LMFDB - Group of Dirichlet characters of modulus 17661

Show commands: PariGP / SageMath

sage: H = DirichletGroup(17661)

pari: g = idealstar(,17661,2)

Character group

sage: G.order() pari: g.no
Order	=	9744
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2436}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{17661}(5888,\cdot)$, $\chi_{17661}(7570,\cdot)$, $\chi_{17661}(16822,\cdot)$

First 32 of 9744 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{17661}(1,\cdot)$	17661.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{17661}(2,\cdot)$	17661.do	2436	yes	$1$	$1$	$e\left(\frac{409}{2436}\right)$	$e\left(\frac{409}{1218}\right)$	$e\left(\frac{328}{609}\right)$	$e\left(\frac{409}{812}\right)$	$e\left(\frac{1721}{2436}\right)$	$e\left(\frac{2273}{2436}\right)$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{409}{609}\right)$	$e\left(\frac{143}{348}\right)$	$e\left(\frac{1063}{2436}\right)$
$\chi_{17661}(4,\cdot)$	17661.dl	1218	no	$1$	$1$	$e\left(\frac{409}{1218}\right)$	$e\left(\frac{409}{609}\right)$	$e\left(\frac{47}{609}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{503}{1218}\right)$	$e\left(\frac{1055}{1218}\right)$	$e\left(\frac{128}{203}\right)$	$e\left(\frac{209}{609}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{1063}{1218}\right)$
$\chi_{17661}(5,\cdot)$	17661.dh	1218	yes	$1$	$1$	$e\left(\frac{328}{609}\right)$	$e\left(\frac{47}{609}\right)$	$e\left(\frac{601}{609}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{320}{609}\right)$	$e\left(\frac{584}{609}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{94}{609}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{376}{609}\right)$
$\chi_{17661}(8,\cdot)$	17661.df	812	no	$1$	$1$	$e\left(\frac{409}{812}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{415}{812}\right)$	$e\left(\frac{97}{812}\right)$	$e\left(\frac{649}{812}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{251}{812}\right)$
$\chi_{17661}(10,\cdot)$	17661.dp	2436	no	$1$	$1$	$e\left(\frac{1721}{2436}\right)$	$e\left(\frac{503}{1218}\right)$	$e\left(\frac{320}{609}\right)$	$e\left(\frac{97}{812}\right)$	$e\left(\frac{565}{2436}\right)$	$e\left(\frac{2173}{2436}\right)$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{503}{609}\right)$	$e\left(\frac{61}{348}\right)$	$e\left(\frac{131}{2436}\right)$
$\chi_{17661}(11,\cdot)$	17661.do	2436	yes	$1$	$1$	$e\left(\frac{2273}{2436}\right)$	$e\left(\frac{1055}{1218}\right)$	$e\left(\frac{584}{609}\right)$	$e\left(\frac{649}{812}\right)$	$e\left(\frac{2173}{2436}\right)$	$e\left(\frac{601}{2436}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{446}{609}\right)$	$e\left(\frac{331}{348}\right)$	$e\left(\frac{1655}{2436}\right)$
$\chi_{17661}(13,\cdot)$	17661.cv	406	no	$-1$	$1$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{128}{203}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{85}{406}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{9}{203}\right)$
$\chi_{17661}(16,\cdot)$	17661.dc	609	no	$1$	$1$	$e\left(\frac{409}{609}\right)$	$e\left(\frac{209}{609}\right)$	$e\left(\frac{94}{609}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{503}{609}\right)$	$e\left(\frac{446}{609}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{418}{609}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{454}{609}\right)$
$\chi_{17661}(17,\cdot)$	17661.cr	348	yes	$-1$	$1$	$e\left(\frac{143}{348}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{61}{348}\right)$	$e\left(\frac{331}{348}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{193}{348}\right)$	$e\left(\frac{287}{348}\right)$
$\chi_{17661}(19,\cdot)$	17661.dp	2436	no	$1$	$1$	$e\left(\frac{1063}{2436}\right)$	$e\left(\frac{1063}{1218}\right)$	$e\left(\frac{376}{609}\right)$	$e\left(\frac{251}{812}\right)$	$e\left(\frac{131}{2436}\right)$	$e\left(\frac{1655}{2436}\right)$	$e\left(\frac{9}{203}\right)$	$e\left(\frac{454}{609}\right)$	$e\left(\frac{287}{348}\right)$	$e\left(\frac{565}{2436}\right)$
$\chi_{17661}(20,\cdot)$	17661.cx	406	yes	$1$	$1$	$e\left(\frac{355}{406}\right)$	$e\left(\frac{152}{203}\right)$	$e\left(\frac{13}{203}\right)$	$e\left(\frac{253}{406}\right)$	$e\left(\frac{381}{406}\right)$	$e\left(\frac{335}{406}\right)$	$e\left(\frac{139}{406}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{199}{406}\right)$
$\chi_{17661}(22,\cdot)$	17661.cy	406	no	$1$	$1$	$e\left(\frac{41}{406}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{123}{406}\right)$	$e\left(\frac{243}{406}\right)$	$e\left(\frac{73}{406}\right)$	$e\left(\frac{173}{203}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{47}{406}\right)$
$\chi_{17661}(23,\cdot)$	17661.dn	1218	yes	$-1$	$1$	$e\left(\frac{191}{1218}\right)$	$e\left(\frac{191}{609}\right)$	$e\left(\frac{233}{1218}\right)$	$e\left(\frac{191}{406}\right)$	$e\left(\frac{212}{609}\right)$	$e\left(\frac{43}{1218}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{382}{609}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{310}{609}\right)$
$\chi_{17661}(25,\cdot)$	17661.dc	609	no	$1$	$1$	$e\left(\frac{47}{609}\right)$	$e\left(\frac{94}{609}\right)$	$e\left(\frac{593}{609}\right)$	$e\left(\frac{47}{203}\right)$	$e\left(\frac{31}{609}\right)$	$e\left(\frac{559}{609}\right)$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{188}{609}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{143}{609}\right)$
$\chi_{17661}(26,\cdot)$	17661.dr	2436	yes	$-1$	$1$	$e\left(\frac{2395}{2436}\right)$	$e\left(\frac{1177}{1218}\right)$	$e\left(\frac{305}{1218}\right)$	$e\left(\frac{771}{812}\right)$	$e\left(\frac{569}{2436}\right)$	$e\left(\frac{2363}{2436}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{568}{609}\right)$	$e\left(\frac{95}{348}\right)$	$e\left(\frac{1171}{2436}\right)$
$\chi_{17661}(31,\cdot)$	17661.dp	2436	no	$1$	$1$	$e\left(\frac{2075}{2436}\right)$	$e\left(\frac{857}{1218}\right)$	$e\left(\frac{251}{609}\right)$	$e\left(\frac{451}{812}\right)$	$e\left(\frac{643}{2436}\right)$	$e\left(\frac{1615}{2436}\right)$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{248}{609}\right)$	$e\left(\frac{115}{348}\right)$	$e\left(\frac{2141}{2436}\right)$
$\chi_{17661}(32,\cdot)$	17661.do	2436	yes	$1$	$1$	$e\left(\frac{2045}{2436}\right)$	$e\left(\frac{827}{1218}\right)$	$e\left(\frac{422}{609}\right)$	$e\left(\frac{421}{812}\right)$	$e\left(\frac{1297}{2436}\right)$	$e\left(\frac{1621}{2436}\right)$	$e\left(\frac{31}{406}\right)$	$e\left(\frac{218}{609}\right)$	$e\left(\frac{19}{348}\right)$	$e\left(\frac{443}{2436}\right)$
$\chi_{17661}(34,\cdot)$	17661.cv	406	no	$-1$	$1$	$e\left(\frac{235}{406}\right)$	$e\left(\frac{32}{203}\right)$	$e\left(\frac{123}{406}\right)$	$e\left(\frac{299}{406}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{359}{406}\right)$	$e\left(\frac{275}{406}\right)$	$e\left(\frac{64}{203}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{53}{203}\right)$
$\chi_{17661}(37,\cdot)$	17661.dq	2436	no	$-1$	$1$	$e\left(\frac{121}{2436}\right)$	$e\left(\frac{121}{1218}\right)$	$e\left(\frac{407}{1218}\right)$	$e\left(\frac{121}{812}\right)$	$e\left(\frac{935}{2436}\right)$	$e\left(\frac{869}{2436}\right)$	$e\left(\frac{223}{406}\right)$	$e\left(\frac{121}{609}\right)$	$e\left(\frac{335}{348}\right)$	$e\left(\frac{109}{2436}\right)$
$\chi_{17661}(38,\cdot)$	17661.dh	1218	yes	$1$	$1$	$e\left(\frac{368}{609}\right)$	$e\left(\frac{127}{609}\right)$	$e\left(\frac{95}{609}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{463}{609}\right)$	$e\left(\frac{373}{609}\right)$	$e\left(\frac{349}{406}\right)$	$e\left(\frac{254}{609}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{407}{609}\right)$
$\chi_{17661}(40,\cdot)$	17661.dp	2436	no	$1$	$1$	$e\left(\frac{103}{2436}\right)$	$e\left(\frac{103}{1218}\right)$	$e\left(\frac{367}{609}\right)$	$e\left(\frac{103}{812}\right)$	$e\left(\frac{1571}{2436}\right)$	$e\left(\frac{1847}{2436}\right)$	$e\left(\frac{32}{203}\right)$	$e\left(\frac{103}{609}\right)$	$e\left(\frac{347}{348}\right)$	$e\left(\frac{2257}{2436}\right)$
$\chi_{17661}(41,\cdot)$	17661.k	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$i$	$i$	$-i$	$1$	$1$	$i$	$-i$
$\chi_{17661}(43,\cdot)$	17661.dd	812	no	$-1$	$1$	$e\left(\frac{321}{812}\right)$	$e\left(\frac{321}{406}\right)$	$e\left(\frac{157}{406}\right)$	$e\left(\frac{151}{812}\right)$	$e\left(\frac{635}{812}\right)$	$e\left(\frac{17}{812}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{61}{812}\right)$
$\chi_{17661}(44,\cdot)$	17661.do	2436	yes	$1$	$1$	$e\left(\frac{655}{2436}\right)$	$e\left(\frac{655}{1218}\right)$	$e\left(\frac{22}{609}\right)$	$e\left(\frac{655}{812}\right)$	$e\left(\frac{743}{2436}\right)$	$e\left(\frac{275}{2436}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{46}{609}\right)$	$e\left(\frac{269}{348}\right)$	$e\left(\frac{1345}{2436}\right)$
$\chi_{17661}(46,\cdot)$	17661.cs	348	no	$-1$	$1$	$e\left(\frac{113}{348}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{19}{348}\right)$	$e\left(\frac{337}{348}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{329}{348}\right)$
$\chi_{17661}(47,\cdot)$	17661.dr	2436	yes	$-1$	$1$	$e\left(\frac{523}{2436}\right)$	$e\left(\frac{523}{1218}\right)$	$e\left(\frac{209}{1218}\right)$	$e\left(\frac{523}{812}\right)$	$e\left(\frac{941}{2436}\right)$	$e\left(\frac{1763}{2436}\right)$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{523}{609}\right)$	$e\left(\frac{299}{348}\right)$	$e\left(\frac{451}{2436}\right)$
$\chi_{17661}(50,\cdot)$	17661.df	812	no	$1$	$1$	$e\left(\frac{199}{812}\right)$	$e\left(\frac{199}{406}\right)$	$e\left(\frac{104}{203}\right)$	$e\left(\frac{597}{812}\right)$	$e\left(\frac{615}{812}\right)$	$e\left(\frac{691}{812}\right)$	$e\left(\frac{97}{406}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{545}{812}\right)$
$\chi_{17661}(52,\cdot)$	17661.di	1218	no	$-1$	$1$	$e\left(\frac{92}{609}\right)$	$e\left(\frac{184}{609}\right)$	$e\left(\frac{961}{1218}\right)$	$e\left(\frac{92}{203}\right)$	$e\left(\frac{1145}{1218}\right)$	$e\left(\frac{550}{609}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{368}{609}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{1117}{1218}\right)$
$\chi_{17661}(53,\cdot)$	17661.dn	1218	yes	$-1$	$1$	$e\left(\frac{355}{1218}\right)$	$e\left(\frac{355}{609}\right)$	$e\left(\frac{229}{1218}\right)$	$e\left(\frac{355}{406}\right)$	$e\left(\frac{292}{609}\right)$	$e\left(\frac{335}{1218}\right)$	$e\left(\frac{57}{203}\right)$	$e\left(\frac{101}{609}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{404}{609}\right)$
$\chi_{17661}(55,\cdot)$	17661.dg	812	no	$1$	$1$	$e\left(\frac{383}{812}\right)$	$e\left(\frac{383}{406}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{337}{812}\right)$	$e\left(\frac{339}{812}\right)$	$e\left(\frac{167}{812}\right)$	$e\left(\frac{152}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{241}{812}\right)$
$\chi_{17661}(59,\cdot)$	17661.cm	174	yes	$1$	$1$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{163}{174}\right)$

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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	$17661$
Structure	\(C_{2}\times C_{2}\times C_{2436}\)
Order	$9744$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{17661}(1,\cdot)\)	17661.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{17661}(2,\cdot)\)	17661.do	2436	yes	\(1\)	\(1\)	\(e\left(\frac{409}{2436}\right)\)	\(e\left(\frac{409}{1218}\right)\)	\(e\left(\frac{328}{609}\right)\)	\(e\left(\frac{409}{812}\right)\)	\(e\left(\frac{1721}{2436}\right)\)	\(e\left(\frac{2273}{2436}\right)\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{409}{609}\right)\)	\(e\left(\frac{143}{348}\right)\)	\(e\left(\frac{1063}{2436}\right)\)
\(\chi_{17661}(4,\cdot)\)	17661.dl	1218	no	\(1\)	\(1\)	\(e\left(\frac{409}{1218}\right)\)	\(e\left(\frac{409}{609}\right)\)	\(e\left(\frac{47}{609}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{503}{1218}\right)\)	\(e\left(\frac{1055}{1218}\right)\)	\(e\left(\frac{128}{203}\right)\)	\(e\left(\frac{209}{609}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{1063}{1218}\right)\)
\(\chi_{17661}(5,\cdot)\)	17661.dh	1218	yes	\(1\)	\(1\)	\(e\left(\frac{328}{609}\right)\)	\(e\left(\frac{47}{609}\right)\)	\(e\left(\frac{601}{609}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{320}{609}\right)\)	\(e\left(\frac{584}{609}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{94}{609}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{376}{609}\right)\)
\(\chi_{17661}(8,\cdot)\)	17661.df	812	no	\(1\)	\(1\)	\(e\left(\frac{409}{812}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{415}{812}\right)\)	\(e\left(\frac{97}{812}\right)\)	\(e\left(\frac{649}{812}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{251}{812}\right)\)
\(\chi_{17661}(10,\cdot)\)	17661.dp	2436	no	\(1\)	\(1\)	\(e\left(\frac{1721}{2436}\right)\)	\(e\left(\frac{503}{1218}\right)\)	\(e\left(\frac{320}{609}\right)\)	\(e\left(\frac{97}{812}\right)\)	\(e\left(\frac{565}{2436}\right)\)	\(e\left(\frac{2173}{2436}\right)\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{503}{609}\right)\)	\(e\left(\frac{61}{348}\right)\)	\(e\left(\frac{131}{2436}\right)\)
\(\chi_{17661}(11,\cdot)\)	17661.do	2436	yes	\(1\)	\(1\)	\(e\left(\frac{2273}{2436}\right)\)	\(e\left(\frac{1055}{1218}\right)\)	\(e\left(\frac{584}{609}\right)\)	\(e\left(\frac{649}{812}\right)\)	\(e\left(\frac{2173}{2436}\right)\)	\(e\left(\frac{601}{2436}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{446}{609}\right)\)	\(e\left(\frac{331}{348}\right)\)	\(e\left(\frac{1655}{2436}\right)\)
\(\chi_{17661}(13,\cdot)\)	17661.cv	406	no	\(-1\)	\(1\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{128}{203}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{85}{406}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{9}{203}\right)\)
\(\chi_{17661}(16,\cdot)\)	17661.dc	609	no	\(1\)	\(1\)	\(e\left(\frac{409}{609}\right)\)	\(e\left(\frac{209}{609}\right)\)	\(e\left(\frac{94}{609}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{503}{609}\right)\)	\(e\left(\frac{446}{609}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{418}{609}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{454}{609}\right)\)
\(\chi_{17661}(17,\cdot)\)	17661.cr	348	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{348}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{61}{348}\right)\)	\(e\left(\frac{331}{348}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{193}{348}\right)\)	\(e\left(\frac{287}{348}\right)\)
\(\chi_{17661}(19,\cdot)\)	17661.dp	2436	no	\(1\)	\(1\)	\(e\left(\frac{1063}{2436}\right)\)	\(e\left(\frac{1063}{1218}\right)\)	\(e\left(\frac{376}{609}\right)\)	\(e\left(\frac{251}{812}\right)\)	\(e\left(\frac{131}{2436}\right)\)	\(e\left(\frac{1655}{2436}\right)\)	\(e\left(\frac{9}{203}\right)\)	\(e\left(\frac{454}{609}\right)\)	\(e\left(\frac{287}{348}\right)\)	\(e\left(\frac{565}{2436}\right)\)
\(\chi_{17661}(20,\cdot)\)	17661.cx	406	yes	\(1\)	\(1\)	\(e\left(\frac{355}{406}\right)\)	\(e\left(\frac{152}{203}\right)\)	\(e\left(\frac{13}{203}\right)\)	\(e\left(\frac{253}{406}\right)\)	\(e\left(\frac{381}{406}\right)\)	\(e\left(\frac{335}{406}\right)\)	\(e\left(\frac{139}{406}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{199}{406}\right)\)
\(\chi_{17661}(22,\cdot)\)	17661.cy	406	no	\(1\)	\(1\)	\(e\left(\frac{41}{406}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{123}{406}\right)\)	\(e\left(\frac{243}{406}\right)\)	\(e\left(\frac{73}{406}\right)\)	\(e\left(\frac{173}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{47}{406}\right)\)
\(\chi_{17661}(23,\cdot)\)	17661.dn	1218	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{1218}\right)\)	\(e\left(\frac{191}{609}\right)\)	\(e\left(\frac{233}{1218}\right)\)	\(e\left(\frac{191}{406}\right)\)	\(e\left(\frac{212}{609}\right)\)	\(e\left(\frac{43}{1218}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{382}{609}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{310}{609}\right)\)
\(\chi_{17661}(25,\cdot)\)	17661.dc	609	no	\(1\)	\(1\)	\(e\left(\frac{47}{609}\right)\)	\(e\left(\frac{94}{609}\right)\)	\(e\left(\frac{593}{609}\right)\)	\(e\left(\frac{47}{203}\right)\)	\(e\left(\frac{31}{609}\right)\)	\(e\left(\frac{559}{609}\right)\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{188}{609}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{143}{609}\right)\)
\(\chi_{17661}(26,\cdot)\)	17661.dr	2436	yes	\(-1\)	\(1\)	\(e\left(\frac{2395}{2436}\right)\)	\(e\left(\frac{1177}{1218}\right)\)	\(e\left(\frac{305}{1218}\right)\)	\(e\left(\frac{771}{812}\right)\)	\(e\left(\frac{569}{2436}\right)\)	\(e\left(\frac{2363}{2436}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{568}{609}\right)\)	\(e\left(\frac{95}{348}\right)\)	\(e\left(\frac{1171}{2436}\right)\)
\(\chi_{17661}(31,\cdot)\)	17661.dp	2436	no	\(1\)	\(1\)	\(e\left(\frac{2075}{2436}\right)\)	\(e\left(\frac{857}{1218}\right)\)	\(e\left(\frac{251}{609}\right)\)	\(e\left(\frac{451}{812}\right)\)	\(e\left(\frac{643}{2436}\right)\)	\(e\left(\frac{1615}{2436}\right)\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{248}{609}\right)\)	\(e\left(\frac{115}{348}\right)\)	\(e\left(\frac{2141}{2436}\right)\)
\(\chi_{17661}(32,\cdot)\)	17661.do	2436	yes	\(1\)	\(1\)	\(e\left(\frac{2045}{2436}\right)\)	\(e\left(\frac{827}{1218}\right)\)	\(e\left(\frac{422}{609}\right)\)	\(e\left(\frac{421}{812}\right)\)	\(e\left(\frac{1297}{2436}\right)\)	\(e\left(\frac{1621}{2436}\right)\)	\(e\left(\frac{31}{406}\right)\)	\(e\left(\frac{218}{609}\right)\)	\(e\left(\frac{19}{348}\right)\)	\(e\left(\frac{443}{2436}\right)\)
\(\chi_{17661}(34,\cdot)\)	17661.cv	406	no	\(-1\)	\(1\)	\(e\left(\frac{235}{406}\right)\)	\(e\left(\frac{32}{203}\right)\)	\(e\left(\frac{123}{406}\right)\)	\(e\left(\frac{299}{406}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{359}{406}\right)\)	\(e\left(\frac{275}{406}\right)\)	\(e\left(\frac{64}{203}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{53}{203}\right)\)
\(\chi_{17661}(37,\cdot)\)	17661.dq	2436	no	\(-1\)	\(1\)	\(e\left(\frac{121}{2436}\right)\)	\(e\left(\frac{121}{1218}\right)\)	\(e\left(\frac{407}{1218}\right)\)	\(e\left(\frac{121}{812}\right)\)	\(e\left(\frac{935}{2436}\right)\)	\(e\left(\frac{869}{2436}\right)\)	\(e\left(\frac{223}{406}\right)\)	\(e\left(\frac{121}{609}\right)\)	\(e\left(\frac{335}{348}\right)\)	\(e\left(\frac{109}{2436}\right)\)
\(\chi_{17661}(38,\cdot)\)	17661.dh	1218	yes	\(1\)	\(1\)	\(e\left(\frac{368}{609}\right)\)	\(e\left(\frac{127}{609}\right)\)	\(e\left(\frac{95}{609}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{463}{609}\right)\)	\(e\left(\frac{373}{609}\right)\)	\(e\left(\frac{349}{406}\right)\)	\(e\left(\frac{254}{609}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{407}{609}\right)\)
\(\chi_{17661}(40,\cdot)\)	17661.dp	2436	no	\(1\)	\(1\)	\(e\left(\frac{103}{2436}\right)\)	\(e\left(\frac{103}{1218}\right)\)	\(e\left(\frac{367}{609}\right)\)	\(e\left(\frac{103}{812}\right)\)	\(e\left(\frac{1571}{2436}\right)\)	\(e\left(\frac{1847}{2436}\right)\)	\(e\left(\frac{32}{203}\right)\)	\(e\left(\frac{103}{609}\right)\)	\(e\left(\frac{347}{348}\right)\)	\(e\left(\frac{2257}{2436}\right)\)
\(\chi_{17661}(41,\cdot)\)	17661.k	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{17661}(43,\cdot)\)	17661.dd	812	no	\(-1\)	\(1\)	\(e\left(\frac{321}{812}\right)\)	\(e\left(\frac{321}{406}\right)\)	\(e\left(\frac{157}{406}\right)\)	\(e\left(\frac{151}{812}\right)\)	\(e\left(\frac{635}{812}\right)\)	\(e\left(\frac{17}{812}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{61}{812}\right)\)
\(\chi_{17661}(44,\cdot)\)	17661.do	2436	yes	\(1\)	\(1\)	\(e\left(\frac{655}{2436}\right)\)	\(e\left(\frac{655}{1218}\right)\)	\(e\left(\frac{22}{609}\right)\)	\(e\left(\frac{655}{812}\right)\)	\(e\left(\frac{743}{2436}\right)\)	\(e\left(\frac{275}{2436}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{46}{609}\right)\)	\(e\left(\frac{269}{348}\right)\)	\(e\left(\frac{1345}{2436}\right)\)
\(\chi_{17661}(46,\cdot)\)	17661.cs	348	no	\(-1\)	\(1\)	\(e\left(\frac{113}{348}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{19}{348}\right)\)	\(e\left(\frac{337}{348}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{329}{348}\right)\)
\(\chi_{17661}(47,\cdot)\)	17661.dr	2436	yes	\(-1\)	\(1\)	\(e\left(\frac{523}{2436}\right)\)	\(e\left(\frac{523}{1218}\right)\)	\(e\left(\frac{209}{1218}\right)\)	\(e\left(\frac{523}{812}\right)\)	\(e\left(\frac{941}{2436}\right)\)	\(e\left(\frac{1763}{2436}\right)\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{523}{609}\right)\)	\(e\left(\frac{299}{348}\right)\)	\(e\left(\frac{451}{2436}\right)\)
\(\chi_{17661}(50,\cdot)\)	17661.df	812	no	\(1\)	\(1\)	\(e\left(\frac{199}{812}\right)\)	\(e\left(\frac{199}{406}\right)\)	\(e\left(\frac{104}{203}\right)\)	\(e\left(\frac{597}{812}\right)\)	\(e\left(\frac{615}{812}\right)\)	\(e\left(\frac{691}{812}\right)\)	\(e\left(\frac{97}{406}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{545}{812}\right)\)
\(\chi_{17661}(52,\cdot)\)	17661.di	1218	no	\(-1\)	\(1\)	\(e\left(\frac{92}{609}\right)\)	\(e\left(\frac{184}{609}\right)\)	\(e\left(\frac{961}{1218}\right)\)	\(e\left(\frac{92}{203}\right)\)	\(e\left(\frac{1145}{1218}\right)\)	\(e\left(\frac{550}{609}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{368}{609}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{1117}{1218}\right)\)
\(\chi_{17661}(53,\cdot)\)	17661.dn	1218	yes	\(-1\)	\(1\)	\(e\left(\frac{355}{1218}\right)\)	\(e\left(\frac{355}{609}\right)\)	\(e\left(\frac{229}{1218}\right)\)	\(e\left(\frac{355}{406}\right)\)	\(e\left(\frac{292}{609}\right)\)	\(e\left(\frac{335}{1218}\right)\)	\(e\left(\frac{57}{203}\right)\)	\(e\left(\frac{101}{609}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{404}{609}\right)\)
\(\chi_{17661}(55,\cdot)\)	17661.dg	812	no	\(1\)	\(1\)	\(e\left(\frac{383}{812}\right)\)	\(e\left(\frac{383}{406}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{337}{812}\right)\)	\(e\left(\frac{339}{812}\right)\)	\(e\left(\frac{167}{812}\right)\)	\(e\left(\frac{152}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{241}{812}\right)\)
\(\chi_{17661}(59,\cdot)\)	17661.cm	174	yes	\(1\)	\(1\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)

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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.