LMFDB - Group of Dirichlet characters of modulus 61347

Show commands: PariGP / SageMath

sage: H = DirichletGroup(61347)

pari: g = idealstar(,61347,2)

Character group

sage: G.order() pari: g.no
Order	=	34320
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{8580}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{61347}(20450,\cdot)$, $\chi_{61347}(50701,\cdot)$, $\chi_{61347}(51547,\cdot)$

First 32 of 34320 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$14$	$16$	$17$	$19$
$\chi_{61347}(1,\cdot)$	61347.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{61347}(2,\cdot)$	61347.hh	8580	yes	$-1$	$1$	$e\left(\frac{4423}{8580}\right)$	$e\left(\frac{133}{4290}\right)$	$e\left(\frac{659}{2860}\right)$	$e\left(\frac{6431}{8580}\right)$	$e\left(\frac{1563}{2860}\right)$	$e\left(\frac{320}{429}\right)$	$e\left(\frac{379}{1430}\right)$	$e\left(\frac{133}{2145}\right)$	$e\left(\frac{3781}{4290}\right)$	$e\left(\frac{113}{660}\right)$
$\chi_{61347}(4,\cdot)$	61347.hb	4290	no	$1$	$1$	$e\left(\frac{133}{4290}\right)$	$e\left(\frac{133}{2145}\right)$	$e\left(\frac{659}{1430}\right)$	$e\left(\frac{2141}{4290}\right)$	$e\left(\frac{133}{1430}\right)$	$e\left(\frac{211}{429}\right)$	$e\left(\frac{379}{715}\right)$	$e\left(\frac{266}{2145}\right)$	$e\left(\frac{1636}{2145}\right)$	$e\left(\frac{113}{330}\right)$
$\chi_{61347}(5,\cdot)$	61347.gw	2860	yes	$1$	$1$	$e\left(\frac{659}{2860}\right)$	$e\left(\frac{659}{1430}\right)$	$e\left(\frac{2291}{2860}\right)$	$e\left(\frac{2523}{2860}\right)$	$e\left(\frac{1977}{2860}\right)$	$e\left(\frac{9}{286}\right)$	$e\left(\frac{161}{1430}\right)$	$e\left(\frac{659}{715}\right)$	$e\left(\frac{634}{715}\right)$	$e\left(\frac{129}{220}\right)$
$\chi_{61347}(7,\cdot)$	61347.hg	8580	no	$1$	$1$	$e\left(\frac{6431}{8580}\right)$	$e\left(\frac{2141}{4290}\right)$	$e\left(\frac{2523}{2860}\right)$	$e\left(\frac{7177}{8580}\right)$	$e\left(\frac{711}{2860}\right)$	$e\left(\frac{271}{429}\right)$	$e\left(\frac{419}{715}\right)$	$e\left(\frac{2141}{2145}\right)$	$e\left(\frac{556}{2145}\right)$	$e\left(\frac{571}{660}\right)$
$\chi_{61347}(8,\cdot)$	61347.gy	2860	yes	$-1$	$1$	$e\left(\frac{1563}{2860}\right)$	$e\left(\frac{133}{1430}\right)$	$e\left(\frac{1977}{2860}\right)$	$e\left(\frac{711}{2860}\right)$	$e\left(\frac{1829}{2860}\right)$	$e\left(\frac{34}{143}\right)$	$e\left(\frac{1137}{1430}\right)$	$e\left(\frac{133}{715}\right)$	$e\left(\frac{921}{1430}\right)$	$e\left(\frac{113}{220}\right)$
$\chi_{61347}(10,\cdot)$	61347.gc	858	no	$-1$	$1$	$e\left(\frac{320}{429}\right)$	$e\left(\frac{211}{429}\right)$	$e\left(\frac{9}{286}\right)$	$e\left(\frac{271}{429}\right)$	$e\left(\frac{34}{143}\right)$	$e\left(\frac{667}{858}\right)$	$e\left(\frac{54}{143}\right)$	$e\left(\frac{422}{429}\right)$	$e\left(\frac{659}{858}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{61347}(14,\cdot)$	61347.go	1430	yes	$-1$	$1$	$e\left(\frac{379}{1430}\right)$	$e\left(\frac{379}{715}\right)$	$e\left(\frac{161}{1430}\right)$	$e\left(\frac{419}{715}\right)$	$e\left(\frac{1137}{1430}\right)$	$e\left(\frac{54}{143}\right)$	$e\left(\frac{1217}{1430}\right)$	$e\left(\frac{43}{715}\right)$	$e\left(\frac{201}{1430}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{61347}(16,\cdot)$	61347.gu	2145	no	$1$	$1$	$e\left(\frac{133}{2145}\right)$	$e\left(\frac{266}{2145}\right)$	$e\left(\frac{659}{715}\right)$	$e\left(\frac{2141}{2145}\right)$	$e\left(\frac{133}{715}\right)$	$e\left(\frac{422}{429}\right)$	$e\left(\frac{43}{715}\right)$	$e\left(\frac{532}{2145}\right)$	$e\left(\frac{1127}{2145}\right)$	$e\left(\frac{113}{165}\right)$
$\chi_{61347}(17,\cdot)$	61347.ha	4290	yes	$1$	$1$	$e\left(\frac{3781}{4290}\right)$	$e\left(\frac{1636}{2145}\right)$	$e\left(\frac{634}{715}\right)$	$e\left(\frac{556}{2145}\right)$	$e\left(\frac{921}{1430}\right)$	$e\left(\frac{659}{858}\right)$	$e\left(\frac{201}{1430}\right)$	$e\left(\frac{1127}{2145}\right)$	$e\left(\frac{2077}{2145}\right)$	$e\left(\frac{133}{165}\right)$
$\chi_{61347}(19,\cdot)$	61347.fw	660	no	$1$	$1$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{469}{660}\right)$
$\chi_{61347}(20,\cdot)$	61347.hj	8580	yes	$1$	$1$	$e\left(\frac{2243}{8580}\right)$	$e\left(\frac{2243}{4290}\right)$	$e\left(\frac{749}{2860}\right)$	$e\left(\frac{3271}{8580}\right)$	$e\left(\frac{2243}{2860}\right)$	$e\left(\frac{449}{858}\right)$	$e\left(\frac{919}{1430}\right)$	$e\left(\frac{98}{2145}\right)$	$e\left(\frac{1393}{2145}\right)$	$e\left(\frac{613}{660}\right)$
$\chi_{61347}(23,\cdot)$	61347.dc	66	no	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{61347}(25,\cdot)$	61347.gp	1430	no	$1$	$1$	$e\left(\frac{659}{1430}\right)$	$e\left(\frac{659}{715}\right)$	$e\left(\frac{861}{1430}\right)$	$e\left(\frac{1093}{1430}\right)$	$e\left(\frac{547}{1430}\right)$	$e\left(\frac{9}{143}\right)$	$e\left(\frac{161}{715}\right)$	$e\left(\frac{603}{715}\right)$	$e\left(\frac{553}{715}\right)$	$e\left(\frac{19}{110}\right)$
$\chi_{61347}(28,\cdot)$	61347.hg	8580	no	$1$	$1$	$e\left(\frac{6697}{8580}\right)$	$e\left(\frac{2407}{4290}\right)$	$e\left(\frac{981}{2860}\right)$	$e\left(\frac{2879}{8580}\right)$	$e\left(\frac{977}{2860}\right)$	$e\left(\frac{53}{429}\right)$	$e\left(\frac{83}{715}\right)$	$e\left(\frac{262}{2145}\right)$	$e\left(\frac{47}{2145}\right)$	$e\left(\frac{137}{660}\right)$
$\chi_{61347}(29,\cdot)$	61347.he	4290	yes	$1$	$1$	$e\left(\frac{1954}{2145}\right)$	$e\left(\frac{1763}{2145}\right)$	$e\left(\frac{349}{1430}\right)$	$e\left(\frac{2221}{4290}\right)$	$e\left(\frac{524}{715}\right)$	$e\left(\frac{133}{858}\right)$	$e\left(\frac{613}{1430}\right)$	$e\left(\frac{1381}{2145}\right)$	$e\left(\frac{1091}{2145}\right)$	$e\left(\frac{163}{330}\right)$
$\chi_{61347}(31,\cdot)$	61347.gv	2860	no	$-1$	$1$	$e\left(\frac{2621}{2860}\right)$	$e\left(\frac{1191}{1430}\right)$	$e\left(\frac{189}{2860}\right)$	$e\left(\frac{2507}{2860}\right)$	$e\left(\frac{2143}{2860}\right)$	$e\left(\frac{281}{286}\right)$	$e\left(\frac{567}{715}\right)$	$e\left(\frac{476}{715}\right)$	$e\left(\frac{1377}{1430}\right)$	$e\left(\frac{141}{220}\right)$
$\chi_{61347}(32,\cdot)$	61347.gq	1716	yes	$-1$	$1$	$e\left(\frac{991}{1716}\right)$	$e\left(\frac{133}{858}\right)$	$e\left(\frac{87}{572}\right)$	$e\left(\frac{1283}{1716}\right)$	$e\left(\frac{419}{572}\right)$	$e\left(\frac{313}{429}\right)$	$e\left(\frac{93}{286}\right)$	$e\left(\frac{133}{429}\right)$	$e\left(\frac{349}{858}\right)$	$e\left(\frac{113}{132}\right)$
$\chi_{61347}(34,\cdot)$	61347.fq	572	no	$-1$	$1$	$e\left(\frac{227}{572}\right)$	$e\left(\frac{227}{286}\right)$	$e\left(\frac{67}{572}\right)$	$e\left(\frac{5}{572}\right)$	$e\left(\frac{109}{572}\right)$	$e\left(\frac{147}{286}\right)$	$e\left(\frac{58}{143}\right)$	$e\left(\frac{84}{143}\right)$	$e\left(\frac{243}{286}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{61347}(35,\cdot)$	61347.he	4290	yes	$1$	$1$	$e\left(\frac{2102}{2145}\right)$	$e\left(\frac{2059}{2145}\right)$	$e\left(\frac{977}{1430}\right)$	$e\left(\frac{3083}{4290}\right)$	$e\left(\frac{672}{715}\right)$	$e\left(\frac{569}{858}\right)$	$e\left(\frac{999}{1430}\right)$	$e\left(\frac{1973}{2145}\right)$	$e\left(\frac{313}{2145}\right)$	$e\left(\frac{149}{330}\right)$
$\chi_{61347}(37,\cdot)$	61347.hi	8580	no	$-1$	$1$	$e\left(\frac{3001}{8580}\right)$	$e\left(\frac{3001}{4290}\right)$	$e\left(\frac{2763}{2860}\right)$	$e\left(\frac{2087}{8580}\right)$	$e\left(\frac{141}{2860}\right)$	$e\left(\frac{271}{858}\right)$	$e\left(\frac{424}{715}\right)$	$e\left(\frac{856}{2145}\right)$	$e\left(\frac{127}{4290}\right)$	$e\left(\frac{401}{660}\right)$
$\chi_{61347}(38,\cdot)$	61347.gj	1430	yes	$-1$	$1$	$e\left(\frac{491}{715}\right)$	$e\left(\frac{267}{715}\right)$	$e\left(\frac{584}{715}\right)$	$e\left(\frac{879}{1430}\right)$	$e\left(\frac{43}{715}\right)$	$e\left(\frac{72}{143}\right)$	$e\left(\frac{431}{1430}\right)$	$e\left(\frac{534}{715}\right)$	$e\left(\frac{983}{1430}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{61347}(40,\cdot)$	61347.dv	130	no	$-1$	$1$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{61347}(41,\cdot)$	61347.hh	8580	yes	$-1$	$1$	$e\left(\frac{2179}{8580}\right)$	$e\left(\frac{2179}{4290}\right)$	$e\left(\frac{2507}{2860}\right)$	$e\left(\frac{6563}{8580}\right)$	$e\left(\frac{2179}{2860}\right)$	$e\left(\frac{56}{429}\right)$	$e\left(\frac{27}{1430}\right)$	$e\left(\frac{34}{2145}\right)$	$e\left(\frac{1273}{4290}\right)$	$e\left(\frac{509}{660}\right)$
$\chi_{61347}(43,\cdot)$	61347.gc	858	no	$-1$	$1$	$e\left(\frac{4}{429}\right)$	$e\left(\frac{8}{429}\right)$	$e\left(\frac{245}{286}\right)$	$e\left(\frac{116}{429}\right)$	$e\left(\frac{4}{143}\right)$	$e\left(\frac{743}{858}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{16}{429}\right)$	$e\left(\frac{271}{858}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{61347}(46,\cdot)$	61347.hg	8580	no	$1$	$1$	$e\left(\frac{4163}{8580}\right)$	$e\left(\frac{4163}{4290}\right)$	$e\left(\frac{919}{2860}\right)$	$e\left(\frac{3181}{8580}\right)$	$e\left(\frac{1303}{2860}\right)$	$e\left(\frac{346}{429}\right)$	$e\left(\frac{612}{715}\right)$	$e\left(\frac{2018}{2145}\right)$	$e\left(\frac{493}{2145}\right)$	$e\left(\frac{103}{660}\right)$
$\chi_{61347}(47,\cdot)$	61347.gw	2860	yes	$1$	$1$	$e\left(\frac{2273}{2860}\right)$	$e\left(\frac{843}{1430}\right)$	$e\left(\frac{177}{2860}\right)$	$e\left(\frac{1281}{2860}\right)$	$e\left(\frac{1099}{2860}\right)$	$e\left(\frac{245}{286}\right)$	$e\left(\frac{347}{1430}\right)$	$e\left(\frac{128}{715}\right)$	$e\left(\frac{83}{715}\right)$	$e\left(\frac{43}{220}\right)$
$\chi_{61347}(49,\cdot)$	61347.hb	4290	no	$1$	$1$	$e\left(\frac{2141}{4290}\right)$	$e\left(\frac{2141}{2145}\right)$	$e\left(\frac{1093}{1430}\right)$	$e\left(\frac{2887}{4290}\right)$	$e\left(\frac{711}{1430}\right)$	$e\left(\frac{113}{429}\right)$	$e\left(\frac{123}{715}\right)$	$e\left(\frac{2137}{2145}\right)$	$e\left(\frac{1112}{2145}\right)$	$e\left(\frac{241}{330}\right)$
$\chi_{61347}(50,\cdot)$	61347.hh	8580	yes	$-1$	$1$	$e\left(\frac{8377}{8580}\right)$	$e\left(\frac{4087}{4290}\right)$	$e\left(\frac{2381}{2860}\right)$	$e\left(\frac{4409}{8580}\right)$	$e\left(\frac{2657}{2860}\right)$	$e\left(\frac{347}{429}\right)$	$e\left(\frac{701}{1430}\right)$	$e\left(\frac{1942}{2145}\right)$	$e\left(\frac{2809}{4290}\right)$	$e\left(\frac{227}{660}\right)$
$\chi_{61347}(53,\cdot)$	61347.go	1430	yes	$-1$	$1$	$e\left(\frac{333}{1430}\right)$	$e\left(\frac{333}{715}\right)$	$e\left(\frac{1047}{1430}\right)$	$e\left(\frac{38}{715}\right)$	$e\left(\frac{999}{1430}\right)$	$e\left(\frac{138}{143}\right)$	$e\left(\frac{409}{1430}\right)$	$e\left(\frac{666}{715}\right)$	$e\left(\frac{37}{1430}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{61347}(56,\cdot)$	61347.ge	858	yes	$-1$	$1$	$e\left(\frac{127}{429}\right)$	$e\left(\frac{254}{429}\right)$	$e\left(\frac{82}{143}\right)$	$e\left(\frac{73}{858}\right)$	$e\left(\frac{127}{143}\right)$	$e\left(\frac{373}{429}\right)$	$e\left(\frac{109}{286}\right)$	$e\left(\frac{79}{429}\right)$	$e\left(\frac{775}{858}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{61347}(58,\cdot)$	61347.hi	8580	no	$-1$	$1$	$e\left(\frac{3659}{8580}\right)$	$e\left(\frac{3659}{4290}\right)$	$e\left(\frac{1357}{2860}\right)$	$e\left(\frac{2293}{8580}\right)$	$e\left(\frac{799}{2860}\right)$	$e\left(\frac{773}{858}\right)$	$e\left(\frac{496}{715}\right)$	$e\left(\frac{1514}{2145}\right)$	$e\left(\frac{1673}{4290}\right)$	$e\left(\frac{439}{660}\right)$

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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	$61347$
Structure	\(C_{2}\times C_{2}\times C_{8580}\)
Order	$34320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{61347}(1,\cdot)\)	61347.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{61347}(2,\cdot)\)	61347.hh	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{4423}{8580}\right)\)	\(e\left(\frac{133}{4290}\right)\)	\(e\left(\frac{659}{2860}\right)\)	\(e\left(\frac{6431}{8580}\right)\)	\(e\left(\frac{1563}{2860}\right)\)	\(e\left(\frac{320}{429}\right)\)	\(e\left(\frac{379}{1430}\right)\)	\(e\left(\frac{133}{2145}\right)\)	\(e\left(\frac{3781}{4290}\right)\)	\(e\left(\frac{113}{660}\right)\)
\(\chi_{61347}(4,\cdot)\)	61347.hb	4290	no	\(1\)	\(1\)	\(e\left(\frac{133}{4290}\right)\)	\(e\left(\frac{133}{2145}\right)\)	\(e\left(\frac{659}{1430}\right)\)	\(e\left(\frac{2141}{4290}\right)\)	\(e\left(\frac{133}{1430}\right)\)	\(e\left(\frac{211}{429}\right)\)	\(e\left(\frac{379}{715}\right)\)	\(e\left(\frac{266}{2145}\right)\)	\(e\left(\frac{1636}{2145}\right)\)	\(e\left(\frac{113}{330}\right)\)
\(\chi_{61347}(5,\cdot)\)	61347.gw	2860	yes	\(1\)	\(1\)	\(e\left(\frac{659}{2860}\right)\)	\(e\left(\frac{659}{1430}\right)\)	\(e\left(\frac{2291}{2860}\right)\)	\(e\left(\frac{2523}{2860}\right)\)	\(e\left(\frac{1977}{2860}\right)\)	\(e\left(\frac{9}{286}\right)\)	\(e\left(\frac{161}{1430}\right)\)	\(e\left(\frac{659}{715}\right)\)	\(e\left(\frac{634}{715}\right)\)	\(e\left(\frac{129}{220}\right)\)
\(\chi_{61347}(7,\cdot)\)	61347.hg	8580	no	\(1\)	\(1\)	\(e\left(\frac{6431}{8580}\right)\)	\(e\left(\frac{2141}{4290}\right)\)	\(e\left(\frac{2523}{2860}\right)\)	\(e\left(\frac{7177}{8580}\right)\)	\(e\left(\frac{711}{2860}\right)\)	\(e\left(\frac{271}{429}\right)\)	\(e\left(\frac{419}{715}\right)\)	\(e\left(\frac{2141}{2145}\right)\)	\(e\left(\frac{556}{2145}\right)\)	\(e\left(\frac{571}{660}\right)\)
\(\chi_{61347}(8,\cdot)\)	61347.gy	2860	yes	\(-1\)	\(1\)	\(e\left(\frac{1563}{2860}\right)\)	\(e\left(\frac{133}{1430}\right)\)	\(e\left(\frac{1977}{2860}\right)\)	\(e\left(\frac{711}{2860}\right)\)	\(e\left(\frac{1829}{2860}\right)\)	\(e\left(\frac{34}{143}\right)\)	\(e\left(\frac{1137}{1430}\right)\)	\(e\left(\frac{133}{715}\right)\)	\(e\left(\frac{921}{1430}\right)\)	\(e\left(\frac{113}{220}\right)\)
\(\chi_{61347}(10,\cdot)\)	61347.gc	858	no	\(-1\)	\(1\)	\(e\left(\frac{320}{429}\right)\)	\(e\left(\frac{211}{429}\right)\)	\(e\left(\frac{9}{286}\right)\)	\(e\left(\frac{271}{429}\right)\)	\(e\left(\frac{34}{143}\right)\)	\(e\left(\frac{667}{858}\right)\)	\(e\left(\frac{54}{143}\right)\)	\(e\left(\frac{422}{429}\right)\)	\(e\left(\frac{659}{858}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{61347}(14,\cdot)\)	61347.go	1430	yes	\(-1\)	\(1\)	\(e\left(\frac{379}{1430}\right)\)	\(e\left(\frac{379}{715}\right)\)	\(e\left(\frac{161}{1430}\right)\)	\(e\left(\frac{419}{715}\right)\)	\(e\left(\frac{1137}{1430}\right)\)	\(e\left(\frac{54}{143}\right)\)	\(e\left(\frac{1217}{1430}\right)\)	\(e\left(\frac{43}{715}\right)\)	\(e\left(\frac{201}{1430}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{61347}(16,\cdot)\)	61347.gu	2145	no	\(1\)	\(1\)	\(e\left(\frac{133}{2145}\right)\)	\(e\left(\frac{266}{2145}\right)\)	\(e\left(\frac{659}{715}\right)\)	\(e\left(\frac{2141}{2145}\right)\)	\(e\left(\frac{133}{715}\right)\)	\(e\left(\frac{422}{429}\right)\)	\(e\left(\frac{43}{715}\right)\)	\(e\left(\frac{532}{2145}\right)\)	\(e\left(\frac{1127}{2145}\right)\)	\(e\left(\frac{113}{165}\right)\)
\(\chi_{61347}(17,\cdot)\)	61347.ha	4290	yes	\(1\)	\(1\)	\(e\left(\frac{3781}{4290}\right)\)	\(e\left(\frac{1636}{2145}\right)\)	\(e\left(\frac{634}{715}\right)\)	\(e\left(\frac{556}{2145}\right)\)	\(e\left(\frac{921}{1430}\right)\)	\(e\left(\frac{659}{858}\right)\)	\(e\left(\frac{201}{1430}\right)\)	\(e\left(\frac{1127}{2145}\right)\)	\(e\left(\frac{2077}{2145}\right)\)	\(e\left(\frac{133}{165}\right)\)
\(\chi_{61347}(19,\cdot)\)	61347.fw	660	no	\(1\)	\(1\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{469}{660}\right)\)
\(\chi_{61347}(20,\cdot)\)	61347.hj	8580	yes	\(1\)	\(1\)	\(e\left(\frac{2243}{8580}\right)\)	\(e\left(\frac{2243}{4290}\right)\)	\(e\left(\frac{749}{2860}\right)\)	\(e\left(\frac{3271}{8580}\right)\)	\(e\left(\frac{2243}{2860}\right)\)	\(e\left(\frac{449}{858}\right)\)	\(e\left(\frac{919}{1430}\right)\)	\(e\left(\frac{98}{2145}\right)\)	\(e\left(\frac{1393}{2145}\right)\)	\(e\left(\frac{613}{660}\right)\)
\(\chi_{61347}(23,\cdot)\)	61347.dc	66	no	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{61347}(25,\cdot)\)	61347.gp	1430	no	\(1\)	\(1\)	\(e\left(\frac{659}{1430}\right)\)	\(e\left(\frac{659}{715}\right)\)	\(e\left(\frac{861}{1430}\right)\)	\(e\left(\frac{1093}{1430}\right)\)	\(e\left(\frac{547}{1430}\right)\)	\(e\left(\frac{9}{143}\right)\)	\(e\left(\frac{161}{715}\right)\)	\(e\left(\frac{603}{715}\right)\)	\(e\left(\frac{553}{715}\right)\)	\(e\left(\frac{19}{110}\right)\)
\(\chi_{61347}(28,\cdot)\)	61347.hg	8580	no	\(1\)	\(1\)	\(e\left(\frac{6697}{8580}\right)\)	\(e\left(\frac{2407}{4290}\right)\)	\(e\left(\frac{981}{2860}\right)\)	\(e\left(\frac{2879}{8580}\right)\)	\(e\left(\frac{977}{2860}\right)\)	\(e\left(\frac{53}{429}\right)\)	\(e\left(\frac{83}{715}\right)\)	\(e\left(\frac{262}{2145}\right)\)	\(e\left(\frac{47}{2145}\right)\)	\(e\left(\frac{137}{660}\right)\)
\(\chi_{61347}(29,\cdot)\)	61347.he	4290	yes	\(1\)	\(1\)	\(e\left(\frac{1954}{2145}\right)\)	\(e\left(\frac{1763}{2145}\right)\)	\(e\left(\frac{349}{1430}\right)\)	\(e\left(\frac{2221}{4290}\right)\)	\(e\left(\frac{524}{715}\right)\)	\(e\left(\frac{133}{858}\right)\)	\(e\left(\frac{613}{1430}\right)\)	\(e\left(\frac{1381}{2145}\right)\)	\(e\left(\frac{1091}{2145}\right)\)	\(e\left(\frac{163}{330}\right)\)
\(\chi_{61347}(31,\cdot)\)	61347.gv	2860	no	\(-1\)	\(1\)	\(e\left(\frac{2621}{2860}\right)\)	\(e\left(\frac{1191}{1430}\right)\)	\(e\left(\frac{189}{2860}\right)\)	\(e\left(\frac{2507}{2860}\right)\)	\(e\left(\frac{2143}{2860}\right)\)	\(e\left(\frac{281}{286}\right)\)	\(e\left(\frac{567}{715}\right)\)	\(e\left(\frac{476}{715}\right)\)	\(e\left(\frac{1377}{1430}\right)\)	\(e\left(\frac{141}{220}\right)\)
\(\chi_{61347}(32,\cdot)\)	61347.gq	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{991}{1716}\right)\)	\(e\left(\frac{133}{858}\right)\)	\(e\left(\frac{87}{572}\right)\)	\(e\left(\frac{1283}{1716}\right)\)	\(e\left(\frac{419}{572}\right)\)	\(e\left(\frac{313}{429}\right)\)	\(e\left(\frac{93}{286}\right)\)	\(e\left(\frac{133}{429}\right)\)	\(e\left(\frac{349}{858}\right)\)	\(e\left(\frac{113}{132}\right)\)
\(\chi_{61347}(34,\cdot)\)	61347.fq	572	no	\(-1\)	\(1\)	\(e\left(\frac{227}{572}\right)\)	\(e\left(\frac{227}{286}\right)\)	\(e\left(\frac{67}{572}\right)\)	\(e\left(\frac{5}{572}\right)\)	\(e\left(\frac{109}{572}\right)\)	\(e\left(\frac{147}{286}\right)\)	\(e\left(\frac{58}{143}\right)\)	\(e\left(\frac{84}{143}\right)\)	\(e\left(\frac{243}{286}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{61347}(35,\cdot)\)	61347.he	4290	yes	\(1\)	\(1\)	\(e\left(\frac{2102}{2145}\right)\)	\(e\left(\frac{2059}{2145}\right)\)	\(e\left(\frac{977}{1430}\right)\)	\(e\left(\frac{3083}{4290}\right)\)	\(e\left(\frac{672}{715}\right)\)	\(e\left(\frac{569}{858}\right)\)	\(e\left(\frac{999}{1430}\right)\)	\(e\left(\frac{1973}{2145}\right)\)	\(e\left(\frac{313}{2145}\right)\)	\(e\left(\frac{149}{330}\right)\)
\(\chi_{61347}(37,\cdot)\)	61347.hi	8580	no	\(-1\)	\(1\)	\(e\left(\frac{3001}{8580}\right)\)	\(e\left(\frac{3001}{4290}\right)\)	\(e\left(\frac{2763}{2860}\right)\)	\(e\left(\frac{2087}{8580}\right)\)	\(e\left(\frac{141}{2860}\right)\)	\(e\left(\frac{271}{858}\right)\)	\(e\left(\frac{424}{715}\right)\)	\(e\left(\frac{856}{2145}\right)\)	\(e\left(\frac{127}{4290}\right)\)	\(e\left(\frac{401}{660}\right)\)
\(\chi_{61347}(38,\cdot)\)	61347.gj	1430	yes	\(-1\)	\(1\)	\(e\left(\frac{491}{715}\right)\)	\(e\left(\frac{267}{715}\right)\)	\(e\left(\frac{584}{715}\right)\)	\(e\left(\frac{879}{1430}\right)\)	\(e\left(\frac{43}{715}\right)\)	\(e\left(\frac{72}{143}\right)\)	\(e\left(\frac{431}{1430}\right)\)	\(e\left(\frac{534}{715}\right)\)	\(e\left(\frac{983}{1430}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{61347}(40,\cdot)\)	61347.dv	130	no	\(-1\)	\(1\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{61347}(41,\cdot)\)	61347.hh	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{2179}{8580}\right)\)	\(e\left(\frac{2179}{4290}\right)\)	\(e\left(\frac{2507}{2860}\right)\)	\(e\left(\frac{6563}{8580}\right)\)	\(e\left(\frac{2179}{2860}\right)\)	\(e\left(\frac{56}{429}\right)\)	\(e\left(\frac{27}{1430}\right)\)	\(e\left(\frac{34}{2145}\right)\)	\(e\left(\frac{1273}{4290}\right)\)	\(e\left(\frac{509}{660}\right)\)
\(\chi_{61347}(43,\cdot)\)	61347.gc	858	no	\(-1\)	\(1\)	\(e\left(\frac{4}{429}\right)\)	\(e\left(\frac{8}{429}\right)\)	\(e\left(\frac{245}{286}\right)\)	\(e\left(\frac{116}{429}\right)\)	\(e\left(\frac{4}{143}\right)\)	\(e\left(\frac{743}{858}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{16}{429}\right)\)	\(e\left(\frac{271}{858}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{61347}(46,\cdot)\)	61347.hg	8580	no	\(1\)	\(1\)	\(e\left(\frac{4163}{8580}\right)\)	\(e\left(\frac{4163}{4290}\right)\)	\(e\left(\frac{919}{2860}\right)\)	\(e\left(\frac{3181}{8580}\right)\)	\(e\left(\frac{1303}{2860}\right)\)	\(e\left(\frac{346}{429}\right)\)	\(e\left(\frac{612}{715}\right)\)	\(e\left(\frac{2018}{2145}\right)\)	\(e\left(\frac{493}{2145}\right)\)	\(e\left(\frac{103}{660}\right)\)
\(\chi_{61347}(47,\cdot)\)	61347.gw	2860	yes	\(1\)	\(1\)	\(e\left(\frac{2273}{2860}\right)\)	\(e\left(\frac{843}{1430}\right)\)	\(e\left(\frac{177}{2860}\right)\)	\(e\left(\frac{1281}{2860}\right)\)	\(e\left(\frac{1099}{2860}\right)\)	\(e\left(\frac{245}{286}\right)\)	\(e\left(\frac{347}{1430}\right)\)	\(e\left(\frac{128}{715}\right)\)	\(e\left(\frac{83}{715}\right)\)	\(e\left(\frac{43}{220}\right)\)
\(\chi_{61347}(49,\cdot)\)	61347.hb	4290	no	\(1\)	\(1\)	\(e\left(\frac{2141}{4290}\right)\)	\(e\left(\frac{2141}{2145}\right)\)	\(e\left(\frac{1093}{1430}\right)\)	\(e\left(\frac{2887}{4290}\right)\)	\(e\left(\frac{711}{1430}\right)\)	\(e\left(\frac{113}{429}\right)\)	\(e\left(\frac{123}{715}\right)\)	\(e\left(\frac{2137}{2145}\right)\)	\(e\left(\frac{1112}{2145}\right)\)	\(e\left(\frac{241}{330}\right)\)
\(\chi_{61347}(50,\cdot)\)	61347.hh	8580	yes	\(-1\)	\(1\)	\(e\left(\frac{8377}{8580}\right)\)	\(e\left(\frac{4087}{4290}\right)\)	\(e\left(\frac{2381}{2860}\right)\)	\(e\left(\frac{4409}{8580}\right)\)	\(e\left(\frac{2657}{2860}\right)\)	\(e\left(\frac{347}{429}\right)\)	\(e\left(\frac{701}{1430}\right)\)	\(e\left(\frac{1942}{2145}\right)\)	\(e\left(\frac{2809}{4290}\right)\)	\(e\left(\frac{227}{660}\right)\)
\(\chi_{61347}(53,\cdot)\)	61347.go	1430	yes	\(-1\)	\(1\)	\(e\left(\frac{333}{1430}\right)\)	\(e\left(\frac{333}{715}\right)\)	\(e\left(\frac{1047}{1430}\right)\)	\(e\left(\frac{38}{715}\right)\)	\(e\left(\frac{999}{1430}\right)\)	\(e\left(\frac{138}{143}\right)\)	\(e\left(\frac{409}{1430}\right)\)	\(e\left(\frac{666}{715}\right)\)	\(e\left(\frac{37}{1430}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{61347}(56,\cdot)\)	61347.ge	858	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{429}\right)\)	\(e\left(\frac{254}{429}\right)\)	\(e\left(\frac{82}{143}\right)\)	\(e\left(\frac{73}{858}\right)\)	\(e\left(\frac{127}{143}\right)\)	\(e\left(\frac{373}{429}\right)\)	\(e\left(\frac{109}{286}\right)\)	\(e\left(\frac{79}{429}\right)\)	\(e\left(\frac{775}{858}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{61347}(58,\cdot)\)	61347.hi	8580	no	\(-1\)	\(1\)	\(e\left(\frac{3659}{8580}\right)\)	\(e\left(\frac{3659}{4290}\right)\)	\(e\left(\frac{1357}{2860}\right)\)	\(e\left(\frac{2293}{8580}\right)\)	\(e\left(\frac{799}{2860}\right)\)	\(e\left(\frac{773}{858}\right)\)	\(e\left(\frac{496}{715}\right)\)	\(e\left(\frac{1514}{2145}\right)\)	\(e\left(\frac{1673}{4290}\right)\)	\(e\left(\frac{439}{660}\right)\)

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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.