LMFDB - Group of Dirichlet characters of modulus 8006

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8006)

pari: g = idealstar(,8006,2)

Character group

sage: G.order() pari: g.no
Order	=	4002
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4002}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8006}(4005,\cdot)$

First 32 of 4002 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8006}(1,\cdot)$	8006.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8006}(3,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{2971}{4002}\right)$	$e\left(\frac{1631}{4002}\right)$	$e\left(\frac{1651}{2001}\right)$	$e\left(\frac{970}{2001}\right)$	$e\left(\frac{171}{667}\right)$	$e\left(\frac{474}{667}\right)$	$e\left(\frac{100}{667}\right)$	$e\left(\frac{344}{667}\right)$	$e\left(\frac{1264}{2001}\right)$	$e\left(\frac{757}{1334}\right)$
$\chi_{8006}(5,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{1631}{4002}\right)$	$e\left(\frac{2761}{4002}\right)$	$e\left(\frac{773}{2001}\right)$	$e\left(\frac{1631}{2001}\right)$	$e\left(\frac{478}{667}\right)$	$e\left(\frac{108}{667}\right)$	$e\left(\frac{65}{667}\right)$	$e\left(\frac{357}{667}\right)$	$e\left(\frac{1622}{2001}\right)$	$e\left(\frac{1059}{1334}\right)$
$\chi_{8006}(7,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1651}{2001}\right)$	$e\left(\frac{773}{2001}\right)$	$e\left(\frac{1841}{2001}\right)$	$e\left(\frac{1301}{2001}\right)$	$e\left(\frac{21}{667}\right)$	$e\left(\frac{655}{667}\right)$	$e\left(\frac{141}{667}\right)$	$e\left(\frac{405}{667}\right)$	$e\left(\frac{635}{2001}\right)$	$e\left(\frac{497}{667}\right)$
$\chi_{8006}(9,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{970}{2001}\right)$	$e\left(\frac{1631}{2001}\right)$	$e\left(\frac{1301}{2001}\right)$	$e\left(\frac{1940}{2001}\right)$	$e\left(\frac{342}{667}\right)$	$e\left(\frac{281}{667}\right)$	$e\left(\frac{200}{667}\right)$	$e\left(\frac{21}{667}\right)$	$e\left(\frac{527}{2001}\right)$	$e\left(\frac{90}{667}\right)$
$\chi_{8006}(11,\cdot)$	8006.m	667	no	$1$	$1$	$e\left(\frac{171}{667}\right)$	$e\left(\frac{478}{667}\right)$	$e\left(\frac{21}{667}\right)$	$e\left(\frac{342}{667}\right)$	$e\left(\frac{196}{667}\right)$	$e\left(\frac{555}{667}\right)$	$e\left(\frac{649}{667}\right)$	$e\left(\frac{445}{667}\right)$	$e\left(\frac{271}{667}\right)$	$e\left(\frac{192}{667}\right)$
$\chi_{8006}(13,\cdot)$	8006.m	667	no	$1$	$1$	$e\left(\frac{474}{667}\right)$	$e\left(\frac{108}{667}\right)$	$e\left(\frac{655}{667}\right)$	$e\left(\frac{281}{667}\right)$	$e\left(\frac{555}{667}\right)$	$e\left(\frac{64}{667}\right)$	$e\left(\frac{582}{667}\right)$	$e\left(\frac{508}{667}\right)$	$e\left(\frac{131}{667}\right)$	$e\left(\frac{462}{667}\right)$
$\chi_{8006}(15,\cdot)$	8006.m	667	no	$1$	$1$	$e\left(\frac{100}{667}\right)$	$e\left(\frac{65}{667}\right)$	$e\left(\frac{141}{667}\right)$	$e\left(\frac{200}{667}\right)$	$e\left(\frac{649}{667}\right)$	$e\left(\frac{582}{667}\right)$	$e\left(\frac{165}{667}\right)$	$e\left(\frac{34}{667}\right)$	$e\left(\frac{295}{667}\right)$	$e\left(\frac{241}{667}\right)$
$\chi_{8006}(17,\cdot)$	8006.m	667	no	$1$	$1$	$e\left(\frac{344}{667}\right)$	$e\left(\frac{357}{667}\right)$	$e\left(\frac{405}{667}\right)$	$e\left(\frac{21}{667}\right)$	$e\left(\frac{445}{667}\right)$	$e\left(\frac{508}{667}\right)$	$e\left(\frac{34}{667}\right)$	$e\left(\frac{197}{667}\right)$	$e\left(\frac{81}{667}\right)$	$e\left(\frac{82}{667}\right)$
$\chi_{8006}(19,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1264}{2001}\right)$	$e\left(\frac{1622}{2001}\right)$	$e\left(\frac{635}{2001}\right)$	$e\left(\frac{527}{2001}\right)$	$e\left(\frac{271}{667}\right)$	$e\left(\frac{131}{667}\right)$	$e\left(\frac{295}{667}\right)$	$e\left(\frac{81}{667}\right)$	$e\left(\frac{794}{2001}\right)$	$e\left(\frac{633}{667}\right)$
$\chi_{8006}(21,\cdot)$	8006.n	1334	no	$-1$	$1$	$e\left(\frac{757}{1334}\right)$	$e\left(\frac{1059}{1334}\right)$	$e\left(\frac{497}{667}\right)$	$e\left(\frac{90}{667}\right)$	$e\left(\frac{192}{667}\right)$	$e\left(\frac{462}{667}\right)$	$e\left(\frac{241}{667}\right)$	$e\left(\frac{82}{667}\right)$	$e\left(\frac{633}{667}\right)$	$e\left(\frac{417}{1334}\right)$
$\chi_{8006}(23,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{881}{4002}\right)$	$e\left(\frac{1273}{4002}\right)$	$e\left(\frac{1745}{2001}\right)$	$e\left(\frac{881}{2001}\right)$	$e\left(\frac{167}{667}\right)$	$e\left(\frac{381}{667}\right)$	$e\left(\frac{359}{667}\right)$	$e\left(\frac{648}{667}\right)$	$e\left(\frac{1016}{2001}\right)$	$e\left(\frac{123}{1334}\right)$
$\chi_{8006}(25,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1631}{2001}\right)$	$e\left(\frac{760}{2001}\right)$	$e\left(\frac{1546}{2001}\right)$	$e\left(\frac{1261}{2001}\right)$	$e\left(\frac{289}{667}\right)$	$e\left(\frac{216}{667}\right)$	$e\left(\frac{130}{667}\right)$	$e\left(\frac{47}{667}\right)$	$e\left(\frac{1243}{2001}\right)$	$e\left(\frac{392}{667}\right)$
$\chi_{8006}(27,\cdot)$	8006.n	1334	no	$-1$	$1$	$e\left(\frac{303}{1334}\right)$	$e\left(\frac{297}{1334}\right)$	$e\left(\frac{317}{667}\right)$	$e\left(\frac{303}{667}\right)$	$e\left(\frac{513}{667}\right)$	$e\left(\frac{88}{667}\right)$	$e\left(\frac{300}{667}\right)$	$e\left(\frac{365}{667}\right)$	$e\left(\frac{597}{667}\right)$	$e\left(\frac{937}{1334}\right)$
$\chi_{8006}(29,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1868}{2001}\right)$	$e\left(\frac{814}{2001}\right)$	$e\left(\frac{1540}{2001}\right)$	$e\left(\frac{1735}{2001}\right)$	$e\left(\frac{48}{667}\right)$	$e\left(\frac{449}{667}\right)$	$e\left(\frac{227}{667}\right)$	$e\left(\frac{354}{667}\right)$	$e\left(\frac{1642}{2001}\right)$	$e\left(\frac{469}{667}\right)$
$\chi_{8006}(31,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{2021}{4002}\right)$	$e\left(\frac{13}{4002}\right)$	$e\left(\frac{1148}{2001}\right)$	$e\left(\frac{20}{2001}\right)$	$e\left(\frac{533}{667}\right)$	$e\left(\frac{553}{667}\right)$	$e\left(\frac{339}{667}\right)$	$e\left(\frac{179}{667}\right)$	$e\left(\frac{1697}{2001}\right)$	$e\left(\frac{105}{1334}\right)$
$\chi_{8006}(33,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{3997}{4002}\right)$	$e\left(\frac{497}{4002}\right)$	$e\left(\frac{1714}{2001}\right)$	$e\left(\frac{1996}{2001}\right)$	$e\left(\frac{367}{667}\right)$	$e\left(\frac{362}{667}\right)$	$e\left(\frac{82}{667}\right)$	$e\left(\frac{122}{667}\right)$	$e\left(\frac{76}{2001}\right)$	$e\left(\frac{1141}{1334}\right)$
$\chi_{8006}(35,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{931}{4002}\right)$	$e\left(\frac{305}{4002}\right)$	$e\left(\frac{613}{2001}\right)$	$e\left(\frac{931}{2001}\right)$	$e\left(\frac{499}{667}\right)$	$e\left(\frac{96}{667}\right)$	$e\left(\frac{206}{667}\right)$	$e\left(\frac{95}{667}\right)$	$e\left(\frac{256}{2001}\right)$	$e\left(\frac{719}{1334}\right)$
$\chi_{8006}(37,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1781}{2001}\right)$	$e\left(\frac{1858}{2001}\right)$	$e\left(\frac{757}{2001}\right)$	$e\left(\frac{1561}{2001}\right)$	$e\left(\frac{280}{667}\right)$	$e\left(\frac{507}{667}\right)$	$e\left(\frac{546}{667}\right)$	$e\left(\frac{64}{667}\right)$	$e\left(\frac{685}{2001}\right)$	$e\left(\frac{179}{667}\right)$
$\chi_{8006}(39,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{1813}{4002}\right)$	$e\left(\frac{2279}{4002}\right)$	$e\left(\frac{1615}{2001}\right)$	$e\left(\frac{1813}{2001}\right)$	$e\left(\frac{59}{667}\right)$	$e\left(\frac{538}{667}\right)$	$e\left(\frac{15}{667}\right)$	$e\left(\frac{185}{667}\right)$	$e\left(\frac{1657}{2001}\right)$	$e\left(\frac{347}{1334}\right)$
$\chi_{8006}(41,\cdot)$	8006.n	1334	no	$-1$	$1$	$e\left(\frac{1195}{1334}\right)$	$e\left(\frac{1277}{1334}\right)$	$e\left(\frac{559}{667}\right)$	$e\left(\frac{528}{667}\right)$	$e\left(\frac{326}{667}\right)$	$e\left(\frac{576}{667}\right)$	$e\left(\frac{569}{667}\right)$	$e\left(\frac{570}{667}\right)$	$e\left(\frac{512}{667}\right)$	$e\left(\frac{979}{1334}\right)$
$\chi_{8006}(43,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{1843}{4002}\right)$	$e\left(\frac{3299}{4002}\right)$	$e\left(\frac{1336}{2001}\right)$	$e\left(\frac{1843}{2001}\right)$	$e\left(\frac{525}{667}\right)$	$e\left(\frac{367}{667}\right)$	$e\left(\frac{190}{667}\right)$	$e\left(\frac{120}{667}\right)$	$e\left(\frac{1201}{2001}\right)$	$e\left(\frac{171}{1334}\right)$
$\chi_{8006}(45,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{3571}{4002}\right)$	$e\left(\frac{2021}{4002}\right)$	$e\left(\frac{73}{2001}\right)$	$e\left(\frac{1570}{2001}\right)$	$e\left(\frac{153}{667}\right)$	$e\left(\frac{389}{667}\right)$	$e\left(\frac{265}{667}\right)$	$e\left(\frac{378}{667}\right)$	$e\left(\frac{148}{2001}\right)$	$e\left(\frac{1239}{1334}\right)$
$\chi_{8006}(47,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{1555}{4002}\right)$	$e\left(\frac{1511}{4002}\right)$	$e\left(\frac{1213}{2001}\right)$	$e\left(\frac{1555}{2001}\right)$	$e\left(\frac{587}{667}\right)$	$e\left(\frac{141}{667}\right)$	$e\left(\frac{511}{667}\right)$	$e\left(\frac{77}{667}\right)$	$e\left(\frac{376}{2001}\right)$	$e\left(\frac{1327}{1334}\right)$
$\chi_{8006}(49,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1301}{2001}\right)$	$e\left(\frac{1546}{2001}\right)$	$e\left(\frac{1681}{2001}\right)$	$e\left(\frac{601}{2001}\right)$	$e\left(\frac{42}{667}\right)$	$e\left(\frac{643}{667}\right)$	$e\left(\frac{282}{667}\right)$	$e\left(\frac{143}{667}\right)$	$e\left(\frac{1270}{2001}\right)$	$e\left(\frac{327}{667}\right)$
$\chi_{8006}(51,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{1033}{4002}\right)$	$e\left(\frac{3773}{4002}\right)$	$e\left(\frac{865}{2001}\right)$	$e\left(\frac{1033}{2001}\right)$	$e\left(\frac{616}{667}\right)$	$e\left(\frac{315}{667}\right)$	$e\left(\frac{134}{667}\right)$	$e\left(\frac{541}{667}\right)$	$e\left(\frac{1507}{2001}\right)$	$e\left(\frac{921}{1334}\right)$
$\chi_{8006}(53,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1952}{2001}\right)$	$e\left(\frac{1669}{2001}\right)$	$e\left(\frac{778}{2001}\right)$	$e\left(\frac{1903}{2001}\right)$	$e\left(\frac{123}{667}\right)$	$e\left(\frac{25}{667}\right)$	$e\left(\frac{540}{667}\right)$	$e\left(\frac{657}{667}\right)$	$e\left(\frac{289}{2001}\right)$	$e\left(\frac{243}{667}\right)$
$\chi_{8006}(55,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{2657}{4002}\right)$	$e\left(\frac{1627}{4002}\right)$	$e\left(\frac{836}{2001}\right)$	$e\left(\frac{656}{2001}\right)$	$e\left(\frac{7}{667}\right)$	$e\left(\frac{663}{667}\right)$	$e\left(\frac{47}{667}\right)$	$e\left(\frac{135}{667}\right)$	$e\left(\frac{434}{2001}\right)$	$e\left(\frac{109}{1334}\right)$
$\chi_{8006}(57,\cdot)$	8006.n	1334	no	$-1$	$1$	$e\left(\frac{499}{1334}\right)$	$e\left(\frac{291}{1334}\right)$	$e\left(\frac{95}{667}\right)$	$e\left(\frac{499}{667}\right)$	$e\left(\frac{442}{667}\right)$	$e\left(\frac{605}{667}\right)$	$e\left(\frac{395}{667}\right)$	$e\left(\frac{425}{667}\right)$	$e\left(\frac{19}{667}\right)$	$e\left(\frac{689}{1334}\right)$
$\chi_{8006}(59,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{1523}{2001}\right)$	$e\left(\frac{1090}{2001}\right)$	$e\left(\frac{1954}{2001}\right)$	$e\left(\frac{1045}{2001}\right)$	$e\left(\frac{2}{667}\right)$	$e\left(\frac{380}{667}\right)$	$e\left(\frac{204}{667}\right)$	$e\left(\frac{515}{667}\right)$	$e\left(\frac{124}{2001}\right)$	$e\left(\frac{492}{667}\right)$
$\chi_{8006}(61,\cdot)$	8006.p	4002	no	$-1$	$1$	$e\left(\frac{2471}{4002}\right)$	$e\left(\frac{3307}{4002}\right)$	$e\left(\frac{965}{2001}\right)$	$e\left(\frac{470}{2001}\right)$	$e\left(\frac{186}{667}\right)$	$e\left(\frac{656}{667}\right)$	$e\left(\frac{296}{667}\right)$	$e\left(\frac{538}{667}\right)$	$e\left(\frac{860}{2001}\right)$	$e\left(\frac{133}{1334}\right)$
$\chi_{8006}(63,\cdot)$	8006.o	2001	no	$1$	$1$	$e\left(\frac{620}{2001}\right)$	$e\left(\frac{403}{2001}\right)$	$e\left(\frac{1141}{2001}\right)$	$e\left(\frac{1240}{2001}\right)$	$e\left(\frac{363}{667}\right)$	$e\left(\frac{269}{667}\right)$	$e\left(\frac{341}{667}\right)$	$e\left(\frac{426}{667}\right)$	$e\left(\frac{1162}{2001}\right)$	$e\left(\frac{587}{667}\right)$

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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	$8006$
Structure	\(C_{4002}\)
Order	$4002$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8006}(1,\cdot)\)	8006.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8006}(3,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{2971}{4002}\right)\)	\(e\left(\frac{1631}{4002}\right)\)	\(e\left(\frac{1651}{2001}\right)\)	\(e\left(\frac{970}{2001}\right)\)	\(e\left(\frac{171}{667}\right)\)	\(e\left(\frac{474}{667}\right)\)	\(e\left(\frac{100}{667}\right)\)	\(e\left(\frac{344}{667}\right)\)	\(e\left(\frac{1264}{2001}\right)\)	\(e\left(\frac{757}{1334}\right)\)
\(\chi_{8006}(5,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{1631}{4002}\right)\)	\(e\left(\frac{2761}{4002}\right)\)	\(e\left(\frac{773}{2001}\right)\)	\(e\left(\frac{1631}{2001}\right)\)	\(e\left(\frac{478}{667}\right)\)	\(e\left(\frac{108}{667}\right)\)	\(e\left(\frac{65}{667}\right)\)	\(e\left(\frac{357}{667}\right)\)	\(e\left(\frac{1622}{2001}\right)\)	\(e\left(\frac{1059}{1334}\right)\)
\(\chi_{8006}(7,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1651}{2001}\right)\)	\(e\left(\frac{773}{2001}\right)\)	\(e\left(\frac{1841}{2001}\right)\)	\(e\left(\frac{1301}{2001}\right)\)	\(e\left(\frac{21}{667}\right)\)	\(e\left(\frac{655}{667}\right)\)	\(e\left(\frac{141}{667}\right)\)	\(e\left(\frac{405}{667}\right)\)	\(e\left(\frac{635}{2001}\right)\)	\(e\left(\frac{497}{667}\right)\)
\(\chi_{8006}(9,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{970}{2001}\right)\)	\(e\left(\frac{1631}{2001}\right)\)	\(e\left(\frac{1301}{2001}\right)\)	\(e\left(\frac{1940}{2001}\right)\)	\(e\left(\frac{342}{667}\right)\)	\(e\left(\frac{281}{667}\right)\)	\(e\left(\frac{200}{667}\right)\)	\(e\left(\frac{21}{667}\right)\)	\(e\left(\frac{527}{2001}\right)\)	\(e\left(\frac{90}{667}\right)\)
\(\chi_{8006}(11,\cdot)\)	8006.m	667	no	\(1\)	\(1\)	\(e\left(\frac{171}{667}\right)\)	\(e\left(\frac{478}{667}\right)\)	\(e\left(\frac{21}{667}\right)\)	\(e\left(\frac{342}{667}\right)\)	\(e\left(\frac{196}{667}\right)\)	\(e\left(\frac{555}{667}\right)\)	\(e\left(\frac{649}{667}\right)\)	\(e\left(\frac{445}{667}\right)\)	\(e\left(\frac{271}{667}\right)\)	\(e\left(\frac{192}{667}\right)\)
\(\chi_{8006}(13,\cdot)\)	8006.m	667	no	\(1\)	\(1\)	\(e\left(\frac{474}{667}\right)\)	\(e\left(\frac{108}{667}\right)\)	\(e\left(\frac{655}{667}\right)\)	\(e\left(\frac{281}{667}\right)\)	\(e\left(\frac{555}{667}\right)\)	\(e\left(\frac{64}{667}\right)\)	\(e\left(\frac{582}{667}\right)\)	\(e\left(\frac{508}{667}\right)\)	\(e\left(\frac{131}{667}\right)\)	\(e\left(\frac{462}{667}\right)\)
\(\chi_{8006}(15,\cdot)\)	8006.m	667	no	\(1\)	\(1\)	\(e\left(\frac{100}{667}\right)\)	\(e\left(\frac{65}{667}\right)\)	\(e\left(\frac{141}{667}\right)\)	\(e\left(\frac{200}{667}\right)\)	\(e\left(\frac{649}{667}\right)\)	\(e\left(\frac{582}{667}\right)\)	\(e\left(\frac{165}{667}\right)\)	\(e\left(\frac{34}{667}\right)\)	\(e\left(\frac{295}{667}\right)\)	\(e\left(\frac{241}{667}\right)\)
\(\chi_{8006}(17,\cdot)\)	8006.m	667	no	\(1\)	\(1\)	\(e\left(\frac{344}{667}\right)\)	\(e\left(\frac{357}{667}\right)\)	\(e\left(\frac{405}{667}\right)\)	\(e\left(\frac{21}{667}\right)\)	\(e\left(\frac{445}{667}\right)\)	\(e\left(\frac{508}{667}\right)\)	\(e\left(\frac{34}{667}\right)\)	\(e\left(\frac{197}{667}\right)\)	\(e\left(\frac{81}{667}\right)\)	\(e\left(\frac{82}{667}\right)\)
\(\chi_{8006}(19,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1264}{2001}\right)\)	\(e\left(\frac{1622}{2001}\right)\)	\(e\left(\frac{635}{2001}\right)\)	\(e\left(\frac{527}{2001}\right)\)	\(e\left(\frac{271}{667}\right)\)	\(e\left(\frac{131}{667}\right)\)	\(e\left(\frac{295}{667}\right)\)	\(e\left(\frac{81}{667}\right)\)	\(e\left(\frac{794}{2001}\right)\)	\(e\left(\frac{633}{667}\right)\)
\(\chi_{8006}(21,\cdot)\)	8006.n	1334	no	\(-1\)	\(1\)	\(e\left(\frac{757}{1334}\right)\)	\(e\left(\frac{1059}{1334}\right)\)	\(e\left(\frac{497}{667}\right)\)	\(e\left(\frac{90}{667}\right)\)	\(e\left(\frac{192}{667}\right)\)	\(e\left(\frac{462}{667}\right)\)	\(e\left(\frac{241}{667}\right)\)	\(e\left(\frac{82}{667}\right)\)	\(e\left(\frac{633}{667}\right)\)	\(e\left(\frac{417}{1334}\right)\)
\(\chi_{8006}(23,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{881}{4002}\right)\)	\(e\left(\frac{1273}{4002}\right)\)	\(e\left(\frac{1745}{2001}\right)\)	\(e\left(\frac{881}{2001}\right)\)	\(e\left(\frac{167}{667}\right)\)	\(e\left(\frac{381}{667}\right)\)	\(e\left(\frac{359}{667}\right)\)	\(e\left(\frac{648}{667}\right)\)	\(e\left(\frac{1016}{2001}\right)\)	\(e\left(\frac{123}{1334}\right)\)
\(\chi_{8006}(25,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1631}{2001}\right)\)	\(e\left(\frac{760}{2001}\right)\)	\(e\left(\frac{1546}{2001}\right)\)	\(e\left(\frac{1261}{2001}\right)\)	\(e\left(\frac{289}{667}\right)\)	\(e\left(\frac{216}{667}\right)\)	\(e\left(\frac{130}{667}\right)\)	\(e\left(\frac{47}{667}\right)\)	\(e\left(\frac{1243}{2001}\right)\)	\(e\left(\frac{392}{667}\right)\)
\(\chi_{8006}(27,\cdot)\)	8006.n	1334	no	\(-1\)	\(1\)	\(e\left(\frac{303}{1334}\right)\)	\(e\left(\frac{297}{1334}\right)\)	\(e\left(\frac{317}{667}\right)\)	\(e\left(\frac{303}{667}\right)\)	\(e\left(\frac{513}{667}\right)\)	\(e\left(\frac{88}{667}\right)\)	\(e\left(\frac{300}{667}\right)\)	\(e\left(\frac{365}{667}\right)\)	\(e\left(\frac{597}{667}\right)\)	\(e\left(\frac{937}{1334}\right)\)
\(\chi_{8006}(29,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1868}{2001}\right)\)	\(e\left(\frac{814}{2001}\right)\)	\(e\left(\frac{1540}{2001}\right)\)	\(e\left(\frac{1735}{2001}\right)\)	\(e\left(\frac{48}{667}\right)\)	\(e\left(\frac{449}{667}\right)\)	\(e\left(\frac{227}{667}\right)\)	\(e\left(\frac{354}{667}\right)\)	\(e\left(\frac{1642}{2001}\right)\)	\(e\left(\frac{469}{667}\right)\)
\(\chi_{8006}(31,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{2021}{4002}\right)\)	\(e\left(\frac{13}{4002}\right)\)	\(e\left(\frac{1148}{2001}\right)\)	\(e\left(\frac{20}{2001}\right)\)	\(e\left(\frac{533}{667}\right)\)	\(e\left(\frac{553}{667}\right)\)	\(e\left(\frac{339}{667}\right)\)	\(e\left(\frac{179}{667}\right)\)	\(e\left(\frac{1697}{2001}\right)\)	\(e\left(\frac{105}{1334}\right)\)
\(\chi_{8006}(33,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{3997}{4002}\right)\)	\(e\left(\frac{497}{4002}\right)\)	\(e\left(\frac{1714}{2001}\right)\)	\(e\left(\frac{1996}{2001}\right)\)	\(e\left(\frac{367}{667}\right)\)	\(e\left(\frac{362}{667}\right)\)	\(e\left(\frac{82}{667}\right)\)	\(e\left(\frac{122}{667}\right)\)	\(e\left(\frac{76}{2001}\right)\)	\(e\left(\frac{1141}{1334}\right)\)
\(\chi_{8006}(35,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{931}{4002}\right)\)	\(e\left(\frac{305}{4002}\right)\)	\(e\left(\frac{613}{2001}\right)\)	\(e\left(\frac{931}{2001}\right)\)	\(e\left(\frac{499}{667}\right)\)	\(e\left(\frac{96}{667}\right)\)	\(e\left(\frac{206}{667}\right)\)	\(e\left(\frac{95}{667}\right)\)	\(e\left(\frac{256}{2001}\right)\)	\(e\left(\frac{719}{1334}\right)\)
\(\chi_{8006}(37,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1781}{2001}\right)\)	\(e\left(\frac{1858}{2001}\right)\)	\(e\left(\frac{757}{2001}\right)\)	\(e\left(\frac{1561}{2001}\right)\)	\(e\left(\frac{280}{667}\right)\)	\(e\left(\frac{507}{667}\right)\)	\(e\left(\frac{546}{667}\right)\)	\(e\left(\frac{64}{667}\right)\)	\(e\left(\frac{685}{2001}\right)\)	\(e\left(\frac{179}{667}\right)\)
\(\chi_{8006}(39,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{1813}{4002}\right)\)	\(e\left(\frac{2279}{4002}\right)\)	\(e\left(\frac{1615}{2001}\right)\)	\(e\left(\frac{1813}{2001}\right)\)	\(e\left(\frac{59}{667}\right)\)	\(e\left(\frac{538}{667}\right)\)	\(e\left(\frac{15}{667}\right)\)	\(e\left(\frac{185}{667}\right)\)	\(e\left(\frac{1657}{2001}\right)\)	\(e\left(\frac{347}{1334}\right)\)
\(\chi_{8006}(41,\cdot)\)	8006.n	1334	no	\(-1\)	\(1\)	\(e\left(\frac{1195}{1334}\right)\)	\(e\left(\frac{1277}{1334}\right)\)	\(e\left(\frac{559}{667}\right)\)	\(e\left(\frac{528}{667}\right)\)	\(e\left(\frac{326}{667}\right)\)	\(e\left(\frac{576}{667}\right)\)	\(e\left(\frac{569}{667}\right)\)	\(e\left(\frac{570}{667}\right)\)	\(e\left(\frac{512}{667}\right)\)	\(e\left(\frac{979}{1334}\right)\)
\(\chi_{8006}(43,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{1843}{4002}\right)\)	\(e\left(\frac{3299}{4002}\right)\)	\(e\left(\frac{1336}{2001}\right)\)	\(e\left(\frac{1843}{2001}\right)\)	\(e\left(\frac{525}{667}\right)\)	\(e\left(\frac{367}{667}\right)\)	\(e\left(\frac{190}{667}\right)\)	\(e\left(\frac{120}{667}\right)\)	\(e\left(\frac{1201}{2001}\right)\)	\(e\left(\frac{171}{1334}\right)\)
\(\chi_{8006}(45,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{3571}{4002}\right)\)	\(e\left(\frac{2021}{4002}\right)\)	\(e\left(\frac{73}{2001}\right)\)	\(e\left(\frac{1570}{2001}\right)\)	\(e\left(\frac{153}{667}\right)\)	\(e\left(\frac{389}{667}\right)\)	\(e\left(\frac{265}{667}\right)\)	\(e\left(\frac{378}{667}\right)\)	\(e\left(\frac{148}{2001}\right)\)	\(e\left(\frac{1239}{1334}\right)\)
\(\chi_{8006}(47,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{1555}{4002}\right)\)	\(e\left(\frac{1511}{4002}\right)\)	\(e\left(\frac{1213}{2001}\right)\)	\(e\left(\frac{1555}{2001}\right)\)	\(e\left(\frac{587}{667}\right)\)	\(e\left(\frac{141}{667}\right)\)	\(e\left(\frac{511}{667}\right)\)	\(e\left(\frac{77}{667}\right)\)	\(e\left(\frac{376}{2001}\right)\)	\(e\left(\frac{1327}{1334}\right)\)
\(\chi_{8006}(49,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1301}{2001}\right)\)	\(e\left(\frac{1546}{2001}\right)\)	\(e\left(\frac{1681}{2001}\right)\)	\(e\left(\frac{601}{2001}\right)\)	\(e\left(\frac{42}{667}\right)\)	\(e\left(\frac{643}{667}\right)\)	\(e\left(\frac{282}{667}\right)\)	\(e\left(\frac{143}{667}\right)\)	\(e\left(\frac{1270}{2001}\right)\)	\(e\left(\frac{327}{667}\right)\)
\(\chi_{8006}(51,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{1033}{4002}\right)\)	\(e\left(\frac{3773}{4002}\right)\)	\(e\left(\frac{865}{2001}\right)\)	\(e\left(\frac{1033}{2001}\right)\)	\(e\left(\frac{616}{667}\right)\)	\(e\left(\frac{315}{667}\right)\)	\(e\left(\frac{134}{667}\right)\)	\(e\left(\frac{541}{667}\right)\)	\(e\left(\frac{1507}{2001}\right)\)	\(e\left(\frac{921}{1334}\right)\)
\(\chi_{8006}(53,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1952}{2001}\right)\)	\(e\left(\frac{1669}{2001}\right)\)	\(e\left(\frac{778}{2001}\right)\)	\(e\left(\frac{1903}{2001}\right)\)	\(e\left(\frac{123}{667}\right)\)	\(e\left(\frac{25}{667}\right)\)	\(e\left(\frac{540}{667}\right)\)	\(e\left(\frac{657}{667}\right)\)	\(e\left(\frac{289}{2001}\right)\)	\(e\left(\frac{243}{667}\right)\)
\(\chi_{8006}(55,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{2657}{4002}\right)\)	\(e\left(\frac{1627}{4002}\right)\)	\(e\left(\frac{836}{2001}\right)\)	\(e\left(\frac{656}{2001}\right)\)	\(e\left(\frac{7}{667}\right)\)	\(e\left(\frac{663}{667}\right)\)	\(e\left(\frac{47}{667}\right)\)	\(e\left(\frac{135}{667}\right)\)	\(e\left(\frac{434}{2001}\right)\)	\(e\left(\frac{109}{1334}\right)\)
\(\chi_{8006}(57,\cdot)\)	8006.n	1334	no	\(-1\)	\(1\)	\(e\left(\frac{499}{1334}\right)\)	\(e\left(\frac{291}{1334}\right)\)	\(e\left(\frac{95}{667}\right)\)	\(e\left(\frac{499}{667}\right)\)	\(e\left(\frac{442}{667}\right)\)	\(e\left(\frac{605}{667}\right)\)	\(e\left(\frac{395}{667}\right)\)	\(e\left(\frac{425}{667}\right)\)	\(e\left(\frac{19}{667}\right)\)	\(e\left(\frac{689}{1334}\right)\)
\(\chi_{8006}(59,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{1523}{2001}\right)\)	\(e\left(\frac{1090}{2001}\right)\)	\(e\left(\frac{1954}{2001}\right)\)	\(e\left(\frac{1045}{2001}\right)\)	\(e\left(\frac{2}{667}\right)\)	\(e\left(\frac{380}{667}\right)\)	\(e\left(\frac{204}{667}\right)\)	\(e\left(\frac{515}{667}\right)\)	\(e\left(\frac{124}{2001}\right)\)	\(e\left(\frac{492}{667}\right)\)
\(\chi_{8006}(61,\cdot)\)	8006.p	4002	no	\(-1\)	\(1\)	\(e\left(\frac{2471}{4002}\right)\)	\(e\left(\frac{3307}{4002}\right)\)	\(e\left(\frac{965}{2001}\right)\)	\(e\left(\frac{470}{2001}\right)\)	\(e\left(\frac{186}{667}\right)\)	\(e\left(\frac{656}{667}\right)\)	\(e\left(\frac{296}{667}\right)\)	\(e\left(\frac{538}{667}\right)\)	\(e\left(\frac{860}{2001}\right)\)	\(e\left(\frac{133}{1334}\right)\)
\(\chi_{8006}(63,\cdot)\)	8006.o	2001	no	\(1\)	\(1\)	\(e\left(\frac{620}{2001}\right)\)	\(e\left(\frac{403}{2001}\right)\)	\(e\left(\frac{1141}{2001}\right)\)	\(e\left(\frac{1240}{2001}\right)\)	\(e\left(\frac{363}{667}\right)\)	\(e\left(\frac{269}{667}\right)\)	\(e\left(\frac{341}{667}\right)\)	\(e\left(\frac{426}{667}\right)\)	\(e\left(\frac{1162}{2001}\right)\)	\(e\left(\frac{587}{667}\right)\)

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L-functions

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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.