LMFDB - Group of Dirichlet characters of modulus 8004

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8004)

pari: g = idealstar(,8004,2)

Character group

sage: G.order() pari: g.no
Order	=	2464
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{308}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8004}(4003,\cdot)$, $\chi_{8004}(2669,\cdot)$, $\chi_{8004}(3133,\cdot)$, $\chi_{8004}(553,\cdot)$

First 32 of 2464 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$31$	$35$	$37$
$\chi_{8004}(1,\cdot)$	8004.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8004}(5,\cdot)$	8004.de	154	no	$1$	$1$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{24}{77}\right)$
$\chi_{8004}(7,\cdot)$	8004.dc	154	no	$1$	$1$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{65}{154}\right)$
$\chi_{8004}(11,\cdot)$	8004.dm	308	yes	$1$	$1$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{1}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{207}{308}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{83}{308}\right)$
$\chi_{8004}(13,\cdot)$	8004.di	154	no	$1$	$1$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{45}{154}\right)$
$\chi_{8004}(17,\cdot)$	8004.cs	44	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{8004}(19,\cdot)$	8004.dr	308	no	$-1$	$1$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{207}{308}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{191}{308}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{281}{308}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{87}{308}\right)$
$\chi_{8004}(25,\cdot)$	8004.cu	77	no	$1$	$1$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{48}{77}\right)$
$\chi_{8004}(31,\cdot)$	8004.dk	308	no	$1$	$1$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{261}{308}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{281}{308}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{257}{308}\right)$
$\chi_{8004}(35,\cdot)$	8004.cv	154	yes	$1$	$1$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{113}{154}\right)$
$\chi_{8004}(37,\cdot)$	8004.do	308	no	$1$	$1$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{83}{308}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{87}{308}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{257}{308}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{113}{308}\right)$
$\chi_{8004}(41,\cdot)$	8004.cn	44	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{8004}(43,\cdot)$	8004.dr	308	no	$-1$	$1$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{47}{308}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{27}{308}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{51}{308}\right)$
$\chi_{8004}(47,\cdot)$	8004.cg	28	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{14}\right)$	$-i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{8004}(49,\cdot)$	8004.cu	77	no	$1$	$1$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{65}{77}\right)$
$\chi_{8004}(53,\cdot)$	8004.df	154	no	$1$	$1$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{153}{154}\right)$
$\chi_{8004}(55,\cdot)$	8004.dk	308	no	$1$	$1$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{171}{308}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{131}{308}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{279}{308}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{179}{308}\right)$
$\chi_{8004}(59,\cdot)$	8004.cb	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{8004}(61,\cdot)$	8004.do	308	no	$1$	$1$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{129}{308}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{61}{308}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{251}{308}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{235}{308}\right)$
$\chi_{8004}(65,\cdot)$	8004.df	154	no	$1$	$1$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{93}{154}\right)$
$\chi_{8004}(67,\cdot)$	8004.cz	154	no	$1$	$1$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{37}{77}\right)$
$\chi_{8004}(71,\cdot)$	8004.cv	154	yes	$1$	$1$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{52}{77}\right)$	$e\left(\frac{129}{154}\right)$
$\chi_{8004}(73,\cdot)$	8004.dn	308	no	$-1$	$1$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{229}{308}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{125}{308}\right)$	$e\left(\frac{61}{77}\right)$	$e\left(\frac{17}{308}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{219}{308}\right)$
$\chi_{8004}(77,\cdot)$	8004.dq	308	no	$1$	$1$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{305}{308}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{303}{308}\right)$	$e\left(\frac{53}{77}\right)$	$e\left(\frac{295}{308}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{213}{308}\right)$
$\chi_{8004}(79,\cdot)$	8004.dr	308	no	$-1$	$1$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{279}{308}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{308}\right)$	$e\left(\frac{76}{77}\right)$	$e\left(\frac{285}{308}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{211}{308}\right)$
$\chi_{8004}(83,\cdot)$	8004.dh	154	yes	$-1$	$1$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{135}{154}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{40}{77}\right)$	$e\left(\frac{117}{154}\right)$
$\chi_{8004}(85,\cdot)$	8004.dn	308	no	$-1$	$1$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{205}{308}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{85}{308}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{221}{308}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{75}{308}\right)$
$\chi_{8004}(89,\cdot)$	8004.dl	308	no	$-1$	$1$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{135}{308}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{225}{308}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{123}{308}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{271}{308}\right)$
$\chi_{8004}(91,\cdot)$	8004.bk	14	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{8004}(95,\cdot)$	8004.dp	308	yes	$-1$	$1$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{69}{308}\right)$	$e\left(\frac{17}{154}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{115}{308}\right)$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{299}{308}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{183}{308}\right)$
$\chi_{8004}(97,\cdot)$	8004.do	308	no	$1$	$1$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{291}{308}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{308}\right)$	$e\left(\frac{18}{77}\right)$	$e\left(\frac{29}{308}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{129}{308}\right)$
$\chi_{8004}(101,\cdot)$	8004.dq	308	no	$1$	$1$	$e\left(\frac{13}{77}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{61}{308}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{307}{308}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{289}{308}\right)$

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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	$8004$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{308}\)
Order	$2464$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\(\chi_{8004}(1,\cdot)\)	8004.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8004}(5,\cdot)\)	8004.de	154	no	\(1\)	\(1\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{24}{77}\right)\)
\(\chi_{8004}(7,\cdot)\)	8004.dc	154	no	\(1\)	\(1\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{65}{154}\right)\)
\(\chi_{8004}(11,\cdot)\)	8004.dm	308	yes	\(1\)	\(1\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{1}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{207}{308}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{83}{308}\right)\)
\(\chi_{8004}(13,\cdot)\)	8004.di	154	no	\(1\)	\(1\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{45}{154}\right)\)
\(\chi_{8004}(17,\cdot)\)	8004.cs	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{8004}(19,\cdot)\)	8004.dr	308	no	\(-1\)	\(1\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{207}{308}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{191}{308}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{281}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{87}{308}\right)\)
\(\chi_{8004}(25,\cdot)\)	8004.cu	77	no	\(1\)	\(1\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)
\(\chi_{8004}(31,\cdot)\)	8004.dk	308	no	\(1\)	\(1\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{261}{308}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{281}{308}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{257}{308}\right)\)
\(\chi_{8004}(35,\cdot)\)	8004.cv	154	yes	\(1\)	\(1\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)
\(\chi_{8004}(37,\cdot)\)	8004.do	308	no	\(1\)	\(1\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{83}{308}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{87}{308}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{257}{308}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{113}{308}\right)\)
\(\chi_{8004}(41,\cdot)\)	8004.cn	44	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{8004}(43,\cdot)\)	8004.dr	308	no	\(-1\)	\(1\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{47}{308}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{27}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{51}{308}\right)\)
\(\chi_{8004}(47,\cdot)\)	8004.cg	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{8004}(49,\cdot)\)	8004.cu	77	no	\(1\)	\(1\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)
\(\chi_{8004}(53,\cdot)\)	8004.df	154	no	\(1\)	\(1\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{153}{154}\right)\)
\(\chi_{8004}(55,\cdot)\)	8004.dk	308	no	\(1\)	\(1\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{171}{308}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{131}{308}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{279}{308}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{179}{308}\right)\)
\(\chi_{8004}(59,\cdot)\)	8004.cb	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{8004}(61,\cdot)\)	8004.do	308	no	\(1\)	\(1\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{129}{308}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{61}{308}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{251}{308}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{235}{308}\right)\)
\(\chi_{8004}(65,\cdot)\)	8004.df	154	no	\(1\)	\(1\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{93}{154}\right)\)
\(\chi_{8004}(67,\cdot)\)	8004.cz	154	no	\(1\)	\(1\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{37}{77}\right)\)
\(\chi_{8004}(71,\cdot)\)	8004.cv	154	yes	\(1\)	\(1\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{52}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)
\(\chi_{8004}(73,\cdot)\)	8004.dn	308	no	\(-1\)	\(1\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{229}{308}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{125}{308}\right)\)	\(e\left(\frac{61}{77}\right)\)	\(e\left(\frac{17}{308}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{219}{308}\right)\)
\(\chi_{8004}(77,\cdot)\)	8004.dq	308	no	\(1\)	\(1\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{305}{308}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{303}{308}\right)\)	\(e\left(\frac{53}{77}\right)\)	\(e\left(\frac{295}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{213}{308}\right)\)
\(\chi_{8004}(79,\cdot)\)	8004.dr	308	no	\(-1\)	\(1\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{279}{308}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{308}\right)\)	\(e\left(\frac{76}{77}\right)\)	\(e\left(\frac{285}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{211}{308}\right)\)
\(\chi_{8004}(83,\cdot)\)	8004.dh	154	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{117}{154}\right)\)
\(\chi_{8004}(85,\cdot)\)	8004.dn	308	no	\(-1\)	\(1\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{205}{308}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{85}{308}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{221}{308}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{75}{308}\right)\)
\(\chi_{8004}(89,\cdot)\)	8004.dl	308	no	\(-1\)	\(1\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{135}{308}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{225}{308}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{123}{308}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{271}{308}\right)\)
\(\chi_{8004}(91,\cdot)\)	8004.bk	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{8004}(95,\cdot)\)	8004.dp	308	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{69}{308}\right)\)	\(e\left(\frac{17}{154}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{115}{308}\right)\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{299}{308}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{183}{308}\right)\)
\(\chi_{8004}(97,\cdot)\)	8004.do	308	no	\(1\)	\(1\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{291}{308}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{308}\right)\)	\(e\left(\frac{18}{77}\right)\)	\(e\left(\frac{29}{308}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{129}{308}\right)\)
\(\chi_{8004}(101,\cdot)\)	8004.dq	308	no	\(1\)	\(1\)	\(e\left(\frac{13}{77}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{61}{308}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{307}{308}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{289}{308}\right)\)

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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.