left(\frac{43}{282}\right)\)	\(e\left(\frac{71}{94}\right)\)	\(e\left(\frac{26}{141}\right)\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{379}{564}\right)\)
\(\chi_{1129}(16,\cdot)\)	1129.k	141	yes	\(1\)	\(1\)	\(e\left(\frac{128}{141}\right)\)	\(e\left(\frac{29}{141}\right)\)	\(e\left(\frac{115}{141}\right)\)	\(e\left(\frac{113}{141}\right)\)	\(e\left(\frac{16}{141}\right)\)	\(e\left(\frac{10}{141}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{58}{141}\right)\)	\(e\left(\frac{100}{141}\right)\)	\(e\left(\frac{8}{141}\right)\)
\(\chi_{1129}(17,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{564}\right)\)	\(e\left(\frac{541}{564}\right)\)	\(e\left(\frac{127}{282}\right)\)	\(e\left(\frac{191}{282}\right)\)	\(e\left(\frac{193}{282}\right)\)	\(e\left(\frac{65}{564}\right)\)	\(e\left(\frac{33}{188}\right)\)	\(e\left(\frac{259}{282}\right)\)	\(e\left(\frac{227}{564}\right)\)	\(e\left(\frac{809}{1128}\right)\)
\(\chi_{1129}(18,\cdot)\)	1129.l	188	yes	\(1\)	\(1\)	\(e\left(\frac{31}{94}\right)\)	\(e\left(\frac{61}{94}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{81}{94}\right)\)	\(e\left(\frac{93}{94}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{11}{94}\right)\)	\(e\left(\frac{45}{188}\right)\)
\(\chi_{1129}(19,\cdot)\)	1129.n	376	yes	\(-1\)	\(1\)	\(e\left(\frac{105}{188}\right)\)	\(e\left(\frac{149}{188}\right)\)	\(e\left(\frac{11}{94}\right)\)	\(e\left(\frac{1}{94}\right)\)	\(e\left(\frac{33}{94}\right)\)	\(e\left(\frac{53}{188}\right)\)	\(e\left(\frac{127}{188}\right)\)	\(e\left(\frac{55}{94}\right)\)	\(e\left(\frac{107}{188}\right)\)	\(e\left(\frac{301}{376}\right)\)
\(\chi_{1129}(20,\cdot)\)	1129.i	47	yes	\(1\)	\(1\)	\(e\left(\frac{19}{47}\right)\)	\(e\left(\frac{1}{47}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{10}{47}\right)\)
\(\chi_{1129}(21,\cdot)\)	1129.j	94	yes	\(1\)	\(1\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{28}{47}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{22}{47}\right)\)	\(e\left(\frac{43}{94}\right)\)
\(\chi_{1129}(22,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{559}{564}\right)\)	\(e\left(\frac{163}{564}\right)\)	\(e\left(\frac{277}{282}\right)\)	\(e\left(\frac{179}{282}\right)\)	\(e\left(\frac{79}{282}\right)\)	\(e\left(\frac{275}{564}\right)\)	\(e\left(\frac{183}{188}\right)\)	\(e\left(\frac{163}{282}\right)\)	\(e\left(\frac{353}{564}\right)\)	\(e\left(\frac{299}{1128}\right)\)
\(\chi_{1129}(23,\cdot)\)	1129.l	188	yes	\(1\)	\(1\)	\(e\left(\frac{65}{94}\right)\)	\(e\left(\frac{43}{94}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{91}{94}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{17}{94}\right)\)	\(e\left(\frac{155}{188}\right)\)
\(\chi_{1129}(24,\cdot)\)	1129.k	141	yes	\(1\)	\(1\)	\(e\left(\frac{68}{141}\right)\)	\(e\left(\frac{11}{141}\right)\)	\(e\left(\frac{136}{141}\right)\)	\(e\left(\frac{38}{141}\right)\)	\(e\left(\frac{79}{141}\right)\)	\(e\left(\frac{67}{141}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{22}{141}\right)\)	\(e\left(\frac{106}{141}\right)\)	\(e\left(\frac{110}{141}\right)\)
\(\chi_{1129}(25,\cdot)\)	1129.k	141	yes	\(1\)	\(1\)	\(e\left(\frac{127}{141}\right)\)	\(e\left(\frac{118}{141}\right)\)	\(e\left(\frac{113}{141}\right)\)	\(e\left(\frac{100}{141}\right)\)	\(e\left(\frac{104}{141}\right)\)	\(e\left(\frac{65}{141}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{95}{141}\right)\)	\(e\left(\frac{86}{141}\right)\)	\(e\left(\frac{52}{141}\right)\)
\(\chi_{1129}(26,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{301}{564}\right)\)	\(e\left(\frac{1}{564}\right)\)	\(e\left(\frac{19}{282}\right)\)	\(e\left(\frac{53}{282}\right)\)	\(e\left(\frac{151}{282}\right)\)	\(e\left(\frac{365}{564}\right)\)	\(e\left(\frac{113}{188}\right)\)	\(e\left(\frac{1}{282}\right)\)	\(e\left(\frac{407}{564}\right)\)	\(e\left(\frac{161}{1128}\right)\)
\(\chi_{1129}(27,\cdot)\)	1129.l	188	yes	\(1\)	\(1\)	\(e\left(\frac{85}{94}\right)\)	\(e\left(\frac{49}{94}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{25}{94}\right)\)	\(e\left(\frac{67}{94}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{15}{94}\right)\)	\(e\left(\frac{181}{188}\right)\)
\(\chi_{1129}(28,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{133}{282}\right)\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{133}{141}\right)\)	\(e\left(\frac{89}{141}\right)\)	\(e\left(\frac{70}{141}\right)\)	\(e\left(\frac{17}{282}\right)\)	\(e\left(\frac{39}{94}\right)\)	\(e\left(\frac{7}{141}\right)\)	\(e\left(\frac{29}{282}\right)\)	\(e\left(\frac{563}{564}\right)\)
\(\chi_{1129}(29,\cdot)\)	1129.p	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{349}{564}\right)\)	\(e\left(\frac{241}{564}\right)\)	\(e\left(\frac{67}{282}\right)\)	\(e\left(\frac{83}{282}\right)\)	\(e\left(\frac{13}{282}\right)\)	\(e\left(\frac{545}{564}\right)\)	\(e\left(\frac{161}{188}\right)\)	\(e\left(\frac{241}{282}\right)\)	\(e\left(\frac{515}{564}\right)\)	\(e\left(\frac{449}{1128}\right)\)
\(\chi_{1129}(30,\cdot)\)	1129.i	47	yes	\(1\)	\(1\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{42}{47}\right)\)	\(e\left(\frac{45}{47}\right)\)	\(e\left(\frac{34}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{33}{47}\right)\)	\(e\left(\frac{44}{47}\right)\)
\(\chi_{1129}(31,\cdot)\)	1129.f	8	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1129}(32,\cdot)\)	1129.o	564	yes	\(1\)	\(1\)	\(e\left(\frac{179}{282}\right)\)	\(e\left(\frac{143}{282}\right)\)	\(e\left(\frac{38}{141}\right)\)	\(e\left(\frac{106}{141}\right)\)	\(e\left(\frac{20}{141}\right)\)	\(e\left(\frac{25}{282}\right)\)	\(e\left(\frac{85}{94}\right)\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{109}{282}\right)\)	\(e\left(\frac{181}{564}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1128 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.