LMFDB - Group of Dirichlet characters of modulus 833952

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(833952)

gp:g = idealstar(,833952,2)

magma:G = FullDirichletGroup(833952);

Character group

Order	=	221184	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{8}\times C_{24}\times C_{144}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{833952}(573343,\cdot)$, $\chi_{833952}(521221,\cdot)$, $\chi_{833952}(277985,\cdot)$, $\chi_{833952}(357409,\cdot)$, $\chi_{833952}(539617,\cdot)$, $\chi_{833952}(742561,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 221184 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{833952}(1,\cdot)$	833952.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{833952}(5,\cdot)$	833952.tfn	144	yes	$1$	$1$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{35}{144}\right)$
$\chi_{833952}(11,\cdot)$	833952.swo	144	yes	$1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{17}{144}\right)$
$\chi_{833952}(13,\cdot)$	833952.nwz	72	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{833952}(19,\cdot)$	833952.pho	72	no	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{833952}(23,\cdot)$	833952.tmq	144	no	$-1$	$1$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{125}{144}\right)$
$\chi_{833952}(25,\cdot)$	833952.ply	72	no	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{833952}(29,\cdot)$	833952.taz	144	no	$-1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{91}{144}\right)$
$\chi_{833952}(31,\cdot)$	833952.tna	144	no	$1$	$1$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{43}{144}\right)$
$\chi_{833952}(37,\cdot)$	833952.spl	144	no	$-1$	$1$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{143}{144}\right)$
$\chi_{833952}(41,\cdot)$	833952.tpe	144	no	$-1$	$1$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{41}{144}\right)$
$\chi_{833952}(43,\cdot)$	833952.fsy	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{833952}(47,\cdot)$	833952.oxi	72	no	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{833952}(53,\cdot)$	833952.qvb	72	yes	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{833952}(55,\cdot)$	833952.kih	36	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{833952}(59,\cdot)$	833952.pvc	72	yes	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{65}{72}\right)$
$\chi_{833952}(61,\cdot)$	833952.ryi	144	no	$1$	$1$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{5}{144}\right)$
$\chi_{833952}(65,\cdot)$	833952.mgc	48	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{833952}(67,\cdot)$	833952.ogz	72	no	$-1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{833952}(71,\cdot)$	833952.tpc	144	no	$-1$	$1$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{19}{144}\right)$
$\chi_{833952}(79,\cdot)$	833952.smy	144	no	$1$	$1$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{85}{144}\right)$
$\chi_{833952}(83,\cdot)$	833952.bct	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{833952}(89,\cdot)$	833952.kgr	36	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{833952}(95,\cdot)$	833952.lqv	48	no	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{833952}(97,\cdot)$	833952.kyl	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{833952}(101,\cdot)$	833952.oga	72	yes	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{833952}(103,\cdot)$	833952.gct	24	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{833952}(107,\cdot)$	833952.tej	144	yes	$1$	$1$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{43}{144}\right)$
$\chi_{833952}(109,\cdot)$	833952.tcb	144	no	$-1$	$1$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{53}{144}\right)$
$\chi_{833952}(113,\cdot)$	833952.tmk	144	no	$-1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{101}{144}\right)$
$\chi_{833952}(115,\cdot)$	833952.nxb	72	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{833952}(121,\cdot)$	833952.qct	72	no	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{17}{72}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$833952$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{8}\times C_{24}\times C_{144}\)
Order	$221184$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{833952}(1,\cdot)\)	833952.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{833952}(5,\cdot)\)	833952.tfn	144	yes	\(1\)	\(1\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)
\(\chi_{833952}(11,\cdot)\)	833952.swo	144	yes	\(1\)	\(1\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)
\(\chi_{833952}(13,\cdot)\)	833952.nwz	72	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{833952}(19,\cdot)\)	833952.pho	72	no	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)
\(\chi_{833952}(23,\cdot)\)	833952.tmq	144	no	\(-1\)	\(1\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)
\(\chi_{833952}(25,\cdot)\)	833952.ply	72	no	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{833952}(29,\cdot)\)	833952.taz	144	no	\(-1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{91}{144}\right)\)
\(\chi_{833952}(31,\cdot)\)	833952.tna	144	no	\(1\)	\(1\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)
\(\chi_{833952}(37,\cdot)\)	833952.spl	144	no	\(-1\)	\(1\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{143}{144}\right)\)
\(\chi_{833952}(41,\cdot)\)	833952.tpe	144	no	\(-1\)	\(1\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{41}{144}\right)\)
\(\chi_{833952}(43,\cdot)\)	833952.fsy	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{833952}(47,\cdot)\)	833952.oxi	72	no	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{833952}(53,\cdot)\)	833952.qvb	72	yes	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)
\(\chi_{833952}(55,\cdot)\)	833952.kih	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{833952}(59,\cdot)\)	833952.pvc	72	yes	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)
\(\chi_{833952}(61,\cdot)\)	833952.ryi	144	no	\(1\)	\(1\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)
\(\chi_{833952}(65,\cdot)\)	833952.mgc	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{833952}(67,\cdot)\)	833952.ogz	72	no	\(-1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{833952}(71,\cdot)\)	833952.tpc	144	no	\(-1\)	\(1\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{19}{144}\right)\)
\(\chi_{833952}(79,\cdot)\)	833952.smy	144	no	\(1\)	\(1\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{85}{144}\right)\)
\(\chi_{833952}(83,\cdot)\)	833952.bct	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{833952}(89,\cdot)\)	833952.kgr	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{833952}(95,\cdot)\)	833952.lqv	48	no	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{833952}(97,\cdot)\)	833952.kyl	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{833952}(101,\cdot)\)	833952.oga	72	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{833952}(103,\cdot)\)	833952.gct	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{833952}(107,\cdot)\)	833952.tej	144	yes	\(1\)	\(1\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)
\(\chi_{833952}(109,\cdot)\)	833952.tcb	144	no	\(-1\)	\(1\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{53}{144}\right)\)
\(\chi_{833952}(113,\cdot)\)	833952.tmk	144	no	\(-1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{101}{144}\right)\)
\(\chi_{833952}(115,\cdot)\)	833952.nxb	72	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{833952}(121,\cdot)\)	833952.qct	72	no	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)

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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.