LMFDB - Group of Dirichlet characters of modulus 164730

Show commands: PariGP / SageMath

sage: H = DirichletGroup(164730)

pari: g = idealstar(,164730,2)

Character group

sage: G.order() pari: g.no
Order	=	39168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{2448}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{164730}(54911,\cdot)$, $\chi_{164730}(32947,\cdot)$, $\chi_{164730}(41041,\cdot)$, $\chi_{164730}(138721,\cdot)$

First 32 of 39168 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	$-1$	$1$	$7$	$11$	$13$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{164730}(1,\cdot)$	164730.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{164730}(7,\cdot)$	164730.ow	816	no	$1$	$1$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{403}{816}\right)$	$e\left(\frac{325}{816}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{635}{816}\right)$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{46}{51}\right)$
$\chi_{164730}(11,\cdot)$	164730.pa	816	no	$1$	$1$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{563}{816}\right)$	$e\left(\frac{329}{816}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{317}{408}\right)$	$e\left(\frac{59}{204}\right)$
$\chi_{164730}(13,\cdot)$	164730.ny	612	no	$1$	$1$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{535}{612}\right)$	$e\left(\frac{76}{153}\right)$	$e\left(\frac{181}{612}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{509}{612}\right)$	$e\left(\frac{335}{612}\right)$	$e\left(\frac{19}{612}\right)$
$\chi_{164730}(23,\cdot)$	164730.qh	2448	no	$-1$	$1$	$e\left(\frac{403}{816}\right)$	$e\left(\frac{563}{816}\right)$	$e\left(\frac{76}{153}\right)$	$e\left(\frac{1957}{2448}\right)$	$e\left(\frac{907}{2448}\right)$	$e\left(\frac{37}{816}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{341}{2448}\right)$	$e\left(\frac{385}{1224}\right)$	$e\left(\frac{19}{153}\right)$
$\chi_{164730}(29,\cdot)$	164730.qm	2448	no	$-1$	$1$	$e\left(\frac{325}{816}\right)$	$e\left(\frac{329}{816}\right)$	$e\left(\frac{181}{612}\right)$	$e\left(\frac{907}{2448}\right)$	$e\left(\frac{1}{2448}\right)$	$e\left(\frac{247}{816}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{887}{2448}\right)$	$e\left(\frac{577}{1224}\right)$	$e\left(\frac{313}{612}\right)$
$\chi_{164730}(31,\cdot)$	164730.pd	816	no	$1$	$1$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{37}{816}\right)$	$e\left(\frac{247}{816}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{401}{816}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{199}{204}\right)$
$\chi_{164730}(37,\cdot)$	164730.mq	272	no	$-1$	$1$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{139}{272}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{209}{272}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{23}{34}\right)$
$\chi_{164730}(41,\cdot)$	164730.qa	2448	no	$-1$	$1$	$e\left(\frac{635}{816}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{509}{612}\right)$	$e\left(\frac{341}{2448}\right)$	$e\left(\frac{887}{2448}\right)$	$e\left(\frac{401}{816}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{961}{2448}\right)$	$e\left(\frac{779}{1224}\right)$	$e\left(\frac{89}{612}\right)$
$\chi_{164730}(43,\cdot)$	164730.pn	1224	no	$-1$	$1$	$e\left(\frac{355}{408}\right)$	$e\left(\frac{317}{408}\right)$	$e\left(\frac{335}{612}\right)$	$e\left(\frac{385}{1224}\right)$	$e\left(\frac{577}{1224}\right)$	$e\left(\frac{331}{408}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{779}{1224}\right)$	$e\left(\frac{77}{306}\right)$	$e\left(\frac{581}{612}\right)$
$\chi_{164730}(47,\cdot)$	164730.ot	612	no	$1$	$1$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{19}{612}\right)$	$e\left(\frac{19}{153}\right)$	$e\left(\frac{313}{612}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{89}{612}\right)$	$e\left(\frac{581}{612}\right)$	$e\left(\frac{43}{612}\right)$
$\chi_{164730}(49,\cdot)$	164730.nv	408	no	$1$	$1$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{403}{408}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{227}{408}\right)$	$e\left(\frac{151}{204}\right)$	$e\left(\frac{41}{51}\right)$
$\chi_{164730}(53,\cdot)$	164730.pk	1224	no	$-1$	$1$	$e\left(\frac{329}{408}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{457}{612}\right)$	$e\left(\frac{1055}{1224}\right)$	$e\left(\frac{71}{1224}\right)$	$e\left(\frac{401}{408}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{1165}{1224}\right)$	$e\left(\frac{29}{153}\right)$	$e\left(\frac{535}{612}\right)$
$\chi_{164730}(59,\cdot)$	164730.pt	1224	no	$1$	$1$	$e\left(\frac{73}{408}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{121}{306}\right)$	$e\left(\frac{1171}{1224}\right)$	$e\left(\frac{1201}{1224}\right)$	$e\left(\frac{235}{408}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{407}{1224}\right)$	$e\left(\frac{499}{612}\right)$	$e\left(\frac{145}{306}\right)$
$\chi_{164730}(61,\cdot)$	164730.qo	2448	no	$-1$	$1$	$e\left(\frac{211}{816}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{115}{612}\right)$	$e\left(\frac{1381}{2448}\right)$	$e\left(\frac{2239}{2448}\right)$	$e\left(\frac{193}{816}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{665}{2448}\right)$	$e\left(\frac{1195}{1224}\right)$	$e\left(\frac{67}{612}\right)$
$\chi_{164730}(67,\cdot)$	164730.od	612	no	$1$	$1$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{37}{612}\right)$	$e\left(\frac{301}{612}\right)$	$e\left(\frac{35}{306}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{146}{153}\right)$	$e\left(\frac{455}{612}\right)$	$e\left(\frac{277}{612}\right)$
$\chi_{164730}(71,\cdot)$	164730.qa	2448	no	$-1$	$1$	$e\left(\frac{641}{816}\right)$	$e\left(\frac{733}{816}\right)$	$e\left(\frac{83}{612}\right)$	$e\left(\frac{2399}{2448}\right)$	$e\left(\frac{533}{2448}\right)$	$e\left(\frac{275}{816}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{307}{2448}\right)$	$e\left(\frac{929}{1224}\right)$	$e\left(\frac{59}{612}\right)$
$\chi_{164730}(73,\cdot)$	164730.qi	2448	no	$1$	$1$	$e\left(\frac{89}{816}\right)$	$e\left(\frac{505}{816}\right)$	$e\left(\frac{79}{306}\right)$	$e\left(\frac{2375}{2448}\right)$	$e\left(\frac{257}{2448}\right)$	$e\left(\frac{647}{816}\right)$	$e\left(\frac{1}{272}\right)$	$e\left(\frac{1519}{2448}\right)$	$e\left(\frac{1103}{1224}\right)$	$e\left(\frac{29}{153}\right)$
$\chi_{164730}(77,\cdot)$	164730.ka	136	no	$1$	$1$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{13}{68}\right)$
$\chi_{164730}(79,\cdot)$	164730.qp	2448	no	$1$	$1$	$e\left(\frac{815}{816}\right)$	$e\left(\frac{643}{816}\right)$	$e\left(\frac{275}{612}\right)$	$e\left(\frac{2105}{2448}\right)$	$e\left(\frac{59}{2448}\right)$	$e\left(\frac{293}{816}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{925}{2448}\right)$	$e\left(\frac{995}{1224}\right)$	$e\left(\frac{413}{612}\right)$
$\chi_{164730}(83,\cdot)$	164730.nq	408	no	$1$	$1$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{193}{204}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{61}{204}\right)$
$\chi_{164730}(89,\cdot)$	164730.ok	612	no	$1$	$1$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{100}{153}\right)$	$e\left(\frac{529}{612}\right)$	$e\left(\frac{91}{612}\right)$	$e\left(\frac{139}{204}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{545}{612}\right)$	$e\left(\frac{14}{153}\right)$	$e\left(\frac{25}{153}\right)$
$\chi_{164730}(91,\cdot)$	164730.qd	2448	no	$1$	$1$	$e\left(\frac{559}{816}\right)$	$e\left(\frac{11}{816}\right)$	$e\left(\frac{601}{612}\right)$	$e\left(\frac{2425}{2448}\right)$	$e\left(\frac{1699}{2448}\right)$	$e\left(\frac{637}{816}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{1493}{2448}\right)$	$e\left(\frac{511}{1224}\right)$	$e\left(\frac{571}{612}\right)$
$\chi_{164730}(97,\cdot)$	164730.qj	2448	no	$-1$	$1$	$e\left(\frac{233}{816}\right)$	$e\left(\frac{529}{816}\right)$	$e\left(\frac{67}{306}\right)$	$e\left(\frac{1991}{2448}\right)$	$e\left(\frac{737}{2448}\right)$	$e\left(\frac{71}{816}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{1327}{2448}\right)$	$e\left(\frac{827}{1224}\right)$	$e\left(\frac{55}{306}\right)$
$\chi_{164730}(101,\cdot)$	164730.mw	306	no	$-1$	$1$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{118}{153}\right)$	$e\left(\frac{13}{153}\right)$	$e\left(\frac{124}{153}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{134}{153}\right)$	$e\left(\frac{41}{153}\right)$	$e\left(\frac{59}{306}\right)$
$\chi_{164730}(103,\cdot)$	164730.lk	204	no	$1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{41}{204}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{125}{204}\right)$
$\chi_{164730}(107,\cdot)$	164730.ox	816	no	$1$	$1$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{781}{816}\right)$	$e\left(\frac{235}{816}\right)$	$e\left(\frac{245}{272}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{773}{816}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{16}{51}\right)$
$\chi_{164730}(109,\cdot)$	164730.qp	2448	no	$1$	$1$	$e\left(\frac{419}{816}\right)$	$e\left(\frac{679}{816}\right)$	$e\left(\frac{443}{612}\right)$	$e\left(\frac{1733}{2448}\right)$	$e\left(\frac{2207}{2448}\right)$	$e\left(\frac{449}{816}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{1657}{2448}\right)$	$e\left(\frac{479}{1224}\right)$	$e\left(\frac{149}{612}\right)$
$\chi_{164730}(113,\cdot)$	164730.mn	272	no	$1$	$1$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{57}{272}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{27}{272}\right)$	$e\left(\frac{205}{272}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{2}{17}\right)$
$\chi_{164730}(121,\cdot)$	164730.nh	408	no	$1$	$1$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{155}{408}\right)$	$e\left(\frac{329}{408}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{103}{408}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{164730}(127,\cdot)$	164730.py	1224	no	$1$	$1$	$e\left(\frac{395}{408}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{571}{612}\right)$	$e\left(\frac{1049}{1224}\right)$	$e\left(\frac{1073}{1224}\right)$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{91}{1224}\right)$	$e\left(\frac{59}{153}\right)$	$e\left(\frac{487}{612}\right)$
$\chi_{164730}(131,\cdot)$	164730.ko	144	no	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{36}\right)$

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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	$164730$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{2448}\)
Order	$39168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{164730}(1,\cdot)\)	164730.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{164730}(7,\cdot)\)	164730.ow	816	no	\(1\)	\(1\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{403}{816}\right)\)	\(e\left(\frac{325}{816}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{635}{816}\right)\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{46}{51}\right)\)
\(\chi_{164730}(11,\cdot)\)	164730.pa	816	no	\(1\)	\(1\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{563}{816}\right)\)	\(e\left(\frac{329}{816}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{317}{408}\right)\)	\(e\left(\frac{59}{204}\right)\)
\(\chi_{164730}(13,\cdot)\)	164730.ny	612	no	\(1\)	\(1\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{535}{612}\right)\)	\(e\left(\frac{76}{153}\right)\)	\(e\left(\frac{181}{612}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{509}{612}\right)\)	\(e\left(\frac{335}{612}\right)\)	\(e\left(\frac{19}{612}\right)\)
\(\chi_{164730}(23,\cdot)\)	164730.qh	2448	no	\(-1\)	\(1\)	\(e\left(\frac{403}{816}\right)\)	\(e\left(\frac{563}{816}\right)\)	\(e\left(\frac{76}{153}\right)\)	\(e\left(\frac{1957}{2448}\right)\)	\(e\left(\frac{907}{2448}\right)\)	\(e\left(\frac{37}{816}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{341}{2448}\right)\)	\(e\left(\frac{385}{1224}\right)\)	\(e\left(\frac{19}{153}\right)\)
\(\chi_{164730}(29,\cdot)\)	164730.qm	2448	no	\(-1\)	\(1\)	\(e\left(\frac{325}{816}\right)\)	\(e\left(\frac{329}{816}\right)\)	\(e\left(\frac{181}{612}\right)\)	\(e\left(\frac{907}{2448}\right)\)	\(e\left(\frac{1}{2448}\right)\)	\(e\left(\frac{247}{816}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{887}{2448}\right)\)	\(e\left(\frac{577}{1224}\right)\)	\(e\left(\frac{313}{612}\right)\)
\(\chi_{164730}(31,\cdot)\)	164730.pd	816	no	\(1\)	\(1\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{37}{816}\right)\)	\(e\left(\frac{247}{816}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{401}{816}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{199}{204}\right)\)
\(\chi_{164730}(37,\cdot)\)	164730.mq	272	no	\(-1\)	\(1\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{139}{272}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{209}{272}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{164730}(41,\cdot)\)	164730.qa	2448	no	\(-1\)	\(1\)	\(e\left(\frac{635}{816}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{509}{612}\right)\)	\(e\left(\frac{341}{2448}\right)\)	\(e\left(\frac{887}{2448}\right)\)	\(e\left(\frac{401}{816}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{961}{2448}\right)\)	\(e\left(\frac{779}{1224}\right)\)	\(e\left(\frac{89}{612}\right)\)
\(\chi_{164730}(43,\cdot)\)	164730.pn	1224	no	\(-1\)	\(1\)	\(e\left(\frac{355}{408}\right)\)	\(e\left(\frac{317}{408}\right)\)	\(e\left(\frac{335}{612}\right)\)	\(e\left(\frac{385}{1224}\right)\)	\(e\left(\frac{577}{1224}\right)\)	\(e\left(\frac{331}{408}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{779}{1224}\right)\)	\(e\left(\frac{77}{306}\right)\)	\(e\left(\frac{581}{612}\right)\)
\(\chi_{164730}(47,\cdot)\)	164730.ot	612	no	\(1\)	\(1\)	\(e\left(\frac{46}{51}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{19}{612}\right)\)	\(e\left(\frac{19}{153}\right)\)	\(e\left(\frac{313}{612}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{89}{612}\right)\)	\(e\left(\frac{581}{612}\right)\)	\(e\left(\frac{43}{612}\right)\)
\(\chi_{164730}(49,\cdot)\)	164730.nv	408	no	\(1\)	\(1\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{403}{408}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{227}{408}\right)\)	\(e\left(\frac{151}{204}\right)\)	\(e\left(\frac{41}{51}\right)\)
\(\chi_{164730}(53,\cdot)\)	164730.pk	1224	no	\(-1\)	\(1\)	\(e\left(\frac{329}{408}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{457}{612}\right)\)	\(e\left(\frac{1055}{1224}\right)\)	\(e\left(\frac{71}{1224}\right)\)	\(e\left(\frac{401}{408}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{1165}{1224}\right)\)	\(e\left(\frac{29}{153}\right)\)	\(e\left(\frac{535}{612}\right)\)
\(\chi_{164730}(59,\cdot)\)	164730.pt	1224	no	\(1\)	\(1\)	\(e\left(\frac{73}{408}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{121}{306}\right)\)	\(e\left(\frac{1171}{1224}\right)\)	\(e\left(\frac{1201}{1224}\right)\)	\(e\left(\frac{235}{408}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{407}{1224}\right)\)	\(e\left(\frac{499}{612}\right)\)	\(e\left(\frac{145}{306}\right)\)
\(\chi_{164730}(61,\cdot)\)	164730.qo	2448	no	\(-1\)	\(1\)	\(e\left(\frac{211}{816}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{115}{612}\right)\)	\(e\left(\frac{1381}{2448}\right)\)	\(e\left(\frac{2239}{2448}\right)\)	\(e\left(\frac{193}{816}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{665}{2448}\right)\)	\(e\left(\frac{1195}{1224}\right)\)	\(e\left(\frac{67}{612}\right)\)
\(\chi_{164730}(67,\cdot)\)	164730.od	612	no	\(1\)	\(1\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{37}{612}\right)\)	\(e\left(\frac{301}{612}\right)\)	\(e\left(\frac{35}{306}\right)\)	\(e\left(\frac{13}{51}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{146}{153}\right)\)	\(e\left(\frac{455}{612}\right)\)	\(e\left(\frac{277}{612}\right)\)
\(\chi_{164730}(71,\cdot)\)	164730.qa	2448	no	\(-1\)	\(1\)	\(e\left(\frac{641}{816}\right)\)	\(e\left(\frac{733}{816}\right)\)	\(e\left(\frac{83}{612}\right)\)	\(e\left(\frac{2399}{2448}\right)\)	\(e\left(\frac{533}{2448}\right)\)	\(e\left(\frac{275}{816}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{307}{2448}\right)\)	\(e\left(\frac{929}{1224}\right)\)	\(e\left(\frac{59}{612}\right)\)
\(\chi_{164730}(73,\cdot)\)	164730.qi	2448	no	\(1\)	\(1\)	\(e\left(\frac{89}{816}\right)\)	\(e\left(\frac{505}{816}\right)\)	\(e\left(\frac{79}{306}\right)\)	\(e\left(\frac{2375}{2448}\right)\)	\(e\left(\frac{257}{2448}\right)\)	\(e\left(\frac{647}{816}\right)\)	\(e\left(\frac{1}{272}\right)\)	\(e\left(\frac{1519}{2448}\right)\)	\(e\left(\frac{1103}{1224}\right)\)	\(e\left(\frac{29}{153}\right)\)
\(\chi_{164730}(77,\cdot)\)	164730.ka	136	no	\(1\)	\(1\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)
\(\chi_{164730}(79,\cdot)\)	164730.qp	2448	no	\(1\)	\(1\)	\(e\left(\frac{815}{816}\right)\)	\(e\left(\frac{643}{816}\right)\)	\(e\left(\frac{275}{612}\right)\)	\(e\left(\frac{2105}{2448}\right)\)	\(e\left(\frac{59}{2448}\right)\)	\(e\left(\frac{293}{816}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{925}{2448}\right)\)	\(e\left(\frac{995}{1224}\right)\)	\(e\left(\frac{413}{612}\right)\)
\(\chi_{164730}(83,\cdot)\)	164730.nq	408	no	\(1\)	\(1\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{193}{204}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{61}{204}\right)\)
\(\chi_{164730}(89,\cdot)\)	164730.ok	612	no	\(1\)	\(1\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{100}{153}\right)\)	\(e\left(\frac{529}{612}\right)\)	\(e\left(\frac{91}{612}\right)\)	\(e\left(\frac{139}{204}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{545}{612}\right)\)	\(e\left(\frac{14}{153}\right)\)	\(e\left(\frac{25}{153}\right)\)
\(\chi_{164730}(91,\cdot)\)	164730.qd	2448	no	\(1\)	\(1\)	\(e\left(\frac{559}{816}\right)\)	\(e\left(\frac{11}{816}\right)\)	\(e\left(\frac{601}{612}\right)\)	\(e\left(\frac{2425}{2448}\right)\)	\(e\left(\frac{1699}{2448}\right)\)	\(e\left(\frac{637}{816}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{1493}{2448}\right)\)	\(e\left(\frac{511}{1224}\right)\)	\(e\left(\frac{571}{612}\right)\)
\(\chi_{164730}(97,\cdot)\)	164730.qj	2448	no	\(-1\)	\(1\)	\(e\left(\frac{233}{816}\right)\)	\(e\left(\frac{529}{816}\right)\)	\(e\left(\frac{67}{306}\right)\)	\(e\left(\frac{1991}{2448}\right)\)	\(e\left(\frac{737}{2448}\right)\)	\(e\left(\frac{71}{816}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{1327}{2448}\right)\)	\(e\left(\frac{827}{1224}\right)\)	\(e\left(\frac{55}{306}\right)\)
\(\chi_{164730}(101,\cdot)\)	164730.mw	306	no	\(-1\)	\(1\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{118}{153}\right)\)	\(e\left(\frac{13}{153}\right)\)	\(e\left(\frac{124}{153}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{134}{153}\right)\)	\(e\left(\frac{41}{153}\right)\)	\(e\left(\frac{59}{306}\right)\)
\(\chi_{164730}(103,\cdot)\)	164730.lk	204	no	\(1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{41}{204}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{125}{204}\right)\)
\(\chi_{164730}(107,\cdot)\)	164730.ox	816	no	\(1\)	\(1\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{781}{816}\right)\)	\(e\left(\frac{235}{816}\right)\)	\(e\left(\frac{245}{272}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{773}{816}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{16}{51}\right)\)
\(\chi_{164730}(109,\cdot)\)	164730.qp	2448	no	\(1\)	\(1\)	\(e\left(\frac{419}{816}\right)\)	\(e\left(\frac{679}{816}\right)\)	\(e\left(\frac{443}{612}\right)\)	\(e\left(\frac{1733}{2448}\right)\)	\(e\left(\frac{2207}{2448}\right)\)	\(e\left(\frac{449}{816}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{1657}{2448}\right)\)	\(e\left(\frac{479}{1224}\right)\)	\(e\left(\frac{149}{612}\right)\)
\(\chi_{164730}(113,\cdot)\)	164730.mn	272	no	\(1\)	\(1\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{57}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{27}{272}\right)\)	\(e\left(\frac{205}{272}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{2}{17}\right)\)
\(\chi_{164730}(121,\cdot)\)	164730.nh	408	no	\(1\)	\(1\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{155}{408}\right)\)	\(e\left(\frac{329}{408}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{103}{408}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)
\(\chi_{164730}(127,\cdot)\)	164730.py	1224	no	\(1\)	\(1\)	\(e\left(\frac{395}{408}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{571}{612}\right)\)	\(e\left(\frac{1049}{1224}\right)\)	\(e\left(\frac{1073}{1224}\right)\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{91}{1224}\right)\)	\(e\left(\frac{59}{153}\right)\)	\(e\left(\frac{487}{612}\right)\)
\(\chi_{164730}(131,\cdot)\)	164730.ko	144	no	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)

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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.