LMFDB - Group of Dirichlet characters of modulus 1568

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1568)

pari: g = idealstar(,1568,2)

Character group

sage: G.order() pari: g.no
Order	=	672
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{168}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1568}(1471,\cdot)$, $\chi_{1568}(197,\cdot)$, $\chi_{1568}(1473,\cdot)$

First 32 of 672 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{1568}(1,\cdot)$	1568.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1568}(3,\cdot)$	1568.cj	168	yes	$1$	$1$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{1568}(5,\cdot)$	1568.cl	168	yes	$-1$	$1$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{1568}(9,\cdot)$	1568.cf	84	no	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{1568}(11,\cdot)$	1568.ci	168	yes	$-1$	$1$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{1568}(13,\cdot)$	1568.cc	56	yes	$-1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{1568}(15,\cdot)$	1568.be	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1568}(17,\cdot)$	1568.bz	42	no	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1568}(19,\cdot)$	1568.bn	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1568}(23,\cdot)$	1568.ch	84	no	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{1568}(25,\cdot)$	1568.cf	84	no	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{1568}(27,\cdot)$	1568.ca	56	yes	$1$	$1$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{1568}(29,\cdot)$	1568.cd	56	yes	$1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{1568}(31,\cdot)$	1568.p	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1568}(33,\cdot)$	1568.bu	42	no	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1568}(37,\cdot)$	1568.ck	168	yes	$1$	$1$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{1568}(39,\cdot)$	1568.ch	84	no	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{1568}(41,\cdot)$	1568.bq	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{1568}(43,\cdot)$	1568.cb	56	yes	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{1568}(45,\cdot)$	1568.cl	168	yes	$-1$	$1$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{1568}(47,\cdot)$	1568.bw	42	no	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1568}(51,\cdot)$	1568.ci	168	yes	$-1$	$1$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{1568}(53,\cdot)$	1568.ck	168	yes	$1$	$1$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{1568}(55,\cdot)$	1568.bs	28	no	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$i$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{1568}(57,\cdot)$	1568.bp	28	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{1568}(59,\cdot)$	1568.cj	168	yes	$1$	$1$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{1568}(61,\cdot)$	1568.cl	168	yes	$-1$	$1$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{1568}(65,\cdot)$	1568.bk	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1568}(67,\cdot)$	1568.bo	24	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1568}(69,\cdot)$	1568.cc	56	yes	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{1568}(71,\cdot)$	1568.br	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$i$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{1568}(73,\cdot)$	1568.ce	84	no	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{42}\right)$

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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	$1568$
Structure	\(C_{2}\times C_{2}\times C_{168}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{1568}(1,\cdot)\)	1568.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1568}(3,\cdot)\)	1568.cj	168	yes	\(1\)	\(1\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{1568}(5,\cdot)\)	1568.cl	168	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{1568}(9,\cdot)\)	1568.cf	84	no	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{1568}(11,\cdot)\)	1568.ci	168	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{1568}(13,\cdot)\)	1568.cc	56	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{1568}(15,\cdot)\)	1568.be	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1568}(17,\cdot)\)	1568.bz	42	no	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1568}(19,\cdot)\)	1568.bn	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1568}(23,\cdot)\)	1568.ch	84	no	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{1568}(25,\cdot)\)	1568.cf	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{1568}(27,\cdot)\)	1568.ca	56	yes	\(1\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{1568}(29,\cdot)\)	1568.cd	56	yes	\(1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{1568}(31,\cdot)\)	1568.p	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1568}(33,\cdot)\)	1568.bu	42	no	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1568}(37,\cdot)\)	1568.ck	168	yes	\(1\)	\(1\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{1568}(39,\cdot)\)	1568.ch	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{1568}(41,\cdot)\)	1568.bq	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{1568}(43,\cdot)\)	1568.cb	56	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{1568}(45,\cdot)\)	1568.cl	168	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{1568}(47,\cdot)\)	1568.bw	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1568}(51,\cdot)\)	1568.ci	168	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{1568}(53,\cdot)\)	1568.ck	168	yes	\(1\)	\(1\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{1568}(55,\cdot)\)	1568.bs	28	no	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(i\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{1568}(57,\cdot)\)	1568.bp	28	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{1568}(59,\cdot)\)	1568.cj	168	yes	\(1\)	\(1\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{1568}(61,\cdot)\)	1568.cl	168	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{1568}(65,\cdot)\)	1568.bk	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1568}(67,\cdot)\)	1568.bo	24	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1568}(69,\cdot)\)	1568.cc	56	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{1568}(71,\cdot)\)	1568.br	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(i\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{1568}(73,\cdot)\)	1568.ce	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)

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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.