LMFDB - Group of Dirichlet characters of modulus 8009

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8009)

pari: g = idealstar(,8009,2)

Character group

sage: G.order() pari: g.no
Order	=	8008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{8008}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8009}(3,\cdot)$

First 32 of 8008 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{8009}(1,\cdot)$	8009.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8009}(2,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{771}{2002}\right)$	$e\left(\frac{2507}{4004}\right)$	$e\left(\frac{771}{1001}\right)$	$e\left(\frac{151}{154}\right)$	$e\left(\frac{45}{4004}\right)$	$e\left(\frac{642}{1001}\right)$	$e\left(\frac{311}{2002}\right)$	$e\left(\frac{505}{2002}\right)$	$e\left(\frac{366}{1001}\right)$	$e\left(\frac{1219}{2002}\right)$
$\chi_{8009}(3,\cdot)$	8009.bf	8008	yes	$-1$	$1$	$e\left(\frac{2507}{4004}\right)$	$e\left(\frac{1}{8008}\right)$	$e\left(\frac{505}{2002}\right)$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{5015}{8008}\right)$	$e\left(\frac{405}{1001}\right)$	$e\left(\frac{3517}{4004}\right)$	$e\left(\frac{1}{4004}\right)$	$e\left(\frac{415}{2002}\right)$	$e\left(\frac{827}{4004}\right)$
$\chi_{8009}(4,\cdot)$	8009.bd	2002	yes	$1$	$1$	$e\left(\frac{771}{1001}\right)$	$e\left(\frac{505}{2002}\right)$	$e\left(\frac{541}{1001}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{45}{2002}\right)$	$e\left(\frac{283}{1001}\right)$	$e\left(\frac{311}{1001}\right)$	$e\left(\frac{505}{1001}\right)$	$e\left(\frac{732}{1001}\right)$	$e\left(\frac{218}{1001}\right)$
$\chi_{8009}(5,\cdot)$	8009.w	308	yes	$1$	$1$	$e\left(\frac{151}{154}\right)$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{173}{308}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{39}{154}\right)$
$\chi_{8009}(6,\cdot)$	8009.bf	8008	yes	$-1$	$1$	$e\left(\frac{45}{4004}\right)$	$e\left(\frac{5015}{8008}\right)$	$e\left(\frac{45}{2002}\right)$	$e\left(\frac{173}{308}\right)$	$e\left(\frac{5105}{8008}\right)$	$e\left(\frac{46}{1001}\right)$	$e\left(\frac{135}{4004}\right)$	$e\left(\frac{1011}{4004}\right)$	$e\left(\frac{1147}{2002}\right)$	$e\left(\frac{3265}{4004}\right)$
$\chi_{8009}(7,\cdot)$	8009.bb	1001	yes	$1$	$1$	$e\left(\frac{642}{1001}\right)$	$e\left(\frac{405}{1001}\right)$	$e\left(\frac{283}{1001}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{46}{1001}\right)$	$e\left(\frac{890}{1001}\right)$	$e\left(\frac{925}{1001}\right)$	$e\left(\frac{810}{1001}\right)$	$e\left(\frac{629}{1001}\right)$	$e\left(\frac{201}{1001}\right)$
$\chi_{8009}(8,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{311}{2002}\right)$	$e\left(\frac{3517}{4004}\right)$	$e\left(\frac{311}{1001}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{135}{4004}\right)$	$e\left(\frac{925}{1001}\right)$	$e\left(\frac{933}{2002}\right)$	$e\left(\frac{1515}{2002}\right)$	$e\left(\frac{97}{1001}\right)$	$e\left(\frac{1655}{2002}\right)$
$\chi_{8009}(9,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{505}{2002}\right)$	$e\left(\frac{1}{4004}\right)$	$e\left(\frac{505}{1001}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{1011}{4004}\right)$	$e\left(\frac{810}{1001}\right)$	$e\left(\frac{1515}{2002}\right)$	$e\left(\frac{1}{2002}\right)$	$e\left(\frac{415}{1001}\right)$	$e\left(\frac{827}{2002}\right)$
$\chi_{8009}(10,\cdot)$	8009.bd	2002	yes	$1$	$1$	$e\left(\frac{366}{1001}\right)$	$e\left(\frac{415}{2002}\right)$	$e\left(\frac{732}{1001}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{1147}{2002}\right)$	$e\left(\frac{629}{1001}\right)$	$e\left(\frac{97}{1001}\right)$	$e\left(\frac{415}{1001}\right)$	$e\left(\frac{106}{1001}\right)$	$e\left(\frac{863}{1001}\right)$
$\chi_{8009}(11,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{1219}{2002}\right)$	$e\left(\frac{827}{4004}\right)$	$e\left(\frac{218}{1001}\right)$	$e\left(\frac{39}{154}\right)$	$e\left(\frac{3265}{4004}\right)$	$e\left(\frac{201}{1001}\right)$	$e\left(\frac{1655}{2002}\right)$	$e\left(\frac{827}{2002}\right)$	$e\left(\frac{863}{1001}\right)$	$e\left(\frac{1247}{2002}\right)$
$\chi_{8009}(12,\cdot)$	8009.bf	8008	yes	$-1$	$1$	$e\left(\frac{1587}{4004}\right)$	$e\left(\frac{2021}{8008}\right)$	$e\left(\frac{1587}{2002}\right)$	$e\left(\frac{167}{308}\right)$	$e\left(\frac{5195}{8008}\right)$	$e\left(\frac{688}{1001}\right)$	$e\left(\frac{757}{4004}\right)$	$e\left(\frac{2021}{4004}\right)$	$e\left(\frac{1879}{2002}\right)$	$e\left(\frac{1699}{4004}\right)$
$\chi_{8009}(13,\cdot)$	8009.v	286	yes	$1$	$1$	$e\left(\frac{85}{143}\right)$	$e\left(\frac{3}{286}\right)$	$e\left(\frac{27}{143}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{173}{286}\right)$	$e\left(\frac{141}{143}\right)$	$e\left(\frac{112}{143}\right)$	$e\left(\frac{3}{143}\right)$	$e\left(\frac{59}{143}\right)$	$e\left(\frac{50}{143}\right)$
$\chi_{8009}(14,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{53}{2002}\right)$	$e\left(\frac{123}{4004}\right)$	$e\left(\frac{53}{1001}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{229}{4004}\right)$	$e\left(\frac{531}{1001}\right)$	$e\left(\frac{159}{2002}\right)$	$e\left(\frac{123}{2002}\right)$	$e\left(\frac{995}{1001}\right)$	$e\left(\frac{1621}{2002}\right)$
$\chi_{8009}(15,\cdot)$	8009.bc	1144	yes	$-1$	$1$	$e\left(\frac{347}{572}\right)$	$e\left(\frac{665}{1144}\right)$	$e\left(\frac{61}{286}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{215}{1144}\right)$	$e\left(\frac{56}{143}\right)$	$e\left(\frac{469}{572}\right)$	$e\left(\frac{93}{572}\right)$	$e\left(\frac{271}{286}\right)$	$e\left(\frac{263}{572}\right)$
$\chi_{8009}(16,\cdot)$	8009.bb	1001	yes	$1$	$1$	$e\left(\frac{541}{1001}\right)$	$e\left(\frac{505}{1001}\right)$	$e\left(\frac{81}{1001}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{45}{1001}\right)$	$e\left(\frac{566}{1001}\right)$	$e\left(\frac{622}{1001}\right)$	$e\left(\frac{9}{1001}\right)$	$e\left(\frac{463}{1001}\right)$	$e\left(\frac{436}{1001}\right)$
$\chi_{8009}(17,\cdot)$	8009.bb	1001	yes	$1$	$1$	$e\left(\frac{932}{1001}\right)$	$e\left(\frac{326}{1001}\right)$	$e\left(\frac{863}{1001}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{257}{1001}\right)$	$e\left(\frac{185}{1001}\right)$	$e\left(\frac{794}{1001}\right)$	$e\left(\frac{652}{1001}\right)$	$e\left(\frac{620}{1001}\right)$	$e\left(\frac{666}{1001}\right)$
$\chi_{8009}(18,\cdot)$	8009.q	91	yes	$1$	$1$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{2}{91}\right)$
$\chi_{8009}(19,\cdot)$	8009.ba	728	yes	$-1$	$1$	$e\left(\frac{265}{364}\right)$	$e\left(\frac{251}{728}\right)$	$e\left(\frac{83}{182}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{53}{728}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{67}{364}\right)$	$e\left(\frac{251}{364}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{97}{364}\right)$
$\chi_{8009}(20,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{1503}{2002}\right)$	$e\left(\frac{3337}{4004}\right)$	$e\left(\frac{502}{1001}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{2339}{4004}\right)$	$e\left(\frac{270}{1001}\right)$	$e\left(\frac{505}{2002}\right)$	$e\left(\frac{1335}{2002}\right)$	$e\left(\frac{472}{1001}\right)$	$e\left(\frac{943}{2002}\right)$
$\chi_{8009}(21,\cdot)$	8009.bc	1144	yes	$-1$	$1$	$e\left(\frac{153}{572}\right)$	$e\left(\frac{463}{1144}\right)$	$e\left(\frac{153}{286}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{769}{1144}\right)$	$e\left(\frac{42}{143}\right)$	$e\left(\frac{459}{572}\right)$	$e\left(\frac{463}{572}\right)$	$e\left(\frac{239}{286}\right)$	$e\left(\frac{233}{572}\right)$
$\chi_{8009}(22,\cdot)$	8009.bd	2002	yes	$1$	$1$	$e\left(\frac{995}{1001}\right)$	$e\left(\frac{1667}{2002}\right)$	$e\left(\frac{989}{1001}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{1655}{2002}\right)$	$e\left(\frac{843}{1001}\right)$	$e\left(\frac{983}{1001}\right)$	$e\left(\frac{666}{1001}\right)$	$e\left(\frac{228}{1001}\right)$	$e\left(\frac{232}{1001}\right)$
$\chi_{8009}(23,\cdot)$	8009.ba	728	yes	$-1$	$1$	$e\left(\frac{305}{364}\right)$	$e\left(\frac{543}{728}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{425}{728}\right)$	$e\left(\frac{59}{91}\right)$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{179}{364}\right)$	$e\left(\frac{29}{182}\right)$	$e\left(\frac{249}{364}\right)$
$\chi_{8009}(24,\cdot)$	8009.bc	1144	yes	$-1$	$1$	$e\left(\frac{447}{572}\right)$	$e\left(\frac{1005}{1144}\right)$	$e\left(\frac{161}{286}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{755}{1144}\right)$	$e\left(\frac{47}{143}\right)$	$e\left(\frac{197}{572}\right)$	$e\left(\frac{433}{572}\right)$	$e\left(\frac{87}{286}\right)$	$e\left(\frac{19}{572}\right)$
$\chi_{8009}(25,\cdot)$	8009.t	154	yes	$1$	$1$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{71}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{39}{77}\right)$
$\chi_{8009}(26,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{1961}{2002}\right)$	$e\left(\frac{2549}{4004}\right)$	$e\left(\frac{960}{1001}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{2467}{4004}\right)$	$e\left(\frac{628}{1001}\right)$	$e\left(\frac{1879}{2002}\right)$	$e\left(\frac{547}{2002}\right)$	$e\left(\frac{779}{1001}\right)$	$e\left(\frac{1919}{2002}\right)$
$\chi_{8009}(27,\cdot)$	8009.bf	8008	yes	$-1$	$1$	$e\left(\frac{3517}{4004}\right)$	$e\left(\frac{3}{8008}\right)$	$e\left(\frac{1515}{2002}\right)$	$e\left(\frac{229}{308}\right)$	$e\left(\frac{7037}{8008}\right)$	$e\left(\frac{214}{1001}\right)$	$e\left(\frac{2543}{4004}\right)$	$e\left(\frac{3}{4004}\right)$	$e\left(\frac{1245}{2002}\right)$	$e\left(\frac{2481}{4004}\right)$
$\chi_{8009}(28,\cdot)$	8009.bd	2002	yes	$1$	$1$	$e\left(\frac{412}{1001}\right)$	$e\left(\frac{1315}{2002}\right)$	$e\left(\frac{824}{1001}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{137}{2002}\right)$	$e\left(\frac{172}{1001}\right)$	$e\left(\frac{235}{1001}\right)$	$e\left(\frac{314}{1001}\right)$	$e\left(\frac{360}{1001}\right)$	$e\left(\frac{419}{1001}\right)$
$\chi_{8009}(29,\cdot)$	8009.bb	1001	yes	$1$	$1$	$e\left(\frac{747}{1001}\right)$	$e\left(\frac{83}{1001}\right)$	$e\left(\frac{493}{1001}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{830}{1001}\right)$	$e\left(\frac{652}{1001}\right)$	$e\left(\frac{239}{1001}\right)$	$e\left(\frac{166}{1001}\right)$	$e\left(\frac{643}{1001}\right)$	$e\left(\frac{145}{1001}\right)$
$\chi_{8009}(30,\cdot)$	8009.ba	728	yes	$-1$	$1$	$e\left(\frac{361}{364}\right)$	$e\left(\frac{151}{728}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{145}{728}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{355}{364}\right)$	$e\left(\frac{151}{364}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{25}{364}\right)$
$\chi_{8009}(31,\cdot)$	8009.bf	8008	yes	$-1$	$1$	$e\left(\frac{849}{4004}\right)$	$e\left(\frac{3859}{8008}\right)$	$e\left(\frac{849}{2002}\right)$	$e\left(\frac{225}{308}\right)$	$e\left(\frac{5557}{8008}\right)$	$e\left(\frac{334}{1001}\right)$	$e\left(\frac{2547}{4004}\right)$	$e\left(\frac{3859}{4004}\right)$	$e\left(\frac{1887}{2002}\right)$	$e\left(\frac{205}{4004}\right)$
$\chi_{8009}(32,\cdot)$	8009.be	4004	yes	$1$	$1$	$e\left(\frac{1853}{2002}\right)$	$e\left(\frac{523}{4004}\right)$	$e\left(\frac{852}{1001}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{225}{4004}\right)$	$e\left(\frac{207}{1001}\right)$	$e\left(\frac{1555}{2002}\right)$	$e\left(\frac{523}{2002}\right)$	$e\left(\frac{829}{1001}\right)$	$e\left(\frac{89}{2002}\right)$

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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	$8009$
Structure	\(C_{8008}\)
Order	$8008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{8009}(1,\cdot)\)	8009.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8009}(2,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{771}{2002}\right)\)	\(e\left(\frac{2507}{4004}\right)\)	\(e\left(\frac{771}{1001}\right)\)	\(e\left(\frac{151}{154}\right)\)	\(e\left(\frac{45}{4004}\right)\)	\(e\left(\frac{642}{1001}\right)\)	\(e\left(\frac{311}{2002}\right)\)	\(e\left(\frac{505}{2002}\right)\)	\(e\left(\frac{366}{1001}\right)\)	\(e\left(\frac{1219}{2002}\right)\)
\(\chi_{8009}(3,\cdot)\)	8009.bf	8008	yes	\(-1\)	\(1\)	\(e\left(\frac{2507}{4004}\right)\)	\(e\left(\frac{1}{8008}\right)\)	\(e\left(\frac{505}{2002}\right)\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{5015}{8008}\right)\)	\(e\left(\frac{405}{1001}\right)\)	\(e\left(\frac{3517}{4004}\right)\)	\(e\left(\frac{1}{4004}\right)\)	\(e\left(\frac{415}{2002}\right)\)	\(e\left(\frac{827}{4004}\right)\)
\(\chi_{8009}(4,\cdot)\)	8009.bd	2002	yes	\(1\)	\(1\)	\(e\left(\frac{771}{1001}\right)\)	\(e\left(\frac{505}{2002}\right)\)	\(e\left(\frac{541}{1001}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{45}{2002}\right)\)	\(e\left(\frac{283}{1001}\right)\)	\(e\left(\frac{311}{1001}\right)\)	\(e\left(\frac{505}{1001}\right)\)	\(e\left(\frac{732}{1001}\right)\)	\(e\left(\frac{218}{1001}\right)\)
\(\chi_{8009}(5,\cdot)\)	8009.w	308	yes	\(1\)	\(1\)	\(e\left(\frac{151}{154}\right)\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{173}{308}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{39}{154}\right)\)
\(\chi_{8009}(6,\cdot)\)	8009.bf	8008	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{4004}\right)\)	\(e\left(\frac{5015}{8008}\right)\)	\(e\left(\frac{45}{2002}\right)\)	\(e\left(\frac{173}{308}\right)\)	\(e\left(\frac{5105}{8008}\right)\)	\(e\left(\frac{46}{1001}\right)\)	\(e\left(\frac{135}{4004}\right)\)	\(e\left(\frac{1011}{4004}\right)\)	\(e\left(\frac{1147}{2002}\right)\)	\(e\left(\frac{3265}{4004}\right)\)
\(\chi_{8009}(7,\cdot)\)	8009.bb	1001	yes	\(1\)	\(1\)	\(e\left(\frac{642}{1001}\right)\)	\(e\left(\frac{405}{1001}\right)\)	\(e\left(\frac{283}{1001}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{46}{1001}\right)\)	\(e\left(\frac{890}{1001}\right)\)	\(e\left(\frac{925}{1001}\right)\)	\(e\left(\frac{810}{1001}\right)\)	\(e\left(\frac{629}{1001}\right)\)	\(e\left(\frac{201}{1001}\right)\)
\(\chi_{8009}(8,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{311}{2002}\right)\)	\(e\left(\frac{3517}{4004}\right)\)	\(e\left(\frac{311}{1001}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{135}{4004}\right)\)	\(e\left(\frac{925}{1001}\right)\)	\(e\left(\frac{933}{2002}\right)\)	\(e\left(\frac{1515}{2002}\right)\)	\(e\left(\frac{97}{1001}\right)\)	\(e\left(\frac{1655}{2002}\right)\)
\(\chi_{8009}(9,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{505}{2002}\right)\)	\(e\left(\frac{1}{4004}\right)\)	\(e\left(\frac{505}{1001}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{1011}{4004}\right)\)	\(e\left(\frac{810}{1001}\right)\)	\(e\left(\frac{1515}{2002}\right)\)	\(e\left(\frac{1}{2002}\right)\)	\(e\left(\frac{415}{1001}\right)\)	\(e\left(\frac{827}{2002}\right)\)
\(\chi_{8009}(10,\cdot)\)	8009.bd	2002	yes	\(1\)	\(1\)	\(e\left(\frac{366}{1001}\right)\)	\(e\left(\frac{415}{2002}\right)\)	\(e\left(\frac{732}{1001}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{1147}{2002}\right)\)	\(e\left(\frac{629}{1001}\right)\)	\(e\left(\frac{97}{1001}\right)\)	\(e\left(\frac{415}{1001}\right)\)	\(e\left(\frac{106}{1001}\right)\)	\(e\left(\frac{863}{1001}\right)\)
\(\chi_{8009}(11,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{1219}{2002}\right)\)	\(e\left(\frac{827}{4004}\right)\)	\(e\left(\frac{218}{1001}\right)\)	\(e\left(\frac{39}{154}\right)\)	\(e\left(\frac{3265}{4004}\right)\)	\(e\left(\frac{201}{1001}\right)\)	\(e\left(\frac{1655}{2002}\right)\)	\(e\left(\frac{827}{2002}\right)\)	\(e\left(\frac{863}{1001}\right)\)	\(e\left(\frac{1247}{2002}\right)\)
\(\chi_{8009}(12,\cdot)\)	8009.bf	8008	yes	\(-1\)	\(1\)	\(e\left(\frac{1587}{4004}\right)\)	\(e\left(\frac{2021}{8008}\right)\)	\(e\left(\frac{1587}{2002}\right)\)	\(e\left(\frac{167}{308}\right)\)	\(e\left(\frac{5195}{8008}\right)\)	\(e\left(\frac{688}{1001}\right)\)	\(e\left(\frac{757}{4004}\right)\)	\(e\left(\frac{2021}{4004}\right)\)	\(e\left(\frac{1879}{2002}\right)\)	\(e\left(\frac{1699}{4004}\right)\)
\(\chi_{8009}(13,\cdot)\)	8009.v	286	yes	\(1\)	\(1\)	\(e\left(\frac{85}{143}\right)\)	\(e\left(\frac{3}{286}\right)\)	\(e\left(\frac{27}{143}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{173}{286}\right)\)	\(e\left(\frac{141}{143}\right)\)	\(e\left(\frac{112}{143}\right)\)	\(e\left(\frac{3}{143}\right)\)	\(e\left(\frac{59}{143}\right)\)	\(e\left(\frac{50}{143}\right)\)
\(\chi_{8009}(14,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{53}{2002}\right)\)	\(e\left(\frac{123}{4004}\right)\)	\(e\left(\frac{53}{1001}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{229}{4004}\right)\)	\(e\left(\frac{531}{1001}\right)\)	\(e\left(\frac{159}{2002}\right)\)	\(e\left(\frac{123}{2002}\right)\)	\(e\left(\frac{995}{1001}\right)\)	\(e\left(\frac{1621}{2002}\right)\)
\(\chi_{8009}(15,\cdot)\)	8009.bc	1144	yes	\(-1\)	\(1\)	\(e\left(\frac{347}{572}\right)\)	\(e\left(\frac{665}{1144}\right)\)	\(e\left(\frac{61}{286}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{215}{1144}\right)\)	\(e\left(\frac{56}{143}\right)\)	\(e\left(\frac{469}{572}\right)\)	\(e\left(\frac{93}{572}\right)\)	\(e\left(\frac{271}{286}\right)\)	\(e\left(\frac{263}{572}\right)\)
\(\chi_{8009}(16,\cdot)\)	8009.bb	1001	yes	\(1\)	\(1\)	\(e\left(\frac{541}{1001}\right)\)	\(e\left(\frac{505}{1001}\right)\)	\(e\left(\frac{81}{1001}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{45}{1001}\right)\)	\(e\left(\frac{566}{1001}\right)\)	\(e\left(\frac{622}{1001}\right)\)	\(e\left(\frac{9}{1001}\right)\)	\(e\left(\frac{463}{1001}\right)\)	\(e\left(\frac{436}{1001}\right)\)
\(\chi_{8009}(17,\cdot)\)	8009.bb	1001	yes	\(1\)	\(1\)	\(e\left(\frac{932}{1001}\right)\)	\(e\left(\frac{326}{1001}\right)\)	\(e\left(\frac{863}{1001}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{257}{1001}\right)\)	\(e\left(\frac{185}{1001}\right)\)	\(e\left(\frac{794}{1001}\right)\)	\(e\left(\frac{652}{1001}\right)\)	\(e\left(\frac{620}{1001}\right)\)	\(e\left(\frac{666}{1001}\right)\)
\(\chi_{8009}(18,\cdot)\)	8009.q	91	yes	\(1\)	\(1\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)
\(\chi_{8009}(19,\cdot)\)	8009.ba	728	yes	\(-1\)	\(1\)	\(e\left(\frac{265}{364}\right)\)	\(e\left(\frac{251}{728}\right)\)	\(e\left(\frac{83}{182}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{53}{728}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{67}{364}\right)\)	\(e\left(\frac{251}{364}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{97}{364}\right)\)
\(\chi_{8009}(20,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{1503}{2002}\right)\)	\(e\left(\frac{3337}{4004}\right)\)	\(e\left(\frac{502}{1001}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{2339}{4004}\right)\)	\(e\left(\frac{270}{1001}\right)\)	\(e\left(\frac{505}{2002}\right)\)	\(e\left(\frac{1335}{2002}\right)\)	\(e\left(\frac{472}{1001}\right)\)	\(e\left(\frac{943}{2002}\right)\)
\(\chi_{8009}(21,\cdot)\)	8009.bc	1144	yes	\(-1\)	\(1\)	\(e\left(\frac{153}{572}\right)\)	\(e\left(\frac{463}{1144}\right)\)	\(e\left(\frac{153}{286}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{769}{1144}\right)\)	\(e\left(\frac{42}{143}\right)\)	\(e\left(\frac{459}{572}\right)\)	\(e\left(\frac{463}{572}\right)\)	\(e\left(\frac{239}{286}\right)\)	\(e\left(\frac{233}{572}\right)\)
\(\chi_{8009}(22,\cdot)\)	8009.bd	2002	yes	\(1\)	\(1\)	\(e\left(\frac{995}{1001}\right)\)	\(e\left(\frac{1667}{2002}\right)\)	\(e\left(\frac{989}{1001}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{1655}{2002}\right)\)	\(e\left(\frac{843}{1001}\right)\)	\(e\left(\frac{983}{1001}\right)\)	\(e\left(\frac{666}{1001}\right)\)	\(e\left(\frac{228}{1001}\right)\)	\(e\left(\frac{232}{1001}\right)\)
\(\chi_{8009}(23,\cdot)\)	8009.ba	728	yes	\(-1\)	\(1\)	\(e\left(\frac{305}{364}\right)\)	\(e\left(\frac{543}{728}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{425}{728}\right)\)	\(e\left(\frac{59}{91}\right)\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{179}{364}\right)\)	\(e\left(\frac{29}{182}\right)\)	\(e\left(\frac{249}{364}\right)\)
\(\chi_{8009}(24,\cdot)\)	8009.bc	1144	yes	\(-1\)	\(1\)	\(e\left(\frac{447}{572}\right)\)	\(e\left(\frac{1005}{1144}\right)\)	\(e\left(\frac{161}{286}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{755}{1144}\right)\)	\(e\left(\frac{47}{143}\right)\)	\(e\left(\frac{197}{572}\right)\)	\(e\left(\frac{433}{572}\right)\)	\(e\left(\frac{87}{286}\right)\)	\(e\left(\frac{19}{572}\right)\)
\(\chi_{8009}(25,\cdot)\)	8009.t	154	yes	\(1\)	\(1\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{71}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)
\(\chi_{8009}(26,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{1961}{2002}\right)\)	\(e\left(\frac{2549}{4004}\right)\)	\(e\left(\frac{960}{1001}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{2467}{4004}\right)\)	\(e\left(\frac{628}{1001}\right)\)	\(e\left(\frac{1879}{2002}\right)\)	\(e\left(\frac{547}{2002}\right)\)	\(e\left(\frac{779}{1001}\right)\)	\(e\left(\frac{1919}{2002}\right)\)
\(\chi_{8009}(27,\cdot)\)	8009.bf	8008	yes	\(-1\)	\(1\)	\(e\left(\frac{3517}{4004}\right)\)	\(e\left(\frac{3}{8008}\right)\)	\(e\left(\frac{1515}{2002}\right)\)	\(e\left(\frac{229}{308}\right)\)	\(e\left(\frac{7037}{8008}\right)\)	\(e\left(\frac{214}{1001}\right)\)	\(e\left(\frac{2543}{4004}\right)\)	\(e\left(\frac{3}{4004}\right)\)	\(e\left(\frac{1245}{2002}\right)\)	\(e\left(\frac{2481}{4004}\right)\)
\(\chi_{8009}(28,\cdot)\)	8009.bd	2002	yes	\(1\)	\(1\)	\(e\left(\frac{412}{1001}\right)\)	\(e\left(\frac{1315}{2002}\right)\)	\(e\left(\frac{824}{1001}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{137}{2002}\right)\)	\(e\left(\frac{172}{1001}\right)\)	\(e\left(\frac{235}{1001}\right)\)	\(e\left(\frac{314}{1001}\right)\)	\(e\left(\frac{360}{1001}\right)\)	\(e\left(\frac{419}{1001}\right)\)
\(\chi_{8009}(29,\cdot)\)	8009.bb	1001	yes	\(1\)	\(1\)	\(e\left(\frac{747}{1001}\right)\)	\(e\left(\frac{83}{1001}\right)\)	\(e\left(\frac{493}{1001}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{830}{1001}\right)\)	\(e\left(\frac{652}{1001}\right)\)	\(e\left(\frac{239}{1001}\right)\)	\(e\left(\frac{166}{1001}\right)\)	\(e\left(\frac{643}{1001}\right)\)	\(e\left(\frac{145}{1001}\right)\)
\(\chi_{8009}(30,\cdot)\)	8009.ba	728	yes	\(-1\)	\(1\)	\(e\left(\frac{361}{364}\right)\)	\(e\left(\frac{151}{728}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{145}{728}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{355}{364}\right)\)	\(e\left(\frac{151}{364}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{25}{364}\right)\)
\(\chi_{8009}(31,\cdot)\)	8009.bf	8008	yes	\(-1\)	\(1\)	\(e\left(\frac{849}{4004}\right)\)	\(e\left(\frac{3859}{8008}\right)\)	\(e\left(\frac{849}{2002}\right)\)	\(e\left(\frac{225}{308}\right)\)	\(e\left(\frac{5557}{8008}\right)\)	\(e\left(\frac{334}{1001}\right)\)	\(e\left(\frac{2547}{4004}\right)\)	\(e\left(\frac{3859}{4004}\right)\)	\(e\left(\frac{1887}{2002}\right)\)	\(e\left(\frac{205}{4004}\right)\)
\(\chi_{8009}(32,\cdot)\)	8009.be	4004	yes	\(1\)	\(1\)	\(e\left(\frac{1853}{2002}\right)\)	\(e\left(\frac{523}{4004}\right)\)	\(e\left(\frac{852}{1001}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{225}{4004}\right)\)	\(e\left(\frac{207}{1001}\right)\)	\(e\left(\frac{1555}{2002}\right)\)	\(e\left(\frac{523}{2002}\right)\)	\(e\left(\frac{829}{1001}\right)\)	\(e\left(\frac{89}{2002}\right)\)

Introduction

L-functions

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First 32 of 8008 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.