LMFDB - Group of Dirichlet characters of modulus 9797

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(9797)

gp:g = idealstar(,9797,2)

magma:G = FullDirichletGroup(9797);

Character group

Order	=	9600	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{4}\times C_{2400}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{9797}(102,\cdot)$, $\chi_{9797}(2426,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 9600 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{9797}(1,\cdot)$	9797.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9797}(2,\cdot)$	9797.ew	1200	yes	$-1$	$1$	$e\left(\frac{31}{600}\right)$	$e\left(\frac{289}{600}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{713}{1200}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{83}{1200}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{353}{600}\right)$
$\chi_{9797}(3,\cdot)$	9797.ex	1200	yes	$-1$	$1$	$e\left(\frac{289}{600}\right)$	$e\left(\frac{391}{600}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{347}{1200}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{977}{1200}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{407}{600}\right)$
$\chi_{9797}(4,\cdot)$	9797.eo	600	yes	$1$	$1$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{113}{600}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{83}{600}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{300}\right)$
$\chi_{9797}(5,\cdot)$	9797.ey	2400	yes	$-1$	$1$	$e\left(\frac{713}{1200}\right)$	$e\left(\frac{347}{1200}\right)$	$e\left(\frac{113}{600}\right)$	$e\left(\frac{1849}{2400}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1159}{2400}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{347}{600}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{19}{1200}\right)$
$\chi_{9797}(6,\cdot)$	9797.cp	60	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{9797}(7,\cdot)$	9797.fa	2400	yes	$1$	$1$	$e\left(\frac{83}{1200}\right)$	$e\left(\frac{977}{1200}\right)$	$e\left(\frac{83}{600}\right)$	$e\left(\frac{1159}{2400}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1969}{2400}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{1129}{1200}\right)$
$\chi_{9797}(8,\cdot)$	9797.ef	400	yes	$-1$	$1$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{93}{200}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{153}{200}\right)$
$\chi_{9797}(9,\cdot)$	9797.eo	600	yes	$1$	$1$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{347}{600}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{107}{300}\right)$
$\chi_{9797}(10,\cdot)$	9797.cw	96	yes	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{9797}(11,\cdot)$	9797.ex	1200	yes	$-1$	$1$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{407}{600}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{19}{1200}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1129}{1200}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{439}{600}\right)$
$\chi_{9797}(12,\cdot)$	9797.ee	400	yes	$-1$	$1$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{381}{400}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{171}{200}\right)$
$\chi_{9797}(13,\cdot)$	9797.fb	2400	yes	$-1$	$1$	$e\left(\frac{617}{1200}\right)$	$e\left(\frac{923}{1200}\right)$	$e\left(\frac{17}{600}\right)$	$e\left(\frac{241}{2400}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{2400}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{1171}{1200}\right)$
$\chi_{9797}(14,\cdot)$	9797.ei	480	yes	$-1$	$1$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{37}{480}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{427}{480}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{127}{240}\right)$
$\chi_{9797}(15,\cdot)$	9797.fa	2400	yes	$1$	$1$	$e\left(\frac{91}{1200}\right)$	$e\left(\frac{1129}{1200}\right)$	$e\left(\frac{91}{600}\right)$	$e\left(\frac{143}{2400}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{713}{2400}\right)$	$e\left(\frac{91}{400}\right)$	$e\left(\frac{529}{600}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{833}{1200}\right)$
$\chi_{9797}(16,\cdot)$	9797.ec	300	yes	$1$	$1$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{150}\right)$
$\chi_{9797}(17,\cdot)$	9797.ei	480	yes	$-1$	$1$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{61}{480}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{211}{480}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{151}{240}\right)$
$\chi_{9797}(18,\cdot)$	9797.ef	400	yes	$-1$	$1$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{69}{400}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{189}{200}\right)$
$\chi_{9797}(19,\cdot)$	9797.et	800	yes	$-1$	$1$	$e\left(\frac{259}{400}\right)$	$e\left(\frac{121}{400}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{707}{800}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{637}{800}\right)$	$e\left(\frac{377}{400}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{17}{400}\right)$
$\chi_{9797}(20,\cdot)$	9797.eq	800	yes	$-1$	$1$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{101}{400}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{767}{800}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{497}{800}\right)$	$e\left(\frac{37}{400}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{77}{400}\right)$
$\chi_{9797}(21,\cdot)$	9797.fb	2400	yes	$-1$	$1$	$e\left(\frac{661}{1200}\right)$	$e\left(\frac{559}{1200}\right)$	$e\left(\frac{61}{600}\right)$	$e\left(\frac{1853}{2400}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1523}{2400}\right)$	$e\left(\frac{261}{400}\right)$	$e\left(\frac{559}{600}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{743}{1200}\right)$
$\chi_{9797}(22,\cdot)$	9797.cz	100	yes	$1$	$1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{8}{25}\right)$	$i$	$e\left(\frac{8}{25}\right)$
$\chi_{9797}(23,\cdot)$	9797.fb	2400	yes	$-1$	$1$	$e\left(\frac{157}{1200}\right)$	$e\left(\frac{583}{1200}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{1061}{2400}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1451}{2400}\right)$	$e\left(\frac{157}{400}\right)$	$e\left(\frac{583}{600}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{191}{1200}\right)$
$\chi_{9797}(24,\cdot)$	9797.ep	600	yes	$1$	$1$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{43}{600}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{600}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{133}{300}\right)$
$\chi_{9797}(25,\cdot)$	9797.ev	1200	yes	$1$	$1$	$e\left(\frac{113}{600}\right)$	$e\left(\frac{347}{600}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{649}{1200}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1159}{1200}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{600}\right)$
$\chi_{9797}(26,\cdot)$	9797.ez	2400	yes	$1$	$1$	$e\left(\frac{679}{1200}\right)$	$e\left(\frac{301}{1200}\right)$	$e\left(\frac{79}{600}\right)$	$e\left(\frac{1667}{2400}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{197}{2400}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{301}{600}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{677}{1200}\right)$
$\chi_{9797}(27,\cdot)$	9797.ee	400	yes	$-1$	$1$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{347}{400}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{177}{400}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{200}\right)$
$\chi_{9797}(28,\cdot)$	9797.es	800	yes	$1$	$1$	$e\left(\frac{69}{400}\right)$	$e\left(\frac{311}{400}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{537}{800}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{767}{800}\right)$	$e\left(\frac{207}{400}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{47}{400}\right)$
$\chi_{9797}(29,\cdot)$	9797.fa	2400	yes	$1$	$1$	$e\left(\frac{617}{1200}\right)$	$e\left(\frac{323}{1200}\right)$	$e\left(\frac{17}{600}\right)$	$e\left(\frac{2341}{2400}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{931}{2400}\right)$	$e\left(\frac{217}{400}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{571}{1200}\right)$
$\chi_{9797}(30,\cdot)$	9797.eq	800	yes	$-1$	$1$	$e\left(\frac{51}{400}\right)$	$e\left(\frac{169}{400}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{523}{800}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{293}{800}\right)$	$e\left(\frac{153}{400}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{113}{400}\right)$
$\chi_{9797}(31,\cdot)$	9797.ev	1200	yes	$1$	$1$	$e\left(\frac{79}{600}\right)$	$e\left(\frac{301}{600}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{497}{1200}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{77}{600}\right)$
$\chi_{9797}(32,\cdot)$	9797.du	240	yes	$-1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{113}{120}\right)$

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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	$9797$
Structure	\(C_{4}\times C_{2400}\)
Order	$9600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{9797}(1,\cdot)\)	9797.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9797}(2,\cdot)\)	9797.ew	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{600}\right)\)	\(e\left(\frac{289}{600}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{713}{1200}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{83}{1200}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{353}{600}\right)\)
\(\chi_{9797}(3,\cdot)\)	9797.ex	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{289}{600}\right)\)	\(e\left(\frac{391}{600}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{347}{1200}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{977}{1200}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{407}{600}\right)\)
\(\chi_{9797}(4,\cdot)\)	9797.eo	600	yes	\(1\)	\(1\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{113}{600}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{83}{600}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{300}\right)\)
\(\chi_{9797}(5,\cdot)\)	9797.ey	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{713}{1200}\right)\)	\(e\left(\frac{347}{1200}\right)\)	\(e\left(\frac{113}{600}\right)\)	\(e\left(\frac{1849}{2400}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1159}{2400}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{347}{600}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{19}{1200}\right)\)
\(\chi_{9797}(6,\cdot)\)	9797.cp	60	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{9797}(7,\cdot)\)	9797.fa	2400	yes	\(1\)	\(1\)	\(e\left(\frac{83}{1200}\right)\)	\(e\left(\frac{977}{1200}\right)\)	\(e\left(\frac{83}{600}\right)\)	\(e\left(\frac{1159}{2400}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1969}{2400}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{377}{600}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{1129}{1200}\right)\)
\(\chi_{9797}(8,\cdot)\)	9797.ef	400	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{93}{200}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{153}{200}\right)\)
\(\chi_{9797}(9,\cdot)\)	9797.eo	600	yes	\(1\)	\(1\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{347}{600}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{377}{600}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{107}{300}\right)\)
\(\chi_{9797}(10,\cdot)\)	9797.cw	96	yes	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{9797}(11,\cdot)\)	9797.ex	1200	yes	\(-1\)	\(1\)	\(e\left(\frac{353}{600}\right)\)	\(e\left(\frac{407}{600}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{19}{1200}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1129}{1200}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{439}{600}\right)\)
\(\chi_{9797}(12,\cdot)\)	9797.ee	400	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{200}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{381}{400}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{171}{200}\right)\)
\(\chi_{9797}(13,\cdot)\)	9797.fb	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{617}{1200}\right)\)	\(e\left(\frac{923}{1200}\right)\)	\(e\left(\frac{17}{600}\right)\)	\(e\left(\frac{241}{2400}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{2400}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{1171}{1200}\right)\)
\(\chi_{9797}(14,\cdot)\)	9797.ei	480	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{37}{480}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{427}{480}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{127}{240}\right)\)
\(\chi_{9797}(15,\cdot)\)	9797.fa	2400	yes	\(1\)	\(1\)	\(e\left(\frac{91}{1200}\right)\)	\(e\left(\frac{1129}{1200}\right)\)	\(e\left(\frac{91}{600}\right)\)	\(e\left(\frac{143}{2400}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{713}{2400}\right)\)	\(e\left(\frac{91}{400}\right)\)	\(e\left(\frac{529}{600}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{833}{1200}\right)\)
\(\chi_{9797}(16,\cdot)\)	9797.ec	300	yes	\(1\)	\(1\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{150}\right)\)
\(\chi_{9797}(17,\cdot)\)	9797.ei	480	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{61}{480}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{211}{480}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{151}{240}\right)\)
\(\chi_{9797}(18,\cdot)\)	9797.ef	400	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{200}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{69}{400}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{189}{200}\right)\)
\(\chi_{9797}(19,\cdot)\)	9797.et	800	yes	\(-1\)	\(1\)	\(e\left(\frac{259}{400}\right)\)	\(e\left(\frac{121}{400}\right)\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{707}{800}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{637}{800}\right)\)	\(e\left(\frac{377}{400}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{17}{400}\right)\)
\(\chi_{9797}(20,\cdot)\)	9797.eq	800	yes	\(-1\)	\(1\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{101}{400}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{767}{800}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{497}{800}\right)\)	\(e\left(\frac{37}{400}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{77}{400}\right)\)
\(\chi_{9797}(21,\cdot)\)	9797.fb	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{661}{1200}\right)\)	\(e\left(\frac{559}{1200}\right)\)	\(e\left(\frac{61}{600}\right)\)	\(e\left(\frac{1853}{2400}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1523}{2400}\right)\)	\(e\left(\frac{261}{400}\right)\)	\(e\left(\frac{559}{600}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{743}{1200}\right)\)
\(\chi_{9797}(22,\cdot)\)	9797.cz	100	yes	\(1\)	\(1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(i\)	\(e\left(\frac{8}{25}\right)\)
\(\chi_{9797}(23,\cdot)\)	9797.fb	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{1200}\right)\)	\(e\left(\frac{583}{1200}\right)\)	\(e\left(\frac{157}{600}\right)\)	\(e\left(\frac{1061}{2400}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1451}{2400}\right)\)	\(e\left(\frac{157}{400}\right)\)	\(e\left(\frac{583}{600}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{191}{1200}\right)\)
\(\chi_{9797}(24,\cdot)\)	9797.ep	600	yes	\(1\)	\(1\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{43}{600}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{600}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{133}{300}\right)\)
\(\chi_{9797}(25,\cdot)\)	9797.ev	1200	yes	\(1\)	\(1\)	\(e\left(\frac{113}{600}\right)\)	\(e\left(\frac{347}{600}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{649}{1200}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1159}{1200}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{600}\right)\)
\(\chi_{9797}(26,\cdot)\)	9797.ez	2400	yes	\(1\)	\(1\)	\(e\left(\frac{679}{1200}\right)\)	\(e\left(\frac{301}{1200}\right)\)	\(e\left(\frac{79}{600}\right)\)	\(e\left(\frac{1667}{2400}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{197}{2400}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{301}{600}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{677}{1200}\right)\)
\(\chi_{9797}(27,\cdot)\)	9797.ee	400	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{347}{400}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{177}{400}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{200}\right)\)
\(\chi_{9797}(28,\cdot)\)	9797.es	800	yes	\(1\)	\(1\)	\(e\left(\frac{69}{400}\right)\)	\(e\left(\frac{311}{400}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{537}{800}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{767}{800}\right)\)	\(e\left(\frac{207}{400}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{47}{400}\right)\)
\(\chi_{9797}(29,\cdot)\)	9797.fa	2400	yes	\(1\)	\(1\)	\(e\left(\frac{617}{1200}\right)\)	\(e\left(\frac{323}{1200}\right)\)	\(e\left(\frac{17}{600}\right)\)	\(e\left(\frac{2341}{2400}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{931}{2400}\right)\)	\(e\left(\frac{217}{400}\right)\)	\(e\left(\frac{323}{600}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{571}{1200}\right)\)
\(\chi_{9797}(30,\cdot)\)	9797.eq	800	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{400}\right)\)	\(e\left(\frac{169}{400}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{523}{800}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{293}{800}\right)\)	\(e\left(\frac{153}{400}\right)\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{113}{400}\right)\)
\(\chi_{9797}(31,\cdot)\)	9797.ev	1200	yes	\(1\)	\(1\)	\(e\left(\frac{79}{600}\right)\)	\(e\left(\frac{301}{600}\right)\)	\(e\left(\frac{79}{300}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{497}{1200}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{77}{600}\right)\)
\(\chi_{9797}(32,\cdot)\)	9797.du	240	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{113}{120}\right)\)

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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.