LMFDB - Group of Dirichlet characters of modulus 277984

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(277984)

gp:g = idealstar(,277984,2)

magma:G = FullDirichletGroup(277984);

Character group

Order	=	110592	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{8}\times C_{24}\times C_{144}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{277984}(17375,\cdot)$, $\chi_{277984}(243237,\cdot)$, $\chi_{277984}(79425,\cdot)$, $\chi_{277984}(261633,\cdot)$, $\chi_{277984}(186593,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 110592 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{277984}(1,\cdot)$	277984.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{277984}(3,\cdot)$	277984.gor	48	yes	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{277984}(5,\cdot)$	277984.jjf	144	yes	$-1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{277984}(9,\cdot)$	277984.dro	24	no	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{277984}(11,\cdot)$	277984.jmk	144	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{277984}(13,\cdot)$	277984.hij	72	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{277984}(15,\cdot)$	277984.hxc	72	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{277984}(19,\cdot)$	277984.iwg	72	yes	$1$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$	$1$
$\chi_{277984}(23,\cdot)$	277984.jey	144	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{277984}(25,\cdot)$	277984.hxk	72	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{277984}(27,\cdot)$	277984.cao	16	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{277984}(29,\cdot)$	277984.jlr	144	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{277984}(31,\cdot)$	277984.jtn	144	no	$1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{277984}(33,\cdot)$	277984.ira	72	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{36}\right)$	$i$
$\chi_{277984}(37,\cdot)$	277984.jhq	144	yes	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{277984}(39,\cdot)$	277984.jer	144	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{277984}(41,\cdot)$	277984.jwe	144	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{277984}(43,\cdot)$	277984.cum	24	no	$1$	$1$	$-i$	$e\left(\frac{23}{24}\right)$	$-1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{277984}(45,\cdot)$	277984.jot	144	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{277984}(47,\cdot)$	277984.hat	72	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{36}\right)$	$1$
$\chi_{277984}(53,\cdot)$	277984.ist	72	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{36}\right)$	$-1$
$\chi_{277984}(55,\cdot)$	277984.ezh	36	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$	$1$
$\chi_{277984}(57,\cdot)$	277984.jdg	144	no	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{277984}(59,\cdot)$	277984.ioq	72	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{36}\right)$	$i$
$\chi_{277984}(61,\cdot)$	277984.ize	144	yes	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{277984}(65,\cdot)$	277984.gme	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{277984}(67,\cdot)$	277984.hkw	72	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{277984}(69,\cdot)$	277984.hmo	72	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{277984}(71,\cdot)$	277984.jwh	144	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{277984}(75,\cdot)$	277984.iyh	144	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{277984}(79,\cdot)$	277984.jge	144	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{277984}(81,\cdot)$	277984.bml	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$

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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 $\F_{q}$
Belyi maps

Modulus	$277984$
Structure	\(C_{2}\times C_{2}\times C_{8}\times C_{24}\times C_{144}\)
Order	$110592$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{277984}(1,\cdot)\)	277984.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{277984}(3,\cdot)\)	277984.gor	48	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{277984}(5,\cdot)\)	277984.jjf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{277984}(9,\cdot)\)	277984.dro	24	no	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{277984}(11,\cdot)\)	277984.jmk	144	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{277984}(13,\cdot)\)	277984.hij	72	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{277984}(15,\cdot)\)	277984.hxc	72	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{277984}(19,\cdot)\)	277984.iwg	72	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)
\(\chi_{277984}(23,\cdot)\)	277984.jey	144	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{277984}(25,\cdot)\)	277984.hxk	72	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{277984}(27,\cdot)\)	277984.cao	16	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{277984}(29,\cdot)\)	277984.jlr	144	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{277984}(31,\cdot)\)	277984.jtn	144	no	\(1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{277984}(33,\cdot)\)	277984.ira	72	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(i\)
\(\chi_{277984}(37,\cdot)\)	277984.jhq	144	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{277984}(39,\cdot)\)	277984.jer	144	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{277984}(41,\cdot)\)	277984.jwe	144	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{277984}(43,\cdot)\)	277984.cum	24	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(-1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{277984}(45,\cdot)\)	277984.jot	144	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{277984}(47,\cdot)\)	277984.hat	72	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(1\)
\(\chi_{277984}(53,\cdot)\)	277984.ist	72	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(-1\)
\(\chi_{277984}(55,\cdot)\)	277984.ezh	36	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)
\(\chi_{277984}(57,\cdot)\)	277984.jdg	144	no	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{277984}(59,\cdot)\)	277984.ioq	72	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(i\)
\(\chi_{277984}(61,\cdot)\)	277984.ize	144	yes	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{277984}(65,\cdot)\)	277984.gme	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{277984}(67,\cdot)\)	277984.hkw	72	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{277984}(69,\cdot)\)	277984.hmo	72	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{277984}(71,\cdot)\)	277984.jwh	144	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{277984}(75,\cdot)\)	277984.iyh	144	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{277984}(79,\cdot)\)	277984.jge	144	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{277984}(81,\cdot)\)	277984.bml	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)

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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.