LMFDB - Group of Dirichlet characters of modulus 3267

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3267)

pari: g = idealstar(,3267,2)

Character group

sage: G.order() pari: g.no
Order	=	1980
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{990}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3267}(3026,\cdot)$, $\chi_{3267}(244,\cdot)$

First 32 of 1980 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{3267}(1,\cdot)$	3267.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3267}(2,\cdot)$	3267.bt	990	yes	$1$	$1$	$e\left(\frac{32}{495}\right)$	$e\left(\frac{64}{495}\right)$	$e\left(\frac{941}{990}\right)$	$e\left(\frac{943}{990}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{359}{990}\right)$	$e\left(\frac{17}{990}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{46}{165}\right)$
$\chi_{3267}(4,\cdot)$	3267.bs	495	yes	$1$	$1$	$e\left(\frac{64}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{359}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{92}{165}\right)$
$\chi_{3267}(5,\cdot)$	3267.bv	990	yes	$-1$	$1$	$e\left(\frac{941}{990}\right)$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{169}{990}\right)$	$e\left(\frac{76}{495}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{83}{495}\right)$	$e\left(\frac{103}{990}\right)$	$e\left(\frac{397}{495}\right)$	$e\left(\frac{43}{330}\right)$
$\chi_{3267}(7,\cdot)$	3267.bu	990	yes	$-1$	$1$	$e\left(\frac{943}{990}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{76}{495}\right)$	$e\left(\frac{661}{990}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{533}{990}\right)$	$e\left(\frac{307}{495}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{149}{330}\right)$
$\chi_{3267}(8,\cdot)$	3267.bp	330	no	$1$	$1$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{3267}(10,\cdot)$	3267.bc	66	no	$-1$	$1$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{3267}(13,\cdot)$	3267.bu	990	yes	$-1$	$1$	$e\left(\frac{359}{990}\right)$	$e\left(\frac{359}{495}\right)$	$e\left(\frac{83}{495}\right)$	$e\left(\frac{533}{990}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{289}{990}\right)$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{223}{495}\right)$	$e\left(\frac{217}{330}\right)$
$\chi_{3267}(14,\cdot)$	3267.bv	990	yes	$-1$	$1$	$e\left(\frac{17}{990}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{103}{990}\right)$	$e\left(\frac{307}{495}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{631}{990}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{241}{330}\right)$
$\chi_{3267}(16,\cdot)$	3267.bs	495	yes	$1$	$1$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{397}{495}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{223}{495}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{19}{165}\right)$
$\chi_{3267}(17,\cdot)$	3267.bp	330	no	$1$	$1$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{3267}(19,\cdot)$	3267.bq	330	no	$-1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{3267}(20,\cdot)$	3267.bv	990	yes	$-1$	$1$	$e\left(\frac{79}{990}\right)$	$e\left(\frac{79}{495}\right)$	$e\left(\frac{71}{990}\right)$	$e\left(\frac{29}{495}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{442}{495}\right)$	$e\left(\frac{137}{990}\right)$	$e\left(\frac{158}{495}\right)$	$e\left(\frac{227}{330}\right)$
$\chi_{3267}(23,\cdot)$	3267.bn	198	yes	$-1$	$1$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{3267}(25,\cdot)$	3267.bs	495	yes	$1$	$1$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{397}{495}\right)$	$e\left(\frac{169}{495}\right)$	$e\left(\frac{152}{495}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{166}{495}\right)$	$e\left(\frac{103}{495}\right)$	$e\left(\frac{299}{495}\right)$	$e\left(\frac{43}{165}\right)$
$\chi_{3267}(26,\cdot)$	3267.bi	110	no	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{3267}(28,\cdot)$	3267.bj	110	no	$-1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{3267}(29,\cdot)$	3267.bt	990	yes	$1$	$1$	$e\left(\frac{104}{495}\right)$	$e\left(\frac{208}{495}\right)$	$e\left(\frac{707}{990}\right)$	$e\left(\frac{961}{990}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{53}{990}\right)$	$e\left(\frac{179}{990}\right)$	$e\left(\frac{416}{495}\right)$	$e\left(\frac{67}{165}\right)$
$\chi_{3267}(31,\cdot)$	3267.bs	495	yes	$1$	$1$	$e\left(\frac{442}{495}\right)$	$e\left(\frac{389}{495}\right)$	$e\left(\frac{203}{495}\right)$	$e\left(\frac{124}{495}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{422}{495}\right)$	$e\left(\frac{71}{495}\right)$	$e\left(\frac{283}{495}\right)$	$e\left(\frac{161}{165}\right)$
$\chi_{3267}(32,\cdot)$	3267.bo	198	yes	$1$	$1$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{64}{99}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{3267}(34,\cdot)$	3267.bh	99	yes	$1$	$1$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{3267}(35,\cdot)$	3267.bp	330	no	$1$	$1$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{3267}(37,\cdot)$	3267.bl	165	no	$1$	$1$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{3267}(38,\cdot)$	3267.bv	990	yes	$-1$	$1$	$e\left(\frac{481}{990}\right)$	$e\left(\frac{481}{495}\right)$	$e\left(\frac{119}{990}\right)$	$e\left(\frac{446}{495}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{383}{990}\right)$	$e\left(\frac{467}{495}\right)$	$e\left(\frac{83}{330}\right)$
$\chi_{3267}(40,\cdot)$	3267.bf	90	no	$-1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{3267}(41,\cdot)$	3267.bt	990	yes	$1$	$1$	$e\left(\frac{76}{495}\right)$	$e\left(\frac{152}{495}\right)$	$e\left(\frac{193}{990}\right)$	$e\left(\frac{569}{990}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{667}{990}\right)$	$e\left(\frac{721}{990}\right)$	$e\left(\frac{304}{495}\right)$	$e\left(\frac{68}{165}\right)$
$\chi_{3267}(43,\cdot)$	3267.bm	198	yes	$-1$	$1$	$e\left(\frac{89}{198}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{31}{66}\right)$
$\chi_{3267}(46,\cdot)$	3267.bq	330	no	$-1$	$1$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{3267}(47,\cdot)$	3267.bv	990	yes	$-1$	$1$	$e\left(\frac{277}{990}\right)$	$e\left(\frac{277}{495}\right)$	$e\left(\frac{863}{990}\right)$	$e\left(\frac{227}{495}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{46}{495}\right)$	$e\left(\frac{731}{990}\right)$	$e\left(\frac{59}{495}\right)$	$e\left(\frac{161}{330}\right)$
$\chi_{3267}(49,\cdot)$	3267.bs	495	yes	$1$	$1$	$e\left(\frac{448}{495}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{152}{495}\right)$	$e\left(\frac{166}{495}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{38}{495}\right)$	$e\left(\frac{119}{495}\right)$	$e\left(\frac{307}{495}\right)$	$e\left(\frac{149}{165}\right)$
$\chi_{3267}(50,\cdot)$	3267.bt	990	yes	$1$	$1$	$e\left(\frac{478}{495}\right)$	$e\left(\frac{461}{495}\right)$	$e\left(\frac{289}{990}\right)$	$e\left(\frac{257}{990}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{691}{990}\right)$	$e\left(\frac{223}{990}\right)$	$e\left(\frac{427}{495}\right)$	$e\left(\frac{89}{165}\right)$
$\chi_{3267}(52,\cdot)$	3267.bu	990	yes	$-1$	$1$	$e\left(\frac{487}{990}\right)$	$e\left(\frac{487}{495}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{439}{990}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{17}{990}\right)$	$e\left(\frac{463}{495}\right)$	$e\left(\frac{479}{495}\right)$	$e\left(\frac{71}{330}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$3267$
Structure	\(C_{2}\times C_{990}\)
Order	$1980$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{3267}(1,\cdot)\)	3267.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3267}(2,\cdot)\)	3267.bt	990	yes	\(1\)	\(1\)	\(e\left(\frac{32}{495}\right)\)	\(e\left(\frac{64}{495}\right)\)	\(e\left(\frac{941}{990}\right)\)	\(e\left(\frac{943}{990}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{359}{990}\right)\)	\(e\left(\frac{17}{990}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{46}{165}\right)\)
\(\chi_{3267}(4,\cdot)\)	3267.bs	495	yes	\(1\)	\(1\)	\(e\left(\frac{64}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{359}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{92}{165}\right)\)
\(\chi_{3267}(5,\cdot)\)	3267.bv	990	yes	\(-1\)	\(1\)	\(e\left(\frac{941}{990}\right)\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{169}{990}\right)\)	\(e\left(\frac{76}{495}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{83}{495}\right)\)	\(e\left(\frac{103}{990}\right)\)	\(e\left(\frac{397}{495}\right)\)	\(e\left(\frac{43}{330}\right)\)
\(\chi_{3267}(7,\cdot)\)	3267.bu	990	yes	\(-1\)	\(1\)	\(e\left(\frac{943}{990}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{76}{495}\right)\)	\(e\left(\frac{661}{990}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{533}{990}\right)\)	\(e\left(\frac{307}{495}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{149}{330}\right)\)
\(\chi_{3267}(8,\cdot)\)	3267.bp	330	no	\(1\)	\(1\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{3267}(10,\cdot)\)	3267.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{3267}(13,\cdot)\)	3267.bu	990	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{990}\right)\)	\(e\left(\frac{359}{495}\right)\)	\(e\left(\frac{83}{495}\right)\)	\(e\left(\frac{533}{990}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{289}{990}\right)\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{223}{495}\right)\)	\(e\left(\frac{217}{330}\right)\)
\(\chi_{3267}(14,\cdot)\)	3267.bv	990	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{990}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{103}{990}\right)\)	\(e\left(\frac{307}{495}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{631}{990}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{241}{330}\right)\)
\(\chi_{3267}(16,\cdot)\)	3267.bs	495	yes	\(1\)	\(1\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{397}{495}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{223}{495}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{19}{165}\right)\)
\(\chi_{3267}(17,\cdot)\)	3267.bp	330	no	\(1\)	\(1\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{3267}(19,\cdot)\)	3267.bq	330	no	\(-1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{3267}(20,\cdot)\)	3267.bv	990	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{990}\right)\)	\(e\left(\frac{79}{495}\right)\)	\(e\left(\frac{71}{990}\right)\)	\(e\left(\frac{29}{495}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{442}{495}\right)\)	\(e\left(\frac{137}{990}\right)\)	\(e\left(\frac{158}{495}\right)\)	\(e\left(\frac{227}{330}\right)\)
\(\chi_{3267}(23,\cdot)\)	3267.bn	198	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{3267}(25,\cdot)\)	3267.bs	495	yes	\(1\)	\(1\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{397}{495}\right)\)	\(e\left(\frac{169}{495}\right)\)	\(e\left(\frac{152}{495}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{166}{495}\right)\)	\(e\left(\frac{103}{495}\right)\)	\(e\left(\frac{299}{495}\right)\)	\(e\left(\frac{43}{165}\right)\)
\(\chi_{3267}(26,\cdot)\)	3267.bi	110	no	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{3267}(28,\cdot)\)	3267.bj	110	no	\(-1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{3267}(29,\cdot)\)	3267.bt	990	yes	\(1\)	\(1\)	\(e\left(\frac{104}{495}\right)\)	\(e\left(\frac{208}{495}\right)\)	\(e\left(\frac{707}{990}\right)\)	\(e\left(\frac{961}{990}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{53}{990}\right)\)	\(e\left(\frac{179}{990}\right)\)	\(e\left(\frac{416}{495}\right)\)	\(e\left(\frac{67}{165}\right)\)
\(\chi_{3267}(31,\cdot)\)	3267.bs	495	yes	\(1\)	\(1\)	\(e\left(\frac{442}{495}\right)\)	\(e\left(\frac{389}{495}\right)\)	\(e\left(\frac{203}{495}\right)\)	\(e\left(\frac{124}{495}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{422}{495}\right)\)	\(e\left(\frac{71}{495}\right)\)	\(e\left(\frac{283}{495}\right)\)	\(e\left(\frac{161}{165}\right)\)
\(\chi_{3267}(32,\cdot)\)	3267.bo	198	yes	\(1\)	\(1\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{64}{99}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{3267}(34,\cdot)\)	3267.bh	99	yes	\(1\)	\(1\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{3267}(35,\cdot)\)	3267.bp	330	no	\(1\)	\(1\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{3267}(37,\cdot)\)	3267.bl	165	no	\(1\)	\(1\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{3267}(38,\cdot)\)	3267.bv	990	yes	\(-1\)	\(1\)	\(e\left(\frac{481}{990}\right)\)	\(e\left(\frac{481}{495}\right)\)	\(e\left(\frac{119}{990}\right)\)	\(e\left(\frac{446}{495}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{383}{990}\right)\)	\(e\left(\frac{467}{495}\right)\)	\(e\left(\frac{83}{330}\right)\)
\(\chi_{3267}(40,\cdot)\)	3267.bf	90	no	\(-1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{3267}(41,\cdot)\)	3267.bt	990	yes	\(1\)	\(1\)	\(e\left(\frac{76}{495}\right)\)	\(e\left(\frac{152}{495}\right)\)	\(e\left(\frac{193}{990}\right)\)	\(e\left(\frac{569}{990}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{667}{990}\right)\)	\(e\left(\frac{721}{990}\right)\)	\(e\left(\frac{304}{495}\right)\)	\(e\left(\frac{68}{165}\right)\)
\(\chi_{3267}(43,\cdot)\)	3267.bm	198	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{198}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{31}{66}\right)\)
\(\chi_{3267}(46,\cdot)\)	3267.bq	330	no	\(-1\)	\(1\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{3267}(47,\cdot)\)	3267.bv	990	yes	\(-1\)	\(1\)	\(e\left(\frac{277}{990}\right)\)	\(e\left(\frac{277}{495}\right)\)	\(e\left(\frac{863}{990}\right)\)	\(e\left(\frac{227}{495}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{46}{495}\right)\)	\(e\left(\frac{731}{990}\right)\)	\(e\left(\frac{59}{495}\right)\)	\(e\left(\frac{161}{330}\right)\)
\(\chi_{3267}(49,\cdot)\)	3267.bs	495	yes	\(1\)	\(1\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{152}{495}\right)\)	\(e\left(\frac{166}{495}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{38}{495}\right)\)	\(e\left(\frac{119}{495}\right)\)	\(e\left(\frac{307}{495}\right)\)	\(e\left(\frac{149}{165}\right)\)
\(\chi_{3267}(50,\cdot)\)	3267.bt	990	yes	\(1\)	\(1\)	\(e\left(\frac{478}{495}\right)\)	\(e\left(\frac{461}{495}\right)\)	\(e\left(\frac{289}{990}\right)\)	\(e\left(\frac{257}{990}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{691}{990}\right)\)	\(e\left(\frac{223}{990}\right)\)	\(e\left(\frac{427}{495}\right)\)	\(e\left(\frac{89}{165}\right)\)
\(\chi_{3267}(52,\cdot)\)	3267.bu	990	yes	\(-1\)	\(1\)	\(e\left(\frac{487}{990}\right)\)	\(e\left(\frac{487}{495}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{439}{990}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{17}{990}\right)\)	\(e\left(\frac{463}{495}\right)\)	\(e\left(\frac{479}{495}\right)\)	\(e\left(\frac{71}{330}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 1980 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.