LMFDB - Group of Dirichlet characters of modulus 67915

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(67915)

gp:g = idealstar(,67915,2)

magma:G = FullDirichletGroup(67915);

Character group

Order	=	50048	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{6256}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{67915}(27167,\cdot)$, $\chi_{67915}(25146,\cdot)$, $\chi_{67915}(44796,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 50048 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{67915}(1,\cdot)$	67915.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{67915}(2,\cdot)$	67915.ey	3128	yes	$-1$	$1$	$e\left(\frac{11}{782}\right)$	$e\left(\frac{859}{3128}\right)$	$e\left(\frac{11}{391}\right)$	$e\left(\frac{903}{3128}\right)$	$e\left(\frac{137}{3128}\right)$	$e\left(\frac{33}{782}\right)$	$e\left(\frac{859}{1564}\right)$	$e\left(\frac{2519}{3128}\right)$	$e\left(\frac{947}{3128}\right)$	$e\left(\frac{1511}{1564}\right)$
$\chi_{67915}(3,\cdot)$	67915.fg	6256	yes	$1$	$1$	$e\left(\frac{859}{3128}\right)$	$e\left(\frac{5939}{6256}\right)$	$e\left(\frac{859}{1564}\right)$	$e\left(\frac{1401}{6256}\right)$	$e\left(\frac{1457}{6256}\right)$	$e\left(\frac{2577}{3128}\right)$	$e\left(\frac{2811}{3128}\right)$	$e\left(\frac{801}{6256}\right)$	$e\left(\frac{3119}{6256}\right)$	$e\left(\frac{589}{782}\right)$
$\chi_{67915}(4,\cdot)$	67915.ew	1564	yes	$1$	$1$	$e\left(\frac{11}{391}\right)$	$e\left(\frac{859}{1564}\right)$	$e\left(\frac{22}{391}\right)$	$e\left(\frac{903}{1564}\right)$	$e\left(\frac{137}{1564}\right)$	$e\left(\frac{33}{391}\right)$	$e\left(\frac{77}{782}\right)$	$e\left(\frac{955}{1564}\right)$	$e\left(\frac{947}{1564}\right)$	$e\left(\frac{729}{782}\right)$
$\chi_{67915}(6,\cdot)$	67915.fk	6256	no	$-1$	$1$	$e\left(\frac{903}{3128}\right)$	$e\left(\frac{1401}{6256}\right)$	$e\left(\frac{903}{1564}\right)$	$e\left(\frac{3207}{6256}\right)$	$e\left(\frac{1731}{6256}\right)$	$e\left(\frac{2709}{3128}\right)$	$e\left(\frac{1401}{3128}\right)$	$e\left(\frac{5839}{6256}\right)$	$e\left(\frac{5013}{6256}\right)$	$e\left(\frac{1125}{1564}\right)$
$\chi_{67915}(7,\cdot)$	67915.fg	6256	yes	$1$	$1$	$e\left(\frac{137}{3128}\right)$	$e\left(\frac{1457}{6256}\right)$	$e\left(\frac{137}{1564}\right)$	$e\left(\frac{1731}{6256}\right)$	$e\left(\frac{5243}{6256}\right)$	$e\left(\frac{411}{3128}\right)$	$e\left(\frac{1457}{3128}\right)$	$e\left(\frac{6107}{6256}\right)$	$e\left(\frac{2005}{6256}\right)$	$e\left(\frac{73}{782}\right)$
$\chi_{67915}(8,\cdot)$	67915.ey	3128	yes	$-1$	$1$	$e\left(\frac{33}{782}\right)$	$e\left(\frac{2577}{3128}\right)$	$e\left(\frac{33}{391}\right)$	$e\left(\frac{2709}{3128}\right)$	$e\left(\frac{411}{3128}\right)$	$e\left(\frac{99}{782}\right)$	$e\left(\frac{1013}{1564}\right)$	$e\left(\frac{1301}{3128}\right)$	$e\left(\frac{2841}{3128}\right)$	$e\left(\frac{1405}{1564}\right)$
$\chi_{67915}(9,\cdot)$	67915.fc	3128	yes	$1$	$1$	$e\left(\frac{859}{1564}\right)$	$e\left(\frac{2811}{3128}\right)$	$e\left(\frac{77}{782}\right)$	$e\left(\frac{1401}{3128}\right)$	$e\left(\frac{1457}{3128}\right)$	$e\left(\frac{1013}{1564}\right)$	$e\left(\frac{1247}{1564}\right)$	$e\left(\frac{801}{3128}\right)$	$e\left(\frac{3119}{3128}\right)$	$e\left(\frac{198}{391}\right)$
$\chi_{67915}(11,\cdot)$	67915.fl	6256	no	$1$	$1$	$e\left(\frac{2519}{3128}\right)$	$e\left(\frac{801}{6256}\right)$	$e\left(\frac{955}{1564}\right)$	$e\left(\frac{5839}{6256}\right)$	$e\left(\frac{6107}{6256}\right)$	$e\left(\frac{1301}{3128}\right)$	$e\left(\frac{801}{3128}\right)$	$e\left(\frac{63}{6256}\right)$	$e\left(\frac{4621}{6256}\right)$	$e\left(\frac{387}{1564}\right)$
$\chi_{67915}(12,\cdot)$	67915.fm	6256	yes	$1$	$1$	$e\left(\frac{947}{3128}\right)$	$e\left(\frac{3119}{6256}\right)$	$e\left(\frac{947}{1564}\right)$	$e\left(\frac{5013}{6256}\right)$	$e\left(\frac{2005}{6256}\right)$	$e\left(\frac{2841}{3128}\right)$	$e\left(\frac{3119}{3128}\right)$	$e\left(\frac{4621}{6256}\right)$	$e\left(\frac{651}{6256}\right)$	$e\left(\frac{268}{391}\right)$
$\chi_{67915}(13,\cdot)$	67915.eo	1564	yes	$1$	$1$	$e\left(\frac{1511}{1564}\right)$	$e\left(\frac{589}{782}\right)$	$e\left(\frac{729}{782}\right)$	$e\left(\frac{1125}{1564}\right)$	$e\left(\frac{73}{782}\right)$	$e\left(\frac{1405}{1564}\right)$	$e\left(\frac{198}{391}\right)$	$e\left(\frac{387}{1564}\right)$	$e\left(\frac{268}{391}\right)$	$e\left(\frac{181}{1564}\right)$
$\chi_{67915}(14,\cdot)$	67915.fj	6256	yes	$-1$	$1$	$e\left(\frac{181}{3128}\right)$	$e\left(\frac{3175}{6256}\right)$	$e\left(\frac{181}{1564}\right)$	$e\left(\frac{3537}{6256}\right)$	$e\left(\frac{5517}{6256}\right)$	$e\left(\frac{543}{3128}\right)$	$e\left(\frac{47}{3128}\right)$	$e\left(\frac{4889}{6256}\right)$	$e\left(\frac{3899}{6256}\right)$	$e\left(\frac{93}{1564}\right)$
$\chi_{67915}(16,\cdot)$	67915.ej	782	no	$1$	$1$	$e\left(\frac{22}{391}\right)$	$e\left(\frac{77}{782}\right)$	$e\left(\frac{44}{391}\right)$	$e\left(\frac{121}{782}\right)$	$e\left(\frac{137}{782}\right)$	$e\left(\frac{66}{391}\right)$	$e\left(\frac{77}{391}\right)$	$e\left(\frac{173}{782}\right)$	$e\left(\frac{165}{782}\right)$	$e\left(\frac{338}{391}\right)$
$\chi_{67915}(18,\cdot)$	67915.et	1564	yes	$-1$	$1$	$e\left(\frac{881}{1564}\right)$	$e\left(\frac{271}{1564}\right)$	$e\left(\frac{99}{782}\right)$	$e\left(\frac{288}{391}\right)$	$e\left(\frac{797}{1564}\right)$	$e\left(\frac{1079}{1564}\right)$	$e\left(\frac{271}{782}\right)$	$e\left(\frac{24}{391}\right)$	$e\left(\frac{469}{1564}\right)$	$e\left(\frac{739}{1564}\right)$
$\chi_{67915}(19,\cdot)$	67915.fa	3128	yes	$-1$	$1$	$e\left(\frac{1389}{1564}\right)$	$e\left(\frac{365}{3128}\right)$	$e\left(\frac{607}{782}\right)$	$e\left(\frac{15}{3128}\right)$	$e\left(\frac{2447}{3128}\right)$	$e\left(\frac{1039}{1564}\right)$	$e\left(\frac{365}{1564}\right)$	$e\left(\frac{99}{3128}\right)$	$e\left(\frac{2793}{3128}\right)$	$e\left(\frac{273}{782}\right)$
$\chi_{67915}(21,\cdot)$	67915.en	1564	no	$1$	$1$	$e\left(\frac{249}{782}\right)$	$e\left(\frac{285}{1564}\right)$	$e\left(\frac{249}{391}\right)$	$e\left(\frac{783}{1564}\right)$	$e\left(\frac{111}{1564}\right)$	$e\left(\frac{747}{782}\right)$	$e\left(\frac{285}{782}\right)$	$e\left(\frac{163}{1564}\right)$	$e\left(\frac{1281}{1564}\right)$	$e\left(\frac{331}{391}\right)$
$\chi_{67915}(22,\cdot)$	67915.fh	6256	yes	$-1$	$1$	$e\left(\frac{2563}{3128}\right)$	$e\left(\frac{2519}{6256}\right)$	$e\left(\frac{999}{1564}\right)$	$e\left(\frac{1389}{6256}\right)$	$e\left(\frac{125}{6256}\right)$	$e\left(\frac{1433}{3128}\right)$	$e\left(\frac{2519}{3128}\right)$	$e\left(\frac{5101}{6256}\right)$	$e\left(\frac{259}{6256}\right)$	$e\left(\frac{167}{782}\right)$
$\chi_{67915}(23,\cdot)$	67915.fh	6256	yes	$-1$	$1$	$e\left(\frac{1497}{3128}\right)$	$e\left(\frac{1525}{6256}\right)$	$e\left(\frac{1497}{1564}\right)$	$e\left(\frac{4519}{6256}\right)$	$e\left(\frac{1911}{6256}\right)$	$e\left(\frac{1363}{3128}\right)$	$e\left(\frac{1525}{3128}\right)$	$e\left(\frac{3863}{6256}\right)$	$e\left(\frac{1257}{6256}\right)$	$e\left(\frac{107}{782}\right)$
$\chi_{67915}(24,\cdot)$	67915.fj	6256	yes	$-1$	$1$	$e\left(\frac{991}{3128}\right)$	$e\left(\frac{4837}{6256}\right)$	$e\left(\frac{991}{1564}\right)$	$e\left(\frac{563}{6256}\right)$	$e\left(\frac{2279}{6256}\right)$	$e\left(\frac{2973}{3128}\right)$	$e\left(\frac{1709}{3128}\right)$	$e\left(\frac{3403}{6256}\right)$	$e\left(\frac{2545}{6256}\right)$	$e\left(\frac{1019}{1564}\right)$
$\chi_{67915}(26,\cdot)$	67915.fd	3128	no	$-1$	$1$	$e\left(\frac{1533}{1564}\right)$	$e\left(\frac{87}{3128}\right)$	$e\left(\frac{751}{782}\right)$	$e\left(\frac{25}{3128}\right)$	$e\left(\frac{429}{3128}\right)$	$e\left(\frac{1471}{1564}\right)$	$e\left(\frac{87}{1564}\right)$	$e\left(\frac{165}{3128}\right)$	$e\left(\frac{3091}{3128}\right)$	$e\left(\frac{32}{391}\right)$
$\chi_{67915}(27,\cdot)$	67915.fg	6256	yes	$1$	$1$	$e\left(\frac{2577}{3128}\right)$	$e\left(\frac{5305}{6256}\right)$	$e\left(\frac{1013}{1564}\right)$	$e\left(\frac{4203}{6256}\right)$	$e\left(\frac{4371}{6256}\right)$	$e\left(\frac{1475}{3128}\right)$	$e\left(\frac{2177}{3128}\right)$	$e\left(\frac{2403}{6256}\right)$	$e\left(\frac{3101}{6256}\right)$	$e\left(\frac{203}{782}\right)$
$\chi_{67915}(28,\cdot)$	67915.fm	6256	yes	$1$	$1$	$e\left(\frac{225}{3128}\right)$	$e\left(\frac{4893}{6256}\right)$	$e\left(\frac{225}{1564}\right)$	$e\left(\frac{5343}{6256}\right)$	$e\left(\frac{5791}{6256}\right)$	$e\left(\frac{675}{3128}\right)$	$e\left(\frac{1765}{3128}\right)$	$e\left(\frac{3671}{6256}\right)$	$e\left(\frac{5793}{6256}\right)$	$e\left(\frac{10}{391}\right)$
$\chi_{67915}(29,\cdot)$	67915.fi	6256	yes	$1$	$1$	$e\left(\frac{1601}{3128}\right)$	$e\left(\frac{1107}{6256}\right)$	$e\left(\frac{37}{1564}\right)$	$e\left(\frac{4309}{6256}\right)$	$e\left(\frac{497}{6256}\right)$	$e\left(\frac{1675}{3128}\right)$	$e\left(\frac{1107}{3128}\right)$	$e\left(\frac{5605}{6256}\right)$	$e\left(\frac{1255}{6256}\right)$	$e\left(\frac{1475}{1564}\right)$
$\chi_{67915}(31,\cdot)$	67915.fl	6256	no	$1$	$1$	$e\left(\frac{1441}{3128}\right)$	$e\left(\frac{2111}{6256}\right)$	$e\left(\frac{1441}{1564}\right)$	$e\left(\frac{4993}{6256}\right)$	$e\left(\frac{1349}{6256}\right)$	$e\left(\frac{1195}{3128}\right)$	$e\left(\frac{2111}{3128}\right)$	$e\left(\frac{1361}{6256}\right)$	$e\left(\frac{1619}{6256}\right)$	$e\left(\frac{317}{1564}\right)$
$\chi_{67915}(32,\cdot)$	67915.ey	3128	yes	$-1$	$1$	$e\left(\frac{55}{782}\right)$	$e\left(\frac{1167}{3128}\right)$	$e\left(\frac{55}{391}\right)$	$e\left(\frac{1387}{3128}\right)$	$e\left(\frac{685}{3128}\right)$	$e\left(\frac{165}{782}\right)$	$e\left(\frac{1167}{1564}\right)$	$e\left(\frac{83}{3128}\right)$	$e\left(\frac{1607}{3128}\right)$	$e\left(\frac{1299}{1564}\right)$
$\chi_{67915}(33,\cdot)$	67915.er	1564	yes	$1$	$1$	$e\left(\frac{125}{1564}\right)$	$e\left(\frac{121}{1564}\right)$	$e\left(\frac{125}{782}\right)$	$e\left(\frac{123}{782}\right)$	$e\left(\frac{327}{1564}\right)$	$e\left(\frac{375}{1564}\right)$	$e\left(\frac{121}{782}\right)$	$e\left(\frac{54}{391}\right)$	$e\left(\frac{371}{1564}\right)$	$e\left(\frac{1}{1564}\right)$
$\chi_{67915}(36,\cdot)$	67915.fb	3128	no	$1$	$1$	$e\left(\frac{903}{1564}\right)$	$e\left(\frac{1401}{3128}\right)$	$e\left(\frac{121}{782}\right)$	$e\left(\frac{79}{3128}\right)$	$e\left(\frac{1731}{3128}\right)$	$e\left(\frac{1145}{1564}\right)$	$e\left(\frac{1401}{1564}\right)$	$e\left(\frac{2711}{3128}\right)$	$e\left(\frac{1885}{3128}\right)$	$e\left(\frac{343}{782}\right)$
$\chi_{67915}(37,\cdot)$	67915.fm	6256	yes	$1$	$1$	$e\left(\frac{2487}{3128}\right)$	$e\left(\frac{3035}{6256}\right)$	$e\left(\frac{923}{1564}\right)$	$e\left(\frac{1753}{6256}\right)$	$e\left(\frac{6121}{6256}\right)$	$e\left(\frac{1205}{3128}\right)$	$e\left(\frac{3035}{3128}\right)$	$e\left(\frac{1873}{6256}\right)$	$e\left(\frac{471}{6256}\right)$	$e\left(\frac{293}{391}\right)$
$\chi_{67915}(38,\cdot)$	67915.cp	92	no	$1$	$1$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{29}{92}\right)$
$\chi_{67915}(39,\cdot)$	67915.fi	6256	yes	$1$	$1$	$e\left(\frac{753}{3128}\right)$	$e\left(\frac{4395}{6256}\right)$	$e\left(\frac{753}{1564}\right)$	$e\left(\frac{5901}{6256}\right)$	$e\left(\frac{2041}{6256}\right)$	$e\left(\frac{2259}{3128}\right)$	$e\left(\frac{1267}{3128}\right)$	$e\left(\frac{2349}{6256}\right)$	$e\left(\frac{1151}{6256}\right)$	$e\left(\frac{1359}{1564}\right)$
$\chi_{67915}(41,\cdot)$	67915.fl	6256	no	$1$	$1$	$e\left(\frac{995}{3128}\right)$	$e\left(\frac{941}{6256}\right)$	$e\left(\frac{995}{1564}\right)$	$e\left(\frac{2931}{6256}\right)$	$e\left(\frac{5503}{6256}\right)$	$e\left(\frac{2985}{3128}\right)$	$e\left(\frac{941}{3128}\right)$	$e\left(\frac{4643}{6256}\right)$	$e\left(\frac{4921}{6256}\right)$	$e\left(\frac{1263}{1564}\right)$
$\chi_{67915}(42,\cdot)$	67915.ff	3128	yes	$-1$	$1$	$e\left(\frac{130}{391}\right)$	$e\left(\frac{1429}{3128}\right)$	$e\left(\frac{260}{391}\right)$	$e\left(\frac{2469}{3128}\right)$	$e\left(\frac{359}{3128}\right)$	$e\left(\frac{390}{391}\right)$	$e\left(\frac{1429}{1564}\right)$	$e\left(\frac{2845}{3128}\right)$	$e\left(\frac{381}{3128}\right)$	$e\left(\frac{1271}{1564}\right)$

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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	$67915$
Structure	\(C_{2}\times C_{4}\times C_{6256}\)
Order	$50048$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{67915}(1,\cdot)\)	67915.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{67915}(2,\cdot)\)	67915.ey	3128	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{782}\right)\)	\(e\left(\frac{859}{3128}\right)\)	\(e\left(\frac{11}{391}\right)\)	\(e\left(\frac{903}{3128}\right)\)	\(e\left(\frac{137}{3128}\right)\)	\(e\left(\frac{33}{782}\right)\)	\(e\left(\frac{859}{1564}\right)\)	\(e\left(\frac{2519}{3128}\right)\)	\(e\left(\frac{947}{3128}\right)\)	\(e\left(\frac{1511}{1564}\right)\)
\(\chi_{67915}(3,\cdot)\)	67915.fg	6256	yes	\(1\)	\(1\)	\(e\left(\frac{859}{3128}\right)\)	\(e\left(\frac{5939}{6256}\right)\)	\(e\left(\frac{859}{1564}\right)\)	\(e\left(\frac{1401}{6256}\right)\)	\(e\left(\frac{1457}{6256}\right)\)	\(e\left(\frac{2577}{3128}\right)\)	\(e\left(\frac{2811}{3128}\right)\)	\(e\left(\frac{801}{6256}\right)\)	\(e\left(\frac{3119}{6256}\right)\)	\(e\left(\frac{589}{782}\right)\)
\(\chi_{67915}(4,\cdot)\)	67915.ew	1564	yes	\(1\)	\(1\)	\(e\left(\frac{11}{391}\right)\)	\(e\left(\frac{859}{1564}\right)\)	\(e\left(\frac{22}{391}\right)\)	\(e\left(\frac{903}{1564}\right)\)	\(e\left(\frac{137}{1564}\right)\)	\(e\left(\frac{33}{391}\right)\)	\(e\left(\frac{77}{782}\right)\)	\(e\left(\frac{955}{1564}\right)\)	\(e\left(\frac{947}{1564}\right)\)	\(e\left(\frac{729}{782}\right)\)
\(\chi_{67915}(6,\cdot)\)	67915.fk	6256	no	\(-1\)	\(1\)	\(e\left(\frac{903}{3128}\right)\)	\(e\left(\frac{1401}{6256}\right)\)	\(e\left(\frac{903}{1564}\right)\)	\(e\left(\frac{3207}{6256}\right)\)	\(e\left(\frac{1731}{6256}\right)\)	\(e\left(\frac{2709}{3128}\right)\)	\(e\left(\frac{1401}{3128}\right)\)	\(e\left(\frac{5839}{6256}\right)\)	\(e\left(\frac{5013}{6256}\right)\)	\(e\left(\frac{1125}{1564}\right)\)
\(\chi_{67915}(7,\cdot)\)	67915.fg	6256	yes	\(1\)	\(1\)	\(e\left(\frac{137}{3128}\right)\)	\(e\left(\frac{1457}{6256}\right)\)	\(e\left(\frac{137}{1564}\right)\)	\(e\left(\frac{1731}{6256}\right)\)	\(e\left(\frac{5243}{6256}\right)\)	\(e\left(\frac{411}{3128}\right)\)	\(e\left(\frac{1457}{3128}\right)\)	\(e\left(\frac{6107}{6256}\right)\)	\(e\left(\frac{2005}{6256}\right)\)	\(e\left(\frac{73}{782}\right)\)
\(\chi_{67915}(8,\cdot)\)	67915.ey	3128	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{782}\right)\)	\(e\left(\frac{2577}{3128}\right)\)	\(e\left(\frac{33}{391}\right)\)	\(e\left(\frac{2709}{3128}\right)\)	\(e\left(\frac{411}{3128}\right)\)	\(e\left(\frac{99}{782}\right)\)	\(e\left(\frac{1013}{1564}\right)\)	\(e\left(\frac{1301}{3128}\right)\)	\(e\left(\frac{2841}{3128}\right)\)	\(e\left(\frac{1405}{1564}\right)\)
\(\chi_{67915}(9,\cdot)\)	67915.fc	3128	yes	\(1\)	\(1\)	\(e\left(\frac{859}{1564}\right)\)	\(e\left(\frac{2811}{3128}\right)\)	\(e\left(\frac{77}{782}\right)\)	\(e\left(\frac{1401}{3128}\right)\)	\(e\left(\frac{1457}{3128}\right)\)	\(e\left(\frac{1013}{1564}\right)\)	\(e\left(\frac{1247}{1564}\right)\)	\(e\left(\frac{801}{3128}\right)\)	\(e\left(\frac{3119}{3128}\right)\)	\(e\left(\frac{198}{391}\right)\)
\(\chi_{67915}(11,\cdot)\)	67915.fl	6256	no	\(1\)	\(1\)	\(e\left(\frac{2519}{3128}\right)\)	\(e\left(\frac{801}{6256}\right)\)	\(e\left(\frac{955}{1564}\right)\)	\(e\left(\frac{5839}{6256}\right)\)	\(e\left(\frac{6107}{6256}\right)\)	\(e\left(\frac{1301}{3128}\right)\)	\(e\left(\frac{801}{3128}\right)\)	\(e\left(\frac{63}{6256}\right)\)	\(e\left(\frac{4621}{6256}\right)\)	\(e\left(\frac{387}{1564}\right)\)
\(\chi_{67915}(12,\cdot)\)	67915.fm	6256	yes	\(1\)	\(1\)	\(e\left(\frac{947}{3128}\right)\)	\(e\left(\frac{3119}{6256}\right)\)	\(e\left(\frac{947}{1564}\right)\)	\(e\left(\frac{5013}{6256}\right)\)	\(e\left(\frac{2005}{6256}\right)\)	\(e\left(\frac{2841}{3128}\right)\)	\(e\left(\frac{3119}{3128}\right)\)	\(e\left(\frac{4621}{6256}\right)\)	\(e\left(\frac{651}{6256}\right)\)	\(e\left(\frac{268}{391}\right)\)
\(\chi_{67915}(13,\cdot)\)	67915.eo	1564	yes	\(1\)	\(1\)	\(e\left(\frac{1511}{1564}\right)\)	\(e\left(\frac{589}{782}\right)\)	\(e\left(\frac{729}{782}\right)\)	\(e\left(\frac{1125}{1564}\right)\)	\(e\left(\frac{73}{782}\right)\)	\(e\left(\frac{1405}{1564}\right)\)	\(e\left(\frac{198}{391}\right)\)	\(e\left(\frac{387}{1564}\right)\)	\(e\left(\frac{268}{391}\right)\)	\(e\left(\frac{181}{1564}\right)\)
\(\chi_{67915}(14,\cdot)\)	67915.fj	6256	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{3128}\right)\)	\(e\left(\frac{3175}{6256}\right)\)	\(e\left(\frac{181}{1564}\right)\)	\(e\left(\frac{3537}{6256}\right)\)	\(e\left(\frac{5517}{6256}\right)\)	\(e\left(\frac{543}{3128}\right)\)	\(e\left(\frac{47}{3128}\right)\)	\(e\left(\frac{4889}{6256}\right)\)	\(e\left(\frac{3899}{6256}\right)\)	\(e\left(\frac{93}{1564}\right)\)
\(\chi_{67915}(16,\cdot)\)	67915.ej	782	no	\(1\)	\(1\)	\(e\left(\frac{22}{391}\right)\)	\(e\left(\frac{77}{782}\right)\)	\(e\left(\frac{44}{391}\right)\)	\(e\left(\frac{121}{782}\right)\)	\(e\left(\frac{137}{782}\right)\)	\(e\left(\frac{66}{391}\right)\)	\(e\left(\frac{77}{391}\right)\)	\(e\left(\frac{173}{782}\right)\)	\(e\left(\frac{165}{782}\right)\)	\(e\left(\frac{338}{391}\right)\)
\(\chi_{67915}(18,\cdot)\)	67915.et	1564	yes	\(-1\)	\(1\)	\(e\left(\frac{881}{1564}\right)\)	\(e\left(\frac{271}{1564}\right)\)	\(e\left(\frac{99}{782}\right)\)	\(e\left(\frac{288}{391}\right)\)	\(e\left(\frac{797}{1564}\right)\)	\(e\left(\frac{1079}{1564}\right)\)	\(e\left(\frac{271}{782}\right)\)	\(e\left(\frac{24}{391}\right)\)	\(e\left(\frac{469}{1564}\right)\)	\(e\left(\frac{739}{1564}\right)\)
\(\chi_{67915}(19,\cdot)\)	67915.fa	3128	yes	\(-1\)	\(1\)	\(e\left(\frac{1389}{1564}\right)\)	\(e\left(\frac{365}{3128}\right)\)	\(e\left(\frac{607}{782}\right)\)	\(e\left(\frac{15}{3128}\right)\)	\(e\left(\frac{2447}{3128}\right)\)	\(e\left(\frac{1039}{1564}\right)\)	\(e\left(\frac{365}{1564}\right)\)	\(e\left(\frac{99}{3128}\right)\)	\(e\left(\frac{2793}{3128}\right)\)	\(e\left(\frac{273}{782}\right)\)
\(\chi_{67915}(21,\cdot)\)	67915.en	1564	no	\(1\)	\(1\)	\(e\left(\frac{249}{782}\right)\)	\(e\left(\frac{285}{1564}\right)\)	\(e\left(\frac{249}{391}\right)\)	\(e\left(\frac{783}{1564}\right)\)	\(e\left(\frac{111}{1564}\right)\)	\(e\left(\frac{747}{782}\right)\)	\(e\left(\frac{285}{782}\right)\)	\(e\left(\frac{163}{1564}\right)\)	\(e\left(\frac{1281}{1564}\right)\)	\(e\left(\frac{331}{391}\right)\)
\(\chi_{67915}(22,\cdot)\)	67915.fh	6256	yes	\(-1\)	\(1\)	\(e\left(\frac{2563}{3128}\right)\)	\(e\left(\frac{2519}{6256}\right)\)	\(e\left(\frac{999}{1564}\right)\)	\(e\left(\frac{1389}{6256}\right)\)	\(e\left(\frac{125}{6256}\right)\)	\(e\left(\frac{1433}{3128}\right)\)	\(e\left(\frac{2519}{3128}\right)\)	\(e\left(\frac{5101}{6256}\right)\)	\(e\left(\frac{259}{6256}\right)\)	\(e\left(\frac{167}{782}\right)\)
\(\chi_{67915}(23,\cdot)\)	67915.fh	6256	yes	\(-1\)	\(1\)	\(e\left(\frac{1497}{3128}\right)\)	\(e\left(\frac{1525}{6256}\right)\)	\(e\left(\frac{1497}{1564}\right)\)	\(e\left(\frac{4519}{6256}\right)\)	\(e\left(\frac{1911}{6256}\right)\)	\(e\left(\frac{1363}{3128}\right)\)	\(e\left(\frac{1525}{3128}\right)\)	\(e\left(\frac{3863}{6256}\right)\)	\(e\left(\frac{1257}{6256}\right)\)	\(e\left(\frac{107}{782}\right)\)
\(\chi_{67915}(24,\cdot)\)	67915.fj	6256	yes	\(-1\)	\(1\)	\(e\left(\frac{991}{3128}\right)\)	\(e\left(\frac{4837}{6256}\right)\)	\(e\left(\frac{991}{1564}\right)\)	\(e\left(\frac{563}{6256}\right)\)	\(e\left(\frac{2279}{6256}\right)\)	\(e\left(\frac{2973}{3128}\right)\)	\(e\left(\frac{1709}{3128}\right)\)	\(e\left(\frac{3403}{6256}\right)\)	\(e\left(\frac{2545}{6256}\right)\)	\(e\left(\frac{1019}{1564}\right)\)
\(\chi_{67915}(26,\cdot)\)	67915.fd	3128	no	\(-1\)	\(1\)	\(e\left(\frac{1533}{1564}\right)\)	\(e\left(\frac{87}{3128}\right)\)	\(e\left(\frac{751}{782}\right)\)	\(e\left(\frac{25}{3128}\right)\)	\(e\left(\frac{429}{3128}\right)\)	\(e\left(\frac{1471}{1564}\right)\)	\(e\left(\frac{87}{1564}\right)\)	\(e\left(\frac{165}{3128}\right)\)	\(e\left(\frac{3091}{3128}\right)\)	\(e\left(\frac{32}{391}\right)\)
\(\chi_{67915}(27,\cdot)\)	67915.fg	6256	yes	\(1\)	\(1\)	\(e\left(\frac{2577}{3128}\right)\)	\(e\left(\frac{5305}{6256}\right)\)	\(e\left(\frac{1013}{1564}\right)\)	\(e\left(\frac{4203}{6256}\right)\)	\(e\left(\frac{4371}{6256}\right)\)	\(e\left(\frac{1475}{3128}\right)\)	\(e\left(\frac{2177}{3128}\right)\)	\(e\left(\frac{2403}{6256}\right)\)	\(e\left(\frac{3101}{6256}\right)\)	\(e\left(\frac{203}{782}\right)\)
\(\chi_{67915}(28,\cdot)\)	67915.fm	6256	yes	\(1\)	\(1\)	\(e\left(\frac{225}{3128}\right)\)	\(e\left(\frac{4893}{6256}\right)\)	\(e\left(\frac{225}{1564}\right)\)	\(e\left(\frac{5343}{6256}\right)\)	\(e\left(\frac{5791}{6256}\right)\)	\(e\left(\frac{675}{3128}\right)\)	\(e\left(\frac{1765}{3128}\right)\)	\(e\left(\frac{3671}{6256}\right)\)	\(e\left(\frac{5793}{6256}\right)\)	\(e\left(\frac{10}{391}\right)\)
\(\chi_{67915}(29,\cdot)\)	67915.fi	6256	yes	\(1\)	\(1\)	\(e\left(\frac{1601}{3128}\right)\)	\(e\left(\frac{1107}{6256}\right)\)	\(e\left(\frac{37}{1564}\right)\)	\(e\left(\frac{4309}{6256}\right)\)	\(e\left(\frac{497}{6256}\right)\)	\(e\left(\frac{1675}{3128}\right)\)	\(e\left(\frac{1107}{3128}\right)\)	\(e\left(\frac{5605}{6256}\right)\)	\(e\left(\frac{1255}{6256}\right)\)	\(e\left(\frac{1475}{1564}\right)\)
\(\chi_{67915}(31,\cdot)\)	67915.fl	6256	no	\(1\)	\(1\)	\(e\left(\frac{1441}{3128}\right)\)	\(e\left(\frac{2111}{6256}\right)\)	\(e\left(\frac{1441}{1564}\right)\)	\(e\left(\frac{4993}{6256}\right)\)	\(e\left(\frac{1349}{6256}\right)\)	\(e\left(\frac{1195}{3128}\right)\)	\(e\left(\frac{2111}{3128}\right)\)	\(e\left(\frac{1361}{6256}\right)\)	\(e\left(\frac{1619}{6256}\right)\)	\(e\left(\frac{317}{1564}\right)\)
\(\chi_{67915}(32,\cdot)\)	67915.ey	3128	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{782}\right)\)	\(e\left(\frac{1167}{3128}\right)\)	\(e\left(\frac{55}{391}\right)\)	\(e\left(\frac{1387}{3128}\right)\)	\(e\left(\frac{685}{3128}\right)\)	\(e\left(\frac{165}{782}\right)\)	\(e\left(\frac{1167}{1564}\right)\)	\(e\left(\frac{83}{3128}\right)\)	\(e\left(\frac{1607}{3128}\right)\)	\(e\left(\frac{1299}{1564}\right)\)
\(\chi_{67915}(33,\cdot)\)	67915.er	1564	yes	\(1\)	\(1\)	\(e\left(\frac{125}{1564}\right)\)	\(e\left(\frac{121}{1564}\right)\)	\(e\left(\frac{125}{782}\right)\)	\(e\left(\frac{123}{782}\right)\)	\(e\left(\frac{327}{1564}\right)\)	\(e\left(\frac{375}{1564}\right)\)	\(e\left(\frac{121}{782}\right)\)	\(e\left(\frac{54}{391}\right)\)	\(e\left(\frac{371}{1564}\right)\)	\(e\left(\frac{1}{1564}\right)\)
\(\chi_{67915}(36,\cdot)\)	67915.fb	3128	no	\(1\)	\(1\)	\(e\left(\frac{903}{1564}\right)\)	\(e\left(\frac{1401}{3128}\right)\)	\(e\left(\frac{121}{782}\right)\)	\(e\left(\frac{79}{3128}\right)\)	\(e\left(\frac{1731}{3128}\right)\)	\(e\left(\frac{1145}{1564}\right)\)	\(e\left(\frac{1401}{1564}\right)\)	\(e\left(\frac{2711}{3128}\right)\)	\(e\left(\frac{1885}{3128}\right)\)	\(e\left(\frac{343}{782}\right)\)
\(\chi_{67915}(37,\cdot)\)	67915.fm	6256	yes	\(1\)	\(1\)	\(e\left(\frac{2487}{3128}\right)\)	\(e\left(\frac{3035}{6256}\right)\)	\(e\left(\frac{923}{1564}\right)\)	\(e\left(\frac{1753}{6256}\right)\)	\(e\left(\frac{6121}{6256}\right)\)	\(e\left(\frac{1205}{3128}\right)\)	\(e\left(\frac{3035}{3128}\right)\)	\(e\left(\frac{1873}{6256}\right)\)	\(e\left(\frac{471}{6256}\right)\)	\(e\left(\frac{293}{391}\right)\)
\(\chi_{67915}(38,\cdot)\)	67915.cp	92	no	\(1\)	\(1\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{29}{92}\right)\)
\(\chi_{67915}(39,\cdot)\)	67915.fi	6256	yes	\(1\)	\(1\)	\(e\left(\frac{753}{3128}\right)\)	\(e\left(\frac{4395}{6256}\right)\)	\(e\left(\frac{753}{1564}\right)\)	\(e\left(\frac{5901}{6256}\right)\)	\(e\left(\frac{2041}{6256}\right)\)	\(e\left(\frac{2259}{3128}\right)\)	\(e\left(\frac{1267}{3128}\right)\)	\(e\left(\frac{2349}{6256}\right)\)	\(e\left(\frac{1151}{6256}\right)\)	\(e\left(\frac{1359}{1564}\right)\)
\(\chi_{67915}(41,\cdot)\)	67915.fl	6256	no	\(1\)	\(1\)	\(e\left(\frac{995}{3128}\right)\)	\(e\left(\frac{941}{6256}\right)\)	\(e\left(\frac{995}{1564}\right)\)	\(e\left(\frac{2931}{6256}\right)\)	\(e\left(\frac{5503}{6256}\right)\)	\(e\left(\frac{2985}{3128}\right)\)	\(e\left(\frac{941}{3128}\right)\)	\(e\left(\frac{4643}{6256}\right)\)	\(e\left(\frac{4921}{6256}\right)\)	\(e\left(\frac{1263}{1564}\right)\)
\(\chi_{67915}(42,\cdot)\)	67915.ff	3128	yes	\(-1\)	\(1\)	\(e\left(\frac{130}{391}\right)\)	\(e\left(\frac{1429}{3128}\right)\)	\(e\left(\frac{260}{391}\right)\)	\(e\left(\frac{2469}{3128}\right)\)	\(e\left(\frac{359}{3128}\right)\)	\(e\left(\frac{390}{391}\right)\)	\(e\left(\frac{1429}{1564}\right)\)	\(e\left(\frac{2845}{3128}\right)\)	\(e\left(\frac{381}{3128}\right)\)	\(e\left(\frac{1271}{1564}\right)\)

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