LMFDB - Group of Dirichlet characters of modulus 1400

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1400)

pari: g = idealstar(,1400,2)

Character group

sage: G.order() pari: g.no
Order	=	480
sage: H.invariants() pari: g.cyc
Structure	=	$C_{60}\times C_{2}\times C_{2}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1400}(351,\cdot)$, $\chi_{1400}(701,\cdot)$, $\chi_{1400}(1177,\cdot)$, $\chi_{1400}(801,\cdot)$

First 32 of 480 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{1400}(1,\cdot)$	1400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1400}(3,\cdot)$	1400.dq	60	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1400}(9,\cdot)$	1400.dc	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1400}(11,\cdot)$	1400.dj	30	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1400}(13,\cdot)$	1400.ct	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1400}(17,\cdot)$	1400.dr	60	no	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1400}(19,\cdot)$	1400.di	30	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1400}(23,\cdot)$	1400.dn	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1400}(27,\cdot)$	1400.cn	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1400}(29,\cdot)$	1400.bt	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1400}(31,\cdot)$	1400.dg	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1400}(33,\cdot)$	1400.dr	60	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{1400}(37,\cdot)$	1400.dm	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1400}(39,\cdot)$	1400.df	30	no	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1400}(41,\cdot)$	1400.bz	10	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1400}(43,\cdot)$	1400.w	4	no	$1$	$1$	$i$	$-1$	$1$	$-i$	$-i$	$-1$	$-i$	$-i$	$1$	$-1$
$\chi_{1400}(47,\cdot)$	1400.dl	60	no	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1400}(51,\cdot)$	1400.ba	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1400}(53,\cdot)$	1400.dm	60	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1400}(57,\cdot)$	1400.v	4	no	$-1$	$1$	$-i$	$-1$	$1$	$-i$	$i$	$-1$	$-i$	$i$	$-1$	$1$
$\chi_{1400}(59,\cdot)$	1400.di	30	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1400}(61,\cdot)$	1400.de	30	yes	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1400}(67,\cdot)$	1400.do	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1400}(69,\cdot)$	1400.cc	10	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1400}(71,\cdot)$	1400.cb	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1400}(73,\cdot)$	1400.dr	60	no	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1400}(79,\cdot)$	1400.df	30	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1400}(81,\cdot)$	1400.cm	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1400}(83,\cdot)$	1400.cn	20	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1400}(87,\cdot)$	1400.dl	60	no	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1400}(89,\cdot)$	1400.dh	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1400}(93,\cdot)$	1400.cj	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$1$	$e\left(\frac{1}{3}\right)$

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	$1400$
Structure	\(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{1400}(1,\cdot)\)	1400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1400}(3,\cdot)\)	1400.dq	60	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1400}(9,\cdot)\)	1400.dc	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1400}(11,\cdot)\)	1400.dj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(13,\cdot)\)	1400.ct	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1400}(17,\cdot)\)	1400.dr	60	no	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1400}(19,\cdot)\)	1400.di	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1400}(23,\cdot)\)	1400.dn	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(27,\cdot)\)	1400.cn	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1400}(29,\cdot)\)	1400.bt	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1400}(31,\cdot)\)	1400.dg	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1400}(33,\cdot)\)	1400.dr	60	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{1400}(37,\cdot)\)	1400.dm	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1400}(39,\cdot)\)	1400.df	30	no	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(41,\cdot)\)	1400.bz	10	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1400}(43,\cdot)\)	1400.w	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)
\(\chi_{1400}(47,\cdot)\)	1400.dl	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1400}(51,\cdot)\)	1400.ba	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1400}(53,\cdot)\)	1400.dm	60	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1400}(57,\cdot)\)	1400.v	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(1\)
\(\chi_{1400}(59,\cdot)\)	1400.di	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1400}(61,\cdot)\)	1400.de	30	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(67,\cdot)\)	1400.do	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1400}(69,\cdot)\)	1400.cc	10	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1400}(71,\cdot)\)	1400.cb	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1400}(73,\cdot)\)	1400.dr	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(79,\cdot)\)	1400.df	30	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1400}(81,\cdot)\)	1400.cm	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1400}(83,\cdot)\)	1400.cn	20	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1400}(87,\cdot)\)	1400.dl	60	no	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1400}(89,\cdot)\)	1400.dh	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(93,\cdot)\)	1400.cj	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{3}\right)\)

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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.