LMFDB - Group of Dirichlet characters of modulus 4004

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4004)

pari: g = idealstar(,4004,2)

Character group

sage: G.order() pari: g.no
Order	=	1440
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4004}(2003,\cdot)$, $\chi_{4004}(3433,\cdot)$, $\chi_{4004}(365,\cdot)$, $\chi_{4004}(925,\cdot)$

First 32 of 1440 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	$-1$	$1$	$3$	$5$	$9$	$15$	$17$	$19$	$23$	$25$	$27$	$29$
$\chi_{4004}(1,\cdot)$	4004.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4004}(3,\cdot)$	4004.ft	30	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{4004}(5,\cdot)$	4004.im	60	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{4004}(9,\cdot)$	4004.fg	15	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{4004}(15,\cdot)$	4004.ih	60	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{4004}(17,\cdot)$	4004.gm	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4004}(19,\cdot)$	4004.ia	60	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4004}(23,\cdot)$	4004.cu	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{4004}(25,\cdot)$	4004.hg	30	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{4004}(27,\cdot)$	4004.dq	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{4004}(29,\cdot)$	4004.gx	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4004}(31,\cdot)$	4004.iw	60	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{4004}(37,\cdot)$	4004.ja	60	no	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{60}\right)$	$-1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{4004}(41,\cdot)$	4004.ij	60	no	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4004}(43,\cdot)$	4004.cj	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{4004}(45,\cdot)$	4004.fa	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{4004}(47,\cdot)$	4004.iw	60	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{4004}(51,\cdot)$	4004.ge	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{4004}(53,\cdot)$	4004.fi	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{4004}(57,\cdot)$	4004.fk	20	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4004}(59,\cdot)$	4004.ir	60	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{60}\right)$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{4004}(61,\cdot)$	4004.hu	30	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4004}(67,\cdot)$	4004.ec	12	no	$1$	$1$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{4004}(69,\cdot)$	4004.fz	30	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{4004}(71,\cdot)$	4004.ih	60	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{4004}(73,\cdot)$	4004.ii	60	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{4004}(75,\cdot)$	4004.hm	30	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{4004}(79,\cdot)$	4004.gq	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4004}(81,\cdot)$	4004.fg	15	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{4004}(83,\cdot)$	4004.fn	20	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{4004}(85,\cdot)$	4004.iz	60	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4004}(87,\cdot)$	4004.cb	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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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	$4004$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{60}\)
Order	$1440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)	\(29\)
\(\chi_{4004}(1,\cdot)\)	4004.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4004}(3,\cdot)\)	4004.ft	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{4004}(5,\cdot)\)	4004.im	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{4004}(9,\cdot)\)	4004.fg	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{4004}(15,\cdot)\)	4004.ih	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(17,\cdot)\)	4004.gm	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4004}(19,\cdot)\)	4004.ia	60	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4004}(23,\cdot)\)	4004.cu	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4004}(25,\cdot)\)	4004.hg	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{4004}(27,\cdot)\)	4004.dq	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{4004}(29,\cdot)\)	4004.gx	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4004}(31,\cdot)\)	4004.iw	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{4004}(37,\cdot)\)	4004.ja	60	no	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(-1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(41,\cdot)\)	4004.ij	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4004}(43,\cdot)\)	4004.cj	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4004}(45,\cdot)\)	4004.fa	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4004}(47,\cdot)\)	4004.iw	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{4004}(51,\cdot)\)	4004.ge	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{4004}(53,\cdot)\)	4004.fi	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{4004}(57,\cdot)\)	4004.fk	20	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4004}(59,\cdot)\)	4004.ir	60	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{4004}(61,\cdot)\)	4004.hu	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4004}(67,\cdot)\)	4004.ec	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4004}(69,\cdot)\)	4004.fz	30	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{4004}(71,\cdot)\)	4004.ih	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{4004}(73,\cdot)\)	4004.ii	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{4004}(75,\cdot)\)	4004.hm	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{4004}(79,\cdot)\)	4004.gq	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4004}(81,\cdot)\)	4004.fg	15	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{4004}(83,\cdot)\)	4004.fn	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{4004}(85,\cdot)\)	4004.iz	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4004}(87,\cdot)\)	4004.cb	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)

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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.