LMFDB - Group of Dirichlet characters of modulus 7623

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7623)

pari: g = idealstar(,7623,2)

Character group

sage: G.order() pari: g.no
Order	=	3960
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{330}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7623}(848,\cdot)$, $\chi_{7623}(4357,\cdot)$, $\chi_{7623}(4600,\cdot)$

First 32 of 3960 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{7623}(1,\cdot)$	7623.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7623}(2,\cdot)$	7623.fg	330	yes	$1$	$1$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{283}{330}\right)$
$\chi_{7623}(4,\cdot)$	7623.fa	165	yes	$1$	$1$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{118}{165}\right)$
$\chi_{7623}(5,\cdot)$	7623.fc	330	yes	$1$	$1$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{76}{165}\right)$
$\chi_{7623}(8,\cdot)$	7623.ew	110	no	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{7623}(10,\cdot)$	7623.dx	66	no	$1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{7623}(13,\cdot)$	7623.fw	330	yes	$1$	$1$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{203}{330}\right)$
$\chi_{7623}(16,\cdot)$	7623.fa	165	yes	$1$	$1$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{71}{165}\right)$
$\chi_{7623}(17,\cdot)$	7623.fj	330	no	$-1$	$1$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{7623}(19,\cdot)$	7623.fx	330	no	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{7623}(20,\cdot)$	7623.fu	330	yes	$1$	$1$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{29}{165}\right)$
$\chi_{7623}(23,\cdot)$	7623.en	66	yes	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{7623}(25,\cdot)$	7623.fb	165	yes	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{152}{165}\right)$
$\chi_{7623}(26,\cdot)$	7623.fr	330	no	$1$	$1$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{7623}(29,\cdot)$	7623.fn	330	no	$1$	$1$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{301}{330}\right)$
$\chi_{7623}(31,\cdot)$	7623.fh	330	yes	$-1$	$1$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{83}{330}\right)$
$\chi_{7623}(32,\cdot)$	7623.em	66	yes	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{7623}(34,\cdot)$	7623.ei	66	yes	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{47}{66}\right)$
$\chi_{7623}(37,\cdot)$	7623.ez	165	no	$1$	$1$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{7623}(38,\cdot)$	7623.fc	330	yes	$1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{116}{165}\right)$
$\chi_{7623}(40,\cdot)$	7623.dh	30	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{7623}(41,\cdot)$	7623.fi	330	yes	$-1$	$1$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{37}{165}\right)$
$\chi_{7623}(43,\cdot)$	7623.eb	66	no	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{7623}(46,\cdot)$	7623.fs	330	no	$-1$	$1$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{7623}(47,\cdot)$	7623.fz	330	yes	$1$	$1$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{7623}(50,\cdot)$	7623.fn	330	no	$1$	$1$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{257}{330}\right)$
$\chi_{7623}(52,\cdot)$	7623.fe	330	yes	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{109}{330}\right)$
$\chi_{7623}(53,\cdot)$	7623.fy	330	no	$-1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{7623}(58,\cdot)$	7623.fb	165	yes	$1$	$1$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{127}{165}\right)$
$\chi_{7623}(59,\cdot)$	7623.fz	330	yes	$1$	$1$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{73}{165}\right)$
$\chi_{7623}(61,\cdot)$	7623.fp	330	yes	$1$	$1$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{157}{330}\right)$
$\chi_{7623}(62,\cdot)$	7623.ex	110	no	$-1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{6}{55}\right)$

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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	$7623$
Structure	\(C_{2}\times C_{6}\times C_{330}\)
Order	$3960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{7623}(1,\cdot)\)	7623.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7623}(2,\cdot)\)	7623.fg	330	yes	\(1\)	\(1\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{283}{330}\right)\)
\(\chi_{7623}(4,\cdot)\)	7623.fa	165	yes	\(1\)	\(1\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)
\(\chi_{7623}(5,\cdot)\)	7623.fc	330	yes	\(1\)	\(1\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)
\(\chi_{7623}(8,\cdot)\)	7623.ew	110	no	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{7623}(10,\cdot)\)	7623.dx	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{7623}(13,\cdot)\)	7623.fw	330	yes	\(1\)	\(1\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{203}{330}\right)\)
\(\chi_{7623}(16,\cdot)\)	7623.fa	165	yes	\(1\)	\(1\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)
\(\chi_{7623}(17,\cdot)\)	7623.fj	330	no	\(-1\)	\(1\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{7623}(19,\cdot)\)	7623.fx	330	no	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{7623}(20,\cdot)\)	7623.fu	330	yes	\(1\)	\(1\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{29}{165}\right)\)
\(\chi_{7623}(23,\cdot)\)	7623.en	66	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{7623}(25,\cdot)\)	7623.fb	165	yes	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)
\(\chi_{7623}(26,\cdot)\)	7623.fr	330	no	\(1\)	\(1\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{7623}(29,\cdot)\)	7623.fn	330	no	\(1\)	\(1\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{301}{330}\right)\)
\(\chi_{7623}(31,\cdot)\)	7623.fh	330	yes	\(-1\)	\(1\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{83}{330}\right)\)
\(\chi_{7623}(32,\cdot)\)	7623.em	66	yes	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{7623}(34,\cdot)\)	7623.ei	66	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)
\(\chi_{7623}(37,\cdot)\)	7623.ez	165	no	\(1\)	\(1\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{7623}(38,\cdot)\)	7623.fc	330	yes	\(1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{116}{165}\right)\)
\(\chi_{7623}(40,\cdot)\)	7623.dh	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{7623}(41,\cdot)\)	7623.fi	330	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{37}{165}\right)\)
\(\chi_{7623}(43,\cdot)\)	7623.eb	66	no	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{7623}(46,\cdot)\)	7623.fs	330	no	\(-1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{7623}(47,\cdot)\)	7623.fz	330	yes	\(1\)	\(1\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{7623}(50,\cdot)\)	7623.fn	330	no	\(1\)	\(1\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{257}{330}\right)\)
\(\chi_{7623}(52,\cdot)\)	7623.fe	330	yes	\(1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)
\(\chi_{7623}(53,\cdot)\)	7623.fy	330	no	\(-1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{7623}(58,\cdot)\)	7623.fb	165	yes	\(1\)	\(1\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)
\(\chi_{7623}(59,\cdot)\)	7623.fz	330	yes	\(1\)	\(1\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{73}{165}\right)\)
\(\chi_{7623}(61,\cdot)\)	7623.fp	330	yes	\(1\)	\(1\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)
\(\chi_{7623}(62,\cdot)\)	7623.ex	110	no	\(-1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)

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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.