LMFDB - Group of Dirichlet characters of modulus 2057

sage:H = DirichletGroup(2057)

pari:g = idealstar(,2057,2)

Character group

sage:G.order() pari:g.no
Order	=	1760
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{880}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2057}(970,\cdot)$, $\chi_{2057}(122,\cdot)$

First 32 of 1760 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{2057}(1,\cdot)$	2057.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2057}(2,\cdot)$	2057.bl	440	yes	$-1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{21}{440}\right)$	$e\left(\frac{411}{440}\right)$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{17}{88}\right)$
$\chi_{2057}(3,\cdot)$	2057.z	80	no	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2057}(4,\cdot)$	2057.bi	220	yes	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{2057}(5,\cdot)$	2057.bn	880	yes	$-1$	$1$	$e\left(\frac{21}{440}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{303}{880}\right)$	$e\left(\frac{493}{880}\right)$	$e\left(\frac{129}{880}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{107}{176}\right)$
$\chi_{2057}(6,\cdot)$	2057.bm	880	yes	$1$	$1$	$e\left(\frac{411}{440}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{493}{880}\right)$	$e\left(\frac{63}{880}\right)$	$e\left(\frac{859}{880}\right)$	$e\left(\frac{353}{440}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{1}{176}\right)$
$\chi_{2057}(7,\cdot)$	2057.bm	880	yes	$1$	$1$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{129}{880}\right)$	$e\left(\frac{859}{880}\right)$	$e\left(\frac{7}{880}\right)$	$e\left(\frac{29}{440}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{117}{176}\right)$
$\chi_{2057}(8,\cdot)$	2057.bl	440	yes	$-1$	$1$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{353}{440}\right)$	$e\left(\frac{29}{440}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{2057}(9,\cdot)$	2057.v	40	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2057}(10,\cdot)$	2057.bh	176	yes	$1$	$1$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{69}{176}\right)$	$e\left(\frac{87}{176}\right)$	$e\left(\frac{147}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{141}{176}\right)$
$\chi_{2057}(12,\cdot)$	2057.bg	176	yes	$-1$	$1$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{107}{176}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{117}{176}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{141}{176}\right)$	$e\left(\frac{35}{176}\right)$
$\chi_{2057}(13,\cdot)$	2057.bj	220	yes	$-1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{2057}(14,\cdot)$	2057.bn	880	yes	$-1$	$1$	$e\left(\frac{417}{440}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{171}{880}\right)$	$e\left(\frac{801}{880}\right)$	$e\left(\frac{613}{880}\right)$	$e\left(\frac{371}{440}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{25}{176}\right)$	$e\left(\frac{151}{176}\right)$
$\chi_{2057}(15,\cdot)$	2057.bk	440	yes	$1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{377}{440}\right)$	$e\left(\frac{307}{440}\right)$	$e\left(\frac{191}{440}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{37}{88}\right)$
$\chi_{2057}(16,\cdot)$	2057.bf	110	yes	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{2057}(18,\cdot)$	2057.bd	110	no	$-1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2057}(19,\cdot)$	2057.bl	440	yes	$-1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{93}{440}\right)$	$e\left(\frac{123}{440}\right)$	$e\left(\frac{399}{440}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{25}{88}\right)$
$\chi_{2057}(20,\cdot)$	2057.bn	880	yes	$-1$	$1$	$e\left(\frac{249}{440}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{387}{880}\right)$	$e\left(\frac{377}{880}\right)$	$e\left(\frac{461}{880}\right)$	$e\left(\frac{307}{440}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{176}\right)$	$e\left(\frac{175}{176}\right)$
$\chi_{2057}(21,\cdot)$	2057.w	44	yes	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$-i$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{11}\right)$	$-1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{2057}(23,\cdot)$	2057.bg	176	yes	$-1$	$1$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{137}{176}\right)$	$e\left(\frac{123}{176}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{95}{176}\right)$	$e\left(\frac{81}{176}\right)$
$\chi_{2057}(24,\cdot)$	2057.bm	880	yes	$1$	$1$	$e\left(\frac{199}{440}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{577}{880}\right)$	$e\left(\frac{827}{880}\right)$	$e\left(\frac{311}{880}\right)$	$e\left(\frac{157}{440}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{176}\right)$	$e\left(\frac{69}{176}\right)$
$\chi_{2057}(25,\cdot)$	2057.bk	440	yes	$1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{303}{440}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{129}{440}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{2057}(26,\cdot)$	2057.bk	440	yes	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{107}{440}\right)$	$e\left(\frac{177}{440}\right)$	$e\left(\frac{381}{440}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{2057}(27,\cdot)$	2057.z	80	no	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2057}(28,\cdot)$	2057.bm	880	yes	$1$	$1$	$e\left(\frac{91}{440}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{213}{880}\right)$	$e\left(\frac{743}{880}\right)$	$e\left(\frac{339}{880}\right)$	$e\left(\frac{273}{440}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{9}{176}\right)$
$\chi_{2057}(29,\cdot)$	2057.bm	880	yes	$1$	$1$	$e\left(\frac{233}{440}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{439}{880}\right)$	$e\left(\frac{829}{880}\right)$	$e\left(\frac{17}{880}\right)$	$e\left(\frac{259}{440}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{5}{176}\right)$	$e\left(\frac{83}{176}\right)$
$\chi_{2057}(30,\cdot)$	2057.bj	220	yes	$-1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{2057}(31,\cdot)$	2057.bn	880	yes	$-1$	$1$	$e\left(\frac{289}{440}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{587}{880}\right)$	$e\left(\frac{17}{880}\right)$	$e\left(\frac{581}{880}\right)$	$e\left(\frac{427}{440}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{57}{176}\right)$	$e\left(\frac{119}{176}\right)$
$\chi_{2057}(32,\cdot)$	2057.bb	88	yes	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{39}{44}\right)$	$-i$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{85}{88}\right)$
$\chi_{2057}(35,\cdot)$	2057.bd	110	no	$-1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{2057}(36,\cdot)$	2057.bk	440	yes	$1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{53}{440}\right)$	$e\left(\frac{63}{440}\right)$	$e\left(\frac{419}{440}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{1}{88}\right)$
$\chi_{2057}(37,\cdot)$	2057.bn	880	yes	$-1$	$1$	$e\left(\frac{113}{440}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{499}{880}\right)$	$e\left(\frac{809}{880}\right)$	$e\left(\frac{317}{880}\right)$	$e\left(\frac{339}{440}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{31}{176}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$2057$
Structure	\(C_{2}\times C_{880}\)
Order	$1760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{2057}(1,\cdot)\)	2057.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2057}(2,\cdot)\)	2057.bl	440	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{21}{440}\right)\)	\(e\left(\frac{411}{440}\right)\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)
\(\chi_{2057}(3,\cdot)\)	2057.z	80	no	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2057}(4,\cdot)\)	2057.bi	220	yes	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{2057}(5,\cdot)\)	2057.bn	880	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{440}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{303}{880}\right)\)	\(e\left(\frac{493}{880}\right)\)	\(e\left(\frac{129}{880}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{107}{176}\right)\)
\(\chi_{2057}(6,\cdot)\)	2057.bm	880	yes	\(1\)	\(1\)	\(e\left(\frac{411}{440}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{493}{880}\right)\)	\(e\left(\frac{63}{880}\right)\)	\(e\left(\frac{859}{880}\right)\)	\(e\left(\frac{353}{440}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{1}{176}\right)\)
\(\chi_{2057}(7,\cdot)\)	2057.bm	880	yes	\(1\)	\(1\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{129}{880}\right)\)	\(e\left(\frac{859}{880}\right)\)	\(e\left(\frac{7}{880}\right)\)	\(e\left(\frac{29}{440}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{117}{176}\right)\)
\(\chi_{2057}(8,\cdot)\)	2057.bl	440	yes	\(-1\)	\(1\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{353}{440}\right)\)	\(e\left(\frac{29}{440}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{2057}(9,\cdot)\)	2057.v	40	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2057}(10,\cdot)\)	2057.bh	176	yes	\(1\)	\(1\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{69}{176}\right)\)	\(e\left(\frac{87}{176}\right)\)	\(e\left(\frac{147}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{141}{176}\right)\)
\(\chi_{2057}(12,\cdot)\)	2057.bg	176	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{107}{176}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{117}{176}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{141}{176}\right)\)	\(e\left(\frac{35}{176}\right)\)
\(\chi_{2057}(13,\cdot)\)	2057.bj	220	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{2057}(14,\cdot)\)	2057.bn	880	yes	\(-1\)	\(1\)	\(e\left(\frac{417}{440}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{171}{880}\right)\)	\(e\left(\frac{801}{880}\right)\)	\(e\left(\frac{613}{880}\right)\)	\(e\left(\frac{371}{440}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{25}{176}\right)\)	\(e\left(\frac{151}{176}\right)\)
\(\chi_{2057}(15,\cdot)\)	2057.bk	440	yes	\(1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{377}{440}\right)\)	\(e\left(\frac{307}{440}\right)\)	\(e\left(\frac{191}{440}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)
\(\chi_{2057}(16,\cdot)\)	2057.bf	110	yes	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{2057}(18,\cdot)\)	2057.bd	110	no	\(-1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2057}(19,\cdot)\)	2057.bl	440	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{93}{440}\right)\)	\(e\left(\frac{123}{440}\right)\)	\(e\left(\frac{399}{440}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)
\(\chi_{2057}(20,\cdot)\)	2057.bn	880	yes	\(-1\)	\(1\)	\(e\left(\frac{249}{440}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{387}{880}\right)\)	\(e\left(\frac{377}{880}\right)\)	\(e\left(\frac{461}{880}\right)\)	\(e\left(\frac{307}{440}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{176}\right)\)	\(e\left(\frac{175}{176}\right)\)
\(\chi_{2057}(21,\cdot)\)	2057.w	44	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(-i\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(-1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{2057}(23,\cdot)\)	2057.bg	176	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{137}{176}\right)\)	\(e\left(\frac{123}{176}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{95}{176}\right)\)	\(e\left(\frac{81}{176}\right)\)
\(\chi_{2057}(24,\cdot)\)	2057.bm	880	yes	\(1\)	\(1\)	\(e\left(\frac{199}{440}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{577}{880}\right)\)	\(e\left(\frac{827}{880}\right)\)	\(e\left(\frac{311}{880}\right)\)	\(e\left(\frac{157}{440}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{176}\right)\)	\(e\left(\frac{69}{176}\right)\)
\(\chi_{2057}(25,\cdot)\)	2057.bk	440	yes	\(1\)	\(1\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{303}{440}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{129}{440}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{2057}(26,\cdot)\)	2057.bk	440	yes	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{107}{440}\right)\)	\(e\left(\frac{177}{440}\right)\)	\(e\left(\frac{381}{440}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{2057}(27,\cdot)\)	2057.z	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2057}(28,\cdot)\)	2057.bm	880	yes	\(1\)	\(1\)	\(e\left(\frac{91}{440}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{213}{880}\right)\)	\(e\left(\frac{743}{880}\right)\)	\(e\left(\frac{339}{880}\right)\)	\(e\left(\frac{273}{440}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{9}{176}\right)\)
\(\chi_{2057}(29,\cdot)\)	2057.bm	880	yes	\(1\)	\(1\)	\(e\left(\frac{233}{440}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{439}{880}\right)\)	\(e\left(\frac{829}{880}\right)\)	\(e\left(\frac{17}{880}\right)\)	\(e\left(\frac{259}{440}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{5}{176}\right)\)	\(e\left(\frac{83}{176}\right)\)
\(\chi_{2057}(30,\cdot)\)	2057.bj	220	yes	\(-1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{2057}(31,\cdot)\)	2057.bn	880	yes	\(-1\)	\(1\)	\(e\left(\frac{289}{440}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{587}{880}\right)\)	\(e\left(\frac{17}{880}\right)\)	\(e\left(\frac{581}{880}\right)\)	\(e\left(\frac{427}{440}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{57}{176}\right)\)	\(e\left(\frac{119}{176}\right)\)
\(\chi_{2057}(32,\cdot)\)	2057.bb	88	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(-i\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)
\(\chi_{2057}(35,\cdot)\)	2057.bd	110	no	\(-1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{2057}(36,\cdot)\)	2057.bk	440	yes	\(1\)	\(1\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{53}{440}\right)\)	\(e\left(\frac{63}{440}\right)\)	\(e\left(\frac{419}{440}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)
\(\chi_{2057}(37,\cdot)\)	2057.bn	880	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{440}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{499}{880}\right)\)	\(e\left(\frac{809}{880}\right)\)	\(e\left(\frac{317}{880}\right)\)	\(e\left(\frac{339}{440}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{31}{176}\right)\)

Introduction

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.