LMFDB - Group of Dirichlet characters of modulus 847

Show commands: PariGP / SageMath

sage: H = DirichletGroup(847)

pari: g = idealstar(,847,2)

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	=	$\chi_{847}(122,\cdot)$, $\chi_{847}(365,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{847}(1,\cdot)$	847.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{847}(2,\cdot)$	847.bf	330	yes	$-1$	$1$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{847}(3,\cdot)$	847.t	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{847}(4,\cdot)$	847.bc	165	yes	$1$	$1$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{847}(5,\cdot)$	847.bd	330	yes	$-1$	$1$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{49}{110}\right)$
$\chi_{847}(6,\cdot)$	847.ba	110	yes	$1$	$1$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{847}(8,\cdot)$	847.z	110	no	$-1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{847}(9,\cdot)$	847.n	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{847}(10,\cdot)$	847.x	66	yes	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{847}(12,\cdot)$	847.y	66	yes	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{847}(13,\cdot)$	847.ba	110	yes	$1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{847}(15,\cdot)$	847.v	55	no	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{847}(16,\cdot)$	847.bc	165	yes	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{847}(17,\cdot)$	847.be	330	yes	$1$	$1$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{847}(18,\cdot)$	847.bf	330	yes	$-1$	$1$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{847}(19,\cdot)$	847.be	330	yes	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{847}(20,\cdot)$	847.bb	110	yes	$-1$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{847}(23,\cdot)$	847.u	33	yes	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{847}(24,\cdot)$	847.be	330	yes	$1$	$1$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{847}(25,\cdot)$	847.bc	165	yes	$1$	$1$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{847}(26,\cdot)$	847.bd	330	yes	$-1$	$1$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{847}(27,\cdot)$	847.j	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$	$e\left(\frac{9}{10}\right)$
$\chi_{847}(29,\cdot)$	847.z	110	no	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{847}(30,\cdot)$	847.bf	330	yes	$-1$	$1$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{847}(31,\cdot)$	847.bd	330	yes	$-1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{847}(32,\cdot)$	847.w	66	yes	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{847}(34,\cdot)$	847.o	22	yes	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$-1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{847}(36,\cdot)$	847.v	55	no	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{847}(37,\cdot)$	847.bc	165	yes	$1$	$1$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{847}(38,\cdot)$	847.bd	330	yes	$-1$	$1$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{847}(39,\cdot)$	847.bf	330	yes	$-1$	$1$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{847}(40,\cdot)$	847.r	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{5}\right)$

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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	$847$
Structure	\(C_{2}\times C_{330}\)
Order	$660$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{847}(1,\cdot)\)	847.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{847}(2,\cdot)\)	847.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{847}(3,\cdot)\)	847.t	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{847}(4,\cdot)\)	847.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{847}(5,\cdot)\)	847.bd	330	yes	\(-1\)	\(1\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{49}{110}\right)\)
\(\chi_{847}(6,\cdot)\)	847.ba	110	yes	\(1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{847}(8,\cdot)\)	847.z	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{847}(9,\cdot)\)	847.n	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{847}(10,\cdot)\)	847.x	66	yes	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{847}(12,\cdot)\)	847.y	66	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{847}(13,\cdot)\)	847.ba	110	yes	\(1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{847}(15,\cdot)\)	847.v	55	no	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{847}(16,\cdot)\)	847.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{847}(17,\cdot)\)	847.be	330	yes	\(1\)	\(1\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{847}(18,\cdot)\)	847.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{847}(19,\cdot)\)	847.be	330	yes	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{847}(20,\cdot)\)	847.bb	110	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{847}(23,\cdot)\)	847.u	33	yes	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{847}(24,\cdot)\)	847.be	330	yes	\(1\)	\(1\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{847}(25,\cdot)\)	847.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{847}(26,\cdot)\)	847.bd	330	yes	\(-1\)	\(1\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{847}(27,\cdot)\)	847.j	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{847}(29,\cdot)\)	847.z	110	no	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{847}(30,\cdot)\)	847.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{847}(31,\cdot)\)	847.bd	330	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{847}(32,\cdot)\)	847.w	66	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{847}(34,\cdot)\)	847.o	22	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(-1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{847}(36,\cdot)\)	847.v	55	no	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{847}(37,\cdot)\)	847.bc	165	yes	\(1\)	\(1\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{847}(38,\cdot)\)	847.bd	330	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{847}(39,\cdot)\)	847.bf	330	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{847}(40,\cdot)\)	847.r	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)

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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.