LMFDB - Group of Dirichlet characters of modulus 185193

Show commands: PariGP / SageMath

sage: H = DirichletGroup(185193)

pari: g = idealstar(,185193,2)

Character group

sage: G.order() pari: g.no
Order	=	116964
sage: H.invariants() pari: g.cyc
Structure	=	$C_{18}\times C_{6498}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{185193}(6860,\cdot)$, $\chi_{185193}(178336,\cdot)$

First 32 of 116964 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{185193}(1,\cdot)$	185193.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{185193}(2,\cdot)$	185193.hc	6498	yes	$1$	$1$	$e\left(\frac{181}{3249}\right)$	$e\left(\frac{362}{3249}\right)$	$e\left(\frac{109}{2166}\right)$	$e\left(\frac{3134}{3249}\right)$	$e\left(\frac{181}{1083}\right)$	$e\left(\frac{689}{6498}\right)$	$e\left(\frac{4111}{6498}\right)$	$e\left(\frac{1849}{6498}\right)$	$e\left(\frac{22}{1083}\right)$	$e\left(\frac{724}{3249}\right)$
$\chi_{185193}(4,\cdot)$	185193.gf	3249	yes	$1$	$1$	$e\left(\frac{362}{3249}\right)$	$e\left(\frac{724}{3249}\right)$	$e\left(\frac{109}{1083}\right)$	$e\left(\frac{3019}{3249}\right)$	$e\left(\frac{362}{1083}\right)$	$e\left(\frac{689}{3249}\right)$	$e\left(\frac{862}{3249}\right)$	$e\left(\frac{1849}{3249}\right)$	$e\left(\frac{44}{1083}\right)$	$e\left(\frac{1448}{3249}\right)$
$\chi_{185193}(5,\cdot)$	185193.gy	6498	yes	$-1$	$1$	$e\left(\frac{109}{2166}\right)$	$e\left(\frac{109}{1083}\right)$	$e\left(\frac{3683}{6498}\right)$	$e\left(\frac{1744}{3249}\right)$	$e\left(\frac{109}{722}\right)$	$e\left(\frac{2005}{3249}\right)$	$e\left(\frac{6431}{6498}\right)$	$e\left(\frac{593}{1083}\right)$	$e\left(\frac{3815}{6498}\right)$	$e\left(\frac{218}{1083}\right)$
$\chi_{185193}(7,\cdot)$	185193.gk	3249	yes	$1$	$1$	$e\left(\frac{3134}{3249}\right)$	$e\left(\frac{3019}{3249}\right)$	$e\left(\frac{1744}{3249}\right)$	$e\left(\frac{1541}{3249}\right)$	$e\left(\frac{968}{1083}\right)$	$e\left(\frac{181}{361}\right)$	$e\left(\frac{1589}{3249}\right)$	$e\left(\frac{1438}{3249}\right)$	$e\left(\frac{1426}{3249}\right)$	$e\left(\frac{2789}{3249}\right)$
$\chi_{185193}(8,\cdot)$	185193.ft	2166	no	$1$	$1$	$e\left(\frac{181}{1083}\right)$	$e\left(\frac{362}{1083}\right)$	$e\left(\frac{109}{722}\right)$	$e\left(\frac{968}{1083}\right)$	$e\left(\frac{181}{361}\right)$	$e\left(\frac{689}{2166}\right)$	$e\left(\frac{1945}{2166}\right)$	$e\left(\frac{1849}{2166}\right)$	$e\left(\frac{22}{361}\right)$	$e\left(\frac{724}{1083}\right)$
$\chi_{185193}(10,\cdot)$	185193.gp	6498	no	$-1$	$1$	$e\left(\frac{689}{6498}\right)$	$e\left(\frac{689}{3249}\right)$	$e\left(\frac{2005}{3249}\right)$	$e\left(\frac{181}{361}\right)$	$e\left(\frac{689}{2166}\right)$	$e\left(\frac{4699}{6498}\right)$	$e\left(\frac{674}{1083}\right)$	$e\left(\frac{5407}{6498}\right)$	$e\left(\frac{3947}{6498}\right)$	$e\left(\frac{1378}{3249}\right)$
$\chi_{185193}(11,\cdot)$	185193.hr	6498	yes	$-1$	$1$	$e\left(\frac{4111}{6498}\right)$	$e\left(\frac{862}{3249}\right)$	$e\left(\frac{6431}{6498}\right)$	$e\left(\frac{1589}{3249}\right)$	$e\left(\frac{1945}{2166}\right)$	$e\left(\frac{674}{1083}\right)$	$e\left(\frac{3355}{6498}\right)$	$e\left(\frac{2719}{3249}\right)$	$e\left(\frac{791}{6498}\right)$	$e\left(\frac{1724}{3249}\right)$
$\chi_{185193}(13,\cdot)$	185193.gz	6498	yes	$-1$	$1$	$e\left(\frac{1849}{6498}\right)$	$e\left(\frac{1849}{3249}\right)$	$e\left(\frac{593}{1083}\right)$	$e\left(\frac{1438}{3249}\right)$	$e\left(\frac{1849}{2166}\right)$	$e\left(\frac{5407}{6498}\right)$	$e\left(\frac{2719}{3249}\right)$	$e\left(\frac{4463}{6498}\right)$	$e\left(\frac{525}{722}\right)$	$e\left(\frac{449}{3249}\right)$
$\chi_{185193}(14,\cdot)$	185193.gx	6498	yes	$1$	$1$	$e\left(\frac{22}{1083}\right)$	$e\left(\frac{44}{1083}\right)$	$e\left(\frac{3815}{6498}\right)$	$e\left(\frac{1426}{3249}\right)$	$e\left(\frac{22}{361}\right)$	$e\left(\frac{3947}{6498}\right)$	$e\left(\frac{791}{6498}\right)$	$e\left(\frac{525}{722}\right)$	$e\left(\frac{1492}{3249}\right)$	$e\left(\frac{88}{1083}\right)$
$\chi_{185193}(16,\cdot)$	185193.gf	3249	yes	$1$	$1$	$e\left(\frac{724}{3249}\right)$	$e\left(\frac{1448}{3249}\right)$	$e\left(\frac{218}{1083}\right)$	$e\left(\frac{2789}{3249}\right)$	$e\left(\frac{724}{1083}\right)$	$e\left(\frac{1378}{3249}\right)$	$e\left(\frac{1724}{3249}\right)$	$e\left(\frac{449}{3249}\right)$	$e\left(\frac{88}{1083}\right)$	$e\left(\frac{2896}{3249}\right)$
$\chi_{185193}(17,\cdot)$	185193.gq	6498	no	$-1$	$1$	$e\left(\frac{5299}{6498}\right)$	$e\left(\frac{2050}{3249}\right)$	$e\left(\frac{3583}{6498}\right)$	$e\left(\frac{596}{1083}\right)$	$e\left(\frac{967}{2166}\right)$	$e\left(\frac{1192}{3249}\right)$	$e\left(\frac{161}{722}\right)$	$e\left(\frac{697}{3249}\right)$	$e\left(\frac{2377}{6498}\right)$	$e\left(\frac{851}{3249}\right)$
$\chi_{185193}(20,\cdot)$	185193.gm	6498	yes	$-1$	$1$	$e\left(\frac{1051}{6498}\right)$	$e\left(\frac{1051}{3249}\right)$	$e\left(\frac{4337}{6498}\right)$	$e\left(\frac{1514}{3249}\right)$	$e\left(\frac{1051}{2166}\right)$	$e\left(\frac{898}{1083}\right)$	$e\left(\frac{1657}{6498}\right)$	$e\left(\frac{379}{3249}\right)$	$e\left(\frac{4079}{6498}\right)$	$e\left(\frac{2102}{3249}\right)$
$\chi_{185193}(22,\cdot)$	185193.gu	6498	yes	$-1$	$1$	$e\left(\frac{497}{722}\right)$	$e\left(\frac{136}{361}\right)$	$e\left(\frac{130}{3249}\right)$	$e\left(\frac{1474}{3249}\right)$	$e\left(\frac{47}{722}\right)$	$e\left(\frac{4733}{6498}\right)$	$e\left(\frac{484}{3249}\right)$	$e\left(\frac{263}{2166}\right)$	$e\left(\frac{923}{6498}\right)$	$e\left(\frac{272}{361}\right)$
$\chi_{185193}(23,\cdot)$	185193.hb	6498	yes	$-1$	$1$	$e\left(\frac{1381}{6498}\right)$	$e\left(\frac{1381}{3249}\right)$	$e\left(\frac{353}{2166}\right)$	$e\left(\frac{2191}{3249}\right)$	$e\left(\frac{1381}{2166}\right)$	$e\left(\frac{1220}{3249}\right)$	$e\left(\frac{5981}{6498}\right)$	$e\left(\frac{58}{3249}\right)$	$e\left(\frac{1921}{2166}\right)$	$e\left(\frac{2762}{3249}\right)$
$\chi_{185193}(25,\cdot)$	185193.gg	3249	yes	$1$	$1$	$e\left(\frac{109}{1083}\right)$	$e\left(\frac{218}{1083}\right)$	$e\left(\frac{434}{3249}\right)$	$e\left(\frac{239}{3249}\right)$	$e\left(\frac{109}{361}\right)$	$e\left(\frac{761}{3249}\right)$	$e\left(\frac{3182}{3249}\right)$	$e\left(\frac{103}{1083}\right)$	$e\left(\frac{566}{3249}\right)$	$e\left(\frac{436}{1083}\right)$
$\chi_{185193}(26,\cdot)$	185193.fv	2166	no	$-1$	$1$	$e\left(\frac{737}{2166}\right)$	$e\left(\frac{737}{1083}\right)$	$e\left(\frac{1295}{2166}\right)$	$e\left(\frac{147}{361}\right)$	$e\left(\frac{15}{722}\right)$	$e\left(\frac{1016}{1083}\right)$	$e\left(\frac{339}{722}\right)$	$e\left(\frac{1052}{1083}\right)$	$e\left(\frac{1619}{2166}\right)$	$e\left(\frac{391}{1083}\right)$
$\chi_{185193}(28,\cdot)$	185193.dr	171	no	$1$	$1$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{52}{171}\right)$
$\chi_{185193}(29,\cdot)$	185193.hl	6498	yes	$1$	$1$	$e\left(\frac{116}{361}\right)$	$e\left(\frac{232}{361}\right)$	$e\left(\frac{3013}{6498}\right)$	$e\left(\frac{2111}{3249}\right)$	$e\left(\frac{348}{361}\right)$	$e\left(\frac{5101}{6498}\right)$	$e\left(\frac{271}{6498}\right)$	$e\left(\frac{661}{2166}\right)$	$e\left(\frac{3155}{3249}\right)$	$e\left(\frac{103}{361}\right)$
$\chi_{185193}(31,\cdot)$	185193.ht	6498	yes	$-1$	$1$	$e\left(\frac{5129}{6498}\right)$	$e\left(\frac{1880}{3249}\right)$	$e\left(\frac{530}{3249}\right)$	$e\left(\frac{1483}{3249}\right)$	$e\left(\frac{797}{2166}\right)$	$e\left(\frac{2063}{2166}\right)$	$e\left(\frac{2362}{3249}\right)$	$e\left(\frac{1495}{6498}\right)$	$e\left(\frac{1597}{6498}\right)$	$e\left(\frac{511}{3249}\right)$
$\chi_{185193}(32,\cdot)$	185193.hc	6498	yes	$1$	$1$	$e\left(\frac{905}{3249}\right)$	$e\left(\frac{1810}{3249}\right)$	$e\left(\frac{545}{2166}\right)$	$e\left(\frac{2674}{3249}\right)$	$e\left(\frac{905}{1083}\right)$	$e\left(\frac{3445}{6498}\right)$	$e\left(\frac{1061}{6498}\right)$	$e\left(\frac{2747}{6498}\right)$	$e\left(\frac{110}{1083}\right)$	$e\left(\frac{371}{3249}\right)$
$\chi_{185193}(34,\cdot)$	185193.gu	6498	yes	$-1$	$1$	$e\left(\frac{629}{722}\right)$	$e\left(\frac{268}{361}\right)$	$e\left(\frac{1955}{3249}\right)$	$e\left(\frac{1673}{3249}\right)$	$e\left(\frac{443}{722}\right)$	$e\left(\frac{3073}{6498}\right)$	$e\left(\frac{2780}{3249}\right)$	$e\left(\frac{1081}{2166}\right)$	$e\left(\frac{2509}{6498}\right)$	$e\left(\frac{175}{361}\right)$
$\chi_{185193}(35,\cdot)$	185193.hp	6498	no	$-1$	$1$	$e\left(\frac{97}{6498}\right)$	$e\left(\frac{97}{3249}\right)$	$e\left(\frac{673}{6498}\right)$	$e\left(\frac{4}{361}\right)$	$e\left(\frac{97}{2166}\right)$	$e\left(\frac{385}{3249}\right)$	$e\left(\frac{1037}{2166}\right)$	$e\left(\frac{3217}{3249}\right)$	$e\left(\frac{169}{6498}\right)$	$e\left(\frac{194}{3249}\right)$
$\chi_{185193}(37,\cdot)$	185193.fo	2166	no	$-1$	$1$	$e\left(\frac{509}{2166}\right)$	$e\left(\frac{509}{1083}\right)$	$e\left(\frac{11}{1083}\right)$	$e\left(\frac{1030}{1083}\right)$	$e\left(\frac{509}{722}\right)$	$e\left(\frac{177}{722}\right)$	$e\left(\frac{613}{1083}\right)$	$e\left(\frac{1819}{2166}\right)$	$e\left(\frac{403}{2166}\right)$	$e\left(\frac{1018}{1083}\right)$
$\chi_{185193}(40,\cdot)$	185193.gu	6498	yes	$-1$	$1$	$e\left(\frac{157}{722}\right)$	$e\left(\frac{157}{361}\right)$	$e\left(\frac{2332}{3249}\right)$	$e\left(\frac{1399}{3249}\right)$	$e\left(\frac{471}{722}\right)$	$e\left(\frac{6077}{6498}\right)$	$e\left(\frac{2884}{3249}\right)$	$e\left(\frac{869}{2166}\right)$	$e\left(\frac{4211}{6498}\right)$	$e\left(\frac{314}{361}\right)$
$\chi_{185193}(41,\cdot)$	185193.gv	6498	yes	$1$	$1$	$e\left(\frac{122}{1083}\right)$	$e\left(\frac{244}{1083}\right)$	$e\left(\frac{743}{6498}\right)$	$e\left(\frac{2821}{3249}\right)$	$e\left(\frac{122}{361}\right)$	$e\left(\frac{1475}{6498}\right)$	$e\left(\frac{2483}{6498}\right)$	$e\left(\frac{1711}{2166}\right)$	$e\left(\frac{3187}{3249}\right)$	$e\left(\frac{488}{1083}\right)$
$\chi_{185193}(43,\cdot)$	185193.gd	3249	yes	$1$	$1$	$e\left(\frac{1774}{3249}\right)$	$e\left(\frac{299}{3249}\right)$	$e\left(\frac{592}{1083}\right)$	$e\left(\frac{2798}{3249}\right)$	$e\left(\frac{691}{1083}\right)$	$e\left(\frac{301}{3249}\right)$	$e\left(\frac{1436}{3249}\right)$	$e\left(\frac{1163}{3249}\right)$	$e\left(\frac{147}{361}\right)$	$e\left(\frac{598}{3249}\right)$
$\chi_{185193}(44,\cdot)$	185193.hp	6498	no	$-1$	$1$	$e\left(\frac{4835}{6498}\right)$	$e\left(\frac{1586}{3249}\right)$	$e\left(\frac{587}{6498}\right)$	$e\left(\frac{151}{361}\right)$	$e\left(\frac{503}{2166}\right)$	$e\left(\frac{2711}{3249}\right)$	$e\left(\frac{1693}{2166}\right)$	$e\left(\frac{1319}{3249}\right)$	$e\left(\frac{1055}{6498}\right)$	$e\left(\frac{3172}{3249}\right)$
$\chi_{185193}(46,\cdot)$	185193.fz	2166	no	$-1$	$1$	$e\left(\frac{581}{2166}\right)$	$e\left(\frac{581}{1083}\right)$	$e\left(\frac{77}{361}\right)$	$e\left(\frac{692}{1083}\right)$	$e\left(\frac{581}{722}\right)$	$e\left(\frac{1043}{2166}\right)$	$e\left(\frac{599}{1083}\right)$	$e\left(\frac{655}{2166}\right)$	$e\left(\frac{655}{722}\right)$	$e\left(\frac{79}{1083}\right)$
$\chi_{185193}(47,\cdot)$	185193.gy	6498	yes	$-1$	$1$	$e\left(\frac{1649}{2166}\right)$	$e\left(\frac{566}{1083}\right)$	$e\left(\frac{3277}{6498}\right)$	$e\left(\frac{1475}{3249}\right)$	$e\left(\frac{205}{722}\right)$	$e\left(\frac{863}{3249}\right)$	$e\left(\frac{1987}{6498}\right)$	$e\left(\frac{178}{1083}\right)$	$e\left(\frac{1399}{6498}\right)$	$e\left(\frac{49}{1083}\right)$
$\chi_{185193}(49,\cdot)$	185193.gk	3249	yes	$1$	$1$	$e\left(\frac{3019}{3249}\right)$	$e\left(\frac{2789}{3249}\right)$	$e\left(\frac{239}{3249}\right)$	$e\left(\frac{3082}{3249}\right)$	$e\left(\frac{853}{1083}\right)$	$e\left(\frac{1}{361}\right)$	$e\left(\frac{3178}{3249}\right)$	$e\left(\frac{2876}{3249}\right)$	$e\left(\frac{2852}{3249}\right)$	$e\left(\frac{2329}{3249}\right)$
$\chi_{185193}(50,\cdot)$	185193.hs	6498	yes	$1$	$1$	$e\left(\frac{508}{3249}\right)$	$e\left(\frac{1016}{3249}\right)$	$e\left(\frac{1195}{6498}\right)$	$e\left(\frac{124}{3249}\right)$	$e\left(\frac{508}{1083}\right)$	$e\left(\frac{737}{2166}\right)$	$e\left(\frac{3977}{6498}\right)$	$e\left(\frac{2467}{6498}\right)$	$e\left(\frac{632}{3249}\right)$	$e\left(\frac{2032}{3249}\right)$

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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	$185193$
Structure	\(C_{18}\times C_{6498}\)
Order	$116964$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{185193}(1,\cdot)\)	185193.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{185193}(2,\cdot)\)	185193.hc	6498	yes	\(1\)	\(1\)	\(e\left(\frac{181}{3249}\right)\)	\(e\left(\frac{362}{3249}\right)\)	\(e\left(\frac{109}{2166}\right)\)	\(e\left(\frac{3134}{3249}\right)\)	\(e\left(\frac{181}{1083}\right)\)	\(e\left(\frac{689}{6498}\right)\)	\(e\left(\frac{4111}{6498}\right)\)	\(e\left(\frac{1849}{6498}\right)\)	\(e\left(\frac{22}{1083}\right)\)	\(e\left(\frac{724}{3249}\right)\)
\(\chi_{185193}(4,\cdot)\)	185193.gf	3249	yes	\(1\)	\(1\)	\(e\left(\frac{362}{3249}\right)\)	\(e\left(\frac{724}{3249}\right)\)	\(e\left(\frac{109}{1083}\right)\)	\(e\left(\frac{3019}{3249}\right)\)	\(e\left(\frac{362}{1083}\right)\)	\(e\left(\frac{689}{3249}\right)\)	\(e\left(\frac{862}{3249}\right)\)	\(e\left(\frac{1849}{3249}\right)\)	\(e\left(\frac{44}{1083}\right)\)	\(e\left(\frac{1448}{3249}\right)\)
\(\chi_{185193}(5,\cdot)\)	185193.gy	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{2166}\right)\)	\(e\left(\frac{109}{1083}\right)\)	\(e\left(\frac{3683}{6498}\right)\)	\(e\left(\frac{1744}{3249}\right)\)	\(e\left(\frac{109}{722}\right)\)	\(e\left(\frac{2005}{3249}\right)\)	\(e\left(\frac{6431}{6498}\right)\)	\(e\left(\frac{593}{1083}\right)\)	\(e\left(\frac{3815}{6498}\right)\)	\(e\left(\frac{218}{1083}\right)\)
\(\chi_{185193}(7,\cdot)\)	185193.gk	3249	yes	\(1\)	\(1\)	\(e\left(\frac{3134}{3249}\right)\)	\(e\left(\frac{3019}{3249}\right)\)	\(e\left(\frac{1744}{3249}\right)\)	\(e\left(\frac{1541}{3249}\right)\)	\(e\left(\frac{968}{1083}\right)\)	\(e\left(\frac{181}{361}\right)\)	\(e\left(\frac{1589}{3249}\right)\)	\(e\left(\frac{1438}{3249}\right)\)	\(e\left(\frac{1426}{3249}\right)\)	\(e\left(\frac{2789}{3249}\right)\)
\(\chi_{185193}(8,\cdot)\)	185193.ft	2166	no	\(1\)	\(1\)	\(e\left(\frac{181}{1083}\right)\)	\(e\left(\frac{362}{1083}\right)\)	\(e\left(\frac{109}{722}\right)\)	\(e\left(\frac{968}{1083}\right)\)	\(e\left(\frac{181}{361}\right)\)	\(e\left(\frac{689}{2166}\right)\)	\(e\left(\frac{1945}{2166}\right)\)	\(e\left(\frac{1849}{2166}\right)\)	\(e\left(\frac{22}{361}\right)\)	\(e\left(\frac{724}{1083}\right)\)
\(\chi_{185193}(10,\cdot)\)	185193.gp	6498	no	\(-1\)	\(1\)	\(e\left(\frac{689}{6498}\right)\)	\(e\left(\frac{689}{3249}\right)\)	\(e\left(\frac{2005}{3249}\right)\)	\(e\left(\frac{181}{361}\right)\)	\(e\left(\frac{689}{2166}\right)\)	\(e\left(\frac{4699}{6498}\right)\)	\(e\left(\frac{674}{1083}\right)\)	\(e\left(\frac{5407}{6498}\right)\)	\(e\left(\frac{3947}{6498}\right)\)	\(e\left(\frac{1378}{3249}\right)\)
\(\chi_{185193}(11,\cdot)\)	185193.hr	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{4111}{6498}\right)\)	\(e\left(\frac{862}{3249}\right)\)	\(e\left(\frac{6431}{6498}\right)\)	\(e\left(\frac{1589}{3249}\right)\)	\(e\left(\frac{1945}{2166}\right)\)	\(e\left(\frac{674}{1083}\right)\)	\(e\left(\frac{3355}{6498}\right)\)	\(e\left(\frac{2719}{3249}\right)\)	\(e\left(\frac{791}{6498}\right)\)	\(e\left(\frac{1724}{3249}\right)\)
\(\chi_{185193}(13,\cdot)\)	185193.gz	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{1849}{6498}\right)\)	\(e\left(\frac{1849}{3249}\right)\)	\(e\left(\frac{593}{1083}\right)\)	\(e\left(\frac{1438}{3249}\right)\)	\(e\left(\frac{1849}{2166}\right)\)	\(e\left(\frac{5407}{6498}\right)\)	\(e\left(\frac{2719}{3249}\right)\)	\(e\left(\frac{4463}{6498}\right)\)	\(e\left(\frac{525}{722}\right)\)	\(e\left(\frac{449}{3249}\right)\)
\(\chi_{185193}(14,\cdot)\)	185193.gx	6498	yes	\(1\)	\(1\)	\(e\left(\frac{22}{1083}\right)\)	\(e\left(\frac{44}{1083}\right)\)	\(e\left(\frac{3815}{6498}\right)\)	\(e\left(\frac{1426}{3249}\right)\)	\(e\left(\frac{22}{361}\right)\)	\(e\left(\frac{3947}{6498}\right)\)	\(e\left(\frac{791}{6498}\right)\)	\(e\left(\frac{525}{722}\right)\)	\(e\left(\frac{1492}{3249}\right)\)	\(e\left(\frac{88}{1083}\right)\)
\(\chi_{185193}(16,\cdot)\)	185193.gf	3249	yes	\(1\)	\(1\)	\(e\left(\frac{724}{3249}\right)\)	\(e\left(\frac{1448}{3249}\right)\)	\(e\left(\frac{218}{1083}\right)\)	\(e\left(\frac{2789}{3249}\right)\)	\(e\left(\frac{724}{1083}\right)\)	\(e\left(\frac{1378}{3249}\right)\)	\(e\left(\frac{1724}{3249}\right)\)	\(e\left(\frac{449}{3249}\right)\)	\(e\left(\frac{88}{1083}\right)\)	\(e\left(\frac{2896}{3249}\right)\)
\(\chi_{185193}(17,\cdot)\)	185193.gq	6498	no	\(-1\)	\(1\)	\(e\left(\frac{5299}{6498}\right)\)	\(e\left(\frac{2050}{3249}\right)\)	\(e\left(\frac{3583}{6498}\right)\)	\(e\left(\frac{596}{1083}\right)\)	\(e\left(\frac{967}{2166}\right)\)	\(e\left(\frac{1192}{3249}\right)\)	\(e\left(\frac{161}{722}\right)\)	\(e\left(\frac{697}{3249}\right)\)	\(e\left(\frac{2377}{6498}\right)\)	\(e\left(\frac{851}{3249}\right)\)
\(\chi_{185193}(20,\cdot)\)	185193.gm	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{1051}{6498}\right)\)	\(e\left(\frac{1051}{3249}\right)\)	\(e\left(\frac{4337}{6498}\right)\)	\(e\left(\frac{1514}{3249}\right)\)	\(e\left(\frac{1051}{2166}\right)\)	\(e\left(\frac{898}{1083}\right)\)	\(e\left(\frac{1657}{6498}\right)\)	\(e\left(\frac{379}{3249}\right)\)	\(e\left(\frac{4079}{6498}\right)\)	\(e\left(\frac{2102}{3249}\right)\)
\(\chi_{185193}(22,\cdot)\)	185193.gu	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{497}{722}\right)\)	\(e\left(\frac{136}{361}\right)\)	\(e\left(\frac{130}{3249}\right)\)	\(e\left(\frac{1474}{3249}\right)\)	\(e\left(\frac{47}{722}\right)\)	\(e\left(\frac{4733}{6498}\right)\)	\(e\left(\frac{484}{3249}\right)\)	\(e\left(\frac{263}{2166}\right)\)	\(e\left(\frac{923}{6498}\right)\)	\(e\left(\frac{272}{361}\right)\)
\(\chi_{185193}(23,\cdot)\)	185193.hb	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{1381}{6498}\right)\)	\(e\left(\frac{1381}{3249}\right)\)	\(e\left(\frac{353}{2166}\right)\)	\(e\left(\frac{2191}{3249}\right)\)	\(e\left(\frac{1381}{2166}\right)\)	\(e\left(\frac{1220}{3249}\right)\)	\(e\left(\frac{5981}{6498}\right)\)	\(e\left(\frac{58}{3249}\right)\)	\(e\left(\frac{1921}{2166}\right)\)	\(e\left(\frac{2762}{3249}\right)\)
\(\chi_{185193}(25,\cdot)\)	185193.gg	3249	yes	\(1\)	\(1\)	\(e\left(\frac{109}{1083}\right)\)	\(e\left(\frac{218}{1083}\right)\)	\(e\left(\frac{434}{3249}\right)\)	\(e\left(\frac{239}{3249}\right)\)	\(e\left(\frac{109}{361}\right)\)	\(e\left(\frac{761}{3249}\right)\)	\(e\left(\frac{3182}{3249}\right)\)	\(e\left(\frac{103}{1083}\right)\)	\(e\left(\frac{566}{3249}\right)\)	\(e\left(\frac{436}{1083}\right)\)
\(\chi_{185193}(26,\cdot)\)	185193.fv	2166	no	\(-1\)	\(1\)	\(e\left(\frac{737}{2166}\right)\)	\(e\left(\frac{737}{1083}\right)\)	\(e\left(\frac{1295}{2166}\right)\)	\(e\left(\frac{147}{361}\right)\)	\(e\left(\frac{15}{722}\right)\)	\(e\left(\frac{1016}{1083}\right)\)	\(e\left(\frac{339}{722}\right)\)	\(e\left(\frac{1052}{1083}\right)\)	\(e\left(\frac{1619}{2166}\right)\)	\(e\left(\frac{391}{1083}\right)\)
\(\chi_{185193}(28,\cdot)\)	185193.dr	171	no	\(1\)	\(1\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)
\(\chi_{185193}(29,\cdot)\)	185193.hl	6498	yes	\(1\)	\(1\)	\(e\left(\frac{116}{361}\right)\)	\(e\left(\frac{232}{361}\right)\)	\(e\left(\frac{3013}{6498}\right)\)	\(e\left(\frac{2111}{3249}\right)\)	\(e\left(\frac{348}{361}\right)\)	\(e\left(\frac{5101}{6498}\right)\)	\(e\left(\frac{271}{6498}\right)\)	\(e\left(\frac{661}{2166}\right)\)	\(e\left(\frac{3155}{3249}\right)\)	\(e\left(\frac{103}{361}\right)\)
\(\chi_{185193}(31,\cdot)\)	185193.ht	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{5129}{6498}\right)\)	\(e\left(\frac{1880}{3249}\right)\)	\(e\left(\frac{530}{3249}\right)\)	\(e\left(\frac{1483}{3249}\right)\)	\(e\left(\frac{797}{2166}\right)\)	\(e\left(\frac{2063}{2166}\right)\)	\(e\left(\frac{2362}{3249}\right)\)	\(e\left(\frac{1495}{6498}\right)\)	\(e\left(\frac{1597}{6498}\right)\)	\(e\left(\frac{511}{3249}\right)\)
\(\chi_{185193}(32,\cdot)\)	185193.hc	6498	yes	\(1\)	\(1\)	\(e\left(\frac{905}{3249}\right)\)	\(e\left(\frac{1810}{3249}\right)\)	\(e\left(\frac{545}{2166}\right)\)	\(e\left(\frac{2674}{3249}\right)\)	\(e\left(\frac{905}{1083}\right)\)	\(e\left(\frac{3445}{6498}\right)\)	\(e\left(\frac{1061}{6498}\right)\)	\(e\left(\frac{2747}{6498}\right)\)	\(e\left(\frac{110}{1083}\right)\)	\(e\left(\frac{371}{3249}\right)\)
\(\chi_{185193}(34,\cdot)\)	185193.gu	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{629}{722}\right)\)	\(e\left(\frac{268}{361}\right)\)	\(e\left(\frac{1955}{3249}\right)\)	\(e\left(\frac{1673}{3249}\right)\)	\(e\left(\frac{443}{722}\right)\)	\(e\left(\frac{3073}{6498}\right)\)	\(e\left(\frac{2780}{3249}\right)\)	\(e\left(\frac{1081}{2166}\right)\)	\(e\left(\frac{2509}{6498}\right)\)	\(e\left(\frac{175}{361}\right)\)
\(\chi_{185193}(35,\cdot)\)	185193.hp	6498	no	\(-1\)	\(1\)	\(e\left(\frac{97}{6498}\right)\)	\(e\left(\frac{97}{3249}\right)\)	\(e\left(\frac{673}{6498}\right)\)	\(e\left(\frac{4}{361}\right)\)	\(e\left(\frac{97}{2166}\right)\)	\(e\left(\frac{385}{3249}\right)\)	\(e\left(\frac{1037}{2166}\right)\)	\(e\left(\frac{3217}{3249}\right)\)	\(e\left(\frac{169}{6498}\right)\)	\(e\left(\frac{194}{3249}\right)\)
\(\chi_{185193}(37,\cdot)\)	185193.fo	2166	no	\(-1\)	\(1\)	\(e\left(\frac{509}{2166}\right)\)	\(e\left(\frac{509}{1083}\right)\)	\(e\left(\frac{11}{1083}\right)\)	\(e\left(\frac{1030}{1083}\right)\)	\(e\left(\frac{509}{722}\right)\)	\(e\left(\frac{177}{722}\right)\)	\(e\left(\frac{613}{1083}\right)\)	\(e\left(\frac{1819}{2166}\right)\)	\(e\left(\frac{403}{2166}\right)\)	\(e\left(\frac{1018}{1083}\right)\)
\(\chi_{185193}(40,\cdot)\)	185193.gu	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{722}\right)\)	\(e\left(\frac{157}{361}\right)\)	\(e\left(\frac{2332}{3249}\right)\)	\(e\left(\frac{1399}{3249}\right)\)	\(e\left(\frac{471}{722}\right)\)	\(e\left(\frac{6077}{6498}\right)\)	\(e\left(\frac{2884}{3249}\right)\)	\(e\left(\frac{869}{2166}\right)\)	\(e\left(\frac{4211}{6498}\right)\)	\(e\left(\frac{314}{361}\right)\)
\(\chi_{185193}(41,\cdot)\)	185193.gv	6498	yes	\(1\)	\(1\)	\(e\left(\frac{122}{1083}\right)\)	\(e\left(\frac{244}{1083}\right)\)	\(e\left(\frac{743}{6498}\right)\)	\(e\left(\frac{2821}{3249}\right)\)	\(e\left(\frac{122}{361}\right)\)	\(e\left(\frac{1475}{6498}\right)\)	\(e\left(\frac{2483}{6498}\right)\)	\(e\left(\frac{1711}{2166}\right)\)	\(e\left(\frac{3187}{3249}\right)\)	\(e\left(\frac{488}{1083}\right)\)
\(\chi_{185193}(43,\cdot)\)	185193.gd	3249	yes	\(1\)	\(1\)	\(e\left(\frac{1774}{3249}\right)\)	\(e\left(\frac{299}{3249}\right)\)	\(e\left(\frac{592}{1083}\right)\)	\(e\left(\frac{2798}{3249}\right)\)	\(e\left(\frac{691}{1083}\right)\)	\(e\left(\frac{301}{3249}\right)\)	\(e\left(\frac{1436}{3249}\right)\)	\(e\left(\frac{1163}{3249}\right)\)	\(e\left(\frac{147}{361}\right)\)	\(e\left(\frac{598}{3249}\right)\)
\(\chi_{185193}(44,\cdot)\)	185193.hp	6498	no	\(-1\)	\(1\)	\(e\left(\frac{4835}{6498}\right)\)	\(e\left(\frac{1586}{3249}\right)\)	\(e\left(\frac{587}{6498}\right)\)	\(e\left(\frac{151}{361}\right)\)	\(e\left(\frac{503}{2166}\right)\)	\(e\left(\frac{2711}{3249}\right)\)	\(e\left(\frac{1693}{2166}\right)\)	\(e\left(\frac{1319}{3249}\right)\)	\(e\left(\frac{1055}{6498}\right)\)	\(e\left(\frac{3172}{3249}\right)\)
\(\chi_{185193}(46,\cdot)\)	185193.fz	2166	no	\(-1\)	\(1\)	\(e\left(\frac{581}{2166}\right)\)	\(e\left(\frac{581}{1083}\right)\)	\(e\left(\frac{77}{361}\right)\)	\(e\left(\frac{692}{1083}\right)\)	\(e\left(\frac{581}{722}\right)\)	\(e\left(\frac{1043}{2166}\right)\)	\(e\left(\frac{599}{1083}\right)\)	\(e\left(\frac{655}{2166}\right)\)	\(e\left(\frac{655}{722}\right)\)	\(e\left(\frac{79}{1083}\right)\)
\(\chi_{185193}(47,\cdot)\)	185193.gy	6498	yes	\(-1\)	\(1\)	\(e\left(\frac{1649}{2166}\right)\)	\(e\left(\frac{566}{1083}\right)\)	\(e\left(\frac{3277}{6498}\right)\)	\(e\left(\frac{1475}{3249}\right)\)	\(e\left(\frac{205}{722}\right)\)	\(e\left(\frac{863}{3249}\right)\)	\(e\left(\frac{1987}{6498}\right)\)	\(e\left(\frac{178}{1083}\right)\)	\(e\left(\frac{1399}{6498}\right)\)	\(e\left(\frac{49}{1083}\right)\)
\(\chi_{185193}(49,\cdot)\)	185193.gk	3249	yes	\(1\)	\(1\)	\(e\left(\frac{3019}{3249}\right)\)	\(e\left(\frac{2789}{3249}\right)\)	\(e\left(\frac{239}{3249}\right)\)	\(e\left(\frac{3082}{3249}\right)\)	\(e\left(\frac{853}{1083}\right)\)	\(e\left(\frac{1}{361}\right)\)	\(e\left(\frac{3178}{3249}\right)\)	\(e\left(\frac{2876}{3249}\right)\)	\(e\left(\frac{2852}{3249}\right)\)	\(e\left(\frac{2329}{3249}\right)\)
\(\chi_{185193}(50,\cdot)\)	185193.hs	6498	yes	\(1\)	\(1\)	\(e\left(\frac{508}{3249}\right)\)	\(e\left(\frac{1016}{3249}\right)\)	\(e\left(\frac{1195}{6498}\right)\)	\(e\left(\frac{124}{3249}\right)\)	\(e\left(\frac{508}{1083}\right)\)	\(e\left(\frac{737}{2166}\right)\)	\(e\left(\frac{3977}{6498}\right)\)	\(e\left(\frac{2467}{6498}\right)\)	\(e\left(\frac{632}{3249}\right)\)	\(e\left(\frac{2032}{3249}\right)\)

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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.