LMFDB - Group of Dirichlet characters of modulus 2550

sage:H = DirichletGroup(2550)

pari:g = idealstar(,2550,2)

Character group

sage:G.order() pari:g.no
Order	=	640
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{80}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2550}(851,\cdot)$, $\chi_{2550}(1327,\cdot)$, $\chi_{2550}(751,\cdot)$

First 32 of 640 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	$-1$	$1$	$7$	$11$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{2550}(1,\cdot)$	2550.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2550}(7,\cdot)$	2550.bl	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(11,\cdot)$	2550.cr	80	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2550}(13,\cdot)$	2550.bs	20	no	$-1$	$1$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-i$
$\chi_{2550}(19,\cdot)$	2550.ce	40	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{40}\right)$	$i$
$\chi_{2550}(23,\cdot)$	2550.cm	80	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(29,\cdot)$	2550.cp	80	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(31,\cdot)$	2550.cq	80	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(37,\cdot)$	2550.cn	80	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2550}(41,\cdot)$	2550.cr	80	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2550}(43,\cdot)$	2550.y	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{2550}(47,\cdot)$	2550.cc	20	no	$1$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$i$
$\chi_{2550}(49,\cdot)$	2550.bc	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{2550}(53,\cdot)$	2550.ci	40	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{21}{40}\right)$	$1$
$\chi_{2550}(59,\cdot)$	2550.cf	40	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{40}\right)$	$-i$
$\chi_{2550}(61,\cdot)$	2550.cq	80	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2550}(67,\cdot)$	2550.cb	20	no	$-1$	$1$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{2550}(71,\cdot)$	2550.cr	80	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(73,\cdot)$	2550.cs	80	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2550}(77,\cdot)$	2550.ci	40	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{40}\right)$	$1$
$\chi_{2550}(79,\cdot)$	2550.co	80	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2550}(83,\cdot)$	2550.ci	40	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{40}\right)$	$1$
$\chi_{2550}(89,\cdot)$	2550.by	20	no	$-1$	$1$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$	$1$
$\chi_{2550}(91,\cdot)$	2550.cq	80	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2550}(97,\cdot)$	2550.cn	80	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2550}(101,\cdot)$	2550.e	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$
$\chi_{2550}(103,\cdot)$	2550.bu	20	no	$-1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$i$
$\chi_{2550}(107,\cdot)$	2550.br	16	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2550}(109,\cdot)$	2550.co	80	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2550}(113,\cdot)$	2550.cm	80	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2550}(121,\cdot)$	2550.cl	40	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{40}\right)$	$-i$
$\chi_{2550}(127,\cdot)$	2550.cj	40	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{40}\right)$	$1$

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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	$2550$
Structure	\(C_{2}\times C_{4}\times C_{80}\)
Order	$640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{2550}(1,\cdot)\)	2550.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2550}(7,\cdot)\)	2550.bl	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(11,\cdot)\)	2550.cr	80	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2550}(13,\cdot)\)	2550.bs	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)
\(\chi_{2550}(19,\cdot)\)	2550.ce	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(i\)
\(\chi_{2550}(23,\cdot)\)	2550.cm	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(29,\cdot)\)	2550.cp	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(31,\cdot)\)	2550.cq	80	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(37,\cdot)\)	2550.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2550}(41,\cdot)\)	2550.cr	80	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2550}(43,\cdot)\)	2550.y	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{2550}(47,\cdot)\)	2550.cc	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(i\)
\(\chi_{2550}(49,\cdot)\)	2550.bc	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{2550}(53,\cdot)\)	2550.ci	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(1\)
\(\chi_{2550}(59,\cdot)\)	2550.cf	40	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(-i\)
\(\chi_{2550}(61,\cdot)\)	2550.cq	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2550}(67,\cdot)\)	2550.cb	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)
\(\chi_{2550}(71,\cdot)\)	2550.cr	80	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(73,\cdot)\)	2550.cs	80	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2550}(77,\cdot)\)	2550.ci	40	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(1\)
\(\chi_{2550}(79,\cdot)\)	2550.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2550}(83,\cdot)\)	2550.ci	40	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(1\)
\(\chi_{2550}(89,\cdot)\)	2550.by	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(1\)
\(\chi_{2550}(91,\cdot)\)	2550.cq	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2550}(97,\cdot)\)	2550.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2550}(101,\cdot)\)	2550.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{2550}(103,\cdot)\)	2550.bu	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)
\(\chi_{2550}(107,\cdot)\)	2550.br	16	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2550}(109,\cdot)\)	2550.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2550}(113,\cdot)\)	2550.cm	80	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2550}(121,\cdot)\)	2550.cl	40	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(-i\)
\(\chi_{2550}(127,\cdot)\)	2550.cj	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(1\)

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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.