LMFDB - Group of Dirichlet characters of modulus 159936

Show commands: PariGP / SageMath

sage: H = DirichletGroup(159936)

pari: g = idealstar(,159936,2)

Character group

sage: G.order() pari: g.no
Order	=	43008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{16}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{159936}(104959,\cdot)$, $\chi_{159936}(109957,\cdot)$, $\chi_{159936}(106625,\cdot)$, $\chi_{159936}(117505,\cdot)$, $\chi_{159936}(94081,\cdot)$

First 32 of 43008 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{159936}(1,\cdot)$	159936.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{159936}(5,\cdot)$	159936.cef	336	yes	$-1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{159936}(11,\cdot)$	159936.cel	336	yes	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{109}{112}\right)$
$\chi_{159936}(13,\cdot)$	159936.bpm	112	no	$-1$	$1$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{79}{112}\right)$	$i$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{159936}(19,\cdot)$	159936.bdd	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$i$
$\chi_{159936}(23,\cdot)$	159936.cce	336	no	$-1$	$1$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{71}{112}\right)$
$\chi_{159936}(25,\cdot)$	159936.bww	168	no	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{159936}(29,\cdot)$	159936.brn	112	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{55}{112}\right)$
$\chi_{159936}(31,\cdot)$	159936.bdl	48	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{29}{48}\right)$	$i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{159936}(37,\cdot)$	159936.bzp	336	no	$-1$	$1$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{111}{112}\right)$
$\chi_{159936}(41,\cdot)$	159936.bqm	112	no	$-1$	$1$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{37}{56}\right)$	$i$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{159936}(43,\cdot)$	159936.bpw	112	no	$-1$	$1$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{159936}(47,\cdot)$	159936.blx	84	no	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{159936}(53,\cdot)$	159936.cdh	336	yes	$-1$	$1$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{159936}(55,\cdot)$	159936.bhy	56	no	$1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{25}{56}\right)$	$-i$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{159936}(59,\cdot)$	159936.cbo	336	yes	$-1$	$1$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{159936}(61,\cdot)$	159936.ccv	336	no	$1$	$1$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{159936}(65,\cdot)$	159936.ccd	336	no	$1$	$1$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{93}{112}\right)$
$\chi_{159936}(67,\cdot)$	159936.bed	48	no	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{159936}(71,\cdot)$	159936.bqp	112	no	$-1$	$1$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{27}{56}\right)$	$-i$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{57}{112}\right)$
$\chi_{159936}(73,\cdot)$	159936.cdr	336	no	$1$	$1$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{159936}(79,\cdot)$	159936.zx	48	no	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{48}\right)$	$-1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{159936}(83,\cdot)$	159936.bpf	112	yes	$-1$	$1$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{159936}(89,\cdot)$	159936.buv	168	no	$1$	$1$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{159936}(95,\cdot)$	159936.cbw	336	no	$-1$	$1$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{47}{112}\right)$
$\chi_{159936}(97,\cdot)$	159936.ps	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{159936}(101,\cdot)$	159936.ccq	336	yes	$1$	$1$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{13}{56}\right)$
$\chi_{159936}(103,\cdot)$	159936.bvc	168	no	$1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{159936}(107,\cdot)$	159936.ccy	336	yes	$-1$	$1$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{293}{336}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{159936}(109,\cdot)$	159936.cee	336	no	$-1$	$1$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{109}{112}\right)$
$\chi_{159936}(113,\cdot)$	159936.bsw	112	no	$1$	$1$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{59}{112}\right)$
$\chi_{159936}(115,\cdot)$	159936.cbc	336	no	$1$	$1$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{45}{56}\right)$

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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	$159936$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{16}\times C_{336}\)
Order	$43008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{159936}(1,\cdot)\)	159936.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{159936}(5,\cdot)\)	159936.cef	336	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{159936}(11,\cdot)\)	159936.cel	336	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{109}{112}\right)\)
\(\chi_{159936}(13,\cdot)\)	159936.bpm	112	no	\(-1\)	\(1\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(i\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{159936}(19,\cdot)\)	159936.bdd	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(i\)
\(\chi_{159936}(23,\cdot)\)	159936.cce	336	no	\(-1\)	\(1\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{71}{112}\right)\)
\(\chi_{159936}(25,\cdot)\)	159936.bww	168	no	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{159936}(29,\cdot)\)	159936.brn	112	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{55}{112}\right)\)
\(\chi_{159936}(31,\cdot)\)	159936.bdl	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{159936}(37,\cdot)\)	159936.bzp	336	no	\(-1\)	\(1\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{111}{112}\right)\)
\(\chi_{159936}(41,\cdot)\)	159936.bqm	112	no	\(-1\)	\(1\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(i\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{159936}(43,\cdot)\)	159936.bpw	112	no	\(-1\)	\(1\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{159936}(47,\cdot)\)	159936.blx	84	no	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{159936}(53,\cdot)\)	159936.cdh	336	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{159936}(55,\cdot)\)	159936.bhy	56	no	\(1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(-i\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{159936}(59,\cdot)\)	159936.cbo	336	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{159936}(61,\cdot)\)	159936.ccv	336	no	\(1\)	\(1\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{159936}(65,\cdot)\)	159936.ccd	336	no	\(1\)	\(1\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{93}{112}\right)\)
\(\chi_{159936}(67,\cdot)\)	159936.bed	48	no	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{159936}(71,\cdot)\)	159936.bqp	112	no	\(-1\)	\(1\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(-i\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)
\(\chi_{159936}(73,\cdot)\)	159936.cdr	336	no	\(1\)	\(1\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{159936}(79,\cdot)\)	159936.zx	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{159936}(83,\cdot)\)	159936.bpf	112	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{159936}(89,\cdot)\)	159936.buv	168	no	\(1\)	\(1\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{159936}(95,\cdot)\)	159936.cbw	336	no	\(-1\)	\(1\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{47}{112}\right)\)
\(\chi_{159936}(97,\cdot)\)	159936.ps	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{159936}(101,\cdot)\)	159936.ccq	336	yes	\(1\)	\(1\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{13}{56}\right)\)
\(\chi_{159936}(103,\cdot)\)	159936.bvc	168	no	\(1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{159936}(107,\cdot)\)	159936.ccy	336	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{293}{336}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{159936}(109,\cdot)\)	159936.cee	336	no	\(-1\)	\(1\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{109}{112}\right)\)
\(\chi_{159936}(113,\cdot)\)	159936.bsw	112	no	\(1\)	\(1\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)
\(\chi_{159936}(115,\cdot)\)	159936.cbc	336	no	\(1\)	\(1\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{45}{56}\right)\)

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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.