LMFDB - Group of Dirichlet characters of modulus 47190

Show commands: PariGP / SageMath

sage: H = DirichletGroup(47190)

pari: g = idealstar(,47190,2)

Character group

sage: G.order() pari: g.no
Order	=	10560
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{660}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{47190}(15731,\cdot)$, $\chi_{47190}(18877,\cdot)$, $\chi_{47190}(3511,\cdot)$, $\chi_{47190}(32671,\cdot)$

First 32 of 10560 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	$-1$	$1$	$7$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{47190}(1,\cdot)$	47190.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{47190}(7,\cdot)$	47190.me	660	no	$-1$	$1$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{133}{660}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{251}{660}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{47190}(17,\cdot)$	47190.ly	660	no	$-1$	$1$	$e\left(\frac{133}{660}\right)$	$e\left(\frac{601}{660}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{199}{220}\right)$
$\chi_{47190}(19,\cdot)$	47190.md	660	no	$1$	$1$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{469}{660}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{71}{660}\right)$	$e\left(\frac{509}{660}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{153}{220}\right)$
$\chi_{47190}(23,\cdot)$	47190.jn	132	no	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{47190}(29,\cdot)$	47190.lb	330	no	$1$	$1$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{47190}(31,\cdot)$	47190.ke	220	no	$-1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{191}{220}\right)$
$\chi_{47190}(37,\cdot)$	47190.lm	660	no	$1$	$1$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{71}{660}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{47190}(41,\cdot)$	47190.mc	660	no	$-1$	$1$	$e\left(\frac{251}{660}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{509}{660}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{259}{660}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{53}{220}\right)$
$\chi_{47190}(43,\cdot)$	47190.jj	132	no	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{47190}(47,\cdot)$	47190.ku	220	no	$-1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{47190}(49,\cdot)$	47190.la	330	no	$1$	$1$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{47190}(53,\cdot)$	47190.ki	220	no	$1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{151}{220}\right)$
$\chi_{47190}(59,\cdot)$	47190.mb	660	no	$1$	$1$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{89}{660}\right)$	$e\left(\frac{71}{660}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{57}{220}\right)$
$\chi_{47190}(61,\cdot)$	47190.lj	330	no	$-1$	$1$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{47190}(67,\cdot)$	47190.iy	132	no	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{47190}(71,\cdot)$	47190.lr	660	no	$1$	$1$	$e\left(\frac{373}{660}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{377}{660}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{109}{220}\right)$
$\chi_{47190}(73,\cdot)$	47190.kt	220	no	$-1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{47190}(79,\cdot)$	47190.iw	110	no	$-1$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{47190}(83,\cdot)$	47190.jy	220	no	$1$	$1$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{47190}(89,\cdot)$	47190.jc	132	no	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{47190}(97,\cdot)$	47190.mh	660	no	$1$	$1$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{493}{660}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{623}{660}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{47190}(101,\cdot)$	47190.kv	330	no	$1$	$1$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{47190}(103,\cdot)$	47190.kj	220	no	$-1$	$1$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{207}{220}\right)$
$\chi_{47190}(107,\cdot)$	47190.lv	660	no	$-1$	$1$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{317}{660}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{421}{660}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{193}{220}\right)$
$\chi_{47190}(109,\cdot)$	47190.go	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{47190}(113,\cdot)$	47190.lx	660	no	$1$	$1$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{277}{660}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{371}{660}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{203}{220}\right)$
$\chi_{47190}(119,\cdot)$	47190.mb	660	no	$1$	$1$	$e\left(\frac{647}{660}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{443}{660}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{193}{660}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{31}{220}\right)$
$\chi_{47190}(127,\cdot)$	47190.lw	660	no	$1$	$1$	$e\left(\frac{53}{660}\right)$	$e\left(\frac{371}{660}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{9}{220}\right)$
$\chi_{47190}(131,\cdot)$	47190.fc	22	no	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{47190}(133,\cdot)$	47190.jg	132	no	$-1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{47190}(137,\cdot)$	47190.lk	660	no	$-1$	$1$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{67}{660}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{167}{660}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{7}{110}\right)$

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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	$47190$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{660}\)
Order	$10560$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{47190}(1,\cdot)\)	47190.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{47190}(7,\cdot)\)	47190.me	660	no	\(-1\)	\(1\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{133}{660}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{251}{660}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{47190}(17,\cdot)\)	47190.ly	660	no	\(-1\)	\(1\)	\(e\left(\frac{133}{660}\right)\)	\(e\left(\frac{601}{660}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{199}{220}\right)\)
\(\chi_{47190}(19,\cdot)\)	47190.md	660	no	\(1\)	\(1\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{469}{660}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{71}{660}\right)\)	\(e\left(\frac{509}{660}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{153}{220}\right)\)
\(\chi_{47190}(23,\cdot)\)	47190.jn	132	no	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{47190}(29,\cdot)\)	47190.lb	330	no	\(1\)	\(1\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{47190}(31,\cdot)\)	47190.ke	220	no	\(-1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{191}{220}\right)\)
\(\chi_{47190}(37,\cdot)\)	47190.lm	660	no	\(1\)	\(1\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{71}{660}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{47190}(41,\cdot)\)	47190.mc	660	no	\(-1\)	\(1\)	\(e\left(\frac{251}{660}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{509}{660}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{259}{660}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{53}{220}\right)\)
\(\chi_{47190}(43,\cdot)\)	47190.jj	132	no	\(1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{47190}(47,\cdot)\)	47190.ku	220	no	\(-1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{47190}(49,\cdot)\)	47190.la	330	no	\(1\)	\(1\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{47190}(53,\cdot)\)	47190.ki	220	no	\(1\)	\(1\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{151}{220}\right)\)
\(\chi_{47190}(59,\cdot)\)	47190.mb	660	no	\(1\)	\(1\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{89}{660}\right)\)	\(e\left(\frac{71}{660}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{57}{220}\right)\)
\(\chi_{47190}(61,\cdot)\)	47190.lj	330	no	\(-1\)	\(1\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{47190}(67,\cdot)\)	47190.iy	132	no	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{47190}(71,\cdot)\)	47190.lr	660	no	\(1\)	\(1\)	\(e\left(\frac{373}{660}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{377}{660}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{109}{220}\right)\)
\(\chi_{47190}(73,\cdot)\)	47190.kt	220	no	\(-1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{47190}(79,\cdot)\)	47190.iw	110	no	\(-1\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{47190}(83,\cdot)\)	47190.jy	220	no	\(1\)	\(1\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{47190}(89,\cdot)\)	47190.jc	132	no	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{47190}(97,\cdot)\)	47190.mh	660	no	\(1\)	\(1\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{493}{660}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{623}{660}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{47190}(101,\cdot)\)	47190.kv	330	no	\(1\)	\(1\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{47190}(103,\cdot)\)	47190.kj	220	no	\(-1\)	\(1\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{207}{220}\right)\)
\(\chi_{47190}(107,\cdot)\)	47190.lv	660	no	\(-1\)	\(1\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{317}{660}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{421}{660}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{193}{220}\right)\)
\(\chi_{47190}(109,\cdot)\)	47190.go	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{47190}(113,\cdot)\)	47190.lx	660	no	\(1\)	\(1\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{277}{660}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{371}{660}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{203}{220}\right)\)
\(\chi_{47190}(119,\cdot)\)	47190.mb	660	no	\(1\)	\(1\)	\(e\left(\frac{647}{660}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{443}{660}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{193}{660}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{31}{220}\right)\)
\(\chi_{47190}(127,\cdot)\)	47190.lw	660	no	\(1\)	\(1\)	\(e\left(\frac{53}{660}\right)\)	\(e\left(\frac{371}{660}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{9}{220}\right)\)
\(\chi_{47190}(131,\cdot)\)	47190.fc	22	no	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{47190}(133,\cdot)\)	47190.jg	132	no	\(-1\)	\(1\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{47190}(137,\cdot)\)	47190.lk	660	no	\(-1\)	\(1\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{67}{660}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{167}{660}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{7}{110}\right)\)

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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.