LMFDB - Group of Dirichlet characters of modulus 508288

sage:H = DirichletGroup(508288)

pari:g = idealstar(,508288,2)

Character group

sage:G.order() pari:g.no
Order	=	218880
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{27360}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{508288}(166783,\cdot)$, $\chi_{508288}(174725,\cdot)$, $\chi_{508288}(323457,\cdot)$, $\chi_{508288}(14081,\cdot)$

First 32 of 218880 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{508288}(1,\cdot)$	508288.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{508288}(3,\cdot)$	508288.wc	27360	yes	$1$	$1$	$e\left(\frac{18479}{27360}\right)$	$e\left(\frac{16037}{27360}\right)$	$e\left(\frac{11}{4560}\right)$	$e\left(\frac{4799}{13680}\right)$	$e\left(\frac{25243}{27360}\right)$	$e\left(\frac{1789}{6840}\right)$	$e\left(\frac{4643}{6840}\right)$	$e\left(\frac{3709}{5472}\right)$	$e\left(\frac{415}{2736}\right)$	$e\left(\frac{2357}{13680}\right)$
$\chi_{508288}(5,\cdot)$	508288.vx	27360	yes	$1$	$1$	$e\left(\frac{16037}{27360}\right)$	$e\left(\frac{311}{27360}\right)$	$e\left(\frac{3953}{4560}\right)$	$e\left(\frac{2357}{13680}\right)$	$e\left(\frac{1369}{27360}\right)$	$e\left(\frac{4087}{6840}\right)$	$e\left(\frac{5369}{6840}\right)$	$e\left(\frac{2479}{5472}\right)$	$e\left(\frac{1309}{2736}\right)$	$e\left(\frac{311}{13680}\right)$
$\chi_{508288}(7,\cdot)$	508288.un	4560	no	$1$	$1$	$e\left(\frac{11}{4560}\right)$	$e\left(\frac{3953}{4560}\right)$	$e\left(\frac{239}{760}\right)$	$e\left(\frac{11}{2280}\right)$	$e\left(\frac{3127}{4560}\right)$	$e\left(\frac{991}{1140}\right)$	$e\left(\frac{197}{1140}\right)$	$e\left(\frac{289}{912}\right)$	$e\left(\frac{415}{456}\right)$	$e\left(\frac{1673}{2280}\right)$
$\chi_{508288}(9,\cdot)$	508288.vv	13680	no	$1$	$1$	$e\left(\frac{4799}{13680}\right)$	$e\left(\frac{2357}{13680}\right)$	$e\left(\frac{11}{2280}\right)$	$e\left(\frac{4799}{6840}\right)$	$e\left(\frac{11563}{13680}\right)$	$e\left(\frac{1789}{3420}\right)$	$e\left(\frac{1223}{3420}\right)$	$e\left(\frac{973}{2736}\right)$	$e\left(\frac{415}{1368}\right)$	$e\left(\frac{2357}{6840}\right)$
$\chi_{508288}(13,\cdot)$	508288.vw	27360	yes	$1$	$1$	$e\left(\frac{25243}{27360}\right)$	$e\left(\frac{1369}{27360}\right)$	$e\left(\frac{3127}{4560}\right)$	$e\left(\frac{11563}{13680}\right)$	$e\left(\frac{17111}{27360}\right)$	$e\left(\frac{6653}{6840}\right)$	$e\left(\frac{2971}{6840}\right)$	$e\left(\frac{3329}{5472}\right)$	$e\left(\frac{35}{2736}\right)$	$e\left(\frac{1369}{13680}\right)$
$\chi_{508288}(15,\cdot)$	508288.uz	6840	no	$1$	$1$	$e\left(\frac{1789}{6840}\right)$	$e\left(\frac{4087}{6840}\right)$	$e\left(\frac{991}{1140}\right)$	$e\left(\frac{1789}{3420}\right)$	$e\left(\frac{6653}{6840}\right)$	$e\left(\frac{1469}{1710}\right)$	$e\left(\frac{793}{1710}\right)$	$e\left(\frac{179}{1368}\right)$	$e\left(\frac{431}{684}\right)$	$e\left(\frac{667}{3420}\right)$
$\chi_{508288}(17,\cdot)$	508288.uy	6840	no	$-1$	$1$	$e\left(\frac{4643}{6840}\right)$	$e\left(\frac{5369}{6840}\right)$	$e\left(\frac{197}{1140}\right)$	$e\left(\frac{1223}{3420}\right)$	$e\left(\frac{2971}{6840}\right)$	$e\left(\frac{793}{1710}\right)$	$e\left(\frac{808}{855}\right)$	$e\left(\frac{1165}{1368}\right)$	$e\left(\frac{499}{684}\right)$	$e\left(\frac{1949}{3420}\right)$
$\chi_{508288}(21,\cdot)$	508288.ut	5472	yes	$1$	$1$	$e\left(\frac{3709}{5472}\right)$	$e\left(\frac{2479}{5472}\right)$	$e\left(\frac{289}{912}\right)$	$e\left(\frac{973}{2736}\right)$	$e\left(\frac{3329}{5472}\right)$	$e\left(\frac{179}{1368}\right)$	$e\left(\frac{1165}{1368}\right)$	$e\left(\frac{5443}{5472}\right)$	$e\left(\frac{169}{2736}\right)$	$e\left(\frac{2479}{2736}\right)$
$\chi_{508288}(23,\cdot)$	508288.tr	2736	no	$-1$	$1$	$e\left(\frac{415}{2736}\right)$	$e\left(\frac{1309}{2736}\right)$	$e\left(\frac{415}{456}\right)$	$e\left(\frac{415}{1368}\right)$	$e\left(\frac{35}{2736}\right)$	$e\left(\frac{431}{684}\right)$	$e\left(\frac{499}{684}\right)$	$e\left(\frac{169}{2736}\right)$	$e\left(\frac{1303}{1368}\right)$	$e\left(\frac{1309}{1368}\right)$
$\chi_{508288}(25,\cdot)$	508288.vv	13680	no	$1$	$1$	$e\left(\frac{2357}{13680}\right)$	$e\left(\frac{311}{13680}\right)$	$e\left(\frac{1673}{2280}\right)$	$e\left(\frac{2357}{6840}\right)$	$e\left(\frac{1369}{13680}\right)$	$e\left(\frac{667}{3420}\right)$	$e\left(\frac{1949}{3420}\right)$	$e\left(\frac{2479}{2736}\right)$	$e\left(\frac{1309}{1368}\right)$	$e\left(\frac{311}{6840}\right)$
$\chi_{508288}(27,\cdot)$	508288.vh	9120	yes	$1$	$1$	$e\left(\frac{239}{9120}\right)$	$e\left(\frac{6917}{9120}\right)$	$e\left(\frac{11}{1520}\right)$	$e\left(\frac{239}{4560}\right)$	$e\left(\frac{7003}{9120}\right)$	$e\left(\frac{1789}{2280}\right)$	$e\left(\frac{83}{2280}\right)$	$e\left(\frac{61}{1824}\right)$	$e\left(\frac{415}{912}\right)$	$e\left(\frac{2357}{4560}\right)$
$\chi_{508288}(29,\cdot)$	508288.vw	27360	yes	$1$	$1$	$e\left(\frac{1111}{27360}\right)$	$e\left(\frac{4813}{27360}\right)$	$e\left(\frac{3619}{4560}\right)$	$e\left(\frac{1111}{13680}\right)$	$e\left(\frac{19427}{27360}\right)$	$e\left(\frac{1481}{6840}\right)$	$e\left(\frac{1087}{6840}\right)$	$e\left(\frac{4565}{5472}\right)$	$e\left(\frac{191}{2736}\right)$	$e\left(\frac{4813}{13680}\right)$
$\chi_{508288}(31,\cdot)$	508288.rd	1140	no	$1$	$1$	$e\left(\frac{227}{1140}\right)$	$e\left(\frac{221}{1140}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{227}{570}\right)$	$e\left(\frac{949}{1140}\right)$	$e\left(\frac{112}{285}\right)$	$e\left(\frac{179}{285}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{221}{570}\right)$
$\chi_{508288}(35,\cdot)$	508288.wd	27360	yes	$1$	$1$	$e\left(\frac{16103}{27360}\right)$	$e\left(\frac{24029}{27360}\right)$	$e\left(\frac{827}{4560}\right)$	$e\left(\frac{2423}{13680}\right)$	$e\left(\frac{20131}{27360}\right)$	$e\left(\frac{3193}{6840}\right)$	$e\left(\frac{6551}{6840}\right)$	$e\left(\frac{4213}{5472}\right)$	$e\left(\frac{1063}{2736}\right)$	$e\left(\frac{10349}{13680}\right)$
$\chi_{508288}(37,\cdot)$	508288.tt	3040	yes	$-1$	$1$	$e\left(\frac{709}{3040}\right)$	$e\left(\frac{327}{3040}\right)$	$e\left(\frac{1443}{1520}\right)$	$e\left(\frac{709}{1520}\right)$	$e\left(\frac{633}{3040}\right)$	$e\left(\frac{259}{760}\right)$	$e\left(\frac{313}{760}\right)$	$e\left(\frac{111}{608}\right)$	$e\left(\frac{45}{304}\right)$	$e\left(\frac{327}{1520}\right)$
$\chi_{508288}(39,\cdot)$	508288.sd	1520	no	$1$	$1$	$e\left(\frac{909}{1520}\right)$	$e\left(\frac{967}{1520}\right)$	$e\left(\frac{523}{760}\right)$	$e\left(\frac{149}{760}\right)$	$e\left(\frac{833}{1520}\right)$	$e\left(\frac{89}{380}\right)$	$e\left(\frac{43}{380}\right)$	$e\left(\frac{87}{304}\right)$	$e\left(\frac{25}{152}\right)$	$e\left(\frac{207}{760}\right)$
$\chi_{508288}(41,\cdot)$	508288.vr	13680	no	$1$	$1$	$e\left(\frac{6067}{13680}\right)$	$e\left(\frac{8041}{13680}\right)$	$e\left(\frac{1963}{2280}\right)$	$e\left(\frac{6067}{6840}\right)$	$e\left(\frac{11159}{13680}\right)$	$e\left(\frac{107}{3420}\right)$	$e\left(\frac{769}{3420}\right)$	$e\left(\frac{833}{2736}\right)$	$e\left(\frac{995}{1368}\right)$	$e\left(\frac{1201}{6840}\right)$
$\chi_{508288}(43,\cdot)$	508288.uu	5472	yes	$1$	$1$	$e\left(\frac{1933}{5472}\right)$	$e\left(\frac{991}{5472}\right)$	$e\left(\frac{793}{912}\right)$	$e\left(\frac{1933}{2736}\right)$	$e\left(\frac{641}{5472}\right)$	$e\left(\frac{731}{1368}\right)$	$e\left(\frac{325}{1368}\right)$	$e\left(\frac{1219}{5472}\right)$	$e\left(\frac{1057}{2736}\right)$	$e\left(\frac{991}{2736}\right)$
$\chi_{508288}(45,\cdot)$	508288.sw	1824	no	$1$	$1$	$e\left(\frac{1709}{1824}\right)$	$e\left(\frac{335}{1824}\right)$	$e\left(\frac{265}{304}\right)$	$e\left(\frac{797}{912}\right)$	$e\left(\frac{1633}{1824}\right)$	$e\left(\frac{55}{456}\right)$	$e\left(\frac{65}{456}\right)$	$e\left(\frac{1475}{1824}\right)$	$e\left(\frac{713}{912}\right)$	$e\left(\frac{335}{912}\right)$
$\chi_{508288}(47,\cdot)$	508288.ve	6840	no	$-1$	$1$	$e\left(\frac{4051}{6840}\right)$	$e\left(\frac{1453}{6840}\right)$	$e\left(\frac{289}{1140}\right)$	$e\left(\frac{631}{3420}\right)$	$e\left(\frac{2987}{6840}\right)$	$e\left(\frac{688}{855}\right)$	$e\left(\frac{1507}{1710}\right)$	$e\left(\frac{1157}{1368}\right)$	$e\left(\frac{581}{684}\right)$	$e\left(\frac{1453}{3420}\right)$
$\chi_{508288}(49,\cdot)$	508288.tj	2280	no	$1$	$1$	$e\left(\frac{11}{2280}\right)$	$e\left(\frac{1673}{2280}\right)$	$e\left(\frac{239}{380}\right)$	$e\left(\frac{11}{1140}\right)$	$e\left(\frac{847}{2280}\right)$	$e\left(\frac{421}{570}\right)$	$e\left(\frac{197}{570}\right)$	$e\left(\frac{289}{456}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{533}{1140}\right)$
$\chi_{508288}(51,\cdot)$	508288.vy	27360	yes	$-1$	$1$	$e\left(\frac{9691}{27360}\right)$	$e\left(\frac{10153}{27360}\right)$	$e\left(\frac{799}{4560}\right)$	$e\left(\frac{9691}{13680}\right)$	$e\left(\frac{9767}{27360}\right)$	$e\left(\frac{4961}{6840}\right)$	$e\left(\frac{4267}{6840}\right)$	$e\left(\frac{2897}{5472}\right)$	$e\left(\frac{2411}{2736}\right)$	$e\left(\frac{10153}{13680}\right)$
$\chi_{508288}(53,\cdot)$	508288.wa	27360	yes	$-1$	$1$	$e\left(\frac{73}{27360}\right)$	$e\left(\frac{23539}{27360}\right)$	$e\left(\frac{757}{4560}\right)$	$e\left(\frac{73}{13680}\right)$	$e\left(\frac{21581}{27360}\right)$	$e\left(\frac{5903}{6840}\right)$	$e\left(\frac{4261}{6840}\right)$	$e\left(\frac{923}{5472}\right)$	$e\left(\frac{1697}{2736}\right)$	$e\left(\frac{9859}{13680}\right)$
$\chi_{508288}(59,\cdot)$	508288.wc	27360	yes	$1$	$1$	$e\left(\frac{7061}{27360}\right)$	$e\left(\frac{3143}{27360}\right)$	$e\left(\frac{2729}{4560}\right)$	$e\left(\frac{7061}{13680}\right)$	$e\left(\frac{7897}{27360}\right)$	$e\left(\frac{2551}{6840}\right)$	$e\left(\frac{1937}{6840}\right)$	$e\left(\frac{4687}{5472}\right)$	$e\left(\frac{565}{2736}\right)$	$e\left(\frac{3143}{13680}\right)$
$\chi_{508288}(61,\cdot)$	508288.wb	27360	yes	$-1$	$1$	$e\left(\frac{10207}{27360}\right)$	$e\left(\frac{16501}{27360}\right)$	$e\left(\frac{2683}{4560}\right)$	$e\left(\frac{10207}{13680}\right)$	$e\left(\frac{8459}{27360}\right)$	$e\left(\frac{6677}{6840}\right)$	$e\left(\frac{3559}{6840}\right)$	$e\left(\frac{5261}{5472}\right)$	$e\left(\frac{1607}{2736}\right)$	$e\left(\frac{2821}{13680}\right)$
$\chi_{508288}(63,\cdot)$	508288.sg	1710	no	$1$	$1$	$e\left(\frac{302}{855}\right)$	$e\left(\frac{67}{1710}\right)$	$e\left(\frac{91}{285}\right)$	$e\left(\frac{604}{855}\right)$	$e\left(\frac{454}{855}\right)$	$e\left(\frac{671}{1710}\right)$	$e\left(\frac{907}{1710}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{67}{855}\right)$
$\chi_{508288}(65,\cdot)$	508288.jk	114	no	$1$	$1$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{7}{57}\right)$
$\chi_{508288}(67,\cdot)$	508288.uv	5472	no	$1$	$1$	$e\left(\frac{3347}{5472}\right)$	$e\left(\frac{401}{5472}\right)$	$e\left(\frac{383}{912}\right)$	$e\left(\frac{611}{2736}\right)$	$e\left(\frac{3727}{5472}\right)$	$e\left(\frac{937}{1368}\right)$	$e\left(\frac{527}{1368}\right)$	$e\left(\frac{173}{5472}\right)$	$e\left(\frac{1775}{2736}\right)$	$e\left(\frac{401}{2736}\right)$
$\chi_{508288}(69,\cdot)$	508288.op	480	no	$-1$	$1$	$e\left(\frac{397}{480}\right)$	$e\left(\frac{31}{480}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{449}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{240}\right)$
$\chi_{508288}(71,\cdot)$	508288.vs	13680	no	$1$	$1$	$e\left(\frac{3361}{13680}\right)$	$e\left(\frac{43}{13680}\right)$	$e\left(\frac{169}{2280}\right)$	$e\left(\frac{3361}{6840}\right)$	$e\left(\frac{7997}{13680}\right)$	$e\left(\frac{851}{3420}\right)$	$e\left(\frac{1897}{3420}\right)$	$e\left(\frac{875}{2736}\right)$	$e\left(\frac{821}{1368}\right)$	$e\left(\frac{43}{6840}\right)$
$\chi_{508288}(73,\cdot)$	508288.vt	13680	no	$-1$	$1$	$e\left(\frac{2503}{13680}\right)$	$e\left(\frac{6349}{13680}\right)$	$e\left(\frac{2047}{2280}\right)$	$e\left(\frac{2503}{6840}\right)$	$e\left(\frac{10331}{13680}\right)$	$e\left(\frac{2213}{3420}\right)$	$e\left(\frac{1921}{3420}\right)$	$e\left(\frac{221}{2736}\right)$	$e\left(\frac{599}{1368}\right)$	$e\left(\frac{6349}{6840}\right)$

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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	$508288$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{27360}\)
Order	$218880$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{508288}(1,\cdot)\)	508288.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{508288}(3,\cdot)\)	508288.wc	27360	yes	\(1\)	\(1\)	\(e\left(\frac{18479}{27360}\right)\)	\(e\left(\frac{16037}{27360}\right)\)	\(e\left(\frac{11}{4560}\right)\)	\(e\left(\frac{4799}{13680}\right)\)	\(e\left(\frac{25243}{27360}\right)\)	\(e\left(\frac{1789}{6840}\right)\)	\(e\left(\frac{4643}{6840}\right)\)	\(e\left(\frac{3709}{5472}\right)\)	\(e\left(\frac{415}{2736}\right)\)	\(e\left(\frac{2357}{13680}\right)\)
\(\chi_{508288}(5,\cdot)\)	508288.vx	27360	yes	\(1\)	\(1\)	\(e\left(\frac{16037}{27360}\right)\)	\(e\left(\frac{311}{27360}\right)\)	\(e\left(\frac{3953}{4560}\right)\)	\(e\left(\frac{2357}{13680}\right)\)	\(e\left(\frac{1369}{27360}\right)\)	\(e\left(\frac{4087}{6840}\right)\)	\(e\left(\frac{5369}{6840}\right)\)	\(e\left(\frac{2479}{5472}\right)\)	\(e\left(\frac{1309}{2736}\right)\)	\(e\left(\frac{311}{13680}\right)\)
\(\chi_{508288}(7,\cdot)\)	508288.un	4560	no	\(1\)	\(1\)	\(e\left(\frac{11}{4560}\right)\)	\(e\left(\frac{3953}{4560}\right)\)	\(e\left(\frac{239}{760}\right)\)	\(e\left(\frac{11}{2280}\right)\)	\(e\left(\frac{3127}{4560}\right)\)	\(e\left(\frac{991}{1140}\right)\)	\(e\left(\frac{197}{1140}\right)\)	\(e\left(\frac{289}{912}\right)\)	\(e\left(\frac{415}{456}\right)\)	\(e\left(\frac{1673}{2280}\right)\)
\(\chi_{508288}(9,\cdot)\)	508288.vv	13680	no	\(1\)	\(1\)	\(e\left(\frac{4799}{13680}\right)\)	\(e\left(\frac{2357}{13680}\right)\)	\(e\left(\frac{11}{2280}\right)\)	\(e\left(\frac{4799}{6840}\right)\)	\(e\left(\frac{11563}{13680}\right)\)	\(e\left(\frac{1789}{3420}\right)\)	\(e\left(\frac{1223}{3420}\right)\)	\(e\left(\frac{973}{2736}\right)\)	\(e\left(\frac{415}{1368}\right)\)	\(e\left(\frac{2357}{6840}\right)\)
\(\chi_{508288}(13,\cdot)\)	508288.vw	27360	yes	\(1\)	\(1\)	\(e\left(\frac{25243}{27360}\right)\)	\(e\left(\frac{1369}{27360}\right)\)	\(e\left(\frac{3127}{4560}\right)\)	\(e\left(\frac{11563}{13680}\right)\)	\(e\left(\frac{17111}{27360}\right)\)	\(e\left(\frac{6653}{6840}\right)\)	\(e\left(\frac{2971}{6840}\right)\)	\(e\left(\frac{3329}{5472}\right)\)	\(e\left(\frac{35}{2736}\right)\)	\(e\left(\frac{1369}{13680}\right)\)
\(\chi_{508288}(15,\cdot)\)	508288.uz	6840	no	\(1\)	\(1\)	\(e\left(\frac{1789}{6840}\right)\)	\(e\left(\frac{4087}{6840}\right)\)	\(e\left(\frac{991}{1140}\right)\)	\(e\left(\frac{1789}{3420}\right)\)	\(e\left(\frac{6653}{6840}\right)\)	\(e\left(\frac{1469}{1710}\right)\)	\(e\left(\frac{793}{1710}\right)\)	\(e\left(\frac{179}{1368}\right)\)	\(e\left(\frac{431}{684}\right)\)	\(e\left(\frac{667}{3420}\right)\)
\(\chi_{508288}(17,\cdot)\)	508288.uy	6840	no	\(-1\)	\(1\)	\(e\left(\frac{4643}{6840}\right)\)	\(e\left(\frac{5369}{6840}\right)\)	\(e\left(\frac{197}{1140}\right)\)	\(e\left(\frac{1223}{3420}\right)\)	\(e\left(\frac{2971}{6840}\right)\)	\(e\left(\frac{793}{1710}\right)\)	\(e\left(\frac{808}{855}\right)\)	\(e\left(\frac{1165}{1368}\right)\)	\(e\left(\frac{499}{684}\right)\)	\(e\left(\frac{1949}{3420}\right)\)
\(\chi_{508288}(21,\cdot)\)	508288.ut	5472	yes	\(1\)	\(1\)	\(e\left(\frac{3709}{5472}\right)\)	\(e\left(\frac{2479}{5472}\right)\)	\(e\left(\frac{289}{912}\right)\)	\(e\left(\frac{973}{2736}\right)\)	\(e\left(\frac{3329}{5472}\right)\)	\(e\left(\frac{179}{1368}\right)\)	\(e\left(\frac{1165}{1368}\right)\)	\(e\left(\frac{5443}{5472}\right)\)	\(e\left(\frac{169}{2736}\right)\)	\(e\left(\frac{2479}{2736}\right)\)
\(\chi_{508288}(23,\cdot)\)	508288.tr	2736	no	\(-1\)	\(1\)	\(e\left(\frac{415}{2736}\right)\)	\(e\left(\frac{1309}{2736}\right)\)	\(e\left(\frac{415}{456}\right)\)	\(e\left(\frac{415}{1368}\right)\)	\(e\left(\frac{35}{2736}\right)\)	\(e\left(\frac{431}{684}\right)\)	\(e\left(\frac{499}{684}\right)\)	\(e\left(\frac{169}{2736}\right)\)	\(e\left(\frac{1303}{1368}\right)\)	\(e\left(\frac{1309}{1368}\right)\)
\(\chi_{508288}(25,\cdot)\)	508288.vv	13680	no	\(1\)	\(1\)	\(e\left(\frac{2357}{13680}\right)\)	\(e\left(\frac{311}{13680}\right)\)	\(e\left(\frac{1673}{2280}\right)\)	\(e\left(\frac{2357}{6840}\right)\)	\(e\left(\frac{1369}{13680}\right)\)	\(e\left(\frac{667}{3420}\right)\)	\(e\left(\frac{1949}{3420}\right)\)	\(e\left(\frac{2479}{2736}\right)\)	\(e\left(\frac{1309}{1368}\right)\)	\(e\left(\frac{311}{6840}\right)\)
\(\chi_{508288}(27,\cdot)\)	508288.vh	9120	yes	\(1\)	\(1\)	\(e\left(\frac{239}{9120}\right)\)	\(e\left(\frac{6917}{9120}\right)\)	\(e\left(\frac{11}{1520}\right)\)	\(e\left(\frac{239}{4560}\right)\)	\(e\left(\frac{7003}{9120}\right)\)	\(e\left(\frac{1789}{2280}\right)\)	\(e\left(\frac{83}{2280}\right)\)	\(e\left(\frac{61}{1824}\right)\)	\(e\left(\frac{415}{912}\right)\)	\(e\left(\frac{2357}{4560}\right)\)
\(\chi_{508288}(29,\cdot)\)	508288.vw	27360	yes	\(1\)	\(1\)	\(e\left(\frac{1111}{27360}\right)\)	\(e\left(\frac{4813}{27360}\right)\)	\(e\left(\frac{3619}{4560}\right)\)	\(e\left(\frac{1111}{13680}\right)\)	\(e\left(\frac{19427}{27360}\right)\)	\(e\left(\frac{1481}{6840}\right)\)	\(e\left(\frac{1087}{6840}\right)\)	\(e\left(\frac{4565}{5472}\right)\)	\(e\left(\frac{191}{2736}\right)\)	\(e\left(\frac{4813}{13680}\right)\)
\(\chi_{508288}(31,\cdot)\)	508288.rd	1140	no	\(1\)	\(1\)	\(e\left(\frac{227}{1140}\right)\)	\(e\left(\frac{221}{1140}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{227}{570}\right)\)	\(e\left(\frac{949}{1140}\right)\)	\(e\left(\frac{112}{285}\right)\)	\(e\left(\frac{179}{285}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{221}{570}\right)\)
\(\chi_{508288}(35,\cdot)\)	508288.wd	27360	yes	\(1\)	\(1\)	\(e\left(\frac{16103}{27360}\right)\)	\(e\left(\frac{24029}{27360}\right)\)	\(e\left(\frac{827}{4560}\right)\)	\(e\left(\frac{2423}{13680}\right)\)	\(e\left(\frac{20131}{27360}\right)\)	\(e\left(\frac{3193}{6840}\right)\)	\(e\left(\frac{6551}{6840}\right)\)	\(e\left(\frac{4213}{5472}\right)\)	\(e\left(\frac{1063}{2736}\right)\)	\(e\left(\frac{10349}{13680}\right)\)
\(\chi_{508288}(37,\cdot)\)	508288.tt	3040	yes	\(-1\)	\(1\)	\(e\left(\frac{709}{3040}\right)\)	\(e\left(\frac{327}{3040}\right)\)	\(e\left(\frac{1443}{1520}\right)\)	\(e\left(\frac{709}{1520}\right)\)	\(e\left(\frac{633}{3040}\right)\)	\(e\left(\frac{259}{760}\right)\)	\(e\left(\frac{313}{760}\right)\)	\(e\left(\frac{111}{608}\right)\)	\(e\left(\frac{45}{304}\right)\)	\(e\left(\frac{327}{1520}\right)\)
\(\chi_{508288}(39,\cdot)\)	508288.sd	1520	no	\(1\)	\(1\)	\(e\left(\frac{909}{1520}\right)\)	\(e\left(\frac{967}{1520}\right)\)	\(e\left(\frac{523}{760}\right)\)	\(e\left(\frac{149}{760}\right)\)	\(e\left(\frac{833}{1520}\right)\)	\(e\left(\frac{89}{380}\right)\)	\(e\left(\frac{43}{380}\right)\)	\(e\left(\frac{87}{304}\right)\)	\(e\left(\frac{25}{152}\right)\)	\(e\left(\frac{207}{760}\right)\)
\(\chi_{508288}(41,\cdot)\)	508288.vr	13680	no	\(1\)	\(1\)	\(e\left(\frac{6067}{13680}\right)\)	\(e\left(\frac{8041}{13680}\right)\)	\(e\left(\frac{1963}{2280}\right)\)	\(e\left(\frac{6067}{6840}\right)\)	\(e\left(\frac{11159}{13680}\right)\)	\(e\left(\frac{107}{3420}\right)\)	\(e\left(\frac{769}{3420}\right)\)	\(e\left(\frac{833}{2736}\right)\)	\(e\left(\frac{995}{1368}\right)\)	\(e\left(\frac{1201}{6840}\right)\)
\(\chi_{508288}(43,\cdot)\)	508288.uu	5472	yes	\(1\)	\(1\)	\(e\left(\frac{1933}{5472}\right)\)	\(e\left(\frac{991}{5472}\right)\)	\(e\left(\frac{793}{912}\right)\)	\(e\left(\frac{1933}{2736}\right)\)	\(e\left(\frac{641}{5472}\right)\)	\(e\left(\frac{731}{1368}\right)\)	\(e\left(\frac{325}{1368}\right)\)	\(e\left(\frac{1219}{5472}\right)\)	\(e\left(\frac{1057}{2736}\right)\)	\(e\left(\frac{991}{2736}\right)\)
\(\chi_{508288}(45,\cdot)\)	508288.sw	1824	no	\(1\)	\(1\)	\(e\left(\frac{1709}{1824}\right)\)	\(e\left(\frac{335}{1824}\right)\)	\(e\left(\frac{265}{304}\right)\)	\(e\left(\frac{797}{912}\right)\)	\(e\left(\frac{1633}{1824}\right)\)	\(e\left(\frac{55}{456}\right)\)	\(e\left(\frac{65}{456}\right)\)	\(e\left(\frac{1475}{1824}\right)\)	\(e\left(\frac{713}{912}\right)\)	\(e\left(\frac{335}{912}\right)\)
\(\chi_{508288}(47,\cdot)\)	508288.ve	6840	no	\(-1\)	\(1\)	\(e\left(\frac{4051}{6840}\right)\)	\(e\left(\frac{1453}{6840}\right)\)	\(e\left(\frac{289}{1140}\right)\)	\(e\left(\frac{631}{3420}\right)\)	\(e\left(\frac{2987}{6840}\right)\)	\(e\left(\frac{688}{855}\right)\)	\(e\left(\frac{1507}{1710}\right)\)	\(e\left(\frac{1157}{1368}\right)\)	\(e\left(\frac{581}{684}\right)\)	\(e\left(\frac{1453}{3420}\right)\)
\(\chi_{508288}(49,\cdot)\)	508288.tj	2280	no	\(1\)	\(1\)	\(e\left(\frac{11}{2280}\right)\)	\(e\left(\frac{1673}{2280}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{11}{1140}\right)\)	\(e\left(\frac{847}{2280}\right)\)	\(e\left(\frac{421}{570}\right)\)	\(e\left(\frac{197}{570}\right)\)	\(e\left(\frac{289}{456}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{533}{1140}\right)\)
\(\chi_{508288}(51,\cdot)\)	508288.vy	27360	yes	\(-1\)	\(1\)	\(e\left(\frac{9691}{27360}\right)\)	\(e\left(\frac{10153}{27360}\right)\)	\(e\left(\frac{799}{4560}\right)\)	\(e\left(\frac{9691}{13680}\right)\)	\(e\left(\frac{9767}{27360}\right)\)	\(e\left(\frac{4961}{6840}\right)\)	\(e\left(\frac{4267}{6840}\right)\)	\(e\left(\frac{2897}{5472}\right)\)	\(e\left(\frac{2411}{2736}\right)\)	\(e\left(\frac{10153}{13680}\right)\)
\(\chi_{508288}(53,\cdot)\)	508288.wa	27360	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{27360}\right)\)	\(e\left(\frac{23539}{27360}\right)\)	\(e\left(\frac{757}{4560}\right)\)	\(e\left(\frac{73}{13680}\right)\)	\(e\left(\frac{21581}{27360}\right)\)	\(e\left(\frac{5903}{6840}\right)\)	\(e\left(\frac{4261}{6840}\right)\)	\(e\left(\frac{923}{5472}\right)\)	\(e\left(\frac{1697}{2736}\right)\)	\(e\left(\frac{9859}{13680}\right)\)
\(\chi_{508288}(59,\cdot)\)	508288.wc	27360	yes	\(1\)	\(1\)	\(e\left(\frac{7061}{27360}\right)\)	\(e\left(\frac{3143}{27360}\right)\)	\(e\left(\frac{2729}{4560}\right)\)	\(e\left(\frac{7061}{13680}\right)\)	\(e\left(\frac{7897}{27360}\right)\)	\(e\left(\frac{2551}{6840}\right)\)	\(e\left(\frac{1937}{6840}\right)\)	\(e\left(\frac{4687}{5472}\right)\)	\(e\left(\frac{565}{2736}\right)\)	\(e\left(\frac{3143}{13680}\right)\)
\(\chi_{508288}(61,\cdot)\)	508288.wb	27360	yes	\(-1\)	\(1\)	\(e\left(\frac{10207}{27360}\right)\)	\(e\left(\frac{16501}{27360}\right)\)	\(e\left(\frac{2683}{4560}\right)\)	\(e\left(\frac{10207}{13680}\right)\)	\(e\left(\frac{8459}{27360}\right)\)	\(e\left(\frac{6677}{6840}\right)\)	\(e\left(\frac{3559}{6840}\right)\)	\(e\left(\frac{5261}{5472}\right)\)	\(e\left(\frac{1607}{2736}\right)\)	\(e\left(\frac{2821}{13680}\right)\)
\(\chi_{508288}(63,\cdot)\)	508288.sg	1710	no	\(1\)	\(1\)	\(e\left(\frac{302}{855}\right)\)	\(e\left(\frac{67}{1710}\right)\)	\(e\left(\frac{91}{285}\right)\)	\(e\left(\frac{604}{855}\right)\)	\(e\left(\frac{454}{855}\right)\)	\(e\left(\frac{671}{1710}\right)\)	\(e\left(\frac{907}{1710}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{67}{855}\right)\)
\(\chi_{508288}(65,\cdot)\)	508288.jk	114	no	\(1\)	\(1\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)
\(\chi_{508288}(67,\cdot)\)	508288.uv	5472	no	\(1\)	\(1\)	\(e\left(\frac{3347}{5472}\right)\)	\(e\left(\frac{401}{5472}\right)\)	\(e\left(\frac{383}{912}\right)\)	\(e\left(\frac{611}{2736}\right)\)	\(e\left(\frac{3727}{5472}\right)\)	\(e\left(\frac{937}{1368}\right)\)	\(e\left(\frac{527}{1368}\right)\)	\(e\left(\frac{173}{5472}\right)\)	\(e\left(\frac{1775}{2736}\right)\)	\(e\left(\frac{401}{2736}\right)\)
\(\chi_{508288}(69,\cdot)\)	508288.op	480	no	\(-1\)	\(1\)	\(e\left(\frac{397}{480}\right)\)	\(e\left(\frac{31}{480}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{449}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{240}\right)\)
\(\chi_{508288}(71,\cdot)\)	508288.vs	13680	no	\(1\)	\(1\)	\(e\left(\frac{3361}{13680}\right)\)	\(e\left(\frac{43}{13680}\right)\)	\(e\left(\frac{169}{2280}\right)\)	\(e\left(\frac{3361}{6840}\right)\)	\(e\left(\frac{7997}{13680}\right)\)	\(e\left(\frac{851}{3420}\right)\)	\(e\left(\frac{1897}{3420}\right)\)	\(e\left(\frac{875}{2736}\right)\)	\(e\left(\frac{821}{1368}\right)\)	\(e\left(\frac{43}{6840}\right)\)
\(\chi_{508288}(73,\cdot)\)	508288.vt	13680	no	\(-1\)	\(1\)	\(e\left(\frac{2503}{13680}\right)\)	\(e\left(\frac{6349}{13680}\right)\)	\(e\left(\frac{2047}{2280}\right)\)	\(e\left(\frac{2503}{6840}\right)\)	\(e\left(\frac{10331}{13680}\right)\)	\(e\left(\frac{2213}{3420}\right)\)	\(e\left(\frac{1921}{3420}\right)\)	\(e\left(\frac{221}{2736}\right)\)	\(e\left(\frac{599}{1368}\right)\)	\(e\left(\frac{6349}{6840}\right)\)

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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.