LMFDB - Group of Dirichlet characters of modulus 704

sage:H = DirichletGroup(704)

pari:g = idealstar(,704,2)

Character group

sage:G.order() pari:g.no
Order	=	320
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{80}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{704}(639,\cdot)$, $\chi_{704}(133,\cdot)$, $\chi_{704}(321,\cdot)$

First 32 of 320 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{704}(1,\cdot)$	704.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{704}(3,\cdot)$	704.bl	80	yes	$-1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{704}(5,\cdot)$	704.bm	80	yes	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{704}(7,\cdot)$	704.bg	40	no	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{704}(9,\cdot)$	704.bj	40	no	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{704}(13,\cdot)$	704.bn	80	yes	$-1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{704}(15,\cdot)$	704.bd	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$1$
$\chi_{704}(17,\cdot)$	704.bc	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$-1$
$\chi_{704}(19,\cdot)$	704.bk	80	yes	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{704}(21,\cdot)$	704.y	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{704}(23,\cdot)$	704.p	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{1}{8}\right)$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{704}(25,\cdot)$	704.bj	40	no	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{704}(27,\cdot)$	704.bl	80	yes	$-1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{704}(29,\cdot)$	704.bn	80	yes	$-1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{704}(31,\cdot)$	704.t	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$
$\chi_{704}(35,\cdot)$	704.bk	80	yes	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{704}(37,\cdot)$	704.bm	80	yes	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{704}(39,\cdot)$	704.bg	40	no	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{704}(41,\cdot)$	704.bi	40	no	$-1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{704}(43,\cdot)$	704.bb	16	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{704}(45,\cdot)$	704.z	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{704}(47,\cdot)$	704.bd	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$-i$	$1$
$\chi_{704}(49,\cdot)$	704.be	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$-1$
$\chi_{704}(51,\cdot)$	704.bk	80	yes	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{704}(53,\cdot)$	704.bm	80	yes	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{704}(57,\cdot)$	704.bi	40	no	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{704}(59,\cdot)$	704.bl	80	yes	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{704}(61,\cdot)$	704.bn	80	yes	$-1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{704}(63,\cdot)$	704.u	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$
$\chi_{704}(65,\cdot)$	704.h	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{704}(67,\cdot)$	704.ba	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{704}(69,\cdot)$	704.bm	80	yes	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$

Click here to search among the remaining 288 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	$704$
Structure	\(C_{2}\times C_{2}\times C_{80}\)
Order	$320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{704}(1,\cdot)\)	704.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{704}(3,\cdot)\)	704.bl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{704}(5,\cdot)\)	704.bm	80	yes	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{704}(7,\cdot)\)	704.bg	40	no	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{704}(9,\cdot)\)	704.bj	40	no	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{704}(13,\cdot)\)	704.bn	80	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{704}(15,\cdot)\)	704.bd	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(1\)
\(\chi_{704}(17,\cdot)\)	704.bc	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(-1\)
\(\chi_{704}(19,\cdot)\)	704.bk	80	yes	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{704}(21,\cdot)\)	704.y	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{704}(23,\cdot)\)	704.p	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{704}(25,\cdot)\)	704.bj	40	no	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{704}(27,\cdot)\)	704.bl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{704}(29,\cdot)\)	704.bn	80	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{704}(31,\cdot)\)	704.t	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{704}(35,\cdot)\)	704.bk	80	yes	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{704}(37,\cdot)\)	704.bm	80	yes	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{704}(39,\cdot)\)	704.bg	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{704}(41,\cdot)\)	704.bi	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{704}(43,\cdot)\)	704.bb	16	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{704}(45,\cdot)\)	704.z	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{704}(47,\cdot)\)	704.bd	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(1\)
\(\chi_{704}(49,\cdot)\)	704.be	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(-1\)
\(\chi_{704}(51,\cdot)\)	704.bk	80	yes	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{704}(53,\cdot)\)	704.bm	80	yes	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{704}(57,\cdot)\)	704.bi	40	no	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{704}(59,\cdot)\)	704.bl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{704}(61,\cdot)\)	704.bn	80	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{704}(63,\cdot)\)	704.u	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{704}(65,\cdot)\)	704.h	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{704}(67,\cdot)\)	704.ba	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{704}(69,\cdot)\)	704.bm	80	yes	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 320 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.