LMFDB - Group of Dirichlet characters of modulus 172800

Show commands: PariGP / SageMath

sage: H = DirichletGroup(172800)

pari: g = idealstar(,172800,2)

Character group

sage: G.order() pari: g.no
Order	=	46080
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{2880}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{172800}(157951,\cdot)$, $\chi_{172800}(29701,\cdot)$, $\chi_{172800}(6401,\cdot)$, $\chi_{172800}(158977,\cdot)$

First 32 of 46080 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{172800}(1,\cdot)$	172800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{172800}(7,\cdot)$	172800.sr	288	no	$1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{115}{144}\right)$
$\chi_{172800}(11,\cdot)$	172800.xy	2880	yes	$1$	$1$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{1669}{2880}\right)$	$e\left(\frac{1151}{2880}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{109}{960}\right)$	$e\left(\frac{1207}{1440}\right)$	$e\left(\frac{1963}{2880}\right)$	$e\left(\frac{349}{360}\right)$	$e\left(\frac{707}{960}\right)$	$e\left(\frac{1183}{1440}\right)$
$\chi_{172800}(13,\cdot)$	172800.xv	2880	yes	$-1$	$1$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{1151}{2880}\right)$	$e\left(\frac{349}{2880}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{311}{960}\right)$	$e\left(\frac{893}{1440}\right)$	$e\left(\frac{1937}{2880}\right)$	$e\left(\frac{131}{360}\right)$	$e\left(\frac{553}{960}\right)$	$e\left(\frac{1277}{1440}\right)$
$\chi_{172800}(17,\cdot)$	172800.rw	240	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{107}{120}\right)$
$\chi_{172800}(19,\cdot)$	172800.ws	960	no	$-1$	$1$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{109}{960}\right)$	$e\left(\frac{311}{960}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{309}{320}\right)$	$e\left(\frac{367}{480}\right)$	$e\left(\frac{643}{960}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{27}{320}\right)$	$e\left(\frac{103}{480}\right)$
$\chi_{172800}(23,\cdot)$	172800.xb	1440	no	$-1$	$1$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{1207}{1440}\right)$	$e\left(\frac{893}{1440}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{367}{480}\right)$	$e\left(\frac{241}{720}\right)$	$e\left(\frac{889}{1440}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{109}{720}\right)$
$\chi_{172800}(29,\cdot)$	172800.xx	2880	yes	$-1$	$1$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{1963}{2880}\right)$	$e\left(\frac{1937}{2880}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{643}{960}\right)$	$e\left(\frac{889}{1440}\right)$	$e\left(\frac{1861}{2880}\right)$	$e\left(\frac{103}{360}\right)$	$e\left(\frac{269}{960}\right)$	$e\left(\frac{721}{1440}\right)$
$\chi_{172800}(31,\cdot)$	172800.ts	360	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{349}{360}\right)$	$e\left(\frac{131}{360}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{103}{360}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{43}{180}\right)$
$\chi_{172800}(37,\cdot)$	172800.wk	960	no	$-1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{707}{960}\right)$	$e\left(\frac{553}{960}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{27}{320}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{269}{960}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{261}{320}\right)$	$e\left(\frac{329}{480}\right)$
$\chi_{172800}(41,\cdot)$	172800.xg	1440	no	$-1$	$1$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1183}{1440}\right)$	$e\left(\frac{1277}{1440}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{103}{480}\right)$	$e\left(\frac{109}{720}\right)$	$e\left(\frac{721}{1440}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{329}{480}\right)$	$e\left(\frac{661}{720}\right)$
$\chi_{172800}(43,\cdot)$	172800.vg	576	no	$1$	$1$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{233}{576}\right)$	$e\left(\frac{475}{576}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{113}{192}\right)$	$e\left(\frac{155}{288}\right)$	$e\left(\frac{551}{576}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{251}{288}\right)$
$\chi_{172800}(47,\cdot)$	172800.wc	720	no	$-1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{427}{720}\right)$	$e\left(\frac{413}{720}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{271}{360}\right)$	$e\left(\frac{469}{720}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{229}{360}\right)$
$\chi_{172800}(49,\cdot)$	172800.pl	144	no	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{172800}(53,\cdot)$	172800.tg	320	no	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{237}{320}\right)$	$e\left(\frac{103}{320}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{33}{320}\right)$	$e\left(\frac{119}{160}\right)$
$\chi_{172800}(59,\cdot)$	172800.xn	2880	yes	$1$	$1$	$e\left(\frac{29}{288}\right)$	$e\left(\frac{2561}{2880}\right)$	$e\left(\frac{19}{2880}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{521}{960}\right)$	$e\left(\frac{1403}{1440}\right)$	$e\left(\frac{1007}{2880}\right)$	$e\left(\frac{281}{360}\right)$	$e\left(\frac{583}{960}\right)$	$e\left(\frac{1427}{1440}\right)$
$\chi_{172800}(61,\cdot)$	172800.xm	2880	yes	$1$	$1$	$e\left(\frac{55}{288}\right)$	$e\left(\frac{1699}{2880}\right)$	$e\left(\frac{761}{2880}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{859}{960}\right)$	$e\left(\frac{1057}{1440}\right)$	$e\left(\frac{13}{2880}\right)$	$e\left(\frac{199}{360}\right)$	$e\left(\frac{917}{960}\right)$	$e\left(\frac{1033}{1440}\right)$
$\chi_{172800}(67,\cdot)$	172800.xq	2880	yes	$1$	$1$	$e\left(\frac{239}{288}\right)$	$e\left(\frac{1187}{2880}\right)$	$e\left(\frac{1033}{2880}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{827}{960}\right)$	$e\left(\frac{1001}{1440}\right)$	$e\left(\frac{2189}{2880}\right)$	$e\left(\frac{347}{360}\right)$	$e\left(\frac{421}{960}\right)$	$e\left(\frac{809}{1440}\right)$
$\chi_{172800}(71,\cdot)$	172800.ur	480	no	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{223}{480}\right)$	$e\left(\frac{77}{480}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{1}{480}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{181}{240}\right)$
$\chi_{172800}(73,\cdot)$	172800.ui	480	no	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{89}{480}\right)$	$e\left(\frac{211}{480}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{203}{240}\right)$
$\chi_{172800}(77,\cdot)$	172800.xo	2880	yes	$1$	$1$	$e\left(\frac{251}{288}\right)$	$e\left(\frac{2639}{2880}\right)$	$e\left(\frac{1741}{2880}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{359}{960}\right)$	$e\left(\frac{77}{1440}\right)$	$e\left(\frac{833}{2880}\right)$	$e\left(\frac{179}{360}\right)$	$e\left(\frac{217}{960}\right)$	$e\left(\frac{893}{1440}\right)$
$\chi_{172800}(79,\cdot)$	172800.vy	720	no	$-1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{277}{720}\right)$	$e\left(\frac{383}{720}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{31}{360}\right)$	$e\left(\frac{499}{720}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{79}{360}\right)$
$\chi_{172800}(83,\cdot)$	172800.xt	2880	yes	$-1$	$1$	$e\left(\frac{67}{288}\right)$	$e\left(\frac{1207}{2880}\right)$	$e\left(\frac{2693}{2880}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{847}{960}\right)$	$e\left(\frac{421}{1440}\right)$	$e\left(\frac{889}{2880}\right)$	$e\left(\frac{247}{360}\right)$	$e\left(\frac{881}{960}\right)$	$e\left(\frac{469}{1440}\right)$
$\chi_{172800}(89,\cdot)$	172800.us	480	no	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{179}{480}\right)$	$e\left(\frac{361}{480}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{413}{480}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{113}{240}\right)$
$\chi_{172800}(91,\cdot)$	172800.wf	960	no	$-1$	$1$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{707}{960}\right)$	$e\left(\frac{313}{960}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{187}{320}\right)$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{269}{960}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{21}{320}\right)$	$e\left(\frac{329}{480}\right)$
$\chi_{172800}(97,\cdot)$	172800.tx	360	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{221}{360}\right)$	$e\left(\frac{109}{360}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{287}{360}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{167}{180}\right)$
$\chi_{172800}(101,\cdot)$	172800.vl	576	no	$-1$	$1$	$e\left(\frac{181}{288}\right)$	$e\left(\frac{5}{576}\right)$	$e\left(\frac{415}{576}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{71}{288}\right)$	$e\left(\frac{395}{576}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{95}{288}\right)$
$\chi_{172800}(103,\cdot)$	172800.wz	1440	no	$1$	$1$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{529}{1440}\right)$	$e\left(\frac{1211}{1440}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{169}{480}\right)$	$e\left(\frac{247}{720}\right)$	$e\left(\frac{1183}{1440}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{47}{480}\right)$	$e\left(\frac{403}{720}\right)$
$\chi_{172800}(107,\cdot)$	172800.lu	64	no	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{172800}(109,\cdot)$	172800.tc	320	no	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{79}{320}\right)$	$e\left(\frac{221}{320}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{117}{320}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{33}{320}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{251}{320}\right)$	$e\left(\frac{13}{160}\right)$
$\chi_{172800}(113,\cdot)$	172800.wa	720	no	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{89}{720}\right)$	$e\left(\frac{151}{720}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{137}{360}\right)$	$e\left(\frac{623}{720}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{143}{360}\right)$
$\chi_{172800}(119,\cdot)$	172800.xh	1440	no	$1$	$1$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{1091}{1440}\right)$	$e\left(\frac{1129}{1440}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{11}{480}\right)$	$e\left(\frac{473}{720}\right)$	$e\left(\frac{797}{1440}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{133}{480}\right)$	$e\left(\frac{497}{720}\right)$

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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	$172800$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{2880}\)
Order	$46080$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{172800}(1,\cdot)\)	172800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{172800}(7,\cdot)\)	172800.sr	288	no	\(1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{115}{144}\right)\)
\(\chi_{172800}(11,\cdot)\)	172800.xy	2880	yes	\(1\)	\(1\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{1669}{2880}\right)\)	\(e\left(\frac{1151}{2880}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{109}{960}\right)\)	\(e\left(\frac{1207}{1440}\right)\)	\(e\left(\frac{1963}{2880}\right)\)	\(e\left(\frac{349}{360}\right)\)	\(e\left(\frac{707}{960}\right)\)	\(e\left(\frac{1183}{1440}\right)\)
\(\chi_{172800}(13,\cdot)\)	172800.xv	2880	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{1151}{2880}\right)\)	\(e\left(\frac{349}{2880}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{311}{960}\right)\)	\(e\left(\frac{893}{1440}\right)\)	\(e\left(\frac{1937}{2880}\right)\)	\(e\left(\frac{131}{360}\right)\)	\(e\left(\frac{553}{960}\right)\)	\(e\left(\frac{1277}{1440}\right)\)
\(\chi_{172800}(17,\cdot)\)	172800.rw	240	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{107}{120}\right)\)
\(\chi_{172800}(19,\cdot)\)	172800.ws	960	no	\(-1\)	\(1\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{109}{960}\right)\)	\(e\left(\frac{311}{960}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{309}{320}\right)\)	\(e\left(\frac{367}{480}\right)\)	\(e\left(\frac{643}{960}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{27}{320}\right)\)	\(e\left(\frac{103}{480}\right)\)
\(\chi_{172800}(23,\cdot)\)	172800.xb	1440	no	\(-1\)	\(1\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{1207}{1440}\right)\)	\(e\left(\frac{893}{1440}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{367}{480}\right)\)	\(e\left(\frac{241}{720}\right)\)	\(e\left(\frac{889}{1440}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{109}{720}\right)\)
\(\chi_{172800}(29,\cdot)\)	172800.xx	2880	yes	\(-1\)	\(1\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{1963}{2880}\right)\)	\(e\left(\frac{1937}{2880}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{643}{960}\right)\)	\(e\left(\frac{889}{1440}\right)\)	\(e\left(\frac{1861}{2880}\right)\)	\(e\left(\frac{103}{360}\right)\)	\(e\left(\frac{269}{960}\right)\)	\(e\left(\frac{721}{1440}\right)\)
\(\chi_{172800}(31,\cdot)\)	172800.ts	360	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{349}{360}\right)\)	\(e\left(\frac{131}{360}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{103}{360}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{43}{180}\right)\)
\(\chi_{172800}(37,\cdot)\)	172800.wk	960	no	\(-1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{707}{960}\right)\)	\(e\left(\frac{553}{960}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{27}{320}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{269}{960}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{261}{320}\right)\)	\(e\left(\frac{329}{480}\right)\)
\(\chi_{172800}(41,\cdot)\)	172800.xg	1440	no	\(-1\)	\(1\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1183}{1440}\right)\)	\(e\left(\frac{1277}{1440}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{103}{480}\right)\)	\(e\left(\frac{109}{720}\right)\)	\(e\left(\frac{721}{1440}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{329}{480}\right)\)	\(e\left(\frac{661}{720}\right)\)
\(\chi_{172800}(43,\cdot)\)	172800.vg	576	no	\(1\)	\(1\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{233}{576}\right)\)	\(e\left(\frac{475}{576}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{113}{192}\right)\)	\(e\left(\frac{155}{288}\right)\)	\(e\left(\frac{551}{576}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{251}{288}\right)\)
\(\chi_{172800}(47,\cdot)\)	172800.wc	720	no	\(-1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{427}{720}\right)\)	\(e\left(\frac{413}{720}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{271}{360}\right)\)	\(e\left(\frac{469}{720}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{229}{360}\right)\)
\(\chi_{172800}(49,\cdot)\)	172800.pl	144	no	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{172800}(53,\cdot)\)	172800.tg	320	no	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{237}{320}\right)\)	\(e\left(\frac{103}{320}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{33}{320}\right)\)	\(e\left(\frac{119}{160}\right)\)
\(\chi_{172800}(59,\cdot)\)	172800.xn	2880	yes	\(1\)	\(1\)	\(e\left(\frac{29}{288}\right)\)	\(e\left(\frac{2561}{2880}\right)\)	\(e\left(\frac{19}{2880}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{521}{960}\right)\)	\(e\left(\frac{1403}{1440}\right)\)	\(e\left(\frac{1007}{2880}\right)\)	\(e\left(\frac{281}{360}\right)\)	\(e\left(\frac{583}{960}\right)\)	\(e\left(\frac{1427}{1440}\right)\)
\(\chi_{172800}(61,\cdot)\)	172800.xm	2880	yes	\(1\)	\(1\)	\(e\left(\frac{55}{288}\right)\)	\(e\left(\frac{1699}{2880}\right)\)	\(e\left(\frac{761}{2880}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{859}{960}\right)\)	\(e\left(\frac{1057}{1440}\right)\)	\(e\left(\frac{13}{2880}\right)\)	\(e\left(\frac{199}{360}\right)\)	\(e\left(\frac{917}{960}\right)\)	\(e\left(\frac{1033}{1440}\right)\)
\(\chi_{172800}(67,\cdot)\)	172800.xq	2880	yes	\(1\)	\(1\)	\(e\left(\frac{239}{288}\right)\)	\(e\left(\frac{1187}{2880}\right)\)	\(e\left(\frac{1033}{2880}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{827}{960}\right)\)	\(e\left(\frac{1001}{1440}\right)\)	\(e\left(\frac{2189}{2880}\right)\)	\(e\left(\frac{347}{360}\right)\)	\(e\left(\frac{421}{960}\right)\)	\(e\left(\frac{809}{1440}\right)\)
\(\chi_{172800}(71,\cdot)\)	172800.ur	480	no	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{223}{480}\right)\)	\(e\left(\frac{77}{480}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{1}{480}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{181}{240}\right)\)
\(\chi_{172800}(73,\cdot)\)	172800.ui	480	no	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{89}{480}\right)\)	\(e\left(\frac{211}{480}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{203}{240}\right)\)
\(\chi_{172800}(77,\cdot)\)	172800.xo	2880	yes	\(1\)	\(1\)	\(e\left(\frac{251}{288}\right)\)	\(e\left(\frac{2639}{2880}\right)\)	\(e\left(\frac{1741}{2880}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{359}{960}\right)\)	\(e\left(\frac{77}{1440}\right)\)	\(e\left(\frac{833}{2880}\right)\)	\(e\left(\frac{179}{360}\right)\)	\(e\left(\frac{217}{960}\right)\)	\(e\left(\frac{893}{1440}\right)\)
\(\chi_{172800}(79,\cdot)\)	172800.vy	720	no	\(-1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{277}{720}\right)\)	\(e\left(\frac{383}{720}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{31}{360}\right)\)	\(e\left(\frac{499}{720}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{79}{360}\right)\)
\(\chi_{172800}(83,\cdot)\)	172800.xt	2880	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{288}\right)\)	\(e\left(\frac{1207}{2880}\right)\)	\(e\left(\frac{2693}{2880}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{847}{960}\right)\)	\(e\left(\frac{421}{1440}\right)\)	\(e\left(\frac{889}{2880}\right)\)	\(e\left(\frac{247}{360}\right)\)	\(e\left(\frac{881}{960}\right)\)	\(e\left(\frac{469}{1440}\right)\)
\(\chi_{172800}(89,\cdot)\)	172800.us	480	no	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{179}{480}\right)\)	\(e\left(\frac{361}{480}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{413}{480}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{113}{240}\right)\)
\(\chi_{172800}(91,\cdot)\)	172800.wf	960	no	\(-1\)	\(1\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{707}{960}\right)\)	\(e\left(\frac{313}{960}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{187}{320}\right)\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{269}{960}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{21}{320}\right)\)	\(e\left(\frac{329}{480}\right)\)
\(\chi_{172800}(97,\cdot)\)	172800.tx	360	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{221}{360}\right)\)	\(e\left(\frac{109}{360}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{287}{360}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{167}{180}\right)\)
\(\chi_{172800}(101,\cdot)\)	172800.vl	576	no	\(-1\)	\(1\)	\(e\left(\frac{181}{288}\right)\)	\(e\left(\frac{5}{576}\right)\)	\(e\left(\frac{415}{576}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{71}{288}\right)\)	\(e\left(\frac{395}{576}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{95}{288}\right)\)
\(\chi_{172800}(103,\cdot)\)	172800.wz	1440	no	\(1\)	\(1\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{529}{1440}\right)\)	\(e\left(\frac{1211}{1440}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{169}{480}\right)\)	\(e\left(\frac{247}{720}\right)\)	\(e\left(\frac{1183}{1440}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{47}{480}\right)\)	\(e\left(\frac{403}{720}\right)\)
\(\chi_{172800}(107,\cdot)\)	172800.lu	64	no	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{172800}(109,\cdot)\)	172800.tc	320	no	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{79}{320}\right)\)	\(e\left(\frac{221}{320}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{117}{320}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{33}{320}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{251}{320}\right)\)	\(e\left(\frac{13}{160}\right)\)
\(\chi_{172800}(113,\cdot)\)	172800.wa	720	no	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{89}{720}\right)\)	\(e\left(\frac{151}{720}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{137}{360}\right)\)	\(e\left(\frac{623}{720}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{143}{360}\right)\)
\(\chi_{172800}(119,\cdot)\)	172800.xh	1440	no	\(1\)	\(1\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{1091}{1440}\right)\)	\(e\left(\frac{1129}{1440}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{11}{480}\right)\)	\(e\left(\frac{473}{720}\right)\)	\(e\left(\frac{797}{1440}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{133}{480}\right)\)	\(e\left(\frac{497}{720}\right)\)

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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.