LMFDB - Group of Dirichlet characters of modulus 9386

sage:H = DirichletGroup(9386)

pari:g = idealstar(,9386,2)

Character group

sage:G.order() pari:g.no
Order	=	4104
sage:H.invariants() pari:g.cyc
Structure	=	$C_{6}\times C_{684}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{9386}(1445,\cdot)$, $\chi_{9386}(3251,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$21$	$23$	$25$
$\chi_{9386}(1,\cdot)$	9386.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9386}(3,\cdot)$	9386.dd	342	no	$-1$	$1$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{100}{171}\right)$
$\chi_{9386}(5,\cdot)$	9386.dq	684	no	$-1$	$1$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{89}{684}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{289}{684}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{203}{684}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{89}{342}\right)$
$\chi_{9386}(7,\cdot)$	9386.cv	228	no	$-1$	$1$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{9386}(9,\cdot)$	9386.cs	171	no	$1$	$1$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{29}{171}\right)$
$\chi_{9386}(11,\cdot)$	9386.cv	228	no	$-1$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{101}{114}\right)$
$\chi_{9386}(15,\cdot)$	9386.dn	684	no	$1$	$1$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{289}{684}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{371}{684}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{517}{684}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{289}{342}\right)$
$\chi_{9386}(17,\cdot)$	9386.dg	342	no	$1$	$1$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{106}{171}\right)$
$\chi_{9386}(21,\cdot)$	9386.dm	684	no	$1$	$1$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{203}{684}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{517}{684}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{659}{684}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{203}{342}\right)$
$\chi_{9386}(23,\cdot)$	9386.dg	342	no	$1$	$1$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{14}{171}\right)$
$\chi_{9386}(25,\cdot)$	9386.dh	342	no	$1$	$1$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{89}{171}\right)$
$\chi_{9386}(27,\cdot)$	9386.ck	114	no	$-1$	$1$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{43}{57}\right)$
$\chi_{9386}(29,\cdot)$	9386.di	342	no	$-1$	$1$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{11}{171}\right)$
$\chi_{9386}(31,\cdot)$	9386.cw	228	no	$1$	$1$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{67}{114}\right)$
$\chi_{9386}(33,\cdot)$	9386.dn	684	no	$1$	$1$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{503}{684}\right)$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{241}{684}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{275}{684}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{161}{342}\right)$
$\chi_{9386}(35,\cdot)$	9386.cu	171	no	$1$	$1$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{46}{171}\right)$
$\chi_{9386}(37,\cdot)$	9386.cx	228	no	$1$	$1$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{91}{228}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{21}{38}\right)$
$\chi_{9386}(41,\cdot)$	9386.do	684	no	$1$	$1$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{137}{684}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{523}{684}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{593}{684}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{137}{342}\right)$
$\chi_{9386}(43,\cdot)$	9386.dg	342	no	$1$	$1$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{94}{171}\right)$
$\chi_{9386}(45,\cdot)$	9386.cv	228	no	$-1$	$1$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{49}{114}\right)$
$\chi_{9386}(47,\cdot)$	9386.dq	684	no	$-1$	$1$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{607}{684}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{311}{684}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{493}{684}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{265}{342}\right)$
$\chi_{9386}(49,\cdot)$	9386.cg	114	no	$1$	$1$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{1}{57}\right)$
$\chi_{9386}(51,\cdot)$	9386.de	342	no	$-1$	$1$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{35}{171}\right)$
$\chi_{9386}(53,\cdot)$	9386.dj	342	no	$-1$	$1$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{104}{171}\right)$
$\chi_{9386}(55,\cdot)$	9386.cs	171	no	$1$	$1$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{25}{171}\right)$
$\chi_{9386}(59,\cdot)$	9386.dn	684	no	$1$	$1$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{23}{684}\right)$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{91}{228}\right)$	$e\left(\frac{181}{684}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{479}{684}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{23}{342}\right)$
$\chi_{9386}(61,\cdot)$	9386.cs	171	no	$1$	$1$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{140}{171}\right)$
$\chi_{9386}(63,\cdot)$	9386.dp	684	no	$-1$	$1$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{403}{684}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{599}{684}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{289}{684}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{61}{342}\right)$
$\chi_{9386}(67,\cdot)$	9386.dn	684	no	$1$	$1$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{157}{684}\right)$	$e\left(\frac{205}{228}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{611}{684}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{385}{684}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{157}{342}\right)$
$\chi_{9386}(69,\cdot)$	9386.l	6	no	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9386}(71,\cdot)$	9386.dn	684	no	$1$	$1$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{233}{684}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{79}{684}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{5}{684}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{233}{342}\right)$
$\chi_{9386}(73,\cdot)$	9386.dq	684	no	$-1$	$1$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{155}{684}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{511}{684}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{269}{684}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{155}{342}\right)$

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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	$9386$
Structure	\(C_{6}\times C_{684}\)
Order	$4104$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{9386}(1,\cdot)\)	9386.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9386}(3,\cdot)\)	9386.dd	342	no	\(-1\)	\(1\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{100}{171}\right)\)
\(\chi_{9386}(5,\cdot)\)	9386.dq	684	no	\(-1\)	\(1\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{89}{684}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{289}{684}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{203}{684}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{89}{342}\right)\)
\(\chi_{9386}(7,\cdot)\)	9386.cv	228	no	\(-1\)	\(1\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{9386}(9,\cdot)\)	9386.cs	171	no	\(1\)	\(1\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{29}{171}\right)\)
\(\chi_{9386}(11,\cdot)\)	9386.cv	228	no	\(-1\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)
\(\chi_{9386}(15,\cdot)\)	9386.dn	684	no	\(1\)	\(1\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{289}{684}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{371}{684}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{517}{684}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{289}{342}\right)\)
\(\chi_{9386}(17,\cdot)\)	9386.dg	342	no	\(1\)	\(1\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)
\(\chi_{9386}(21,\cdot)\)	9386.dm	684	no	\(1\)	\(1\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{203}{684}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{517}{684}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{659}{684}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{203}{342}\right)\)
\(\chi_{9386}(23,\cdot)\)	9386.dg	342	no	\(1\)	\(1\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{14}{171}\right)\)
\(\chi_{9386}(25,\cdot)\)	9386.dh	342	no	\(1\)	\(1\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{89}{171}\right)\)
\(\chi_{9386}(27,\cdot)\)	9386.ck	114	no	\(-1\)	\(1\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)
\(\chi_{9386}(29,\cdot)\)	9386.di	342	no	\(-1\)	\(1\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{11}{171}\right)\)
\(\chi_{9386}(31,\cdot)\)	9386.cw	228	no	\(1\)	\(1\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{67}{114}\right)\)
\(\chi_{9386}(33,\cdot)\)	9386.dn	684	no	\(1\)	\(1\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{503}{684}\right)\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{241}{684}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{275}{684}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{161}{342}\right)\)
\(\chi_{9386}(35,\cdot)\)	9386.cu	171	no	\(1\)	\(1\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)
\(\chi_{9386}(37,\cdot)\)	9386.cx	228	no	\(1\)	\(1\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{91}{228}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)
\(\chi_{9386}(41,\cdot)\)	9386.do	684	no	\(1\)	\(1\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{137}{684}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{523}{684}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{593}{684}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{137}{342}\right)\)
\(\chi_{9386}(43,\cdot)\)	9386.dg	342	no	\(1\)	\(1\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{94}{171}\right)\)
\(\chi_{9386}(45,\cdot)\)	9386.cv	228	no	\(-1\)	\(1\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{49}{114}\right)\)
\(\chi_{9386}(47,\cdot)\)	9386.dq	684	no	\(-1\)	\(1\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{607}{684}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{311}{684}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{493}{684}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{265}{342}\right)\)
\(\chi_{9386}(49,\cdot)\)	9386.cg	114	no	\(1\)	\(1\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)
\(\chi_{9386}(51,\cdot)\)	9386.de	342	no	\(-1\)	\(1\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{35}{171}\right)\)
\(\chi_{9386}(53,\cdot)\)	9386.dj	342	no	\(-1\)	\(1\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{104}{171}\right)\)
\(\chi_{9386}(55,\cdot)\)	9386.cs	171	no	\(1\)	\(1\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{25}{171}\right)\)
\(\chi_{9386}(59,\cdot)\)	9386.dn	684	no	\(1\)	\(1\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{23}{684}\right)\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{91}{228}\right)\)	\(e\left(\frac{181}{684}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{479}{684}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{23}{342}\right)\)
\(\chi_{9386}(61,\cdot)\)	9386.cs	171	no	\(1\)	\(1\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)
\(\chi_{9386}(63,\cdot)\)	9386.dp	684	no	\(-1\)	\(1\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{403}{684}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{599}{684}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{289}{684}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{61}{342}\right)\)
\(\chi_{9386}(67,\cdot)\)	9386.dn	684	no	\(1\)	\(1\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{157}{684}\right)\)	\(e\left(\frac{205}{228}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{611}{684}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{385}{684}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{157}{342}\right)\)
\(\chi_{9386}(69,\cdot)\)	9386.l	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9386}(71,\cdot)\)	9386.dn	684	no	\(1\)	\(1\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{233}{684}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{79}{684}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{5}{684}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{233}{342}\right)\)
\(\chi_{9386}(73,\cdot)\)	9386.dq	684	no	\(-1\)	\(1\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{155}{684}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{511}{684}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{269}{684}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{155}{342}\right)\)

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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.