LMFDB - Group of Dirichlet characters of modulus 779609

Show commands: PariGP / SageMath

sage: H = DirichletGroup(779609)

pari: g = idealstar(,779609,2)

Character group

sage: G.order() pari: g.no
Order	=	779608
sage: H.invariants() pari: g.cyc
Structure	=	$C_{779608}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{779609}(3,\cdot)$

First 32 of 779608 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{779609}(1,\cdot)$	779609.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{779609}(2,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{115353}{194902}\right)$	$e\left(\frac{155099}{389804}\right)$	$e\left(\frac{17902}{97451}\right)$	$e\left(\frac{36605}{97451}\right)$	$e\left(\frac{385805}{389804}\right)$	$e\left(\frac{103525}{389804}\right)$	$e\left(\frac{151157}{194902}\right)$	$e\left(\frac{155099}{194902}\right)$	$e\left(\frac{188563}{194902}\right)$	$e\left(\frac{149447}{389804}\right)$
$\chi_{779609}(3,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{155099}{389804}\right)$	$e\left(\frac{1}{779608}\right)$	$e\left(\frac{155099}{194902}\right)$	$e\left(\frac{78012}{97451}\right)$	$e\left(\frac{310199}{779608}\right)$	$e\left(\frac{632583}{779608}\right)$	$e\left(\frac{75493}{389804}\right)$	$e\left(\frac{1}{389804}\right)$	$e\left(\frac{77343}{389804}\right)$	$e\left(\frac{295133}{779608}\right)$
$\chi_{779609}(4,\cdot)$	779609.bd	194902	yes	$1$	$1$	$e\left(\frac{17902}{97451}\right)$	$e\left(\frac{155099}{194902}\right)$	$e\left(\frac{35804}{97451}\right)$	$e\left(\frac{73210}{97451}\right)$	$e\left(\frac{190903}{194902}\right)$	$e\left(\frac{103525}{194902}\right)$	$e\left(\frac{53706}{97451}\right)$	$e\left(\frac{57648}{97451}\right)$	$e\left(\frac{91112}{97451}\right)$	$e\left(\frac{149447}{194902}\right)$
$\chi_{779609}(5,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{36605}{97451}\right)$	$e\left(\frac{78012}{97451}\right)$	$e\left(\frac{73210}{97451}\right)$	$e\left(\frac{67748}{97451}\right)$	$e\left(\frac{17166}{97451}\right)$	$e\left(\frac{73498}{97451}\right)$	$e\left(\frac{12364}{97451}\right)$	$e\left(\frac{58573}{97451}\right)$	$e\left(\frac{6902}{97451}\right)$	$e\left(\frac{44885}{97451}\right)$
$\chi_{779609}(6,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{385805}{389804}\right)$	$e\left(\frac{310199}{779608}\right)$	$e\left(\frac{190903}{194902}\right)$	$e\left(\frac{17166}{97451}\right)$	$e\left(\frac{302201}{779608}\right)$	$e\left(\frac{60025}{779608}\right)$	$e\left(\frac{377807}{389804}\right)$	$e\left(\frac{310199}{389804}\right)$	$e\left(\frac{64665}{389804}\right)$	$e\left(\frac{594027}{779608}\right)$
$\chi_{779609}(7,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{103525}{389804}\right)$	$e\left(\frac{632583}{779608}\right)$	$e\left(\frac{103525}{194902}\right)$	$e\left(\frac{73498}{97451}\right)$	$e\left(\frac{60025}{779608}\right)$	$e\left(\frac{159609}{779608}\right)$	$e\left(\frac{310575}{389804}\right)$	$e\left(\frac{242779}{389804}\right)$	$e\left(\frac{7713}{389804}\right)$	$e\left(\frac{272347}{779608}\right)$
$\chi_{779609}(8,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{151157}{194902}\right)$	$e\left(\frac{75493}{389804}\right)$	$e\left(\frac{53706}{97451}\right)$	$e\left(\frac{12364}{97451}\right)$	$e\left(\frac{377807}{389804}\right)$	$e\left(\frac{310575}{389804}\right)$	$e\left(\frac{63667}{194902}\right)$	$e\left(\frac{75493}{194902}\right)$	$e\left(\frac{175885}{194902}\right)$	$e\left(\frac{58537}{389804}\right)$
$\chi_{779609}(9,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{155099}{194902}\right)$	$e\left(\frac{1}{389804}\right)$	$e\left(\frac{57648}{97451}\right)$	$e\left(\frac{58573}{97451}\right)$	$e\left(\frac{310199}{389804}\right)$	$e\left(\frac{242779}{389804}\right)$	$e\left(\frac{75493}{194902}\right)$	$e\left(\frac{1}{194902}\right)$	$e\left(\frac{77343}{194902}\right)$	$e\left(\frac{295133}{389804}\right)$
$\chi_{779609}(10,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{188563}{194902}\right)$	$e\left(\frac{77343}{389804}\right)$	$e\left(\frac{91112}{97451}\right)$	$e\left(\frac{6902}{97451}\right)$	$e\left(\frac{64665}{389804}\right)$	$e\left(\frac{7713}{389804}\right)$	$e\left(\frac{175885}{194902}\right)$	$e\left(\frac{77343}{194902}\right)$	$e\left(\frac{7465}{194902}\right)$	$e\left(\frac{328987}{389804}\right)$
$\chi_{779609}(11,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{149447}{389804}\right)$	$e\left(\frac{295133}{779608}\right)$	$e\left(\frac{149447}{194902}\right)$	$e\left(\frac{44885}{97451}\right)$	$e\left(\frac{594027}{779608}\right)$	$e\left(\frac{272347}{779608}\right)$	$e\left(\frac{58537}{389804}\right)$	$e\left(\frac{295133}{389804}\right)$	$e\left(\frac{328987}{389804}\right)$	$e\left(\frac{224673}{779608}\right)$
$\chi_{779609}(12,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{226707}{389804}\right)$	$e\left(\frac{620397}{779608}\right)$	$e\left(\frac{31805}{194902}\right)$	$e\left(\frac{53771}{97451}\right)$	$e\left(\frac{294203}{779608}\right)$	$e\left(\frac{267075}{779608}\right)$	$e\left(\frac{290317}{389804}\right)$	$e\left(\frac{230593}{389804}\right)$	$e\left(\frac{51987}{389804}\right)$	$e\left(\frac{113313}{779608}\right)$
$\chi_{779609}(13,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{93964}{97451}\right)$	$e\left(\frac{38729}{97451}\right)$	$e\left(\frac{90477}{97451}\right)$	$e\left(\frac{37356}{97451}\right)$	$e\left(\frac{35242}{97451}\right)$	$e\left(\frac{28156}{97451}\right)$	$e\left(\frac{86990}{97451}\right)$	$e\left(\frac{77458}{97451}\right)$	$e\left(\frac{33869}{97451}\right)$	$e\left(\frac{80716}{97451}\right)$
$\chi_{779609}(14,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{334231}{389804}\right)$	$e\left(\frac{163173}{779608}\right)$	$e\left(\frac{139329}{194902}\right)$	$e\left(\frac{12652}{97451}\right)$	$e\left(\frac{52027}{779608}\right)$	$e\left(\frac{366659}{779608}\right)$	$e\left(\frac{223085}{389804}\right)$	$e\left(\frac{163173}{389804}\right)$	$e\left(\frac{384839}{389804}\right)$	$e\left(\frac{571241}{779608}\right)$
$\chi_{779609}(15,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{301519}{389804}\right)$	$e\left(\frac{624097}{779608}\right)$	$e\left(\frac{106617}{194902}\right)$	$e\left(\frac{48309}{97451}\right)$	$e\left(\frac{447527}{779608}\right)$	$e\left(\frac{440959}{779608}\right)$	$e\left(\frac{124949}{389804}\right)$	$e\left(\frac{234293}{389804}\right)$	$e\left(\frac{104951}{389804}\right)$	$e\left(\frac{654213}{779608}\right)$
$\chi_{779609}(16,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{35804}{97451}\right)$	$e\left(\frac{57648}{97451}\right)$	$e\left(\frac{71608}{97451}\right)$	$e\left(\frac{48969}{97451}\right)$	$e\left(\frac{93452}{97451}\right)$	$e\left(\frac{6074}{97451}\right)$	$e\left(\frac{9961}{97451}\right)$	$e\left(\frac{17845}{97451}\right)$	$e\left(\frac{84773}{97451}\right)$	$e\left(\frac{51996}{97451}\right)$
$\chi_{779609}(17,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{334893}{389804}\right)$	$e\left(\frac{302679}{779608}\right)$	$e\left(\frac{139991}{194902}\right)$	$e\left(\frac{21946}{97451}\right)$	$e\left(\frac{192857}{779608}\right)$	$e\left(\frac{203881}{779608}\right)$	$e\left(\frac{225071}{389804}\right)$	$e\left(\frac{302679}{389804}\right)$	$e\left(\frac{32873}{389804}\right)$	$e\left(\frac{737843}{779608}\right)$
$\chi_{779609}(18,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{37775}{97451}\right)$	$e\left(\frac{38775}{97451}\right)$	$e\left(\frac{75550}{97451}\right)$	$e\left(\frac{95178}{97451}\right)$	$e\left(\frac{76550}{97451}\right)$	$e\left(\frac{86576}{97451}\right)$	$e\left(\frac{15874}{97451}\right)$	$e\left(\frac{77550}{97451}\right)$	$e\left(\frac{35502}{97451}\right)$	$e\left(\frac{13694}{97451}\right)$
$\chi_{779609}(19,\cdot)$	779609.bd	194902	yes	$1$	$1$	$e\left(\frac{83898}{97451}\right)$	$e\left(\frac{143409}{194902}\right)$	$e\left(\frac{70345}{97451}\right)$	$e\left(\frac{17922}{97451}\right)$	$e\left(\frac{116303}{194902}\right)$	$e\left(\frac{179939}{194902}\right)$	$e\left(\frac{56792}{97451}\right)$	$e\left(\frac{45958}{97451}\right)$	$e\left(\frac{4369}{97451}\right)$	$e\left(\frac{4979}{194902}\right)$
$\chi_{779609}(20,\cdot)$	779609.bd	194902	yes	$1$	$1$	$e\left(\frac{54507}{97451}\right)$	$e\left(\frac{116221}{194902}\right)$	$e\left(\frac{11563}{97451}\right)$	$e\left(\frac{43507}{97451}\right)$	$e\left(\frac{30333}{194902}\right)$	$e\left(\frac{55619}{194902}\right)$	$e\left(\frac{66070}{97451}\right)$	$e\left(\frac{18770}{97451}\right)$	$e\left(\frac{563}{97451}\right)$	$e\left(\frac{44315}{194902}\right)$
$\chi_{779609}(21,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{64656}{97451}\right)$	$e\left(\frac{79073}{97451}\right)$	$e\left(\frac{31861}{97451}\right)$	$e\left(\frac{54059}{97451}\right)$	$e\left(\frac{46278}{97451}\right)$	$e\left(\frac{1573}{97451}\right)$	$e\left(\frac{96517}{97451}\right)$	$e\left(\frac{60695}{97451}\right)$	$e\left(\frac{21264}{97451}\right)$	$e\left(\frac{70935}{97451}\right)$
$\chi_{779609}(22,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{380153}{389804}\right)$	$e\left(\frac{605331}{779608}\right)$	$e\left(\frac{185251}{194902}\right)$	$e\left(\frac{81490}{97451}\right)$	$e\left(\frac{586029}{779608}\right)$	$e\left(\frac{479397}{779608}\right)$	$e\left(\frac{360851}{389804}\right)$	$e\left(\frac{215527}{389804}\right)$	$e\left(\frac{316309}{389804}\right)$	$e\left(\frac{523567}{779608}\right)$
$\chi_{779609}(23,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{94014}{97451}\right)$	$e\left(\frac{19561}{97451}\right)$	$e\left(\frac{90577}{97451}\right)$	$e\left(\frac{60184}{97451}\right)$	$e\left(\frac{16124}{97451}\right)$	$e\left(\frac{17887}{97451}\right)$	$e\left(\frac{87140}{97451}\right)$	$e\left(\frac{39122}{97451}\right)$	$e\left(\frac{56747}{97451}\right)$	$e\left(\frac{1922}{97451}\right)$
$\chi_{779609}(24,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{67609}{389804}\right)$	$e\left(\frac{150987}{779608}\right)$	$e\left(\frac{67609}{194902}\right)$	$e\left(\frac{90376}{97451}\right)$	$e\left(\frac{286205}{779608}\right)$	$e\left(\frac{474125}{779608}\right)$	$e\left(\frac{202827}{389804}\right)$	$e\left(\frac{150987}{389804}\right)$	$e\left(\frac{39309}{389804}\right)$	$e\left(\frac{412207}{779608}\right)$
$\chi_{779609}(25,\cdot)$	779609.bc	97451	yes	$1$	$1$	$e\left(\frac{73210}{97451}\right)$	$e\left(\frac{58573}{97451}\right)$	$e\left(\frac{48969}{97451}\right)$	$e\left(\frac{38045}{97451}\right)$	$e\left(\frac{34332}{97451}\right)$	$e\left(\frac{49545}{97451}\right)$	$e\left(\frac{24728}{97451}\right)$	$e\left(\frac{19695}{97451}\right)$	$e\left(\frac{13804}{97451}\right)$	$e\left(\frac{89770}{97451}\right)$
$\chi_{779609}(26,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{108379}{194902}\right)$	$e\left(\frac{310015}{389804}\right)$	$e\left(\frac{10928}{97451}\right)$	$e\left(\frac{73961}{97451}\right)$	$e\left(\frac{136969}{389804}\right)$	$e\left(\frac{216149}{389804}\right)$	$e\left(\frac{130235}{194902}\right)$	$e\left(\frac{115113}{194902}\right)$	$e\left(\frac{61399}{194902}\right)$	$e\left(\frac{82507}{389804}\right)$
$\chi_{779609}(27,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{75493}{389804}\right)$	$e\left(\frac{3}{779608}\right)$	$e\left(\frac{75493}{194902}\right)$	$e\left(\frac{39134}{97451}\right)$	$e\left(\frac{150989}{779608}\right)$	$e\left(\frac{338533}{779608}\right)$	$e\left(\frac{226479}{389804}\right)$	$e\left(\frac{3}{389804}\right)$	$e\left(\frac{232029}{389804}\right)$	$e\left(\frac{105791}{779608}\right)$
$\chi_{779609}(28,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{175133}{389804}\right)$	$e\left(\frac{473371}{779608}\right)$	$e\left(\frac{175133}{194902}\right)$	$e\left(\frac{49257}{97451}\right)$	$e\left(\frac{44029}{779608}\right)$	$e\left(\frac{573709}{779608}\right)$	$e\left(\frac{135595}{389804}\right)$	$e\left(\frac{83567}{389804}\right)$	$e\left(\frac{372161}{389804}\right)$	$e\left(\frac{90527}{779608}\right)$
$\chi_{779609}(29,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{176337}{389804}\right)$	$e\left(\frac{220703}{779608}\right)$	$e\left(\frac{176337}{194902}\right)$	$e\left(\frac{34658}{97451}\right)$	$e\left(\frac{573377}{779608}\right)$	$e\left(\frac{765209}{779608}\right)$	$e\left(\frac{139207}{389804}\right)$	$e\left(\frac{220703}{389804}\right)$	$e\left(\frac{314969}{389804}\right)$	$e\left(\frac{490099}{779608}\right)$
$\chi_{779609}(30,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{142421}{389804}\right)$	$e\left(\frac{154687}{779608}\right)$	$e\left(\frac{142421}{194902}\right)$	$e\left(\frac{84914}{97451}\right)$	$e\left(\frac{439529}{779608}\right)$	$e\left(\frac{648009}{779608}\right)$	$e\left(\frac{37459}{389804}\right)$	$e\left(\frac{154687}{389804}\right)$	$e\left(\frac{92273}{389804}\right)$	$e\left(\frac{173499}{779608}\right)$
$\chi_{779609}(31,\cdot)$	779609.bf	779608	yes	$-1$	$1$	$e\left(\frac{71049}{389804}\right)$	$e\left(\frac{320059}{779608}\right)$	$e\left(\frac{71049}{194902}\right)$	$e\left(\frac{34743}{97451}\right)$	$e\left(\frac{462157}{779608}\right)$	$e\left(\frac{464405}{779608}\right)$	$e\left(\frac{213147}{389804}\right)$	$e\left(\frac{320059}{389804}\right)$	$e\left(\frac{210021}{389804}\right)$	$e\left(\frac{328743}{779608}\right)$
$\chi_{779609}(32,\cdot)$	779609.be	389804	yes	$1$	$1$	$e\left(\frac{186961}{194902}\right)$	$e\left(\frac{385691}{389804}\right)$	$e\left(\frac{89510}{97451}\right)$	$e\left(\frac{85574}{97451}\right)$	$e\left(\frac{369809}{389804}\right)$	$e\left(\frac{127821}{389804}\right)$	$e\left(\frac{171079}{194902}\right)$	$e\left(\frac{190789}{194902}\right)$	$e\left(\frac{163207}{194902}\right)$	$e\left(\frac{357431}{389804}\right)$

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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	$779609$
Structure	\(C_{779608}\)
Order	$779608$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{779609}(1,\cdot)\)	779609.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{779609}(2,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{115353}{194902}\right)\)	\(e\left(\frac{155099}{389804}\right)\)	\(e\left(\frac{17902}{97451}\right)\)	\(e\left(\frac{36605}{97451}\right)\)	\(e\left(\frac{385805}{389804}\right)\)	\(e\left(\frac{103525}{389804}\right)\)	\(e\left(\frac{151157}{194902}\right)\)	\(e\left(\frac{155099}{194902}\right)\)	\(e\left(\frac{188563}{194902}\right)\)	\(e\left(\frac{149447}{389804}\right)\)
\(\chi_{779609}(3,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{155099}{389804}\right)\)	\(e\left(\frac{1}{779608}\right)\)	\(e\left(\frac{155099}{194902}\right)\)	\(e\left(\frac{78012}{97451}\right)\)	\(e\left(\frac{310199}{779608}\right)\)	\(e\left(\frac{632583}{779608}\right)\)	\(e\left(\frac{75493}{389804}\right)\)	\(e\left(\frac{1}{389804}\right)\)	\(e\left(\frac{77343}{389804}\right)\)	\(e\left(\frac{295133}{779608}\right)\)
\(\chi_{779609}(4,\cdot)\)	779609.bd	194902	yes	\(1\)	\(1\)	\(e\left(\frac{17902}{97451}\right)\)	\(e\left(\frac{155099}{194902}\right)\)	\(e\left(\frac{35804}{97451}\right)\)	\(e\left(\frac{73210}{97451}\right)\)	\(e\left(\frac{190903}{194902}\right)\)	\(e\left(\frac{103525}{194902}\right)\)	\(e\left(\frac{53706}{97451}\right)\)	\(e\left(\frac{57648}{97451}\right)\)	\(e\left(\frac{91112}{97451}\right)\)	\(e\left(\frac{149447}{194902}\right)\)
\(\chi_{779609}(5,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{36605}{97451}\right)\)	\(e\left(\frac{78012}{97451}\right)\)	\(e\left(\frac{73210}{97451}\right)\)	\(e\left(\frac{67748}{97451}\right)\)	\(e\left(\frac{17166}{97451}\right)\)	\(e\left(\frac{73498}{97451}\right)\)	\(e\left(\frac{12364}{97451}\right)\)	\(e\left(\frac{58573}{97451}\right)\)	\(e\left(\frac{6902}{97451}\right)\)	\(e\left(\frac{44885}{97451}\right)\)
\(\chi_{779609}(6,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{385805}{389804}\right)\)	\(e\left(\frac{310199}{779608}\right)\)	\(e\left(\frac{190903}{194902}\right)\)	\(e\left(\frac{17166}{97451}\right)\)	\(e\left(\frac{302201}{779608}\right)\)	\(e\left(\frac{60025}{779608}\right)\)	\(e\left(\frac{377807}{389804}\right)\)	\(e\left(\frac{310199}{389804}\right)\)	\(e\left(\frac{64665}{389804}\right)\)	\(e\left(\frac{594027}{779608}\right)\)
\(\chi_{779609}(7,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{103525}{389804}\right)\)	\(e\left(\frac{632583}{779608}\right)\)	\(e\left(\frac{103525}{194902}\right)\)	\(e\left(\frac{73498}{97451}\right)\)	\(e\left(\frac{60025}{779608}\right)\)	\(e\left(\frac{159609}{779608}\right)\)	\(e\left(\frac{310575}{389804}\right)\)	\(e\left(\frac{242779}{389804}\right)\)	\(e\left(\frac{7713}{389804}\right)\)	\(e\left(\frac{272347}{779608}\right)\)
\(\chi_{779609}(8,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{151157}{194902}\right)\)	\(e\left(\frac{75493}{389804}\right)\)	\(e\left(\frac{53706}{97451}\right)\)	\(e\left(\frac{12364}{97451}\right)\)	\(e\left(\frac{377807}{389804}\right)\)	\(e\left(\frac{310575}{389804}\right)\)	\(e\left(\frac{63667}{194902}\right)\)	\(e\left(\frac{75493}{194902}\right)\)	\(e\left(\frac{175885}{194902}\right)\)	\(e\left(\frac{58537}{389804}\right)\)
\(\chi_{779609}(9,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{155099}{194902}\right)\)	\(e\left(\frac{1}{389804}\right)\)	\(e\left(\frac{57648}{97451}\right)\)	\(e\left(\frac{58573}{97451}\right)\)	\(e\left(\frac{310199}{389804}\right)\)	\(e\left(\frac{242779}{389804}\right)\)	\(e\left(\frac{75493}{194902}\right)\)	\(e\left(\frac{1}{194902}\right)\)	\(e\left(\frac{77343}{194902}\right)\)	\(e\left(\frac{295133}{389804}\right)\)
\(\chi_{779609}(10,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{188563}{194902}\right)\)	\(e\left(\frac{77343}{389804}\right)\)	\(e\left(\frac{91112}{97451}\right)\)	\(e\left(\frac{6902}{97451}\right)\)	\(e\left(\frac{64665}{389804}\right)\)	\(e\left(\frac{7713}{389804}\right)\)	\(e\left(\frac{175885}{194902}\right)\)	\(e\left(\frac{77343}{194902}\right)\)	\(e\left(\frac{7465}{194902}\right)\)	\(e\left(\frac{328987}{389804}\right)\)
\(\chi_{779609}(11,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{149447}{389804}\right)\)	\(e\left(\frac{295133}{779608}\right)\)	\(e\left(\frac{149447}{194902}\right)\)	\(e\left(\frac{44885}{97451}\right)\)	\(e\left(\frac{594027}{779608}\right)\)	\(e\left(\frac{272347}{779608}\right)\)	\(e\left(\frac{58537}{389804}\right)\)	\(e\left(\frac{295133}{389804}\right)\)	\(e\left(\frac{328987}{389804}\right)\)	\(e\left(\frac{224673}{779608}\right)\)
\(\chi_{779609}(12,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{226707}{389804}\right)\)	\(e\left(\frac{620397}{779608}\right)\)	\(e\left(\frac{31805}{194902}\right)\)	\(e\left(\frac{53771}{97451}\right)\)	\(e\left(\frac{294203}{779608}\right)\)	\(e\left(\frac{267075}{779608}\right)\)	\(e\left(\frac{290317}{389804}\right)\)	\(e\left(\frac{230593}{389804}\right)\)	\(e\left(\frac{51987}{389804}\right)\)	\(e\left(\frac{113313}{779608}\right)\)
\(\chi_{779609}(13,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{93964}{97451}\right)\)	\(e\left(\frac{38729}{97451}\right)\)	\(e\left(\frac{90477}{97451}\right)\)	\(e\left(\frac{37356}{97451}\right)\)	\(e\left(\frac{35242}{97451}\right)\)	\(e\left(\frac{28156}{97451}\right)\)	\(e\left(\frac{86990}{97451}\right)\)	\(e\left(\frac{77458}{97451}\right)\)	\(e\left(\frac{33869}{97451}\right)\)	\(e\left(\frac{80716}{97451}\right)\)
\(\chi_{779609}(14,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{334231}{389804}\right)\)	\(e\left(\frac{163173}{779608}\right)\)	\(e\left(\frac{139329}{194902}\right)\)	\(e\left(\frac{12652}{97451}\right)\)	\(e\left(\frac{52027}{779608}\right)\)	\(e\left(\frac{366659}{779608}\right)\)	\(e\left(\frac{223085}{389804}\right)\)	\(e\left(\frac{163173}{389804}\right)\)	\(e\left(\frac{384839}{389804}\right)\)	\(e\left(\frac{571241}{779608}\right)\)
\(\chi_{779609}(15,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{301519}{389804}\right)\)	\(e\left(\frac{624097}{779608}\right)\)	\(e\left(\frac{106617}{194902}\right)\)	\(e\left(\frac{48309}{97451}\right)\)	\(e\left(\frac{447527}{779608}\right)\)	\(e\left(\frac{440959}{779608}\right)\)	\(e\left(\frac{124949}{389804}\right)\)	\(e\left(\frac{234293}{389804}\right)\)	\(e\left(\frac{104951}{389804}\right)\)	\(e\left(\frac{654213}{779608}\right)\)
\(\chi_{779609}(16,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{35804}{97451}\right)\)	\(e\left(\frac{57648}{97451}\right)\)	\(e\left(\frac{71608}{97451}\right)\)	\(e\left(\frac{48969}{97451}\right)\)	\(e\left(\frac{93452}{97451}\right)\)	\(e\left(\frac{6074}{97451}\right)\)	\(e\left(\frac{9961}{97451}\right)\)	\(e\left(\frac{17845}{97451}\right)\)	\(e\left(\frac{84773}{97451}\right)\)	\(e\left(\frac{51996}{97451}\right)\)
\(\chi_{779609}(17,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{334893}{389804}\right)\)	\(e\left(\frac{302679}{779608}\right)\)	\(e\left(\frac{139991}{194902}\right)\)	\(e\left(\frac{21946}{97451}\right)\)	\(e\left(\frac{192857}{779608}\right)\)	\(e\left(\frac{203881}{779608}\right)\)	\(e\left(\frac{225071}{389804}\right)\)	\(e\left(\frac{302679}{389804}\right)\)	\(e\left(\frac{32873}{389804}\right)\)	\(e\left(\frac{737843}{779608}\right)\)
\(\chi_{779609}(18,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{37775}{97451}\right)\)	\(e\left(\frac{38775}{97451}\right)\)	\(e\left(\frac{75550}{97451}\right)\)	\(e\left(\frac{95178}{97451}\right)\)	\(e\left(\frac{76550}{97451}\right)\)	\(e\left(\frac{86576}{97451}\right)\)	\(e\left(\frac{15874}{97451}\right)\)	\(e\left(\frac{77550}{97451}\right)\)	\(e\left(\frac{35502}{97451}\right)\)	\(e\left(\frac{13694}{97451}\right)\)
\(\chi_{779609}(19,\cdot)\)	779609.bd	194902	yes	\(1\)	\(1\)	\(e\left(\frac{83898}{97451}\right)\)	\(e\left(\frac{143409}{194902}\right)\)	\(e\left(\frac{70345}{97451}\right)\)	\(e\left(\frac{17922}{97451}\right)\)	\(e\left(\frac{116303}{194902}\right)\)	\(e\left(\frac{179939}{194902}\right)\)	\(e\left(\frac{56792}{97451}\right)\)	\(e\left(\frac{45958}{97451}\right)\)	\(e\left(\frac{4369}{97451}\right)\)	\(e\left(\frac{4979}{194902}\right)\)
\(\chi_{779609}(20,\cdot)\)	779609.bd	194902	yes	\(1\)	\(1\)	\(e\left(\frac{54507}{97451}\right)\)	\(e\left(\frac{116221}{194902}\right)\)	\(e\left(\frac{11563}{97451}\right)\)	\(e\left(\frac{43507}{97451}\right)\)	\(e\left(\frac{30333}{194902}\right)\)	\(e\left(\frac{55619}{194902}\right)\)	\(e\left(\frac{66070}{97451}\right)\)	\(e\left(\frac{18770}{97451}\right)\)	\(e\left(\frac{563}{97451}\right)\)	\(e\left(\frac{44315}{194902}\right)\)
\(\chi_{779609}(21,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{64656}{97451}\right)\)	\(e\left(\frac{79073}{97451}\right)\)	\(e\left(\frac{31861}{97451}\right)\)	\(e\left(\frac{54059}{97451}\right)\)	\(e\left(\frac{46278}{97451}\right)\)	\(e\left(\frac{1573}{97451}\right)\)	\(e\left(\frac{96517}{97451}\right)\)	\(e\left(\frac{60695}{97451}\right)\)	\(e\left(\frac{21264}{97451}\right)\)	\(e\left(\frac{70935}{97451}\right)\)
\(\chi_{779609}(22,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{380153}{389804}\right)\)	\(e\left(\frac{605331}{779608}\right)\)	\(e\left(\frac{185251}{194902}\right)\)	\(e\left(\frac{81490}{97451}\right)\)	\(e\left(\frac{586029}{779608}\right)\)	\(e\left(\frac{479397}{779608}\right)\)	\(e\left(\frac{360851}{389804}\right)\)	\(e\left(\frac{215527}{389804}\right)\)	\(e\left(\frac{316309}{389804}\right)\)	\(e\left(\frac{523567}{779608}\right)\)
\(\chi_{779609}(23,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{94014}{97451}\right)\)	\(e\left(\frac{19561}{97451}\right)\)	\(e\left(\frac{90577}{97451}\right)\)	\(e\left(\frac{60184}{97451}\right)\)	\(e\left(\frac{16124}{97451}\right)\)	\(e\left(\frac{17887}{97451}\right)\)	\(e\left(\frac{87140}{97451}\right)\)	\(e\left(\frac{39122}{97451}\right)\)	\(e\left(\frac{56747}{97451}\right)\)	\(e\left(\frac{1922}{97451}\right)\)
\(\chi_{779609}(24,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{67609}{389804}\right)\)	\(e\left(\frac{150987}{779608}\right)\)	\(e\left(\frac{67609}{194902}\right)\)	\(e\left(\frac{90376}{97451}\right)\)	\(e\left(\frac{286205}{779608}\right)\)	\(e\left(\frac{474125}{779608}\right)\)	\(e\left(\frac{202827}{389804}\right)\)	\(e\left(\frac{150987}{389804}\right)\)	\(e\left(\frac{39309}{389804}\right)\)	\(e\left(\frac{412207}{779608}\right)\)
\(\chi_{779609}(25,\cdot)\)	779609.bc	97451	yes	\(1\)	\(1\)	\(e\left(\frac{73210}{97451}\right)\)	\(e\left(\frac{58573}{97451}\right)\)	\(e\left(\frac{48969}{97451}\right)\)	\(e\left(\frac{38045}{97451}\right)\)	\(e\left(\frac{34332}{97451}\right)\)	\(e\left(\frac{49545}{97451}\right)\)	\(e\left(\frac{24728}{97451}\right)\)	\(e\left(\frac{19695}{97451}\right)\)	\(e\left(\frac{13804}{97451}\right)\)	\(e\left(\frac{89770}{97451}\right)\)
\(\chi_{779609}(26,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{108379}{194902}\right)\)	\(e\left(\frac{310015}{389804}\right)\)	\(e\left(\frac{10928}{97451}\right)\)	\(e\left(\frac{73961}{97451}\right)\)	\(e\left(\frac{136969}{389804}\right)\)	\(e\left(\frac{216149}{389804}\right)\)	\(e\left(\frac{130235}{194902}\right)\)	\(e\left(\frac{115113}{194902}\right)\)	\(e\left(\frac{61399}{194902}\right)\)	\(e\left(\frac{82507}{389804}\right)\)
\(\chi_{779609}(27,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{75493}{389804}\right)\)	\(e\left(\frac{3}{779608}\right)\)	\(e\left(\frac{75493}{194902}\right)\)	\(e\left(\frac{39134}{97451}\right)\)	\(e\left(\frac{150989}{779608}\right)\)	\(e\left(\frac{338533}{779608}\right)\)	\(e\left(\frac{226479}{389804}\right)\)	\(e\left(\frac{3}{389804}\right)\)	\(e\left(\frac{232029}{389804}\right)\)	\(e\left(\frac{105791}{779608}\right)\)
\(\chi_{779609}(28,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{175133}{389804}\right)\)	\(e\left(\frac{473371}{779608}\right)\)	\(e\left(\frac{175133}{194902}\right)\)	\(e\left(\frac{49257}{97451}\right)\)	\(e\left(\frac{44029}{779608}\right)\)	\(e\left(\frac{573709}{779608}\right)\)	\(e\left(\frac{135595}{389804}\right)\)	\(e\left(\frac{83567}{389804}\right)\)	\(e\left(\frac{372161}{389804}\right)\)	\(e\left(\frac{90527}{779608}\right)\)
\(\chi_{779609}(29,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{176337}{389804}\right)\)	\(e\left(\frac{220703}{779608}\right)\)	\(e\left(\frac{176337}{194902}\right)\)	\(e\left(\frac{34658}{97451}\right)\)	\(e\left(\frac{573377}{779608}\right)\)	\(e\left(\frac{765209}{779608}\right)\)	\(e\left(\frac{139207}{389804}\right)\)	\(e\left(\frac{220703}{389804}\right)\)	\(e\left(\frac{314969}{389804}\right)\)	\(e\left(\frac{490099}{779608}\right)\)
\(\chi_{779609}(30,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{142421}{389804}\right)\)	\(e\left(\frac{154687}{779608}\right)\)	\(e\left(\frac{142421}{194902}\right)\)	\(e\left(\frac{84914}{97451}\right)\)	\(e\left(\frac{439529}{779608}\right)\)	\(e\left(\frac{648009}{779608}\right)\)	\(e\left(\frac{37459}{389804}\right)\)	\(e\left(\frac{154687}{389804}\right)\)	\(e\left(\frac{92273}{389804}\right)\)	\(e\left(\frac{173499}{779608}\right)\)
\(\chi_{779609}(31,\cdot)\)	779609.bf	779608	yes	\(-1\)	\(1\)	\(e\left(\frac{71049}{389804}\right)\)	\(e\left(\frac{320059}{779608}\right)\)	\(e\left(\frac{71049}{194902}\right)\)	\(e\left(\frac{34743}{97451}\right)\)	\(e\left(\frac{462157}{779608}\right)\)	\(e\left(\frac{464405}{779608}\right)\)	\(e\left(\frac{213147}{389804}\right)\)	\(e\left(\frac{320059}{389804}\right)\)	\(e\left(\frac{210021}{389804}\right)\)	\(e\left(\frac{328743}{779608}\right)\)
\(\chi_{779609}(32,\cdot)\)	779609.be	389804	yes	\(1\)	\(1\)	\(e\left(\frac{186961}{194902}\right)\)	\(e\left(\frac{385691}{389804}\right)\)	\(e\left(\frac{89510}{97451}\right)\)	\(e\left(\frac{85574}{97451}\right)\)	\(e\left(\frac{369809}{389804}\right)\)	\(e\left(\frac{127821}{389804}\right)\)	\(e\left(\frac{171079}{194902}\right)\)	\(e\left(\frac{190789}{194902}\right)\)	\(e\left(\frac{163207}{194902}\right)\)	\(e\left(\frac{357431}{389804}\right)\)

Introduction

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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.