LMFDB - Group of Dirichlet characters of modulus 8712

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8712)

pari: g = idealstar(,8712,2)

Character group

sage: G.order() pari: g.no
Order	=	2640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{330}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8712}(6535,\cdot)$, $\chi_{8712}(4357,\cdot)$, $\chi_{8712}(1937,\cdot)$, $\chi_{8712}(5689,\cdot)$

First 32 of 2640 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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8712}(1,\cdot)$	8712.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8712}(5,\cdot)$	8712.ek	330	yes	$-1$	$1$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{8712}(7,\cdot)$	8712.el	330	no	$1$	$1$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{8712}(13,\cdot)$	8712.ev	330	yes	$-1$	$1$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{8712}(17,\cdot)$	8712.dt	110	no	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{8712}(19,\cdot)$	8712.dz	110	no	$1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{8712}(23,\cdot)$	8712.dh	66	no	$1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{8712}(25,\cdot)$	8712.ei	165	no	$1$	$1$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{8712}(29,\cdot)$	8712.en	330	yes	$1$	$1$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{8712}(31,\cdot)$	8712.em	330	no	$-1$	$1$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{8712}(35,\cdot)$	8712.eh	110	no	$-1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{8712}(37,\cdot)$	8712.dx	110	no	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{8712}(41,\cdot)$	8712.ew	330	no	$1$	$1$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{8712}(43,\cdot)$	8712.dl	66	yes	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{8712}(47,\cdot)$	8712.eu	330	no	$1$	$1$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{8712}(49,\cdot)$	8712.ei	165	no	$1$	$1$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{8712}(53,\cdot)$	8712.ef	110	no	$-1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{8712}(59,\cdot)$	8712.ep	330	yes	$1$	$1$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{8712}(61,\cdot)$	8712.ev	330	yes	$-1$	$1$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{8712}(65,\cdot)$	8712.df	66	no	$1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{8712}(67,\cdot)$	8712.de	66	yes	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{8712}(71,\cdot)$	8712.dv	110	no	$1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{8712}(73,\cdot)$	8712.eb	110	no	$-1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{8712}(79,\cdot)$	8712.el	330	no	$1$	$1$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{8712}(83,\cdot)$	8712.ej	330	yes	$-1$	$1$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{8712}(85,\cdot)$	8712.ev	330	yes	$-1$	$1$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{8712}(89,\cdot)$	8712.cf	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{8712}(91,\cdot)$	8712.du	110	no	$-1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{8712}(95,\cdot)$	8712.et	330	no	$-1$	$1$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{8712}(97,\cdot)$	8712.ei	165	no	$1$	$1$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{8712}(101,\cdot)$	8712.en	330	yes	$1$	$1$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{8712}(103,\cdot)$	8712.em	330	no	$-1$	$1$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{37}{110}\right)$

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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	$8712$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{330}\)
Order	$2640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8712}(1,\cdot)\)	8712.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8712}(5,\cdot)\)	8712.ek	330	yes	\(-1\)	\(1\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{8712}(7,\cdot)\)	8712.el	330	no	\(1\)	\(1\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{8712}(13,\cdot)\)	8712.ev	330	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{8712}(17,\cdot)\)	8712.dt	110	no	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{8712}(19,\cdot)\)	8712.dz	110	no	\(1\)	\(1\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{8712}(23,\cdot)\)	8712.dh	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{8712}(25,\cdot)\)	8712.ei	165	no	\(1\)	\(1\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{8712}(29,\cdot)\)	8712.en	330	yes	\(1\)	\(1\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{8712}(31,\cdot)\)	8712.em	330	no	\(-1\)	\(1\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{8712}(35,\cdot)\)	8712.eh	110	no	\(-1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{8712}(37,\cdot)\)	8712.dx	110	no	\(1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{8712}(41,\cdot)\)	8712.ew	330	no	\(1\)	\(1\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{8712}(43,\cdot)\)	8712.dl	66	yes	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{8712}(47,\cdot)\)	8712.eu	330	no	\(1\)	\(1\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{8712}(49,\cdot)\)	8712.ei	165	no	\(1\)	\(1\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{8712}(53,\cdot)\)	8712.ef	110	no	\(-1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{8712}(59,\cdot)\)	8712.ep	330	yes	\(1\)	\(1\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{8712}(61,\cdot)\)	8712.ev	330	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{8712}(65,\cdot)\)	8712.df	66	no	\(1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{8712}(67,\cdot)\)	8712.de	66	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{8712}(71,\cdot)\)	8712.dv	110	no	\(1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{8712}(73,\cdot)\)	8712.eb	110	no	\(-1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{8712}(79,\cdot)\)	8712.el	330	no	\(1\)	\(1\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{8712}(83,\cdot)\)	8712.ej	330	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{8712}(85,\cdot)\)	8712.ev	330	yes	\(-1\)	\(1\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{8712}(89,\cdot)\)	8712.cf	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{8712}(91,\cdot)\)	8712.du	110	no	\(-1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{8712}(95,\cdot)\)	8712.et	330	no	\(-1\)	\(1\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{8712}(97,\cdot)\)	8712.ei	165	no	\(1\)	\(1\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{8712}(101,\cdot)\)	8712.en	330	yes	\(1\)	\(1\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{8712}(103,\cdot)\)	8712.em	330	no	\(-1\)	\(1\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{37}{110}\right)\)

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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.