LMFDB - Group of Dirichlet characters of modulus 9680

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(9680)

gp:g = idealstar(,9680,2)

magma:G = FullDirichletGroup(9680);

Character group

Order	=	3520	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{220}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{9680}(3631,\cdot)$, $\chi_{9680}(2421,\cdot)$, $\chi_{9680}(1937,\cdot)$, $\chi_{9680}(4721,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 3520 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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{9680}(1,\cdot)$	9680.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9680}(3,\cdot)$	9680.ci	20	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$-i$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{9680}(7,\cdot)$	9680.fs	220	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{9680}(9,\cdot)$	9680.bt	10	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{9680}(13,\cdot)$	9680.gd	220	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{79}{220}\right)$
$\chi_{9680}(17,\cdot)$	9680.fv	220	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{9680}(19,\cdot)$	9680.fz	220	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{220}\right)$
$\chi_{9680}(21,\cdot)$	9680.dz	44	no	$-1$	$1$	$-i$	$e\left(\frac{6}{11}\right)$	$-1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$i$	$e\left(\frac{19}{44}\right)$
$\chi_{9680}(23,\cdot)$	9680.eg	44	no	$1$	$1$	$i$	$e\left(\frac{31}{44}\right)$	$-1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{44}\right)$	$-i$	$e\left(\frac{9}{11}\right)$
$\chi_{9680}(27,\cdot)$	9680.ci	20	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{9680}(29,\cdot)$	9680.fm	220	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{193}{220}\right)$
$\chi_{9680}(31,\cdot)$	9680.fb	110	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{9680}(37,\cdot)$	9680.gb	220	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{163}{220}\right)$
$\chi_{9680}(39,\cdot)$	9680.ez	110	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{9680}(41,\cdot)$	9680.fa	110	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{9680}(43,\cdot)$	9680.dv	44	yes	$-1$	$1$	$-1$	$e\left(\frac{15}{44}\right)$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{44}\right)$	$-1$	$e\left(\frac{5}{44}\right)$
$\chi_{9680}(47,\cdot)$	9680.ft	220	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{9680}(49,\cdot)$	9680.ey	110	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{9680}(51,\cdot)$	9680.fk	220	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{93}{220}\right)$
$\chi_{9680}(53,\cdot)$	9680.fj	220	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{139}{220}\right)$
$\chi_{9680}(57,\cdot)$	9680.fp	220	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{9680}(59,\cdot)$	9680.fl	220	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{153}{220}\right)$
$\chi_{9680}(61,\cdot)$	9680.fx	220	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{220}\right)$
$\chi_{9680}(63,\cdot)$	9680.fq	220	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{9680}(67,\cdot)$	9680.dt	44	yes	$1$	$1$	$-1$	$e\left(\frac{27}{44}\right)$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{44}\right)$	$-1$	$e\left(\frac{9}{44}\right)$
$\chi_{9680}(69,\cdot)$	9680.fw	220	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{220}\right)$
$\chi_{9680}(71,\cdot)$	9680.es	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{9680}(73,\cdot)$	9680.fp	220	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{9680}(79,\cdot)$	9680.eu	110	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{9680}(81,\cdot)$	9680.bo	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9680}(83,\cdot)$	9680.fi	220	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{51}{220}\right)$
$\chi_{9680}(87,\cdot)$	9680.eb	44	no	$-1$	$1$	$-i$	$e\left(\frac{19}{44}\right)$	$-1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{44}\right)$	$i$	$e\left(\frac{5}{22}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$9680$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{220}\)
Order	$3520$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{9680}(1,\cdot)\)	9680.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9680}(3,\cdot)\)	9680.ci	20	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{9680}(7,\cdot)\)	9680.fs	220	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{9680}(9,\cdot)\)	9680.bt	10	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{9680}(13,\cdot)\)	9680.gd	220	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{79}{220}\right)\)
\(\chi_{9680}(17,\cdot)\)	9680.fv	220	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{9680}(19,\cdot)\)	9680.fz	220	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{220}\right)\)
\(\chi_{9680}(21,\cdot)\)	9680.dz	44	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{6}{11}\right)\)	\(-1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(i\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{9680}(23,\cdot)\)	9680.eg	44	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{31}{44}\right)\)	\(-1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(-i\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{9680}(27,\cdot)\)	9680.ci	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{9680}(29,\cdot)\)	9680.fm	220	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{193}{220}\right)\)
\(\chi_{9680}(31,\cdot)\)	9680.fb	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{9680}(37,\cdot)\)	9680.gb	220	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)
\(\chi_{9680}(39,\cdot)\)	9680.ez	110	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{9680}(41,\cdot)\)	9680.fa	110	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{9680}(43,\cdot)\)	9680.dv	44	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{15}{44}\right)\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(-1\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{9680}(47,\cdot)\)	9680.ft	220	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{9680}(49,\cdot)\)	9680.ey	110	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{9680}(51,\cdot)\)	9680.fk	220	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{93}{220}\right)\)
\(\chi_{9680}(53,\cdot)\)	9680.fj	220	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{139}{220}\right)\)
\(\chi_{9680}(57,\cdot)\)	9680.fp	220	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{9680}(59,\cdot)\)	9680.fl	220	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{153}{220}\right)\)
\(\chi_{9680}(61,\cdot)\)	9680.fx	220	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{220}\right)\)
\(\chi_{9680}(63,\cdot)\)	9680.fq	220	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{9680}(67,\cdot)\)	9680.dt	44	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{27}{44}\right)\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(-1\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{9680}(69,\cdot)\)	9680.fw	220	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{220}\right)\)
\(\chi_{9680}(71,\cdot)\)	9680.es	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{9680}(73,\cdot)\)	9680.fp	220	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{9680}(79,\cdot)\)	9680.eu	110	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{9680}(81,\cdot)\)	9680.bo	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9680}(83,\cdot)\)	9680.fi	220	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{51}{220}\right)\)
\(\chi_{9680}(87,\cdot)\)	9680.eb	44	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{19}{44}\right)\)	\(-1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(i\)	\(e\left(\frac{5}{22}\right)\)

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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.