LMFDB - Group of Dirichlet characters of modulus 54450

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(54450)

gp:g = idealstar(,54450,2)

magma:G = FullDirichletGroup(54450);

Character group

Order	=	13200	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{10}\times C_{660}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{54450}(30251,\cdot)$, $\chi_{54450}(37027,\cdot)$, $\chi_{54450}(14401,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 13200 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{54450}(1,\cdot)$	54450.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{54450}(7,\cdot)$	54450.mp	660	no	$1$	$1$	$e\left(\frac{239}{660}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{54450}(13,\cdot)$	54450.mn	660	no	$1$	$1$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{257}{660}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{71}{132}\right)$
$\chi_{54450}(17,\cdot)$	54450.kb	220	no	$-1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{54450}(19,\cdot)$	54450.it	110	no	$-1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{54450}(23,\cdot)$	54450.mc	660	no	$1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{257}{660}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{503}{660}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{65}{132}\right)$
$\chi_{54450}(29,\cdot)$	54450.kq	330	no	$1$	$1$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{54450}(31,\cdot)$	54450.jh	165	no	$1$	$1$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{54450}(37,\cdot)$	54450.jp	220	no	$-1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{54450}(41,\cdot)$	54450.lu	330	no	$1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{54450}(43,\cdot)$	54450.jd	132	no	$1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{54450}(47,\cdot)$	54450.mf	660	no	$1$	$1$	$e\left(\frac{101}{660}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{361}{660}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{91}{132}\right)$
$\chi_{54450}(49,\cdot)$	54450.lm	330	no	$1$	$1$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{54450}(53,\cdot)$	54450.jv	220	no	$1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{54450}(59,\cdot)$	54450.lg	330	no	$-1$	$1$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{54450}(61,\cdot)$	54450.lv	330	no	$-1$	$1$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{54450}(67,\cdot)$	54450.mh	660	no	$-1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{54450}(71,\cdot)$	54450.in	110	no	$-1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{54450}(73,\cdot)$	54450.jm	220	no	$1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{54450}(79,\cdot)$	54450.lc	330	no	$-1$	$1$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{54450}(83,\cdot)$	54450.ms	660	no	$-1$	$1$	$e\left(\frac{173}{660}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{619}{660}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{54450}(89,\cdot)$	54450.jb	110	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{54450}(91,\cdot)$	54450.ge	55	no	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{54450}(97,\cdot)$	54450.mk	660	no	$-1$	$1$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{391}{660}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{54450}(101,\cdot)$	54450.lq	330	no	$1$	$1$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{54450}(103,\cdot)$	54450.ml	660	no	$-1$	$1$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{221}{660}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{101}{660}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{54450}(107,\cdot)$	54450.ka	220	no	$-1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{54450}(109,\cdot)$	54450.ho	110	no	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{54450}(113,\cdot)$	54450.mx	660	no	$1$	$1$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{641}{660}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{347}{660}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{101}{132}\right)$
$\chi_{54450}(119,\cdot)$	54450.lp	330	no	$-1$	$1$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{54450}(127,\cdot)$	54450.kg	220	no	$1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{54450}(131,\cdot)$	54450.km	330	no	$1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{25}{66}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$54450$
Structure	\(C_{2}\times C_{10}\times C_{660}\)
Order	$13200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{54450}(1,\cdot)\)	54450.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{54450}(7,\cdot)\)	54450.mp	660	no	\(1\)	\(1\)	\(e\left(\frac{239}{660}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{54450}(13,\cdot)\)	54450.mn	660	no	\(1\)	\(1\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{257}{660}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{71}{132}\right)\)
\(\chi_{54450}(17,\cdot)\)	54450.kb	220	no	\(-1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{54450}(19,\cdot)\)	54450.it	110	no	\(-1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{54450}(23,\cdot)\)	54450.mc	660	no	\(1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{257}{660}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{503}{660}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{65}{132}\right)\)
\(\chi_{54450}(29,\cdot)\)	54450.kq	330	no	\(1\)	\(1\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{54450}(31,\cdot)\)	54450.jh	165	no	\(1\)	\(1\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{54450}(37,\cdot)\)	54450.jp	220	no	\(-1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{54450}(41,\cdot)\)	54450.lu	330	no	\(1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{54450}(43,\cdot)\)	54450.jd	132	no	\(1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{54450}(47,\cdot)\)	54450.mf	660	no	\(1\)	\(1\)	\(e\left(\frac{101}{660}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{361}{660}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{91}{132}\right)\)
\(\chi_{54450}(49,\cdot)\)	54450.lm	330	no	\(1\)	\(1\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{54450}(53,\cdot)\)	54450.jv	220	no	\(1\)	\(1\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{54450}(59,\cdot)\)	54450.lg	330	no	\(-1\)	\(1\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{54450}(61,\cdot)\)	54450.lv	330	no	\(-1\)	\(1\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{54450}(67,\cdot)\)	54450.mh	660	no	\(-1\)	\(1\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{107}{132}\right)\)
\(\chi_{54450}(71,\cdot)\)	54450.in	110	no	\(-1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{54450}(73,\cdot)\)	54450.jm	220	no	\(1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{54450}(79,\cdot)\)	54450.lc	330	no	\(-1\)	\(1\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{54450}(83,\cdot)\)	54450.ms	660	no	\(-1\)	\(1\)	\(e\left(\frac{173}{660}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{619}{660}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{54450}(89,\cdot)\)	54450.jb	110	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{54450}(91,\cdot)\)	54450.ge	55	no	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{54450}(97,\cdot)\)	54450.mk	660	no	\(-1\)	\(1\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{391}{660}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{54450}(101,\cdot)\)	54450.lq	330	no	\(1\)	\(1\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{54450}(103,\cdot)\)	54450.ml	660	no	\(-1\)	\(1\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{221}{660}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{101}{660}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{54450}(107,\cdot)\)	54450.ka	220	no	\(-1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{54450}(109,\cdot)\)	54450.ho	110	no	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{54450}(113,\cdot)\)	54450.mx	660	no	\(1\)	\(1\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{641}{660}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{347}{660}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{101}{132}\right)\)
\(\chi_{54450}(119,\cdot)\)	54450.lp	330	no	\(-1\)	\(1\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{54450}(127,\cdot)\)	54450.kg	220	no	\(1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{54450}(131,\cdot)\)	54450.km	330	no	\(1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{25}{66}\right)\)

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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.