LMFDB - Group of Dirichlet characters of modulus 254144

sage:H = DirichletGroup(254144)

pari:g = idealstar(,254144,2)

Character group

sage:G.order() pari:g.no
Order	=	109440
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{13680}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{254144}(166783,\cdot)$, $\chi_{254144}(174725,\cdot)$, $\chi_{254144}(69313,\cdot)$, $\chi_{254144}(14081,\cdot)$

First 32 of 109440 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{254144}(1,\cdot)$	254144.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{254144}(3,\cdot)$	254144.si	13680	yes	$1$	$1$	$e\left(\frac{13087}{13680}\right)$	$e\left(\frac{9301}{13680}\right)$	$e\left(\frac{2143}{2280}\right)$	$e\left(\frac{6247}{6840}\right)$	$e\left(\frac{4499}{13680}\right)$	$e\left(\frac{2177}{3420}\right)$	$e\left(\frac{1039}{3420}\right)$	$e\left(\frac{2453}{2736}\right)$	$e\left(\frac{635}{1368}\right)$	$e\left(\frac{2461}{6840}\right)$
$\chi_{254144}(5,\cdot)$	254144.sl	13680	yes	$1$	$1$	$e\left(\frac{9301}{13680}\right)$	$e\left(\frac{583}{13680}\right)$	$e\left(\frac{409}{2280}\right)$	$e\left(\frac{2461}{6840}\right)$	$e\left(\frac{7097}{13680}\right)$	$e\left(\frac{2471}{3420}\right)$	$e\left(\frac{2257}{3420}\right)$	$e\left(\frac{2351}{2736}\right)$	$e\left(\frac{1253}{1368}\right)$	$e\left(\frac{583}{6840}\right)$
$\chi_{254144}(7,\cdot)$	254144.qq	2280	no	$1$	$1$	$e\left(\frac{2143}{2280}\right)$	$e\left(\frac{409}{2280}\right)$	$e\left(\frac{167}{380}\right)$	$e\left(\frac{1003}{1140}\right)$	$e\left(\frac{851}{2280}\right)$	$e\left(\frac{34}{285}\right)$	$e\left(\frac{263}{285}\right)$	$e\left(\frac{173}{456}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{409}{1140}\right)$
$\chi_{254144}(9,\cdot)$	254144.ry	6840	no	$1$	$1$	$e\left(\frac{6247}{6840}\right)$	$e\left(\frac{2461}{6840}\right)$	$e\left(\frac{1003}{1140}\right)$	$e\left(\frac{2827}{3420}\right)$	$e\left(\frac{4499}{6840}\right)$	$e\left(\frac{467}{1710}\right)$	$e\left(\frac{1039}{1710}\right)$	$e\left(\frac{1085}{1368}\right)$	$e\left(\frac{635}{684}\right)$	$e\left(\frac{2461}{3420}\right)$
$\chi_{254144}(13,\cdot)$	254144.sh	13680	yes	$1$	$1$	$e\left(\frac{4499}{13680}\right)$	$e\left(\frac{7097}{13680}\right)$	$e\left(\frac{851}{2280}\right)$	$e\left(\frac{4499}{6840}\right)$	$e\left(\frac{8983}{13680}\right)$	$e\left(\frac{2899}{3420}\right)$	$e\left(\frac{1913}{3420}\right)$	$e\left(\frac{1921}{2736}\right)$	$e\left(\frac{787}{1368}\right)$	$e\left(\frac{257}{6840}\right)$
$\chi_{254144}(15,\cdot)$	254144.rg	3420	no	$1$	$1$	$e\left(\frac{2177}{3420}\right)$	$e\left(\frac{2471}{3420}\right)$	$e\left(\frac{34}{285}\right)$	$e\left(\frac{467}{1710}\right)$	$e\left(\frac{2899}{3420}\right)$	$e\left(\frac{307}{855}\right)$	$e\left(\frac{824}{855}\right)$	$e\left(\frac{517}{684}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{761}{1710}\right)$
$\chi_{254144}(17,\cdot)$	254144.rh	3420	no	$-1$	$1$	$e\left(\frac{1039}{3420}\right)$	$e\left(\frac{2257}{3420}\right)$	$e\left(\frac{263}{285}\right)$	$e\left(\frac{1039}{1710}\right)$	$e\left(\frac{1913}{3420}\right)$	$e\left(\frac{824}{855}\right)$	$e\left(\frac{761}{1710}\right)$	$e\left(\frac{155}{684}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{547}{1710}\right)$
$\chi_{254144}(21,\cdot)$	254144.re	2736	yes	$1$	$1$	$e\left(\frac{2453}{2736}\right)$	$e\left(\frac{2351}{2736}\right)$	$e\left(\frac{173}{456}\right)$	$e\left(\frac{1085}{1368}\right)$	$e\left(\frac{1921}{2736}\right)$	$e\left(\frac{517}{684}\right)$	$e\left(\frac{155}{684}\right)$	$e\left(\frac{755}{2736}\right)$	$e\left(\frac{1025}{1368}\right)$	$e\left(\frac{983}{1368}\right)$
$\chi_{254144}(23,\cdot)$	254144.po	1368	no	$-1$	$1$	$e\left(\frac{635}{1368}\right)$	$e\left(\frac{1253}{1368}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{635}{684}\right)$	$e\left(\frac{787}{1368}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{1025}{1368}\right)$	$e\left(\frac{53}{684}\right)$	$e\left(\frac{569}{684}\right)$
$\chi_{254144}(25,\cdot)$	254144.ry	6840	no	$1$	$1$	$e\left(\frac{2461}{6840}\right)$	$e\left(\frac{583}{6840}\right)$	$e\left(\frac{409}{1140}\right)$	$e\left(\frac{2461}{3420}\right)$	$e\left(\frac{257}{6840}\right)$	$e\left(\frac{761}{1710}\right)$	$e\left(\frac{547}{1710}\right)$	$e\left(\frac{983}{1368}\right)$	$e\left(\frac{569}{684}\right)$	$e\left(\frac{583}{3420}\right)$
$\chi_{254144}(27,\cdot)$	254144.rq	4560	yes	$1$	$1$	$e\left(\frac{3967}{4560}\right)$	$e\left(\frac{181}{4560}\right)$	$e\left(\frac{623}{760}\right)$	$e\left(\frac{1687}{2280}\right)$	$e\left(\frac{4499}{4560}\right)$	$e\left(\frac{1037}{1140}\right)$	$e\left(\frac{1039}{1140}\right)$	$e\left(\frac{629}{912}\right)$	$e\left(\frac{179}{456}\right)$	$e\left(\frac{181}{2280}\right)$
$\chi_{254144}(29,\cdot)$	254144.sh	13680	yes	$1$	$1$	$e\left(\frac{7823}{13680}\right)$	$e\left(\frac{269}{13680}\right)$	$e\left(\frac{527}{2280}\right)$	$e\left(\frac{983}{6840}\right)$	$e\left(\frac{5011}{13680}\right)$	$e\left(\frac{2023}{3420}\right)$	$e\left(\frac{2681}{3420}\right)$	$e\left(\frac{2197}{2736}\right)$	$e\left(\frac{1207}{1368}\right)$	$e\left(\frac{269}{6840}\right)$
$\chi_{254144}(31,\cdot)$	254144.ns	570	no	$1$	$1$	$e\left(\frac{541}{570}\right)$	$e\left(\frac{253}{570}\right)$	$e\left(\frac{113}{190}\right)$	$e\left(\frac{256}{285}\right)$	$e\left(\frac{166}{285}\right)$	$e\left(\frac{112}{285}\right)$	$e\left(\frac{179}{285}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{253}{285}\right)$
$\chi_{254144}(35,\cdot)$	254144.se	13680	yes	$1$	$1$	$e\left(\frac{8479}{13680}\right)$	$e\left(\frac{3037}{13680}\right)$	$e\left(\frac{1411}{2280}\right)$	$e\left(\frac{1639}{6840}\right)$	$e\left(\frac{12203}{13680}\right)$	$e\left(\frac{2879}{3420}\right)$	$e\left(\frac{1993}{3420}\right)$	$e\left(\frac{653}{2736}\right)$	$e\left(\frac{275}{1368}\right)$	$e\left(\frac{3037}{6840}\right)$
$\chi_{254144}(37,\cdot)$	254144.qa	1520	yes	$-1$	$1$	$e\left(\frac{877}{1520}\right)$	$e\left(\frac{1351}{1520}\right)$	$e\left(\frac{579}{760}\right)$	$e\left(\frac{117}{760}\right)$	$e\left(\frac{1409}{1520}\right)$	$e\left(\frac{177}{380}\right)$	$e\left(\frac{109}{380}\right)$	$e\left(\frac{103}{304}\right)$	$e\left(\frac{13}{152}\right)$	$e\left(\frac{591}{760}\right)$
$\chi_{254144}(39,\cdot)$	254144.ot	760	no	$1$	$1$	$e\left(\frac{217}{760}\right)$	$e\left(\frac{151}{760}\right)$	$e\left(\frac{119}{380}\right)$	$e\left(\frac{217}{380}\right)$	$e\left(\frac{749}{760}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{91}{152}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{151}{380}\right)$
$\chi_{254144}(41,\cdot)$	254144.sd	6840	no	$1$	$1$	$e\left(\frac{1751}{6840}\right)$	$e\left(\frac{3593}{6840}\right)$	$e\left(\frac{269}{1140}\right)$	$e\left(\frac{1751}{3420}\right)$	$e\left(\frac{6007}{6840}\right)$	$e\left(\frac{668}{855}\right)$	$e\left(\frac{406}{855}\right)$	$e\left(\frac{673}{1368}\right)$	$e\left(\frac{583}{684}\right)$	$e\left(\frac{173}{3420}\right)$
$\chi_{254144}(43,\cdot)$	254144.rd	2736	yes	$1$	$1$	$e\left(\frac{197}{2736}\right)$	$e\left(\frac{239}{2736}\right)$	$e\left(\frac{425}{456}\right)$	$e\left(\frac{197}{1368}\right)$	$e\left(\frac{1945}{2736}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{419}{684}\right)$	$e\left(\frac{11}{2736}\right)$	$e\left(\frac{101}{1368}\right)$	$e\left(\frac{239}{1368}\right)$
$\chi_{254144}(45,\cdot)$	254144.pb	912	no	$1$	$1$	$e\left(\frac{541}{912}\right)$	$e\left(\frac{367}{912}\right)$	$e\left(\frac{9}{152}\right)$	$e\left(\frac{85}{456}\right)$	$e\left(\frac{161}{912}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{595}{912}\right)$	$e\left(\frac{385}{456}\right)$	$e\left(\frac{367}{456}\right)$
$\chi_{254144}(47,\cdot)$	254144.rj	3420	no	$-1$	$1$	$e\left(\frac{2453}{3420}\right)$	$e\left(\frac{2009}{3420}\right)$	$e\left(\frac{1}{285}\right)$	$e\left(\frac{743}{1710}\right)$	$e\left(\frac{211}{3420}\right)$	$e\left(\frac{521}{1710}\right)$	$e\left(\frac{326}{855}\right)$	$e\left(\frac{493}{684}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{299}{1710}\right)$
$\chi_{254144}(49,\cdot)$	254144.pd	1140	no	$1$	$1$	$e\left(\frac{1003}{1140}\right)$	$e\left(\frac{409}{1140}\right)$	$e\left(\frac{167}{190}\right)$	$e\left(\frac{433}{570}\right)$	$e\left(\frac{851}{1140}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{241}{285}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{409}{570}\right)$
$\chi_{254144}(51,\cdot)$	254144.sk	13680	yes	$-1$	$1$	$e\left(\frac{3563}{13680}\right)$	$e\left(\frac{4649}{13680}\right)$	$e\left(\frac{1967}{2280}\right)$	$e\left(\frac{3563}{6840}\right)$	$e\left(\frac{12151}{13680}\right)$	$e\left(\frac{2053}{3420}\right)$	$e\left(\frac{2561}{3420}\right)$	$e\left(\frac{337}{2736}\right)$	$e\left(\frac{607}{1368}\right)$	$e\left(\frac{4649}{6840}\right)$
$\chi_{254144}(53,\cdot)$	254144.sf	13680	yes	$-1$	$1$	$e\left(\frac{6449}{13680}\right)$	$e\left(\frac{227}{13680}\right)$	$e\left(\frac{1661}{2280}\right)$	$e\left(\frac{6449}{6840}\right)$	$e\left(\frac{1813}{13680}\right)$	$e\left(\frac{1669}{3420}\right)$	$e\left(\frac{3413}{3420}\right)$	$e\left(\frac{547}{2736}\right)$	$e\left(\frac{1105}{1368}\right)$	$e\left(\frac{227}{6840}\right)$
$\chi_{254144}(59,\cdot)$	254144.si	13680	yes	$1$	$1$	$e\left(\frac{11653}{13680}\right)$	$e\left(\frac{8839}{13680}\right)$	$e\left(\frac{2077}{2280}\right)$	$e\left(\frac{4813}{6840}\right)$	$e\left(\frac{3521}{13680}\right)$	$e\left(\frac{1703}{3420}\right)$	$e\left(\frac{541}{3420}\right)$	$e\left(\frac{2087}{2736}\right)$	$e\left(\frac{881}{1368}\right)$	$e\left(\frac{1999}{6840}\right)$
$\chi_{254144}(61,\cdot)$	254144.sj	13680	yes	$-1$	$1$	$e\left(\frac{2111}{13680}\right)$	$e\left(\frac{2693}{13680}\right)$	$e\left(\frac{1199}{2280}\right)$	$e\left(\frac{2111}{6840}\right)$	$e\left(\frac{2947}{13680}\right)$	$e\left(\frac{1201}{3420}\right)$	$e\left(\frac{497}{3420}\right)$	$e\left(\frac{1861}{2736}\right)$	$e\left(\frac{1231}{1368}\right)$	$e\left(\frac{2693}{6840}\right)$
$\chi_{254144}(63,\cdot)$	254144.qh	1710	no	$1$	$1$	$e\left(\frac{1459}{1710}\right)$	$e\left(\frac{461}{855}\right)$	$e\left(\frac{91}{285}\right)$	$e\left(\frac{604}{855}\right)$	$e\left(\frac{53}{1710}\right)$	$e\left(\frac{671}{1710}\right)$	$e\left(\frac{907}{1710}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{67}{855}\right)$
$\chi_{254144}(65,\cdot)$	254144.iq	114	no	$1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{7}{57}\right)$
$\chi_{254144}(67,\cdot)$	254144.qz	2736	no	$1$	$1$	$e\left(\frac{1075}{2736}\right)$	$e\left(\frac{1825}{2736}\right)$	$e\left(\frac{163}{456}\right)$	$e\left(\frac{1075}{1368}\right)$	$e\left(\frac{1607}{2736}\right)$	$e\left(\frac{41}{684}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{2053}{2736}\right)$	$e\left(\frac{1315}{1368}\right)$	$e\left(\frac{457}{1368}\right)$
$\chi_{254144}(69,\cdot)$	254144.lg	240	no	$-1$	$1$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{120}\right)$
$\chi_{254144}(71,\cdot)$	254144.rx	6840	no	$1$	$1$	$e\left(\frac{4673}{6840}\right)$	$e\left(\frac{5579}{6840}\right)$	$e\left(\frac{227}{1140}\right)$	$e\left(\frac{1253}{3420}\right)$	$e\left(\frac{5281}{6840}\right)$	$e\left(\frac{853}{1710}\right)$	$e\left(\frac{521}{1710}\right)$	$e\left(\frac{1207}{1368}\right)$	$e\left(\frac{667}{684}\right)$	$e\left(\frac{2159}{3420}\right)$
$\chi_{254144}(73,\cdot)$	254144.rw	6840	no	$-1$	$1$	$e\left(\frac{1679}{6840}\right)$	$e\left(\frac{1037}{6840}\right)$	$e\left(\frac{881}{1140}\right)$	$e\left(\frac{1679}{3420}\right)$	$e\left(\frac{463}{6840}\right)$	$e\left(\frac{679}{1710}\right)$	$e\left(\frac{694}{855}\right)$	$e\left(\frac{25}{1368}\right)$	$e\left(\frac{43}{684}\right)$	$e\left(\frac{1037}{3420}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$254144$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{13680}\)
Order	$109440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{254144}(1,\cdot)\)	254144.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{254144}(3,\cdot)\)	254144.si	13680	yes	\(1\)	\(1\)	\(e\left(\frac{13087}{13680}\right)\)	\(e\left(\frac{9301}{13680}\right)\)	\(e\left(\frac{2143}{2280}\right)\)	\(e\left(\frac{6247}{6840}\right)\)	\(e\left(\frac{4499}{13680}\right)\)	\(e\left(\frac{2177}{3420}\right)\)	\(e\left(\frac{1039}{3420}\right)\)	\(e\left(\frac{2453}{2736}\right)\)	\(e\left(\frac{635}{1368}\right)\)	\(e\left(\frac{2461}{6840}\right)\)
\(\chi_{254144}(5,\cdot)\)	254144.sl	13680	yes	\(1\)	\(1\)	\(e\left(\frac{9301}{13680}\right)\)	\(e\left(\frac{583}{13680}\right)\)	\(e\left(\frac{409}{2280}\right)\)	\(e\left(\frac{2461}{6840}\right)\)	\(e\left(\frac{7097}{13680}\right)\)	\(e\left(\frac{2471}{3420}\right)\)	\(e\left(\frac{2257}{3420}\right)\)	\(e\left(\frac{2351}{2736}\right)\)	\(e\left(\frac{1253}{1368}\right)\)	\(e\left(\frac{583}{6840}\right)\)
\(\chi_{254144}(7,\cdot)\)	254144.qq	2280	no	\(1\)	\(1\)	\(e\left(\frac{2143}{2280}\right)\)	\(e\left(\frac{409}{2280}\right)\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{1003}{1140}\right)\)	\(e\left(\frac{851}{2280}\right)\)	\(e\left(\frac{34}{285}\right)\)	\(e\left(\frac{263}{285}\right)\)	\(e\left(\frac{173}{456}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{409}{1140}\right)\)
\(\chi_{254144}(9,\cdot)\)	254144.ry	6840	no	\(1\)	\(1\)	\(e\left(\frac{6247}{6840}\right)\)	\(e\left(\frac{2461}{6840}\right)\)	\(e\left(\frac{1003}{1140}\right)\)	\(e\left(\frac{2827}{3420}\right)\)	\(e\left(\frac{4499}{6840}\right)\)	\(e\left(\frac{467}{1710}\right)\)	\(e\left(\frac{1039}{1710}\right)\)	\(e\left(\frac{1085}{1368}\right)\)	\(e\left(\frac{635}{684}\right)\)	\(e\left(\frac{2461}{3420}\right)\)
\(\chi_{254144}(13,\cdot)\)	254144.sh	13680	yes	\(1\)	\(1\)	\(e\left(\frac{4499}{13680}\right)\)	\(e\left(\frac{7097}{13680}\right)\)	\(e\left(\frac{851}{2280}\right)\)	\(e\left(\frac{4499}{6840}\right)\)	\(e\left(\frac{8983}{13680}\right)\)	\(e\left(\frac{2899}{3420}\right)\)	\(e\left(\frac{1913}{3420}\right)\)	\(e\left(\frac{1921}{2736}\right)\)	\(e\left(\frac{787}{1368}\right)\)	\(e\left(\frac{257}{6840}\right)\)
\(\chi_{254144}(15,\cdot)\)	254144.rg	3420	no	\(1\)	\(1\)	\(e\left(\frac{2177}{3420}\right)\)	\(e\left(\frac{2471}{3420}\right)\)	\(e\left(\frac{34}{285}\right)\)	\(e\left(\frac{467}{1710}\right)\)	\(e\left(\frac{2899}{3420}\right)\)	\(e\left(\frac{307}{855}\right)\)	\(e\left(\frac{824}{855}\right)\)	\(e\left(\frac{517}{684}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{761}{1710}\right)\)
\(\chi_{254144}(17,\cdot)\)	254144.rh	3420	no	\(-1\)	\(1\)	\(e\left(\frac{1039}{3420}\right)\)	\(e\left(\frac{2257}{3420}\right)\)	\(e\left(\frac{263}{285}\right)\)	\(e\left(\frac{1039}{1710}\right)\)	\(e\left(\frac{1913}{3420}\right)\)	\(e\left(\frac{824}{855}\right)\)	\(e\left(\frac{761}{1710}\right)\)	\(e\left(\frac{155}{684}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{547}{1710}\right)\)
\(\chi_{254144}(21,\cdot)\)	254144.re	2736	yes	\(1\)	\(1\)	\(e\left(\frac{2453}{2736}\right)\)	\(e\left(\frac{2351}{2736}\right)\)	\(e\left(\frac{173}{456}\right)\)	\(e\left(\frac{1085}{1368}\right)\)	\(e\left(\frac{1921}{2736}\right)\)	\(e\left(\frac{517}{684}\right)\)	\(e\left(\frac{155}{684}\right)\)	\(e\left(\frac{755}{2736}\right)\)	\(e\left(\frac{1025}{1368}\right)\)	\(e\left(\frac{983}{1368}\right)\)
\(\chi_{254144}(23,\cdot)\)	254144.po	1368	no	\(-1\)	\(1\)	\(e\left(\frac{635}{1368}\right)\)	\(e\left(\frac{1253}{1368}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{635}{684}\right)\)	\(e\left(\frac{787}{1368}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{1025}{1368}\right)\)	\(e\left(\frac{53}{684}\right)\)	\(e\left(\frac{569}{684}\right)\)
\(\chi_{254144}(25,\cdot)\)	254144.ry	6840	no	\(1\)	\(1\)	\(e\left(\frac{2461}{6840}\right)\)	\(e\left(\frac{583}{6840}\right)\)	\(e\left(\frac{409}{1140}\right)\)	\(e\left(\frac{2461}{3420}\right)\)	\(e\left(\frac{257}{6840}\right)\)	\(e\left(\frac{761}{1710}\right)\)	\(e\left(\frac{547}{1710}\right)\)	\(e\left(\frac{983}{1368}\right)\)	\(e\left(\frac{569}{684}\right)\)	\(e\left(\frac{583}{3420}\right)\)
\(\chi_{254144}(27,\cdot)\)	254144.rq	4560	yes	\(1\)	\(1\)	\(e\left(\frac{3967}{4560}\right)\)	\(e\left(\frac{181}{4560}\right)\)	\(e\left(\frac{623}{760}\right)\)	\(e\left(\frac{1687}{2280}\right)\)	\(e\left(\frac{4499}{4560}\right)\)	\(e\left(\frac{1037}{1140}\right)\)	\(e\left(\frac{1039}{1140}\right)\)	\(e\left(\frac{629}{912}\right)\)	\(e\left(\frac{179}{456}\right)\)	\(e\left(\frac{181}{2280}\right)\)
\(\chi_{254144}(29,\cdot)\)	254144.sh	13680	yes	\(1\)	\(1\)	\(e\left(\frac{7823}{13680}\right)\)	\(e\left(\frac{269}{13680}\right)\)	\(e\left(\frac{527}{2280}\right)\)	\(e\left(\frac{983}{6840}\right)\)	\(e\left(\frac{5011}{13680}\right)\)	\(e\left(\frac{2023}{3420}\right)\)	\(e\left(\frac{2681}{3420}\right)\)	\(e\left(\frac{2197}{2736}\right)\)	\(e\left(\frac{1207}{1368}\right)\)	\(e\left(\frac{269}{6840}\right)\)
\(\chi_{254144}(31,\cdot)\)	254144.ns	570	no	\(1\)	\(1\)	\(e\left(\frac{541}{570}\right)\)	\(e\left(\frac{253}{570}\right)\)	\(e\left(\frac{113}{190}\right)\)	\(e\left(\frac{256}{285}\right)\)	\(e\left(\frac{166}{285}\right)\)	\(e\left(\frac{112}{285}\right)\)	\(e\left(\frac{179}{285}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{253}{285}\right)\)
\(\chi_{254144}(35,\cdot)\)	254144.se	13680	yes	\(1\)	\(1\)	\(e\left(\frac{8479}{13680}\right)\)	\(e\left(\frac{3037}{13680}\right)\)	\(e\left(\frac{1411}{2280}\right)\)	\(e\left(\frac{1639}{6840}\right)\)	\(e\left(\frac{12203}{13680}\right)\)	\(e\left(\frac{2879}{3420}\right)\)	\(e\left(\frac{1993}{3420}\right)\)	\(e\left(\frac{653}{2736}\right)\)	\(e\left(\frac{275}{1368}\right)\)	\(e\left(\frac{3037}{6840}\right)\)
\(\chi_{254144}(37,\cdot)\)	254144.qa	1520	yes	\(-1\)	\(1\)	\(e\left(\frac{877}{1520}\right)\)	\(e\left(\frac{1351}{1520}\right)\)	\(e\left(\frac{579}{760}\right)\)	\(e\left(\frac{117}{760}\right)\)	\(e\left(\frac{1409}{1520}\right)\)	\(e\left(\frac{177}{380}\right)\)	\(e\left(\frac{109}{380}\right)\)	\(e\left(\frac{103}{304}\right)\)	\(e\left(\frac{13}{152}\right)\)	\(e\left(\frac{591}{760}\right)\)
\(\chi_{254144}(39,\cdot)\)	254144.ot	760	no	\(1\)	\(1\)	\(e\left(\frac{217}{760}\right)\)	\(e\left(\frac{151}{760}\right)\)	\(e\left(\frac{119}{380}\right)\)	\(e\left(\frac{217}{380}\right)\)	\(e\left(\frac{749}{760}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{91}{152}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{151}{380}\right)\)
\(\chi_{254144}(41,\cdot)\)	254144.sd	6840	no	\(1\)	\(1\)	\(e\left(\frac{1751}{6840}\right)\)	\(e\left(\frac{3593}{6840}\right)\)	\(e\left(\frac{269}{1140}\right)\)	\(e\left(\frac{1751}{3420}\right)\)	\(e\left(\frac{6007}{6840}\right)\)	\(e\left(\frac{668}{855}\right)\)	\(e\left(\frac{406}{855}\right)\)	\(e\left(\frac{673}{1368}\right)\)	\(e\left(\frac{583}{684}\right)\)	\(e\left(\frac{173}{3420}\right)\)
\(\chi_{254144}(43,\cdot)\)	254144.rd	2736	yes	\(1\)	\(1\)	\(e\left(\frac{197}{2736}\right)\)	\(e\left(\frac{239}{2736}\right)\)	\(e\left(\frac{425}{456}\right)\)	\(e\left(\frac{197}{1368}\right)\)	\(e\left(\frac{1945}{2736}\right)\)	\(e\left(\frac{109}{684}\right)\)	\(e\left(\frac{419}{684}\right)\)	\(e\left(\frac{11}{2736}\right)\)	\(e\left(\frac{101}{1368}\right)\)	\(e\left(\frac{239}{1368}\right)\)
\(\chi_{254144}(45,\cdot)\)	254144.pb	912	no	\(1\)	\(1\)	\(e\left(\frac{541}{912}\right)\)	\(e\left(\frac{367}{912}\right)\)	\(e\left(\frac{9}{152}\right)\)	\(e\left(\frac{85}{456}\right)\)	\(e\left(\frac{161}{912}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{595}{912}\right)\)	\(e\left(\frac{385}{456}\right)\)	\(e\left(\frac{367}{456}\right)\)
\(\chi_{254144}(47,\cdot)\)	254144.rj	3420	no	\(-1\)	\(1\)	\(e\left(\frac{2453}{3420}\right)\)	\(e\left(\frac{2009}{3420}\right)\)	\(e\left(\frac{1}{285}\right)\)	\(e\left(\frac{743}{1710}\right)\)	\(e\left(\frac{211}{3420}\right)\)	\(e\left(\frac{521}{1710}\right)\)	\(e\left(\frac{326}{855}\right)\)	\(e\left(\frac{493}{684}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{299}{1710}\right)\)
\(\chi_{254144}(49,\cdot)\)	254144.pd	1140	no	\(1\)	\(1\)	\(e\left(\frac{1003}{1140}\right)\)	\(e\left(\frac{409}{1140}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{433}{570}\right)\)	\(e\left(\frac{851}{1140}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{241}{285}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{409}{570}\right)\)
\(\chi_{254144}(51,\cdot)\)	254144.sk	13680	yes	\(-1\)	\(1\)	\(e\left(\frac{3563}{13680}\right)\)	\(e\left(\frac{4649}{13680}\right)\)	\(e\left(\frac{1967}{2280}\right)\)	\(e\left(\frac{3563}{6840}\right)\)	\(e\left(\frac{12151}{13680}\right)\)	\(e\left(\frac{2053}{3420}\right)\)	\(e\left(\frac{2561}{3420}\right)\)	\(e\left(\frac{337}{2736}\right)\)	\(e\left(\frac{607}{1368}\right)\)	\(e\left(\frac{4649}{6840}\right)\)
\(\chi_{254144}(53,\cdot)\)	254144.sf	13680	yes	\(-1\)	\(1\)	\(e\left(\frac{6449}{13680}\right)\)	\(e\left(\frac{227}{13680}\right)\)	\(e\left(\frac{1661}{2280}\right)\)	\(e\left(\frac{6449}{6840}\right)\)	\(e\left(\frac{1813}{13680}\right)\)	\(e\left(\frac{1669}{3420}\right)\)	\(e\left(\frac{3413}{3420}\right)\)	\(e\left(\frac{547}{2736}\right)\)	\(e\left(\frac{1105}{1368}\right)\)	\(e\left(\frac{227}{6840}\right)\)
\(\chi_{254144}(59,\cdot)\)	254144.si	13680	yes	\(1\)	\(1\)	\(e\left(\frac{11653}{13680}\right)\)	\(e\left(\frac{8839}{13680}\right)\)	\(e\left(\frac{2077}{2280}\right)\)	\(e\left(\frac{4813}{6840}\right)\)	\(e\left(\frac{3521}{13680}\right)\)	\(e\left(\frac{1703}{3420}\right)\)	\(e\left(\frac{541}{3420}\right)\)	\(e\left(\frac{2087}{2736}\right)\)	\(e\left(\frac{881}{1368}\right)\)	\(e\left(\frac{1999}{6840}\right)\)
\(\chi_{254144}(61,\cdot)\)	254144.sj	13680	yes	\(-1\)	\(1\)	\(e\left(\frac{2111}{13680}\right)\)	\(e\left(\frac{2693}{13680}\right)\)	\(e\left(\frac{1199}{2280}\right)\)	\(e\left(\frac{2111}{6840}\right)\)	\(e\left(\frac{2947}{13680}\right)\)	\(e\left(\frac{1201}{3420}\right)\)	\(e\left(\frac{497}{3420}\right)\)	\(e\left(\frac{1861}{2736}\right)\)	\(e\left(\frac{1231}{1368}\right)\)	\(e\left(\frac{2693}{6840}\right)\)
\(\chi_{254144}(63,\cdot)\)	254144.qh	1710	no	\(1\)	\(1\)	\(e\left(\frac{1459}{1710}\right)\)	\(e\left(\frac{461}{855}\right)\)	\(e\left(\frac{91}{285}\right)\)	\(e\left(\frac{604}{855}\right)\)	\(e\left(\frac{53}{1710}\right)\)	\(e\left(\frac{671}{1710}\right)\)	\(e\left(\frac{907}{1710}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{67}{855}\right)\)
\(\chi_{254144}(65,\cdot)\)	254144.iq	114	no	\(1\)	\(1\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)
\(\chi_{254144}(67,\cdot)\)	254144.qz	2736	no	\(1\)	\(1\)	\(e\left(\frac{1075}{2736}\right)\)	\(e\left(\frac{1825}{2736}\right)\)	\(e\left(\frac{163}{456}\right)\)	\(e\left(\frac{1075}{1368}\right)\)	\(e\left(\frac{1607}{2736}\right)\)	\(e\left(\frac{41}{684}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{2053}{2736}\right)\)	\(e\left(\frac{1315}{1368}\right)\)	\(e\left(\frac{457}{1368}\right)\)
\(\chi_{254144}(69,\cdot)\)	254144.lg	240	no	\(-1\)	\(1\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{120}\right)\)
\(\chi_{254144}(71,\cdot)\)	254144.rx	6840	no	\(1\)	\(1\)	\(e\left(\frac{4673}{6840}\right)\)	\(e\left(\frac{5579}{6840}\right)\)	\(e\left(\frac{227}{1140}\right)\)	\(e\left(\frac{1253}{3420}\right)\)	\(e\left(\frac{5281}{6840}\right)\)	\(e\left(\frac{853}{1710}\right)\)	\(e\left(\frac{521}{1710}\right)\)	\(e\left(\frac{1207}{1368}\right)\)	\(e\left(\frac{667}{684}\right)\)	\(e\left(\frac{2159}{3420}\right)\)
\(\chi_{254144}(73,\cdot)\)	254144.rw	6840	no	\(-1\)	\(1\)	\(e\left(\frac{1679}{6840}\right)\)	\(e\left(\frac{1037}{6840}\right)\)	\(e\left(\frac{881}{1140}\right)\)	\(e\left(\frac{1679}{3420}\right)\)	\(e\left(\frac{463}{6840}\right)\)	\(e\left(\frac{679}{1710}\right)\)	\(e\left(\frac{694}{855}\right)\)	\(e\left(\frac{25}{1368}\right)\)	\(e\left(\frac{43}{684}\right)\)	\(e\left(\frac{1037}{3420}\right)\)

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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.