LMFDB - Group of Dirichlet characters of modulus 228672

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(228672)

gp:g = idealstar(,228672,2)

magma:G = FullDirichletGroup(228672);

Character group

Order	=	76032	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{1584}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{228672}(21439,\cdot)$, $\chi_{228672}(185797,\cdot)$, $\chi_{228672}(25409,\cdot)$, $\chi_{228672}(169921,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 76032 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{228672}(1,\cdot)$	228672.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{228672}(5,\cdot)$	228672.bry	1584	yes	$1$	$1$	$e\left(\frac{367}{1584}\right)$	$e\left(\frac{625}{792}\right)$	$e\left(\frac{791}{1584}\right)$	$e\left(\frac{1361}{1584}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1205}{1584}\right)$	$e\left(\frac{445}{792}\right)$	$e\left(\frac{367}{792}\right)$	$e\left(\frac{1577}{1584}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{228672}(7,\cdot)$	228672.bpn	792	no	$1$	$1$	$e\left(\frac{625}{792}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{479}{792}\right)$	$e\left(\frac{491}{792}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{173}{792}\right)$	$e\left(\frac{289}{396}\right)$	$e\left(\frac{229}{396}\right)$	$e\left(\frac{581}{792}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{228672}(11,\cdot)$	228672.brq	1584	yes	$1$	$1$	$e\left(\frac{791}{1584}\right)$	$e\left(\frac{479}{792}\right)$	$e\left(\frac{1147}{1584}\right)$	$e\left(\frac{1153}{1584}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{1489}{1584}\right)$	$e\left(\frac{425}{792}\right)$	$e\left(\frac{791}{792}\right)$	$e\left(\frac{109}{1584}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{228672}(13,\cdot)$	228672.brz	1584	yes	$-1$	$1$	$e\left(\frac{1361}{1584}\right)$	$e\left(\frac{491}{792}\right)$	$e\left(\frac{1153}{1584}\right)$	$e\left(\frac{775}{1584}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{331}{1584}\right)$	$e\left(\frac{263}{792}\right)$	$e\left(\frac{569}{792}\right)$	$e\left(\frac{943}{1584}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{228672}(17,\cdot)$	228672.bcj	132	no	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{228672}(19,\cdot)$	228672.brb	1584	no	$-1$	$1$	$e\left(\frac{1205}{1584}\right)$	$e\left(\frac{173}{792}\right)$	$e\left(\frac{1489}{1584}\right)$	$e\left(\frac{331}{1584}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{1483}{1584}\right)$	$e\left(\frac{167}{792}\right)$	$e\left(\frac{413}{792}\right)$	$e\left(\frac{919}{1584}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{228672}(23,\cdot)$	228672.bot	792	no	$1$	$1$	$e\left(\frac{445}{792}\right)$	$e\left(\frac{289}{396}\right)$	$e\left(\frac{425}{792}\right)$	$e\left(\frac{263}{792}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{167}{792}\right)$	$e\left(\frac{31}{396}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{203}{792}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{228672}(25,\cdot)$	228672.bqg	792	no	$1$	$1$	$e\left(\frac{367}{792}\right)$	$e\left(\frac{229}{396}\right)$	$e\left(\frac{791}{792}\right)$	$e\left(\frac{569}{792}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{413}{792}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{367}{396}\right)$	$e\left(\frac{785}{792}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{228672}(29,\cdot)$	228672.brj	1584	yes	$-1$	$1$	$e\left(\frac{1577}{1584}\right)$	$e\left(\frac{581}{792}\right)$	$e\left(\frac{109}{1584}\right)$	$e\left(\frac{943}{1584}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{919}{1584}\right)$	$e\left(\frac{203}{792}\right)$	$e\left(\frac{785}{792}\right)$	$e\left(\frac{1555}{1584}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{228672}(31,\cdot)$	228672.un	66	no	$-1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{228672}(35,\cdot)$	228672.tl	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{48}\right)$	$i$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{48}\right)$	$1$
$\chi_{228672}(37,\cdot)$	228672.bru	1584	no	$1$	$1$	$e\left(\frac{1307}{1584}\right)$	$e\left(\frac{23}{792}\right)$	$e\left(\frac{919}{1584}\right)$	$e\left(\frac{1525}{1584}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{877}{1584}\right)$	$e\left(\frac{773}{792}\right)$	$e\left(\frac{515}{792}\right)$	$e\left(\frac{889}{1584}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{228672}(41,\cdot)$	228672.xf	72	no	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{228672}(43,\cdot)$	228672.bns	528	yes	$-1$	$1$	$e\left(\frac{181}{528}\right)$	$e\left(\frac{25}{264}\right)$	$e\left(\frac{425}{528}\right)$	$e\left(\frac{73}{176}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{211}{528}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{181}{264}\right)$	$e\left(\frac{335}{528}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{228672}(47,\cdot)$	228672.bjo	396	no	$1$	$1$	$e\left(\frac{211}{396}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{137}{396}\right)$	$e\left(\frac{191}{396}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{113}{396}\right)$	$e\left(\frac{85}{198}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{365}{396}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{228672}(49,\cdot)$	228672.bjs	396	no	$1$	$1$	$e\left(\frac{229}{396}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{83}{396}\right)$	$e\left(\frac{95}{396}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{173}{396}\right)$	$e\left(\frac{91}{198}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{185}{396}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{228672}(53,\cdot)$	228672.bms	528	no	$1$	$1$	$e\left(\frac{185}{528}\right)$	$e\left(\frac{23}{264}\right)$	$e\left(\frac{193}{528}\right)$	$e\left(\frac{7}{528}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{528}\right)$	$e\left(\frac{179}{264}\right)$	$e\left(\frac{185}{264}\right)$	$e\left(\frac{31}{528}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{228672}(55,\cdot)$	228672.bje	264	no	$1$	$1$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{59}{264}\right)$	$e\left(\frac{155}{264}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{185}{264}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{228672}(59,\cdot)$	228672.bqs	1584	yes	$-1$	$1$	$e\left(\frac{1351}{1584}\right)$	$e\left(\frac{529}{792}\right)$	$e\left(\frac{1535}{1584}\right)$	$e\left(\frac{953}{1584}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1229}{1584}\right)$	$e\left(\frac{25}{792}\right)$	$e\left(\frac{559}{792}\right)$	$e\left(\frac{1241}{1584}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{228672}(61,\cdot)$	228672.brz	1584	yes	$-1$	$1$	$e\left(\frac{1213}{1584}\right)$	$e\left(\frac{103}{792}\right)$	$e\left(\frac{1421}{1584}\right)$	$e\left(\frac{1403}{1584}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1055}{1584}\right)$	$e\left(\frac{331}{792}\right)$	$e\left(\frac{421}{792}\right)$	$e\left(\frac{1235}{1584}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{228672}(65,\cdot)$	228672.uh	66	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{228672}(67,\cdot)$	228672.bro	1584	yes	$-1$	$1$	$e\left(\frac{1241}{1584}\right)$	$e\left(\frac{353}{792}\right)$	$e\left(\frac{1381}{1584}\right)$	$e\left(\frac{535}{1584}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{1207}{1584}\right)$	$e\left(\frac{179}{792}\right)$	$e\left(\frac{449}{792}\right)$	$e\left(\frac{163}{1584}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{228672}(71,\cdot)$	228672.bjf	264	no	$-1$	$1$	$e\left(\frac{139}{264}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{245}{264}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{71}{264}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{227}{264}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{228672}(73,\cdot)$	228672.bor	792	no	$1$	$1$	$e\left(\frac{745}{792}\right)$	$e\left(\frac{337}{396}\right)$	$e\left(\frac{53}{792}\right)$	$e\left(\frac{599}{792}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{23}{792}\right)$	$e\left(\frac{307}{396}\right)$	$e\left(\frac{349}{396}\right)$	$e\left(\frac{371}{792}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{228672}(77,\cdot)$	228672.bqo	1584	yes	$1$	$1$	$e\left(\frac{457}{1584}\right)$	$e\left(\frac{283}{792}\right)$	$e\left(\frac{521}{1584}\right)$	$e\left(\frac{551}{1584}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{251}{1584}\right)$	$e\left(\frac{211}{792}\right)$	$e\left(\frac{457}{792}\right)$	$e\left(\frac{1271}{1584}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{228672}(79,\cdot)$	228672.oh	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{228672}(83,\cdot)$	228672.bnn	528	yes	$1$	$1$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{17}{176}\right)$	$e\left(\frac{241}{528}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{233}{528}\right)$	$e\left(\frac{185}{264}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{119}{176}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{228672}(85,\cdot)$	228672.bdx	144	yes	$1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{228672}(89,\cdot)$	228672.bpd	792	no	$1$	$1$	$e\left(\frac{425}{792}\right)$	$e\left(\frac{17}{99}\right)$	$e\left(\frac{595}{792}\right)$	$e\left(\frac{751}{792}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{445}{792}\right)$	$e\left(\frac{17}{396}\right)$	$e\left(\frac{29}{396}\right)$	$e\left(\frac{205}{792}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{228672}(91,\cdot)$	228672.bra	1584	no	$-1$	$1$	$e\left(\frac{1027}{1584}\right)$	$e\left(\frac{295}{792}\right)$	$e\left(\frac{527}{1584}\right)$	$e\left(\frac{173}{1584}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{677}{1584}\right)$	$e\left(\frac{49}{792}\right)$	$e\left(\frac{235}{792}\right)$	$e\left(\frac{521}{1584}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{228672}(95,\cdot)$	228672.bau	132	no	$-1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{47}{66}\right)$

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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	$228672$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{1584}\)
Order	$76032$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{228672}(1,\cdot)\)	228672.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{228672}(5,\cdot)\)	228672.bry	1584	yes	\(1\)	\(1\)	\(e\left(\frac{367}{1584}\right)\)	\(e\left(\frac{625}{792}\right)\)	\(e\left(\frac{791}{1584}\right)\)	\(e\left(\frac{1361}{1584}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1205}{1584}\right)\)	\(e\left(\frac{445}{792}\right)\)	\(e\left(\frac{367}{792}\right)\)	\(e\left(\frac{1577}{1584}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{228672}(7,\cdot)\)	228672.bpn	792	no	\(1\)	\(1\)	\(e\left(\frac{625}{792}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{479}{792}\right)\)	\(e\left(\frac{491}{792}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{173}{792}\right)\)	\(e\left(\frac{289}{396}\right)\)	\(e\left(\frac{229}{396}\right)\)	\(e\left(\frac{581}{792}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{228672}(11,\cdot)\)	228672.brq	1584	yes	\(1\)	\(1\)	\(e\left(\frac{791}{1584}\right)\)	\(e\left(\frac{479}{792}\right)\)	\(e\left(\frac{1147}{1584}\right)\)	\(e\left(\frac{1153}{1584}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{1489}{1584}\right)\)	\(e\left(\frac{425}{792}\right)\)	\(e\left(\frac{791}{792}\right)\)	\(e\left(\frac{109}{1584}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{228672}(13,\cdot)\)	228672.brz	1584	yes	\(-1\)	\(1\)	\(e\left(\frac{1361}{1584}\right)\)	\(e\left(\frac{491}{792}\right)\)	\(e\left(\frac{1153}{1584}\right)\)	\(e\left(\frac{775}{1584}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{331}{1584}\right)\)	\(e\left(\frac{263}{792}\right)\)	\(e\left(\frac{569}{792}\right)\)	\(e\left(\frac{943}{1584}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{228672}(17,\cdot)\)	228672.bcj	132	no	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{228672}(19,\cdot)\)	228672.brb	1584	no	\(-1\)	\(1\)	\(e\left(\frac{1205}{1584}\right)\)	\(e\left(\frac{173}{792}\right)\)	\(e\left(\frac{1489}{1584}\right)\)	\(e\left(\frac{331}{1584}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{1483}{1584}\right)\)	\(e\left(\frac{167}{792}\right)\)	\(e\left(\frac{413}{792}\right)\)	\(e\left(\frac{919}{1584}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{228672}(23,\cdot)\)	228672.bot	792	no	\(1\)	\(1\)	\(e\left(\frac{445}{792}\right)\)	\(e\left(\frac{289}{396}\right)\)	\(e\left(\frac{425}{792}\right)\)	\(e\left(\frac{263}{792}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{167}{792}\right)\)	\(e\left(\frac{31}{396}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{203}{792}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{228672}(25,\cdot)\)	228672.bqg	792	no	\(1\)	\(1\)	\(e\left(\frac{367}{792}\right)\)	\(e\left(\frac{229}{396}\right)\)	\(e\left(\frac{791}{792}\right)\)	\(e\left(\frac{569}{792}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{413}{792}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{367}{396}\right)\)	\(e\left(\frac{785}{792}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{228672}(29,\cdot)\)	228672.brj	1584	yes	\(-1\)	\(1\)	\(e\left(\frac{1577}{1584}\right)\)	\(e\left(\frac{581}{792}\right)\)	\(e\left(\frac{109}{1584}\right)\)	\(e\left(\frac{943}{1584}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{919}{1584}\right)\)	\(e\left(\frac{203}{792}\right)\)	\(e\left(\frac{785}{792}\right)\)	\(e\left(\frac{1555}{1584}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{228672}(31,\cdot)\)	228672.un	66	no	\(-1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{228672}(35,\cdot)\)	228672.tl	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(i\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(1\)
\(\chi_{228672}(37,\cdot)\)	228672.bru	1584	no	\(1\)	\(1\)	\(e\left(\frac{1307}{1584}\right)\)	\(e\left(\frac{23}{792}\right)\)	\(e\left(\frac{919}{1584}\right)\)	\(e\left(\frac{1525}{1584}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{877}{1584}\right)\)	\(e\left(\frac{773}{792}\right)\)	\(e\left(\frac{515}{792}\right)\)	\(e\left(\frac{889}{1584}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{228672}(41,\cdot)\)	228672.xf	72	no	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{228672}(43,\cdot)\)	228672.bns	528	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{528}\right)\)	\(e\left(\frac{25}{264}\right)\)	\(e\left(\frac{425}{528}\right)\)	\(e\left(\frac{73}{176}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{211}{528}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{181}{264}\right)\)	\(e\left(\frac{335}{528}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{228672}(47,\cdot)\)	228672.bjo	396	no	\(1\)	\(1\)	\(e\left(\frac{211}{396}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{137}{396}\right)\)	\(e\left(\frac{191}{396}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{113}{396}\right)\)	\(e\left(\frac{85}{198}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{365}{396}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{228672}(49,\cdot)\)	228672.bjs	396	no	\(1\)	\(1\)	\(e\left(\frac{229}{396}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{83}{396}\right)\)	\(e\left(\frac{95}{396}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{173}{396}\right)\)	\(e\left(\frac{91}{198}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{185}{396}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{228672}(53,\cdot)\)	228672.bms	528	no	\(1\)	\(1\)	\(e\left(\frac{185}{528}\right)\)	\(e\left(\frac{23}{264}\right)\)	\(e\left(\frac{193}{528}\right)\)	\(e\left(\frac{7}{528}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{528}\right)\)	\(e\left(\frac{179}{264}\right)\)	\(e\left(\frac{185}{264}\right)\)	\(e\left(\frac{31}{528}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{228672}(55,\cdot)\)	228672.bje	264	no	\(1\)	\(1\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{59}{264}\right)\)	\(e\left(\frac{155}{264}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{185}{264}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{228672}(59,\cdot)\)	228672.bqs	1584	yes	\(-1\)	\(1\)	\(e\left(\frac{1351}{1584}\right)\)	\(e\left(\frac{529}{792}\right)\)	\(e\left(\frac{1535}{1584}\right)\)	\(e\left(\frac{953}{1584}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{1229}{1584}\right)\)	\(e\left(\frac{25}{792}\right)\)	\(e\left(\frac{559}{792}\right)\)	\(e\left(\frac{1241}{1584}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{228672}(61,\cdot)\)	228672.brz	1584	yes	\(-1\)	\(1\)	\(e\left(\frac{1213}{1584}\right)\)	\(e\left(\frac{103}{792}\right)\)	\(e\left(\frac{1421}{1584}\right)\)	\(e\left(\frac{1403}{1584}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1055}{1584}\right)\)	\(e\left(\frac{331}{792}\right)\)	\(e\left(\frac{421}{792}\right)\)	\(e\left(\frac{1235}{1584}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{228672}(65,\cdot)\)	228672.uh	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{228672}(67,\cdot)\)	228672.bro	1584	yes	\(-1\)	\(1\)	\(e\left(\frac{1241}{1584}\right)\)	\(e\left(\frac{353}{792}\right)\)	\(e\left(\frac{1381}{1584}\right)\)	\(e\left(\frac{535}{1584}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{1207}{1584}\right)\)	\(e\left(\frac{179}{792}\right)\)	\(e\left(\frac{449}{792}\right)\)	\(e\left(\frac{163}{1584}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{228672}(71,\cdot)\)	228672.bjf	264	no	\(-1\)	\(1\)	\(e\left(\frac{139}{264}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{245}{264}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{71}{264}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{227}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{228672}(73,\cdot)\)	228672.bor	792	no	\(1\)	\(1\)	\(e\left(\frac{745}{792}\right)\)	\(e\left(\frac{337}{396}\right)\)	\(e\left(\frac{53}{792}\right)\)	\(e\left(\frac{599}{792}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{23}{792}\right)\)	\(e\left(\frac{307}{396}\right)\)	\(e\left(\frac{349}{396}\right)\)	\(e\left(\frac{371}{792}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{228672}(77,\cdot)\)	228672.bqo	1584	yes	\(1\)	\(1\)	\(e\left(\frac{457}{1584}\right)\)	\(e\left(\frac{283}{792}\right)\)	\(e\left(\frac{521}{1584}\right)\)	\(e\left(\frac{551}{1584}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{251}{1584}\right)\)	\(e\left(\frac{211}{792}\right)\)	\(e\left(\frac{457}{792}\right)\)	\(e\left(\frac{1271}{1584}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{228672}(79,\cdot)\)	228672.oh	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{228672}(83,\cdot)\)	228672.bnn	528	yes	\(1\)	\(1\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{17}{176}\right)\)	\(e\left(\frac{241}{528}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{233}{528}\right)\)	\(e\left(\frac{185}{264}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{119}{176}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{228672}(85,\cdot)\)	228672.bdx	144	yes	\(1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{228672}(89,\cdot)\)	228672.bpd	792	no	\(1\)	\(1\)	\(e\left(\frac{425}{792}\right)\)	\(e\left(\frac{17}{99}\right)\)	\(e\left(\frac{595}{792}\right)\)	\(e\left(\frac{751}{792}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{445}{792}\right)\)	\(e\left(\frac{17}{396}\right)\)	\(e\left(\frac{29}{396}\right)\)	\(e\left(\frac{205}{792}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{228672}(91,\cdot)\)	228672.bra	1584	no	\(-1\)	\(1\)	\(e\left(\frac{1027}{1584}\right)\)	\(e\left(\frac{295}{792}\right)\)	\(e\left(\frac{527}{1584}\right)\)	\(e\left(\frac{173}{1584}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{677}{1584}\right)\)	\(e\left(\frac{49}{792}\right)\)	\(e\left(\frac{235}{792}\right)\)	\(e\left(\frac{521}{1584}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{228672}(95,\cdot)\)	228672.bau	132	no	\(-1\)	\(1\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)

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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.