LMFDB - Group of Dirichlet characters of modulus 82800

Show commands: PariGP / SageMath

sage: H = DirichletGroup(82800)

pari: g = idealstar(,82800,2)

Character group

sage: G.order() pari: g.no
Order	=	21120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{660}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{82800}(10351,\cdot)$, $\chi_{82800}(62101,\cdot)$, $\chi_{82800}(46001,\cdot)$, $\chi_{82800}(76177,\cdot)$, $\chi_{82800}(28801,\cdot)$

First 32 of 21120 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{82800}(1,\cdot)$	82800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{82800}(7,\cdot)$	82800.sg	132	no	$-1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{97}{132}\right)$
$\chi_{82800}(11,\cdot)$	82800.xb	660	yes	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{263}{660}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{581}{660}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{61}{132}\right)$
$\chi_{82800}(13,\cdot)$	82800.xt	660	yes	$-1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{619}{660}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{82800}(17,\cdot)$	82800.vg	220	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{82800}(19,\cdot)$	82800.tx	220	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{82800}(29,\cdot)$	82800.yn	660	yes	$-1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{581}{660}\right)$	$e\left(\frac{619}{660}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{227}{660}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{82800}(31,\cdot)$	82800.vz	330	no	$-1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{82800}(37,\cdot)$	82800.up	220	no	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{82800}(41,\cdot)$	82800.wi	330	no	$-1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{82800}(43,\cdot)$	82800.sw	132	no	$-1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{82800}(47,\cdot)$	82800.oy	60	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{82800}(49,\cdot)$	82800.px	66	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{82800}(53,\cdot)$	82800.uw	220	no	$-1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{82800}(59,\cdot)$	82800.xa	660	yes	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{413}{660}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{289}{660}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{101}{132}\right)$
$\chi_{82800}(61,\cdot)$	82800.yj	660	yes	$-1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{37}{132}\right)$
$\chi_{82800}(67,\cdot)$	82800.xp	660	yes	$-1$	$1$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{199}{660}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{343}{660}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{82800}(71,\cdot)$	82800.rh	110	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{82800}(73,\cdot)$	82800.ui	220	no	$-1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{82800}(77,\cdot)$	82800.xm	660	yes	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{553}{660}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{61}{660}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{82800}(79,\cdot)$	82800.vv	330	no	$1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{82800}(83,\cdot)$	82800.xy	660	yes	$1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{82800}(89,\cdot)$	82800.qw	110	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{82800}(91,\cdot)$	82800.ht	20	no	$1$	$1$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{82800}(97,\cdot)$	82800.yg	660	no	$1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{82800}(101,\cdot)$	82800.sd	132	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{25}{132}\right)$
$\chi_{82800}(103,\cdot)$	82800.yf	660	no	$-1$	$1$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{359}{660}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{83}{132}\right)$
$\chi_{82800}(107,\cdot)$	82800.mv	44	no	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{82800}(109,\cdot)$	82800.vo	220	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{82800}(113,\cdot)$	82800.xg	660	no	$-1$	$1$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{653}{660}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{71}{132}\right)$
$\chi_{82800}(119,\cdot)$	82800.wo	330	no	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{82800}(121,\cdot)$	82800.wt	330	no	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{61}{66}\right)$

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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	$82800$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{660}\)
Order	$21120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{82800}(1,\cdot)\)	82800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{82800}(7,\cdot)\)	82800.sg	132	no	\(-1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)
\(\chi_{82800}(11,\cdot)\)	82800.xb	660	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{263}{660}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{581}{660}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{61}{132}\right)\)
\(\chi_{82800}(13,\cdot)\)	82800.xt	660	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{619}{660}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{82800}(17,\cdot)\)	82800.vg	220	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{82800}(19,\cdot)\)	82800.tx	220	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{82800}(29,\cdot)\)	82800.yn	660	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{581}{660}\right)\)	\(e\left(\frac{619}{660}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{227}{660}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{82800}(31,\cdot)\)	82800.vz	330	no	\(-1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{82800}(37,\cdot)\)	82800.up	220	no	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{82800}(41,\cdot)\)	82800.wi	330	no	\(-1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{82800}(43,\cdot)\)	82800.sw	132	no	\(-1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{82800}(47,\cdot)\)	82800.oy	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{82800}(49,\cdot)\)	82800.px	66	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{82800}(53,\cdot)\)	82800.uw	220	no	\(-1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{82800}(59,\cdot)\)	82800.xa	660	yes	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{413}{660}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{289}{660}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{101}{132}\right)\)
\(\chi_{82800}(61,\cdot)\)	82800.yj	660	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{37}{132}\right)\)
\(\chi_{82800}(67,\cdot)\)	82800.xp	660	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{199}{660}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{343}{660}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{82800}(71,\cdot)\)	82800.rh	110	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{82800}(73,\cdot)\)	82800.ui	220	no	\(-1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{82800}(77,\cdot)\)	82800.xm	660	yes	\(1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{553}{660}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{61}{660}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{82800}(79,\cdot)\)	82800.vv	330	no	\(1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{82800}(83,\cdot)\)	82800.xy	660	yes	\(1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{82800}(89,\cdot)\)	82800.qw	110	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{82800}(91,\cdot)\)	82800.ht	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)
\(\chi_{82800}(97,\cdot)\)	82800.yg	660	no	\(1\)	\(1\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{85}{132}\right)\)
\(\chi_{82800}(101,\cdot)\)	82800.sd	132	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{25}{132}\right)\)
\(\chi_{82800}(103,\cdot)\)	82800.yf	660	no	\(-1\)	\(1\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{359}{660}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{83}{132}\right)\)
\(\chi_{82800}(107,\cdot)\)	82800.mv	44	no	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{82800}(109,\cdot)\)	82800.vo	220	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{82800}(113,\cdot)\)	82800.xg	660	no	\(-1\)	\(1\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{653}{660}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{71}{132}\right)\)
\(\chi_{82800}(119,\cdot)\)	82800.wo	330	no	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{82800}(121,\cdot)\)	82800.wt	330	no	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{61}{66}\right)\)

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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.