LMFDB - Group of Dirichlet characters of modulus 1089

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1089)

pari: g = idealstar(,1089,2)

Character group

sage: G.order() pari: g.no
Order	=	660
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{330}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1089}(848,\cdot)$, $\chi_{1089}(244,\cdot)$

First 32 of 660 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{1089}(1,\cdot)$	1089.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1089}(2,\cdot)$	1089.bd	330	yes	$1$	$1$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{1089}(4,\cdot)$	1089.bc	165	yes	$1$	$1$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{1089}(5,\cdot)$	1089.bf	330	yes	$-1$	$1$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{1089}(7,\cdot)$	1089.be	330	yes	$-1$	$1$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{1089}(8,\cdot)$	1089.bb	110	no	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{1089}(10,\cdot)$	1089.p	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1089}(13,\cdot)$	1089.be	330	yes	$-1$	$1$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{1089}(14,\cdot)$	1089.bf	330	yes	$-1$	$1$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{1089}(16,\cdot)$	1089.bc	165	yes	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{1089}(17,\cdot)$	1089.bb	110	no	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{1089}(19,\cdot)$	1089.ba	110	no	$-1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{1089}(20,\cdot)$	1089.bf	330	yes	$-1$	$1$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{1089}(23,\cdot)$	1089.w	66	yes	$-1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1089}(25,\cdot)$	1089.bc	165	yes	$1$	$1$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{1089}(26,\cdot)$	1089.z	110	no	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{1089}(28,\cdot)$	1089.ba	110	no	$-1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{1089}(29,\cdot)$	1089.bd	330	yes	$1$	$1$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{1089}(31,\cdot)$	1089.bc	165	yes	$1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{1089}(32,\cdot)$	1089.y	66	yes	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1089}(34,\cdot)$	1089.u	33	yes	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{1089}(35,\cdot)$	1089.bb	110	no	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{1089}(37,\cdot)$	1089.v	55	no	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{1089}(38,\cdot)$	1089.bf	330	yes	$-1$	$1$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{1089}(40,\cdot)$	1089.s	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1089}(41,\cdot)$	1089.bd	330	yes	$1$	$1$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{1089}(43,\cdot)$	1089.x	66	yes	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{1089}(46,\cdot)$	1089.ba	110	no	$-1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{1089}(47,\cdot)$	1089.bf	330	yes	$-1$	$1$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{1089}(49,\cdot)$	1089.bc	165	yes	$1$	$1$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{1089}(50,\cdot)$	1089.bd	330	yes	$1$	$1$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{1089}(52,\cdot)$	1089.be	330	yes	$-1$	$1$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{97}{110}\right)$

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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	$1089$
Structure	\(C_{2}\times C_{330}\)
Order	$660$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{1089}(1,\cdot)\)	1089.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1089}(2,\cdot)\)	1089.bd	330	yes	\(1\)	\(1\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{1089}(4,\cdot)\)	1089.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{1089}(5,\cdot)\)	1089.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{1089}(7,\cdot)\)	1089.be	330	yes	\(-1\)	\(1\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{1089}(8,\cdot)\)	1089.bb	110	no	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{1089}(10,\cdot)\)	1089.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1089}(13,\cdot)\)	1089.be	330	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{1089}(14,\cdot)\)	1089.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{1089}(16,\cdot)\)	1089.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{1089}(17,\cdot)\)	1089.bb	110	no	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{1089}(19,\cdot)\)	1089.ba	110	no	\(-1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{1089}(20,\cdot)\)	1089.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{1089}(23,\cdot)\)	1089.w	66	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1089}(25,\cdot)\)	1089.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{1089}(26,\cdot)\)	1089.z	110	no	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{1089}(28,\cdot)\)	1089.ba	110	no	\(-1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{1089}(29,\cdot)\)	1089.bd	330	yes	\(1\)	\(1\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{1089}(31,\cdot)\)	1089.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{1089}(32,\cdot)\)	1089.y	66	yes	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1089}(34,\cdot)\)	1089.u	33	yes	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{1089}(35,\cdot)\)	1089.bb	110	no	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{1089}(37,\cdot)\)	1089.v	55	no	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{1089}(38,\cdot)\)	1089.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{1089}(40,\cdot)\)	1089.s	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1089}(41,\cdot)\)	1089.bd	330	yes	\(1\)	\(1\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{1089}(43,\cdot)\)	1089.x	66	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{1089}(46,\cdot)\)	1089.ba	110	no	\(-1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{1089}(47,\cdot)\)	1089.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{1089}(49,\cdot)\)	1089.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{1089}(50,\cdot)\)	1089.bd	330	yes	\(1\)	\(1\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{1089}(52,\cdot)\)	1089.be	330	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.