LMFDB - Group of Dirichlet characters of modulus 20736

Show commands: PariGP / SageMath

sage: H = DirichletGroup(20736)

pari: g = idealstar(,20736,2)

Character group

sage: G.order() pari: g.no
Order	=	6912
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1728}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{20736}(12799,\cdot)$, $\chi_{20736}(15877,\cdot)$, $\chi_{20736}(6401,\cdot)$

First 32 of 6912 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{20736}(1,\cdot)$	20736.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{20736}(5,\cdot)$	20736.eg	1728	yes	$-1$	$1$	$e\left(\frac{1403}{1728}\right)$	$e\left(\frac{839}{864}\right)$	$e\left(\frac{1495}{1728}\right)$	$e\left(\frac{245}{1728}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{463}{576}\right)$	$e\left(\frac{781}{864}\right)$	$e\left(\frac{539}{864}\right)$	$e\left(\frac{1177}{1728}\right)$	$e\left(\frac{139}{216}\right)$
$\chi_{20736}(7,\cdot)$	20736.ea	864	no	$-1$	$1$	$e\left(\frac{839}{864}\right)$	$e\left(\frac{347}{432}\right)$	$e\left(\frac{547}{864}\right)$	$e\left(\frac{617}{864}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{91}{288}\right)$	$e\left(\frac{409}{432}\right)$	$e\left(\frac{407}{432}\right)$	$e\left(\frac{157}{864}\right)$	$e\left(\frac{73}{108}\right)$
$\chi_{20736}(11,\cdot)$	20736.eh	1728	yes	$1$	$1$	$e\left(\frac{1495}{1728}\right)$	$e\left(\frac{547}{864}\right)$	$e\left(\frac{899}{1728}\right)$	$e\left(\frac{601}{1728}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{347}{576}\right)$	$e\left(\frac{641}{864}\right)$	$e\left(\frac{631}{864}\right)$	$e\left(\frac{461}{1728}\right)$	$e\left(\frac{203}{216}\right)$
$\chi_{20736}(13,\cdot)$	20736.ee	1728	yes	$1$	$1$	$e\left(\frac{245}{1728}\right)$	$e\left(\frac{617}{864}\right)$	$e\left(\frac{601}{1728}\right)$	$e\left(\frac{1211}{1728}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{1}{576}\right)$	$e\left(\frac{787}{864}\right)$	$e\left(\frac{245}{864}\right)$	$e\left(\frac{1399}{1728}\right)$	$e\left(\frac{181}{216}\right)$
$\chi_{20736}(17,\cdot)$	20736.dd	144	no	$-1$	$1$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{20736}(19,\cdot)$	20736.dx	576	no	$-1$	$1$	$e\left(\frac{463}{576}\right)$	$e\left(\frac{91}{288}\right)$	$e\left(\frac{347}{576}\right)$	$e\left(\frac{1}{576}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{89}{288}\right)$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{53}{576}\right)$	$e\left(\frac{11}{72}\right)$
$\chi_{20736}(23,\cdot)$	20736.eb	864	no	$1$	$1$	$e\left(\frac{781}{864}\right)$	$e\left(\frac{409}{432}\right)$	$e\left(\frac{641}{864}\right)$	$e\left(\frac{787}{864}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{89}{288}\right)$	$e\left(\frac{347}{432}\right)$	$e\left(\frac{349}{432}\right)$	$e\left(\frac{383}{864}\right)$	$e\left(\frac{35}{108}\right)$
$\chi_{20736}(25,\cdot)$	20736.ec	864	no	$1$	$1$	$e\left(\frac{539}{864}\right)$	$e\left(\frac{407}{432}\right)$	$e\left(\frac{631}{864}\right)$	$e\left(\frac{245}{864}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{349}{432}\right)$	$e\left(\frac{107}{432}\right)$	$e\left(\frac{313}{864}\right)$	$e\left(\frac{31}{108}\right)$
$\chi_{20736}(29,\cdot)$	20736.eg	1728	yes	$-1$	$1$	$e\left(\frac{1177}{1728}\right)$	$e\left(\frac{157}{864}\right)$	$e\left(\frac{461}{1728}\right)$	$e\left(\frac{1399}{1728}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{53}{576}\right)$	$e\left(\frac{383}{864}\right)$	$e\left(\frac{313}{864}\right)$	$e\left(\frac{1283}{1728}\right)$	$e\left(\frac{17}{216}\right)$
$\chi_{20736}(31,\cdot)$	20736.dm	216	no	$-1$	$1$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{20736}(35,\cdot)$	20736.dw	576	no	$1$	$1$	$e\left(\frac{451}{576}\right)$	$e\left(\frac{223}{288}\right)$	$e\left(\frac{287}{576}\right)$	$e\left(\frac{493}{576}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{245}{288}\right)$	$e\left(\frac{163}{288}\right)$	$e\left(\frac{497}{576}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{20736}(37,\cdot)$	20736.dz	576	no	$1$	$1$	$e\left(\frac{161}{576}\right)$	$e\left(\frac{101}{288}\right)$	$e\left(\frac{181}{576}\right)$	$e\left(\frac{335}{576}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{7}{288}\right)$	$e\left(\frac{161}{288}\right)$	$e\left(\frac{475}{576}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{20736}(41,\cdot)$	20736.ed	864	no	$-1$	$1$	$e\left(\frac{469}{864}\right)$	$e\left(\frac{169}{432}\right)$	$e\left(\frac{89}{864}\right)$	$e\left(\frac{331}{864}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{113}{288}\right)$	$e\left(\frac{155}{432}\right)$	$e\left(\frac{37}{432}\right)$	$e\left(\frac{407}{864}\right)$	$e\left(\frac{41}{108}\right)$
$\chi_{20736}(43,\cdot)$	20736.ef	1728	yes	$-1$	$1$	$e\left(\frac{559}{1728}\right)$	$e\left(\frac{475}{864}\right)$	$e\left(\frac{1403}{1728}\right)$	$e\left(\frac{97}{1728}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{563}{576}\right)$	$e\left(\frac{281}{864}\right)$	$e\left(\frac{559}{864}\right)$	$e\left(\frac{533}{1728}\right)$	$e\left(\frac{59}{216}\right)$
$\chi_{20736}(47,\cdot)$	20736.dv	432	no	$1$	$1$	$e\left(\frac{289}{432}\right)$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{269}{432}\right)$	$e\left(\frac{151}{432}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{73}{216}\right)$	$e\left(\frac{155}{432}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{20736}(49,\cdot)$	20736.ds	432	no	$1$	$1$	$e\left(\frac{407}{432}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{115}{432}\right)$	$e\left(\frac{185}{432}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{157}{432}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{20736}(53,\cdot)$	20736.dh	192	no	$-1$	$1$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{20736}(55,\cdot)$	20736.cw	96	no	$-1$	$1$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{20736}(59,\cdot)$	20736.eh	1728	yes	$1$	$1$	$e\left(\frac{1259}{1728}\right)$	$e\left(\frac{263}{864}\right)$	$e\left(\frac{1639}{1728}\right)$	$e\left(\frac{965}{1728}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{31}{576}\right)$	$e\left(\frac{493}{864}\right)$	$e\left(\frac{395}{864}\right)$	$e\left(\frac{1321}{1728}\right)$	$e\left(\frac{175}{216}\right)$
$\chi_{20736}(61,\cdot)$	20736.ee	1728	yes	$1$	$1$	$e\left(\frac{769}{1728}\right)$	$e\left(\frac{325}{864}\right)$	$e\left(\frac{1301}{1728}\right)$	$e\left(\frac{1135}{1728}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{29}{576}\right)$	$e\left(\frac{647}{864}\right)$	$e\left(\frac{769}{864}\right)$	$e\left(\frac{251}{1728}\right)$	$e\left(\frac{137}{216}\right)$
$\chi_{20736}(65,\cdot)$	20736.da	108	no	$-1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{20736}(67,\cdot)$	20736.ef	1728	yes	$-1$	$1$	$e\left(\frac{929}{1728}\right)$	$e\left(\frac{437}{864}\right)$	$e\left(\frac{1429}{1728}\right)$	$e\left(\frac{1679}{1728}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{541}{576}\right)$	$e\left(\frac{535}{864}\right)$	$e\left(\frac{65}{864}\right)$	$e\left(\frac{283}{1728}\right)$	$e\left(\frac{37}{216}\right)$
$\chi_{20736}(71,\cdot)$	20736.dq	288	no	$1$	$1$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{89}{288}\right)$	$e\left(\frac{187}{288}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{263}{288}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{20736}(73,\cdot)$	20736.dp	288	no	$1$	$1$	$e\left(\frac{179}{288}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{271}{288}\right)$	$e\left(\frac{29}{288}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{20736}(77,\cdot)$	20736.eg	1728	yes	$-1$	$1$	$e\left(\frac{1445}{1728}\right)$	$e\left(\frac{377}{864}\right)$	$e\left(\frac{265}{1728}\right)$	$e\left(\frac{107}{1728}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{529}{576}\right)$	$e\left(\frac{595}{864}\right)$	$e\left(\frac{581}{864}\right)$	$e\left(\frac{775}{1728}\right)$	$e\left(\frac{133}{216}\right)$
$\chi_{20736}(79,\cdot)$	20736.dt	432	no	$-1$	$1$	$e\left(\frac{319}{432}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{131}{432}\right)$	$e\left(\frac{145}{432}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{125}{216}\right)$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{53}{432}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{20736}(83,\cdot)$	20736.eh	1728	yes	$1$	$1$	$e\left(\frac{61}{1728}\right)$	$e\left(\frac{769}{864}\right)$	$e\left(\frac{929}{1728}\right)$	$e\left(\frac{1363}{1728}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{233}{576}\right)$	$e\left(\frac{203}{864}\right)$	$e\left(\frac{61}{864}\right)$	$e\left(\frac{1103}{1728}\right)$	$e\left(\frac{161}{216}\right)$
$\chi_{20736}(85,\cdot)$	20736.ee	1728	yes	$1$	$1$	$e\left(\frac{527}{1728}\right)$	$e\left(\frac{107}{864}\right)$	$e\left(\frac{1723}{1728}\right)$	$e\left(\frac{1025}{1728}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{115}{576}\right)$	$e\left(\frac{649}{864}\right)$	$e\left(\frac{527}{864}\right)$	$e\left(\frac{181}{1728}\right)$	$e\left(\frac{79}{216}\right)$
$\chi_{20736}(89,\cdot)$	20736.do	288	no	$-1$	$1$	$e\left(\frac{17}{288}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{47}{288}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{43}{288}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{20736}(91,\cdot)$	20736.dx	576	no	$-1$	$1$	$e\left(\frac{65}{576}\right)$	$e\left(\frac{149}{288}\right)$	$e\left(\frac{565}{576}\right)$	$e\left(\frac{239}{576}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{247}{288}\right)$	$e\left(\frac{65}{288}\right)$	$e\left(\frac{571}{576}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{20736}(95,\cdot)$	20736.dk	216	no	$1$	$1$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{43}{54}\right)$

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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	$20736$
Structure	\(C_{2}\times C_{2}\times C_{1728}\)
Order	$6912$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{20736}(1,\cdot)\)	20736.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{20736}(5,\cdot)\)	20736.eg	1728	yes	\(-1\)	\(1\)	\(e\left(\frac{1403}{1728}\right)\)	\(e\left(\frac{839}{864}\right)\)	\(e\left(\frac{1495}{1728}\right)\)	\(e\left(\frac{245}{1728}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{463}{576}\right)\)	\(e\left(\frac{781}{864}\right)\)	\(e\left(\frac{539}{864}\right)\)	\(e\left(\frac{1177}{1728}\right)\)	\(e\left(\frac{139}{216}\right)\)
\(\chi_{20736}(7,\cdot)\)	20736.ea	864	no	\(-1\)	\(1\)	\(e\left(\frac{839}{864}\right)\)	\(e\left(\frac{347}{432}\right)\)	\(e\left(\frac{547}{864}\right)\)	\(e\left(\frac{617}{864}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{91}{288}\right)\)	\(e\left(\frac{409}{432}\right)\)	\(e\left(\frac{407}{432}\right)\)	\(e\left(\frac{157}{864}\right)\)	\(e\left(\frac{73}{108}\right)\)
\(\chi_{20736}(11,\cdot)\)	20736.eh	1728	yes	\(1\)	\(1\)	\(e\left(\frac{1495}{1728}\right)\)	\(e\left(\frac{547}{864}\right)\)	\(e\left(\frac{899}{1728}\right)\)	\(e\left(\frac{601}{1728}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{347}{576}\right)\)	\(e\left(\frac{641}{864}\right)\)	\(e\left(\frac{631}{864}\right)\)	\(e\left(\frac{461}{1728}\right)\)	\(e\left(\frac{203}{216}\right)\)
\(\chi_{20736}(13,\cdot)\)	20736.ee	1728	yes	\(1\)	\(1\)	\(e\left(\frac{245}{1728}\right)\)	\(e\left(\frac{617}{864}\right)\)	\(e\left(\frac{601}{1728}\right)\)	\(e\left(\frac{1211}{1728}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{1}{576}\right)\)	\(e\left(\frac{787}{864}\right)\)	\(e\left(\frac{245}{864}\right)\)	\(e\left(\frac{1399}{1728}\right)\)	\(e\left(\frac{181}{216}\right)\)
\(\chi_{20736}(17,\cdot)\)	20736.dd	144	no	\(-1\)	\(1\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{20736}(19,\cdot)\)	20736.dx	576	no	\(-1\)	\(1\)	\(e\left(\frac{463}{576}\right)\)	\(e\left(\frac{91}{288}\right)\)	\(e\left(\frac{347}{576}\right)\)	\(e\left(\frac{1}{576}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{89}{288}\right)\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{53}{576}\right)\)	\(e\left(\frac{11}{72}\right)\)
\(\chi_{20736}(23,\cdot)\)	20736.eb	864	no	\(1\)	\(1\)	\(e\left(\frac{781}{864}\right)\)	\(e\left(\frac{409}{432}\right)\)	\(e\left(\frac{641}{864}\right)\)	\(e\left(\frac{787}{864}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{89}{288}\right)\)	\(e\left(\frac{347}{432}\right)\)	\(e\left(\frac{349}{432}\right)\)	\(e\left(\frac{383}{864}\right)\)	\(e\left(\frac{35}{108}\right)\)
\(\chi_{20736}(25,\cdot)\)	20736.ec	864	no	\(1\)	\(1\)	\(e\left(\frac{539}{864}\right)\)	\(e\left(\frac{407}{432}\right)\)	\(e\left(\frac{631}{864}\right)\)	\(e\left(\frac{245}{864}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{349}{432}\right)\)	\(e\left(\frac{107}{432}\right)\)	\(e\left(\frac{313}{864}\right)\)	\(e\left(\frac{31}{108}\right)\)
\(\chi_{20736}(29,\cdot)\)	20736.eg	1728	yes	\(-1\)	\(1\)	\(e\left(\frac{1177}{1728}\right)\)	\(e\left(\frac{157}{864}\right)\)	\(e\left(\frac{461}{1728}\right)\)	\(e\left(\frac{1399}{1728}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{53}{576}\right)\)	\(e\left(\frac{383}{864}\right)\)	\(e\left(\frac{313}{864}\right)\)	\(e\left(\frac{1283}{1728}\right)\)	\(e\left(\frac{17}{216}\right)\)
\(\chi_{20736}(31,\cdot)\)	20736.dm	216	no	\(-1\)	\(1\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{20736}(35,\cdot)\)	20736.dw	576	no	\(1\)	\(1\)	\(e\left(\frac{451}{576}\right)\)	\(e\left(\frac{223}{288}\right)\)	\(e\left(\frac{287}{576}\right)\)	\(e\left(\frac{493}{576}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{245}{288}\right)\)	\(e\left(\frac{163}{288}\right)\)	\(e\left(\frac{497}{576}\right)\)	\(e\left(\frac{23}{72}\right)\)
\(\chi_{20736}(37,\cdot)\)	20736.dz	576	no	\(1\)	\(1\)	\(e\left(\frac{161}{576}\right)\)	\(e\left(\frac{101}{288}\right)\)	\(e\left(\frac{181}{576}\right)\)	\(e\left(\frac{335}{576}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{7}{288}\right)\)	\(e\left(\frac{161}{288}\right)\)	\(e\left(\frac{475}{576}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{20736}(41,\cdot)\)	20736.ed	864	no	\(-1\)	\(1\)	\(e\left(\frac{469}{864}\right)\)	\(e\left(\frac{169}{432}\right)\)	\(e\left(\frac{89}{864}\right)\)	\(e\left(\frac{331}{864}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{113}{288}\right)\)	\(e\left(\frac{155}{432}\right)\)	\(e\left(\frac{37}{432}\right)\)	\(e\left(\frac{407}{864}\right)\)	\(e\left(\frac{41}{108}\right)\)
\(\chi_{20736}(43,\cdot)\)	20736.ef	1728	yes	\(-1\)	\(1\)	\(e\left(\frac{559}{1728}\right)\)	\(e\left(\frac{475}{864}\right)\)	\(e\left(\frac{1403}{1728}\right)\)	\(e\left(\frac{97}{1728}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{563}{576}\right)\)	\(e\left(\frac{281}{864}\right)\)	\(e\left(\frac{559}{864}\right)\)	\(e\left(\frac{533}{1728}\right)\)	\(e\left(\frac{59}{216}\right)\)
\(\chi_{20736}(47,\cdot)\)	20736.dv	432	no	\(1\)	\(1\)	\(e\left(\frac{289}{432}\right)\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{269}{432}\right)\)	\(e\left(\frac{151}{432}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{73}{216}\right)\)	\(e\left(\frac{155}{432}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{20736}(49,\cdot)\)	20736.ds	432	no	\(1\)	\(1\)	\(e\left(\frac{407}{432}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{115}{432}\right)\)	\(e\left(\frac{185}{432}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{157}{432}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{20736}(53,\cdot)\)	20736.dh	192	no	\(-1\)	\(1\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{20736}(55,\cdot)\)	20736.cw	96	no	\(-1\)	\(1\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{20736}(59,\cdot)\)	20736.eh	1728	yes	\(1\)	\(1\)	\(e\left(\frac{1259}{1728}\right)\)	\(e\left(\frac{263}{864}\right)\)	\(e\left(\frac{1639}{1728}\right)\)	\(e\left(\frac{965}{1728}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{31}{576}\right)\)	\(e\left(\frac{493}{864}\right)\)	\(e\left(\frac{395}{864}\right)\)	\(e\left(\frac{1321}{1728}\right)\)	\(e\left(\frac{175}{216}\right)\)
\(\chi_{20736}(61,\cdot)\)	20736.ee	1728	yes	\(1\)	\(1\)	\(e\left(\frac{769}{1728}\right)\)	\(e\left(\frac{325}{864}\right)\)	\(e\left(\frac{1301}{1728}\right)\)	\(e\left(\frac{1135}{1728}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{29}{576}\right)\)	\(e\left(\frac{647}{864}\right)\)	\(e\left(\frac{769}{864}\right)\)	\(e\left(\frac{251}{1728}\right)\)	\(e\left(\frac{137}{216}\right)\)
\(\chi_{20736}(65,\cdot)\)	20736.da	108	no	\(-1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{20736}(67,\cdot)\)	20736.ef	1728	yes	\(-1\)	\(1\)	\(e\left(\frac{929}{1728}\right)\)	\(e\left(\frac{437}{864}\right)\)	\(e\left(\frac{1429}{1728}\right)\)	\(e\left(\frac{1679}{1728}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{541}{576}\right)\)	\(e\left(\frac{535}{864}\right)\)	\(e\left(\frac{65}{864}\right)\)	\(e\left(\frac{283}{1728}\right)\)	\(e\left(\frac{37}{216}\right)\)
\(\chi_{20736}(71,\cdot)\)	20736.dq	288	no	\(1\)	\(1\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{89}{288}\right)\)	\(e\left(\frac{187}{288}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{263}{288}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{20736}(73,\cdot)\)	20736.dp	288	no	\(1\)	\(1\)	\(e\left(\frac{179}{288}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{271}{288}\right)\)	\(e\left(\frac{29}{288}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{20736}(77,\cdot)\)	20736.eg	1728	yes	\(-1\)	\(1\)	\(e\left(\frac{1445}{1728}\right)\)	\(e\left(\frac{377}{864}\right)\)	\(e\left(\frac{265}{1728}\right)\)	\(e\left(\frac{107}{1728}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{529}{576}\right)\)	\(e\left(\frac{595}{864}\right)\)	\(e\left(\frac{581}{864}\right)\)	\(e\left(\frac{775}{1728}\right)\)	\(e\left(\frac{133}{216}\right)\)
\(\chi_{20736}(79,\cdot)\)	20736.dt	432	no	\(-1\)	\(1\)	\(e\left(\frac{319}{432}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{131}{432}\right)\)	\(e\left(\frac{145}{432}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{125}{216}\right)\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{53}{432}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{20736}(83,\cdot)\)	20736.eh	1728	yes	\(1\)	\(1\)	\(e\left(\frac{61}{1728}\right)\)	\(e\left(\frac{769}{864}\right)\)	\(e\left(\frac{929}{1728}\right)\)	\(e\left(\frac{1363}{1728}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{233}{576}\right)\)	\(e\left(\frac{203}{864}\right)\)	\(e\left(\frac{61}{864}\right)\)	\(e\left(\frac{1103}{1728}\right)\)	\(e\left(\frac{161}{216}\right)\)
\(\chi_{20736}(85,\cdot)\)	20736.ee	1728	yes	\(1\)	\(1\)	\(e\left(\frac{527}{1728}\right)\)	\(e\left(\frac{107}{864}\right)\)	\(e\left(\frac{1723}{1728}\right)\)	\(e\left(\frac{1025}{1728}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{115}{576}\right)\)	\(e\left(\frac{649}{864}\right)\)	\(e\left(\frac{527}{864}\right)\)	\(e\left(\frac{181}{1728}\right)\)	\(e\left(\frac{79}{216}\right)\)
\(\chi_{20736}(89,\cdot)\)	20736.do	288	no	\(-1\)	\(1\)	\(e\left(\frac{17}{288}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{47}{288}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{43}{288}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{20736}(91,\cdot)\)	20736.dx	576	no	\(-1\)	\(1\)	\(e\left(\frac{65}{576}\right)\)	\(e\left(\frac{149}{288}\right)\)	\(e\left(\frac{565}{576}\right)\)	\(e\left(\frac{239}{576}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{247}{288}\right)\)	\(e\left(\frac{65}{288}\right)\)	\(e\left(\frac{571}{576}\right)\)	\(e\left(\frac{37}{72}\right)\)
\(\chi_{20736}(95,\cdot)\)	20736.dk	216	no	\(1\)	\(1\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{43}{54}\right)\)

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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.