LMFDB - Group of Dirichlet characters of modulus 518400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(518400)

pari: g = idealstar(,518400,2)

Character group

sage: G.order() pari: g.no
Order	=	138240
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{8640}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{518400}(157951,\cdot)$, $\chi_{518400}(202501,\cdot)$, $\chi_{518400}(6401,\cdot)$, $\chi_{518400}(331777,\cdot)$

First 32 of 138240 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{518400}(1,\cdot)$	518400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{518400}(7,\cdot)$	518400.baq	864	no	$1$	$1$	$e\left(\frac{23}{432}\right)$	$e\left(\frac{547}{864}\right)$	$e\left(\frac{401}{864}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{235}{288}\right)$	$e\left(\frac{301}{432}\right)$	$e\left(\frac{589}{864}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{169}{432}\right)$
$\chi_{518400}(11,\cdot)$	518400.bfr	8640	yes	$1$	$1$	$e\left(\frac{547}{864}\right)$	$e\left(\frac{2767}{8640}\right)$	$e\left(\frac{4733}{8640}\right)$	$e\left(\frac{383}{720}\right)$	$e\left(\frac{7}{2880}\right)$	$e\left(\frac{2341}{4320}\right)$	$e\left(\frac{7489}{8640}\right)$	$e\left(\frac{367}{1080}\right)$	$e\left(\frac{1481}{2880}\right)$	$e\left(\frac{1309}{4320}\right)$
$\chi_{518400}(13,\cdot)$	518400.bfn	8640	yes	$-1$	$1$	$e\left(\frac{401}{864}\right)$	$e\left(\frac{4733}{8640}\right)$	$e\left(\frac{6487}{8640}\right)$	$e\left(\frac{577}{720}\right)$	$e\left(\frac{293}{2880}\right)$	$e\left(\frac{1559}{4320}\right)$	$e\left(\frac{6131}{8640}\right)$	$e\left(\frac{473}{1080}\right)$	$e\left(\frac{379}{2880}\right)$	$e\left(\frac{791}{4320}\right)$
$\chi_{518400}(17,\cdot)$	518400.bai	720	no	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{383}{720}\right)$	$e\left(\frac{577}{720}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{359}{360}\right)$	$e\left(\frac{521}{720}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{41}{360}\right)$
$\chi_{518400}(19,\cdot)$	518400.bef	2880	no	$-1$	$1$	$e\left(\frac{235}{288}\right)$	$e\left(\frac{7}{2880}\right)$	$e\left(\frac{293}{2880}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{607}{960}\right)$	$e\left(\frac{301}{1440}\right)$	$e\left(\frac{2569}{2880}\right)$	$e\left(\frac{127}{360}\right)$	$e\left(\frac{401}{960}\right)$	$e\left(\frac{1429}{1440}\right)$
$\chi_{518400}(23,\cdot)$	518400.bfb	4320	no	$-1$	$1$	$e\left(\frac{301}{432}\right)$	$e\left(\frac{2341}{4320}\right)$	$e\left(\frac{1559}{4320}\right)$	$e\left(\frac{359}{360}\right)$	$e\left(\frac{301}{1440}\right)$	$e\left(\frac{1843}{2160}\right)$	$e\left(\frac{2347}{4320}\right)$	$e\left(\frac{391}{540}\right)$	$e\left(\frac{1403}{1440}\right)$	$e\left(\frac{1207}{2160}\right)$
$\chi_{518400}(29,\cdot)$	518400.bft	8640	yes	$-1$	$1$	$e\left(\frac{589}{864}\right)$	$e\left(\frac{7489}{8640}\right)$	$e\left(\frac{6131}{8640}\right)$	$e\left(\frac{521}{720}\right)$	$e\left(\frac{2569}{2880}\right)$	$e\left(\frac{2347}{4320}\right)$	$e\left(\frac{8143}{8640}\right)$	$e\left(\frac{949}{1080}\right)$	$e\left(\frac{2087}{2880}\right)$	$e\left(\frac{3763}{4320}\right)$
$\chi_{518400}(31,\cdot)$	518400.bbw	1080	no	$-1$	$1$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{367}{1080}\right)$	$e\left(\frac{473}{1080}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{127}{360}\right)$	$e\left(\frac{391}{540}\right)$	$e\left(\frac{949}{1080}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{101}{360}\right)$	$e\left(\frac{529}{540}\right)$
$\chi_{518400}(37,\cdot)$	518400.bep	2880	no	$-1$	$1$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{1481}{2880}\right)$	$e\left(\frac{379}{2880}\right)$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{401}{960}\right)$	$e\left(\frac{1403}{1440}\right)$	$e\left(\frac{2087}{2880}\right)$	$e\left(\frac{101}{360}\right)$	$e\left(\frac{463}{960}\right)$	$e\left(\frac{347}{1440}\right)$
$\chi_{518400}(41,\cdot)$	518400.bew	4320	no	$-1$	$1$	$e\left(\frac{169}{432}\right)$	$e\left(\frac{1309}{4320}\right)$	$e\left(\frac{791}{4320}\right)$	$e\left(\frac{41}{360}\right)$	$e\left(\frac{1429}{1440}\right)$	$e\left(\frac{1207}{2160}\right)$	$e\left(\frac{3763}{4320}\right)$	$e\left(\frac{529}{540}\right)$	$e\left(\frac{347}{1440}\right)$	$e\left(\frac{1903}{2160}\right)$
$\chi_{518400}(43,\cdot)$	518400.bdl	1728	no	$1$	$1$	$e\left(\frac{259}{864}\right)$	$e\left(\frac{1403}{1728}\right)$	$e\left(\frac{529}{1728}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{275}{576}\right)$	$e\left(\frac{497}{864}\right)$	$e\left(\frac{1397}{1728}\right)$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{397}{576}\right)$	$e\left(\frac{593}{864}\right)$
$\chi_{518400}(47,\cdot)$	518400.bdp	2160	no	$-1$	$1$	$e\left(\frac{151}{216}\right)$	$e\left(\frac{481}{2160}\right)$	$e\left(\frac{1079}{2160}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{601}{720}\right)$	$e\left(\frac{973}{1080}\right)$	$e\left(\frac{127}{2160}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{203}{720}\right)$	$e\left(\frac{967}{1080}\right)$
$\chi_{518400}(49,\cdot)$	518400.xh	432	no	$1$	$1$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{115}{432}\right)$	$e\left(\frac{401}{432}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{157}{432}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{169}{216}\right)$
$\chi_{518400}(53,\cdot)$	518400.bbn	960	no	$1$	$1$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{71}{960}\right)$	$e\left(\frac{949}{960}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{53}{480}\right)$	$e\left(\frac{137}{960}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{33}{320}\right)$	$e\left(\frac{197}{480}\right)$
$\chi_{518400}(59,\cdot)$	518400.bfp	8640	yes	$1$	$1$	$e\left(\frac{695}{864}\right)$	$e\left(\frac{1283}{8640}\right)$	$e\left(\frac{7417}{8640}\right)$	$e\left(\frac{427}{720}\right)$	$e\left(\frac{1883}{2880}\right)$	$e\left(\frac{1169}{4320}\right)$	$e\left(\frac{1421}{8640}\right)$	$e\left(\frac{443}{1080}\right)$	$e\left(\frac{2389}{2880}\right)$	$e\left(\frac{2201}{4320}\right)$
$\chi_{518400}(61,\cdot)$	518400.bfu	8640	yes	$1$	$1$	$e\left(\frac{325}{864}\right)$	$e\left(\frac{4777}{8640}\right)$	$e\left(\frac{7403}{8640}\right)$	$e\left(\frac{353}{720}\right)$	$e\left(\frac{1297}{2880}\right)$	$e\left(\frac{2371}{4320}\right)$	$e\left(\frac{6439}{8640}\right)$	$e\left(\frac{37}{1080}\right)$	$e\left(\frac{191}{2880}\right)$	$e\left(\frac{2779}{4320}\right)$
$\chi_{518400}(67,\cdot)$	518400.bfm	8640	yes	$1$	$1$	$e\left(\frac{653}{864}\right)$	$e\left(\frac{1961}{8640}\right)$	$e\left(\frac{2779}{8640}\right)$	$e\left(\frac{469}{720}\right)$	$e\left(\frac{1841}{2880}\right)$	$e\left(\frac{3323}{4320}\right)$	$e\left(\frac{4007}{8640}\right)$	$e\left(\frac{401}{1080}\right)$	$e\left(\frac{2863}{2880}\right)$	$e\left(\frac{827}{4320}\right)$
$\chi_{518400}(71,\cdot)$	518400.bci	1440	no	$1$	$1$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{1309}{1440}\right)$	$e\left(\frac{71}{1440}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{127}{720}\right)$	$e\left(\frac{163}{1440}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{463}{720}\right)$
$\chi_{518400}(73,\cdot)$	518400.bcm	1440	no	$-1$	$1$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{1067}{1440}\right)$	$e\left(\frac{793}{1440}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{467}{480}\right)$	$e\left(\frac{701}{720}\right)$	$e\left(\frac{629}{1440}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{181}{480}\right)$	$e\left(\frac{689}{720}\right)$
$\chi_{518400}(77,\cdot)$	518400.bfz	8640	yes	$1$	$1$	$e\left(\frac{593}{864}\right)$	$e\left(\frac{8237}{8640}\right)$	$e\left(\frac{103}{8640}\right)$	$e\left(\frac{673}{720}\right)$	$e\left(\frac{2357}{2880}\right)$	$e\left(\frac{1031}{4320}\right)$	$e\left(\frac{4739}{8640}\right)$	$e\left(\frac{17}{1080}\right)$	$e\left(\frac{331}{2880}\right)$	$e\left(\frac{2999}{4320}\right)$
$\chi_{518400}(79,\cdot)$	518400.beb	2160	no	$-1$	$1$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{1951}{2160}\right)$	$e\left(\frac{509}{2160}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{631}{720}\right)$	$e\left(\frac{733}{1080}\right)$	$e\left(\frac{697}{2160}\right)$	$e\left(\frac{23}{135}\right)$	$e\left(\frac{713}{720}\right)$	$e\left(\frac{277}{1080}\right)$
$\chi_{518400}(83,\cdot)$	518400.bfy	8640	yes	$-1$	$1$	$e\left(\frac{553}{864}\right)$	$e\left(\frac{8101}{8640}\right)$	$e\left(\frac{5519}{8640}\right)$	$e\left(\frac{449}{720}\right)$	$e\left(\frac{301}{2880}\right)$	$e\left(\frac{3823}{4320}\right)$	$e\left(\frac{8107}{8640}\right)$	$e\left(\frac{1021}{1080}\right)$	$e\left(\frac{1043}{2880}\right)$	$e\left(\frac{1567}{4320}\right)$
$\chi_{518400}(89,\cdot)$	518400.bcj	1440	no	$-1$	$1$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{1337}{1440}\right)$	$e\left(\frac{1243}{1440}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{17}{480}\right)$	$e\left(\frac{611}{720}\right)$	$e\left(\frac{1079}{1440}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{271}{480}\right)$	$e\left(\frac{419}{720}\right)$
$\chi_{518400}(91,\cdot)$	518400.beq	2880	no	$-1$	$1$	$e\left(\frac{149}{288}\right)$	$e\left(\frac{521}{2880}\right)$	$e\left(\frac{619}{2880}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{881}{960}\right)$	$e\left(\frac{83}{1440}\right)$	$e\left(\frac{1127}{2880}\right)$	$e\left(\frac{41}{360}\right)$	$e\left(\frac{703}{960}\right)$	$e\left(\frac{827}{1440}\right)$
$\chi_{518400}(97,\cdot)$	518400.bbs	1080	no	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{743}{1080}\right)$	$e\left(\frac{127}{1080}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{83}{360}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{341}{1080}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{139}{360}\right)$	$e\left(\frac{41}{540}\right)$
$\chi_{518400}(101,\cdot)$	518400.bde	1728	no	$-1$	$1$	$e\left(\frac{703}{864}\right)$	$e\left(\frac{1679}{1728}\right)$	$e\left(\frac{541}{1728}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{263}{576}\right)$	$e\left(\frac{53}{864}\right)$	$e\left(\frac{737}{1728}\right)$	$e\left(\frac{83}{216}\right)$	$e\left(\frac{553}{576}\right)$	$e\left(\frac{221}{864}\right)$
$\chi_{518400}(103,\cdot)$	518400.bez	4320	no	$1$	$1$	$e\left(\frac{307}{432}\right)$	$e\left(\frac{2707}{4320}\right)$	$e\left(\frac{2993}{4320}\right)$	$e\left(\frac{353}{360}\right)$	$e\left(\frac{667}{1440}\right)$	$e\left(\frac{1381}{2160}\right)$	$e\left(\frac{2749}{4320}\right)$	$e\left(\frac{397}{540}\right)$	$e\left(\frac{461}{1440}\right)$	$e\left(\frac{169}{2160}\right)$
$\chi_{518400}(107,\cdot)$	518400.tb	192	no	$-1$	$1$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{518400}(109,\cdot)$	518400.bbf	960	no	$1$	$1$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{557}{960}\right)$	$e\left(\frac{343}{960}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{117}{320}\right)$	$e\left(\frac{191}{480}\right)$	$e\left(\frac{419}{960}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{251}{320}\right)$	$e\left(\frac{359}{480}\right)$
$\chi_{518400}(113,\cdot)$	518400.bdo	2160	no	$1$	$1$	$e\left(\frac{185}{216}\right)$	$e\left(\frac{1547}{2160}\right)$	$e\left(\frac{1573}{2160}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{707}{720}\right)$	$e\left(\frac{371}{1080}\right)$	$e\left(\frac{29}{2160}\right)$	$e\left(\frac{257}{270}\right)$	$e\left(\frac{1}{720}\right)$	$e\left(\frac{629}{1080}\right)$
$\chi_{518400}(119,\cdot)$	518400.bex	4320	no	$1$	$1$	$e\left(\frac{197}{432}\right)$	$e\left(\frac{713}{4320}\right)$	$e\left(\frac{1147}{4320}\right)$	$e\left(\frac{97}{360}\right)$	$e\left(\frac{1313}{1440}\right)$	$e\left(\frac{1499}{2160}\right)$	$e\left(\frac{1751}{4320}\right)$	$e\left(\frac{323}{540}\right)$	$e\left(\frac{79}{1440}\right)$	$e\left(\frac{1091}{2160}\right)$

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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	$518400$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{8640}\)
Order	$138240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{518400}(1,\cdot)\)	518400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{518400}(7,\cdot)\)	518400.baq	864	no	\(1\)	\(1\)	\(e\left(\frac{23}{432}\right)\)	\(e\left(\frac{547}{864}\right)\)	\(e\left(\frac{401}{864}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{235}{288}\right)\)	\(e\left(\frac{301}{432}\right)\)	\(e\left(\frac{589}{864}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{169}{432}\right)\)
\(\chi_{518400}(11,\cdot)\)	518400.bfr	8640	yes	\(1\)	\(1\)	\(e\left(\frac{547}{864}\right)\)	\(e\left(\frac{2767}{8640}\right)\)	\(e\left(\frac{4733}{8640}\right)\)	\(e\left(\frac{383}{720}\right)\)	\(e\left(\frac{7}{2880}\right)\)	\(e\left(\frac{2341}{4320}\right)\)	\(e\left(\frac{7489}{8640}\right)\)	\(e\left(\frac{367}{1080}\right)\)	\(e\left(\frac{1481}{2880}\right)\)	\(e\left(\frac{1309}{4320}\right)\)
\(\chi_{518400}(13,\cdot)\)	518400.bfn	8640	yes	\(-1\)	\(1\)	\(e\left(\frac{401}{864}\right)\)	\(e\left(\frac{4733}{8640}\right)\)	\(e\left(\frac{6487}{8640}\right)\)	\(e\left(\frac{577}{720}\right)\)	\(e\left(\frac{293}{2880}\right)\)	\(e\left(\frac{1559}{4320}\right)\)	\(e\left(\frac{6131}{8640}\right)\)	\(e\left(\frac{473}{1080}\right)\)	\(e\left(\frac{379}{2880}\right)\)	\(e\left(\frac{791}{4320}\right)\)
\(\chi_{518400}(17,\cdot)\)	518400.bai	720	no	\(1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{383}{720}\right)\)	\(e\left(\frac{577}{720}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{359}{360}\right)\)	\(e\left(\frac{521}{720}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{41}{360}\right)\)
\(\chi_{518400}(19,\cdot)\)	518400.bef	2880	no	\(-1\)	\(1\)	\(e\left(\frac{235}{288}\right)\)	\(e\left(\frac{7}{2880}\right)\)	\(e\left(\frac{293}{2880}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{607}{960}\right)\)	\(e\left(\frac{301}{1440}\right)\)	\(e\left(\frac{2569}{2880}\right)\)	\(e\left(\frac{127}{360}\right)\)	\(e\left(\frac{401}{960}\right)\)	\(e\left(\frac{1429}{1440}\right)\)
\(\chi_{518400}(23,\cdot)\)	518400.bfb	4320	no	\(-1\)	\(1\)	\(e\left(\frac{301}{432}\right)\)	\(e\left(\frac{2341}{4320}\right)\)	\(e\left(\frac{1559}{4320}\right)\)	\(e\left(\frac{359}{360}\right)\)	\(e\left(\frac{301}{1440}\right)\)	\(e\left(\frac{1843}{2160}\right)\)	\(e\left(\frac{2347}{4320}\right)\)	\(e\left(\frac{391}{540}\right)\)	\(e\left(\frac{1403}{1440}\right)\)	\(e\left(\frac{1207}{2160}\right)\)
\(\chi_{518400}(29,\cdot)\)	518400.bft	8640	yes	\(-1\)	\(1\)	\(e\left(\frac{589}{864}\right)\)	\(e\left(\frac{7489}{8640}\right)\)	\(e\left(\frac{6131}{8640}\right)\)	\(e\left(\frac{521}{720}\right)\)	\(e\left(\frac{2569}{2880}\right)\)	\(e\left(\frac{2347}{4320}\right)\)	\(e\left(\frac{8143}{8640}\right)\)	\(e\left(\frac{949}{1080}\right)\)	\(e\left(\frac{2087}{2880}\right)\)	\(e\left(\frac{3763}{4320}\right)\)
\(\chi_{518400}(31,\cdot)\)	518400.bbw	1080	no	\(-1\)	\(1\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{367}{1080}\right)\)	\(e\left(\frac{473}{1080}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{127}{360}\right)\)	\(e\left(\frac{391}{540}\right)\)	\(e\left(\frac{949}{1080}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{101}{360}\right)\)	\(e\left(\frac{529}{540}\right)\)
\(\chi_{518400}(37,\cdot)\)	518400.bep	2880	no	\(-1\)	\(1\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{1481}{2880}\right)\)	\(e\left(\frac{379}{2880}\right)\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{401}{960}\right)\)	\(e\left(\frac{1403}{1440}\right)\)	\(e\left(\frac{2087}{2880}\right)\)	\(e\left(\frac{101}{360}\right)\)	\(e\left(\frac{463}{960}\right)\)	\(e\left(\frac{347}{1440}\right)\)
\(\chi_{518400}(41,\cdot)\)	518400.bew	4320	no	\(-1\)	\(1\)	\(e\left(\frac{169}{432}\right)\)	\(e\left(\frac{1309}{4320}\right)\)	\(e\left(\frac{791}{4320}\right)\)	\(e\left(\frac{41}{360}\right)\)	\(e\left(\frac{1429}{1440}\right)\)	\(e\left(\frac{1207}{2160}\right)\)	\(e\left(\frac{3763}{4320}\right)\)	\(e\left(\frac{529}{540}\right)\)	\(e\left(\frac{347}{1440}\right)\)	\(e\left(\frac{1903}{2160}\right)\)
\(\chi_{518400}(43,\cdot)\)	518400.bdl	1728	no	\(1\)	\(1\)	\(e\left(\frac{259}{864}\right)\)	\(e\left(\frac{1403}{1728}\right)\)	\(e\left(\frac{529}{1728}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{275}{576}\right)\)	\(e\left(\frac{497}{864}\right)\)	\(e\left(\frac{1397}{1728}\right)\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{397}{576}\right)\)	\(e\left(\frac{593}{864}\right)\)
\(\chi_{518400}(47,\cdot)\)	518400.bdp	2160	no	\(-1\)	\(1\)	\(e\left(\frac{151}{216}\right)\)	\(e\left(\frac{481}{2160}\right)\)	\(e\left(\frac{1079}{2160}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{601}{720}\right)\)	\(e\left(\frac{973}{1080}\right)\)	\(e\left(\frac{127}{2160}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{203}{720}\right)\)	\(e\left(\frac{967}{1080}\right)\)
\(\chi_{518400}(49,\cdot)\)	518400.xh	432	no	\(1\)	\(1\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{115}{432}\right)\)	\(e\left(\frac{401}{432}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{157}{432}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{169}{216}\right)\)
\(\chi_{518400}(53,\cdot)\)	518400.bbn	960	no	\(1\)	\(1\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{71}{960}\right)\)	\(e\left(\frac{949}{960}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{53}{480}\right)\)	\(e\left(\frac{137}{960}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{33}{320}\right)\)	\(e\left(\frac{197}{480}\right)\)
\(\chi_{518400}(59,\cdot)\)	518400.bfp	8640	yes	\(1\)	\(1\)	\(e\left(\frac{695}{864}\right)\)	\(e\left(\frac{1283}{8640}\right)\)	\(e\left(\frac{7417}{8640}\right)\)	\(e\left(\frac{427}{720}\right)\)	\(e\left(\frac{1883}{2880}\right)\)	\(e\left(\frac{1169}{4320}\right)\)	\(e\left(\frac{1421}{8640}\right)\)	\(e\left(\frac{443}{1080}\right)\)	\(e\left(\frac{2389}{2880}\right)\)	\(e\left(\frac{2201}{4320}\right)\)
\(\chi_{518400}(61,\cdot)\)	518400.bfu	8640	yes	\(1\)	\(1\)	\(e\left(\frac{325}{864}\right)\)	\(e\left(\frac{4777}{8640}\right)\)	\(e\left(\frac{7403}{8640}\right)\)	\(e\left(\frac{353}{720}\right)\)	\(e\left(\frac{1297}{2880}\right)\)	\(e\left(\frac{2371}{4320}\right)\)	\(e\left(\frac{6439}{8640}\right)\)	\(e\left(\frac{37}{1080}\right)\)	\(e\left(\frac{191}{2880}\right)\)	\(e\left(\frac{2779}{4320}\right)\)
\(\chi_{518400}(67,\cdot)\)	518400.bfm	8640	yes	\(1\)	\(1\)	\(e\left(\frac{653}{864}\right)\)	\(e\left(\frac{1961}{8640}\right)\)	\(e\left(\frac{2779}{8640}\right)\)	\(e\left(\frac{469}{720}\right)\)	\(e\left(\frac{1841}{2880}\right)\)	\(e\left(\frac{3323}{4320}\right)\)	\(e\left(\frac{4007}{8640}\right)\)	\(e\left(\frac{401}{1080}\right)\)	\(e\left(\frac{2863}{2880}\right)\)	\(e\left(\frac{827}{4320}\right)\)
\(\chi_{518400}(71,\cdot)\)	518400.bci	1440	no	\(1\)	\(1\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{1309}{1440}\right)\)	\(e\left(\frac{71}{1440}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{127}{720}\right)\)	\(e\left(\frac{163}{1440}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{107}{480}\right)\)	\(e\left(\frac{463}{720}\right)\)
\(\chi_{518400}(73,\cdot)\)	518400.bcm	1440	no	\(-1\)	\(1\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{1067}{1440}\right)\)	\(e\left(\frac{793}{1440}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{467}{480}\right)\)	\(e\left(\frac{701}{720}\right)\)	\(e\left(\frac{629}{1440}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{181}{480}\right)\)	\(e\left(\frac{689}{720}\right)\)
\(\chi_{518400}(77,\cdot)\)	518400.bfz	8640	yes	\(1\)	\(1\)	\(e\left(\frac{593}{864}\right)\)	\(e\left(\frac{8237}{8640}\right)\)	\(e\left(\frac{103}{8640}\right)\)	\(e\left(\frac{673}{720}\right)\)	\(e\left(\frac{2357}{2880}\right)\)	\(e\left(\frac{1031}{4320}\right)\)	\(e\left(\frac{4739}{8640}\right)\)	\(e\left(\frac{17}{1080}\right)\)	\(e\left(\frac{331}{2880}\right)\)	\(e\left(\frac{2999}{4320}\right)\)
\(\chi_{518400}(79,\cdot)\)	518400.beb	2160	no	\(-1\)	\(1\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{1951}{2160}\right)\)	\(e\left(\frac{509}{2160}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{631}{720}\right)\)	\(e\left(\frac{733}{1080}\right)\)	\(e\left(\frac{697}{2160}\right)\)	\(e\left(\frac{23}{135}\right)\)	\(e\left(\frac{713}{720}\right)\)	\(e\left(\frac{277}{1080}\right)\)
\(\chi_{518400}(83,\cdot)\)	518400.bfy	8640	yes	\(-1\)	\(1\)	\(e\left(\frac{553}{864}\right)\)	\(e\left(\frac{8101}{8640}\right)\)	\(e\left(\frac{5519}{8640}\right)\)	\(e\left(\frac{449}{720}\right)\)	\(e\left(\frac{301}{2880}\right)\)	\(e\left(\frac{3823}{4320}\right)\)	\(e\left(\frac{8107}{8640}\right)\)	\(e\left(\frac{1021}{1080}\right)\)	\(e\left(\frac{1043}{2880}\right)\)	\(e\left(\frac{1567}{4320}\right)\)
\(\chi_{518400}(89,\cdot)\)	518400.bcj	1440	no	\(-1\)	\(1\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{1337}{1440}\right)\)	\(e\left(\frac{1243}{1440}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{17}{480}\right)\)	\(e\left(\frac{611}{720}\right)\)	\(e\left(\frac{1079}{1440}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{271}{480}\right)\)	\(e\left(\frac{419}{720}\right)\)
\(\chi_{518400}(91,\cdot)\)	518400.beq	2880	no	\(-1\)	\(1\)	\(e\left(\frac{149}{288}\right)\)	\(e\left(\frac{521}{2880}\right)\)	\(e\left(\frac{619}{2880}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{881}{960}\right)\)	\(e\left(\frac{83}{1440}\right)\)	\(e\left(\frac{1127}{2880}\right)\)	\(e\left(\frac{41}{360}\right)\)	\(e\left(\frac{703}{960}\right)\)	\(e\left(\frac{827}{1440}\right)\)
\(\chi_{518400}(97,\cdot)\)	518400.bbs	1080	no	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{743}{1080}\right)\)	\(e\left(\frac{127}{1080}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{83}{360}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{341}{1080}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{139}{360}\right)\)	\(e\left(\frac{41}{540}\right)\)
\(\chi_{518400}(101,\cdot)\)	518400.bde	1728	no	\(-1\)	\(1\)	\(e\left(\frac{703}{864}\right)\)	\(e\left(\frac{1679}{1728}\right)\)	\(e\left(\frac{541}{1728}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{263}{576}\right)\)	\(e\left(\frac{53}{864}\right)\)	\(e\left(\frac{737}{1728}\right)\)	\(e\left(\frac{83}{216}\right)\)	\(e\left(\frac{553}{576}\right)\)	\(e\left(\frac{221}{864}\right)\)
\(\chi_{518400}(103,\cdot)\)	518400.bez	4320	no	\(1\)	\(1\)	\(e\left(\frac{307}{432}\right)\)	\(e\left(\frac{2707}{4320}\right)\)	\(e\left(\frac{2993}{4320}\right)\)	\(e\left(\frac{353}{360}\right)\)	\(e\left(\frac{667}{1440}\right)\)	\(e\left(\frac{1381}{2160}\right)\)	\(e\left(\frac{2749}{4320}\right)\)	\(e\left(\frac{397}{540}\right)\)	\(e\left(\frac{461}{1440}\right)\)	\(e\left(\frac{169}{2160}\right)\)
\(\chi_{518400}(107,\cdot)\)	518400.tb	192	no	\(-1\)	\(1\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{518400}(109,\cdot)\)	518400.bbf	960	no	\(1\)	\(1\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{557}{960}\right)\)	\(e\left(\frac{343}{960}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{117}{320}\right)\)	\(e\left(\frac{191}{480}\right)\)	\(e\left(\frac{419}{960}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{251}{320}\right)\)	\(e\left(\frac{359}{480}\right)\)
\(\chi_{518400}(113,\cdot)\)	518400.bdo	2160	no	\(1\)	\(1\)	\(e\left(\frac{185}{216}\right)\)	\(e\left(\frac{1547}{2160}\right)\)	\(e\left(\frac{1573}{2160}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{707}{720}\right)\)	\(e\left(\frac{371}{1080}\right)\)	\(e\left(\frac{29}{2160}\right)\)	\(e\left(\frac{257}{270}\right)\)	\(e\left(\frac{1}{720}\right)\)	\(e\left(\frac{629}{1080}\right)\)
\(\chi_{518400}(119,\cdot)\)	518400.bex	4320	no	\(1\)	\(1\)	\(e\left(\frac{197}{432}\right)\)	\(e\left(\frac{713}{4320}\right)\)	\(e\left(\frac{1147}{4320}\right)\)	\(e\left(\frac{97}{360}\right)\)	\(e\left(\frac{1313}{1440}\right)\)	\(e\left(\frac{1499}{2160}\right)\)	\(e\left(\frac{1751}{4320}\right)\)	\(e\left(\frac{323}{540}\right)\)	\(e\left(\frac{79}{1440}\right)\)	\(e\left(\frac{1091}{2160}\right)\)

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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.