LMFDB - Group of Dirichlet characters of modulus 6500

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(6500)

gp:g = idealstar(,6500,2)

magma:G = FullDirichletGroup(6500);

Character group

Order	=	2400	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{300}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{6500}(3251,\cdot)$, $\chi_{6500}(5877,\cdot)$, $\chi_{6500}(5501,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 2400 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{6500}(1,\cdot)$	6500.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6500}(3,\cdot)$	6500.ek	300	yes	$1$	$1$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{101}{150}\right)$
$\chi_{6500}(7,\cdot)$	6500.dg	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{6500}(9,\cdot)$	6500.dx	150	no	$1$	$1$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{26}{75}\right)$
$\chi_{6500}(11,\cdot)$	6500.em	300	yes	$1$	$1$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{34}{75}\right)$
$\chi_{6500}(17,\cdot)$	6500.ei	300	no	$-1$	$1$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{139}{150}\right)$
$\chi_{6500}(19,\cdot)$	6500.eg	300	yes	$1$	$1$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{62}{75}\right)$
$\chi_{6500}(21,\cdot)$	6500.du	100	no	$-1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{6500}(23,\cdot)$	6500.el	300	yes	$1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{83}{150}\right)$
$\chi_{6500}(27,\cdot)$	6500.dr	100	no	$1$	$1$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{6500}(29,\cdot)$	6500.dx	150	no	$1$	$1$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{58}{75}\right)$
$\chi_{6500}(31,\cdot)$	6500.dn	100	yes	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{6500}(33,\cdot)$	6500.ef	300	no	$1$	$1$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{150}\right)$
$\chi_{6500}(37,\cdot)$	6500.ep	300	no	$1$	$1$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{47}{150}\right)$
$\chi_{6500}(41,\cdot)$	6500.eh	300	no	$-1$	$1$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{46}{75}\right)$
$\chi_{6500}(43,\cdot)$	6500.df	60	no	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{6500}(47,\cdot)$	6500.dv	100	yes	$-1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{6500}(49,\cdot)$	6500.ck	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{6500}(51,\cdot)$	6500.bi	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{6500}(53,\cdot)$	6500.dq	100	no	$-1$	$1$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{6500}(57,\cdot)$	6500.m	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$i$	$i$	$i$	$i$	$-1$
$\chi_{6500}(59,\cdot)$	6500.eg	300	yes	$1$	$1$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{56}{75}\right)$
$\chi_{6500}(61,\cdot)$	6500.dk	75	no	$1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{29}{75}\right)$
$\chi_{6500}(63,\cdot)$	6500.eo	300	yes	$-1$	$1$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{6500}(67,\cdot)$	6500.eo	300	yes	$-1$	$1$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{59}{150}\right)$
$\chi_{6500}(69,\cdot)$	6500.eb	150	no	$1$	$1$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{17}{75}\right)$
$\chi_{6500}(71,\cdot)$	6500.em	300	yes	$1$	$1$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{75}\right)$
$\chi_{6500}(73,\cdot)$	6500.dw	100	no	$1$	$1$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{6500}(77,\cdot)$	6500.dp	100	no	$-1$	$1$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{6500}(79,\cdot)$	6500.cr	50	no	$-1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{6500}(81,\cdot)$	6500.dk	75	no	$1$	$1$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{52}{75}\right)$
$\chi_{6500}(83,\cdot)$	6500.dv	100	yes	$-1$	$1$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{33}{50}\right)$

Click here to search among the remaining 2368 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	$6500$
Structure	\(C_{2}\times C_{4}\times C_{300}\)
Order	$2400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{6500}(1,\cdot)\)	6500.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6500}(3,\cdot)\)	6500.ek	300	yes	\(1\)	\(1\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)
\(\chi_{6500}(7,\cdot)\)	6500.dg	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{6500}(9,\cdot)\)	6500.dx	150	no	\(1\)	\(1\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{26}{75}\right)\)
\(\chi_{6500}(11,\cdot)\)	6500.em	300	yes	\(1\)	\(1\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{34}{75}\right)\)
\(\chi_{6500}(17,\cdot)\)	6500.ei	300	no	\(-1\)	\(1\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{139}{150}\right)\)
\(\chi_{6500}(19,\cdot)\)	6500.eg	300	yes	\(1\)	\(1\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{62}{75}\right)\)
\(\chi_{6500}(21,\cdot)\)	6500.du	100	no	\(-1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{6500}(23,\cdot)\)	6500.el	300	yes	\(1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)
\(\chi_{6500}(27,\cdot)\)	6500.dr	100	no	\(1\)	\(1\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{6500}(29,\cdot)\)	6500.dx	150	no	\(1\)	\(1\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{58}{75}\right)\)
\(\chi_{6500}(31,\cdot)\)	6500.dn	100	yes	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)
\(\chi_{6500}(33,\cdot)\)	6500.ef	300	no	\(1\)	\(1\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{150}\right)\)
\(\chi_{6500}(37,\cdot)\)	6500.ep	300	no	\(1\)	\(1\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{47}{150}\right)\)
\(\chi_{6500}(41,\cdot)\)	6500.eh	300	no	\(-1\)	\(1\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{46}{75}\right)\)
\(\chi_{6500}(43,\cdot)\)	6500.df	60	no	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{6500}(47,\cdot)\)	6500.dv	100	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{6500}(49,\cdot)\)	6500.ck	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{6500}(51,\cdot)\)	6500.bi	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{6500}(53,\cdot)\)	6500.dq	100	no	\(-1\)	\(1\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{6500}(57,\cdot)\)	6500.m	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{6500}(59,\cdot)\)	6500.eg	300	yes	\(1\)	\(1\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{56}{75}\right)\)
\(\chi_{6500}(61,\cdot)\)	6500.dk	75	no	\(1\)	\(1\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{29}{75}\right)\)
\(\chi_{6500}(63,\cdot)\)	6500.eo	300	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{6500}(67,\cdot)\)	6500.eo	300	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{289}{300}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{59}{150}\right)\)
\(\chi_{6500}(69,\cdot)\)	6500.eb	150	no	\(1\)	\(1\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{17}{75}\right)\)
\(\chi_{6500}(71,\cdot)\)	6500.em	300	yes	\(1\)	\(1\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{75}\right)\)
\(\chi_{6500}(73,\cdot)\)	6500.dw	100	no	\(1\)	\(1\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{6500}(77,\cdot)\)	6500.dp	100	no	\(-1\)	\(1\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{6500}(79,\cdot)\)	6500.cr	50	no	\(-1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)
\(\chi_{6500}(81,\cdot)\)	6500.dk	75	no	\(1\)	\(1\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{52}{75}\right)\)
\(\chi_{6500}(83,\cdot)\)	6500.dv	100	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 2400 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.