LMFDB - Group of Dirichlet characters of modulus 18225

sage:H = DirichletGroup(18225)

pari:g = idealstar(,18225,2)

Character group

sage:G.order() pari:g.no
Order	=	9720
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4860}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{18225}(4376,\cdot)$, $\chi_{18225}(13852,\cdot)$

First 32 of 9720 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(1,\cdot)$	18225.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{18225}(2,\cdot)$	18225.cs	4860	yes	$1$	$1$	$e\left(\frac{253}{4860}\right)$	$e\left(\frac{253}{2430}\right)$	$e\left(\frac{59}{972}\right)$	$e\left(\frac{253}{1620}\right)$	$e\left(\frac{929}{2430}\right)$	$e\left(\frac{3077}{4860}\right)$	$e\left(\frac{137}{1215}\right)$	$e\left(\frac{253}{1215}\right)$	$e\left(\frac{1163}{1620}\right)$	$e\left(\frac{449}{810}\right)$
$\chi_{18225}(4,\cdot)$	18225.cp	2430	yes	$1$	$1$	$e\left(\frac{253}{2430}\right)$	$e\left(\frac{253}{1215}\right)$	$e\left(\frac{59}{486}\right)$	$e\left(\frac{253}{810}\right)$	$e\left(\frac{929}{1215}\right)$	$e\left(\frac{647}{2430}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{506}{1215}\right)$	$e\left(\frac{353}{810}\right)$	$e\left(\frac{44}{405}\right)$
$\chi_{18225}(7,\cdot)$	18225.ck	972	no	$-1$	$1$	$e\left(\frac{59}{972}\right)$	$e\left(\frac{59}{486}\right)$	$e\left(\frac{647}{972}\right)$	$e\left(\frac{59}{324}\right)$	$e\left(\frac{104}{243}\right)$	$e\left(\frac{877}{972}\right)$	$e\left(\frac{353}{486}\right)$	$e\left(\frac{59}{243}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{49}{162}\right)$
$\chi_{18225}(8,\cdot)$	18225.cn	1620	no	$1$	$1$	$e\left(\frac{253}{1620}\right)$	$e\left(\frac{253}{810}\right)$	$e\left(\frac{59}{324}\right)$	$e\left(\frac{253}{540}\right)$	$e\left(\frac{119}{810}\right)$	$e\left(\frac{1457}{1620}\right)$	$e\left(\frac{137}{405}\right)$	$e\left(\frac{253}{405}\right)$	$e\left(\frac{83}{540}\right)$	$e\left(\frac{179}{270}\right)$
$\chi_{18225}(11,\cdot)$	18225.cq	2430	yes	$-1$	$1$	$e\left(\frac{929}{2430}\right)$	$e\left(\frac{929}{1215}\right)$	$e\left(\frac{104}{243}\right)$	$e\left(\frac{119}{810}\right)$	$e\left(\frac{1439}{2430}\right)$	$e\left(\frac{638}{1215}\right)$	$e\left(\frac{1969}{2430}\right)$	$e\left(\frac{643}{1215}\right)$	$e\left(\frac{499}{810}\right)$	$e\left(\frac{232}{405}\right)$
$\chi_{18225}(13,\cdot)$	18225.ct	4860	yes	$-1$	$1$	$e\left(\frac{3077}{4860}\right)$	$e\left(\frac{647}{2430}\right)$	$e\left(\frac{877}{972}\right)$	$e\left(\frac{1457}{1620}\right)$	$e\left(\frac{638}{1215}\right)$	$e\left(\frac{4123}{4860}\right)$	$e\left(\frac{1301}{2430}\right)$	$e\left(\frac{647}{1215}\right)$	$e\left(\frac{1447}{1620}\right)$	$e\left(\frac{271}{810}\right)$
$\chi_{18225}(14,\cdot)$	18225.cr	2430	yes	$-1$	$1$	$e\left(\frac{137}{1215}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{353}{486}\right)$	$e\left(\frac{137}{405}\right)$	$e\left(\frac{1969}{2430}\right)$	$e\left(\frac{1301}{2430}\right)$	$e\left(\frac{2039}{2430}\right)$	$e\left(\frac{548}{1215}\right)$	$e\left(\frac{292}{405}\right)$	$e\left(\frac{347}{405}\right)$
$\chi_{18225}(16,\cdot)$	18225.cm	1215	yes	$1$	$1$	$e\left(\frac{253}{1215}\right)$	$e\left(\frac{506}{1215}\right)$	$e\left(\frac{59}{243}\right)$	$e\left(\frac{253}{405}\right)$	$e\left(\frac{643}{1215}\right)$	$e\left(\frac{647}{1215}\right)$	$e\left(\frac{548}{1215}\right)$	$e\left(\frac{1012}{1215}\right)$	$e\left(\frac{353}{405}\right)$	$e\left(\frac{88}{405}\right)$
$\chi_{18225}(17,\cdot)$	18225.cn	1620	no	$1$	$1$	$e\left(\frac{1163}{1620}\right)$	$e\left(\frac{353}{810}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{83}{540}\right)$	$e\left(\frac{499}{810}\right)$	$e\left(\frac{1447}{1620}\right)$	$e\left(\frac{292}{405}\right)$	$e\left(\frac{353}{405}\right)$	$e\left(\frac{373}{540}\right)$	$e\left(\frac{79}{270}\right)$
$\chi_{18225}(19,\cdot)$	18225.cj	810	no	$1$	$1$	$e\left(\frac{449}{810}\right)$	$e\left(\frac{44}{405}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{179}{270}\right)$	$e\left(\frac{232}{405}\right)$	$e\left(\frac{271}{810}\right)$	$e\left(\frac{347}{405}\right)$	$e\left(\frac{88}{405}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{37}{135}\right)$
$\chi_{18225}(22,\cdot)$	18225.ct	4860	yes	$-1$	$1$	$e\left(\frac{2111}{4860}\right)$	$e\left(\frac{2111}{2430}\right)$	$e\left(\frac{475}{972}\right)$	$e\left(\frac{491}{1620}\right)$	$e\left(\frac{1184}{1215}\right)$	$e\left(\frac{769}{4860}\right)$	$e\left(\frac{2243}{2430}\right)$	$e\left(\frac{896}{1215}\right)$	$e\left(\frac{541}{1620}\right)$	$e\left(\frac{103}{810}\right)$
$\chi_{18225}(23,\cdot)$	18225.cs	4860	yes	$1$	$1$	$e\left(\frac{1703}{4860}\right)$	$e\left(\frac{1703}{2430}\right)$	$e\left(\frac{109}{972}\right)$	$e\left(\frac{83}{1620}\right)$	$e\left(\frac{769}{2430}\right)$	$e\left(\frac{907}{4860}\right)$	$e\left(\frac{562}{1215}\right)$	$e\left(\frac{488}{1215}\right)$	$e\left(\frac{913}{1620}\right)$	$e\left(\frac{349}{810}\right)$
$\chi_{18225}(26,\cdot)$	18225.bf	54	no	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{18225}(28,\cdot)$	18225.cf	540	no	$-1$	$1$	$e\left(\frac{89}{540}\right)$	$e\left(\frac{89}{270}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{26}{135}\right)$	$e\left(\frac{91}{540}\right)$	$e\left(\frac{257}{270}\right)$	$e\left(\frac{89}{135}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{18225}(29,\cdot)$	18225.cr	2430	yes	$-1$	$1$	$e\left(\frac{619}{1215}\right)$	$e\left(\frac{23}{1215}\right)$	$e\left(\frac{403}{486}\right)$	$e\left(\frac{214}{405}\right)$	$e\left(\frac{1163}{2430}\right)$	$e\left(\frac{2047}{2430}\right)$	$e\left(\frac{823}{2430}\right)$	$e\left(\frac{46}{1215}\right)$	$e\left(\frac{329}{405}\right)$	$e\left(\frac{4}{405}\right)$
$\chi_{18225}(31,\cdot)$	18225.cm	1215	yes	$1$	$1$	$e\left(\frac{131}{1215}\right)$	$e\left(\frac{262}{1215}\right)$	$e\left(\frac{214}{243}\right)$	$e\left(\frac{131}{405}\right)$	$e\left(\frac{866}{1215}\right)$	$e\left(\frac{724}{1215}\right)$	$e\left(\frac{1201}{1215}\right)$	$e\left(\frac{524}{1215}\right)$	$e\left(\frac{226}{405}\right)$	$e\left(\frac{116}{405}\right)$
$\chi_{18225}(32,\cdot)$	18225.cl	972	no	$1$	$1$	$e\left(\frac{253}{972}\right)$	$e\left(\frac{253}{486}\right)$	$e\left(\frac{295}{972}\right)$	$e\left(\frac{253}{324}\right)$	$e\left(\frac{443}{486}\right)$	$e\left(\frac{161}{972}\right)$	$e\left(\frac{137}{243}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{191}{324}\right)$	$e\left(\frac{125}{162}\right)$
$\chi_{18225}(34,\cdot)$	18225.cp	2430	yes	$1$	$1$	$e\left(\frac{1871}{2430}\right)$	$e\left(\frac{656}{1215}\right)$	$e\left(\frac{31}{486}\right)$	$e\left(\frac{251}{810}\right)$	$e\left(\frac{1213}{1215}\right)$	$e\left(\frac{1279}{2430}\right)$	$e\left(\frac{1013}{1215}\right)$	$e\left(\frac{97}{1215}\right)$	$e\left(\frac{331}{810}\right)$	$e\left(\frac{343}{405}\right)$
$\chi_{18225}(37,\cdot)$	18225.co	1620	no	$-1$	$1$	$e\left(\frac{1589}{1620}\right)$	$e\left(\frac{779}{810}\right)$	$e\left(\frac{133}{324}\right)$	$e\left(\frac{509}{540}\right)$	$e\left(\frac{176}{405}\right)$	$e\left(\frac{1291}{1620}\right)$	$e\left(\frac{317}{810}\right)$	$e\left(\frac{374}{405}\right)$	$e\left(\frac{199}{540}\right)$	$e\left(\frac{247}{270}\right)$
$\chi_{18225}(38,\cdot)$	18225.cs	4860	yes	$1$	$1$	$e\left(\frac{2947}{4860}\right)$	$e\left(\frac{517}{2430}\right)$	$e\left(\frac{353}{972}\right)$	$e\left(\frac{1327}{1620}\right)$	$e\left(\frac{2321}{2430}\right)$	$e\left(\frac{4703}{4860}\right)$	$e\left(\frac{1178}{1215}\right)$	$e\left(\frac{517}{1215}\right)$	$e\left(\frac{17}{1620}\right)$	$e\left(\frac{671}{810}\right)$
$\chi_{18225}(41,\cdot)$	18225.cq	2430	yes	$-1$	$1$	$e\left(\frac{1561}{2430}\right)$	$e\left(\frac{346}{1215}\right)$	$e\left(\frac{73}{243}\right)$	$e\left(\frac{751}{810}\right)$	$e\left(\frac{961}{2430}\right)$	$e\left(\frac{817}{1215}\right)$	$e\left(\frac{2291}{2430}\right)$	$e\left(\frac{692}{1215}\right)$	$e\left(\frac{161}{810}\right)$	$e\left(\frac{113}{405}\right)$
$\chi_{18225}(43,\cdot)$	18225.ck	972	no	$-1$	$1$	$e\left(\frac{665}{972}\right)$	$e\left(\frac{179}{486}\right)$	$e\left(\frac{785}{972}\right)$	$e\left(\frac{17}{324}\right)$	$e\left(\frac{89}{243}\right)$	$e\left(\frac{379}{972}\right)$	$e\left(\frac{239}{486}\right)$	$e\left(\frac{179}{243}\right)$	$e\left(\frac{187}{324}\right)$	$e\left(\frac{91}{162}\right)$
$\chi_{18225}(44,\cdot)$	18225.ci	810	no	$-1$	$1$	$e\left(\frac{197}{405}\right)$	$e\left(\frac{394}{405}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{62}{135}\right)$	$e\left(\frac{289}{810}\right)$	$e\left(\frac{641}{810}\right)$	$e\left(\frac{29}{810}\right)$	$e\left(\frac{383}{405}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{92}{135}\right)$
$\chi_{18225}(46,\cdot)$	18225.cb	405	no	$1$	$1$	$e\left(\frac{163}{405}\right)$	$e\left(\frac{326}{405}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{28}{135}\right)$	$e\left(\frac{283}{405}\right)$	$e\left(\frac{332}{405}\right)$	$e\left(\frac{233}{405}\right)$	$e\left(\frac{247}{405}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{133}{135}\right)$
$\chi_{18225}(47,\cdot)$	18225.cs	4860	yes	$1$	$1$	$e\left(\frac{3121}{4860}\right)$	$e\left(\frac{691}{2430}\right)$	$e\left(\frac{359}{972}\right)$	$e\left(\frac{1501}{1620}\right)$	$e\left(\frac{1913}{2430}\right)$	$e\left(\frac{749}{4860}\right)$	$e\left(\frac{14}{1215}\right)$	$e\left(\frac{691}{1215}\right)$	$e\left(\frac{311}{1620}\right)$	$e\left(\frac{173}{810}\right)$
$\chi_{18225}(49,\cdot)$	18225.ce	486	no	$1$	$1$	$e\left(\frac{59}{486}\right)$	$e\left(\frac{59}{243}\right)$	$e\left(\frac{161}{486}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{208}{243}\right)$	$e\left(\frac{391}{486}\right)$	$e\left(\frac{110}{243}\right)$	$e\left(\frac{118}{243}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{49}{81}\right)$
$\chi_{18225}(52,\cdot)$	18225.ct	4860	yes	$-1$	$1$	$e\left(\frac{3583}{4860}\right)$	$e\left(\frac{1153}{2430}\right)$	$e\left(\frac{23}{972}\right)$	$e\left(\frac{343}{1620}\right)$	$e\left(\frac{352}{1215}\right)$	$e\left(\frac{557}{4860}\right)$	$e\left(\frac{1849}{2430}\right)$	$e\left(\frac{1153}{1215}\right)$	$e\left(\frac{533}{1620}\right)$	$e\left(\frac{359}{810}\right)$
$\chi_{18225}(53,\cdot)$	18225.cg	540	no	$1$	$1$	$e\left(\frac{119}{540}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{331}{540}\right)$	$e\left(\frac{121}{135}\right)$	$e\left(\frac{119}{135}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{18225}(56,\cdot)$	18225.cq	2430	yes	$-1$	$1$	$e\left(\frac{527}{2430}\right)$	$e\left(\frac{527}{1215}\right)$	$e\left(\frac{206}{243}\right)$	$e\left(\frac{527}{810}\right)$	$e\left(\frac{1397}{2430}\right)$	$e\left(\frac{974}{1215}\right)$	$e\left(\frac{157}{2430}\right)$	$e\left(\frac{1054}{1215}\right)$	$e\left(\frac{127}{810}\right)$	$e\left(\frac{391}{405}\right)$
$\chi_{18225}(58,\cdot)$	18225.ct	4860	yes	$-1$	$1$	$e\left(\frac{2729}{4860}\right)$	$e\left(\frac{299}{2430}\right)$	$e\left(\frac{865}{972}\right)$	$e\left(\frac{1109}{1620}\right)$	$e\left(\frac{1046}{1215}\right)$	$e\left(\frac{2311}{4860}\right)$	$e\left(\frac{1097}{2430}\right)$	$e\left(\frac{299}{1215}\right)$	$e\left(\frac{859}{1620}\right)$	$e\left(\frac{457}{810}\right)$
$\chi_{18225}(59,\cdot)$	18225.cr	2430	yes	$-1$	$1$	$e\left(\frac{818}{1215}\right)$	$e\left(\frac{421}{1215}\right)$	$e\left(\frac{467}{486}\right)$	$e\left(\frac{8}{405}\right)$	$e\left(\frac{1531}{2430}\right)$	$e\left(\frac{1019}{2430}\right)$	$e\left(\frac{1541}{2430}\right)$	$e\left(\frac{842}{1215}\right)$	$e\left(\frac{88}{405}\right)$	$e\left(\frac{38}{405}\right)$

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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	$18225$
Structure	\(C_{2}\times C_{4860}\)
Order	$9720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(1,\cdot)\)	18225.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{18225}(2,\cdot)\)	18225.cs	4860	yes	\(1\)	\(1\)	\(e\left(\frac{253}{4860}\right)\)	\(e\left(\frac{253}{2430}\right)\)	\(e\left(\frac{59}{972}\right)\)	\(e\left(\frac{253}{1620}\right)\)	\(e\left(\frac{929}{2430}\right)\)	\(e\left(\frac{3077}{4860}\right)\)	\(e\left(\frac{137}{1215}\right)\)	\(e\left(\frac{253}{1215}\right)\)	\(e\left(\frac{1163}{1620}\right)\)	\(e\left(\frac{449}{810}\right)\)
\(\chi_{18225}(4,\cdot)\)	18225.cp	2430	yes	\(1\)	\(1\)	\(e\left(\frac{253}{2430}\right)\)	\(e\left(\frac{253}{1215}\right)\)	\(e\left(\frac{59}{486}\right)\)	\(e\left(\frac{253}{810}\right)\)	\(e\left(\frac{929}{1215}\right)\)	\(e\left(\frac{647}{2430}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{506}{1215}\right)\)	\(e\left(\frac{353}{810}\right)\)	\(e\left(\frac{44}{405}\right)\)
\(\chi_{18225}(7,\cdot)\)	18225.ck	972	no	\(-1\)	\(1\)	\(e\left(\frac{59}{972}\right)\)	\(e\left(\frac{59}{486}\right)\)	\(e\left(\frac{647}{972}\right)\)	\(e\left(\frac{59}{324}\right)\)	\(e\left(\frac{104}{243}\right)\)	\(e\left(\frac{877}{972}\right)\)	\(e\left(\frac{353}{486}\right)\)	\(e\left(\frac{59}{243}\right)\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{49}{162}\right)\)
\(\chi_{18225}(8,\cdot)\)	18225.cn	1620	no	\(1\)	\(1\)	\(e\left(\frac{253}{1620}\right)\)	\(e\left(\frac{253}{810}\right)\)	\(e\left(\frac{59}{324}\right)\)	\(e\left(\frac{253}{540}\right)\)	\(e\left(\frac{119}{810}\right)\)	\(e\left(\frac{1457}{1620}\right)\)	\(e\left(\frac{137}{405}\right)\)	\(e\left(\frac{253}{405}\right)\)	\(e\left(\frac{83}{540}\right)\)	\(e\left(\frac{179}{270}\right)\)
\(\chi_{18225}(11,\cdot)\)	18225.cq	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{929}{2430}\right)\)	\(e\left(\frac{929}{1215}\right)\)	\(e\left(\frac{104}{243}\right)\)	\(e\left(\frac{119}{810}\right)\)	\(e\left(\frac{1439}{2430}\right)\)	\(e\left(\frac{638}{1215}\right)\)	\(e\left(\frac{1969}{2430}\right)\)	\(e\left(\frac{643}{1215}\right)\)	\(e\left(\frac{499}{810}\right)\)	\(e\left(\frac{232}{405}\right)\)
\(\chi_{18225}(13,\cdot)\)	18225.ct	4860	yes	\(-1\)	\(1\)	\(e\left(\frac{3077}{4860}\right)\)	\(e\left(\frac{647}{2430}\right)\)	\(e\left(\frac{877}{972}\right)\)	\(e\left(\frac{1457}{1620}\right)\)	\(e\left(\frac{638}{1215}\right)\)	\(e\left(\frac{4123}{4860}\right)\)	\(e\left(\frac{1301}{2430}\right)\)	\(e\left(\frac{647}{1215}\right)\)	\(e\left(\frac{1447}{1620}\right)\)	\(e\left(\frac{271}{810}\right)\)
\(\chi_{18225}(14,\cdot)\)	18225.cr	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{1215}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{353}{486}\right)\)	\(e\left(\frac{137}{405}\right)\)	\(e\left(\frac{1969}{2430}\right)\)	\(e\left(\frac{1301}{2430}\right)\)	\(e\left(\frac{2039}{2430}\right)\)	\(e\left(\frac{548}{1215}\right)\)	\(e\left(\frac{292}{405}\right)\)	\(e\left(\frac{347}{405}\right)\)
\(\chi_{18225}(16,\cdot)\)	18225.cm	1215	yes	\(1\)	\(1\)	\(e\left(\frac{253}{1215}\right)\)	\(e\left(\frac{506}{1215}\right)\)	\(e\left(\frac{59}{243}\right)\)	\(e\left(\frac{253}{405}\right)\)	\(e\left(\frac{643}{1215}\right)\)	\(e\left(\frac{647}{1215}\right)\)	\(e\left(\frac{548}{1215}\right)\)	\(e\left(\frac{1012}{1215}\right)\)	\(e\left(\frac{353}{405}\right)\)	\(e\left(\frac{88}{405}\right)\)
\(\chi_{18225}(17,\cdot)\)	18225.cn	1620	no	\(1\)	\(1\)	\(e\left(\frac{1163}{1620}\right)\)	\(e\left(\frac{353}{810}\right)\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{83}{540}\right)\)	\(e\left(\frac{499}{810}\right)\)	\(e\left(\frac{1447}{1620}\right)\)	\(e\left(\frac{292}{405}\right)\)	\(e\left(\frac{353}{405}\right)\)	\(e\left(\frac{373}{540}\right)\)	\(e\left(\frac{79}{270}\right)\)
\(\chi_{18225}(19,\cdot)\)	18225.cj	810	no	\(1\)	\(1\)	\(e\left(\frac{449}{810}\right)\)	\(e\left(\frac{44}{405}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{179}{270}\right)\)	\(e\left(\frac{232}{405}\right)\)	\(e\left(\frac{271}{810}\right)\)	\(e\left(\frac{347}{405}\right)\)	\(e\left(\frac{88}{405}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{37}{135}\right)\)
\(\chi_{18225}(22,\cdot)\)	18225.ct	4860	yes	\(-1\)	\(1\)	\(e\left(\frac{2111}{4860}\right)\)	\(e\left(\frac{2111}{2430}\right)\)	\(e\left(\frac{475}{972}\right)\)	\(e\left(\frac{491}{1620}\right)\)	\(e\left(\frac{1184}{1215}\right)\)	\(e\left(\frac{769}{4860}\right)\)	\(e\left(\frac{2243}{2430}\right)\)	\(e\left(\frac{896}{1215}\right)\)	\(e\left(\frac{541}{1620}\right)\)	\(e\left(\frac{103}{810}\right)\)
\(\chi_{18225}(23,\cdot)\)	18225.cs	4860	yes	\(1\)	\(1\)	\(e\left(\frac{1703}{4860}\right)\)	\(e\left(\frac{1703}{2430}\right)\)	\(e\left(\frac{109}{972}\right)\)	\(e\left(\frac{83}{1620}\right)\)	\(e\left(\frac{769}{2430}\right)\)	\(e\left(\frac{907}{4860}\right)\)	\(e\left(\frac{562}{1215}\right)\)	\(e\left(\frac{488}{1215}\right)\)	\(e\left(\frac{913}{1620}\right)\)	\(e\left(\frac{349}{810}\right)\)
\(\chi_{18225}(26,\cdot)\)	18225.bf	54	no	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{18225}(28,\cdot)\)	18225.cf	540	no	\(-1\)	\(1\)	\(e\left(\frac{89}{540}\right)\)	\(e\left(\frac{89}{270}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{26}{135}\right)\)	\(e\left(\frac{91}{540}\right)\)	\(e\left(\frac{257}{270}\right)\)	\(e\left(\frac{89}{135}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{18225}(29,\cdot)\)	18225.cr	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{619}{1215}\right)\)	\(e\left(\frac{23}{1215}\right)\)	\(e\left(\frac{403}{486}\right)\)	\(e\left(\frac{214}{405}\right)\)	\(e\left(\frac{1163}{2430}\right)\)	\(e\left(\frac{2047}{2430}\right)\)	\(e\left(\frac{823}{2430}\right)\)	\(e\left(\frac{46}{1215}\right)\)	\(e\left(\frac{329}{405}\right)\)	\(e\left(\frac{4}{405}\right)\)
\(\chi_{18225}(31,\cdot)\)	18225.cm	1215	yes	\(1\)	\(1\)	\(e\left(\frac{131}{1215}\right)\)	\(e\left(\frac{262}{1215}\right)\)	\(e\left(\frac{214}{243}\right)\)	\(e\left(\frac{131}{405}\right)\)	\(e\left(\frac{866}{1215}\right)\)	\(e\left(\frac{724}{1215}\right)\)	\(e\left(\frac{1201}{1215}\right)\)	\(e\left(\frac{524}{1215}\right)\)	\(e\left(\frac{226}{405}\right)\)	\(e\left(\frac{116}{405}\right)\)
\(\chi_{18225}(32,\cdot)\)	18225.cl	972	no	\(1\)	\(1\)	\(e\left(\frac{253}{972}\right)\)	\(e\left(\frac{253}{486}\right)\)	\(e\left(\frac{295}{972}\right)\)	\(e\left(\frac{253}{324}\right)\)	\(e\left(\frac{443}{486}\right)\)	\(e\left(\frac{161}{972}\right)\)	\(e\left(\frac{137}{243}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{191}{324}\right)\)	\(e\left(\frac{125}{162}\right)\)
\(\chi_{18225}(34,\cdot)\)	18225.cp	2430	yes	\(1\)	\(1\)	\(e\left(\frac{1871}{2430}\right)\)	\(e\left(\frac{656}{1215}\right)\)	\(e\left(\frac{31}{486}\right)\)	\(e\left(\frac{251}{810}\right)\)	\(e\left(\frac{1213}{1215}\right)\)	\(e\left(\frac{1279}{2430}\right)\)	\(e\left(\frac{1013}{1215}\right)\)	\(e\left(\frac{97}{1215}\right)\)	\(e\left(\frac{331}{810}\right)\)	\(e\left(\frac{343}{405}\right)\)
\(\chi_{18225}(37,\cdot)\)	18225.co	1620	no	\(-1\)	\(1\)	\(e\left(\frac{1589}{1620}\right)\)	\(e\left(\frac{779}{810}\right)\)	\(e\left(\frac{133}{324}\right)\)	\(e\left(\frac{509}{540}\right)\)	\(e\left(\frac{176}{405}\right)\)	\(e\left(\frac{1291}{1620}\right)\)	\(e\left(\frac{317}{810}\right)\)	\(e\left(\frac{374}{405}\right)\)	\(e\left(\frac{199}{540}\right)\)	\(e\left(\frac{247}{270}\right)\)
\(\chi_{18225}(38,\cdot)\)	18225.cs	4860	yes	\(1\)	\(1\)	\(e\left(\frac{2947}{4860}\right)\)	\(e\left(\frac{517}{2430}\right)\)	\(e\left(\frac{353}{972}\right)\)	\(e\left(\frac{1327}{1620}\right)\)	\(e\left(\frac{2321}{2430}\right)\)	\(e\left(\frac{4703}{4860}\right)\)	\(e\left(\frac{1178}{1215}\right)\)	\(e\left(\frac{517}{1215}\right)\)	\(e\left(\frac{17}{1620}\right)\)	\(e\left(\frac{671}{810}\right)\)
\(\chi_{18225}(41,\cdot)\)	18225.cq	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1561}{2430}\right)\)	\(e\left(\frac{346}{1215}\right)\)	\(e\left(\frac{73}{243}\right)\)	\(e\left(\frac{751}{810}\right)\)	\(e\left(\frac{961}{2430}\right)\)	\(e\left(\frac{817}{1215}\right)\)	\(e\left(\frac{2291}{2430}\right)\)	\(e\left(\frac{692}{1215}\right)\)	\(e\left(\frac{161}{810}\right)\)	\(e\left(\frac{113}{405}\right)\)
\(\chi_{18225}(43,\cdot)\)	18225.ck	972	no	\(-1\)	\(1\)	\(e\left(\frac{665}{972}\right)\)	\(e\left(\frac{179}{486}\right)\)	\(e\left(\frac{785}{972}\right)\)	\(e\left(\frac{17}{324}\right)\)	\(e\left(\frac{89}{243}\right)\)	\(e\left(\frac{379}{972}\right)\)	\(e\left(\frac{239}{486}\right)\)	\(e\left(\frac{179}{243}\right)\)	\(e\left(\frac{187}{324}\right)\)	\(e\left(\frac{91}{162}\right)\)
\(\chi_{18225}(44,\cdot)\)	18225.ci	810	no	\(-1\)	\(1\)	\(e\left(\frac{197}{405}\right)\)	\(e\left(\frac{394}{405}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{62}{135}\right)\)	\(e\left(\frac{289}{810}\right)\)	\(e\left(\frac{641}{810}\right)\)	\(e\left(\frac{29}{810}\right)\)	\(e\left(\frac{383}{405}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{92}{135}\right)\)
\(\chi_{18225}(46,\cdot)\)	18225.cb	405	no	\(1\)	\(1\)	\(e\left(\frac{163}{405}\right)\)	\(e\left(\frac{326}{405}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{28}{135}\right)\)	\(e\left(\frac{283}{405}\right)\)	\(e\left(\frac{332}{405}\right)\)	\(e\left(\frac{233}{405}\right)\)	\(e\left(\frac{247}{405}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{133}{135}\right)\)
\(\chi_{18225}(47,\cdot)\)	18225.cs	4860	yes	\(1\)	\(1\)	\(e\left(\frac{3121}{4860}\right)\)	\(e\left(\frac{691}{2430}\right)\)	\(e\left(\frac{359}{972}\right)\)	\(e\left(\frac{1501}{1620}\right)\)	\(e\left(\frac{1913}{2430}\right)\)	\(e\left(\frac{749}{4860}\right)\)	\(e\left(\frac{14}{1215}\right)\)	\(e\left(\frac{691}{1215}\right)\)	\(e\left(\frac{311}{1620}\right)\)	\(e\left(\frac{173}{810}\right)\)
\(\chi_{18225}(49,\cdot)\)	18225.ce	486	no	\(1\)	\(1\)	\(e\left(\frac{59}{486}\right)\)	\(e\left(\frac{59}{243}\right)\)	\(e\left(\frac{161}{486}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{208}{243}\right)\)	\(e\left(\frac{391}{486}\right)\)	\(e\left(\frac{110}{243}\right)\)	\(e\left(\frac{118}{243}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)
\(\chi_{18225}(52,\cdot)\)	18225.ct	4860	yes	\(-1\)	\(1\)	\(e\left(\frac{3583}{4860}\right)\)	\(e\left(\frac{1153}{2430}\right)\)	\(e\left(\frac{23}{972}\right)\)	\(e\left(\frac{343}{1620}\right)\)	\(e\left(\frac{352}{1215}\right)\)	\(e\left(\frac{557}{4860}\right)\)	\(e\left(\frac{1849}{2430}\right)\)	\(e\left(\frac{1153}{1215}\right)\)	\(e\left(\frac{533}{1620}\right)\)	\(e\left(\frac{359}{810}\right)\)
\(\chi_{18225}(53,\cdot)\)	18225.cg	540	no	\(1\)	\(1\)	\(e\left(\frac{119}{540}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{331}{540}\right)\)	\(e\left(\frac{121}{135}\right)\)	\(e\left(\frac{119}{135}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{18225}(56,\cdot)\)	18225.cq	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{527}{2430}\right)\)	\(e\left(\frac{527}{1215}\right)\)	\(e\left(\frac{206}{243}\right)\)	\(e\left(\frac{527}{810}\right)\)	\(e\left(\frac{1397}{2430}\right)\)	\(e\left(\frac{974}{1215}\right)\)	\(e\left(\frac{157}{2430}\right)\)	\(e\left(\frac{1054}{1215}\right)\)	\(e\left(\frac{127}{810}\right)\)	\(e\left(\frac{391}{405}\right)\)
\(\chi_{18225}(58,\cdot)\)	18225.ct	4860	yes	\(-1\)	\(1\)	\(e\left(\frac{2729}{4860}\right)\)	\(e\left(\frac{299}{2430}\right)\)	\(e\left(\frac{865}{972}\right)\)	\(e\left(\frac{1109}{1620}\right)\)	\(e\left(\frac{1046}{1215}\right)\)	\(e\left(\frac{2311}{4860}\right)\)	\(e\left(\frac{1097}{2430}\right)\)	\(e\left(\frac{299}{1215}\right)\)	\(e\left(\frac{859}{1620}\right)\)	\(e\left(\frac{457}{810}\right)\)
\(\chi_{18225}(59,\cdot)\)	18225.cr	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{818}{1215}\right)\)	\(e\left(\frac{421}{1215}\right)\)	\(e\left(\frac{467}{486}\right)\)	\(e\left(\frac{8}{405}\right)\)	\(e\left(\frac{1531}{2430}\right)\)	\(e\left(\frac{1019}{2430}\right)\)	\(e\left(\frac{1541}{2430}\right)\)	\(e\left(\frac{842}{1215}\right)\)	\(e\left(\frac{88}{405}\right)\)	\(e\left(\frac{38}{405}\right)\)

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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.