LMFDB - Group of Dirichlet characters of modulus 144000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(144000)

pari: g = idealstar(,144000,2)

Character group

sage: G.order() pari: g.no
Order	=	38400
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{2400}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{144000}(42751,\cdot)$, $\chi_{144000}(58501,\cdot)$, $\chi_{144000}(64001,\cdot)$, $\chi_{144000}(101377,\cdot)$

First 32 of 38400 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{144000}(1,\cdot)$	144000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{144000}(7,\cdot)$	144000.pf	240	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{120}\right)$
$\chi_{144000}(11,\cdot)$	144000.ue	2400	yes	$1$	$1$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{499}{2400}\right)$	$e\left(\frac{1961}{2400}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{219}{800}\right)$	$e\left(\frac{97}{1200}\right)$	$e\left(\frac{13}{2400}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{357}{800}\right)$	$e\left(\frac{1153}{1200}\right)$
$\chi_{144000}(13,\cdot)$	144000.ty	2400	yes	$-1$	$1$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{1961}{2400}\right)$	$e\left(\frac{2179}{2400}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{641}{800}\right)$	$e\left(\frac{383}{1200}\right)$	$e\left(\frac{407}{2400}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{23}{800}\right)$	$e\left(\frac{1067}{1200}\right)$
$\chi_{144000}(17,\cdot)$	144000.on	200	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{77}{200}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{87}{100}\right)$
$\chi_{144000}(19,\cdot)$	144000.tb	800	no	$-1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{219}{800}\right)$	$e\left(\frac{641}{800}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{217}{800}\right)$	$e\left(\frac{57}{400}\right)$	$e\left(\frac{453}{800}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{151}{800}\right)$	$e\left(\frac{193}{400}\right)$
$\chi_{144000}(23,\cdot)$	144000.tc	1200	no	$-1$	$1$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{97}{1200}\right)$	$e\left(\frac{383}{1200}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{57}{400}\right)$	$e\left(\frac{241}{600}\right)$	$e\left(\frac{1039}{1200}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{371}{400}\right)$	$e\left(\frac{559}{600}\right)$
$\chi_{144000}(29,\cdot)$	144000.tv	2400	yes	$-1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{13}{2400}\right)$	$e\left(\frac{407}{2400}\right)$	$e\left(\frac{77}{200}\right)$	$e\left(\frac{453}{800}\right)$	$e\left(\frac{1039}{1200}\right)$	$e\left(\frac{931}{2400}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{59}{800}\right)$	$e\left(\frac{511}{1200}\right)$
$\chi_{144000}(31,\cdot)$	144000.qp	300	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{43}{150}\right)$
$\chi_{144000}(37,\cdot)$	144000.sr	800	no	$-1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{357}{800}\right)$	$e\left(\frac{23}{800}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{151}{800}\right)$	$e\left(\frac{371}{400}\right)$	$e\left(\frac{59}{800}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{753}{800}\right)$	$e\left(\frac{79}{400}\right)$
$\chi_{144000}(41,\cdot)$	144000.tg	1200	no	$-1$	$1$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1153}{1200}\right)$	$e\left(\frac{1067}{1200}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{193}{400}\right)$	$e\left(\frac{559}{600}\right)$	$e\left(\frac{511}{1200}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{79}{400}\right)$	$e\left(\frac{391}{600}\right)$
$\chi_{144000}(43,\cdot)$	144000.ru	480	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{191}{480}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{17}{480}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{77}{240}\right)$
$\chi_{144000}(47,\cdot)$	144000.ry	600	no	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{473}{600}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{259}{600}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{229}{300}\right)$
$\chi_{144000}(49,\cdot)$	144000.mx	120	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{144000}(53,\cdot)$	144000.sw	800	no	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{561}{800}\right)$	$e\left(\frac{379}{800}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{523}{800}\right)$	$e\left(\frac{183}{400}\right)$	$e\left(\frac{207}{800}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{269}{800}\right)$	$e\left(\frac{267}{400}\right)$
$\chi_{144000}(59,\cdot)$	144000.tu	2400	yes	$1$	$1$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{791}{2400}\right)$	$e\left(\frac{2149}{2400}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{671}{800}\right)$	$e\left(\frac{773}{1200}\right)$	$e\left(\frac{617}{2400}\right)$	$e\left(\frac{221}{300}\right)$	$e\left(\frac{113}{800}\right)$	$e\left(\frac{77}{1200}\right)$
$\chi_{144000}(61,\cdot)$	144000.ug	2400	yes	$1$	$1$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{1669}{2400}\right)$	$e\left(\frac{191}{2400}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{589}{800}\right)$	$e\left(\frac{7}{1200}\right)$	$e\left(\frac{1003}{2400}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{67}{800}\right)$	$e\left(\frac{943}{1200}\right)$
$\chi_{144000}(67,\cdot)$	144000.tz	2400	yes	$1$	$1$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{437}{2400}\right)$	$e\left(\frac{1543}{2400}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{397}{800}\right)$	$e\left(\frac{611}{1200}\right)$	$e\left(\frac{1019}{2400}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{491}{800}\right)$	$e\left(\frac{239}{1200}\right)$
$\chi_{144000}(71,\cdot)$	144000.ra	400	no	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{107}{400}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{59}{400}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{31}{400}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{111}{200}\right)$
$\chi_{144000}(73,\cdot)$	144000.qt	400	no	$-1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{239}{400}\right)$	$e\left(\frac{321}{400}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{393}{400}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{231}{400}\right)$	$e\left(\frac{133}{200}\right)$
$\chi_{144000}(77,\cdot)$	144000.ub	2400	yes	$1$	$1$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{1289}{2400}\right)$	$e\left(\frac{2371}{2400}\right)$	$e\left(\frac{31}{200}\right)$	$e\left(\frac{209}{800}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{1943}{2400}\right)$	$e\left(\frac{209}{300}\right)$	$e\left(\frac{727}{800}\right)$	$e\left(\frac{83}{1200}\right)$
$\chi_{144000}(79,\cdot)$	144000.sg	600	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{367}{600}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{229}{600}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{49}{300}\right)$
$\chi_{144000}(83,\cdot)$	144000.ua	2400	yes	$-1$	$1$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{2257}{2400}\right)$	$e\left(\frac{923}{2400}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{217}{800}\right)$	$e\left(\frac{871}{1200}\right)$	$e\left(\frac{1759}{2400}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{751}{800}\right)$	$e\left(\frac{379}{1200}\right)$
$\chi_{144000}(89,\cdot)$	144000.qu	400	no	$-1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{189}{400}\right)$	$e\left(\frac{71}{400}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{327}{400}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{243}{400}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{81}{400}\right)$	$e\left(\frac{83}{200}\right)$
$\chi_{144000}(91,\cdot)$	144000.sn	800	no	$-1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{117}{800}\right)$	$e\left(\frac{63}{800}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{631}{800}\right)$	$e\left(\frac{351}{400}\right)$	$e\left(\frac{779}{800}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{393}{800}\right)$	$e\left(\frac{399}{400}\right)$
$\chi_{144000}(97,\cdot)$	144000.qk	300	no	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{150}\right)$
$\chi_{144000}(101,\cdot)$	144000.rn	480	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{323}{480}\right)$	$e\left(\frac{457}{480}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{461}{480}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{69}{160}\right)$	$e\left(\frac{161}{240}\right)$
$\chi_{144000}(103,\cdot)$	144000.te	1200	no	$1$	$1$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{799}{1200}\right)$	$e\left(\frac{161}{1200}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{319}{400}\right)$	$e\left(\frac{247}{600}\right)$	$e\left(\frac{913}{1200}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{157}{400}\right)$	$e\left(\frac{253}{600}\right)$
$\chi_{144000}(107,\cdot)$	144000.ok	160	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{87}{160}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{123}{160}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{144000}(109,\cdot)$	144000.ta	800	no	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{107}{800}\right)$	$e\left(\frac{673}{800}\right)$	$e\left(\frac{109}{200}\right)$	$e\left(\frac{201}{800}\right)$	$e\left(\frac{321}{400}\right)$	$e\left(\frac{709}{800}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{503}{800}\right)$	$e\left(\frac{129}{400}\right)$
$\chi_{144000}(113,\cdot)$	144000.sk	600	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{331}{600}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{473}{600}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{263}{300}\right)$
$\chi_{144000}(119,\cdot)$	144000.tm	1200	no	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{821}{1200}\right)$	$e\left(\frac{919}{1200}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{101}{400}\right)$	$e\left(\frac{563}{600}\right)$	$e\left(\frac{227}{1200}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{203}{400}\right)$	$e\left(\frac{587}{600}\right)$

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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	$144000$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{2400}\)
Order	$38400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{144000}(1,\cdot)\)	144000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{144000}(7,\cdot)\)	144000.pf	240	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{120}\right)\)
\(\chi_{144000}(11,\cdot)\)	144000.ue	2400	yes	\(1\)	\(1\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{499}{2400}\right)\)	\(e\left(\frac{1961}{2400}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{219}{800}\right)\)	\(e\left(\frac{97}{1200}\right)\)	\(e\left(\frac{13}{2400}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{357}{800}\right)\)	\(e\left(\frac{1153}{1200}\right)\)
\(\chi_{144000}(13,\cdot)\)	144000.ty	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{1961}{2400}\right)\)	\(e\left(\frac{2179}{2400}\right)\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{641}{800}\right)\)	\(e\left(\frac{383}{1200}\right)\)	\(e\left(\frac{407}{2400}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{23}{800}\right)\)	\(e\left(\frac{1067}{1200}\right)\)
\(\chi_{144000}(17,\cdot)\)	144000.on	200	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{77}{200}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{87}{100}\right)\)
\(\chi_{144000}(19,\cdot)\)	144000.tb	800	no	\(-1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{219}{800}\right)\)	\(e\left(\frac{641}{800}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{217}{800}\right)\)	\(e\left(\frac{57}{400}\right)\)	\(e\left(\frac{453}{800}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{151}{800}\right)\)	\(e\left(\frac{193}{400}\right)\)
\(\chi_{144000}(23,\cdot)\)	144000.tc	1200	no	\(-1\)	\(1\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{97}{1200}\right)\)	\(e\left(\frac{383}{1200}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{57}{400}\right)\)	\(e\left(\frac{241}{600}\right)\)	\(e\left(\frac{1039}{1200}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{371}{400}\right)\)	\(e\left(\frac{559}{600}\right)\)
\(\chi_{144000}(29,\cdot)\)	144000.tv	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{13}{2400}\right)\)	\(e\left(\frac{407}{2400}\right)\)	\(e\left(\frac{77}{200}\right)\)	\(e\left(\frac{453}{800}\right)\)	\(e\left(\frac{1039}{1200}\right)\)	\(e\left(\frac{931}{2400}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{59}{800}\right)\)	\(e\left(\frac{511}{1200}\right)\)
\(\chi_{144000}(31,\cdot)\)	144000.qp	300	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{43}{150}\right)\)
\(\chi_{144000}(37,\cdot)\)	144000.sr	800	no	\(-1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{357}{800}\right)\)	\(e\left(\frac{23}{800}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{151}{800}\right)\)	\(e\left(\frac{371}{400}\right)\)	\(e\left(\frac{59}{800}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{753}{800}\right)\)	\(e\left(\frac{79}{400}\right)\)
\(\chi_{144000}(41,\cdot)\)	144000.tg	1200	no	\(-1\)	\(1\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1153}{1200}\right)\)	\(e\left(\frac{1067}{1200}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{193}{400}\right)\)	\(e\left(\frac{559}{600}\right)\)	\(e\left(\frac{511}{1200}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{79}{400}\right)\)	\(e\left(\frac{391}{600}\right)\)
\(\chi_{144000}(43,\cdot)\)	144000.ru	480	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{191}{480}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{17}{480}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{77}{240}\right)\)
\(\chi_{144000}(47,\cdot)\)	144000.ry	600	no	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{157}{600}\right)\)	\(e\left(\frac{473}{600}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{117}{200}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{259}{600}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{229}{300}\right)\)
\(\chi_{144000}(49,\cdot)\)	144000.mx	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{144000}(53,\cdot)\)	144000.sw	800	no	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{561}{800}\right)\)	\(e\left(\frac{379}{800}\right)\)	\(e\left(\frac{157}{200}\right)\)	\(e\left(\frac{523}{800}\right)\)	\(e\left(\frac{183}{400}\right)\)	\(e\left(\frac{207}{800}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{269}{800}\right)\)	\(e\left(\frac{267}{400}\right)\)
\(\chi_{144000}(59,\cdot)\)	144000.tu	2400	yes	\(1\)	\(1\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{791}{2400}\right)\)	\(e\left(\frac{2149}{2400}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{671}{800}\right)\)	\(e\left(\frac{773}{1200}\right)\)	\(e\left(\frac{617}{2400}\right)\)	\(e\left(\frac{221}{300}\right)\)	\(e\left(\frac{113}{800}\right)\)	\(e\left(\frac{77}{1200}\right)\)
\(\chi_{144000}(61,\cdot)\)	144000.ug	2400	yes	\(1\)	\(1\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{1669}{2400}\right)\)	\(e\left(\frac{191}{2400}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{589}{800}\right)\)	\(e\left(\frac{7}{1200}\right)\)	\(e\left(\frac{1003}{2400}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{67}{800}\right)\)	\(e\left(\frac{943}{1200}\right)\)
\(\chi_{144000}(67,\cdot)\)	144000.tz	2400	yes	\(1\)	\(1\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{437}{2400}\right)\)	\(e\left(\frac{1543}{2400}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{397}{800}\right)\)	\(e\left(\frac{611}{1200}\right)\)	\(e\left(\frac{1019}{2400}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{491}{800}\right)\)	\(e\left(\frac{239}{1200}\right)\)
\(\chi_{144000}(71,\cdot)\)	144000.ra	400	no	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{107}{400}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{59}{400}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{31}{400}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{111}{200}\right)\)
\(\chi_{144000}(73,\cdot)\)	144000.qt	400	no	\(-1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{239}{400}\right)\)	\(e\left(\frac{321}{400}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{393}{400}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{231}{400}\right)\)	\(e\left(\frac{133}{200}\right)\)
\(\chi_{144000}(77,\cdot)\)	144000.ub	2400	yes	\(1\)	\(1\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{1289}{2400}\right)\)	\(e\left(\frac{2371}{2400}\right)\)	\(e\left(\frac{31}{200}\right)\)	\(e\left(\frac{209}{800}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{1943}{2400}\right)\)	\(e\left(\frac{209}{300}\right)\)	\(e\left(\frac{727}{800}\right)\)	\(e\left(\frac{83}{1200}\right)\)
\(\chi_{144000}(79,\cdot)\)	144000.sg	600	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{367}{600}\right)\)	\(e\left(\frac{413}{600}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{229}{600}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{49}{300}\right)\)
\(\chi_{144000}(83,\cdot)\)	144000.ua	2400	yes	\(-1\)	\(1\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{2257}{2400}\right)\)	\(e\left(\frac{923}{2400}\right)\)	\(e\left(\frac{3}{200}\right)\)	\(e\left(\frac{217}{800}\right)\)	\(e\left(\frac{871}{1200}\right)\)	\(e\left(\frac{1759}{2400}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{751}{800}\right)\)	\(e\left(\frac{379}{1200}\right)\)
\(\chi_{144000}(89,\cdot)\)	144000.qu	400	no	\(-1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{189}{400}\right)\)	\(e\left(\frac{71}{400}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{327}{400}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{243}{400}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{81}{400}\right)\)	\(e\left(\frac{83}{200}\right)\)
\(\chi_{144000}(91,\cdot)\)	144000.sn	800	no	\(-1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{117}{800}\right)\)	\(e\left(\frac{63}{800}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{631}{800}\right)\)	\(e\left(\frac{351}{400}\right)\)	\(e\left(\frac{779}{800}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{393}{800}\right)\)	\(e\left(\frac{399}{400}\right)\)
\(\chi_{144000}(97,\cdot)\)	144000.qk	300	no	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{150}\right)\)
\(\chi_{144000}(101,\cdot)\)	144000.rn	480	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{323}{480}\right)\)	\(e\left(\frac{457}{480}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{461}{480}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{69}{160}\right)\)	\(e\left(\frac{161}{240}\right)\)
\(\chi_{144000}(103,\cdot)\)	144000.te	1200	no	\(1\)	\(1\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{799}{1200}\right)\)	\(e\left(\frac{161}{1200}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{319}{400}\right)\)	\(e\left(\frac{247}{600}\right)\)	\(e\left(\frac{913}{1200}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{157}{400}\right)\)	\(e\left(\frac{253}{600}\right)\)
\(\chi_{144000}(107,\cdot)\)	144000.ok	160	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{87}{160}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{123}{160}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{144000}(109,\cdot)\)	144000.ta	800	no	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{107}{800}\right)\)	\(e\left(\frac{673}{800}\right)\)	\(e\left(\frac{109}{200}\right)\)	\(e\left(\frac{201}{800}\right)\)	\(e\left(\frac{321}{400}\right)\)	\(e\left(\frac{709}{800}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{503}{800}\right)\)	\(e\left(\frac{129}{400}\right)\)
\(\chi_{144000}(113,\cdot)\)	144000.sk	600	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{179}{600}\right)\)	\(e\left(\frac{331}{600}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{99}{200}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{473}{600}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{263}{300}\right)\)
\(\chi_{144000}(119,\cdot)\)	144000.tm	1200	no	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{821}{1200}\right)\)	\(e\left(\frac{919}{1200}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{101}{400}\right)\)	\(e\left(\frac{563}{600}\right)\)	\(e\left(\frac{227}{1200}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{203}{400}\right)\)	\(e\left(\frac{587}{600}\right)\)

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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.