LMFDB - Group of Dirichlet characters of modulus 864900

Show commands: PariGP / SageMath

sage: H = DirichletGroup(864900)

pari: g = idealstar(,864900,2)

Character group

sage: G.order() pari: g.no
Order	=	223200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{30}\times C_{1860}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{864900}(432451,\cdot)$, $\chi_{864900}(384401,\cdot)$, $\chi_{864900}(207577,\cdot)$, $\chi_{864900}(113401,\cdot)$

First 32 of 223200 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$37$	$41$	$43$
$\chi_{864900}(1,\cdot)$	864900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{864900}(7,\cdot)$	864900.cjw	1860	no	$1$	$1$	$e\left(\frac{601}{620}\right)$	$e\left(\frac{649}{930}\right)$	$e\left(\frac{497}{620}\right)$	$e\left(\frac{1157}{1860}\right)$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{257}{1860}\right)$	$e\left(\frac{857}{930}\right)$	$e\left(\frac{13}{372}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{563}{620}\right)$
$\chi_{864900}(11,\cdot)$	864900.bzb	930	yes	$-1$	$1$	$e\left(\frac{649}{930}\right)$	$e\left(\frac{201}{310}\right)$	$e\left(\frac{749}{930}\right)$	$e\left(\frac{184}{465}\right)$	$e\left(\frac{209}{930}\right)$	$e\left(\frac{65}{186}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{191}{930}\right)$	$e\left(\frac{683}{930}\right)$	$e\left(\frac{431}{465}\right)$
$\chi_{864900}(13,\cdot)$	864900.cki	1860	no	$1$	$1$	$e\left(\frac{497}{620}\right)$	$e\left(\frac{749}{930}\right)$	$e\left(\frac{77}{124}\right)$	$e\left(\frac{305}{372}\right)$	$e\left(\frac{347}{930}\right)$	$e\left(\frac{1171}{1860}\right)$	$e\left(\frac{68}{465}\right)$	$e\left(\frac{1093}{1860}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{561}{620}\right)$
$\chi_{864900}(17,\cdot)$	864900.cic	1860	no	$-1$	$1$	$e\left(\frac{1157}{1860}\right)$	$e\left(\frac{184}{465}\right)$	$e\left(\frac{305}{372}\right)$	$e\left(\frac{97}{372}\right)$	$e\left(\frac{919}{930}\right)$	$e\left(\frac{409}{620}\right)$	$e\left(\frac{189}{310}\right)$	$e\left(\frac{1091}{1860}\right)$	$e\left(\frac{881}{930}\right)$	$e\left(\frac{1301}{1860}\right)$
$\chi_{864900}(19,\cdot)$	864900.bxb	930	no	$-1$	$1$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{209}{930}\right)$	$e\left(\frac{347}{930}\right)$	$e\left(\frac{919}{930}\right)$	$e\left(\frac{877}{930}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{223}{930}\right)$	$e\left(\frac{292}{465}\right)$	$e\left(\frac{263}{465}\right)$
$\chi_{864900}(23,\cdot)$	864900.cfl	1860	yes	$1$	$1$	$e\left(\frac{257}{1860}\right)$	$e\left(\frac{65}{186}\right)$	$e\left(\frac{1171}{1860}\right)$	$e\left(\frac{409}{620}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{1591}{1860}\right)$	$e\left(\frac{811}{930}\right)$	$e\left(\frac{39}{620}\right)$	$e\left(\frac{269}{930}\right)$	$e\left(\frac{461}{1860}\right)$
$\chi_{864900}(29,\cdot)$	864900.cci	930	no	$1$	$1$	$e\left(\frac{857}{930}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{68}{465}\right)$	$e\left(\frac{189}{310}\right)$	$e\left(\frac{13}{31}\right)$	$e\left(\frac{811}{930}\right)$	$e\left(\frac{421}{465}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{703}{930}\right)$	$e\left(\frac{433}{465}\right)$
$\chi_{864900}(37,\cdot)$	864900.ckn	1860	no	$1$	$1$	$e\left(\frac{13}{372}\right)$	$e\left(\frac{191}{930}\right)$	$e\left(\frac{1093}{1860}\right)$	$e\left(\frac{1091}{1860}\right)$	$e\left(\frac{223}{930}\right)$	$e\left(\frac{39}{620}\right)$	$e\left(\frac{2}{155}\right)$	$e\left(\frac{1403}{1860}\right)$	$e\left(\frac{112}{465}\right)$	$e\left(\frac{349}{372}\right)$
$\chi_{864900}(41,\cdot)$	864900.cdt	930	no	$-1$	$1$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{683}{930}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{881}{930}\right)$	$e\left(\frac{292}{465}\right)$	$e\left(\frac{269}{930}\right)$	$e\left(\frac{703}{930}\right)$	$e\left(\frac{112}{465}\right)$	$e\left(\frac{53}{62}\right)$	$e\left(\frac{11}{155}\right)$
$\chi_{864900}(43,\cdot)$	864900.chg	1860	no	$-1$	$1$	$e\left(\frac{563}{620}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{561}{620}\right)$	$e\left(\frac{1301}{1860}\right)$	$e\left(\frac{263}{465}\right)$	$e\left(\frac{461}{1860}\right)$	$e\left(\frac{433}{465}\right)$	$e\left(\frac{349}{372}\right)$	$e\left(\frac{11}{155}\right)$	$e\left(\frac{139}{620}\right)$
$\chi_{864900}(47,\cdot)$	864900.cix	1860	yes	$-1$	$1$	$e\left(\frac{691}{1860}\right)$	$e\left(\frac{178}{465}\right)$	$e\left(\frac{551}{1860}\right)$	$e\left(\frac{409}{620}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{343}{372}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{163}{620}\right)$	$e\left(\frac{331}{930}\right)$	$e\left(\frac{1453}{1860}\right)$
$\chi_{864900}(49,\cdot)$	864900.bsw	930	no	$1$	$1$	$e\left(\frac{291}{310}\right)$	$e\left(\frac{184}{465}\right)$	$e\left(\frac{187}{310}\right)$	$e\left(\frac{227}{930}\right)$	$e\left(\frac{382}{465}\right)$	$e\left(\frac{257}{930}\right)$	$e\left(\frac{392}{465}\right)$	$e\left(\frac{13}{186}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{253}{310}\right)$
$\chi_{864900}(53,\cdot)$	864900.chw	1860	no	$-1$	$1$	$e\left(\frac{727}{1860}\right)$	$e\left(\frac{332}{465}\right)$	$e\left(\frac{1763}{1860}\right)$	$e\left(\frac{1051}{1860}\right)$	$e\left(\frac{617}{930}\right)$	$e\left(\frac{523}{620}\right)$	$e\left(\frac{153}{310}\right)$	$e\left(\frac{709}{1860}\right)$	$e\left(\frac{83}{186}\right)$	$e\left(\frac{631}{1860}\right)$
$\chi_{864900}(59,\cdot)$	864900.bxj	930	yes	$1$	$1$	$e\left(\frac{334}{465}\right)$	$e\left(\frac{99}{155}\right)$	$e\left(\frac{131}{186}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{37}{930}\right)$	$e\left(\frac{353}{930}\right)$	$e\left(\frac{601}{930}\right)$	$e\left(\frac{469}{930}\right)$	$e\left(\frac{193}{930}\right)$	$e\left(\frac{382}{465}\right)$
$\chi_{864900}(61,\cdot)$	864900.ces	930	no	$-1$	$1$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{689}{930}\right)$	$e\left(\frac{421}{930}\right)$	$e\left(\frac{299}{310}\right)$	$e\left(\frac{82}{155}\right)$	$e\left(\frac{829}{930}\right)$	$e\left(\frac{23}{930}\right)$	$e\left(\frac{37}{310}\right)$	$e\left(\frac{8}{465}\right)$	$e\left(\frac{49}{186}\right)$
$\chi_{864900}(67,\cdot)$	864900.cjy	1860	yes	$1$	$1$	$e\left(\frac{73}{124}\right)$	$e\left(\frac{647}{930}\right)$	$e\left(\frac{157}{620}\right)$	$e\left(\frac{1477}{1860}\right)$	$e\left(\frac{103}{465}\right)$	$e\left(\frac{49}{1860}\right)$	$e\left(\frac{319}{930}\right)$	$e\left(\frac{781}{1860}\right)$	$e\left(\frac{28}{155}\right)$	$e\left(\frac{95}{124}\right)$
$\chi_{864900}(71,\cdot)$	864900.bzu	930	no	$1$	$1$	$e\left(\frac{641}{930}\right)$	$e\left(\frac{407}{465}\right)$	$e\left(\frac{152}{465}\right)$	$e\left(\frac{383}{930}\right)$	$e\left(\frac{797}{930}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{273}{310}\right)$	$e\left(\frac{121}{465}\right)$	$e\left(\frac{125}{186}\right)$	$e\left(\frac{683}{930}\right)$
$\chi_{864900}(73,\cdot)$	864900.ckc	1860	no	$1$	$1$	$e\left(\frac{1363}{1860}\right)$	$e\left(\frac{763}{930}\right)$	$e\left(\frac{1103}{1860}\right)$	$e\left(\frac{1021}{1860}\right)$	$e\left(\frac{29}{930}\right)$	$e\left(\frac{109}{124}\right)$	$e\left(\frac{4}{31}\right)$	$e\left(\frac{1537}{1860}\right)$	$e\left(\frac{314}{465}\right)$	$e\left(\frac{679}{1860}\right)$
$\chi_{864900}(77,\cdot)$	864900.cgs	1860	no	$-1$	$1$	$e\left(\frac{1241}{1860}\right)$	$e\left(\frac{161}{465}\right)$	$e\left(\frac{1129}{1860}\right)$	$e\left(\frac{11}{620}\right)$	$e\left(\frac{197}{310}\right)$	$e\left(\frac{907}{1860}\right)$	$e\left(\frac{97}{930}\right)$	$e\left(\frac{149}{620}\right)$	$e\left(\frac{79}{186}\right)$	$e\left(\frac{1553}{1860}\right)$
$\chi_{864900}(79,\cdot)$	864900.cdg	930	yes	$1$	$1$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{347}{465}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{419}{465}\right)$	$e\left(\frac{157}{930}\right)$	$e\left(\frac{97}{930}\right)$	$e\left(\frac{779}{930}\right)$	$e\left(\frac{11}{465}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{171}{310}\right)$
$\chi_{864900}(83,\cdot)$	864900.cfx	1860	yes	$1$	$1$	$e\left(\frac{149}{1860}\right)$	$e\left(\frac{193}{310}\right)$	$e\left(\frac{139}{1860}\right)$	$e\left(\frac{763}{1860}\right)$	$e\left(\frac{211}{465}\right)$	$e\left(\frac{319}{372}\right)$	$e\left(\frac{175}{186}\right)$	$e\left(\frac{1441}{1860}\right)$	$e\left(\frac{389}{930}\right)$	$e\left(\frac{137}{1860}\right)$
$\chi_{864900}(89,\cdot)$	864900.blm	310	no	$1$	$1$	$e\left(\frac{273}{310}\right)$	$e\left(\frac{83}{155}\right)$	$e\left(\frac{54}{155}\right)$	$e\left(\frac{81}{310}\right)$	$e\left(\frac{19}{155}\right)$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{116}{155}\right)$	$e\left(\frac{251}{310}\right)$	$e\left(\frac{22}{155}\right)$
$\chi_{864900}(91,\cdot)$	864900.blc	310	no	$1$	$1$	$e\left(\frac{239}{310}\right)$	$e\left(\frac{78}{155}\right)$	$e\left(\frac{131}{310}\right)$	$e\left(\frac{137}{310}\right)$	$e\left(\frac{243}{310}\right)$	$e\left(\frac{119}{155}\right)$	$e\left(\frac{21}{310}\right)$	$e\left(\frac{193}{310}\right)$	$e\left(\frac{2}{31}\right)$	$e\left(\frac{126}{155}\right)$
$\chi_{864900}(97,\cdot)$	864900.cgu	1860	no	$-1$	$1$	$e\left(\frac{973}{1860}\right)$	$e\left(\frac{196}{465}\right)$	$e\left(\frac{211}{372}\right)$	$e\left(\frac{107}{124}\right)$	$e\left(\frac{287}{310}\right)$	$e\left(\frac{623}{1860}\right)$	$e\left(\frac{203}{930}\right)$	$e\left(\frac{83}{620}\right)$	$e\left(\frac{107}{465}\right)$	$e\left(\frac{439}{1860}\right)$
$\chi_{864900}(101,\cdot)$	864900.bwk	930	no	$-1$	$1$	$e\left(\frac{448}{465}\right)$	$e\left(\frac{641}{930}\right)$	$e\left(\frac{461}{465}\right)$	$e\left(\frac{153}{310}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{379}{930}\right)$	$e\left(\frac{503}{930}\right)$	$e\left(\frac{8}{31}\right)$	$e\left(\frac{823}{930}\right)$	$e\left(\frac{259}{465}\right)$
$\chi_{864900}(103,\cdot)$	864900.cft	1860	yes	$1$	$1$	$e\left(\frac{23}{620}\right)$	$e\left(\frac{85}{186}\right)$	$e\left(\frac{299}{620}\right)$	$e\left(\frac{1099}{1860}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{1327}{1860}\right)$	$e\left(\frac{307}{930}\right)$	$e\left(\frac{1579}{1860}\right)$	$e\left(\frac{63}{155}\right)$	$e\left(\frac{69}{620}\right)$
$\chi_{864900}(107,\cdot)$	864900.chq	1860	no	$-1$	$1$	$e\left(\frac{1547}{1860}\right)$	$e\left(\frac{13}{465}\right)$	$e\left(\frac{1759}{1860}\right)$	$e\left(\frac{1823}{1860}\right)$	$e\left(\frac{59}{465}\right)$	$e\left(\frac{581}{620}\right)$	$e\left(\frac{153}{155}\right)$	$e\left(\frac{265}{372}\right)$	$e\left(\frac{923}{930}\right)$	$e\left(\frac{1541}{1860}\right)$
$\chi_{864900}(109,\cdot)$	864900.blo	310	no	$1$	$1$	$e\left(\frac{121}{310}\right)$	$e\left(\frac{119}{155}\right)$	$e\left(\frac{17}{62}\right)$	$e\left(\frac{5}{62}\right)$	$e\left(\frac{87}{155}\right)$	$e\left(\frac{131}{310}\right)$	$e\left(\frac{81}{155}\right)$	$e\left(\frac{23}{310}\right)$	$e\left(\frac{148}{155}\right)$	$e\left(\frac{53}{310}\right)$
$\chi_{864900}(113,\cdot)$	864900.cfm	1860	no	$1$	$1$	$e\left(\frac{441}{620}\right)$	$e\left(\frac{7}{186}\right)$	$e\left(\frac{463}{620}\right)$	$e\left(\frac{73}{1860}\right)$	$e\left(\frac{151}{186}\right)$	$e\left(\frac{199}{1860}\right)$	$e\left(\frac{197}{465}\right)$	$e\left(\frac{583}{1860}\right)$	$e\left(\frac{37}{310}\right)$	$e\left(\frac{83}{620}\right)$
$\chi_{864900}(119,\cdot)$	864900.cee	930	yes	$-1$	$1$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{29}{310}\right)$	$e\left(\frac{289}{465}\right)$	$e\left(\frac{821}{930}\right)$	$e\left(\frac{371}{930}\right)$	$e\left(\frac{371}{465}\right)$	$e\left(\frac{247}{465}\right)$	$e\left(\frac{289}{465}\right)$	$e\left(\frac{593}{930}\right)$	$e\left(\frac{113}{186}\right)$
$\chi_{864900}(121,\cdot)$	864900.bpc	465	no	$1$	$1$	$e\left(\frac{184}{465}\right)$	$e\left(\frac{46}{155}\right)$	$e\left(\frac{284}{465}\right)$	$e\left(\frac{368}{465}\right)$	$e\left(\frac{209}{465}\right)$	$e\left(\frac{65}{93}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{218}{465}\right)$	$e\left(\frac{397}{465}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$864900$
Structure	\(C_{2}\times C_{2}\times C_{30}\times C_{1860}\)
Order	$223200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(37\)	\(41\)	\(43\)
\(\chi_{864900}(1,\cdot)\)	864900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{864900}(7,\cdot)\)	864900.cjw	1860	no	\(1\)	\(1\)	\(e\left(\frac{601}{620}\right)\)	\(e\left(\frac{649}{930}\right)\)	\(e\left(\frac{497}{620}\right)\)	\(e\left(\frac{1157}{1860}\right)\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{257}{1860}\right)\)	\(e\left(\frac{857}{930}\right)\)	\(e\left(\frac{13}{372}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{563}{620}\right)\)
\(\chi_{864900}(11,\cdot)\)	864900.bzb	930	yes	\(-1\)	\(1\)	\(e\left(\frac{649}{930}\right)\)	\(e\left(\frac{201}{310}\right)\)	\(e\left(\frac{749}{930}\right)\)	\(e\left(\frac{184}{465}\right)\)	\(e\left(\frac{209}{930}\right)\)	\(e\left(\frac{65}{186}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{191}{930}\right)\)	\(e\left(\frac{683}{930}\right)\)	\(e\left(\frac{431}{465}\right)\)
\(\chi_{864900}(13,\cdot)\)	864900.cki	1860	no	\(1\)	\(1\)	\(e\left(\frac{497}{620}\right)\)	\(e\left(\frac{749}{930}\right)\)	\(e\left(\frac{77}{124}\right)\)	\(e\left(\frac{305}{372}\right)\)	\(e\left(\frac{347}{930}\right)\)	\(e\left(\frac{1171}{1860}\right)\)	\(e\left(\frac{68}{465}\right)\)	\(e\left(\frac{1093}{1860}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{561}{620}\right)\)
\(\chi_{864900}(17,\cdot)\)	864900.cic	1860	no	\(-1\)	\(1\)	\(e\left(\frac{1157}{1860}\right)\)	\(e\left(\frac{184}{465}\right)\)	\(e\left(\frac{305}{372}\right)\)	\(e\left(\frac{97}{372}\right)\)	\(e\left(\frac{919}{930}\right)\)	\(e\left(\frac{409}{620}\right)\)	\(e\left(\frac{189}{310}\right)\)	\(e\left(\frac{1091}{1860}\right)\)	\(e\left(\frac{881}{930}\right)\)	\(e\left(\frac{1301}{1860}\right)\)
\(\chi_{864900}(19,\cdot)\)	864900.bxb	930	no	\(-1\)	\(1\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{209}{930}\right)\)	\(e\left(\frac{347}{930}\right)\)	\(e\left(\frac{919}{930}\right)\)	\(e\left(\frac{877}{930}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{223}{930}\right)\)	\(e\left(\frac{292}{465}\right)\)	\(e\left(\frac{263}{465}\right)\)
\(\chi_{864900}(23,\cdot)\)	864900.cfl	1860	yes	\(1\)	\(1\)	\(e\left(\frac{257}{1860}\right)\)	\(e\left(\frac{65}{186}\right)\)	\(e\left(\frac{1171}{1860}\right)\)	\(e\left(\frac{409}{620}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{1591}{1860}\right)\)	\(e\left(\frac{811}{930}\right)\)	\(e\left(\frac{39}{620}\right)\)	\(e\left(\frac{269}{930}\right)\)	\(e\left(\frac{461}{1860}\right)\)
\(\chi_{864900}(29,\cdot)\)	864900.cci	930	no	\(1\)	\(1\)	\(e\left(\frac{857}{930}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{68}{465}\right)\)	\(e\left(\frac{189}{310}\right)\)	\(e\left(\frac{13}{31}\right)\)	\(e\left(\frac{811}{930}\right)\)	\(e\left(\frac{421}{465}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{703}{930}\right)\)	\(e\left(\frac{433}{465}\right)\)
\(\chi_{864900}(37,\cdot)\)	864900.ckn	1860	no	\(1\)	\(1\)	\(e\left(\frac{13}{372}\right)\)	\(e\left(\frac{191}{930}\right)\)	\(e\left(\frac{1093}{1860}\right)\)	\(e\left(\frac{1091}{1860}\right)\)	\(e\left(\frac{223}{930}\right)\)	\(e\left(\frac{39}{620}\right)\)	\(e\left(\frac{2}{155}\right)\)	\(e\left(\frac{1403}{1860}\right)\)	\(e\left(\frac{112}{465}\right)\)	\(e\left(\frac{349}{372}\right)\)
\(\chi_{864900}(41,\cdot)\)	864900.cdt	930	no	\(-1\)	\(1\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{683}{930}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{881}{930}\right)\)	\(e\left(\frac{292}{465}\right)\)	\(e\left(\frac{269}{930}\right)\)	\(e\left(\frac{703}{930}\right)\)	\(e\left(\frac{112}{465}\right)\)	\(e\left(\frac{53}{62}\right)\)	\(e\left(\frac{11}{155}\right)\)
\(\chi_{864900}(43,\cdot)\)	864900.chg	1860	no	\(-1\)	\(1\)	\(e\left(\frac{563}{620}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{561}{620}\right)\)	\(e\left(\frac{1301}{1860}\right)\)	\(e\left(\frac{263}{465}\right)\)	\(e\left(\frac{461}{1860}\right)\)	\(e\left(\frac{433}{465}\right)\)	\(e\left(\frac{349}{372}\right)\)	\(e\left(\frac{11}{155}\right)\)	\(e\left(\frac{139}{620}\right)\)
\(\chi_{864900}(47,\cdot)\)	864900.cix	1860	yes	\(-1\)	\(1\)	\(e\left(\frac{691}{1860}\right)\)	\(e\left(\frac{178}{465}\right)\)	\(e\left(\frac{551}{1860}\right)\)	\(e\left(\frac{409}{620}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{343}{372}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{163}{620}\right)\)	\(e\left(\frac{331}{930}\right)\)	\(e\left(\frac{1453}{1860}\right)\)
\(\chi_{864900}(49,\cdot)\)	864900.bsw	930	no	\(1\)	\(1\)	\(e\left(\frac{291}{310}\right)\)	\(e\left(\frac{184}{465}\right)\)	\(e\left(\frac{187}{310}\right)\)	\(e\left(\frac{227}{930}\right)\)	\(e\left(\frac{382}{465}\right)\)	\(e\left(\frac{257}{930}\right)\)	\(e\left(\frac{392}{465}\right)\)	\(e\left(\frac{13}{186}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{253}{310}\right)\)
\(\chi_{864900}(53,\cdot)\)	864900.chw	1860	no	\(-1\)	\(1\)	\(e\left(\frac{727}{1860}\right)\)	\(e\left(\frac{332}{465}\right)\)	\(e\left(\frac{1763}{1860}\right)\)	\(e\left(\frac{1051}{1860}\right)\)	\(e\left(\frac{617}{930}\right)\)	\(e\left(\frac{523}{620}\right)\)	\(e\left(\frac{153}{310}\right)\)	\(e\left(\frac{709}{1860}\right)\)	\(e\left(\frac{83}{186}\right)\)	\(e\left(\frac{631}{1860}\right)\)
\(\chi_{864900}(59,\cdot)\)	864900.bxj	930	yes	\(1\)	\(1\)	\(e\left(\frac{334}{465}\right)\)	\(e\left(\frac{99}{155}\right)\)	\(e\left(\frac{131}{186}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{37}{930}\right)\)	\(e\left(\frac{353}{930}\right)\)	\(e\left(\frac{601}{930}\right)\)	\(e\left(\frac{469}{930}\right)\)	\(e\left(\frac{193}{930}\right)\)	\(e\left(\frac{382}{465}\right)\)
\(\chi_{864900}(61,\cdot)\)	864900.ces	930	no	\(-1\)	\(1\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{689}{930}\right)\)	\(e\left(\frac{421}{930}\right)\)	\(e\left(\frac{299}{310}\right)\)	\(e\left(\frac{82}{155}\right)\)	\(e\left(\frac{829}{930}\right)\)	\(e\left(\frac{23}{930}\right)\)	\(e\left(\frac{37}{310}\right)\)	\(e\left(\frac{8}{465}\right)\)	\(e\left(\frac{49}{186}\right)\)
\(\chi_{864900}(67,\cdot)\)	864900.cjy	1860	yes	\(1\)	\(1\)	\(e\left(\frac{73}{124}\right)\)	\(e\left(\frac{647}{930}\right)\)	\(e\left(\frac{157}{620}\right)\)	\(e\left(\frac{1477}{1860}\right)\)	\(e\left(\frac{103}{465}\right)\)	\(e\left(\frac{49}{1860}\right)\)	\(e\left(\frac{319}{930}\right)\)	\(e\left(\frac{781}{1860}\right)\)	\(e\left(\frac{28}{155}\right)\)	\(e\left(\frac{95}{124}\right)\)
\(\chi_{864900}(71,\cdot)\)	864900.bzu	930	no	\(1\)	\(1\)	\(e\left(\frac{641}{930}\right)\)	\(e\left(\frac{407}{465}\right)\)	\(e\left(\frac{152}{465}\right)\)	\(e\left(\frac{383}{930}\right)\)	\(e\left(\frac{797}{930}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{273}{310}\right)\)	\(e\left(\frac{121}{465}\right)\)	\(e\left(\frac{125}{186}\right)\)	\(e\left(\frac{683}{930}\right)\)
\(\chi_{864900}(73,\cdot)\)	864900.ckc	1860	no	\(1\)	\(1\)	\(e\left(\frac{1363}{1860}\right)\)	\(e\left(\frac{763}{930}\right)\)	\(e\left(\frac{1103}{1860}\right)\)	\(e\left(\frac{1021}{1860}\right)\)	\(e\left(\frac{29}{930}\right)\)	\(e\left(\frac{109}{124}\right)\)	\(e\left(\frac{4}{31}\right)\)	\(e\left(\frac{1537}{1860}\right)\)	\(e\left(\frac{314}{465}\right)\)	\(e\left(\frac{679}{1860}\right)\)
\(\chi_{864900}(77,\cdot)\)	864900.cgs	1860	no	\(-1\)	\(1\)	\(e\left(\frac{1241}{1860}\right)\)	\(e\left(\frac{161}{465}\right)\)	\(e\left(\frac{1129}{1860}\right)\)	\(e\left(\frac{11}{620}\right)\)	\(e\left(\frac{197}{310}\right)\)	\(e\left(\frac{907}{1860}\right)\)	\(e\left(\frac{97}{930}\right)\)	\(e\left(\frac{149}{620}\right)\)	\(e\left(\frac{79}{186}\right)\)	\(e\left(\frac{1553}{1860}\right)\)
\(\chi_{864900}(79,\cdot)\)	864900.cdg	930	yes	\(1\)	\(1\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{347}{465}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{419}{465}\right)\)	\(e\left(\frac{157}{930}\right)\)	\(e\left(\frac{97}{930}\right)\)	\(e\left(\frac{779}{930}\right)\)	\(e\left(\frac{11}{465}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{171}{310}\right)\)
\(\chi_{864900}(83,\cdot)\)	864900.cfx	1860	yes	\(1\)	\(1\)	\(e\left(\frac{149}{1860}\right)\)	\(e\left(\frac{193}{310}\right)\)	\(e\left(\frac{139}{1860}\right)\)	\(e\left(\frac{763}{1860}\right)\)	\(e\left(\frac{211}{465}\right)\)	\(e\left(\frac{319}{372}\right)\)	\(e\left(\frac{175}{186}\right)\)	\(e\left(\frac{1441}{1860}\right)\)	\(e\left(\frac{389}{930}\right)\)	\(e\left(\frac{137}{1860}\right)\)
\(\chi_{864900}(89,\cdot)\)	864900.blm	310	no	\(1\)	\(1\)	\(e\left(\frac{273}{310}\right)\)	\(e\left(\frac{83}{155}\right)\)	\(e\left(\frac{54}{155}\right)\)	\(e\left(\frac{81}{310}\right)\)	\(e\left(\frac{19}{155}\right)\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{116}{155}\right)\)	\(e\left(\frac{251}{310}\right)\)	\(e\left(\frac{22}{155}\right)\)
\(\chi_{864900}(91,\cdot)\)	864900.blc	310	no	\(1\)	\(1\)	\(e\left(\frac{239}{310}\right)\)	\(e\left(\frac{78}{155}\right)\)	\(e\left(\frac{131}{310}\right)\)	\(e\left(\frac{137}{310}\right)\)	\(e\left(\frac{243}{310}\right)\)	\(e\left(\frac{119}{155}\right)\)	\(e\left(\frac{21}{310}\right)\)	\(e\left(\frac{193}{310}\right)\)	\(e\left(\frac{2}{31}\right)\)	\(e\left(\frac{126}{155}\right)\)
\(\chi_{864900}(97,\cdot)\)	864900.cgu	1860	no	\(-1\)	\(1\)	\(e\left(\frac{973}{1860}\right)\)	\(e\left(\frac{196}{465}\right)\)	\(e\left(\frac{211}{372}\right)\)	\(e\left(\frac{107}{124}\right)\)	\(e\left(\frac{287}{310}\right)\)	\(e\left(\frac{623}{1860}\right)\)	\(e\left(\frac{203}{930}\right)\)	\(e\left(\frac{83}{620}\right)\)	\(e\left(\frac{107}{465}\right)\)	\(e\left(\frac{439}{1860}\right)\)
\(\chi_{864900}(101,\cdot)\)	864900.bwk	930	no	\(-1\)	\(1\)	\(e\left(\frac{448}{465}\right)\)	\(e\left(\frac{641}{930}\right)\)	\(e\left(\frac{461}{465}\right)\)	\(e\left(\frac{153}{310}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{379}{930}\right)\)	\(e\left(\frac{503}{930}\right)\)	\(e\left(\frac{8}{31}\right)\)	\(e\left(\frac{823}{930}\right)\)	\(e\left(\frac{259}{465}\right)\)
\(\chi_{864900}(103,\cdot)\)	864900.cft	1860	yes	\(1\)	\(1\)	\(e\left(\frac{23}{620}\right)\)	\(e\left(\frac{85}{186}\right)\)	\(e\left(\frac{299}{620}\right)\)	\(e\left(\frac{1099}{1860}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{1327}{1860}\right)\)	\(e\left(\frac{307}{930}\right)\)	\(e\left(\frac{1579}{1860}\right)\)	\(e\left(\frac{63}{155}\right)\)	\(e\left(\frac{69}{620}\right)\)
\(\chi_{864900}(107,\cdot)\)	864900.chq	1860	no	\(-1\)	\(1\)	\(e\left(\frac{1547}{1860}\right)\)	\(e\left(\frac{13}{465}\right)\)	\(e\left(\frac{1759}{1860}\right)\)	\(e\left(\frac{1823}{1860}\right)\)	\(e\left(\frac{59}{465}\right)\)	\(e\left(\frac{581}{620}\right)\)	\(e\left(\frac{153}{155}\right)\)	\(e\left(\frac{265}{372}\right)\)	\(e\left(\frac{923}{930}\right)\)	\(e\left(\frac{1541}{1860}\right)\)
\(\chi_{864900}(109,\cdot)\)	864900.blo	310	no	\(1\)	\(1\)	\(e\left(\frac{121}{310}\right)\)	\(e\left(\frac{119}{155}\right)\)	\(e\left(\frac{17}{62}\right)\)	\(e\left(\frac{5}{62}\right)\)	\(e\left(\frac{87}{155}\right)\)	\(e\left(\frac{131}{310}\right)\)	\(e\left(\frac{81}{155}\right)\)	\(e\left(\frac{23}{310}\right)\)	\(e\left(\frac{148}{155}\right)\)	\(e\left(\frac{53}{310}\right)\)
\(\chi_{864900}(113,\cdot)\)	864900.cfm	1860	no	\(1\)	\(1\)	\(e\left(\frac{441}{620}\right)\)	\(e\left(\frac{7}{186}\right)\)	\(e\left(\frac{463}{620}\right)\)	\(e\left(\frac{73}{1860}\right)\)	\(e\left(\frac{151}{186}\right)\)	\(e\left(\frac{199}{1860}\right)\)	\(e\left(\frac{197}{465}\right)\)	\(e\left(\frac{583}{1860}\right)\)	\(e\left(\frac{37}{310}\right)\)	\(e\left(\frac{83}{620}\right)\)
\(\chi_{864900}(119,\cdot)\)	864900.cee	930	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{29}{310}\right)\)	\(e\left(\frac{289}{465}\right)\)	\(e\left(\frac{821}{930}\right)\)	\(e\left(\frac{371}{930}\right)\)	\(e\left(\frac{371}{465}\right)\)	\(e\left(\frac{247}{465}\right)\)	\(e\left(\frac{289}{465}\right)\)	\(e\left(\frac{593}{930}\right)\)	\(e\left(\frac{113}{186}\right)\)
\(\chi_{864900}(121,\cdot)\)	864900.bpc	465	no	\(1\)	\(1\)	\(e\left(\frac{184}{465}\right)\)	\(e\left(\frac{46}{155}\right)\)	\(e\left(\frac{284}{465}\right)\)	\(e\left(\frac{368}{465}\right)\)	\(e\left(\frac{209}{465}\right)\)	\(e\left(\frac{65}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{218}{465}\right)\)	\(e\left(\frac{397}{465}\right)\)

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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.