LMFDB - Group of Dirichlet characters of modulus 8100

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(8100)

gp:g = idealstar(,8100,2)

magma:G = FullDirichletGroup(8100);

Character group

Order	=	2160	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{540}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{8100}(4051,\cdot)$, $\chi_{8100}(6401,\cdot)$, $\chi_{8100}(7777,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2160 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8100}(1,\cdot)$	8100.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8100}(7,\cdot)$	8100.db	108	no	$1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{8100}(11,\cdot)$	8100.di	270	yes	$1$	$1$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{58}{135}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{128}{135}\right)$	$e\left(\frac{137}{270}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{259}{270}\right)$
$\chi_{8100}(13,\cdot)$	8100.dp	540	no	$-1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{127}{540}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{43}{540}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{88}{135}\right)$
$\chi_{8100}(17,\cdot)$	8100.dd	180	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{8100}(19,\cdot)$	8100.cr	90	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{8100}(23,\cdot)$	8100.dq	540	yes	$-1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{128}{135}\right)$	$e\left(\frac{43}{540}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{427}{540}\right)$	$e\left(\frac{86}{135}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{269}{270}\right)$
$\chi_{8100}(29,\cdot)$	8100.dl	270	no	$-1$	$1$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{137}{270}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{86}{135}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{68}{135}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{193}{270}\right)$
$\chi_{8100}(31,\cdot)$	8100.dm	270	yes	$-1$	$1$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{68}{135}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{31}{135}\right)$
$\chi_{8100}(37,\cdot)$	8100.de	180	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{8100}(41,\cdot)$	8100.dk	270	no	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{259}{270}\right)$	$e\left(\frac{88}{135}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{221}{270}\right)$
$\chi_{8100}(43,\cdot)$	8100.db	108	no	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{8100}(47,\cdot)$	8100.dq	540	yes	$-1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{106}{135}\right)$	$e\left(\frac{101}{540}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{149}{540}\right)$	$e\left(\frac{67}{135}\right)$	$e\left(\frac{241}{270}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{73}{270}\right)$
$\chi_{8100}(49,\cdot)$	8100.cm	54	no	$1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{8100}(53,\cdot)$	8100.co	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{8100}(59,\cdot)$	8100.dn	270	yes	$1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{270}\right)$
$\chi_{8100}(61,\cdot)$	8100.dc	135	no	$1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{43}{135}\right)$	$e\left(\frac{122}{135}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{89}{135}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{32}{135}\right)$
$\chi_{8100}(67,\cdot)$	8100.do	540	yes	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{469}{540}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{331}{540}\right)$	$e\left(\frac{121}{270}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{106}{135}\right)$
$\chi_{8100}(71,\cdot)$	8100.cs	90	no	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{8100}(73,\cdot)$	8100.de	180	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{8100}(77,\cdot)$	8100.dr	540	no	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{211}{270}\right)$	$e\left(\frac{133}{540}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{247}{540}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{19}{135}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{179}{270}\right)$
$\chi_{8100}(79,\cdot)$	8100.dh	270	yes	$-1$	$1$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{13}{270}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{41}{135}\right)$	$e\left(\frac{52}{135}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{119}{135}\right)$
$\chi_{8100}(83,\cdot)$	8100.dq	540	yes	$-1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{19}{135}\right)$	$e\left(\frac{539}{540}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{191}{540}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{19}{270}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{157}{270}\right)$
$\chi_{8100}(89,\cdot)$	8100.cx	90	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{8100}(91,\cdot)$	8100.cw	90	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{8100}(97,\cdot)$	8100.dp	540	no	$-1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{401}{540}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{89}{540}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{44}{135}\right)$
$\chi_{8100}(101,\cdot)$	8100.cl	54	no	$-1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{8100}(103,\cdot)$	8100.do	540	yes	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{127}{270}\right)$	$e\left(\frac{391}{540}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{109}{540}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{131}{270}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{19}{135}\right)$
$\chi_{8100}(107,\cdot)$	8100.be	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{8100}(109,\cdot)$	8100.bz	30	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{8100}(113,\cdot)$	8100.dr	540	no	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{109}{270}\right)$	$e\left(\frac{427}{540}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{253}{540}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{61}{135}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{191}{270}\right)$
$\chi_{8100}(119,\cdot)$	8100.dn	270	yes	$1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{94}{135}\right)$	$e\left(\frac{97}{270}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{187}{270}\right)$

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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	$8100$
Structure	\(C_{2}\times C_{2}\times C_{540}\)
Order	$2160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8100}(1,\cdot)\)	8100.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8100}(7,\cdot)\)	8100.db	108	no	\(1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{8100}(11,\cdot)\)	8100.di	270	yes	\(1\)	\(1\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{58}{135}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{128}{135}\right)\)	\(e\left(\frac{137}{270}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{259}{270}\right)\)
\(\chi_{8100}(13,\cdot)\)	8100.dp	540	no	\(-1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{127}{540}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{43}{540}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{88}{135}\right)\)
\(\chi_{8100}(17,\cdot)\)	8100.dd	180	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{8100}(19,\cdot)\)	8100.cr	90	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{8100}(23,\cdot)\)	8100.dq	540	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{128}{135}\right)\)	\(e\left(\frac{43}{540}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{427}{540}\right)\)	\(e\left(\frac{86}{135}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{269}{270}\right)\)
\(\chi_{8100}(29,\cdot)\)	8100.dl	270	no	\(-1\)	\(1\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{137}{270}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{86}{135}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{68}{135}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{193}{270}\right)\)
\(\chi_{8100}(31,\cdot)\)	8100.dm	270	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{68}{135}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{31}{135}\right)\)
\(\chi_{8100}(37,\cdot)\)	8100.de	180	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{8100}(41,\cdot)\)	8100.dk	270	no	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{88}{135}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{221}{270}\right)\)
\(\chi_{8100}(43,\cdot)\)	8100.db	108	no	\(1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{8100}(47,\cdot)\)	8100.dq	540	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{106}{135}\right)\)	\(e\left(\frac{101}{540}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{149}{540}\right)\)	\(e\left(\frac{67}{135}\right)\)	\(e\left(\frac{241}{270}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{73}{270}\right)\)
\(\chi_{8100}(49,\cdot)\)	8100.cm	54	no	\(1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{8100}(53,\cdot)\)	8100.co	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{8100}(59,\cdot)\)	8100.dn	270	yes	\(1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{270}\right)\)
\(\chi_{8100}(61,\cdot)\)	8100.dc	135	no	\(1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{43}{135}\right)\)	\(e\left(\frac{122}{135}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{89}{135}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{32}{135}\right)\)
\(\chi_{8100}(67,\cdot)\)	8100.do	540	yes	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{469}{540}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{331}{540}\right)\)	\(e\left(\frac{121}{270}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{106}{135}\right)\)
\(\chi_{8100}(71,\cdot)\)	8100.cs	90	no	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{8100}(73,\cdot)\)	8100.de	180	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{8100}(77,\cdot)\)	8100.dr	540	no	\(1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{211}{270}\right)\)	\(e\left(\frac{133}{540}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{247}{540}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{19}{135}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{179}{270}\right)\)
\(\chi_{8100}(79,\cdot)\)	8100.dh	270	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{13}{270}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{41}{135}\right)\)	\(e\left(\frac{52}{135}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{119}{135}\right)\)
\(\chi_{8100}(83,\cdot)\)	8100.dq	540	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{19}{135}\right)\)	\(e\left(\frac{539}{540}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{191}{540}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{19}{270}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{157}{270}\right)\)
\(\chi_{8100}(89,\cdot)\)	8100.cx	90	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{8100}(91,\cdot)\)	8100.cw	90	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{8100}(97,\cdot)\)	8100.dp	540	no	\(-1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{401}{540}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{89}{540}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{44}{135}\right)\)
\(\chi_{8100}(101,\cdot)\)	8100.cl	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{8100}(103,\cdot)\)	8100.do	540	yes	\(1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{127}{270}\right)\)	\(e\left(\frac{391}{540}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{109}{540}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{131}{270}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{19}{135}\right)\)
\(\chi_{8100}(107,\cdot)\)	8100.be	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8100}(109,\cdot)\)	8100.bz	30	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{8100}(113,\cdot)\)	8100.dr	540	no	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{109}{270}\right)\)	\(e\left(\frac{427}{540}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{253}{540}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{61}{135}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{191}{270}\right)\)
\(\chi_{8100}(119,\cdot)\)	8100.dn	270	yes	\(1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{94}{135}\right)\)	\(e\left(\frac{97}{270}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{187}{270}\right)\)

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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.