LMFDB - Group of Dirichlet characters of modulus 53312

Show commands: PariGP / SageMath

sage: H = DirichletGroup(53312)

pari: g = idealstar(,53312,2)

Character group

sage: G.order() pari: g.no
Order	=	21504
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{16}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{53312}(51647,\cdot)$, $\chi_{53312}(3333,\cdot)$, $\chi_{53312}(10881,\cdot)$, $\chi_{53312}(40769,\cdot)$

First 32 of 21504 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{53312}(1,\cdot)$	53312.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{53312}(3,\cdot)$	53312.bca	336	yes	$-1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{53312}(5,\cdot)$	53312.bce	336	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{53312}(9,\cdot)$	53312.yl	168	no	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{53312}(11,\cdot)$	53312.yx	336	yes	$1$	$1$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{53312}(13,\cdot)$	53312.uj	112	yes	$-1$	$1$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{61}{112}\right)$
$\chi_{53312}(15,\cdot)$	53312.rc	56	no	$-1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{28}\right)$	$-1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{53312}(19,\cdot)$	53312.ne	48	no	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{53312}(23,\cdot)$	53312.bai	336	no	$1$	$1$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{53312}(25,\cdot)$	53312.yp	168	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{53312}(27,\cdot)$	53312.tj	112	yes	$-1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{53312}(29,\cdot)$	53312.vh	112	yes	$-1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{53312}(31,\cdot)$	53312.ob	48	no	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{53312}(33,\cdot)$	53312.md	42	no	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{53312}(37,\cdot)$	53312.zb	336	yes	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{53312}(39,\cdot)$	53312.bas	336	no	$1$	$1$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{111}{112}\right)$
$\chi_{53312}(41,\cdot)$	53312.ue	112	no	$1$	$1$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{19}{56}\right)$	$i$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{53312}(43,\cdot)$	53312.vw	112	yes	$-1$	$1$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{53312}(45,\cdot)$	53312.zc	336	yes	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{53312}(47,\cdot)$	53312.sf	84	no	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{53312}(53,\cdot)$	53312.bbo	336	yes	$1$	$1$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{71}{336}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{17}{112}\right)$
$\chi_{53312}(55,\cdot)$	53312.rl	56	no	$1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{53312}(57,\cdot)$	53312.ty	112	no	$-1$	$1$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{47}{56}\right)$	$-1$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{112}\right)$
$\chi_{53312}(59,\cdot)$	53312.bbs	336	yes	$1$	$1$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{97}{112}\right)$
$\chi_{53312}(61,\cdot)$	53312.zc	336	yes	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{53312}(65,\cdot)$	53312.baq	336	no	$-1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{53312}(67,\cdot)$	53312.ot	48	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{53312}(69,\cdot)$	53312.vc	112	no	$-1$	$1$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{53312}(71,\cdot)$	53312.uq	112	no	$1$	$1$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{29}{56}\right)$	$-i$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{53312}(73,\cdot)$	53312.bbn	336	no	$1$	$1$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{107}{112}\right)$
$\chi_{53312}(75,\cdot)$	53312.zw	336	yes	$-1$	$1$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{53312}(79,\cdot)$	53312.na	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$

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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	$53312$
Structure	\(C_{2}\times C_{2}\times C_{16}\times C_{336}\)
Order	$21504$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{53312}(1,\cdot)\)	53312.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{53312}(3,\cdot)\)	53312.bca	336	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{53312}(5,\cdot)\)	53312.bce	336	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{53312}(9,\cdot)\)	53312.yl	168	no	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{53312}(11,\cdot)\)	53312.yx	336	yes	\(1\)	\(1\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{53312}(13,\cdot)\)	53312.uj	112	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)
\(\chi_{53312}(15,\cdot)\)	53312.rc	56	no	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{53312}(19,\cdot)\)	53312.ne	48	no	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{53312}(23,\cdot)\)	53312.bai	336	no	\(1\)	\(1\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{53312}(25,\cdot)\)	53312.yp	168	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{53312}(27,\cdot)\)	53312.tj	112	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{53312}(29,\cdot)\)	53312.vh	112	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{53312}(31,\cdot)\)	53312.ob	48	no	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{53312}(33,\cdot)\)	53312.md	42	no	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{53312}(37,\cdot)\)	53312.zb	336	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{53312}(39,\cdot)\)	53312.bas	336	no	\(1\)	\(1\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{111}{112}\right)\)
\(\chi_{53312}(41,\cdot)\)	53312.ue	112	no	\(1\)	\(1\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(i\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{53312}(43,\cdot)\)	53312.vw	112	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{53312}(45,\cdot)\)	53312.zc	336	yes	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{53312}(47,\cdot)\)	53312.sf	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{53312}(53,\cdot)\)	53312.bbo	336	yes	\(1\)	\(1\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{71}{336}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{17}{112}\right)\)
\(\chi_{53312}(55,\cdot)\)	53312.rl	56	no	\(1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{53312}(57,\cdot)\)	53312.ty	112	no	\(-1\)	\(1\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(-1\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)
\(\chi_{53312}(59,\cdot)\)	53312.bbs	336	yes	\(1\)	\(1\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)
\(\chi_{53312}(61,\cdot)\)	53312.zc	336	yes	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{53312}(65,\cdot)\)	53312.baq	336	no	\(-1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{53312}(67,\cdot)\)	53312.ot	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{53312}(69,\cdot)\)	53312.vc	112	no	\(-1\)	\(1\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{53312}(71,\cdot)\)	53312.uq	112	no	\(1\)	\(1\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(-i\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{53312}(73,\cdot)\)	53312.bbn	336	no	\(1\)	\(1\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{107}{112}\right)\)
\(\chi_{53312}(75,\cdot)\)	53312.zw	336	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{53312}(79,\cdot)\)	53312.na	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)

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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.