LMFDB - Group of Dirichlet characters of modulus 583

Show commands: PariGP / SageMath

sage: H = DirichletGroup(583)

pari: g = idealstar(,583,2)

Character group

sage: G.order() pari: g.no
Order	=	520
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{260}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{583}(266,\cdot)$, $\chi_{583}(320,\cdot)$

First 32 of 520 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{583}(1,\cdot)$	583.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{583}(2,\cdot)$	583.x	260	yes	$1$	$1$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{583}(3,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{249}{260}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{583}(4,\cdot)$	583.t	130	yes	$1$	$1$	$e\left(\frac{31}{130}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{583}(5,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{147}{260}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{52}\right)$
$\chi_{583}(6,\cdot)$	583.v	130	yes	$-1$	$1$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{583}(7,\cdot)$	583.v	130	yes	$-1$	$1$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{583}(8,\cdot)$	583.x	260	yes	$1$	$1$	$e\left(\frac{93}{260}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{93}{130}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{583}(9,\cdot)$	583.t	130	yes	$1$	$1$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{23}{65}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{583}(10,\cdot)$	583.o	26	yes	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{583}(12,\cdot)$	583.r	52	no	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{49}{52}\right)$
$\chi_{583}(13,\cdot)$	583.u	130	yes	$-1$	$1$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{89}{130}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{583}(14,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{23}{260}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{52}\right)$
$\chi_{583}(15,\cdot)$	583.s	65	yes	$1$	$1$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{34}{65}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{3}{65}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{583}(16,\cdot)$	583.s	65	yes	$1$	$1$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{62}{65}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{57}{65}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{583}(17,\cdot)$	583.v	130	yes	$-1$	$1$	$e\left(\frac{6}{65}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{12}{65}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{583}(18,\cdot)$	583.x	260	yes	$1$	$1$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{21}{65}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{41}{52}\right)$
$\chi_{583}(19,\cdot)$	583.x	260	yes	$1$	$1$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{129}{260}\right)$	$e\left(\frac{3}{130}\right)$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{9}{260}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{583}(20,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{141}{260}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{179}{260}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{163}{260}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{47}{52}\right)$
$\chi_{583}(21,\cdot)$	583.q	52	yes	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{583}(23,\cdot)$	583.e	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$i$	$-1$	$-1$	$i$	$-1$	$1$	$i$
$\chi_{583}(24,\cdot)$	583.u	130	yes	$-1$	$1$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{63}{65}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{583}(25,\cdot)$	583.t	130	yes	$1$	$1$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{14}{65}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{583}(26,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{177}{260}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{47}{130}\right)$	$e\left(\frac{103}{260}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{17}{130}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{583}(27,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{227}{260}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{69}{130}\right)$	$e\left(\frac{37}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{33}{52}\right)$
$\chi_{583}(28,\cdot)$	583.u	130	yes	$-1$	$1$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{4}{65}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{81}{130}\right)$	$e\left(\frac{56}{65}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{583}(29,\cdot)$	583.v	130	yes	$-1$	$1$	$e\left(\frac{38}{65}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{49}{130}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{49}{65}\right)$	$e\left(\frac{18}{65}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{583}(30,\cdot)$	583.l	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$-i$
$\chi_{583}(31,\cdot)$	583.w	260	yes	$-1$	$1$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{61}{130}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{107}{130}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{183}{260}\right)$	$e\left(\frac{23}{130}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{583}(32,\cdot)$	583.q	52	yes	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{583}(34,\cdot)$	583.r	52	no	$-1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{583}(35,\cdot)$	583.x	260	yes	$1$	$1$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{193}{260}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{1}{65}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{15}{52}\right)$

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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	$583$
Structure	\(C_{2}\times C_{260}\)
Order	$520$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{583}(1,\cdot)\)	583.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{583}(2,\cdot)\)	583.x	260	yes	\(1\)	\(1\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{583}(3,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{249}{260}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{583}(4,\cdot)\)	583.t	130	yes	\(1\)	\(1\)	\(e\left(\frac{31}{130}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{583}(5,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{147}{260}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)
\(\chi_{583}(6,\cdot)\)	583.v	130	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{583}(7,\cdot)\)	583.v	130	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{583}(8,\cdot)\)	583.x	260	yes	\(1\)	\(1\)	\(e\left(\frac{93}{260}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{93}{130}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{583}(9,\cdot)\)	583.t	130	yes	\(1\)	\(1\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{23}{65}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{583}(10,\cdot)\)	583.o	26	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{583}(12,\cdot)\)	583.r	52	no	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)
\(\chi_{583}(13,\cdot)\)	583.u	130	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{89}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{583}(14,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{260}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)
\(\chi_{583}(15,\cdot)\)	583.s	65	yes	\(1\)	\(1\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{34}{65}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{3}{65}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{583}(16,\cdot)\)	583.s	65	yes	\(1\)	\(1\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{62}{65}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{57}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{583}(17,\cdot)\)	583.v	130	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{65}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{12}{65}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{583}(18,\cdot)\)	583.x	260	yes	\(1\)	\(1\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{21}{65}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)
\(\chi_{583}(19,\cdot)\)	583.x	260	yes	\(1\)	\(1\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{129}{260}\right)\)	\(e\left(\frac{3}{130}\right)\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{9}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{583}(20,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{141}{260}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{179}{260}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{163}{260}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)
\(\chi_{583}(21,\cdot)\)	583.q	52	yes	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{583}(23,\cdot)\)	583.e	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(i\)
\(\chi_{583}(24,\cdot)\)	583.u	130	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{583}(25,\cdot)\)	583.t	130	yes	\(1\)	\(1\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{14}{65}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{583}(26,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{177}{260}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{47}{130}\right)\)	\(e\left(\frac{103}{260}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{17}{130}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{583}(27,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{227}{260}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{69}{130}\right)\)	\(e\left(\frac{37}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)
\(\chi_{583}(28,\cdot)\)	583.u	130	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{4}{65}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{81}{130}\right)\)	\(e\left(\frac{56}{65}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{583}(29,\cdot)\)	583.v	130	yes	\(-1\)	\(1\)	\(e\left(\frac{38}{65}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{49}{130}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{49}{65}\right)\)	\(e\left(\frac{18}{65}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{583}(30,\cdot)\)	583.l	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(-i\)
\(\chi_{583}(31,\cdot)\)	583.w	260	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{61}{130}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{107}{130}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{183}{260}\right)\)	\(e\left(\frac{23}{130}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{583}(32,\cdot)\)	583.q	52	yes	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{583}(34,\cdot)\)	583.r	52	no	\(-1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{583}(35,\cdot)\)	583.x	260	yes	\(1\)	\(1\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{193}{260}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{1}{65}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)

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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.