LMFDB - Group of Dirichlet characters of modulus 61952

sage:H = DirichletGroup(61952)

pari:g = idealstar(,61952,2)

Character group

sage:G.order() pari:g.no
Order	=	28160
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{7040}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{61952}(13311,\cdot)$, $\chi_{61952}(35333,\cdot)$, $\chi_{61952}(6657,\cdot)$

First 32 of 28160 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{61952}(1,\cdot)$	61952.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{61952}(3,\cdot)$	61952.dx	640	no	$-1$	$1$	$e\left(\frac{301}{640}\right)$	$e\left(\frac{303}{640}\right)$	$e\left(\frac{107}{320}\right)$	$e\left(\frac{301}{320}\right)$	$e\left(\frac{97}{640}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{121}{640}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{61952}(5,\cdot)$	61952.eu	7040	yes	$1$	$1$	$e\left(\frac{303}{640}\right)$	$e\left(\frac{5559}{7040}\right)$	$e\left(\frac{1011}{3520}\right)$	$e\left(\frac{303}{320}\right)$	$e\left(\frac{5721}{7040}\right)$	$e\left(\frac{463}{1760}\right)$	$e\left(\frac{321}{1760}\right)$	$e\left(\frac{113}{7040}\right)$	$e\left(\frac{1071}{1408}\right)$	$e\left(\frac{141}{704}\right)$
$\chi_{61952}(7,\cdot)$	61952.er	3520	no	$1$	$1$	$e\left(\frac{107}{320}\right)$	$e\left(\frac{1011}{3520}\right)$	$e\left(\frac{1279}{1760}\right)$	$e\left(\frac{107}{160}\right)$	$e\left(\frac{2109}{3520}\right)$	$e\left(\frac{547}{880}\right)$	$e\left(\frac{269}{880}\right)$	$e\left(\frac{277}{3520}\right)$	$e\left(\frac{43}{704}\right)$	$e\left(\frac{17}{352}\right)$
$\chi_{61952}(9,\cdot)$	61952.dn	320	no	$1$	$1$	$e\left(\frac{301}{320}\right)$	$e\left(\frac{303}{320}\right)$	$e\left(\frac{107}{160}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{97}{320}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{121}{320}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{61952}(13,\cdot)$	61952.ew	7040	yes	$-1$	$1$	$e\left(\frac{97}{640}\right)$	$e\left(\frac{5721}{7040}\right)$	$e\left(\frac{2109}{3520}\right)$	$e\left(\frac{97}{320}\right)$	$e\left(\frac{6999}{7040}\right)$	$e\left(\frac{1697}{1760}\right)$	$e\left(\frac{479}{1760}\right)$	$e\left(\frac{1087}{7040}\right)$	$e\left(\frac{1057}{1408}\right)$	$e\left(\frac{291}{704}\right)$
$\chi_{61952}(15,\cdot)$	61952.ep	1760	no	$-1$	$1$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{463}{1760}\right)$	$e\left(\frac{547}{880}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1697}{1760}\right)$	$e\left(\frac{91}{440}\right)$	$e\left(\frac{17}{440}\right)$	$e\left(\frac{361}{1760}\right)$	$e\left(\frac{199}{352}\right)$	$e\left(\frac{93}{176}\right)$
$\chi_{61952}(17,\cdot)$	61952.eo	1760	no	$-1$	$1$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{321}{1760}\right)$	$e\left(\frac{269}{880}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{479}{1760}\right)$	$e\left(\frac{17}{440}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{7}{1760}\right)$	$e\left(\frac{57}{352}\right)$	$e\left(\frac{43}{176}\right)$
$\chi_{61952}(19,\cdot)$	61952.ev	7040	yes	$1$	$1$	$e\left(\frac{121}{640}\right)$	$e\left(\frac{113}{7040}\right)$	$e\left(\frac{277}{3520}\right)$	$e\left(\frac{121}{320}\right)$	$e\left(\frac{1087}{7040}\right)$	$e\left(\frac{361}{1760}\right)$	$e\left(\frac{7}{1760}\right)$	$e\left(\frac{1831}{7040}\right)$	$e\left(\frac{377}{1408}\right)$	$e\left(\frac{587}{704}\right)$
$\chi_{61952}(21,\cdot)$	61952.ej	1408	yes	$-1$	$1$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{1071}{1408}\right)$	$e\left(\frac{43}{704}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{1057}{1408}\right)$	$e\left(\frac{199}{352}\right)$	$e\left(\frac{57}{352}\right)$	$e\left(\frac{377}{1408}\right)$	$e\left(\frac{1219}{1408}\right)$	$e\left(\frac{265}{704}\right)$
$\chi_{61952}(23,\cdot)$	61952.eb	704	no	$-1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{141}{704}\right)$	$e\left(\frac{17}{352}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{291}{704}\right)$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{43}{176}\right)$	$e\left(\frac{587}{704}\right)$	$e\left(\frac{265}{704}\right)$	$e\left(\frac{203}{352}\right)$
$\chi_{61952}(25,\cdot)$	61952.eq	3520	no	$1$	$1$	$e\left(\frac{303}{320}\right)$	$e\left(\frac{2039}{3520}\right)$	$e\left(\frac{1011}{1760}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{2201}{3520}\right)$	$e\left(\frac{463}{880}\right)$	$e\left(\frac{321}{880}\right)$	$e\left(\frac{113}{3520}\right)$	$e\left(\frac{367}{704}\right)$	$e\left(\frac{141}{352}\right)$
$\chi_{61952}(27,\cdot)$	61952.dx	640	no	$-1$	$1$	$e\left(\frac{263}{640}\right)$	$e\left(\frac{269}{640}\right)$	$e\left(\frac{1}{320}\right)$	$e\left(\frac{263}{320}\right)$	$e\left(\frac{291}{640}\right)$	$e\left(\frac{133}{160}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{363}{640}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{63}{64}\right)$
$\chi_{61952}(29,\cdot)$	61952.ew	7040	yes	$-1$	$1$	$e\left(\frac{149}{640}\right)$	$e\left(\frac{2797}{7040}\right)$	$e\left(\frac{673}{3520}\right)$	$e\left(\frac{149}{320}\right)$	$e\left(\frac{1923}{7040}\right)$	$e\left(\frac{1109}{1760}\right)$	$e\left(\frac{843}{1760}\right)$	$e\left(\frac{6539}{7040}\right)$	$e\left(\frac{597}{1408}\right)$	$e\left(\frac{191}{704}\right)$
$\chi_{61952}(31,\cdot)$	61952.eg	880	no	$-1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{807}{880}\right)$	$e\left(\frac{263}{440}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{793}{880}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{729}{880}\right)$	$e\left(\frac{15}{176}\right)$	$e\left(\frac{9}{88}\right)$
$\chi_{61952}(35,\cdot)$	61952.ev	7040	yes	$1$	$1$	$e\left(\frac{517}{640}\right)$	$e\left(\frac{541}{7040}\right)$	$e\left(\frac{49}{3520}\right)$	$e\left(\frac{197}{320}\right)$	$e\left(\frac{2899}{7040}\right)$	$e\left(\frac{1557}{1760}\right)$	$e\left(\frac{859}{1760}\right)$	$e\left(\frac{667}{7040}\right)$	$e\left(\frac{1157}{1408}\right)$	$e\left(\frac{175}{704}\right)$
$\chi_{61952}(37,\cdot)$	61952.eu	7040	yes	$1$	$1$	$e\left(\frac{279}{640}\right)$	$e\left(\frac{3167}{7040}\right)$	$e\left(\frac{443}{3520}\right)$	$e\left(\frac{279}{320}\right)$	$e\left(\frac{1713}{7040}\right)$	$e\left(\frac{1559}{1760}\right)$	$e\left(\frac{313}{1760}\right)$	$e\left(\frac{1289}{7040}\right)$	$e\left(\frac{791}{1408}\right)$	$e\left(\frac{325}{704}\right)$
$\chi_{61952}(39,\cdot)$	61952.er	3520	no	$1$	$1$	$e\left(\frac{199}{320}\right)$	$e\left(\frac{1007}{3520}\right)$	$e\left(\frac{1643}{1760}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{513}{3520}\right)$	$e\left(\frac{799}{880}\right)$	$e\left(\frac{113}{880}\right)$	$e\left(\frac{1209}{3520}\right)$	$e\left(\frac{391}{704}\right)$	$e\left(\frac{261}{352}\right)$
$\chi_{61952}(41,\cdot)$	61952.et	3520	no	$-1$	$1$	$e\left(\frac{273}{320}\right)$	$e\left(\frac{1609}{3520}\right)$	$e\left(\frac{541}{1760}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{1351}{3520}\right)$	$e\left(\frac{273}{880}\right)$	$e\left(\frac{711}{880}\right)$	$e\left(\frac{3503}{3520}\right)$	$e\left(\frac{113}{704}\right)$	$e\left(\frac{147}{352}\right)$
$\chi_{61952}(43,\cdot)$	61952.ek	1408	yes	$1$	$1$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{415}{1408}\right)$	$e\left(\frac{251}{704}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1201}{1408}\right)$	$e\left(\frac{167}{352}\right)$	$e\left(\frac{169}{352}\right)$	$e\left(\frac{457}{1408}\right)$	$e\left(\frac{755}{1408}\right)$	$e\left(\frac{57}{704}\right)$
$\chi_{61952}(45,\cdot)$	61952.el	1408	yes	$1$	$1$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{1037}{1408}\right)$	$e\left(\frac{673}{704}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{163}{1408}\right)$	$e\left(\frac{53}{352}\right)$	$e\left(\frac{315}{352}\right)$	$e\left(\frac{555}{1408}\right)$	$e\left(\frac{521}{1408}\right)$	$e\left(\frac{603}{704}\right)$
$\chi_{61952}(47,\cdot)$	61952.ep	1760	no	$-1$	$1$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{477}{1760}\right)$	$e\left(\frac{153}{880}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{243}{1760}\right)$	$e\left(\frac{89}{440}\right)$	$e\left(\frac{123}{440}\right)$	$e\left(\frac{619}{1760}\right)$	$e\left(\frac{37}{352}\right)$	$e\left(\frac{119}{176}\right)$
$\chi_{61952}(49,\cdot)$	61952.en	1760	no	$1$	$1$	$e\left(\frac{107}{160}\right)$	$e\left(\frac{1011}{1760}\right)$	$e\left(\frac{399}{880}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{349}{1760}\right)$	$e\left(\frac{107}{440}\right)$	$e\left(\frac{269}{440}\right)$	$e\left(\frac{277}{1760}\right)$	$e\left(\frac{43}{352}\right)$	$e\left(\frac{17}{176}\right)$
$\chi_{61952}(51,\cdot)$	61952.ev	7040	yes	$1$	$1$	$e\left(\frac{209}{640}\right)$	$e\left(\frac{4617}{7040}\right)$	$e\left(\frac{2253}{3520}\right)$	$e\left(\frac{209}{320}\right)$	$e\left(\frac{2983}{7040}\right)$	$e\left(\frac{1729}{1760}\right)$	$e\left(\frac{1423}{1760}\right)$	$e\left(\frac{1359}{7040}\right)$	$e\left(\frac{1361}{1408}\right)$	$e\left(\frac{403}{704}\right)$
$\chi_{61952}(53,\cdot)$	61952.eu	7040	yes	$1$	$1$	$e\left(\frac{107}{640}\right)$	$e\left(\frac{2451}{7040}\right)$	$e\left(\frac{2239}{3520}\right)$	$e\left(\frac{107}{320}\right)$	$e\left(\frac{4669}{7040}\right)$	$e\left(\frac{907}{1760}\right)$	$e\left(\frac{549}{1760}\right)$	$e\left(\frac{6197}{7040}\right)$	$e\left(\frac{1131}{1408}\right)$	$e\left(\frac{1}{704}\right)$
$\chi_{61952}(57,\cdot)$	61952.et	3520	no	$-1$	$1$	$e\left(\frac{211}{320}\right)$	$e\left(\frac{1723}{3520}\right)$	$e\left(\frac{727}{1760}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{1077}{3520}\right)$	$e\left(\frac{131}{880}\right)$	$e\left(\frac{757}{880}\right)$	$e\left(\frac{1581}{3520}\right)$	$e\left(\frac{51}{704}\right)$	$e\left(\frac{57}{352}\right)$
$\chi_{61952}(59,\cdot)$	61952.ex	7040	yes	$-1$	$1$	$e\left(\frac{159}{640}\right)$	$e\left(\frac{1127}{7040}\right)$	$e\left(\frac{1283}{3520}\right)$	$e\left(\frac{159}{320}\right)$	$e\left(\frac{4393}{7040}\right)$	$e\left(\frac{719}{1760}\right)$	$e\left(\frac{1713}{1760}\right)$	$e\left(\frac{1409}{7040}\right)$	$e\left(\frac{863}{1408}\right)$	$e\left(\frac{509}{704}\right)$
$\chi_{61952}(61,\cdot)$	61952.ew	7040	yes	$-1$	$1$	$e\left(\frac{573}{640}\right)$	$e\left(\frac{6869}{7040}\right)$	$e\left(\frac{3241}{3520}\right)$	$e\left(\frac{253}{320}\right)$	$e\left(\frac{411}{7040}\right)$	$e\left(\frac{1533}{1760}\right)$	$e\left(\frac{1251}{1760}\right)$	$e\left(\frac{1123}{7040}\right)$	$e\left(\frac{1149}{1408}\right)$	$e\left(\frac{311}{704}\right)$
$\chi_{61952}(63,\cdot)$	61952.dv	440	no	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{103}{440}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{397}{440}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{201}{440}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{61952}(65,\cdot)$	61952.cl	88	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{39}{44}\right)$	$i$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{61952}(67,\cdot)$	61952.ei	1408	yes	$-1$	$1$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{241}{1408}\right)$	$e\left(\frac{245}{704}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{767}{1408}\right)$	$e\left(\frac{41}{352}\right)$	$e\left(\frac{247}{352}\right)$	$e\left(\frac{871}{1408}\right)$	$e\left(\frac{413}{1408}\right)$	$e\left(\frac{503}{704}\right)$
$\chi_{61952}(69,\cdot)$	61952.eu	7040	yes	$1$	$1$	$e\left(\frac{511}{640}\right)$	$e\left(\frac{4743}{7040}\right)$	$e\left(\frac{1347}{3520}\right)$	$e\left(\frac{191}{320}\right)$	$e\left(\frac{3977}{7040}\right)$	$e\left(\frac{831}{1760}\right)$	$e\left(\frac{177}{1760}\right)$	$e\left(\frac{161}{7040}\right)$	$e\left(\frac{255}{1408}\right)$	$e\left(\frac{637}{704}\right)$

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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	$61952$
Structure	\(C_{2}\times C_{2}\times C_{7040}\)
Order	$28160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{61952}(1,\cdot)\)	61952.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{61952}(3,\cdot)\)	61952.dx	640	no	\(-1\)	\(1\)	\(e\left(\frac{301}{640}\right)\)	\(e\left(\frac{303}{640}\right)\)	\(e\left(\frac{107}{320}\right)\)	\(e\left(\frac{301}{320}\right)\)	\(e\left(\frac{97}{640}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{121}{640}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{61952}(5,\cdot)\)	61952.eu	7040	yes	\(1\)	\(1\)	\(e\left(\frac{303}{640}\right)\)	\(e\left(\frac{5559}{7040}\right)\)	\(e\left(\frac{1011}{3520}\right)\)	\(e\left(\frac{303}{320}\right)\)	\(e\left(\frac{5721}{7040}\right)\)	\(e\left(\frac{463}{1760}\right)\)	\(e\left(\frac{321}{1760}\right)\)	\(e\left(\frac{113}{7040}\right)\)	\(e\left(\frac{1071}{1408}\right)\)	\(e\left(\frac{141}{704}\right)\)
\(\chi_{61952}(7,\cdot)\)	61952.er	3520	no	\(1\)	\(1\)	\(e\left(\frac{107}{320}\right)\)	\(e\left(\frac{1011}{3520}\right)\)	\(e\left(\frac{1279}{1760}\right)\)	\(e\left(\frac{107}{160}\right)\)	\(e\left(\frac{2109}{3520}\right)\)	\(e\left(\frac{547}{880}\right)\)	\(e\left(\frac{269}{880}\right)\)	\(e\left(\frac{277}{3520}\right)\)	\(e\left(\frac{43}{704}\right)\)	\(e\left(\frac{17}{352}\right)\)
\(\chi_{61952}(9,\cdot)\)	61952.dn	320	no	\(1\)	\(1\)	\(e\left(\frac{301}{320}\right)\)	\(e\left(\frac{303}{320}\right)\)	\(e\left(\frac{107}{160}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{97}{320}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{121}{320}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{61952}(13,\cdot)\)	61952.ew	7040	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{640}\right)\)	\(e\left(\frac{5721}{7040}\right)\)	\(e\left(\frac{2109}{3520}\right)\)	\(e\left(\frac{97}{320}\right)\)	\(e\left(\frac{6999}{7040}\right)\)	\(e\left(\frac{1697}{1760}\right)\)	\(e\left(\frac{479}{1760}\right)\)	\(e\left(\frac{1087}{7040}\right)\)	\(e\left(\frac{1057}{1408}\right)\)	\(e\left(\frac{291}{704}\right)\)
\(\chi_{61952}(15,\cdot)\)	61952.ep	1760	no	\(-1\)	\(1\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{463}{1760}\right)\)	\(e\left(\frac{547}{880}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1697}{1760}\right)\)	\(e\left(\frac{91}{440}\right)\)	\(e\left(\frac{17}{440}\right)\)	\(e\left(\frac{361}{1760}\right)\)	\(e\left(\frac{199}{352}\right)\)	\(e\left(\frac{93}{176}\right)\)
\(\chi_{61952}(17,\cdot)\)	61952.eo	1760	no	\(-1\)	\(1\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{321}{1760}\right)\)	\(e\left(\frac{269}{880}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{479}{1760}\right)\)	\(e\left(\frac{17}{440}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{7}{1760}\right)\)	\(e\left(\frac{57}{352}\right)\)	\(e\left(\frac{43}{176}\right)\)
\(\chi_{61952}(19,\cdot)\)	61952.ev	7040	yes	\(1\)	\(1\)	\(e\left(\frac{121}{640}\right)\)	\(e\left(\frac{113}{7040}\right)\)	\(e\left(\frac{277}{3520}\right)\)	\(e\left(\frac{121}{320}\right)\)	\(e\left(\frac{1087}{7040}\right)\)	\(e\left(\frac{361}{1760}\right)\)	\(e\left(\frac{7}{1760}\right)\)	\(e\left(\frac{1831}{7040}\right)\)	\(e\left(\frac{377}{1408}\right)\)	\(e\left(\frac{587}{704}\right)\)
\(\chi_{61952}(21,\cdot)\)	61952.ej	1408	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{1071}{1408}\right)\)	\(e\left(\frac{43}{704}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{1057}{1408}\right)\)	\(e\left(\frac{199}{352}\right)\)	\(e\left(\frac{57}{352}\right)\)	\(e\left(\frac{377}{1408}\right)\)	\(e\left(\frac{1219}{1408}\right)\)	\(e\left(\frac{265}{704}\right)\)
\(\chi_{61952}(23,\cdot)\)	61952.eb	704	no	\(-1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{141}{704}\right)\)	\(e\left(\frac{17}{352}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{291}{704}\right)\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{43}{176}\right)\)	\(e\left(\frac{587}{704}\right)\)	\(e\left(\frac{265}{704}\right)\)	\(e\left(\frac{203}{352}\right)\)
\(\chi_{61952}(25,\cdot)\)	61952.eq	3520	no	\(1\)	\(1\)	\(e\left(\frac{303}{320}\right)\)	\(e\left(\frac{2039}{3520}\right)\)	\(e\left(\frac{1011}{1760}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{2201}{3520}\right)\)	\(e\left(\frac{463}{880}\right)\)	\(e\left(\frac{321}{880}\right)\)	\(e\left(\frac{113}{3520}\right)\)	\(e\left(\frac{367}{704}\right)\)	\(e\left(\frac{141}{352}\right)\)
\(\chi_{61952}(27,\cdot)\)	61952.dx	640	no	\(-1\)	\(1\)	\(e\left(\frac{263}{640}\right)\)	\(e\left(\frac{269}{640}\right)\)	\(e\left(\frac{1}{320}\right)\)	\(e\left(\frac{263}{320}\right)\)	\(e\left(\frac{291}{640}\right)\)	\(e\left(\frac{133}{160}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{363}{640}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{63}{64}\right)\)
\(\chi_{61952}(29,\cdot)\)	61952.ew	7040	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{640}\right)\)	\(e\left(\frac{2797}{7040}\right)\)	\(e\left(\frac{673}{3520}\right)\)	\(e\left(\frac{149}{320}\right)\)	\(e\left(\frac{1923}{7040}\right)\)	\(e\left(\frac{1109}{1760}\right)\)	\(e\left(\frac{843}{1760}\right)\)	\(e\left(\frac{6539}{7040}\right)\)	\(e\left(\frac{597}{1408}\right)\)	\(e\left(\frac{191}{704}\right)\)
\(\chi_{61952}(31,\cdot)\)	61952.eg	880	no	\(-1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{807}{880}\right)\)	\(e\left(\frac{263}{440}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{793}{880}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{729}{880}\right)\)	\(e\left(\frac{15}{176}\right)\)	\(e\left(\frac{9}{88}\right)\)
\(\chi_{61952}(35,\cdot)\)	61952.ev	7040	yes	\(1\)	\(1\)	\(e\left(\frac{517}{640}\right)\)	\(e\left(\frac{541}{7040}\right)\)	\(e\left(\frac{49}{3520}\right)\)	\(e\left(\frac{197}{320}\right)\)	\(e\left(\frac{2899}{7040}\right)\)	\(e\left(\frac{1557}{1760}\right)\)	\(e\left(\frac{859}{1760}\right)\)	\(e\left(\frac{667}{7040}\right)\)	\(e\left(\frac{1157}{1408}\right)\)	\(e\left(\frac{175}{704}\right)\)
\(\chi_{61952}(37,\cdot)\)	61952.eu	7040	yes	\(1\)	\(1\)	\(e\left(\frac{279}{640}\right)\)	\(e\left(\frac{3167}{7040}\right)\)	\(e\left(\frac{443}{3520}\right)\)	\(e\left(\frac{279}{320}\right)\)	\(e\left(\frac{1713}{7040}\right)\)	\(e\left(\frac{1559}{1760}\right)\)	\(e\left(\frac{313}{1760}\right)\)	\(e\left(\frac{1289}{7040}\right)\)	\(e\left(\frac{791}{1408}\right)\)	\(e\left(\frac{325}{704}\right)\)
\(\chi_{61952}(39,\cdot)\)	61952.er	3520	no	\(1\)	\(1\)	\(e\left(\frac{199}{320}\right)\)	\(e\left(\frac{1007}{3520}\right)\)	\(e\left(\frac{1643}{1760}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{513}{3520}\right)\)	\(e\left(\frac{799}{880}\right)\)	\(e\left(\frac{113}{880}\right)\)	\(e\left(\frac{1209}{3520}\right)\)	\(e\left(\frac{391}{704}\right)\)	\(e\left(\frac{261}{352}\right)\)
\(\chi_{61952}(41,\cdot)\)	61952.et	3520	no	\(-1\)	\(1\)	\(e\left(\frac{273}{320}\right)\)	\(e\left(\frac{1609}{3520}\right)\)	\(e\left(\frac{541}{1760}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{1351}{3520}\right)\)	\(e\left(\frac{273}{880}\right)\)	\(e\left(\frac{711}{880}\right)\)	\(e\left(\frac{3503}{3520}\right)\)	\(e\left(\frac{113}{704}\right)\)	\(e\left(\frac{147}{352}\right)\)
\(\chi_{61952}(43,\cdot)\)	61952.ek	1408	yes	\(1\)	\(1\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{415}{1408}\right)\)	\(e\left(\frac{251}{704}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1201}{1408}\right)\)	\(e\left(\frac{167}{352}\right)\)	\(e\left(\frac{169}{352}\right)\)	\(e\left(\frac{457}{1408}\right)\)	\(e\left(\frac{755}{1408}\right)\)	\(e\left(\frac{57}{704}\right)\)
\(\chi_{61952}(45,\cdot)\)	61952.el	1408	yes	\(1\)	\(1\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{1037}{1408}\right)\)	\(e\left(\frac{673}{704}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{163}{1408}\right)\)	\(e\left(\frac{53}{352}\right)\)	\(e\left(\frac{315}{352}\right)\)	\(e\left(\frac{555}{1408}\right)\)	\(e\left(\frac{521}{1408}\right)\)	\(e\left(\frac{603}{704}\right)\)
\(\chi_{61952}(47,\cdot)\)	61952.ep	1760	no	\(-1\)	\(1\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{477}{1760}\right)\)	\(e\left(\frac{153}{880}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{243}{1760}\right)\)	\(e\left(\frac{89}{440}\right)\)	\(e\left(\frac{123}{440}\right)\)	\(e\left(\frac{619}{1760}\right)\)	\(e\left(\frac{37}{352}\right)\)	\(e\left(\frac{119}{176}\right)\)
\(\chi_{61952}(49,\cdot)\)	61952.en	1760	no	\(1\)	\(1\)	\(e\left(\frac{107}{160}\right)\)	\(e\left(\frac{1011}{1760}\right)\)	\(e\left(\frac{399}{880}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{349}{1760}\right)\)	\(e\left(\frac{107}{440}\right)\)	\(e\left(\frac{269}{440}\right)\)	\(e\left(\frac{277}{1760}\right)\)	\(e\left(\frac{43}{352}\right)\)	\(e\left(\frac{17}{176}\right)\)
\(\chi_{61952}(51,\cdot)\)	61952.ev	7040	yes	\(1\)	\(1\)	\(e\left(\frac{209}{640}\right)\)	\(e\left(\frac{4617}{7040}\right)\)	\(e\left(\frac{2253}{3520}\right)\)	\(e\left(\frac{209}{320}\right)\)	\(e\left(\frac{2983}{7040}\right)\)	\(e\left(\frac{1729}{1760}\right)\)	\(e\left(\frac{1423}{1760}\right)\)	\(e\left(\frac{1359}{7040}\right)\)	\(e\left(\frac{1361}{1408}\right)\)	\(e\left(\frac{403}{704}\right)\)
\(\chi_{61952}(53,\cdot)\)	61952.eu	7040	yes	\(1\)	\(1\)	\(e\left(\frac{107}{640}\right)\)	\(e\left(\frac{2451}{7040}\right)\)	\(e\left(\frac{2239}{3520}\right)\)	\(e\left(\frac{107}{320}\right)\)	\(e\left(\frac{4669}{7040}\right)\)	\(e\left(\frac{907}{1760}\right)\)	\(e\left(\frac{549}{1760}\right)\)	\(e\left(\frac{6197}{7040}\right)\)	\(e\left(\frac{1131}{1408}\right)\)	\(e\left(\frac{1}{704}\right)\)
\(\chi_{61952}(57,\cdot)\)	61952.et	3520	no	\(-1\)	\(1\)	\(e\left(\frac{211}{320}\right)\)	\(e\left(\frac{1723}{3520}\right)\)	\(e\left(\frac{727}{1760}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{1077}{3520}\right)\)	\(e\left(\frac{131}{880}\right)\)	\(e\left(\frac{757}{880}\right)\)	\(e\left(\frac{1581}{3520}\right)\)	\(e\left(\frac{51}{704}\right)\)	\(e\left(\frac{57}{352}\right)\)
\(\chi_{61952}(59,\cdot)\)	61952.ex	7040	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{640}\right)\)	\(e\left(\frac{1127}{7040}\right)\)	\(e\left(\frac{1283}{3520}\right)\)	\(e\left(\frac{159}{320}\right)\)	\(e\left(\frac{4393}{7040}\right)\)	\(e\left(\frac{719}{1760}\right)\)	\(e\left(\frac{1713}{1760}\right)\)	\(e\left(\frac{1409}{7040}\right)\)	\(e\left(\frac{863}{1408}\right)\)	\(e\left(\frac{509}{704}\right)\)
\(\chi_{61952}(61,\cdot)\)	61952.ew	7040	yes	\(-1\)	\(1\)	\(e\left(\frac{573}{640}\right)\)	\(e\left(\frac{6869}{7040}\right)\)	\(e\left(\frac{3241}{3520}\right)\)	\(e\left(\frac{253}{320}\right)\)	\(e\left(\frac{411}{7040}\right)\)	\(e\left(\frac{1533}{1760}\right)\)	\(e\left(\frac{1251}{1760}\right)\)	\(e\left(\frac{1123}{7040}\right)\)	\(e\left(\frac{1149}{1408}\right)\)	\(e\left(\frac{311}{704}\right)\)
\(\chi_{61952}(63,\cdot)\)	61952.dv	440	no	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{103}{440}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{397}{440}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{201}{440}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{61952}(65,\cdot)\)	61952.cl	88	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(i\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{61952}(67,\cdot)\)	61952.ei	1408	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{128}\right)\)	\(e\left(\frac{241}{1408}\right)\)	\(e\left(\frac{245}{704}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{767}{1408}\right)\)	\(e\left(\frac{41}{352}\right)\)	\(e\left(\frac{247}{352}\right)\)	\(e\left(\frac{871}{1408}\right)\)	\(e\left(\frac{413}{1408}\right)\)	\(e\left(\frac{503}{704}\right)\)
\(\chi_{61952}(69,\cdot)\)	61952.eu	7040	yes	\(1\)	\(1\)	\(e\left(\frac{511}{640}\right)\)	\(e\left(\frac{4743}{7040}\right)\)	\(e\left(\frac{1347}{3520}\right)\)	\(e\left(\frac{191}{320}\right)\)	\(e\left(\frac{3977}{7040}\right)\)	\(e\left(\frac{831}{1760}\right)\)	\(e\left(\frac{177}{1760}\right)\)	\(e\left(\frac{161}{7040}\right)\)	\(e\left(\frac{255}{1408}\right)\)	\(e\left(\frac{637}{704}\right)\)

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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.