LMFDB - Group of Dirichlet characters of modulus 4235

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4235)

pari: g = idealstar(,4235,2)

Character group

sage: G.order() pari: g.no
Order	=	2640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{660}\times C_{2}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4235}(2542,\cdot)$, $\chi_{4235}(1816,\cdot)$, $\chi_{4235}(2906,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$12$	$13$	$16$	$17$
$\chi_{4235}(1,\cdot)$	4235.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4235}(2,\cdot)$	4235.do	660	yes	$1$	$1$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{19}{660}\right)$
$\chi_{4235}(3,\cdot)$	4235.ci	60	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{4235}(4,\cdot)$	4235.dk	330	yes	$1$	$1$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{19}{330}\right)$
$\chi_{4235}(6,\cdot)$	4235.cu	110	no	$1$	$1$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{4235}(8,\cdot)$	4235.de	220	no	$1$	$1$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{19}{220}\right)$
$\chi_{4235}(9,\cdot)$	4235.bu	30	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4235}(12,\cdot)$	4235.da	132	yes	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{23}{132}\right)$
$\chi_{4235}(13,\cdot)$	4235.df	220	yes	$-1$	$1$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{53}{220}\right)$
$\chi_{4235}(16,\cdot)$	4235.dc	165	no	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{19}{165}\right)$
$\chi_{4235}(17,\cdot)$	4235.dr	660	yes	$-1$	$1$	$e\left(\frac{19}{660}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{161}{660}\right)$
$\chi_{4235}(18,\cdot)$	4235.do	660	yes	$1$	$1$	$e\left(\frac{457}{660}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{173}{660}\right)$
$\chi_{4235}(19,\cdot)$	4235.dj	330	yes	$1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{101}{330}\right)$
$\chi_{4235}(23,\cdot)$	4235.cz	132	yes	$-1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{4235}(24,\cdot)$	4235.dj	330	yes	$1$	$1$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{67}{330}\right)$
$\chi_{4235}(26,\cdot)$	4235.dh	330	no	$-1$	$1$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{89}{330}\right)$
$\chi_{4235}(27,\cdot)$	4235.bl	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{4235}(29,\cdot)$	4235.cx	110	no	$-1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{4235}(31,\cdot)$	4235.dh	330	no	$-1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{157}{330}\right)$
$\chi_{4235}(32,\cdot)$	4235.db	132	yes	$1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{19}{132}\right)$
$\chi_{4235}(34,\cdot)$	4235.br	22	yes	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{4235}(36,\cdot)$	4235.cf	55	no	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{4235}(37,\cdot)$	4235.dq	660	yes	$-1$	$1$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{193}{660}\right)$
$\chi_{4235}(38,\cdot)$	4235.dp	660	yes	$1$	$1$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{221}{660}\right)$
$\chi_{4235}(39,\cdot)$	4235.di	330	yes	$-1$	$1$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{59}{165}\right)$
$\chi_{4235}(41,\cdot)$	4235.cu	110	no	$1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{4235}(43,\cdot)$	4235.cd	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$i$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{41}{44}\right)$	$-1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{4235}(46,\cdot)$	4235.dm	330	no	$-1$	$1$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{97}{330}\right)$
$\chi_{4235}(47,\cdot)$	4235.dp	660	yes	$1$	$1$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{487}{660}\right)$
$\chi_{4235}(48,\cdot)$	4235.dd	220	yes	$1$	$1$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{51}{220}\right)$
$\chi_{4235}(51,\cdot)$	4235.dm	330	no	$-1$	$1$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{119}{330}\right)$
$\chi_{4235}(52,\cdot)$	4235.dr	660	yes	$-1$	$1$	$e\left(\frac{343}{660}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{197}{660}\right)$

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	$4235$
Structure	\(C_{660}\times C_{2}\times C_{2}\)
Order	$2640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(12\)	\(13\)	\(16\)	\(17\)
\(\chi_{4235}(1,\cdot)\)	4235.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4235}(2,\cdot)\)	4235.do	660	yes	\(1\)	\(1\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{19}{660}\right)\)
\(\chi_{4235}(3,\cdot)\)	4235.ci	60	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{4235}(4,\cdot)\)	4235.dk	330	yes	\(1\)	\(1\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{19}{330}\right)\)
\(\chi_{4235}(6,\cdot)\)	4235.cu	110	no	\(1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{4235}(8,\cdot)\)	4235.de	220	no	\(1\)	\(1\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)
\(\chi_{4235}(9,\cdot)\)	4235.bu	30	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4235}(12,\cdot)\)	4235.da	132	yes	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)
\(\chi_{4235}(13,\cdot)\)	4235.df	220	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{53}{220}\right)\)
\(\chi_{4235}(16,\cdot)\)	4235.dc	165	no	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)
\(\chi_{4235}(17,\cdot)\)	4235.dr	660	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{660}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{161}{660}\right)\)
\(\chi_{4235}(18,\cdot)\)	4235.do	660	yes	\(1\)	\(1\)	\(e\left(\frac{457}{660}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{173}{660}\right)\)
\(\chi_{4235}(19,\cdot)\)	4235.dj	330	yes	\(1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)
\(\chi_{4235}(23,\cdot)\)	4235.cz	132	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)
\(\chi_{4235}(24,\cdot)\)	4235.dj	330	yes	\(1\)	\(1\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{67}{330}\right)\)
\(\chi_{4235}(26,\cdot)\)	4235.dh	330	no	\(-1\)	\(1\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)
\(\chi_{4235}(27,\cdot)\)	4235.bl	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{4235}(29,\cdot)\)	4235.cx	110	no	\(-1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{4235}(31,\cdot)\)	4235.dh	330	no	\(-1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)
\(\chi_{4235}(32,\cdot)\)	4235.db	132	yes	\(1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)
\(\chi_{4235}(34,\cdot)\)	4235.br	22	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{4235}(36,\cdot)\)	4235.cf	55	no	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{4235}(37,\cdot)\)	4235.dq	660	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{193}{660}\right)\)
\(\chi_{4235}(38,\cdot)\)	4235.dp	660	yes	\(1\)	\(1\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{221}{660}\right)\)
\(\chi_{4235}(39,\cdot)\)	4235.di	330	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)
\(\chi_{4235}(41,\cdot)\)	4235.cu	110	no	\(1\)	\(1\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{4235}(43,\cdot)\)	4235.cd	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(i\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(-1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{4235}(46,\cdot)\)	4235.dm	330	no	\(-1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)
\(\chi_{4235}(47,\cdot)\)	4235.dp	660	yes	\(1\)	\(1\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{487}{660}\right)\)
\(\chi_{4235}(48,\cdot)\)	4235.dd	220	yes	\(1\)	\(1\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{51}{220}\right)\)
\(\chi_{4235}(51,\cdot)\)	4235.dm	330	no	\(-1\)	\(1\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{119}{330}\right)\)
\(\chi_{4235}(52,\cdot)\)	4235.dr	660	yes	\(-1\)	\(1\)	\(e\left(\frac{343}{660}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{197}{660}\right)\)

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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.