LMFDB - Group of Dirichlet characters of modulus 2593

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2593)

pari: g = idealstar(,2593,2)

Character group

sage: G.order() pari: g.no
Order	=	2592
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2592}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2593}(7,\cdot)$

First 32 of 2592 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2593}(1,\cdot)$	2593.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2593}(2,\cdot)$	2593.r	81	yes	$1$	$1$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{7}{81}\right)$	$1$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{46}{81}\right)$
$\chi_{2593}(3,\cdot)$	2593.ba	648	yes	$1$	$1$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{85}{648}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{613}{648}\right)$	$e\left(\frac{593}{648}\right)$
$\chi_{2593}(4,\cdot)$	2593.r	81	yes	$1$	$1$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{14}{81}\right)$	$1$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{11}{81}\right)$
$\chi_{2593}(5,\cdot)$	2593.m	32	yes	$-1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{32}\right)$	$1$	$i$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{2593}(6,\cdot)$	2593.ba	648	yes	$1$	$1$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{341}{648}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{317}{648}\right)$	$e\left(\frac{313}{648}\right)$
$\chi_{2593}(7,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{85}{648}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{341}{648}\right)$	$e\left(\frac{1}{2592}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{85}{324}\right)$	$e\left(\frac{1753}{2592}\right)$	$e\left(\frac{533}{2592}\right)$
$\chi_{2593}(8,\cdot)$	2593.l	27	yes	$1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{27}\right)$	$1$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2593}(9,\cdot)$	2593.y	324	yes	$1$	$1$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{23}{81}\right)$	$i$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{85}{324}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{289}{324}\right)$	$e\left(\frac{269}{324}\right)$
$\chi_{2593}(10,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{613}{648}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{317}{648}\right)$	$e\left(\frac{1753}{2592}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{289}{324}\right)$	$e\left(\frac{1489}{2592}\right)$	$e\left(\frac{1229}{2592}\right)$
$\chi_{2593}(11,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{593}{648}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{313}{648}\right)$	$e\left(\frac{533}{2592}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{269}{324}\right)$	$e\left(\frac{1229}{2592}\right)$	$e\left(\frac{1561}{2592}\right)$
$\chi_{2593}(12,\cdot)$	2593.w	216	yes	$1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{7}{216}\right)$	$e\left(\frac{11}{216}\right)$
$\chi_{2593}(13,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{595}{648}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{443}{648}\right)$	$e\left(\frac{655}{2592}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{2551}{2592}\right)$	$e\left(\frac{1787}{2592}\right)$
$\chi_{2593}(14,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{293}{648}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{253}{648}\right)$	$e\left(\frac{1025}{2592}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{293}{324}\right)$	$e\left(\frac{569}{2592}\right)$	$e\left(\frac{2005}{2592}\right)$
$\chi_{2593}(15,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{145}{648}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{353}{648}\right)$	$e\left(\frac{1069}{2592}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{145}{324}\right)$	$e\left(\frac{2533}{2592}\right)$	$e\left(\frac{2129}{2592}\right)$
$\chi_{2593}(16,\cdot)$	2593.r	81	yes	$1$	$1$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{28}{81}\right)$	$1$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{22}{81}\right)$
$\chi_{2593}(17,\cdot)$	2593.ba	648	yes	$1$	$1$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{623}{648}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{239}{648}\right)$	$e\left(\frac{283}{648}\right)$
$\chi_{2593}(18,\cdot)$	2593.t	108	yes	$1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{10}{27}\right)$	$i$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{43}{108}\right)$
$\chi_{2593}(19,\cdot)$	2593.w	216	yes	$1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{41}{216}\right)$
$\chi_{2593}(20,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{173}{648}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{229}{648}\right)$	$e\left(\frac{185}{2592}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{173}{324}\right)$	$e\left(\frac{305}{2592}\right)$	$e\left(\frac{109}{2592}\right)$
$\chi_{2593}(21,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{473}{648}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{289}{648}\right)$	$e\left(\frac{341}{2592}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{149}{324}\right)$	$e\left(\frac{1613}{2592}\right)$	$e\left(\frac{313}{2592}\right)$
$\chi_{2593}(22,\cdot)$	2593.x	288	yes	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{288}\right)$	$e\left(\frac{49}{288}\right)$
$\chi_{2593}(23,\cdot)$	2593.bb	864	yes	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{761}{864}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{17}{864}\right)$	$e\left(\frac{397}{864}\right)$
$\chi_{2593}(24,\cdot)$	2593.ba	648	yes	$1$	$1$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{205}{648}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{373}{648}\right)$	$e\left(\frac{401}{648}\right)$
$\chi_{2593}(25,\cdot)$	2593.i	16	yes	$1$	$1$	$1$	$i$	$1$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$1$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2593}(26,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{155}{648}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{355}{648}\right)$	$e\left(\frac{1679}{2592}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{155}{324}\right)$	$e\left(\frac{1367}{2592}\right)$	$e\left(\frac{667}{2592}\right)$
$\chi_{2593}(27,\cdot)$	2593.w	216	yes	$1$	$1$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{161}{216}\right)$
$\chi_{2593}(28,\cdot)$	2593.bb	864	yes	$-1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{55}{216}\right)$	$e\left(\frac{683}{864}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{659}{864}\right)$	$e\left(\frac{295}{864}\right)$
$\chi_{2593}(29,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{479}{648}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{31}{648}\right)$	$e\left(\frac{59}{2592}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{155}{324}\right)$	$e\left(\frac{2339}{2592}\right)$	$e\left(\frac{343}{2592}\right)$
$\chi_{2593}(30,\cdot)$	2593.bd	2592	yes	$-1$	$1$	$e\left(\frac{70}{81}\right)$	$e\left(\frac{353}{648}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{265}{648}\right)$	$e\left(\frac{2093}{2592}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{1349}{2592}\right)$	$e\left(\frac{1009}{2592}\right)$
$\chi_{2593}(31,\cdot)$	2593.r	81	yes	$1$	$1$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{43}{81}\right)$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{62}{81}\right)$	$e\left(\frac{28}{81}\right)$
$\chi_{2593}(32,\cdot)$	2593.r	81	yes	$1$	$1$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{35}{81}\right)$	$1$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{68}{81}\right)$

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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	$2593$
Structure	\(C_{2592}\)
Order	$2592$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2593}(1,\cdot)\)	2593.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2593}(2,\cdot)\)	2593.r	81	yes	\(1\)	\(1\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(1\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)
\(\chi_{2593}(3,\cdot)\)	2593.ba	648	yes	\(1\)	\(1\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{85}{648}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{613}{648}\right)\)	\(e\left(\frac{593}{648}\right)\)
\(\chi_{2593}(4,\cdot)\)	2593.r	81	yes	\(1\)	\(1\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(1\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)
\(\chi_{2593}(5,\cdot)\)	2593.m	32	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{2593}(6,\cdot)\)	2593.ba	648	yes	\(1\)	\(1\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{341}{648}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{317}{648}\right)\)	\(e\left(\frac{313}{648}\right)\)
\(\chi_{2593}(7,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{85}{648}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{341}{648}\right)\)	\(e\left(\frac{1}{2592}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{85}{324}\right)\)	\(e\left(\frac{1753}{2592}\right)\)	\(e\left(\frac{533}{2592}\right)\)
\(\chi_{2593}(8,\cdot)\)	2593.l	27	yes	\(1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(1\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2593}(9,\cdot)\)	2593.y	324	yes	\(1\)	\(1\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(i\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{85}{324}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{289}{324}\right)\)	\(e\left(\frac{269}{324}\right)\)
\(\chi_{2593}(10,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{613}{648}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{317}{648}\right)\)	\(e\left(\frac{1753}{2592}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{289}{324}\right)\)	\(e\left(\frac{1489}{2592}\right)\)	\(e\left(\frac{1229}{2592}\right)\)
\(\chi_{2593}(11,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{593}{648}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{313}{648}\right)\)	\(e\left(\frac{533}{2592}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{269}{324}\right)\)	\(e\left(\frac{1229}{2592}\right)\)	\(e\left(\frac{1561}{2592}\right)\)
\(\chi_{2593}(12,\cdot)\)	2593.w	216	yes	\(1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{7}{216}\right)\)	\(e\left(\frac{11}{216}\right)\)
\(\chi_{2593}(13,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{595}{648}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{443}{648}\right)\)	\(e\left(\frac{655}{2592}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{271}{324}\right)\)	\(e\left(\frac{2551}{2592}\right)\)	\(e\left(\frac{1787}{2592}\right)\)
\(\chi_{2593}(14,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{293}{648}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{253}{648}\right)\)	\(e\left(\frac{1025}{2592}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{293}{324}\right)\)	\(e\left(\frac{569}{2592}\right)\)	\(e\left(\frac{2005}{2592}\right)\)
\(\chi_{2593}(15,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{145}{648}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{353}{648}\right)\)	\(e\left(\frac{1069}{2592}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{145}{324}\right)\)	\(e\left(\frac{2533}{2592}\right)\)	\(e\left(\frac{2129}{2592}\right)\)
\(\chi_{2593}(16,\cdot)\)	2593.r	81	yes	\(1\)	\(1\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(1\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{22}{81}\right)\)
\(\chi_{2593}(17,\cdot)\)	2593.ba	648	yes	\(1\)	\(1\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{61}{162}\right)\)	\(e\left(\frac{623}{648}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{239}{648}\right)\)	\(e\left(\frac{283}{648}\right)\)
\(\chi_{2593}(18,\cdot)\)	2593.t	108	yes	\(1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(i\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{43}{108}\right)\)
\(\chi_{2593}(19,\cdot)\)	2593.w	216	yes	\(1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{41}{216}\right)\)
\(\chi_{2593}(20,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{173}{648}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{229}{648}\right)\)	\(e\left(\frac{185}{2592}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{173}{324}\right)\)	\(e\left(\frac{305}{2592}\right)\)	\(e\left(\frac{109}{2592}\right)\)
\(\chi_{2593}(21,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{473}{648}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{289}{648}\right)\)	\(e\left(\frac{341}{2592}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{149}{324}\right)\)	\(e\left(\frac{1613}{2592}\right)\)	\(e\left(\frac{313}{2592}\right)\)
\(\chi_{2593}(22,\cdot)\)	2593.x	288	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{288}\right)\)	\(e\left(\frac{49}{288}\right)\)
\(\chi_{2593}(23,\cdot)\)	2593.bb	864	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{761}{864}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{17}{864}\right)\)	\(e\left(\frac{397}{864}\right)\)
\(\chi_{2593}(24,\cdot)\)	2593.ba	648	yes	\(1\)	\(1\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{205}{648}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{373}{648}\right)\)	\(e\left(\frac{401}{648}\right)\)
\(\chi_{2593}(25,\cdot)\)	2593.i	16	yes	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2593}(26,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{155}{648}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{355}{648}\right)\)	\(e\left(\frac{1679}{2592}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{155}{324}\right)\)	\(e\left(\frac{1367}{2592}\right)\)	\(e\left(\frac{667}{2592}\right)\)
\(\chi_{2593}(27,\cdot)\)	2593.w	216	yes	\(1\)	\(1\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{161}{216}\right)\)
\(\chi_{2593}(28,\cdot)\)	2593.bb	864	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{55}{216}\right)\)	\(e\left(\frac{683}{864}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{659}{864}\right)\)	\(e\left(\frac{295}{864}\right)\)
\(\chi_{2593}(29,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{479}{648}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{31}{648}\right)\)	\(e\left(\frac{59}{2592}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{155}{324}\right)\)	\(e\left(\frac{2339}{2592}\right)\)	\(e\left(\frac{343}{2592}\right)\)
\(\chi_{2593}(30,\cdot)\)	2593.bd	2592	yes	\(-1\)	\(1\)	\(e\left(\frac{70}{81}\right)\)	\(e\left(\frac{353}{648}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{265}{648}\right)\)	\(e\left(\frac{2093}{2592}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{29}{324}\right)\)	\(e\left(\frac{1349}{2592}\right)\)	\(e\left(\frac{1009}{2592}\right)\)
\(\chi_{2593}(31,\cdot)\)	2593.r	81	yes	\(1\)	\(1\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{62}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)
\(\chi_{2593}(32,\cdot)\)	2593.r	81	yes	\(1\)	\(1\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(1\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)

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L-functions

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Character group

First 32 of 2592 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.