LMFDB - Group of Dirichlet characters of modulus 818921

Show commands: PariGP / SageMath

sage: H = DirichletGroup(818921)

pari: g = idealstar(,818921,2)

Character group

sage: G.order() pari: g.no
Order	=	796752
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{199188}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{818921}(354129,\cdot)$, $\chi_{818921}(464795,\cdot)$

First 32 of 796752 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{818921}(1,\cdot)$	818921.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{818921}(2,\cdot)$	818921.eo	199188	yes	$1$	$1$	$e\left(\frac{2771}{99594}\right)$	$e\left(\frac{123077}{199188}\right)$	$e\left(\frac{2771}{49797}\right)$	$e\left(\frac{70969}{99594}\right)$	$e\left(\frac{14291}{22132}\right)$	$e\left(\frac{118655}{199188}\right)$	$e\left(\frac{2771}{33198}\right)$	$e\left(\frac{23483}{99594}\right)$	$e\left(\frac{12290}{16599}\right)$	$e\left(\frac{241}{16599}\right)$
$\chi_{818921}(3,\cdot)$	818921.ek	199188	yes	$-1$	$1$	$e\left(\frac{123077}{199188}\right)$	$e\left(\frac{133945}{199188}\right)$	$e\left(\frac{23483}{99594}\right)$	$e\left(\frac{89875}{199188}\right)$	$e\left(\frac{3213}{11066}\right)$	$e\left(\frac{19765}{199188}\right)$	$e\left(\frac{56681}{66396}\right)$	$e\left(\frac{34351}{99594}\right)$	$e\left(\frac{1147}{16599}\right)$	$e\left(\frac{10261}{33198}\right)$
$\chi_{818921}(4,\cdot)$	818921.eh	99594	yes	$1$	$1$	$e\left(\frac{2771}{49797}\right)$	$e\left(\frac{23483}{99594}\right)$	$e\left(\frac{5542}{49797}\right)$	$e\left(\frac{21172}{49797}\right)$	$e\left(\frac{3225}{11066}\right)$	$e\left(\frac{19061}{99594}\right)$	$e\left(\frac{2771}{16599}\right)$	$e\left(\frac{23483}{49797}\right)$	$e\left(\frac{7981}{16599}\right)$	$e\left(\frac{482}{16599}\right)$
$\chi_{818921}(5,\cdot)$	818921.eo	199188	yes	$1$	$1$	$e\left(\frac{70969}{99594}\right)$	$e\left(\frac{89875}{199188}\right)$	$e\left(\frac{21172}{49797}\right)$	$e\left(\frac{88607}{99594}\right)$	$e\left(\frac{3625}{22132}\right)$	$e\left(\frac{48361}{199188}\right)$	$e\left(\frac{4573}{33198}\right)$	$e\left(\frac{89875}{99594}\right)$	$e\left(\frac{9997}{16599}\right)$	$e\left(\frac{11294}{16599}\right)$
$\chi_{818921}(6,\cdot)$	818921.ds	22132	yes	$-1$	$1$	$e\left(\frac{14291}{22132}\right)$	$e\left(\frac{3213}{11066}\right)$	$e\left(\frac{3225}{11066}\right)$	$e\left(\frac{3625}{22132}\right)$	$e\left(\frac{20717}{22132}\right)$	$e\left(\frac{3845}{5533}\right)$	$e\left(\frac{20741}{22132}\right)$	$e\left(\frac{3213}{5533}\right)$	$e\left(\frac{4479}{5533}\right)$	$e\left(\frac{3581}{11066}\right)$
$\chi_{818921}(7,\cdot)$	818921.ep	199188	yes	$-1$	$1$	$e\left(\frac{118655}{199188}\right)$	$e\left(\frac{19765}{199188}\right)$	$e\left(\frac{19061}{99594}\right)$	$e\left(\frac{48361}{199188}\right)$	$e\left(\frac{3845}{5533}\right)$	$e\left(\frac{197041}{199188}\right)$	$e\left(\frac{52259}{66396}\right)$	$e\left(\frac{19765}{99594}\right)$	$e\left(\frac{13918}{16599}\right)$	$e\left(\frac{31645}{33198}\right)$
$\chi_{818921}(8,\cdot)$	818921.eg	66396	yes	$1$	$1$	$e\left(\frac{2771}{33198}\right)$	$e\left(\frac{56681}{66396}\right)$	$e\left(\frac{2771}{16599}\right)$	$e\left(\frac{4573}{33198}\right)$	$e\left(\frac{20741}{22132}\right)$	$e\left(\frac{52259}{66396}\right)$	$e\left(\frac{2771}{11066}\right)$	$e\left(\frac{23483}{33198}\right)$	$e\left(\frac{1224}{5533}\right)$	$e\left(\frac{241}{5533}\right)$
$\chi_{818921}(9,\cdot)$	818921.ej	99594	yes	$1$	$1$	$e\left(\frac{23483}{99594}\right)$	$e\left(\frac{34351}{99594}\right)$	$e\left(\frac{23483}{49797}\right)$	$e\left(\frac{89875}{99594}\right)$	$e\left(\frac{3213}{5533}\right)$	$e\left(\frac{19765}{99594}\right)$	$e\left(\frac{23483}{33198}\right)$	$e\left(\frac{34351}{49797}\right)$	$e\left(\frac{2294}{16599}\right)$	$e\left(\frac{10261}{16599}\right)$
$\chi_{818921}(10,\cdot)$	818921.dk	16599	yes	$1$	$1$	$e\left(\frac{12290}{16599}\right)$	$e\left(\frac{1147}{16599}\right)$	$e\left(\frac{7981}{16599}\right)$	$e\left(\frac{9997}{16599}\right)$	$e\left(\frac{4479}{5533}\right)$	$e\left(\frac{13918}{16599}\right)$	$e\left(\frac{1224}{5533}\right)$	$e\left(\frac{2294}{16599}\right)$	$e\left(\frac{1896}{5533}\right)$	$e\left(\frac{3845}{5533}\right)$
$\chi_{818921}(11,\cdot)$	818921.dx	33198	yes	$1$	$1$	$e\left(\frac{241}{16599}\right)$	$e\left(\frac{10261}{33198}\right)$	$e\left(\frac{482}{16599}\right)$	$e\left(\frac{11294}{16599}\right)$	$e\left(\frac{3581}{11066}\right)$	$e\left(\frac{31645}{33198}\right)$	$e\left(\frac{241}{5533}\right)$	$e\left(\frac{10261}{16599}\right)$	$e\left(\frac{3845}{5533}\right)$	$e\left(\frac{3067}{5533}\right)$
$\chi_{818921}(12,\cdot)$	818921.ep	199188	yes	$-1$	$1$	$e\left(\frac{134161}{199188}\right)$	$e\left(\frac{180911}{199188}\right)$	$e\left(\frac{34567}{99594}\right)$	$e\left(\frac{174563}{199188}\right)$	$e\left(\frac{3219}{5533}\right)$	$e\left(\frac{57887}{199188}\right)$	$e\left(\frac{1369}{66396}\right)$	$e\left(\frac{81317}{99594}\right)$	$e\left(\frac{9128}{16599}\right)$	$e\left(\frac{11225}{33198}\right)$
$\chi_{818921}(13,\cdot)$	818921.el	199188	yes	$1$	$1$	$e\left(\frac{34568}{49797}\right)$	$e\left(\frac{122377}{199188}\right)$	$e\left(\frac{19339}{49797}\right)$	$e\left(\frac{43402}{49797}\right)$	$e\left(\frac{6829}{22132}\right)$	$e\left(\frac{871}{199188}\right)$	$e\left(\frac{1370}{16599}\right)$	$e\left(\frac{22783}{99594}\right)$	$e\left(\frac{9391}{16599}\right)$	$e\left(\frac{9032}{16599}\right)$
$\chi_{818921}(14,\cdot)$	818921.ef	66396	yes	$-1$	$1$	$e\left(\frac{41399}{66396}\right)$	$e\left(\frac{23807}{33198}\right)$	$e\left(\frac{8201}{33198}\right)$	$e\left(\frac{63433}{66396}\right)$	$e\left(\frac{7539}{22132}\right)$	$e\left(\frac{9709}{16599}\right)$	$e\left(\frac{19267}{22132}\right)$	$e\left(\frac{7208}{16599}\right)$	$e\left(\frac{3203}{5533}\right)$	$e\left(\frac{10709}{11066}\right)$
$\chi_{818921}(15,\cdot)$	818921.em	199188	yes	$-1$	$1$	$e\left(\frac{65827}{199188}\right)$	$e\left(\frac{6158}{49797}\right)$	$e\left(\frac{65827}{99594}\right)$	$e\left(\frac{67901}{199188}\right)$	$e\left(\frac{10051}{22132}\right)$	$e\left(\frac{34063}{99594}\right)$	$e\left(\frac{65827}{66396}\right)$	$e\left(\frac{12316}{49797}\right)$	$e\left(\frac{11144}{16599}\right)$	$e\left(\frac{32849}{33198}\right)$
$\chi_{818921}(16,\cdot)$	818921.ea	49797	yes	$1$	$1$	$e\left(\frac{5542}{49797}\right)$	$e\left(\frac{23483}{49797}\right)$	$e\left(\frac{11084}{49797}\right)$	$e\left(\frac{42344}{49797}\right)$	$e\left(\frac{3225}{5533}\right)$	$e\left(\frac{19061}{49797}\right)$	$e\left(\frac{5542}{16599}\right)$	$e\left(\frac{46966}{49797}\right)$	$e\left(\frac{15962}{16599}\right)$	$e\left(\frac{964}{16599}\right)$
$\chi_{818921}(17,\cdot)$	818921.do	18108	yes	$-1$	$1$	$e\left(\frac{4259}{18108}\right)$	$e\left(\frac{4306}{4527}\right)$	$e\left(\frac{4259}{9054}\right)$	$e\left(\frac{17101}{18108}\right)$	$e\left(\frac{375}{2012}\right)$	$e\left(\frac{6881}{9054}\right)$	$e\left(\frac{4259}{6036}\right)$	$e\left(\frac{4085}{4527}\right)$	$e\left(\frac{271}{1509}\right)$	$e\left(\frac{793}{3018}\right)$
$\chi_{818921}(18,\cdot)$	818921.el	199188	yes	$1$	$1$	$e\left(\frac{13127}{49797}\right)$	$e\left(\frac{191779}{199188}\right)$	$e\left(\frac{26254}{49797}\right)$	$e\left(\frac{30625}{49797}\right)$	$e\left(\frac{5011}{22132}\right)$	$e\left(\frac{158185}{199188}\right)$	$e\left(\frac{13127}{16599}\right)$	$e\left(\frac{92185}{99594}\right)$	$e\left(\frac{14584}{16599}\right)$	$e\left(\frac{10502}{16599}\right)$
$\chi_{818921}(19,\cdot)$	818921.em	199188	yes	$-1$	$1$	$e\left(\frac{33437}{199188}\right)$	$e\left(\frac{26644}{49797}\right)$	$e\left(\frac{33437}{99594}\right)$	$e\left(\frac{91027}{199188}\right)$	$e\left(\frac{15557}{22132}\right)$	$e\left(\frac{57281}{99594}\right)$	$e\left(\frac{33437}{66396}\right)$	$e\left(\frac{3491}{49797}\right)$	$e\left(\frac{10372}{16599}\right)$	$e\left(\frac{23251}{33198}\right)$
$\chi_{818921}(20,\cdot)$	818921.eo	199188	yes	$1$	$1$	$e\left(\frac{76511}{99594}\right)$	$e\left(\frac{136841}{199188}\right)$	$e\left(\frac{26714}{49797}\right)$	$e\left(\frac{31357}{99594}\right)$	$e\left(\frac{10075}{22132}\right)$	$e\left(\frac{86483}{199188}\right)$	$e\left(\frac{10115}{33198}\right)$	$e\left(\frac{37247}{99594}\right)$	$e\left(\frac{1379}{16599}\right)$	$e\left(\frac{11776}{16599}\right)$
$\chi_{818921}(21,\cdot)$	818921.eh	99594	yes	$1$	$1$	$e\left(\frac{10636}{49797}\right)$	$e\left(\frac{76855}{99594}\right)$	$e\left(\frac{21272}{49797}\right)$	$e\left(\frac{34559}{49797}\right)$	$e\left(\frac{10903}{11066}\right)$	$e\left(\frac{8809}{99594}\right)$	$e\left(\frac{10636}{16599}\right)$	$e\left(\frac{27058}{49797}\right)$	$e\left(\frac{15065}{16599}\right)$	$e\left(\frac{4354}{16599}\right)$
$\chi_{818921}(22,\cdot)$	818921.eo	199188	yes	$1$	$1$	$e\left(\frac{4217}{99594}\right)$	$e\left(\frac{184643}{199188}\right)$	$e\left(\frac{4217}{49797}\right)$	$e\left(\frac{39139}{99594}\right)$	$e\left(\frac{21453}{22132}\right)$	$e\left(\frac{109337}{199188}\right)$	$e\left(\frac{4217}{33198}\right)$	$e\left(\frac{85049}{99594}\right)$	$e\left(\frac{7226}{16599}\right)$	$e\left(\frac{9442}{16599}\right)$
$\chi_{818921}(23,\cdot)$	818921.cy	6036	yes	$1$	$1$	$e\left(\frac{521}{3018}\right)$	$e\left(\frac{1883}{6036}\right)$	$e\left(\frac{521}{1509}\right)$	$e\left(\frac{1693}{3018}\right)$	$e\left(\frac{975}{2012}\right)$	$e\left(\frac{5321}{6036}\right)$	$e\left(\frac{521}{1006}\right)$	$e\left(\frac{1883}{3018}\right)$	$e\left(\frac{369}{503}\right)$	$e\left(\frac{461}{503}\right)$
$\chi_{818921}(24,\cdot)$	818921.em	199188	yes	$-1$	$1$	$e\left(\frac{139703}{199188}\right)$	$e\left(\frac{26200}{49797}\right)$	$e\left(\frac{40109}{99594}\right)$	$e\left(\frac{117313}{199188}\right)$	$e\left(\frac{5035}{22132}\right)$	$e\left(\frac{88271}{99594}\right)$	$e\left(\frac{6911}{66396}\right)$	$e\left(\frac{2603}{49797}\right)$	$e\left(\frac{4819}{16599}\right)$	$e\left(\frac{11707}{33198}\right)$
$\chi_{818921}(25,\cdot)$	818921.eh	99594	yes	$1$	$1$	$e\left(\frac{21172}{49797}\right)$	$e\left(\frac{89875}{99594}\right)$	$e\left(\frac{42344}{49797}\right)$	$e\left(\frac{38810}{49797}\right)$	$e\left(\frac{3625}{11066}\right)$	$e\left(\frac{48361}{99594}\right)$	$e\left(\frac{4573}{16599}\right)$	$e\left(\frac{40078}{49797}\right)$	$e\left(\frac{3395}{16599}\right)$	$e\left(\frac{5989}{16599}\right)$
$\chi_{818921}(26,\cdot)$	818921.ct	3018	yes	$1$	$1$	$e\left(\frac{2179}{3018}\right)$	$e\left(\frac{701}{3018}\right)$	$e\left(\frac{670}{1509}\right)$	$e\left(\frac{1763}{3018}\right)$	$e\left(\frac{480}{503}\right)$	$e\left(\frac{1811}{3018}\right)$	$e\left(\frac{167}{1006}\right)$	$e\left(\frac{701}{1509}\right)$	$e\left(\frac{154}{503}\right)$	$e\left(\frac{281}{503}\right)$
$\chi_{818921}(27,\cdot)$	818921.ed	66396	yes	$-1$	$1$	$e\left(\frac{56681}{66396}\right)$	$e\left(\frac{1153}{66396}\right)$	$e\left(\frac{23483}{33198}\right)$	$e\left(\frac{23479}{66396}\right)$	$e\left(\frac{9639}{11066}\right)$	$e\left(\frac{19765}{66396}\right)$	$e\left(\frac{12417}{22132}\right)$	$e\left(\frac{1153}{33198}\right)$	$e\left(\frac{1147}{5533}\right)$	$e\left(\frac{10261}{11066}\right)$
$\chi_{818921}(28,\cdot)$	818921.ek	199188	yes	$-1$	$1$	$e\left(\frac{129739}{199188}\right)$	$e\left(\frac{66731}{199188}\right)$	$e\left(\frac{30145}{99594}\right)$	$e\left(\frac{133049}{199188}\right)$	$e\left(\frac{10915}{11066}\right)$	$e\left(\frac{35975}{199188}\right)$	$e\left(\frac{63343}{66396}\right)$	$e\left(\frac{66731}{99594}\right)$	$e\left(\frac{5300}{16599}\right)$	$e\left(\frac{32609}{33198}\right)$
$\chi_{818921}(29,\cdot)$	818921.ef	66396	yes	$-1$	$1$	$e\left(\frac{4399}{66396}\right)$	$e\left(\frac{3415}{33198}\right)$	$e\left(\frac{4399}{33198}\right)$	$e\left(\frac{4001}{66396}\right)$	$e\left(\frac{3743}{22132}\right)$	$e\left(\frac{16508}{16599}\right)$	$e\left(\frac{4399}{22132}\right)$	$e\left(\frac{3415}{16599}\right)$	$e\left(\frac{700}{5533}\right)$	$e\left(\frac{131}{11066}\right)$
$\chi_{818921}(30,\cdot)$	818921.ek	199188	yes	$-1$	$1$	$e\left(\frac{71369}{199188}\right)$	$e\left(\frac{147709}{199188}\right)$	$e\left(\frac{71369}{99594}\right)$	$e\left(\frac{10651}{199188}\right)$	$e\left(\frac{1105}{11066}\right)$	$e\left(\frac{186781}{199188}\right)$	$e\left(\frac{4973}{66396}\right)$	$e\left(\frac{48115}{99594}\right)$	$e\left(\frac{6835}{16599}\right)$	$e\left(\frac{133}{33198}\right)$
$\chi_{818921}(31,\cdot)$	818921.dw	22132	yes	$1$	$1$	$e\left(\frac{3357}{5533}\right)$	$e\left(\frac{18279}{22132}\right)$	$e\left(\frac{1181}{5533}\right)$	$e\left(\frac{3130}{5533}\right)$	$e\left(\frac{9575}{22132}\right)$	$e\left(\frac{4925}{22132}\right)$	$e\left(\frac{4538}{5533}\right)$	$e\left(\frac{7213}{11066}\right)$	$e\left(\frac{954}{5533}\right)$	$e\left(\frac{5314}{5533}\right)$
$\chi_{818921}(32,\cdot)$	818921.eo	199188	yes	$1$	$1$	$e\left(\frac{13855}{99594}\right)$	$e\left(\frac{17821}{199188}\right)$	$e\left(\frac{13855}{49797}\right)$	$e\left(\frac{56063}{99594}\right)$	$e\left(\frac{5059}{22132}\right)$	$e\left(\frac{194899}{199188}\right)$	$e\left(\frac{13855}{33198}\right)$	$e\left(\frac{17821}{99594}\right)$	$e\left(\frac{11653}{16599}\right)$	$e\left(\frac{1205}{16599}\right)$

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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	$818921$
Structure	\(C_{4}\times C_{199188}\)
Order	$796752$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{818921}(1,\cdot)\)	818921.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{818921}(2,\cdot)\)	818921.eo	199188	yes	\(1\)	\(1\)	\(e\left(\frac{2771}{99594}\right)\)	\(e\left(\frac{123077}{199188}\right)\)	\(e\left(\frac{2771}{49797}\right)\)	\(e\left(\frac{70969}{99594}\right)\)	\(e\left(\frac{14291}{22132}\right)\)	\(e\left(\frac{118655}{199188}\right)\)	\(e\left(\frac{2771}{33198}\right)\)	\(e\left(\frac{23483}{99594}\right)\)	\(e\left(\frac{12290}{16599}\right)\)	\(e\left(\frac{241}{16599}\right)\)
\(\chi_{818921}(3,\cdot)\)	818921.ek	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{123077}{199188}\right)\)	\(e\left(\frac{133945}{199188}\right)\)	\(e\left(\frac{23483}{99594}\right)\)	\(e\left(\frac{89875}{199188}\right)\)	\(e\left(\frac{3213}{11066}\right)\)	\(e\left(\frac{19765}{199188}\right)\)	\(e\left(\frac{56681}{66396}\right)\)	\(e\left(\frac{34351}{99594}\right)\)	\(e\left(\frac{1147}{16599}\right)\)	\(e\left(\frac{10261}{33198}\right)\)
\(\chi_{818921}(4,\cdot)\)	818921.eh	99594	yes	\(1\)	\(1\)	\(e\left(\frac{2771}{49797}\right)\)	\(e\left(\frac{23483}{99594}\right)\)	\(e\left(\frac{5542}{49797}\right)\)	\(e\left(\frac{21172}{49797}\right)\)	\(e\left(\frac{3225}{11066}\right)\)	\(e\left(\frac{19061}{99594}\right)\)	\(e\left(\frac{2771}{16599}\right)\)	\(e\left(\frac{23483}{49797}\right)\)	\(e\left(\frac{7981}{16599}\right)\)	\(e\left(\frac{482}{16599}\right)\)
\(\chi_{818921}(5,\cdot)\)	818921.eo	199188	yes	\(1\)	\(1\)	\(e\left(\frac{70969}{99594}\right)\)	\(e\left(\frac{89875}{199188}\right)\)	\(e\left(\frac{21172}{49797}\right)\)	\(e\left(\frac{88607}{99594}\right)\)	\(e\left(\frac{3625}{22132}\right)\)	\(e\left(\frac{48361}{199188}\right)\)	\(e\left(\frac{4573}{33198}\right)\)	\(e\left(\frac{89875}{99594}\right)\)	\(e\left(\frac{9997}{16599}\right)\)	\(e\left(\frac{11294}{16599}\right)\)
\(\chi_{818921}(6,\cdot)\)	818921.ds	22132	yes	\(-1\)	\(1\)	\(e\left(\frac{14291}{22132}\right)\)	\(e\left(\frac{3213}{11066}\right)\)	\(e\left(\frac{3225}{11066}\right)\)	\(e\left(\frac{3625}{22132}\right)\)	\(e\left(\frac{20717}{22132}\right)\)	\(e\left(\frac{3845}{5533}\right)\)	\(e\left(\frac{20741}{22132}\right)\)	\(e\left(\frac{3213}{5533}\right)\)	\(e\left(\frac{4479}{5533}\right)\)	\(e\left(\frac{3581}{11066}\right)\)
\(\chi_{818921}(7,\cdot)\)	818921.ep	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{118655}{199188}\right)\)	\(e\left(\frac{19765}{199188}\right)\)	\(e\left(\frac{19061}{99594}\right)\)	\(e\left(\frac{48361}{199188}\right)\)	\(e\left(\frac{3845}{5533}\right)\)	\(e\left(\frac{197041}{199188}\right)\)	\(e\left(\frac{52259}{66396}\right)\)	\(e\left(\frac{19765}{99594}\right)\)	\(e\left(\frac{13918}{16599}\right)\)	\(e\left(\frac{31645}{33198}\right)\)
\(\chi_{818921}(8,\cdot)\)	818921.eg	66396	yes	\(1\)	\(1\)	\(e\left(\frac{2771}{33198}\right)\)	\(e\left(\frac{56681}{66396}\right)\)	\(e\left(\frac{2771}{16599}\right)\)	\(e\left(\frac{4573}{33198}\right)\)	\(e\left(\frac{20741}{22132}\right)\)	\(e\left(\frac{52259}{66396}\right)\)	\(e\left(\frac{2771}{11066}\right)\)	\(e\left(\frac{23483}{33198}\right)\)	\(e\left(\frac{1224}{5533}\right)\)	\(e\left(\frac{241}{5533}\right)\)
\(\chi_{818921}(9,\cdot)\)	818921.ej	99594	yes	\(1\)	\(1\)	\(e\left(\frac{23483}{99594}\right)\)	\(e\left(\frac{34351}{99594}\right)\)	\(e\left(\frac{23483}{49797}\right)\)	\(e\left(\frac{89875}{99594}\right)\)	\(e\left(\frac{3213}{5533}\right)\)	\(e\left(\frac{19765}{99594}\right)\)	\(e\left(\frac{23483}{33198}\right)\)	\(e\left(\frac{34351}{49797}\right)\)	\(e\left(\frac{2294}{16599}\right)\)	\(e\left(\frac{10261}{16599}\right)\)
\(\chi_{818921}(10,\cdot)\)	818921.dk	16599	yes	\(1\)	\(1\)	\(e\left(\frac{12290}{16599}\right)\)	\(e\left(\frac{1147}{16599}\right)\)	\(e\left(\frac{7981}{16599}\right)\)	\(e\left(\frac{9997}{16599}\right)\)	\(e\left(\frac{4479}{5533}\right)\)	\(e\left(\frac{13918}{16599}\right)\)	\(e\left(\frac{1224}{5533}\right)\)	\(e\left(\frac{2294}{16599}\right)\)	\(e\left(\frac{1896}{5533}\right)\)	\(e\left(\frac{3845}{5533}\right)\)
\(\chi_{818921}(11,\cdot)\)	818921.dx	33198	yes	\(1\)	\(1\)	\(e\left(\frac{241}{16599}\right)\)	\(e\left(\frac{10261}{33198}\right)\)	\(e\left(\frac{482}{16599}\right)\)	\(e\left(\frac{11294}{16599}\right)\)	\(e\left(\frac{3581}{11066}\right)\)	\(e\left(\frac{31645}{33198}\right)\)	\(e\left(\frac{241}{5533}\right)\)	\(e\left(\frac{10261}{16599}\right)\)	\(e\left(\frac{3845}{5533}\right)\)	\(e\left(\frac{3067}{5533}\right)\)
\(\chi_{818921}(12,\cdot)\)	818921.ep	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{134161}{199188}\right)\)	\(e\left(\frac{180911}{199188}\right)\)	\(e\left(\frac{34567}{99594}\right)\)	\(e\left(\frac{174563}{199188}\right)\)	\(e\left(\frac{3219}{5533}\right)\)	\(e\left(\frac{57887}{199188}\right)\)	\(e\left(\frac{1369}{66396}\right)\)	\(e\left(\frac{81317}{99594}\right)\)	\(e\left(\frac{9128}{16599}\right)\)	\(e\left(\frac{11225}{33198}\right)\)
\(\chi_{818921}(13,\cdot)\)	818921.el	199188	yes	\(1\)	\(1\)	\(e\left(\frac{34568}{49797}\right)\)	\(e\left(\frac{122377}{199188}\right)\)	\(e\left(\frac{19339}{49797}\right)\)	\(e\left(\frac{43402}{49797}\right)\)	\(e\left(\frac{6829}{22132}\right)\)	\(e\left(\frac{871}{199188}\right)\)	\(e\left(\frac{1370}{16599}\right)\)	\(e\left(\frac{22783}{99594}\right)\)	\(e\left(\frac{9391}{16599}\right)\)	\(e\left(\frac{9032}{16599}\right)\)
\(\chi_{818921}(14,\cdot)\)	818921.ef	66396	yes	\(-1\)	\(1\)	\(e\left(\frac{41399}{66396}\right)\)	\(e\left(\frac{23807}{33198}\right)\)	\(e\left(\frac{8201}{33198}\right)\)	\(e\left(\frac{63433}{66396}\right)\)	\(e\left(\frac{7539}{22132}\right)\)	\(e\left(\frac{9709}{16599}\right)\)	\(e\left(\frac{19267}{22132}\right)\)	\(e\left(\frac{7208}{16599}\right)\)	\(e\left(\frac{3203}{5533}\right)\)	\(e\left(\frac{10709}{11066}\right)\)
\(\chi_{818921}(15,\cdot)\)	818921.em	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{65827}{199188}\right)\)	\(e\left(\frac{6158}{49797}\right)\)	\(e\left(\frac{65827}{99594}\right)\)	\(e\left(\frac{67901}{199188}\right)\)	\(e\left(\frac{10051}{22132}\right)\)	\(e\left(\frac{34063}{99594}\right)\)	\(e\left(\frac{65827}{66396}\right)\)	\(e\left(\frac{12316}{49797}\right)\)	\(e\left(\frac{11144}{16599}\right)\)	\(e\left(\frac{32849}{33198}\right)\)
\(\chi_{818921}(16,\cdot)\)	818921.ea	49797	yes	\(1\)	\(1\)	\(e\left(\frac{5542}{49797}\right)\)	\(e\left(\frac{23483}{49797}\right)\)	\(e\left(\frac{11084}{49797}\right)\)	\(e\left(\frac{42344}{49797}\right)\)	\(e\left(\frac{3225}{5533}\right)\)	\(e\left(\frac{19061}{49797}\right)\)	\(e\left(\frac{5542}{16599}\right)\)	\(e\left(\frac{46966}{49797}\right)\)	\(e\left(\frac{15962}{16599}\right)\)	\(e\left(\frac{964}{16599}\right)\)
\(\chi_{818921}(17,\cdot)\)	818921.do	18108	yes	\(-1\)	\(1\)	\(e\left(\frac{4259}{18108}\right)\)	\(e\left(\frac{4306}{4527}\right)\)	\(e\left(\frac{4259}{9054}\right)\)	\(e\left(\frac{17101}{18108}\right)\)	\(e\left(\frac{375}{2012}\right)\)	\(e\left(\frac{6881}{9054}\right)\)	\(e\left(\frac{4259}{6036}\right)\)	\(e\left(\frac{4085}{4527}\right)\)	\(e\left(\frac{271}{1509}\right)\)	\(e\left(\frac{793}{3018}\right)\)
\(\chi_{818921}(18,\cdot)\)	818921.el	199188	yes	\(1\)	\(1\)	\(e\left(\frac{13127}{49797}\right)\)	\(e\left(\frac{191779}{199188}\right)\)	\(e\left(\frac{26254}{49797}\right)\)	\(e\left(\frac{30625}{49797}\right)\)	\(e\left(\frac{5011}{22132}\right)\)	\(e\left(\frac{158185}{199188}\right)\)	\(e\left(\frac{13127}{16599}\right)\)	\(e\left(\frac{92185}{99594}\right)\)	\(e\left(\frac{14584}{16599}\right)\)	\(e\left(\frac{10502}{16599}\right)\)
\(\chi_{818921}(19,\cdot)\)	818921.em	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{33437}{199188}\right)\)	\(e\left(\frac{26644}{49797}\right)\)	\(e\left(\frac{33437}{99594}\right)\)	\(e\left(\frac{91027}{199188}\right)\)	\(e\left(\frac{15557}{22132}\right)\)	\(e\left(\frac{57281}{99594}\right)\)	\(e\left(\frac{33437}{66396}\right)\)	\(e\left(\frac{3491}{49797}\right)\)	\(e\left(\frac{10372}{16599}\right)\)	\(e\left(\frac{23251}{33198}\right)\)
\(\chi_{818921}(20,\cdot)\)	818921.eo	199188	yes	\(1\)	\(1\)	\(e\left(\frac{76511}{99594}\right)\)	\(e\left(\frac{136841}{199188}\right)\)	\(e\left(\frac{26714}{49797}\right)\)	\(e\left(\frac{31357}{99594}\right)\)	\(e\left(\frac{10075}{22132}\right)\)	\(e\left(\frac{86483}{199188}\right)\)	\(e\left(\frac{10115}{33198}\right)\)	\(e\left(\frac{37247}{99594}\right)\)	\(e\left(\frac{1379}{16599}\right)\)	\(e\left(\frac{11776}{16599}\right)\)
\(\chi_{818921}(21,\cdot)\)	818921.eh	99594	yes	\(1\)	\(1\)	\(e\left(\frac{10636}{49797}\right)\)	\(e\left(\frac{76855}{99594}\right)\)	\(e\left(\frac{21272}{49797}\right)\)	\(e\left(\frac{34559}{49797}\right)\)	\(e\left(\frac{10903}{11066}\right)\)	\(e\left(\frac{8809}{99594}\right)\)	\(e\left(\frac{10636}{16599}\right)\)	\(e\left(\frac{27058}{49797}\right)\)	\(e\left(\frac{15065}{16599}\right)\)	\(e\left(\frac{4354}{16599}\right)\)
\(\chi_{818921}(22,\cdot)\)	818921.eo	199188	yes	\(1\)	\(1\)	\(e\left(\frac{4217}{99594}\right)\)	\(e\left(\frac{184643}{199188}\right)\)	\(e\left(\frac{4217}{49797}\right)\)	\(e\left(\frac{39139}{99594}\right)\)	\(e\left(\frac{21453}{22132}\right)\)	\(e\left(\frac{109337}{199188}\right)\)	\(e\left(\frac{4217}{33198}\right)\)	\(e\left(\frac{85049}{99594}\right)\)	\(e\left(\frac{7226}{16599}\right)\)	\(e\left(\frac{9442}{16599}\right)\)
\(\chi_{818921}(23,\cdot)\)	818921.cy	6036	yes	\(1\)	\(1\)	\(e\left(\frac{521}{3018}\right)\)	\(e\left(\frac{1883}{6036}\right)\)	\(e\left(\frac{521}{1509}\right)\)	\(e\left(\frac{1693}{3018}\right)\)	\(e\left(\frac{975}{2012}\right)\)	\(e\left(\frac{5321}{6036}\right)\)	\(e\left(\frac{521}{1006}\right)\)	\(e\left(\frac{1883}{3018}\right)\)	\(e\left(\frac{369}{503}\right)\)	\(e\left(\frac{461}{503}\right)\)
\(\chi_{818921}(24,\cdot)\)	818921.em	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{139703}{199188}\right)\)	\(e\left(\frac{26200}{49797}\right)\)	\(e\left(\frac{40109}{99594}\right)\)	\(e\left(\frac{117313}{199188}\right)\)	\(e\left(\frac{5035}{22132}\right)\)	\(e\left(\frac{88271}{99594}\right)\)	\(e\left(\frac{6911}{66396}\right)\)	\(e\left(\frac{2603}{49797}\right)\)	\(e\left(\frac{4819}{16599}\right)\)	\(e\left(\frac{11707}{33198}\right)\)
\(\chi_{818921}(25,\cdot)\)	818921.eh	99594	yes	\(1\)	\(1\)	\(e\left(\frac{21172}{49797}\right)\)	\(e\left(\frac{89875}{99594}\right)\)	\(e\left(\frac{42344}{49797}\right)\)	\(e\left(\frac{38810}{49797}\right)\)	\(e\left(\frac{3625}{11066}\right)\)	\(e\left(\frac{48361}{99594}\right)\)	\(e\left(\frac{4573}{16599}\right)\)	\(e\left(\frac{40078}{49797}\right)\)	\(e\left(\frac{3395}{16599}\right)\)	\(e\left(\frac{5989}{16599}\right)\)
\(\chi_{818921}(26,\cdot)\)	818921.ct	3018	yes	\(1\)	\(1\)	\(e\left(\frac{2179}{3018}\right)\)	\(e\left(\frac{701}{3018}\right)\)	\(e\left(\frac{670}{1509}\right)\)	\(e\left(\frac{1763}{3018}\right)\)	\(e\left(\frac{480}{503}\right)\)	\(e\left(\frac{1811}{3018}\right)\)	\(e\left(\frac{167}{1006}\right)\)	\(e\left(\frac{701}{1509}\right)\)	\(e\left(\frac{154}{503}\right)\)	\(e\left(\frac{281}{503}\right)\)
\(\chi_{818921}(27,\cdot)\)	818921.ed	66396	yes	\(-1\)	\(1\)	\(e\left(\frac{56681}{66396}\right)\)	\(e\left(\frac{1153}{66396}\right)\)	\(e\left(\frac{23483}{33198}\right)\)	\(e\left(\frac{23479}{66396}\right)\)	\(e\left(\frac{9639}{11066}\right)\)	\(e\left(\frac{19765}{66396}\right)\)	\(e\left(\frac{12417}{22132}\right)\)	\(e\left(\frac{1153}{33198}\right)\)	\(e\left(\frac{1147}{5533}\right)\)	\(e\left(\frac{10261}{11066}\right)\)
\(\chi_{818921}(28,\cdot)\)	818921.ek	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{129739}{199188}\right)\)	\(e\left(\frac{66731}{199188}\right)\)	\(e\left(\frac{30145}{99594}\right)\)	\(e\left(\frac{133049}{199188}\right)\)	\(e\left(\frac{10915}{11066}\right)\)	\(e\left(\frac{35975}{199188}\right)\)	\(e\left(\frac{63343}{66396}\right)\)	\(e\left(\frac{66731}{99594}\right)\)	\(e\left(\frac{5300}{16599}\right)\)	\(e\left(\frac{32609}{33198}\right)\)
\(\chi_{818921}(29,\cdot)\)	818921.ef	66396	yes	\(-1\)	\(1\)	\(e\left(\frac{4399}{66396}\right)\)	\(e\left(\frac{3415}{33198}\right)\)	\(e\left(\frac{4399}{33198}\right)\)	\(e\left(\frac{4001}{66396}\right)\)	\(e\left(\frac{3743}{22132}\right)\)	\(e\left(\frac{16508}{16599}\right)\)	\(e\left(\frac{4399}{22132}\right)\)	\(e\left(\frac{3415}{16599}\right)\)	\(e\left(\frac{700}{5533}\right)\)	\(e\left(\frac{131}{11066}\right)\)
\(\chi_{818921}(30,\cdot)\)	818921.ek	199188	yes	\(-1\)	\(1\)	\(e\left(\frac{71369}{199188}\right)\)	\(e\left(\frac{147709}{199188}\right)\)	\(e\left(\frac{71369}{99594}\right)\)	\(e\left(\frac{10651}{199188}\right)\)	\(e\left(\frac{1105}{11066}\right)\)	\(e\left(\frac{186781}{199188}\right)\)	\(e\left(\frac{4973}{66396}\right)\)	\(e\left(\frac{48115}{99594}\right)\)	\(e\left(\frac{6835}{16599}\right)\)	\(e\left(\frac{133}{33198}\right)\)
\(\chi_{818921}(31,\cdot)\)	818921.dw	22132	yes	\(1\)	\(1\)	\(e\left(\frac{3357}{5533}\right)\)	\(e\left(\frac{18279}{22132}\right)\)	\(e\left(\frac{1181}{5533}\right)\)	\(e\left(\frac{3130}{5533}\right)\)	\(e\left(\frac{9575}{22132}\right)\)	\(e\left(\frac{4925}{22132}\right)\)	\(e\left(\frac{4538}{5533}\right)\)	\(e\left(\frac{7213}{11066}\right)\)	\(e\left(\frac{954}{5533}\right)\)	\(e\left(\frac{5314}{5533}\right)\)
\(\chi_{818921}(32,\cdot)\)	818921.eo	199188	yes	\(1\)	\(1\)	\(e\left(\frac{13855}{99594}\right)\)	\(e\left(\frac{17821}{199188}\right)\)	\(e\left(\frac{13855}{49797}\right)\)	\(e\left(\frac{56063}{99594}\right)\)	\(e\left(\frac{5059}{22132}\right)\)	\(e\left(\frac{194899}{199188}\right)\)	\(e\left(\frac{13855}{33198}\right)\)	\(e\left(\frac{17821}{99594}\right)\)	\(e\left(\frac{11653}{16599}\right)\)	\(e\left(\frac{1205}{16599}\right)\)

Introduction

L-functions

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Character group

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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.