LMFDB - Group of Dirichlet characters of modulus 21780

Show commands: PariGP / SageMath

sage: H = DirichletGroup(21780)

pari: g = idealstar(,21780,2)

Character group

sage: G.order() pari: g.no
Order	=	5280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{660}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{21780}(10891,\cdot)$, $\chi_{21780}(19361,\cdot)$, $\chi_{21780}(4357,\cdot)$, $\chi_{21780}(14401,\cdot)$

First 32 of 5280 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{21780}(1,\cdot)$	21780.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{21780}(7,\cdot)$	21780.hd	660	yes	$-1$	$1$	$e\left(\frac{569}{660}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{21780}(13,\cdot)$	21780.hg	660	no	$1$	$1$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{71}{132}\right)$
$\chi_{21780}(17,\cdot)$	21780.gk	220	no	$-1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{21780}(19,\cdot)$	21780.fo	110	no	$1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{21780}(23,\cdot)$	21780.fy	132	yes	$-1$	$1$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{131}{132}\right)$
$\chi_{21780}(29,\cdot)$	21780.gn	330	no	$1$	$1$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{21780}(31,\cdot)$	21780.gw	330	no	$-1$	$1$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{21780}(37,\cdot)$	21780.gg	220	no	$-1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{21780}(41,\cdot)$	21780.ha	330	no	$1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{37}{66}\right)$
$\chi_{21780}(43,\cdot)$	21780.gc	132	yes	$-1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{13}{132}\right)$
$\chi_{21780}(47,\cdot)$	21780.hh	660	yes	$-1$	$1$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{25}{132}\right)$
$\chi_{21780}(49,\cdot)$	21780.gz	330	no	$1$	$1$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{21780}(53,\cdot)$	21780.gi	220	no	$1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{21780}(59,\cdot)$	21780.gs	330	yes	$1$	$1$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{21780}(61,\cdot)$	21780.gy	330	no	$-1$	$1$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{21780}(67,\cdot)$	21780.fw	132	yes	$1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{21780}(71,\cdot)$	21780.fl	110	no	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{21780}(73,\cdot)$	21780.gm	220	no	$1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{21780}(79,\cdot)$	21780.gx	330	yes	$1$	$1$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{21780}(83,\cdot)$	21780.hf	660	yes	$1$	$1$	$e\left(\frac{503}{660}\right)$	$e\left(\frac{139}{660}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{21780}(89,\cdot)$	21780.dh	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{21780}(91,\cdot)$	21780.fn	110	no	$-1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{21780}(97,\cdot)$	21780.he	660	no	$-1$	$1$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{91}{660}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{21780}(101,\cdot)$	21780.ha	330	no	$1$	$1$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{21780}(103,\cdot)$	21780.hj	660	yes	$1$	$1$	$e\left(\frac{229}{660}\right)$	$e\left(\frac{617}{660}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{21780}(107,\cdot)$	21780.gf	220	no	$1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{21780}(109,\cdot)$	21780.cw	22	no	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{21780}(113,\cdot)$	21780.hc	660	no	$1$	$1$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{101}{132}\right)$
$\chi_{21780}(119,\cdot)$	21780.gs	330	yes	$1$	$1$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{21780}(127,\cdot)$	21780.gh	220	no	$-1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{21780}(131,\cdot)$	21780.fa	66	no	$-1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{29}{33}\right)$

Click here to search among the remaining 5248 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 $\F_{q}$

Modulus	$21780$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{660}\)
Order	$5280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{21780}(1,\cdot)\)	21780.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{21780}(7,\cdot)\)	21780.hd	660	yes	\(-1\)	\(1\)	\(e\left(\frac{569}{660}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{21780}(13,\cdot)\)	21780.hg	660	no	\(1\)	\(1\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{71}{132}\right)\)
\(\chi_{21780}(17,\cdot)\)	21780.gk	220	no	\(-1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{21780}(19,\cdot)\)	21780.fo	110	no	\(1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{21780}(23,\cdot)\)	21780.fy	132	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)
\(\chi_{21780}(29,\cdot)\)	21780.gn	330	no	\(1\)	\(1\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{21780}(31,\cdot)\)	21780.gw	330	no	\(-1\)	\(1\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{21780}(37,\cdot)\)	21780.gg	220	no	\(-1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{21780}(41,\cdot)\)	21780.ha	330	no	\(1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{37}{66}\right)\)
\(\chi_{21780}(43,\cdot)\)	21780.gc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{13}{132}\right)\)
\(\chi_{21780}(47,\cdot)\)	21780.hh	660	yes	\(-1\)	\(1\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{25}{132}\right)\)
\(\chi_{21780}(49,\cdot)\)	21780.gz	330	no	\(1\)	\(1\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{21780}(53,\cdot)\)	21780.gi	220	no	\(1\)	\(1\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{21780}(59,\cdot)\)	21780.gs	330	yes	\(1\)	\(1\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{21780}(61,\cdot)\)	21780.gy	330	no	\(-1\)	\(1\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{21780}(67,\cdot)\)	21780.fw	132	yes	\(1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{21780}(71,\cdot)\)	21780.fl	110	no	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{21780}(73,\cdot)\)	21780.gm	220	no	\(1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{21780}(79,\cdot)\)	21780.gx	330	yes	\(1\)	\(1\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{21780}(83,\cdot)\)	21780.hf	660	yes	\(1\)	\(1\)	\(e\left(\frac{503}{660}\right)\)	\(e\left(\frac{139}{660}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{21780}(89,\cdot)\)	21780.dh	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{21780}(91,\cdot)\)	21780.fn	110	no	\(-1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{21780}(97,\cdot)\)	21780.he	660	no	\(-1\)	\(1\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{91}{660}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{21780}(101,\cdot)\)	21780.ha	330	no	\(1\)	\(1\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{21780}(103,\cdot)\)	21780.hj	660	yes	\(1\)	\(1\)	\(e\left(\frac{229}{660}\right)\)	\(e\left(\frac{617}{660}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{107}{132}\right)\)
\(\chi_{21780}(107,\cdot)\)	21780.gf	220	no	\(1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{21780}(109,\cdot)\)	21780.cw	22	no	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{21780}(113,\cdot)\)	21780.hc	660	no	\(1\)	\(1\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{101}{132}\right)\)
\(\chi_{21780}(119,\cdot)\)	21780.gs	330	yes	\(1\)	\(1\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{21780}(127,\cdot)\)	21780.gh	220	no	\(-1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{21780}(131,\cdot)\)	21780.fa	66	no	\(-1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 5280 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.