LMFDB - Group of Dirichlet characters of modulus 9067

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9067)

pari: g = idealstar(,9067,2)

Character group

sage: G.order() pari: g.no
Order	=	9066
sage: H.invariants() pari: g.cyc
Structure	=	$C_{9066}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9067}(3,\cdot)$

First 32 of 9066 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{9067}(1,\cdot)$	9067.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9067}(2,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{1553}{3022}\right)$	$e\left(\frac{2935}{3022}\right)$	$e\left(\frac{42}{1511}\right)$	$e\left(\frac{847}{3022}\right)$	$e\left(\frac{733}{1511}\right)$	$e\left(\frac{1027}{3022}\right)$	$e\left(\frac{1637}{3022}\right)$	$e\left(\frac{1424}{1511}\right)$	$e\left(\frac{1200}{1511}\right)$	$e\left(\frac{15}{3022}\right)$
$\chi_{9067}(3,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{2935}{3022}\right)$	$e\left(\frac{1}{9066}\right)$	$e\left(\frac{1424}{1511}\right)$	$e\left(\frac{25}{9066}\right)$	$e\left(\frac{4403}{4533}\right)$	$e\left(\frac{355}{3022}\right)$	$e\left(\frac{2761}{3022}\right)$	$e\left(\frac{1}{4533}\right)$	$e\left(\frac{4415}{4533}\right)$	$e\left(\frac{2883}{3022}\right)$
$\chi_{9067}(4,\cdot)$	9067.e	1511	yes	$1$	$1$	$e\left(\frac{42}{1511}\right)$	$e\left(\frac{1424}{1511}\right)$	$e\left(\frac{84}{1511}\right)$	$e\left(\frac{847}{1511}\right)$	$e\left(\frac{1466}{1511}\right)$	$e\left(\frac{1027}{1511}\right)$	$e\left(\frac{126}{1511}\right)$	$e\left(\frac{1337}{1511}\right)$	$e\left(\frac{889}{1511}\right)$	$e\left(\frac{15}{1511}\right)$
$\chi_{9067}(5,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{847}{3022}\right)$	$e\left(\frac{25}{9066}\right)$	$e\left(\frac{847}{1511}\right)$	$e\left(\frac{625}{9066}\right)$	$e\left(\frac{1283}{4533}\right)$	$e\left(\frac{2831}{3022}\right)$	$e\left(\frac{2541}{3022}\right)$	$e\left(\frac{25}{4533}\right)$	$e\left(\frac{1583}{4533}\right)$	$e\left(\frac{2569}{3022}\right)$
$\chi_{9067}(6,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{733}{1511}\right)$	$e\left(\frac{4403}{4533}\right)$	$e\left(\frac{1466}{1511}\right)$	$e\left(\frac{1283}{4533}\right)$	$e\left(\frac{2069}{4533}\right)$	$e\left(\frac{691}{1511}\right)$	$e\left(\frac{688}{1511}\right)$	$e\left(\frac{4273}{4533}\right)$	$e\left(\frac{3482}{4533}\right)$	$e\left(\frac{1449}{1511}\right)$
$\chi_{9067}(7,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{1027}{3022}\right)$	$e\left(\frac{355}{3022}\right)$	$e\left(\frac{1027}{1511}\right)$	$e\left(\frac{2831}{3022}\right)$	$e\left(\frac{691}{1511}\right)$	$e\left(\frac{325}{3022}\right)$	$e\left(\frac{59}{3022}\right)$	$e\left(\frac{355}{1511}\right)$	$e\left(\frac{418}{1511}\right)$	$e\left(\frac{43}{3022}\right)$
$\chi_{9067}(8,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{1637}{3022}\right)$	$e\left(\frac{2761}{3022}\right)$	$e\left(\frac{126}{1511}\right)$	$e\left(\frac{2541}{3022}\right)$	$e\left(\frac{688}{1511}\right)$	$e\left(\frac{59}{3022}\right)$	$e\left(\frac{1889}{3022}\right)$	$e\left(\frac{1250}{1511}\right)$	$e\left(\frac{578}{1511}\right)$	$e\left(\frac{45}{3022}\right)$
$\chi_{9067}(9,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{1424}{1511}\right)$	$e\left(\frac{1}{4533}\right)$	$e\left(\frac{1337}{1511}\right)$	$e\left(\frac{25}{4533}\right)$	$e\left(\frac{4273}{4533}\right)$	$e\left(\frac{355}{1511}\right)$	$e\left(\frac{1250}{1511}\right)$	$e\left(\frac{2}{4533}\right)$	$e\left(\frac{4297}{4533}\right)$	$e\left(\frac{1372}{1511}\right)$
$\chi_{9067}(10,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{1200}{1511}\right)$	$e\left(\frac{4415}{4533}\right)$	$e\left(\frac{889}{1511}\right)$	$e\left(\frac{1583}{4533}\right)$	$e\left(\frac{3482}{4533}\right)$	$e\left(\frac{418}{1511}\right)$	$e\left(\frac{578}{1511}\right)$	$e\left(\frac{4297}{4533}\right)$	$e\left(\frac{650}{4533}\right)$	$e\left(\frac{1292}{1511}\right)$
$\chi_{9067}(11,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{15}{3022}\right)$	$e\left(\frac{2883}{3022}\right)$	$e\left(\frac{15}{1511}\right)$	$e\left(\frac{2569}{3022}\right)$	$e\left(\frac{1449}{1511}\right)$	$e\left(\frac{43}{3022}\right)$	$e\left(\frac{45}{3022}\right)$	$e\left(\frac{1372}{1511}\right)$	$e\left(\frac{1292}{1511}\right)$	$e\left(\frac{545}{3022}\right)$
$\chi_{9067}(12,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{3019}{3022}\right)$	$e\left(\frac{8545}{9066}\right)$	$e\left(\frac{1508}{1511}\right)$	$e\left(\frac{5107}{9066}\right)$	$e\left(\frac{4268}{4533}\right)$	$e\left(\frac{2409}{3022}\right)$	$e\left(\frac{3013}{3022}\right)$	$e\left(\frac{4012}{4533}\right)$	$e\left(\frac{2549}{4533}\right)$	$e\left(\frac{2913}{3022}\right)$
$\chi_{9067}(13,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{145}{3022}\right)$	$e\left(\frac{8057}{9066}\right)$	$e\left(\frac{145}{1511}\right)$	$e\left(\frac{1973}{9066}\right)$	$e\left(\frac{4246}{4533}\right)$	$e\left(\frac{1423}{3022}\right)$	$e\left(\frac{435}{3022}\right)$	$e\left(\frac{3524}{4533}\right)$	$e\left(\frac{1204}{4533}\right)$	$e\left(\frac{1239}{3022}\right)$
$\chi_{9067}(14,\cdot)$	9067.e	1511	yes	$1$	$1$	$e\left(\frac{1290}{1511}\right)$	$e\left(\frac{134}{1511}\right)$	$e\left(\frac{1069}{1511}\right)$	$e\left(\frac{328}{1511}\right)$	$e\left(\frac{1424}{1511}\right)$	$e\left(\frac{676}{1511}\right)$	$e\left(\frac{848}{1511}\right)$	$e\left(\frac{268}{1511}\right)$	$e\left(\frac{107}{1511}\right)$	$e\left(\frac{29}{1511}\right)$
$\chi_{9067}(15,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{380}{1511}\right)$	$e\left(\frac{13}{4533}\right)$	$e\left(\frac{760}{1511}\right)$	$e\left(\frac{325}{4533}\right)$	$e\left(\frac{1153}{4533}\right)$	$e\left(\frac{82}{1511}\right)$	$e\left(\frac{1140}{1511}\right)$	$e\left(\frac{26}{4533}\right)$	$e\left(\frac{1465}{4533}\right)$	$e\left(\frac{1215}{1511}\right)$
$\chi_{9067}(16,\cdot)$	9067.e	1511	yes	$1$	$1$	$e\left(\frac{84}{1511}\right)$	$e\left(\frac{1337}{1511}\right)$	$e\left(\frac{168}{1511}\right)$	$e\left(\frac{183}{1511}\right)$	$e\left(\frac{1421}{1511}\right)$	$e\left(\frac{543}{1511}\right)$	$e\left(\frac{252}{1511}\right)$	$e\left(\frac{1163}{1511}\right)$	$e\left(\frac{267}{1511}\right)$	$e\left(\frac{30}{1511}\right)$
$\chi_{9067}(17,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{2587}{3022}\right)$	$e\left(\frac{6049}{9066}\right)$	$e\left(\frac{1076}{1511}\right)$	$e\left(\frac{6169}{9066}\right)$	$e\left(\frac{2372}{4533}\right)$	$e\left(\frac{1775}{3022}\right)$	$e\left(\frac{1717}{3022}\right)$	$e\left(\frac{1516}{4533}\right)$	$e\left(\frac{2432}{4533}\right)$	$e\left(\frac{2327}{3022}\right)$
$\chi_{9067}(18,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{1379}{3022}\right)$	$e\left(\frac{8807}{9066}\right)$	$e\left(\frac{1379}{1511}\right)$	$e\left(\frac{2591}{9066}\right)$	$e\left(\frac{1939}{4533}\right)$	$e\left(\frac{1737}{3022}\right)$	$e\left(\frac{1115}{3022}\right)$	$e\left(\frac{4274}{4533}\right)$	$e\left(\frac{3364}{4533}\right)$	$e\left(\frac{2759}{3022}\right)$
$\chi_{9067}(19,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{1155}{3022}\right)$	$e\left(\frac{7177}{9066}\right)$	$e\left(\frac{1155}{1511}\right)$	$e\left(\frac{7171}{9066}\right)$	$e\left(\frac{788}{4533}\right)$	$e\left(\frac{289}{3022}\right)$	$e\left(\frac{443}{3022}\right)$	$e\left(\frac{2644}{4533}\right)$	$e\left(\frac{785}{4533}\right)$	$e\left(\frac{2679}{3022}\right)$
$\chi_{9067}(20,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{931}{3022}\right)$	$e\left(\frac{8569}{9066}\right)$	$e\left(\frac{931}{1511}\right)$	$e\left(\frac{5707}{9066}\right)$	$e\left(\frac{1148}{4533}\right)$	$e\left(\frac{1863}{3022}\right)$	$e\left(\frac{2793}{3022}\right)$	$e\left(\frac{4036}{4533}\right)$	$e\left(\frac{4250}{4533}\right)$	$e\left(\frac{2599}{3022}\right)$
$\chi_{9067}(21,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{470}{1511}\right)$	$e\left(\frac{533}{4533}\right)$	$e\left(\frac{940}{1511}\right)$	$e\left(\frac{4259}{4533}\right)$	$e\left(\frac{1943}{4533}\right)$	$e\left(\frac{340}{1511}\right)$	$e\left(\frac{1410}{1511}\right)$	$e\left(\frac{1066}{4533}\right)$	$e\left(\frac{1136}{4533}\right)$	$e\left(\frac{1463}{1511}\right)$
$\chi_{9067}(22,\cdot)$	9067.e	1511	yes	$1$	$1$	$e\left(\frac{784}{1511}\right)$	$e\left(\frac{1398}{1511}\right)$	$e\left(\frac{57}{1511}\right)$	$e\left(\frac{197}{1511}\right)$	$e\left(\frac{671}{1511}\right)$	$e\left(\frac{535}{1511}\right)$	$e\left(\frac{841}{1511}\right)$	$e\left(\frac{1285}{1511}\right)$	$e\left(\frac{981}{1511}\right)$	$e\left(\frac{280}{1511}\right)$
$\chi_{9067}(23,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{160}{1511}\right)$	$e\left(\frac{85}{4533}\right)$	$e\left(\frac{320}{1511}\right)$	$e\left(\frac{2125}{4533}\right)$	$e\left(\frac{565}{4533}\right)$	$e\left(\frac{1466}{1511}\right)$	$e\left(\frac{480}{1511}\right)$	$e\left(\frac{170}{4533}\right)$	$e\left(\frac{2605}{4533}\right)$	$e\left(\frac{273}{1511}\right)$
$\chi_{9067}(24,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{775}{1511}\right)$	$e\left(\frac{4142}{4533}\right)$	$e\left(\frac{39}{1511}\right)$	$e\left(\frac{3824}{4533}\right)$	$e\left(\frac{1934}{4533}\right)$	$e\left(\frac{207}{1511}\right)$	$e\left(\frac{814}{1511}\right)$	$e\left(\frac{3751}{4533}\right)$	$e\left(\frac{1616}{4533}\right)$	$e\left(\frac{1464}{1511}\right)$
$\chi_{9067}(25,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{847}{1511}\right)$	$e\left(\frac{25}{4533}\right)$	$e\left(\frac{183}{1511}\right)$	$e\left(\frac{625}{4533}\right)$	$e\left(\frac{2566}{4533}\right)$	$e\left(\frac{1320}{1511}\right)$	$e\left(\frac{1030}{1511}\right)$	$e\left(\frac{50}{4533}\right)$	$e\left(\frac{3166}{4533}\right)$	$e\left(\frac{1058}{1511}\right)$
$\chi_{9067}(26,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{849}{1511}\right)$	$e\left(\frac{3898}{4533}\right)$	$e\left(\frac{187}{1511}\right)$	$e\left(\frac{2257}{4533}\right)$	$e\left(\frac{1912}{4533}\right)$	$e\left(\frac{1225}{1511}\right)$	$e\left(\frac{1036}{1511}\right)$	$e\left(\frac{3263}{4533}\right)$	$e\left(\frac{271}{4533}\right)$	$e\left(\frac{627}{1511}\right)$
$\chi_{9067}(27,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{2761}{3022}\right)$	$e\left(\frac{1}{3022}\right)$	$e\left(\frac{1250}{1511}\right)$	$e\left(\frac{25}{3022}\right)$	$e\left(\frac{1381}{1511}\right)$	$e\left(\frac{1065}{3022}\right)$	$e\left(\frac{2239}{3022}\right)$	$e\left(\frac{1}{1511}\right)$	$e\left(\frac{1393}{1511}\right)$	$e\left(\frac{2605}{3022}\right)$
$\chi_{9067}(28,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{1111}{3022}\right)$	$e\left(\frac{181}{3022}\right)$	$e\left(\frac{1111}{1511}\right)$	$e\left(\frac{1503}{3022}\right)$	$e\left(\frac{646}{1511}\right)$	$e\left(\frac{2379}{3022}\right)$	$e\left(\frac{311}{3022}\right)$	$e\left(\frac{181}{1511}\right)$	$e\left(\frac{1307}{1511}\right)$	$e\left(\frac{73}{3022}\right)$
$\chi_{9067}(29,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{971}{3022}\right)$	$e\left(\frac{4435}{9066}\right)$	$e\left(\frac{971}{1511}\right)$	$e\left(\frac{2083}{9066}\right)$	$e\left(\frac{3674}{4533}\right)$	$e\left(\frac{2985}{3022}\right)$	$e\left(\frac{2913}{3022}\right)$	$e\left(\frac{4435}{4533}\right)$	$e\left(\frac{2498}{4533}\right)$	$e\left(\frac{23}{3022}\right)$
$\chi_{9067}(30,\cdot)$	9067.h	9066	yes	$-1$	$1$	$e\left(\frac{2313}{3022}\right)$	$e\left(\frac{8831}{9066}\right)$	$e\left(\frac{802}{1511}\right)$	$e\left(\frac{3191}{9066}\right)$	$e\left(\frac{3352}{4533}\right)$	$e\left(\frac{1191}{3022}\right)$	$e\left(\frac{895}{3022}\right)$	$e\left(\frac{4298}{4533}\right)$	$e\left(\frac{532}{4533}\right)$	$e\left(\frac{2445}{3022}\right)$
$\chi_{9067}(31,\cdot)$	9067.g	4533	yes	$1$	$1$	$e\left(\frac{1102}{1511}\right)$	$e\left(\frac{491}{4533}\right)$	$e\left(\frac{693}{1511}\right)$	$e\left(\frac{3209}{4533}\right)$	$e\left(\frac{3797}{4533}\right)$	$e\left(\frac{540}{1511}\right)$	$e\left(\frac{284}{1511}\right)$	$e\left(\frac{982}{4533}\right)$	$e\left(\frac{1982}{4533}\right)$	$e\left(\frac{1257}{1511}\right)$
$\chi_{9067}(32,\cdot)$	9067.f	3022	yes	$-1$	$1$	$e\left(\frac{1721}{3022}\right)$	$e\left(\frac{2587}{3022}\right)$	$e\left(\frac{210}{1511}\right)$	$e\left(\frac{1213}{3022}\right)$	$e\left(\frac{643}{1511}\right)$	$e\left(\frac{2113}{3022}\right)$	$e\left(\frac{2141}{3022}\right)$	$e\left(\frac{1076}{1511}\right)$	$e\left(\frac{1467}{1511}\right)$	$e\left(\frac{75}{3022}\right)$

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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	$9067$
Structure	\(C_{9066}\)
Order	$9066$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{9067}(1,\cdot)\)	9067.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9067}(2,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{1553}{3022}\right)\)	\(e\left(\frac{2935}{3022}\right)\)	\(e\left(\frac{42}{1511}\right)\)	\(e\left(\frac{847}{3022}\right)\)	\(e\left(\frac{733}{1511}\right)\)	\(e\left(\frac{1027}{3022}\right)\)	\(e\left(\frac{1637}{3022}\right)\)	\(e\left(\frac{1424}{1511}\right)\)	\(e\left(\frac{1200}{1511}\right)\)	\(e\left(\frac{15}{3022}\right)\)
\(\chi_{9067}(3,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{2935}{3022}\right)\)	\(e\left(\frac{1}{9066}\right)\)	\(e\left(\frac{1424}{1511}\right)\)	\(e\left(\frac{25}{9066}\right)\)	\(e\left(\frac{4403}{4533}\right)\)	\(e\left(\frac{355}{3022}\right)\)	\(e\left(\frac{2761}{3022}\right)\)	\(e\left(\frac{1}{4533}\right)\)	\(e\left(\frac{4415}{4533}\right)\)	\(e\left(\frac{2883}{3022}\right)\)
\(\chi_{9067}(4,\cdot)\)	9067.e	1511	yes	\(1\)	\(1\)	\(e\left(\frac{42}{1511}\right)\)	\(e\left(\frac{1424}{1511}\right)\)	\(e\left(\frac{84}{1511}\right)\)	\(e\left(\frac{847}{1511}\right)\)	\(e\left(\frac{1466}{1511}\right)\)	\(e\left(\frac{1027}{1511}\right)\)	\(e\left(\frac{126}{1511}\right)\)	\(e\left(\frac{1337}{1511}\right)\)	\(e\left(\frac{889}{1511}\right)\)	\(e\left(\frac{15}{1511}\right)\)
\(\chi_{9067}(5,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{847}{3022}\right)\)	\(e\left(\frac{25}{9066}\right)\)	\(e\left(\frac{847}{1511}\right)\)	\(e\left(\frac{625}{9066}\right)\)	\(e\left(\frac{1283}{4533}\right)\)	\(e\left(\frac{2831}{3022}\right)\)	\(e\left(\frac{2541}{3022}\right)\)	\(e\left(\frac{25}{4533}\right)\)	\(e\left(\frac{1583}{4533}\right)\)	\(e\left(\frac{2569}{3022}\right)\)
\(\chi_{9067}(6,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{733}{1511}\right)\)	\(e\left(\frac{4403}{4533}\right)\)	\(e\left(\frac{1466}{1511}\right)\)	\(e\left(\frac{1283}{4533}\right)\)	\(e\left(\frac{2069}{4533}\right)\)	\(e\left(\frac{691}{1511}\right)\)	\(e\left(\frac{688}{1511}\right)\)	\(e\left(\frac{4273}{4533}\right)\)	\(e\left(\frac{3482}{4533}\right)\)	\(e\left(\frac{1449}{1511}\right)\)
\(\chi_{9067}(7,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{1027}{3022}\right)\)	\(e\left(\frac{355}{3022}\right)\)	\(e\left(\frac{1027}{1511}\right)\)	\(e\left(\frac{2831}{3022}\right)\)	\(e\left(\frac{691}{1511}\right)\)	\(e\left(\frac{325}{3022}\right)\)	\(e\left(\frac{59}{3022}\right)\)	\(e\left(\frac{355}{1511}\right)\)	\(e\left(\frac{418}{1511}\right)\)	\(e\left(\frac{43}{3022}\right)\)
\(\chi_{9067}(8,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{1637}{3022}\right)\)	\(e\left(\frac{2761}{3022}\right)\)	\(e\left(\frac{126}{1511}\right)\)	\(e\left(\frac{2541}{3022}\right)\)	\(e\left(\frac{688}{1511}\right)\)	\(e\left(\frac{59}{3022}\right)\)	\(e\left(\frac{1889}{3022}\right)\)	\(e\left(\frac{1250}{1511}\right)\)	\(e\left(\frac{578}{1511}\right)\)	\(e\left(\frac{45}{3022}\right)\)
\(\chi_{9067}(9,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{1424}{1511}\right)\)	\(e\left(\frac{1}{4533}\right)\)	\(e\left(\frac{1337}{1511}\right)\)	\(e\left(\frac{25}{4533}\right)\)	\(e\left(\frac{4273}{4533}\right)\)	\(e\left(\frac{355}{1511}\right)\)	\(e\left(\frac{1250}{1511}\right)\)	\(e\left(\frac{2}{4533}\right)\)	\(e\left(\frac{4297}{4533}\right)\)	\(e\left(\frac{1372}{1511}\right)\)
\(\chi_{9067}(10,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{1200}{1511}\right)\)	\(e\left(\frac{4415}{4533}\right)\)	\(e\left(\frac{889}{1511}\right)\)	\(e\left(\frac{1583}{4533}\right)\)	\(e\left(\frac{3482}{4533}\right)\)	\(e\left(\frac{418}{1511}\right)\)	\(e\left(\frac{578}{1511}\right)\)	\(e\left(\frac{4297}{4533}\right)\)	\(e\left(\frac{650}{4533}\right)\)	\(e\left(\frac{1292}{1511}\right)\)
\(\chi_{9067}(11,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{3022}\right)\)	\(e\left(\frac{2883}{3022}\right)\)	\(e\left(\frac{15}{1511}\right)\)	\(e\left(\frac{2569}{3022}\right)\)	\(e\left(\frac{1449}{1511}\right)\)	\(e\left(\frac{43}{3022}\right)\)	\(e\left(\frac{45}{3022}\right)\)	\(e\left(\frac{1372}{1511}\right)\)	\(e\left(\frac{1292}{1511}\right)\)	\(e\left(\frac{545}{3022}\right)\)
\(\chi_{9067}(12,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{3019}{3022}\right)\)	\(e\left(\frac{8545}{9066}\right)\)	\(e\left(\frac{1508}{1511}\right)\)	\(e\left(\frac{5107}{9066}\right)\)	\(e\left(\frac{4268}{4533}\right)\)	\(e\left(\frac{2409}{3022}\right)\)	\(e\left(\frac{3013}{3022}\right)\)	\(e\left(\frac{4012}{4533}\right)\)	\(e\left(\frac{2549}{4533}\right)\)	\(e\left(\frac{2913}{3022}\right)\)
\(\chi_{9067}(13,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{145}{3022}\right)\)	\(e\left(\frac{8057}{9066}\right)\)	\(e\left(\frac{145}{1511}\right)\)	\(e\left(\frac{1973}{9066}\right)\)	\(e\left(\frac{4246}{4533}\right)\)	\(e\left(\frac{1423}{3022}\right)\)	\(e\left(\frac{435}{3022}\right)\)	\(e\left(\frac{3524}{4533}\right)\)	\(e\left(\frac{1204}{4533}\right)\)	\(e\left(\frac{1239}{3022}\right)\)
\(\chi_{9067}(14,\cdot)\)	9067.e	1511	yes	\(1\)	\(1\)	\(e\left(\frac{1290}{1511}\right)\)	\(e\left(\frac{134}{1511}\right)\)	\(e\left(\frac{1069}{1511}\right)\)	\(e\left(\frac{328}{1511}\right)\)	\(e\left(\frac{1424}{1511}\right)\)	\(e\left(\frac{676}{1511}\right)\)	\(e\left(\frac{848}{1511}\right)\)	\(e\left(\frac{268}{1511}\right)\)	\(e\left(\frac{107}{1511}\right)\)	\(e\left(\frac{29}{1511}\right)\)
\(\chi_{9067}(15,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{380}{1511}\right)\)	\(e\left(\frac{13}{4533}\right)\)	\(e\left(\frac{760}{1511}\right)\)	\(e\left(\frac{325}{4533}\right)\)	\(e\left(\frac{1153}{4533}\right)\)	\(e\left(\frac{82}{1511}\right)\)	\(e\left(\frac{1140}{1511}\right)\)	\(e\left(\frac{26}{4533}\right)\)	\(e\left(\frac{1465}{4533}\right)\)	\(e\left(\frac{1215}{1511}\right)\)
\(\chi_{9067}(16,\cdot)\)	9067.e	1511	yes	\(1\)	\(1\)	\(e\left(\frac{84}{1511}\right)\)	\(e\left(\frac{1337}{1511}\right)\)	\(e\left(\frac{168}{1511}\right)\)	\(e\left(\frac{183}{1511}\right)\)	\(e\left(\frac{1421}{1511}\right)\)	\(e\left(\frac{543}{1511}\right)\)	\(e\left(\frac{252}{1511}\right)\)	\(e\left(\frac{1163}{1511}\right)\)	\(e\left(\frac{267}{1511}\right)\)	\(e\left(\frac{30}{1511}\right)\)
\(\chi_{9067}(17,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{2587}{3022}\right)\)	\(e\left(\frac{6049}{9066}\right)\)	\(e\left(\frac{1076}{1511}\right)\)	\(e\left(\frac{6169}{9066}\right)\)	\(e\left(\frac{2372}{4533}\right)\)	\(e\left(\frac{1775}{3022}\right)\)	\(e\left(\frac{1717}{3022}\right)\)	\(e\left(\frac{1516}{4533}\right)\)	\(e\left(\frac{2432}{4533}\right)\)	\(e\left(\frac{2327}{3022}\right)\)
\(\chi_{9067}(18,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{1379}{3022}\right)\)	\(e\left(\frac{8807}{9066}\right)\)	\(e\left(\frac{1379}{1511}\right)\)	\(e\left(\frac{2591}{9066}\right)\)	\(e\left(\frac{1939}{4533}\right)\)	\(e\left(\frac{1737}{3022}\right)\)	\(e\left(\frac{1115}{3022}\right)\)	\(e\left(\frac{4274}{4533}\right)\)	\(e\left(\frac{3364}{4533}\right)\)	\(e\left(\frac{2759}{3022}\right)\)
\(\chi_{9067}(19,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{1155}{3022}\right)\)	\(e\left(\frac{7177}{9066}\right)\)	\(e\left(\frac{1155}{1511}\right)\)	\(e\left(\frac{7171}{9066}\right)\)	\(e\left(\frac{788}{4533}\right)\)	\(e\left(\frac{289}{3022}\right)\)	\(e\left(\frac{443}{3022}\right)\)	\(e\left(\frac{2644}{4533}\right)\)	\(e\left(\frac{785}{4533}\right)\)	\(e\left(\frac{2679}{3022}\right)\)
\(\chi_{9067}(20,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{931}{3022}\right)\)	\(e\left(\frac{8569}{9066}\right)\)	\(e\left(\frac{931}{1511}\right)\)	\(e\left(\frac{5707}{9066}\right)\)	\(e\left(\frac{1148}{4533}\right)\)	\(e\left(\frac{1863}{3022}\right)\)	\(e\left(\frac{2793}{3022}\right)\)	\(e\left(\frac{4036}{4533}\right)\)	\(e\left(\frac{4250}{4533}\right)\)	\(e\left(\frac{2599}{3022}\right)\)
\(\chi_{9067}(21,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{470}{1511}\right)\)	\(e\left(\frac{533}{4533}\right)\)	\(e\left(\frac{940}{1511}\right)\)	\(e\left(\frac{4259}{4533}\right)\)	\(e\left(\frac{1943}{4533}\right)\)	\(e\left(\frac{340}{1511}\right)\)	\(e\left(\frac{1410}{1511}\right)\)	\(e\left(\frac{1066}{4533}\right)\)	\(e\left(\frac{1136}{4533}\right)\)	\(e\left(\frac{1463}{1511}\right)\)
\(\chi_{9067}(22,\cdot)\)	9067.e	1511	yes	\(1\)	\(1\)	\(e\left(\frac{784}{1511}\right)\)	\(e\left(\frac{1398}{1511}\right)\)	\(e\left(\frac{57}{1511}\right)\)	\(e\left(\frac{197}{1511}\right)\)	\(e\left(\frac{671}{1511}\right)\)	\(e\left(\frac{535}{1511}\right)\)	\(e\left(\frac{841}{1511}\right)\)	\(e\left(\frac{1285}{1511}\right)\)	\(e\left(\frac{981}{1511}\right)\)	\(e\left(\frac{280}{1511}\right)\)
\(\chi_{9067}(23,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{160}{1511}\right)\)	\(e\left(\frac{85}{4533}\right)\)	\(e\left(\frac{320}{1511}\right)\)	\(e\left(\frac{2125}{4533}\right)\)	\(e\left(\frac{565}{4533}\right)\)	\(e\left(\frac{1466}{1511}\right)\)	\(e\left(\frac{480}{1511}\right)\)	\(e\left(\frac{170}{4533}\right)\)	\(e\left(\frac{2605}{4533}\right)\)	\(e\left(\frac{273}{1511}\right)\)
\(\chi_{9067}(24,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{775}{1511}\right)\)	\(e\left(\frac{4142}{4533}\right)\)	\(e\left(\frac{39}{1511}\right)\)	\(e\left(\frac{3824}{4533}\right)\)	\(e\left(\frac{1934}{4533}\right)\)	\(e\left(\frac{207}{1511}\right)\)	\(e\left(\frac{814}{1511}\right)\)	\(e\left(\frac{3751}{4533}\right)\)	\(e\left(\frac{1616}{4533}\right)\)	\(e\left(\frac{1464}{1511}\right)\)
\(\chi_{9067}(25,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{847}{1511}\right)\)	\(e\left(\frac{25}{4533}\right)\)	\(e\left(\frac{183}{1511}\right)\)	\(e\left(\frac{625}{4533}\right)\)	\(e\left(\frac{2566}{4533}\right)\)	\(e\left(\frac{1320}{1511}\right)\)	\(e\left(\frac{1030}{1511}\right)\)	\(e\left(\frac{50}{4533}\right)\)	\(e\left(\frac{3166}{4533}\right)\)	\(e\left(\frac{1058}{1511}\right)\)
\(\chi_{9067}(26,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{849}{1511}\right)\)	\(e\left(\frac{3898}{4533}\right)\)	\(e\left(\frac{187}{1511}\right)\)	\(e\left(\frac{2257}{4533}\right)\)	\(e\left(\frac{1912}{4533}\right)\)	\(e\left(\frac{1225}{1511}\right)\)	\(e\left(\frac{1036}{1511}\right)\)	\(e\left(\frac{3263}{4533}\right)\)	\(e\left(\frac{271}{4533}\right)\)	\(e\left(\frac{627}{1511}\right)\)
\(\chi_{9067}(27,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{2761}{3022}\right)\)	\(e\left(\frac{1}{3022}\right)\)	\(e\left(\frac{1250}{1511}\right)\)	\(e\left(\frac{25}{3022}\right)\)	\(e\left(\frac{1381}{1511}\right)\)	\(e\left(\frac{1065}{3022}\right)\)	\(e\left(\frac{2239}{3022}\right)\)	\(e\left(\frac{1}{1511}\right)\)	\(e\left(\frac{1393}{1511}\right)\)	\(e\left(\frac{2605}{3022}\right)\)
\(\chi_{9067}(28,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{1111}{3022}\right)\)	\(e\left(\frac{181}{3022}\right)\)	\(e\left(\frac{1111}{1511}\right)\)	\(e\left(\frac{1503}{3022}\right)\)	\(e\left(\frac{646}{1511}\right)\)	\(e\left(\frac{2379}{3022}\right)\)	\(e\left(\frac{311}{3022}\right)\)	\(e\left(\frac{181}{1511}\right)\)	\(e\left(\frac{1307}{1511}\right)\)	\(e\left(\frac{73}{3022}\right)\)
\(\chi_{9067}(29,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{971}{3022}\right)\)	\(e\left(\frac{4435}{9066}\right)\)	\(e\left(\frac{971}{1511}\right)\)	\(e\left(\frac{2083}{9066}\right)\)	\(e\left(\frac{3674}{4533}\right)\)	\(e\left(\frac{2985}{3022}\right)\)	\(e\left(\frac{2913}{3022}\right)\)	\(e\left(\frac{4435}{4533}\right)\)	\(e\left(\frac{2498}{4533}\right)\)	\(e\left(\frac{23}{3022}\right)\)
\(\chi_{9067}(30,\cdot)\)	9067.h	9066	yes	\(-1\)	\(1\)	\(e\left(\frac{2313}{3022}\right)\)	\(e\left(\frac{8831}{9066}\right)\)	\(e\left(\frac{802}{1511}\right)\)	\(e\left(\frac{3191}{9066}\right)\)	\(e\left(\frac{3352}{4533}\right)\)	\(e\left(\frac{1191}{3022}\right)\)	\(e\left(\frac{895}{3022}\right)\)	\(e\left(\frac{4298}{4533}\right)\)	\(e\left(\frac{532}{4533}\right)\)	\(e\left(\frac{2445}{3022}\right)\)
\(\chi_{9067}(31,\cdot)\)	9067.g	4533	yes	\(1\)	\(1\)	\(e\left(\frac{1102}{1511}\right)\)	\(e\left(\frac{491}{4533}\right)\)	\(e\left(\frac{693}{1511}\right)\)	\(e\left(\frac{3209}{4533}\right)\)	\(e\left(\frac{3797}{4533}\right)\)	\(e\left(\frac{540}{1511}\right)\)	\(e\left(\frac{284}{1511}\right)\)	\(e\left(\frac{982}{4533}\right)\)	\(e\left(\frac{1982}{4533}\right)\)	\(e\left(\frac{1257}{1511}\right)\)
\(\chi_{9067}(32,\cdot)\)	9067.f	3022	yes	\(-1\)	\(1\)	\(e\left(\frac{1721}{3022}\right)\)	\(e\left(\frac{2587}{3022}\right)\)	\(e\left(\frac{210}{1511}\right)\)	\(e\left(\frac{1213}{3022}\right)\)	\(e\left(\frac{643}{1511}\right)\)	\(e\left(\frac{2113}{3022}\right)\)	\(e\left(\frac{2141}{3022}\right)\)	\(e\left(\frac{1076}{1511}\right)\)	\(e\left(\frac{1467}{1511}\right)\)	\(e\left(\frac{75}{3022}\right)\)

Introduction

L-functions

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Properties

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Character group

First 32 of 9066 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.