LMFDB - Group of Dirichlet characters of modulus 2557

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2557)

pari: g = idealstar(,2557,2)

Character group

sage: G.order() pari: g.no
Order	=	2556
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2556}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2557}(2,\cdot)$

First 32 of 2556 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2557}(1,\cdot)$	2557.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2557}(2,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{1}{2556}\right)$	$e\left(\frac{595}{639}\right)$	$e\left(\frac{1}{1278}\right)$	$e\left(\frac{2371}{2556}\right)$	$e\left(\frac{2381}{2556}\right)$	$e\left(\frac{1021}{1278}\right)$	$e\left(\frac{1}{852}\right)$	$e\left(\frac{551}{639}\right)$	$e\left(\frac{593}{639}\right)$	$e\left(\frac{566}{639}\right)$
$\chi_{2557}(3,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{595}{639}\right)$	$e\left(\frac{76}{639}\right)$	$e\left(\frac{551}{639}\right)$	$e\left(\frac{472}{639}\right)$	$e\left(\frac{32}{639}\right)$	$e\left(\frac{251}{639}\right)$	$e\left(\frac{169}{213}\right)$	$e\left(\frac{152}{639}\right)$	$e\left(\frac{428}{639}\right)$	$e\left(\frac{68}{639}\right)$
$\chi_{2557}(4,\cdot)$	2557.q	1278	yes	$1$	$1$	$e\left(\frac{1}{1278}\right)$	$e\left(\frac{551}{639}\right)$	$e\left(\frac{1}{639}\right)$	$e\left(\frac{1093}{1278}\right)$	$e\left(\frac{1103}{1278}\right)$	$e\left(\frac{382}{639}\right)$	$e\left(\frac{1}{426}\right)$	$e\left(\frac{463}{639}\right)$	$e\left(\frac{547}{639}\right)$	$e\left(\frac{493}{639}\right)$
$\chi_{2557}(5,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{2371}{2556}\right)$	$e\left(\frac{472}{639}\right)$	$e\left(\frac{1093}{1278}\right)$	$e\left(\frac{997}{2556}\right)$	$e\left(\frac{1703}{2556}\right)$	$e\left(\frac{259}{1278}\right)$	$e\left(\frac{667}{852}\right)$	$e\left(\frac{305}{639}\right)$	$e\left(\frac{203}{639}\right)$	$e\left(\frac{86}{639}\right)$
$\chi_{2557}(6,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{2381}{2556}\right)$	$e\left(\frac{32}{639}\right)$	$e\left(\frac{1103}{1278}\right)$	$e\left(\frac{1703}{2556}\right)$	$e\left(\frac{2509}{2556}\right)$	$e\left(\frac{245}{1278}\right)$	$e\left(\frac{677}{852}\right)$	$e\left(\frac{64}{639}\right)$	$e\left(\frac{382}{639}\right)$	$e\left(\frac{634}{639}\right)$
$\chi_{2557}(7,\cdot)$	2557.q	1278	yes	$1$	$1$	$e\left(\frac{1021}{1278}\right)$	$e\left(\frac{251}{639}\right)$	$e\left(\frac{382}{639}\right)$	$e\left(\frac{259}{1278}\right)$	$e\left(\frac{245}{1278}\right)$	$e\left(\frac{232}{639}\right)$	$e\left(\frac{169}{426}\right)$	$e\left(\frac{502}{639}\right)$	$e\left(\frac{1}{639}\right)$	$e\left(\frac{460}{639}\right)$
$\chi_{2557}(8,\cdot)$	2557.p	852	yes	$-1$	$1$	$e\left(\frac{1}{852}\right)$	$e\left(\frac{169}{213}\right)$	$e\left(\frac{1}{426}\right)$	$e\left(\frac{667}{852}\right)$	$e\left(\frac{677}{852}\right)$	$e\left(\frac{169}{426}\right)$	$e\left(\frac{1}{284}\right)$	$e\left(\frac{125}{213}\right)$	$e\left(\frac{167}{213}\right)$	$e\left(\frac{140}{213}\right)$
$\chi_{2557}(9,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{551}{639}\right)$	$e\left(\frac{152}{639}\right)$	$e\left(\frac{463}{639}\right)$	$e\left(\frac{305}{639}\right)$	$e\left(\frac{64}{639}\right)$	$e\left(\frac{502}{639}\right)$	$e\left(\frac{125}{213}\right)$	$e\left(\frac{304}{639}\right)$	$e\left(\frac{217}{639}\right)$	$e\left(\frac{136}{639}\right)$
$\chi_{2557}(10,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{593}{639}\right)$	$e\left(\frac{428}{639}\right)$	$e\left(\frac{547}{639}\right)$	$e\left(\frac{203}{639}\right)$	$e\left(\frac{382}{639}\right)$	$e\left(\frac{1}{639}\right)$	$e\left(\frac{167}{213}\right)$	$e\left(\frac{217}{639}\right)$	$e\left(\frac{157}{639}\right)$	$e\left(\frac{13}{639}\right)$
$\chi_{2557}(11,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{566}{639}\right)$	$e\left(\frac{68}{639}\right)$	$e\left(\frac{493}{639}\right)$	$e\left(\frac{86}{639}\right)$	$e\left(\frac{634}{639}\right)$	$e\left(\frac{460}{639}\right)$	$e\left(\frac{140}{213}\right)$	$e\left(\frac{136}{639}\right)$	$e\left(\frac{13}{639}\right)$	$e\left(\frac{229}{639}\right)$
$\chi_{2557}(12,\cdot)$	2557.n	426	yes	$1$	$1$	$e\left(\frac{397}{426}\right)$	$e\left(\frac{209}{213}\right)$	$e\left(\frac{184}{213}\right)$	$e\left(\frac{253}{426}\right)$	$e\left(\frac{389}{426}\right)$	$e\left(\frac{211}{213}\right)$	$e\left(\frac{113}{142}\right)$	$e\left(\frac{205}{213}\right)$	$e\left(\frac{112}{213}\right)$	$e\left(\frac{187}{213}\right)$
$\chi_{2557}(13,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{488}{639}\right)$	$e\left(\frac{377}{639}\right)$	$e\left(\frac{337}{639}\right)$	$e\left(\frac{458}{639}\right)$	$e\left(\frac{226}{639}\right)$	$e\left(\frac{295}{639}\right)$	$e\left(\frac{62}{213}\right)$	$e\left(\frac{115}{639}\right)$	$e\left(\frac{307}{639}\right)$	$e\left(\frac{1}{639}\right)$
$\chi_{2557}(14,\cdot)$	2557.m	284	yes	$-1$	$1$	$e\left(\frac{227}{284}\right)$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{85}{142}\right)$	$e\left(\frac{37}{284}\right)$	$e\left(\frac{35}{284}\right)$	$e\left(\frac{23}{142}\right)$	$e\left(\frac{113}{284}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{66}{71}\right)$	$e\left(\frac{43}{71}\right)$
$\chi_{2557}(15,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{2195}{2556}\right)$	$e\left(\frac{548}{639}\right)$	$e\left(\frac{917}{1278}\right)$	$e\left(\frac{329}{2556}\right)$	$e\left(\frac{1831}{2556}\right)$	$e\left(\frac{761}{1278}\right)$	$e\left(\frac{491}{852}\right)$	$e\left(\frac{457}{639}\right)$	$e\left(\frac{631}{639}\right)$	$e\left(\frac{154}{639}\right)$
$\chi_{2557}(16,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{1}{639}\right)$	$e\left(\frac{463}{639}\right)$	$e\left(\frac{2}{639}\right)$	$e\left(\frac{454}{639}\right)$	$e\left(\frac{464}{639}\right)$	$e\left(\frac{125}{639}\right)$	$e\left(\frac{1}{213}\right)$	$e\left(\frac{287}{639}\right)$	$e\left(\frac{455}{639}\right)$	$e\left(\frac{347}{639}\right)$
$\chi_{2557}(17,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{1309}{2556}\right)$	$e\left(\frac{553}{639}\right)$	$e\left(\frac{31}{1278}\right)$	$e\left(\frac{655}{2556}\right)$	$e\left(\frac{965}{2556}\right)$	$e\left(\frac{979}{1278}\right)$	$e\left(\frac{457}{852}\right)$	$e\left(\frac{467}{639}\right)$	$e\left(\frac{491}{639}\right)$	$e\left(\frac{293}{639}\right)$
$\chi_{2557}(18,\cdot)$	2557.m	284	yes	$-1$	$1$	$e\left(\frac{245}{284}\right)$	$e\left(\frac{12}{71}\right)$	$e\left(\frac{103}{142}\right)$	$e\left(\frac{115}{284}\right)$	$e\left(\frac{9}{284}\right)$	$e\left(\frac{83}{142}\right)$	$e\left(\frac{167}{284}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{7}{71}\right)$
$\chi_{2557}(19,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{179}{639}\right)$	$e\left(\frac{446}{639}\right)$	$e\left(\frac{358}{639}\right)$	$e\left(\frac{113}{639}\right)$	$e\left(\frac{625}{639}\right)$	$e\left(\frac{10}{639}\right)$	$e\left(\frac{179}{213}\right)$	$e\left(\frac{253}{639}\right)$	$e\left(\frac{292}{639}\right)$	$e\left(\frac{130}{639}\right)$
$\chi_{2557}(20,\cdot)$	2557.p	852	yes	$-1$	$1$	$e\left(\frac{791}{852}\right)$	$e\left(\frac{128}{213}\right)$	$e\left(\frac{365}{426}\right)$	$e\left(\frac{209}{852}\right)$	$e\left(\frac{451}{852}\right)$	$e\left(\frac{341}{426}\right)$	$e\left(\frac{223}{284}\right)$	$e\left(\frac{43}{213}\right)$	$e\left(\frac{37}{213}\right)$	$e\left(\frac{193}{213}\right)$
$\chi_{2557}(21,\cdot)$	2557.n	426	yes	$1$	$1$	$e\left(\frac{311}{426}\right)$	$e\left(\frac{109}{213}\right)$	$e\left(\frac{98}{213}\right)$	$e\left(\frac{401}{426}\right)$	$e\left(\frac{103}{426}\right)$	$e\left(\frac{161}{213}\right)$	$e\left(\frac{27}{142}\right)$	$e\left(\frac{5}{213}\right)$	$e\left(\frac{143}{213}\right)$	$e\left(\frac{176}{213}\right)$
$\chi_{2557}(22,\cdot)$	2557.p	852	yes	$-1$	$1$	$e\left(\frac{755}{852}\right)$	$e\left(\frac{8}{213}\right)$	$e\left(\frac{329}{426}\right)$	$e\left(\frac{53}{852}\right)$	$e\left(\frac{787}{852}\right)$	$e\left(\frac{221}{426}\right)$	$e\left(\frac{187}{284}\right)$	$e\left(\frac{16}{213}\right)$	$e\left(\frac{202}{213}\right)$	$e\left(\frac{52}{213}\right)$
$\chi_{2557}(23,\cdot)$	2557.q	1278	yes	$1$	$1$	$e\left(\frac{613}{1278}\right)$	$e\left(\frac{371}{639}\right)$	$e\left(\frac{613}{639}\right)$	$e\left(\frac{337}{1278}\right)$	$e\left(\frac{77}{1278}\right)$	$e\left(\frac{292}{639}\right)$	$e\left(\frac{187}{426}\right)$	$e\left(\frac{103}{639}\right)$	$e\left(\frac{475}{639}\right)$	$e\left(\frac{601}{639}\right)$
$\chi_{2557}(24,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{2383}{2556}\right)$	$e\left(\frac{583}{639}\right)$	$e\left(\frac{1105}{1278}\right)$	$e\left(\frac{1333}{2556}\right)$	$e\left(\frac{2159}{2556}\right)$	$e\left(\frac{1009}{1278}\right)$	$e\left(\frac{679}{852}\right)$	$e\left(\frac{527}{639}\right)$	$e\left(\frac{290}{639}\right)$	$e\left(\frac{488}{639}\right)$
$\chi_{2557}(25,\cdot)$	2557.q	1278	yes	$1$	$1$	$e\left(\frac{1093}{1278}\right)$	$e\left(\frac{305}{639}\right)$	$e\left(\frac{454}{639}\right)$	$e\left(\frac{997}{1278}\right)$	$e\left(\frac{425}{1278}\right)$	$e\left(\frac{259}{639}\right)$	$e\left(\frac{241}{426}\right)$	$e\left(\frac{610}{639}\right)$	$e\left(\frac{406}{639}\right)$	$e\left(\frac{172}{639}\right)$
$\chi_{2557}(26,\cdot)$	2557.m	284	yes	$-1$	$1$	$e\left(\frac{217}{284}\right)$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{75}{142}\right)$	$e\left(\frac{183}{284}\right)$	$e\left(\frac{81}{284}\right)$	$e\left(\frac{37}{142}\right)$	$e\left(\frac{83}{284}\right)$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{29}{71}\right)$	$e\left(\frac{63}{71}\right)$
$\chi_{2557}(27,\cdot)$	2557.l	213	yes	$1$	$1$	$e\left(\frac{169}{213}\right)$	$e\left(\frac{76}{213}\right)$	$e\left(\frac{125}{213}\right)$	$e\left(\frac{46}{213}\right)$	$e\left(\frac{32}{213}\right)$	$e\left(\frac{38}{213}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{152}{213}\right)$	$e\left(\frac{2}{213}\right)$	$e\left(\frac{68}{213}\right)$
$\chi_{2557}(28,\cdot)$	2557.o	639	yes	$1$	$1$	$e\left(\frac{511}{639}\right)$	$e\left(\frac{163}{639}\right)$	$e\left(\frac{383}{639}\right)$	$e\left(\frac{37}{639}\right)$	$e\left(\frac{35}{639}\right)$	$e\left(\frac{614}{639}\right)$	$e\left(\frac{85}{213}\right)$	$e\left(\frac{326}{639}\right)$	$e\left(\frac{548}{639}\right)$	$e\left(\frac{314}{639}\right)$
$\chi_{2557}(29,\cdot)$	2557.q	1278	yes	$1$	$1$	$e\left(\frac{691}{1278}\right)$	$e\left(\frac{536}{639}\right)$	$e\left(\frac{52}{639}\right)$	$e\left(\frac{1243}{1278}\right)$	$e\left(\frac{485}{1278}\right)$	$e\left(\frac{55}{639}\right)$	$e\left(\frac{265}{426}\right)$	$e\left(\frac{433}{639}\right)$	$e\left(\frac{328}{639}\right)$	$e\left(\frac{76}{639}\right)$
$\chi_{2557}(30,\cdot)$	2557.j	71	yes	$1$	$1$	$e\left(\frac{61}{71}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{51}{71}\right)$	$e\left(\frac{4}{71}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{28}{71}\right)$	$e\left(\frac{41}{71}\right)$	$e\left(\frac{41}{71}\right)$	$e\left(\frac{65}{71}\right)$	$e\left(\frac{9}{71}\right)$
$\chi_{2557}(31,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{653}{2556}\right)$	$e\left(\frac{23}{639}\right)$	$e\left(\frac{653}{1278}\right)$	$e\left(\frac{1883}{2556}\right)$	$e\left(\frac{745}{2556}\right)$	$e\left(\frac{875}{1278}\right)$	$e\left(\frac{653}{852}\right)$	$e\left(\frac{46}{639}\right)$	$e\left(\frac{634}{639}\right)$	$e\left(\frac{256}{639}\right)$
$\chi_{2557}(32,\cdot)$	2557.r	2556	yes	$-1$	$1$	$e\left(\frac{5}{2556}\right)$	$e\left(\frac{419}{639}\right)$	$e\left(\frac{5}{1278}\right)$	$e\left(\frac{1631}{2556}\right)$	$e\left(\frac{1681}{2556}\right)$	$e\left(\frac{1271}{1278}\right)$	$e\left(\frac{5}{852}\right)$	$e\left(\frac{199}{639}\right)$	$e\left(\frac{409}{639}\right)$	$e\left(\frac{274}{639}\right)$

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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	$2557$
Structure	\(C_{2556}\)
Order	$2556$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2557}(1,\cdot)\)	2557.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2557}(2,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{2556}\right)\)	\(e\left(\frac{595}{639}\right)\)	\(e\left(\frac{1}{1278}\right)\)	\(e\left(\frac{2371}{2556}\right)\)	\(e\left(\frac{2381}{2556}\right)\)	\(e\left(\frac{1021}{1278}\right)\)	\(e\left(\frac{1}{852}\right)\)	\(e\left(\frac{551}{639}\right)\)	\(e\left(\frac{593}{639}\right)\)	\(e\left(\frac{566}{639}\right)\)
\(\chi_{2557}(3,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{595}{639}\right)\)	\(e\left(\frac{76}{639}\right)\)	\(e\left(\frac{551}{639}\right)\)	\(e\left(\frac{472}{639}\right)\)	\(e\left(\frac{32}{639}\right)\)	\(e\left(\frac{251}{639}\right)\)	\(e\left(\frac{169}{213}\right)\)	\(e\left(\frac{152}{639}\right)\)	\(e\left(\frac{428}{639}\right)\)	\(e\left(\frac{68}{639}\right)\)
\(\chi_{2557}(4,\cdot)\)	2557.q	1278	yes	\(1\)	\(1\)	\(e\left(\frac{1}{1278}\right)\)	\(e\left(\frac{551}{639}\right)\)	\(e\left(\frac{1}{639}\right)\)	\(e\left(\frac{1093}{1278}\right)\)	\(e\left(\frac{1103}{1278}\right)\)	\(e\left(\frac{382}{639}\right)\)	\(e\left(\frac{1}{426}\right)\)	\(e\left(\frac{463}{639}\right)\)	\(e\left(\frac{547}{639}\right)\)	\(e\left(\frac{493}{639}\right)\)
\(\chi_{2557}(5,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{2371}{2556}\right)\)	\(e\left(\frac{472}{639}\right)\)	\(e\left(\frac{1093}{1278}\right)\)	\(e\left(\frac{997}{2556}\right)\)	\(e\left(\frac{1703}{2556}\right)\)	\(e\left(\frac{259}{1278}\right)\)	\(e\left(\frac{667}{852}\right)\)	\(e\left(\frac{305}{639}\right)\)	\(e\left(\frac{203}{639}\right)\)	\(e\left(\frac{86}{639}\right)\)
\(\chi_{2557}(6,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{2381}{2556}\right)\)	\(e\left(\frac{32}{639}\right)\)	\(e\left(\frac{1103}{1278}\right)\)	\(e\left(\frac{1703}{2556}\right)\)	\(e\left(\frac{2509}{2556}\right)\)	\(e\left(\frac{245}{1278}\right)\)	\(e\left(\frac{677}{852}\right)\)	\(e\left(\frac{64}{639}\right)\)	\(e\left(\frac{382}{639}\right)\)	\(e\left(\frac{634}{639}\right)\)
\(\chi_{2557}(7,\cdot)\)	2557.q	1278	yes	\(1\)	\(1\)	\(e\left(\frac{1021}{1278}\right)\)	\(e\left(\frac{251}{639}\right)\)	\(e\left(\frac{382}{639}\right)\)	\(e\left(\frac{259}{1278}\right)\)	\(e\left(\frac{245}{1278}\right)\)	\(e\left(\frac{232}{639}\right)\)	\(e\left(\frac{169}{426}\right)\)	\(e\left(\frac{502}{639}\right)\)	\(e\left(\frac{1}{639}\right)\)	\(e\left(\frac{460}{639}\right)\)
\(\chi_{2557}(8,\cdot)\)	2557.p	852	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{852}\right)\)	\(e\left(\frac{169}{213}\right)\)	\(e\left(\frac{1}{426}\right)\)	\(e\left(\frac{667}{852}\right)\)	\(e\left(\frac{677}{852}\right)\)	\(e\left(\frac{169}{426}\right)\)	\(e\left(\frac{1}{284}\right)\)	\(e\left(\frac{125}{213}\right)\)	\(e\left(\frac{167}{213}\right)\)	\(e\left(\frac{140}{213}\right)\)
\(\chi_{2557}(9,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{551}{639}\right)\)	\(e\left(\frac{152}{639}\right)\)	\(e\left(\frac{463}{639}\right)\)	\(e\left(\frac{305}{639}\right)\)	\(e\left(\frac{64}{639}\right)\)	\(e\left(\frac{502}{639}\right)\)	\(e\left(\frac{125}{213}\right)\)	\(e\left(\frac{304}{639}\right)\)	\(e\left(\frac{217}{639}\right)\)	\(e\left(\frac{136}{639}\right)\)
\(\chi_{2557}(10,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{593}{639}\right)\)	\(e\left(\frac{428}{639}\right)\)	\(e\left(\frac{547}{639}\right)\)	\(e\left(\frac{203}{639}\right)\)	\(e\left(\frac{382}{639}\right)\)	\(e\left(\frac{1}{639}\right)\)	\(e\left(\frac{167}{213}\right)\)	\(e\left(\frac{217}{639}\right)\)	\(e\left(\frac{157}{639}\right)\)	\(e\left(\frac{13}{639}\right)\)
\(\chi_{2557}(11,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{566}{639}\right)\)	\(e\left(\frac{68}{639}\right)\)	\(e\left(\frac{493}{639}\right)\)	\(e\left(\frac{86}{639}\right)\)	\(e\left(\frac{634}{639}\right)\)	\(e\left(\frac{460}{639}\right)\)	\(e\left(\frac{140}{213}\right)\)	\(e\left(\frac{136}{639}\right)\)	\(e\left(\frac{13}{639}\right)\)	\(e\left(\frac{229}{639}\right)\)
\(\chi_{2557}(12,\cdot)\)	2557.n	426	yes	\(1\)	\(1\)	\(e\left(\frac{397}{426}\right)\)	\(e\left(\frac{209}{213}\right)\)	\(e\left(\frac{184}{213}\right)\)	\(e\left(\frac{253}{426}\right)\)	\(e\left(\frac{389}{426}\right)\)	\(e\left(\frac{211}{213}\right)\)	\(e\left(\frac{113}{142}\right)\)	\(e\left(\frac{205}{213}\right)\)	\(e\left(\frac{112}{213}\right)\)	\(e\left(\frac{187}{213}\right)\)
\(\chi_{2557}(13,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{488}{639}\right)\)	\(e\left(\frac{377}{639}\right)\)	\(e\left(\frac{337}{639}\right)\)	\(e\left(\frac{458}{639}\right)\)	\(e\left(\frac{226}{639}\right)\)	\(e\left(\frac{295}{639}\right)\)	\(e\left(\frac{62}{213}\right)\)	\(e\left(\frac{115}{639}\right)\)	\(e\left(\frac{307}{639}\right)\)	\(e\left(\frac{1}{639}\right)\)
\(\chi_{2557}(14,\cdot)\)	2557.m	284	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{284}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{85}{142}\right)\)	\(e\left(\frac{37}{284}\right)\)	\(e\left(\frac{35}{284}\right)\)	\(e\left(\frac{23}{142}\right)\)	\(e\left(\frac{113}{284}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{66}{71}\right)\)	\(e\left(\frac{43}{71}\right)\)
\(\chi_{2557}(15,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{2195}{2556}\right)\)	\(e\left(\frac{548}{639}\right)\)	\(e\left(\frac{917}{1278}\right)\)	\(e\left(\frac{329}{2556}\right)\)	\(e\left(\frac{1831}{2556}\right)\)	\(e\left(\frac{761}{1278}\right)\)	\(e\left(\frac{491}{852}\right)\)	\(e\left(\frac{457}{639}\right)\)	\(e\left(\frac{631}{639}\right)\)	\(e\left(\frac{154}{639}\right)\)
\(\chi_{2557}(16,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{1}{639}\right)\)	\(e\left(\frac{463}{639}\right)\)	\(e\left(\frac{2}{639}\right)\)	\(e\left(\frac{454}{639}\right)\)	\(e\left(\frac{464}{639}\right)\)	\(e\left(\frac{125}{639}\right)\)	\(e\left(\frac{1}{213}\right)\)	\(e\left(\frac{287}{639}\right)\)	\(e\left(\frac{455}{639}\right)\)	\(e\left(\frac{347}{639}\right)\)
\(\chi_{2557}(17,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{1309}{2556}\right)\)	\(e\left(\frac{553}{639}\right)\)	\(e\left(\frac{31}{1278}\right)\)	\(e\left(\frac{655}{2556}\right)\)	\(e\left(\frac{965}{2556}\right)\)	\(e\left(\frac{979}{1278}\right)\)	\(e\left(\frac{457}{852}\right)\)	\(e\left(\frac{467}{639}\right)\)	\(e\left(\frac{491}{639}\right)\)	\(e\left(\frac{293}{639}\right)\)
\(\chi_{2557}(18,\cdot)\)	2557.m	284	yes	\(-1\)	\(1\)	\(e\left(\frac{245}{284}\right)\)	\(e\left(\frac{12}{71}\right)\)	\(e\left(\frac{103}{142}\right)\)	\(e\left(\frac{115}{284}\right)\)	\(e\left(\frac{9}{284}\right)\)	\(e\left(\frac{83}{142}\right)\)	\(e\left(\frac{167}{284}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{7}{71}\right)\)
\(\chi_{2557}(19,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{179}{639}\right)\)	\(e\left(\frac{446}{639}\right)\)	\(e\left(\frac{358}{639}\right)\)	\(e\left(\frac{113}{639}\right)\)	\(e\left(\frac{625}{639}\right)\)	\(e\left(\frac{10}{639}\right)\)	\(e\left(\frac{179}{213}\right)\)	\(e\left(\frac{253}{639}\right)\)	\(e\left(\frac{292}{639}\right)\)	\(e\left(\frac{130}{639}\right)\)
\(\chi_{2557}(20,\cdot)\)	2557.p	852	yes	\(-1\)	\(1\)	\(e\left(\frac{791}{852}\right)\)	\(e\left(\frac{128}{213}\right)\)	\(e\left(\frac{365}{426}\right)\)	\(e\left(\frac{209}{852}\right)\)	\(e\left(\frac{451}{852}\right)\)	\(e\left(\frac{341}{426}\right)\)	\(e\left(\frac{223}{284}\right)\)	\(e\left(\frac{43}{213}\right)\)	\(e\left(\frac{37}{213}\right)\)	\(e\left(\frac{193}{213}\right)\)
\(\chi_{2557}(21,\cdot)\)	2557.n	426	yes	\(1\)	\(1\)	\(e\left(\frac{311}{426}\right)\)	\(e\left(\frac{109}{213}\right)\)	\(e\left(\frac{98}{213}\right)\)	\(e\left(\frac{401}{426}\right)\)	\(e\left(\frac{103}{426}\right)\)	\(e\left(\frac{161}{213}\right)\)	\(e\left(\frac{27}{142}\right)\)	\(e\left(\frac{5}{213}\right)\)	\(e\left(\frac{143}{213}\right)\)	\(e\left(\frac{176}{213}\right)\)
\(\chi_{2557}(22,\cdot)\)	2557.p	852	yes	\(-1\)	\(1\)	\(e\left(\frac{755}{852}\right)\)	\(e\left(\frac{8}{213}\right)\)	\(e\left(\frac{329}{426}\right)\)	\(e\left(\frac{53}{852}\right)\)	\(e\left(\frac{787}{852}\right)\)	\(e\left(\frac{221}{426}\right)\)	\(e\left(\frac{187}{284}\right)\)	\(e\left(\frac{16}{213}\right)\)	\(e\left(\frac{202}{213}\right)\)	\(e\left(\frac{52}{213}\right)\)
\(\chi_{2557}(23,\cdot)\)	2557.q	1278	yes	\(1\)	\(1\)	\(e\left(\frac{613}{1278}\right)\)	\(e\left(\frac{371}{639}\right)\)	\(e\left(\frac{613}{639}\right)\)	\(e\left(\frac{337}{1278}\right)\)	\(e\left(\frac{77}{1278}\right)\)	\(e\left(\frac{292}{639}\right)\)	\(e\left(\frac{187}{426}\right)\)	\(e\left(\frac{103}{639}\right)\)	\(e\left(\frac{475}{639}\right)\)	\(e\left(\frac{601}{639}\right)\)
\(\chi_{2557}(24,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{2383}{2556}\right)\)	\(e\left(\frac{583}{639}\right)\)	\(e\left(\frac{1105}{1278}\right)\)	\(e\left(\frac{1333}{2556}\right)\)	\(e\left(\frac{2159}{2556}\right)\)	\(e\left(\frac{1009}{1278}\right)\)	\(e\left(\frac{679}{852}\right)\)	\(e\left(\frac{527}{639}\right)\)	\(e\left(\frac{290}{639}\right)\)	\(e\left(\frac{488}{639}\right)\)
\(\chi_{2557}(25,\cdot)\)	2557.q	1278	yes	\(1\)	\(1\)	\(e\left(\frac{1093}{1278}\right)\)	\(e\left(\frac{305}{639}\right)\)	\(e\left(\frac{454}{639}\right)\)	\(e\left(\frac{997}{1278}\right)\)	\(e\left(\frac{425}{1278}\right)\)	\(e\left(\frac{259}{639}\right)\)	\(e\left(\frac{241}{426}\right)\)	\(e\left(\frac{610}{639}\right)\)	\(e\left(\frac{406}{639}\right)\)	\(e\left(\frac{172}{639}\right)\)
\(\chi_{2557}(26,\cdot)\)	2557.m	284	yes	\(-1\)	\(1\)	\(e\left(\frac{217}{284}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{75}{142}\right)\)	\(e\left(\frac{183}{284}\right)\)	\(e\left(\frac{81}{284}\right)\)	\(e\left(\frac{37}{142}\right)\)	\(e\left(\frac{83}{284}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{29}{71}\right)\)	\(e\left(\frac{63}{71}\right)\)
\(\chi_{2557}(27,\cdot)\)	2557.l	213	yes	\(1\)	\(1\)	\(e\left(\frac{169}{213}\right)\)	\(e\left(\frac{76}{213}\right)\)	\(e\left(\frac{125}{213}\right)\)	\(e\left(\frac{46}{213}\right)\)	\(e\left(\frac{32}{213}\right)\)	\(e\left(\frac{38}{213}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{152}{213}\right)\)	\(e\left(\frac{2}{213}\right)\)	\(e\left(\frac{68}{213}\right)\)
\(\chi_{2557}(28,\cdot)\)	2557.o	639	yes	\(1\)	\(1\)	\(e\left(\frac{511}{639}\right)\)	\(e\left(\frac{163}{639}\right)\)	\(e\left(\frac{383}{639}\right)\)	\(e\left(\frac{37}{639}\right)\)	\(e\left(\frac{35}{639}\right)\)	\(e\left(\frac{614}{639}\right)\)	\(e\left(\frac{85}{213}\right)\)	\(e\left(\frac{326}{639}\right)\)	\(e\left(\frac{548}{639}\right)\)	\(e\left(\frac{314}{639}\right)\)
\(\chi_{2557}(29,\cdot)\)	2557.q	1278	yes	\(1\)	\(1\)	\(e\left(\frac{691}{1278}\right)\)	\(e\left(\frac{536}{639}\right)\)	\(e\left(\frac{52}{639}\right)\)	\(e\left(\frac{1243}{1278}\right)\)	\(e\left(\frac{485}{1278}\right)\)	\(e\left(\frac{55}{639}\right)\)	\(e\left(\frac{265}{426}\right)\)	\(e\left(\frac{433}{639}\right)\)	\(e\left(\frac{328}{639}\right)\)	\(e\left(\frac{76}{639}\right)\)
\(\chi_{2557}(30,\cdot)\)	2557.j	71	yes	\(1\)	\(1\)	\(e\left(\frac{61}{71}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{51}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{28}{71}\right)\)	\(e\left(\frac{41}{71}\right)\)	\(e\left(\frac{41}{71}\right)\)	\(e\left(\frac{65}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)
\(\chi_{2557}(31,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{653}{2556}\right)\)	\(e\left(\frac{23}{639}\right)\)	\(e\left(\frac{653}{1278}\right)\)	\(e\left(\frac{1883}{2556}\right)\)	\(e\left(\frac{745}{2556}\right)\)	\(e\left(\frac{875}{1278}\right)\)	\(e\left(\frac{653}{852}\right)\)	\(e\left(\frac{46}{639}\right)\)	\(e\left(\frac{634}{639}\right)\)	\(e\left(\frac{256}{639}\right)\)
\(\chi_{2557}(32,\cdot)\)	2557.r	2556	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{2556}\right)\)	\(e\left(\frac{419}{639}\right)\)	\(e\left(\frac{5}{1278}\right)\)	\(e\left(\frac{1631}{2556}\right)\)	\(e\left(\frac{1681}{2556}\right)\)	\(e\left(\frac{1271}{1278}\right)\)	\(e\left(\frac{5}{852}\right)\)	\(e\left(\frac{199}{639}\right)\)	\(e\left(\frac{409}{639}\right)\)	\(e\left(\frac{274}{639}\right)\)

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L-functions

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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.