LMFDB - Group of Dirichlet characters of modulus 1275

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1275)

pari: g = idealstar(,1275,2)

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	=	$\chi_{1275}(851,\cdot)$, $\chi_{1275}(52,\cdot)$, $\chi_{1275}(751,\cdot)$

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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$19$	$22$
$\chi_{1275}(1,\cdot)$	1275.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1275}(2,\cdot)$	1275.ce	40	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{1275}(4,\cdot)$	1275.bt	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1275}(7,\cdot)$	1275.bl	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1275}(8,\cdot)$	1275.ce	40	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{1275}(11,\cdot)$	1275.cp	80	yes	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{1275}(13,\cdot)$	1275.bu	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1275}(14,\cdot)$	1275.cr	80	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{1275}(16,\cdot)$	1275.bd	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1275}(19,\cdot)$	1275.cg	40	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{1275}(22,\cdot)$	1275.cn	80	no	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{1275}(23,\cdot)$	1275.cm	80	yes	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{1275}(26,\cdot)$	1275.y	8	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{1275}(28,\cdot)$	1275.cn	80	no	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{1275}(29,\cdot)$	1275.cr	80	yes	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{1275}(31,\cdot)$	1275.co	80	no	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{1275}(32,\cdot)$	1275.bb	8	no	$1$	$1$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$
$\chi_{1275}(37,\cdot)$	1275.cn	80	no	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{1275}(38,\cdot)$	1275.ca	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1275}(41,\cdot)$	1275.cp	80	yes	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{1275}(43,\cdot)$	1275.v	8	no	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{1275}(44,\cdot)$	1275.cr	80	yes	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{1275}(46,\cdot)$	1275.co	80	no	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{1275}(47,\cdot)$	1275.ca	20	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1275}(49,\cdot)$	1275.ba	8	no	$1$	$1$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{1275}(52,\cdot)$	1275.bx	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1275}(53,\cdot)$	1275.cl	40	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{1275}(56,\cdot)$	1275.cp	80	yes	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{1275}(58,\cdot)$	1275.cn	80	no	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{1275}(59,\cdot)$	1275.ch	40	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{1275}(61,\cdot)$	1275.co	80	no	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{1275}(62,\cdot)$	1275.ct	80	yes	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{67}{80}\right)$

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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	$1275$
Structure	\(C_{2}\times C_{4}\times C_{80}\)
Order	$640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(19\)	\(22\)
\(\chi_{1275}(1,\cdot)\)	1275.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1275}(2,\cdot)\)	1275.ce	40	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{1275}(4,\cdot)\)	1275.bt	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1275}(7,\cdot)\)	1275.bl	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1275}(8,\cdot)\)	1275.ce	40	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{1275}(11,\cdot)\)	1275.cp	80	yes	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{1275}(13,\cdot)\)	1275.bu	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1275}(14,\cdot)\)	1275.cr	80	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{1275}(16,\cdot)\)	1275.bd	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1275}(19,\cdot)\)	1275.cg	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{1275}(22,\cdot)\)	1275.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{1275}(23,\cdot)\)	1275.cm	80	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{1275}(26,\cdot)\)	1275.y	8	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1275}(28,\cdot)\)	1275.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{1275}(29,\cdot)\)	1275.cr	80	yes	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{1275}(31,\cdot)\)	1275.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{1275}(32,\cdot)\)	1275.bb	8	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1275}(37,\cdot)\)	1275.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{1275}(38,\cdot)\)	1275.ca	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1275}(41,\cdot)\)	1275.cp	80	yes	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)
\(\chi_{1275}(43,\cdot)\)	1275.v	8	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1275}(44,\cdot)\)	1275.cr	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{1275}(46,\cdot)\)	1275.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{1275}(47,\cdot)\)	1275.ca	20	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1275}(49,\cdot)\)	1275.ba	8	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1275}(52,\cdot)\)	1275.bx	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1275}(53,\cdot)\)	1275.cl	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{1275}(56,\cdot)\)	1275.cp	80	yes	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{1275}(58,\cdot)\)	1275.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{1275}(59,\cdot)\)	1275.ch	40	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{1275}(61,\cdot)\)	1275.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{1275}(62,\cdot)\)	1275.ct	80	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)

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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.