LMFDB - Group of Dirichlet characters of modulus 7581

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(7581)

pari: g = idealstar(,7581,2)

Character group

sage: G.order() pari: g.no
Order	=	4104
sage: H.invariants() pari: g.cyc
Structure	=	$C_{342}\times C_{6}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7581}(2528,\cdot)$, $\chi_{7581}(6499,\cdot)$, $\chi_{7581}(1807,\cdot)$

First 32 of 4104 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$20$
$\chi_{7581}(1,\cdot)$	7581.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7581}(2,\cdot)$	7581.ex	342	yes	$1$	$1$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{7}{38}\right)$
$\chi_{7581}(4,\cdot)$	7581.ea	171	no	$1$	$1$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{7581}(5,\cdot)$	7581.en	342	yes	$1$	$1$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{7581}(8,\cdot)$	7581.ds	114	no	$1$	$1$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{21}{38}\right)$
$\chi_{7581}(10,\cdot)$	7581.ee	342	no	$1$	$1$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{35}{38}\right)$
$\chi_{7581}(11,\cdot)$	7581.dy	114	yes	$-1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{11}{38}\right)$
$\chi_{7581}(13,\cdot)$	7581.em	342	no	$1$	$1$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{23}{38}\right)$
$\chi_{7581}(16,\cdot)$	7581.ea	171	no	$1$	$1$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{7581}(17,\cdot)$	7581.eg	342	yes	$1$	$1$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{7581}(20,\cdot)$	7581.cr	38	yes	$1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{2}{19}\right)$
$\chi_{7581}(22,\cdot)$	7581.ej	342	no	$-1$	$1$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{7581}(23,\cdot)$	7581.eh	342	yes	$-1$	$1$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{15}{38}\right)$
$\chi_{7581}(25,\cdot)$	7581.ea	171	no	$1$	$1$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{7581}(26,\cdot)$	7581.dw	114	yes	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{7581}(29,\cdot)$	7581.es	342	no	$1$	$1$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{5}{38}\right)$
$\chi_{7581}(31,\cdot)$	7581.df	114	no	$1$	$1$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{31}{38}\right)$
$\chi_{7581}(32,\cdot)$	7581.ex	342	yes	$1$	$1$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{35}{38}\right)$
$\chi_{7581}(34,\cdot)$	7581.em	342	no	$1$	$1$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{31}{38}\right)$
$\chi_{7581}(37,\cdot)$	7581.dl	114	no	$-1$	$1$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{7581}(40,\cdot)$	7581.ee	342	no	$1$	$1$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{11}{38}\right)$
$\chi_{7581}(41,\cdot)$	7581.er	342	yes	$-1$	$1$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{16}{19}\right)$
$\chi_{7581}(43,\cdot)$	7581.ec	171	no	$1$	$1$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{7581}(44,\cdot)$	7581.eh	342	yes	$-1$	$1$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{25}{38}\right)$
$\chi_{7581}(46,\cdot)$	7581.dx	114	no	$-1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{11}{19}\right)$
$\chi_{7581}(47,\cdot)$	7581.eg	342	yes	$1$	$1$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{7581}(50,\cdot)$	7581.ds	114	no	$1$	$1$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{25}{38}\right)$
$\chi_{7581}(52,\cdot)$	7581.el	342	no	$1$	$1$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{37}{38}\right)$
$\chi_{7581}(53,\cdot)$	7581.ex	342	yes	$1$	$1$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{11}{38}\right)$
$\chi_{7581}(55,\cdot)$	7581.eu	342	no	$-1$	$1$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{1}{38}\right)$
$\chi_{7581}(58,\cdot)$	7581.cw	57	no	$1$	$1$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{6}{19}\right)$
$\chi_{7581}(59,\cdot)$	7581.eq	342	yes	$-1$	$1$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{16}{19}\right)$

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	$7581$
Structure	\(C_{342}\times C_{6}\times C_{2}\)
Order	$4104$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(20\)
\(\chi_{7581}(1,\cdot)\)	7581.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7581}(2,\cdot)\)	7581.ex	342	yes	\(1\)	\(1\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{7}{38}\right)\)
\(\chi_{7581}(4,\cdot)\)	7581.ea	171	no	\(1\)	\(1\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{7581}(5,\cdot)\)	7581.en	342	yes	\(1\)	\(1\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{7581}(8,\cdot)\)	7581.ds	114	no	\(1\)	\(1\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)
\(\chi_{7581}(10,\cdot)\)	7581.ee	342	no	\(1\)	\(1\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{35}{38}\right)\)
\(\chi_{7581}(11,\cdot)\)	7581.dy	114	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{11}{38}\right)\)
\(\chi_{7581}(13,\cdot)\)	7581.em	342	no	\(1\)	\(1\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{23}{38}\right)\)
\(\chi_{7581}(16,\cdot)\)	7581.ea	171	no	\(1\)	\(1\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{7581}(17,\cdot)\)	7581.eg	342	yes	\(1\)	\(1\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{7581}(20,\cdot)\)	7581.cr	38	yes	\(1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)
\(\chi_{7581}(22,\cdot)\)	7581.ej	342	no	\(-1\)	\(1\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{7581}(23,\cdot)\)	7581.eh	342	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{15}{38}\right)\)
\(\chi_{7581}(25,\cdot)\)	7581.ea	171	no	\(1\)	\(1\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{7581}(26,\cdot)\)	7581.dw	114	yes	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{7581}(29,\cdot)\)	7581.es	342	no	\(1\)	\(1\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{5}{38}\right)\)
\(\chi_{7581}(31,\cdot)\)	7581.df	114	no	\(1\)	\(1\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)
\(\chi_{7581}(32,\cdot)\)	7581.ex	342	yes	\(1\)	\(1\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{35}{38}\right)\)
\(\chi_{7581}(34,\cdot)\)	7581.em	342	no	\(1\)	\(1\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{31}{38}\right)\)
\(\chi_{7581}(37,\cdot)\)	7581.dl	114	no	\(-1\)	\(1\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{7581}(40,\cdot)\)	7581.ee	342	no	\(1\)	\(1\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{11}{38}\right)\)
\(\chi_{7581}(41,\cdot)\)	7581.er	342	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{16}{19}\right)\)
\(\chi_{7581}(43,\cdot)\)	7581.ec	171	no	\(1\)	\(1\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{7581}(44,\cdot)\)	7581.eh	342	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{25}{38}\right)\)
\(\chi_{7581}(46,\cdot)\)	7581.dx	114	no	\(-1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)
\(\chi_{7581}(47,\cdot)\)	7581.eg	342	yes	\(1\)	\(1\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{7581}(50,\cdot)\)	7581.ds	114	no	\(1\)	\(1\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)
\(\chi_{7581}(52,\cdot)\)	7581.el	342	no	\(1\)	\(1\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{37}{38}\right)\)
\(\chi_{7581}(53,\cdot)\)	7581.ex	342	yes	\(1\)	\(1\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{11}{38}\right)\)
\(\chi_{7581}(55,\cdot)\)	7581.eu	342	no	\(-1\)	\(1\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{1}{38}\right)\)
\(\chi_{7581}(58,\cdot)\)	7581.cw	57	no	\(1\)	\(1\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)
\(\chi_{7581}(59,\cdot)\)	7581.eq	342	yes	\(-1\)	\(1\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{16}{19}\right)\)

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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.