LMFDB - Group of Dirichlet characters of modulus 6897

sage:H = DirichletGroup(6897)

pari:g = idealstar(,6897,2)

Character group

sage:G.order() pari:g.no
Order	=	3960
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{990}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6897}(2300,\cdot)$, $\chi_{6897}(970,\cdot)$, $\chi_{6897}(3631,\cdot)$

First 32 of 3960 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{6897}(1,\cdot)$	6897.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6897}(2,\cdot)$	6897.dq	990	yes	$-1$	$1$	$e\left(\frac{559}{990}\right)$	$e\left(\frac{64}{495}\right)$	$e\left(\frac{61}{990}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{97}{495}\right)$	$e\left(\frac{476}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{248}{495}\right)$
$\chi_{6897}(4,\cdot)$	6897.dk	495	no	$1$	$1$	$e\left(\frac{64}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{61}{495}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{194}{495}\right)$	$e\left(\frac{457}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{1}{495}\right)$
$\chi_{6897}(5,\cdot)$	6897.dm	990	yes	$-1$	$1$	$e\left(\frac{61}{990}\right)$	$e\left(\frac{61}{495}\right)$	$e\left(\frac{499}{990}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{193}{495}\right)$	$e\left(\frac{103}{990}\right)$	$e\left(\frac{122}{495}\right)$	$e\left(\frac{349}{990}\right)$
$\chi_{6897}(7,\cdot)$	6897.dg	330	no	$-1$	$1$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{149}{330}\right)$
$\chi_{6897}(8,\cdot)$	6897.di	330	yes	$-1$	$1$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{83}{165}\right)$
$\chi_{6897}(10,\cdot)$	6897.cy	198	no	$1$	$1$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{169}{198}\right)$
$\chi_{6897}(13,\cdot)$	6897.dp	990	no	$1$	$1$	$e\left(\frac{97}{495}\right)$	$e\left(\frac{194}{495}\right)$	$e\left(\frac{193}{495}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{62}{495}\right)$	$e\left(\frac{287}{990}\right)$	$e\left(\frac{388}{495}\right)$	$e\left(\frac{761}{990}\right)$
$\chi_{6897}(14,\cdot)$	6897.dl	990	yes	$1$	$1$	$e\left(\frac{476}{495}\right)$	$e\left(\frac{457}{495}\right)$	$e\left(\frac{103}{990}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{287}{990}\right)$	$e\left(\frac{398}{495}\right)$	$e\left(\frac{419}{495}\right)$	$e\left(\frac{943}{990}\right)$
$\chi_{6897}(16,\cdot)$	6897.dk	495	no	$1$	$1$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{122}{495}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{388}{495}\right)$	$e\left(\frac{419}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{2}{495}\right)$
$\chi_{6897}(17,\cdot)$	6897.do	990	yes	$1$	$1$	$e\left(\frac{248}{495}\right)$	$e\left(\frac{1}{495}\right)$	$e\left(\frac{349}{990}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{169}{198}\right)$	$e\left(\frac{761}{990}\right)$	$e\left(\frac{943}{990}\right)$	$e\left(\frac{2}{495}\right)$	$e\left(\frac{437}{495}\right)$
$\chi_{6897}(20,\cdot)$	6897.cp	110	no	$-1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{6897}(23,\cdot)$	6897.db	198	yes	$-1$	$1$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{61}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{157}{198}\right)$
$\chi_{6897}(25,\cdot)$	6897.dk	495	no	$1$	$1$	$e\left(\frac{61}{495}\right)$	$e\left(\frac{122}{495}\right)$	$e\left(\frac{4}{495}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{386}{495}\right)$	$e\left(\frac{103}{495}\right)$	$e\left(\frac{244}{495}\right)$	$e\left(\frac{349}{495}\right)$
$\chi_{6897}(26,\cdot)$	6897.dj	330	yes	$-1$	$1$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{89}{330}\right)$
$\chi_{6897}(28,\cdot)$	6897.dr	990	no	$-1$	$1$	$e\left(\frac{521}{990}\right)$	$e\left(\frac{26}{495}\right)$	$e\left(\frac{82}{495}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{481}{990}\right)$	$e\left(\frac{379}{495}\right)$	$e\left(\frac{52}{495}\right)$	$e\left(\frac{449}{990}\right)$
$\chi_{6897}(29,\cdot)$	6897.dq	990	yes	$-1$	$1$	$e\left(\frac{593}{990}\right)$	$e\left(\frac{98}{495}\right)$	$e\left(\frac{47}{990}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{164}{495}\right)$	$e\left(\frac{172}{495}\right)$	$e\left(\frac{196}{495}\right)$	$e\left(\frac{256}{495}\right)$
$\chi_{6897}(31,\cdot)$	6897.dh	330	no	$-1$	$1$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{106}{165}\right)$
$\chi_{6897}(32,\cdot)$	6897.cx	198	yes	$-1$	$1$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{50}{99}\right)$
$\chi_{6897}(34,\cdot)$	6897.da	198	no	$-1$	$1$	$e\left(\frac{13}{198}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{38}{99}\right)$
$\chi_{6897}(35,\cdot)$	6897.do	990	yes	$1$	$1$	$e\left(\frac{227}{495}\right)$	$e\left(\frac{454}{495}\right)$	$e\left(\frac{541}{990}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{479}{990}\right)$	$e\left(\frac{937}{990}\right)$	$e\left(\frac{413}{495}\right)$	$e\left(\frac{398}{495}\right)$
$\chi_{6897}(37,\cdot)$	6897.cr	110	no	$-1$	$1$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{6897}(40,\cdot)$	6897.ci	90	no	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{6897}(41,\cdot)$	6897.dq	990	yes	$-1$	$1$	$e\left(\frac{427}{990}\right)$	$e\left(\frac{427}{495}\right)$	$e\left(\frac{523}{990}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{95}{99}\right)$	$e\left(\frac{361}{495}\right)$	$e\left(\frac{113}{495}\right)$	$e\left(\frac{359}{495}\right)$	$e\left(\frac{479}{495}\right)$
$\chi_{6897}(43,\cdot)$	6897.cw	198	no	$-1$	$1$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{4}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{5}{198}\right)$
$\chi_{6897}(46,\cdot)$	6897.dd	330	no	$1$	$1$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{97}{330}\right)$
$\chi_{6897}(47,\cdot)$	6897.dm	990	yes	$-1$	$1$	$e\left(\frac{827}{990}\right)$	$e\left(\frac{332}{495}\right)$	$e\left(\frac{533}{990}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{101}{495}\right)$	$e\left(\frac{731}{990}\right)$	$e\left(\frac{169}{495}\right)$	$e\left(\frac{593}{990}\right)$
$\chi_{6897}(49,\cdot)$	6897.cv	165	no	$1$	$1$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{149}{165}\right)$
$\chi_{6897}(50,\cdot)$	6897.di	330	yes	$-1$	$1$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{34}{165}\right)$
$\chi_{6897}(52,\cdot)$	6897.dp	990	no	$1$	$1$	$e\left(\frac{161}{495}\right)$	$e\left(\frac{322}{495}\right)$	$e\left(\frac{254}{495}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{211}{990}\right)$	$e\left(\frac{149}{495}\right)$	$e\left(\frac{763}{990}\right)$
$\chi_{6897}(53,\cdot)$	6897.dl	990	yes	$1$	$1$	$e\left(\frac{37}{495}\right)$	$e\left(\frac{74}{495}\right)$	$e\left(\frac{581}{990}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{379}{990}\right)$	$e\left(\frac{241}{495}\right)$	$e\left(\frac{148}{495}\right)$	$e\left(\frac{821}{990}\right)$
$\chi_{6897}(56,\cdot)$	6897.bj	22	yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$

Click here to search among the remaining 3928 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	$6897$
Structure	\(C_{2}\times C_{2}\times C_{990}\)
Order	$3960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{6897}(1,\cdot)\)	6897.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6897}(2,\cdot)\)	6897.dq	990	yes	\(-1\)	\(1\)	\(e\left(\frac{559}{990}\right)\)	\(e\left(\frac{64}{495}\right)\)	\(e\left(\frac{61}{990}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{97}{495}\right)\)	\(e\left(\frac{476}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{248}{495}\right)\)
\(\chi_{6897}(4,\cdot)\)	6897.dk	495	no	\(1\)	\(1\)	\(e\left(\frac{64}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{61}{495}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{194}{495}\right)\)	\(e\left(\frac{457}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{1}{495}\right)\)
\(\chi_{6897}(5,\cdot)\)	6897.dm	990	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{990}\right)\)	\(e\left(\frac{61}{495}\right)\)	\(e\left(\frac{499}{990}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{193}{495}\right)\)	\(e\left(\frac{103}{990}\right)\)	\(e\left(\frac{122}{495}\right)\)	\(e\left(\frac{349}{990}\right)\)
\(\chi_{6897}(7,\cdot)\)	6897.dg	330	no	\(-1\)	\(1\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{149}{330}\right)\)
\(\chi_{6897}(8,\cdot)\)	6897.di	330	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{83}{165}\right)\)
\(\chi_{6897}(10,\cdot)\)	6897.cy	198	no	\(1\)	\(1\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{169}{198}\right)\)
\(\chi_{6897}(13,\cdot)\)	6897.dp	990	no	\(1\)	\(1\)	\(e\left(\frac{97}{495}\right)\)	\(e\left(\frac{194}{495}\right)\)	\(e\left(\frac{193}{495}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{62}{495}\right)\)	\(e\left(\frac{287}{990}\right)\)	\(e\left(\frac{388}{495}\right)\)	\(e\left(\frac{761}{990}\right)\)
\(\chi_{6897}(14,\cdot)\)	6897.dl	990	yes	\(1\)	\(1\)	\(e\left(\frac{476}{495}\right)\)	\(e\left(\frac{457}{495}\right)\)	\(e\left(\frac{103}{990}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{287}{990}\right)\)	\(e\left(\frac{398}{495}\right)\)	\(e\left(\frac{419}{495}\right)\)	\(e\left(\frac{943}{990}\right)\)
\(\chi_{6897}(16,\cdot)\)	6897.dk	495	no	\(1\)	\(1\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{122}{495}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{388}{495}\right)\)	\(e\left(\frac{419}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{2}{495}\right)\)
\(\chi_{6897}(17,\cdot)\)	6897.do	990	yes	\(1\)	\(1\)	\(e\left(\frac{248}{495}\right)\)	\(e\left(\frac{1}{495}\right)\)	\(e\left(\frac{349}{990}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{169}{198}\right)\)	\(e\left(\frac{761}{990}\right)\)	\(e\left(\frac{943}{990}\right)\)	\(e\left(\frac{2}{495}\right)\)	\(e\left(\frac{437}{495}\right)\)
\(\chi_{6897}(20,\cdot)\)	6897.cp	110	no	\(-1\)	\(1\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{6897}(23,\cdot)\)	6897.db	198	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{61}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{157}{198}\right)\)
\(\chi_{6897}(25,\cdot)\)	6897.dk	495	no	\(1\)	\(1\)	\(e\left(\frac{61}{495}\right)\)	\(e\left(\frac{122}{495}\right)\)	\(e\left(\frac{4}{495}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{386}{495}\right)\)	\(e\left(\frac{103}{495}\right)\)	\(e\left(\frac{244}{495}\right)\)	\(e\left(\frac{349}{495}\right)\)
\(\chi_{6897}(26,\cdot)\)	6897.dj	330	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)
\(\chi_{6897}(28,\cdot)\)	6897.dr	990	no	\(-1\)	\(1\)	\(e\left(\frac{521}{990}\right)\)	\(e\left(\frac{26}{495}\right)\)	\(e\left(\frac{82}{495}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{481}{990}\right)\)	\(e\left(\frac{379}{495}\right)\)	\(e\left(\frac{52}{495}\right)\)	\(e\left(\frac{449}{990}\right)\)
\(\chi_{6897}(29,\cdot)\)	6897.dq	990	yes	\(-1\)	\(1\)	\(e\left(\frac{593}{990}\right)\)	\(e\left(\frac{98}{495}\right)\)	\(e\left(\frac{47}{990}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{164}{495}\right)\)	\(e\left(\frac{172}{495}\right)\)	\(e\left(\frac{196}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)
\(\chi_{6897}(31,\cdot)\)	6897.dh	330	no	\(-1\)	\(1\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)
\(\chi_{6897}(32,\cdot)\)	6897.cx	198	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)
\(\chi_{6897}(34,\cdot)\)	6897.da	198	no	\(-1\)	\(1\)	\(e\left(\frac{13}{198}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{38}{99}\right)\)
\(\chi_{6897}(35,\cdot)\)	6897.do	990	yes	\(1\)	\(1\)	\(e\left(\frac{227}{495}\right)\)	\(e\left(\frac{454}{495}\right)\)	\(e\left(\frac{541}{990}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{479}{990}\right)\)	\(e\left(\frac{937}{990}\right)\)	\(e\left(\frac{413}{495}\right)\)	\(e\left(\frac{398}{495}\right)\)
\(\chi_{6897}(37,\cdot)\)	6897.cr	110	no	\(-1\)	\(1\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{6897}(40,\cdot)\)	6897.ci	90	no	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{6897}(41,\cdot)\)	6897.dq	990	yes	\(-1\)	\(1\)	\(e\left(\frac{427}{990}\right)\)	\(e\left(\frac{427}{495}\right)\)	\(e\left(\frac{523}{990}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{95}{99}\right)\)	\(e\left(\frac{361}{495}\right)\)	\(e\left(\frac{113}{495}\right)\)	\(e\left(\frac{359}{495}\right)\)	\(e\left(\frac{479}{495}\right)\)
\(\chi_{6897}(43,\cdot)\)	6897.cw	198	no	\(-1\)	\(1\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{4}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{5}{198}\right)\)
\(\chi_{6897}(46,\cdot)\)	6897.dd	330	no	\(1\)	\(1\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)
\(\chi_{6897}(47,\cdot)\)	6897.dm	990	yes	\(-1\)	\(1\)	\(e\left(\frac{827}{990}\right)\)	\(e\left(\frac{332}{495}\right)\)	\(e\left(\frac{533}{990}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{101}{495}\right)\)	\(e\left(\frac{731}{990}\right)\)	\(e\left(\frac{169}{495}\right)\)	\(e\left(\frac{593}{990}\right)\)
\(\chi_{6897}(49,\cdot)\)	6897.cv	165	no	\(1\)	\(1\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)
\(\chi_{6897}(50,\cdot)\)	6897.di	330	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{34}{165}\right)\)
\(\chi_{6897}(52,\cdot)\)	6897.dp	990	no	\(1\)	\(1\)	\(e\left(\frac{161}{495}\right)\)	\(e\left(\frac{322}{495}\right)\)	\(e\left(\frac{254}{495}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{211}{990}\right)\)	\(e\left(\frac{149}{495}\right)\)	\(e\left(\frac{763}{990}\right)\)
\(\chi_{6897}(53,\cdot)\)	6897.dl	990	yes	\(1\)	\(1\)	\(e\left(\frac{37}{495}\right)\)	\(e\left(\frac{74}{495}\right)\)	\(e\left(\frac{581}{990}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{379}{990}\right)\)	\(e\left(\frac{241}{495}\right)\)	\(e\left(\frac{148}{495}\right)\)	\(e\left(\frac{821}{990}\right)\)
\(\chi_{6897}(56,\cdot)\)	6897.bj	22	yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 3960 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.