LMFDB - Group of Dirichlet characters of modulus 32487

Show commands: PariGP / SageMath

sage: H = DirichletGroup(32487)

pari: g = idealstar(,32487,2)

Character group

sage: G.order() pari: g.no
Order	=	16128
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{32487}(21659,\cdot)$, $\chi_{32487}(22543,\cdot)$, $\chi_{32487}(22492,\cdot)$, $\chi_{32487}(19111,\cdot)$

First 32 of 16128 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$19$	$20$	$22$
$\chi_{32487}(1,\cdot)$	32487.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{32487}(2,\cdot)$	32487.zc	168	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{151}{168}\right)$
$\chi_{32487}(4,\cdot)$	32487.sm	84	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{32487}(5,\cdot)$	32487.zp	336	yes	$1$	$1$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{15}{112}\right)$
$\chi_{32487}(8,\cdot)$	32487.sl	56	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{32487}(10,\cdot)$	32487.bac	336	no	$1$	$1$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{11}{336}\right)$
$\chi_{32487}(11,\cdot)$	32487.baw	336	yes	$-1$	$1$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{239}{336}\right)$
$\chi_{32487}(16,\cdot)$	32487.nc	42	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{32487}(19,\cdot)$	32487.jw	24	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{32487}(20,\cdot)$	32487.zi	336	yes	$1$	$1$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{313}{336}\right)$
$\chi_{32487}(22,\cdot)$	32487.bai	336	no	$-1$	$1$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{205}{336}\right)$
$\chi_{32487}(23,\cdot)$	32487.bbl	336	yes	$1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{23}{336}\right)$
$\chi_{32487}(25,\cdot)$	32487.xs	168	no	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{32487}(29,\cdot)$	32487.bab	336	yes	$1$	$1$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{5}{336}\right)$
$\chi_{32487}(31,\cdot)$	32487.qi	48	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{32487}(32,\cdot)$	32487.zc	168	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{83}{168}\right)$
$\chi_{32487}(37,\cdot)$	32487.bbq	336	no	$1$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{89}{336}\right)$
$\chi_{32487}(38,\cdot)$	32487.sw	84	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{32487}(40,\cdot)$	32487.zv	336	no	$1$	$1$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{93}{112}\right)$
$\chi_{32487}(41,\cdot)$	32487.zi	336	yes	$1$	$1$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{181}{336}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{227}{336}\right)$
$\chi_{32487}(43,\cdot)$	32487.yf	168	no	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{65}{168}\right)$
$\chi_{32487}(44,\cdot)$	32487.zm	336	yes	$-1$	$1$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{181}{336}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{57}{112}\right)$
$\chi_{32487}(46,\cdot)$	32487.bbq	336	no	$1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{169}{336}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{325}{336}\right)$
$\chi_{32487}(47,\cdot)$	32487.tk	84	yes	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{32487}(50,\cdot)$	32487.gs	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{32487}(53,\cdot)$	32487.ya	168	no	$-1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{32487}(55,\cdot)$	32487.sv	84	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{32487}(58,\cdot)$	32487.baq	336	no	$1$	$1$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{307}{336}\right)$
$\chi_{32487}(59,\cdot)$	32487.zf	168	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{149}{168}\right)$
$\chi_{32487}(61,\cdot)$	32487.bae	336	no	$1$	$1$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{187}{336}\right)$
$\chi_{32487}(62,\cdot)$	32487.bag	336	yes	$-1$	$1$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{239}{336}\right)$
$\chi_{32487}(64,\cdot)$	32487.mh	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{7}\right)$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{28}\right)$

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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	$32487$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{336}\)
Order	$16128$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(16\)	\(19\)	\(20\)	\(22\)
\(\chi_{32487}(1,\cdot)\)	32487.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{32487}(2,\cdot)\)	32487.zc	168	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{151}{168}\right)\)
\(\chi_{32487}(4,\cdot)\)	32487.sm	84	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{32487}(5,\cdot)\)	32487.zp	336	yes	\(1\)	\(1\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{15}{112}\right)\)
\(\chi_{32487}(8,\cdot)\)	32487.sl	56	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{32487}(10,\cdot)\)	32487.bac	336	no	\(1\)	\(1\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{11}{336}\right)\)
\(\chi_{32487}(11,\cdot)\)	32487.baw	336	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{239}{336}\right)\)
\(\chi_{32487}(16,\cdot)\)	32487.nc	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{32487}(19,\cdot)\)	32487.jw	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{32487}(20,\cdot)\)	32487.zi	336	yes	\(1\)	\(1\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{313}{336}\right)\)
\(\chi_{32487}(22,\cdot)\)	32487.bai	336	no	\(-1\)	\(1\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{205}{336}\right)\)
\(\chi_{32487}(23,\cdot)\)	32487.bbl	336	yes	\(1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{23}{336}\right)\)
\(\chi_{32487}(25,\cdot)\)	32487.xs	168	no	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{32487}(29,\cdot)\)	32487.bab	336	yes	\(1\)	\(1\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{5}{336}\right)\)
\(\chi_{32487}(31,\cdot)\)	32487.qi	48	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{32487}(32,\cdot)\)	32487.zc	168	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{83}{168}\right)\)
\(\chi_{32487}(37,\cdot)\)	32487.bbq	336	no	\(1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{89}{336}\right)\)
\(\chi_{32487}(38,\cdot)\)	32487.sw	84	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{32487}(40,\cdot)\)	32487.zv	336	no	\(1\)	\(1\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)
\(\chi_{32487}(41,\cdot)\)	32487.zi	336	yes	\(1\)	\(1\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{181}{336}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{227}{336}\right)\)
\(\chi_{32487}(43,\cdot)\)	32487.yf	168	no	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{65}{168}\right)\)
\(\chi_{32487}(44,\cdot)\)	32487.zm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{181}{336}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)
\(\chi_{32487}(46,\cdot)\)	32487.bbq	336	no	\(1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{169}{336}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{325}{336}\right)\)
\(\chi_{32487}(47,\cdot)\)	32487.tk	84	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{32487}(50,\cdot)\)	32487.gs	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{32487}(53,\cdot)\)	32487.ya	168	no	\(-1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{32487}(55,\cdot)\)	32487.sv	84	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{32487}(58,\cdot)\)	32487.baq	336	no	\(1\)	\(1\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{307}{336}\right)\)
\(\chi_{32487}(59,\cdot)\)	32487.zf	168	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{149}{168}\right)\)
\(\chi_{32487}(61,\cdot)\)	32487.bae	336	no	\(1\)	\(1\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{187}{336}\right)\)
\(\chi_{32487}(62,\cdot)\)	32487.bag	336	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{239}{336}\right)\)
\(\chi_{32487}(64,\cdot)\)	32487.mh	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)

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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.