LMFDB - Group of Dirichlet characters of modulus 4232

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(4232)

gp:g = idealstar(,4232,2)

magma:G = FullDirichletGroup(4232);

Character group

Order	=	2024	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{506}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{4232}(3175,\cdot)$, $\chi_{4232}(2117,\cdot)$, $\chi_{4232}(2121,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2024 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4232}(1,\cdot)$	4232.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4232}(3,\cdot)$	4232.be	506	yes	$-1$	$1$	$e\left(\frac{128}{253}\right)$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{43}{506}\right)$
$\chi_{4232}(5,\cdot)$	4232.bc	506	yes	$-1$	$1$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{129}{506}\right)$	$e\left(\frac{16}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{199}{253}\right)$
$\chi_{4232}(7,\cdot)$	4232.ba	506	no	$1$	$1$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{129}{506}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{489}{506}\right)$
$\chi_{4232}(9,\cdot)$	4232.y	253	no	$1$	$1$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{16}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{43}{253}\right)$
$\chi_{4232}(11,\cdot)$	4232.bf	506	yes	$1$	$1$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{42}{253}\right)$
$\chi_{4232}(13,\cdot)$	4232.z	506	yes	$1$	$1$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{427}{506}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{479}{506}\right)$
$\chi_{4232}(15,\cdot)$	4232.ba	506	no	$1$	$1$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{441}{506}\right)$
$\chi_{4232}(17,\cdot)$	4232.bd	506	no	$-1$	$1$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{335}{506}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{157}{506}\right)$
$\chi_{4232}(19,\cdot)$	4232.bf	506	yes	$1$	$1$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{125}{253}\right)$
$\chi_{4232}(21,\cdot)$	4232.bc	506	yes	$-1$	$1$	$e\left(\frac{43}{506}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{42}{253}\right)$	$e\left(\frac{479}{506}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{13}{253}\right)$
$\chi_{4232}(25,\cdot)$	4232.y	253	no	$1$	$1$	$e\left(\frac{16}{253}\right)$	$e\left(\frac{1}{253}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{190}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{145}{253}\right)$
$\chi_{4232}(27,\cdot)$	4232.be	506	yes	$-1$	$1$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{265}{506}\right)$	$e\left(\frac{57}{506}\right)$	$e\left(\frac{190}{253}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{129}{506}\right)$
$\chi_{4232}(29,\cdot)$	4232.z	506	yes	$1$	$1$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{403}{506}\right)$	$e\left(\frac{61}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{305}{506}\right)$	$e\left(\frac{417}{506}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{245}{506}\right)$
$\chi_{4232}(31,\cdot)$	4232.bb	506	no	$-1$	$1$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{127}{253}\right)$
$\chi_{4232}(33,\cdot)$	4232.bd	506	no	$-1$	$1$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{465}{506}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{127}{506}\right)$
$\chi_{4232}(35,\cdot)$	4232.be	506	yes	$-1$	$1$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{159}{506}\right)$	$e\left(\frac{439}{506}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{381}{506}\right)$
$\chi_{4232}(37,\cdot)$	4232.bc	506	yes	$-1$	$1$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{47}{506}\right)$	$e\left(\frac{149}{253}\right)$	$e\left(\frac{122}{253}\right)$	$e\left(\frac{283}{506}\right)$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{98}{253}\right)$
$\chi_{4232}(39,\cdot)$	4232.bb	506	no	$-1$	$1$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{8}{253}\right)$
$\chi_{4232}(41,\cdot)$	4232.y	253	no	$1$	$1$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{105}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{87}{253}\right)$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{45}{253}\right)$
$\chi_{4232}(43,\cdot)$	4232.bf	506	yes	$1$	$1$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{140}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{323}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{317}{506}\right)$	$e\left(\frac{60}{253}\right)$
$\chi_{4232}(45,\cdot)$	4232.u	46	yes	$-1$	$1$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{4232}(47,\cdot)$	4232.v	46	no	$-1$	$1$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{4232}(49,\cdot)$	4232.y	253	no	$1$	$1$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{236}{253}\right)$
$\chi_{4232}(51,\cdot)$	4232.bf	506	yes	$1$	$1$	$e\left(\frac{107}{253}\right)$	$e\left(\frac{149}{253}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{471}{506}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{100}{253}\right)$
$\chi_{4232}(53,\cdot)$	4232.bc	506	yes	$-1$	$1$	$e\left(\frac{73}{506}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{13}{506}\right)$	$e\left(\frac{125}{506}\right)$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{228}{253}\right)$
$\chi_{4232}(55,\cdot)$	4232.bb	506	no	$-1$	$1$	$e\left(\frac{369}{506}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{113}{506}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{241}{253}\right)$
$\chi_{4232}(57,\cdot)$	4232.bd	506	no	$-1$	$1$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{96}{253}\right)$	$e\left(\frac{153}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{293}{506}\right)$
$\chi_{4232}(59,\cdot)$	4232.be	506	yes	$-1$	$1$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{421}{506}\right)$	$e\left(\frac{167}{506}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{295}{506}\right)$	$e\left(\frac{73}{506}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{325}{506}\right)$
$\chi_{4232}(61,\cdot)$	4232.bc	506	yes	$-1$	$1$	$e\left(\frac{85}{506}\right)$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{37}{506}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{61}{253}\right)$
$\chi_{4232}(63,\cdot)$	4232.o	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{4232}(65,\cdot)$	4232.bd	506	no	$-1$	$1$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{245}{506}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{211}{506}\right)$	$e\left(\frac{479}{506}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{371}{506}\right)$

Click here to search among the remaining 1992 characters.

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	$4232$
Structure	\(C_{2}\times C_{2}\times C_{506}\)
Order	$2024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4232}(1,\cdot)\)	4232.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4232}(3,\cdot)\)	4232.be	506	yes	\(-1\)	\(1\)	\(e\left(\frac{128}{253}\right)\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{43}{506}\right)\)
\(\chi_{4232}(5,\cdot)\)	4232.bc	506	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{129}{506}\right)\)	\(e\left(\frac{16}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)
\(\chi_{4232}(7,\cdot)\)	4232.ba	506	no	\(1\)	\(1\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{129}{506}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{489}{506}\right)\)
\(\chi_{4232}(9,\cdot)\)	4232.y	253	no	\(1\)	\(1\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{16}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{43}{253}\right)\)
\(\chi_{4232}(11,\cdot)\)	4232.bf	506	yes	\(1\)	\(1\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{42}{253}\right)\)
\(\chi_{4232}(13,\cdot)\)	4232.z	506	yes	\(1\)	\(1\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{427}{506}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{479}{506}\right)\)
\(\chi_{4232}(15,\cdot)\)	4232.ba	506	no	\(1\)	\(1\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{441}{506}\right)\)
\(\chi_{4232}(17,\cdot)\)	4232.bd	506	no	\(-1\)	\(1\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{335}{506}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{157}{506}\right)\)
\(\chi_{4232}(19,\cdot)\)	4232.bf	506	yes	\(1\)	\(1\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{125}{253}\right)\)
\(\chi_{4232}(21,\cdot)\)	4232.bc	506	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{506}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{42}{253}\right)\)	\(e\left(\frac{479}{506}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{13}{253}\right)\)
\(\chi_{4232}(25,\cdot)\)	4232.y	253	no	\(1\)	\(1\)	\(e\left(\frac{16}{253}\right)\)	\(e\left(\frac{1}{253}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{190}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)
\(\chi_{4232}(27,\cdot)\)	4232.be	506	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{265}{506}\right)\)	\(e\left(\frac{57}{506}\right)\)	\(e\left(\frac{190}{253}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{129}{506}\right)\)
\(\chi_{4232}(29,\cdot)\)	4232.z	506	yes	\(1\)	\(1\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{403}{506}\right)\)	\(e\left(\frac{61}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{305}{506}\right)\)	\(e\left(\frac{417}{506}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{245}{506}\right)\)
\(\chi_{4232}(31,\cdot)\)	4232.bb	506	no	\(-1\)	\(1\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{127}{253}\right)\)
\(\chi_{4232}(33,\cdot)\)	4232.bd	506	no	\(-1\)	\(1\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{465}{506}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)
\(\chi_{4232}(35,\cdot)\)	4232.be	506	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{159}{506}\right)\)	\(e\left(\frac{439}{506}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{381}{506}\right)\)
\(\chi_{4232}(37,\cdot)\)	4232.bc	506	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{47}{506}\right)\)	\(e\left(\frac{149}{253}\right)\)	\(e\left(\frac{122}{253}\right)\)	\(e\left(\frac{283}{506}\right)\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)
\(\chi_{4232}(39,\cdot)\)	4232.bb	506	no	\(-1\)	\(1\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{8}{253}\right)\)
\(\chi_{4232}(41,\cdot)\)	4232.y	253	no	\(1\)	\(1\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{105}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{87}{253}\right)\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)
\(\chi_{4232}(43,\cdot)\)	4232.bf	506	yes	\(1\)	\(1\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{140}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{323}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{317}{506}\right)\)	\(e\left(\frac{60}{253}\right)\)
\(\chi_{4232}(45,\cdot)\)	4232.u	46	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{4232}(47,\cdot)\)	4232.v	46	no	\(-1\)	\(1\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{4232}(49,\cdot)\)	4232.y	253	no	\(1\)	\(1\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)
\(\chi_{4232}(51,\cdot)\)	4232.bf	506	yes	\(1\)	\(1\)	\(e\left(\frac{107}{253}\right)\)	\(e\left(\frac{149}{253}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{471}{506}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)
\(\chi_{4232}(53,\cdot)\)	4232.bc	506	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{506}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{13}{506}\right)\)	\(e\left(\frac{125}{506}\right)\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{228}{253}\right)\)
\(\chi_{4232}(55,\cdot)\)	4232.bb	506	no	\(-1\)	\(1\)	\(e\left(\frac{369}{506}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{113}{506}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{241}{253}\right)\)
\(\chi_{4232}(57,\cdot)\)	4232.bd	506	no	\(-1\)	\(1\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{96}{253}\right)\)	\(e\left(\frac{153}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)
\(\chi_{4232}(59,\cdot)\)	4232.be	506	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{421}{506}\right)\)	\(e\left(\frac{167}{506}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{295}{506}\right)\)	\(e\left(\frac{73}{506}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{325}{506}\right)\)
\(\chi_{4232}(61,\cdot)\)	4232.bc	506	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{506}\right)\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{37}{506}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{61}{253}\right)\)
\(\chi_{4232}(63,\cdot)\)	4232.o	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{4232}(65,\cdot)\)	4232.bd	506	no	\(-1\)	\(1\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{245}{506}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{211}{506}\right)\)	\(e\left(\frac{479}{506}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{371}{506}\right)\)

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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.