LMFDB - Group of Dirichlet characters of modulus 1700

sage:H = DirichletGroup(1700)

pari:g = idealstar(,1700,2)

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	=	$\chi_{1700}(851,\cdot)$, $\chi_{1700}(477,\cdot)$, $\chi_{1700}(1601,\cdot)$

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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{1700}(1,\cdot)$	1700.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1700}(3,\cdot)$	1700.ct	80	yes	$-1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{1700}(7,\cdot)$	1700.bk	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1700}(9,\cdot)$	1700.ce	40	no	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{1700}(11,\cdot)$	1700.cq	80	yes	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{1700}(13,\cdot)$	1700.cc	20	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1700}(19,\cdot)$	1700.cf	40	yes	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{1700}(21,\cdot)$	1700.bx	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1700}(23,\cdot)$	1700.cm	80	yes	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{1700}(27,\cdot)$	1700.ct	80	yes	$-1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{1700}(29,\cdot)$	1700.co	80	no	$-1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{1700}(31,\cdot)$	1700.cq	80	yes	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{1700}(33,\cdot)$	1700.cb	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1700}(37,\cdot)$	1700.cn	80	no	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{1700}(39,\cdot)$	1700.cp	80	yes	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{1700}(41,\cdot)$	1700.cr	80	no	$-1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{1700}(43,\cdot)$	1700.ba	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1700}(47,\cdot)$	1700.cd	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1700}(49,\cdot)$	1700.bc	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1700}(53,\cdot)$	1700.cj	40	no	$-1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{1700}(57,\cdot)$	1700.bl	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1700}(59,\cdot)$	1700.cf	40	yes	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{1700}(61,\cdot)$	1700.cr	80	no	$-1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{1700}(63,\cdot)$	1700.ct	80	yes	$-1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{1700}(67,\cdot)$	1700.bu	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1700}(69,\cdot)$	1700.bg	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1700}(71,\cdot)$	1700.cq	80	yes	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{1700}(73,\cdot)$	1700.cs	80	no	$1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{1700}(77,\cdot)$	1700.cj	40	no	$-1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{1700}(79,\cdot)$	1700.cp	80	yes	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{1700}(81,\cdot)$	1700.bx	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1700}(83,\cdot)$	1700.ch	40	yes	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{40}\right)$

Click here to search among the remaining 608 characters.

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	$1700$
Structure	\(C_{2}\times C_{4}\times C_{80}\)
Order	$640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1700}(1,\cdot)\)	1700.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1700}(3,\cdot)\)	1700.ct	80	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{1700}(7,\cdot)\)	1700.bk	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1700}(9,\cdot)\)	1700.ce	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{1700}(11,\cdot)\)	1700.cq	80	yes	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{1700}(13,\cdot)\)	1700.cc	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1700}(19,\cdot)\)	1700.cf	40	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{1700}(21,\cdot)\)	1700.bx	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1700}(23,\cdot)\)	1700.cm	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{1700}(27,\cdot)\)	1700.ct	80	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{1700}(29,\cdot)\)	1700.co	80	no	\(-1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{1700}(31,\cdot)\)	1700.cq	80	yes	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{1700}(33,\cdot)\)	1700.cb	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1700}(37,\cdot)\)	1700.cn	80	no	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{1700}(39,\cdot)\)	1700.cp	80	yes	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{1700}(41,\cdot)\)	1700.cr	80	no	\(-1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{1700}(43,\cdot)\)	1700.ba	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1700}(47,\cdot)\)	1700.cd	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1700}(49,\cdot)\)	1700.bc	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1700}(53,\cdot)\)	1700.cj	40	no	\(-1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{1700}(57,\cdot)\)	1700.bl	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1700}(59,\cdot)\)	1700.cf	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{1700}(61,\cdot)\)	1700.cr	80	no	\(-1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{1700}(63,\cdot)\)	1700.ct	80	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{1700}(67,\cdot)\)	1700.bu	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1700}(69,\cdot)\)	1700.bg	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1700}(71,\cdot)\)	1700.cq	80	yes	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{1700}(73,\cdot)\)	1700.cs	80	no	\(1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{1700}(77,\cdot)\)	1700.cj	40	no	\(-1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{1700}(79,\cdot)\)	1700.cp	80	yes	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{1700}(81,\cdot)\)	1700.bx	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1700}(83,\cdot)\)	1700.ch	40	yes	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 640 characters

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