LMFDB - Group of Dirichlet characters of modulus 968

Show commands: PariGP / SageMath

sage: H = DirichletGroup(968)

pari: g = idealstar(,968,2)

Character group

sage: G.order() pari: g.no
Order	=	440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{110}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{968}(727,\cdot)$, $\chi_{968}(485,\cdot)$, $\chi_{968}(849,\cdot)$

First 32 of 440 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{968}(1,\cdot)$	968.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{968}(3,\cdot)$	968.l	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$
$\chi_{968}(5,\cdot)$	968.bd	110	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{968}(7,\cdot)$	968.bf	110	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{968}(9,\cdot)$	968.i	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$
$\chi_{968}(13,\cdot)$	968.bc	110	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{968}(15,\cdot)$	968.be	110	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{968}(17,\cdot)$	968.bb	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{968}(19,\cdot)$	968.ba	110	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{968}(21,\cdot)$	968.u	22	yes	$-1$	$1$	$-1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{22}\right)$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{968}(23,\cdot)$	968.s	22	no	$-1$	$1$	$-1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{22}\right)$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{968}(25,\cdot)$	968.y	55	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{968}(27,\cdot)$	968.l	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$
$\chi_{968}(29,\cdot)$	968.bc	110	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{968}(31,\cdot)$	968.be	110	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{968}(35,\cdot)$	968.ba	110	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{968}(37,\cdot)$	968.bd	110	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{968}(39,\cdot)$	968.bf	110	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{968}(41,\cdot)$	968.bb	110	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{968}(43,\cdot)$	968.w	22	yes	$1$	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{11}\right)$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{968}(45,\cdot)$	968.t	22	yes	$1$	$1$	$-1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{10}{11}\right)$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{968}(47,\cdot)$	968.be	110	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{968}(49,\cdot)$	968.y	55	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{968}(51,\cdot)$	968.ba	110	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{968}(53,\cdot)$	968.bd	110	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{968}(57,\cdot)$	968.bb	110	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{968}(59,\cdot)$	968.z	110	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{968}(61,\cdot)$	968.bc	110	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{968}(63,\cdot)$	968.bf	110	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{968}(65,\cdot)$	968.v	22	no	$-1$	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{968}(67,\cdot)$	968.x	22	yes	$-1$	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{22}\right)$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{968}(69,\cdot)$	968.bd	110	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$

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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	$968$
Structure	\(C_{2}\times C_{2}\times C_{110}\)
Order	$440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{968}(1,\cdot)\)	968.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{968}(3,\cdot)\)	968.l	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{968}(5,\cdot)\)	968.bd	110	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{968}(7,\cdot)\)	968.bf	110	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{968}(9,\cdot)\)	968.i	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(1\)
\(\chi_{968}(13,\cdot)\)	968.bc	110	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{968}(15,\cdot)\)	968.be	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{968}(17,\cdot)\)	968.bb	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{968}(19,\cdot)\)	968.ba	110	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{968}(21,\cdot)\)	968.u	22	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{968}(23,\cdot)\)	968.s	22	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{968}(25,\cdot)\)	968.y	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{968}(27,\cdot)\)	968.l	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{968}(29,\cdot)\)	968.bc	110	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{968}(31,\cdot)\)	968.be	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{968}(35,\cdot)\)	968.ba	110	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{968}(37,\cdot)\)	968.bd	110	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{968}(39,\cdot)\)	968.bf	110	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{968}(41,\cdot)\)	968.bb	110	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{968}(43,\cdot)\)	968.w	22	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{968}(45,\cdot)\)	968.t	22	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{968}(47,\cdot)\)	968.be	110	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{968}(49,\cdot)\)	968.y	55	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{968}(51,\cdot)\)	968.ba	110	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{968}(53,\cdot)\)	968.bd	110	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{968}(57,\cdot)\)	968.bb	110	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{968}(59,\cdot)\)	968.z	110	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{968}(61,\cdot)\)	968.bc	110	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{968}(63,\cdot)\)	968.bf	110	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{968}(65,\cdot)\)	968.v	22	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{968}(67,\cdot)\)	968.x	22	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{968}(69,\cdot)\)	968.bd	110	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)

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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.