LMFDB - Group of Dirichlet characters of modulus 2001

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2001)

pari: g = idealstar(,2001,2)

Character group

sage: G.order() pari: g.no
Order	=	1232
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{308}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2001}(668,\cdot)$, $\chi_{2001}(1132,\cdot)$, $\chi_{2001}(553,\cdot)$

First 32 of 1232 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2001}(1,\cdot)$	2001.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2001}(2,\cdot)$	2001.bv	308	yes	$1$	$1$	$e\left(\frac{221}{308}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{47}{308}\right)$	$e\left(\frac{29}{308}\right)$	$e\left(\frac{65}{308}\right)$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{269}{308}\right)$	$e\left(\frac{67}{77}\right)$
$\chi_{2001}(4,\cdot)$	2001.bo	154	no	$1$	$1$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{57}{77}\right)$
$\chi_{2001}(5,\cdot)$	2001.br	154	yes	$1$	$1$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{39}{77}\right)$
$\chi_{2001}(7,\cdot)$	2001.bp	154	no	$-1$	$1$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{48}{77}\right)$
$\chi_{2001}(8,\cdot)$	2001.bv	308	yes	$1$	$1$	$e\left(\frac{47}{308}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{141}{308}\right)$	$e\left(\frac{87}{308}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{191}{308}\right)$	$e\left(\frac{47}{77}\right)$
$\chi_{2001}(10,\cdot)$	2001.bu	308	no	$1$	$1$	$e\left(\frac{29}{308}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{69}{154}\right)$	$e\left(\frac{87}{308}\right)$	$e\left(\frac{93}{308}\right)$	$e\left(\frac{235}{308}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{167}{308}\right)$	$e\left(\frac{29}{77}\right)$
$\chi_{2001}(11,\cdot)$	2001.bs	308	yes	$-1$	$1$	$e\left(\frac{65}{308}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{235}{308}\right)$	$e\left(\frac{155}{308}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{65}{77}\right)$
$\chi_{2001}(13,\cdot)$	2001.bo	154	no	$1$	$1$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{37}{77}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{51}{77}\right)$
$\chi_{2001}(14,\cdot)$	2001.bs	308	yes	$-1$	$1$	$e\left(\frac{269}{308}\right)$	$e\left(\frac{115}{154}\right)$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{191}{308}\right)$	$e\left(\frac{167}{308}\right)$	$e\left(\frac{215}{308}\right)$	$e\left(\frac{111}{154}\right)$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{38}{77}\right)$
$\chi_{2001}(16,\cdot)$	2001.bk	77	no	$1$	$1$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{37}{77}\right)$
$\chi_{2001}(17,\cdot)$	2001.bj	44	yes	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{2001}(19,\cdot)$	2001.bu	308	no	$1$	$1$	$e\left(\frac{211}{308}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{17}{308}\right)$	$e\left(\frac{135}{308}\right)$	$e\left(\frac{53}{308}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{153}{308}\right)$	$e\left(\frac{57}{77}\right)$
$\chi_{2001}(20,\cdot)$	2001.bn	154	yes	$1$	$1$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{19}{77}\right)$
$\chi_{2001}(22,\cdot)$	2001.u	14	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2001}(25,\cdot)$	2001.bk	77	no	$1$	$1$	$e\left(\frac{58}{77}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{51}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{20}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{43}{77}\right)$	$e\left(\frac{26}{77}\right)$	$e\left(\frac{1}{77}\right)$
$\chi_{2001}(26,\cdot)$	2001.bv	308	yes	$1$	$1$	$e\left(\frac{195}{308}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{12}{77}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{277}{308}\right)$	$e\left(\frac{243}{308}\right)$	$e\left(\frac{3}{308}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{183}{308}\right)$	$e\left(\frac{41}{77}\right)$
$\chi_{2001}(28,\cdot)$	2001.bb	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2001}(31,\cdot)$	2001.bt	308	no	$-1$	$1$	$e\left(\frac{179}{308}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{229}{308}\right)$	$e\left(\frac{197}{308}\right)$	$e\left(\frac{107}{308}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{59}{308}\right)$	$e\left(\frac{25}{77}\right)$
$\chi_{2001}(32,\cdot)$	2001.bv	308	yes	$1$	$1$	$e\left(\frac{181}{308}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{60}{77}\right)$	$e\left(\frac{235}{308}\right)$	$e\left(\frac{145}{308}\right)$	$e\left(\frac{17}{308}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{113}{308}\right)$	$e\left(\frac{27}{77}\right)$
$\chi_{2001}(34,\cdot)$	2001.bl	154	no	$-1$	$1$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{23}{77}\right)$	$e\left(\frac{25}{77}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{32}{77}\right)$
$\chi_{2001}(35,\cdot)$	2001.bq	154	yes	$-1$	$1$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{46}{77}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{29}{77}\right)$	$e\left(\frac{10}{77}\right)$
$\chi_{2001}(37,\cdot)$	2001.bu	308	no	$1$	$1$	$e\left(\frac{5}{308}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{65}{154}\right)$	$e\left(\frac{15}{308}\right)$	$e\left(\frac{101}{308}\right)$	$e\left(\frac{83}{308}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{135}{308}\right)$	$e\left(\frac{5}{77}\right)$
$\chi_{2001}(38,\cdot)$	2001.br	154	yes	$1$	$1$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{16}{77}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{19}{77}\right)$	$e\left(\frac{57}{154}\right)$	$e\left(\frac{47}{77}\right)$
$\chi_{2001}(40,\cdot)$	2001.bu	308	no	$1$	$1$	$e\left(\frac{163}{308}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{181}{308}\right)$	$e\left(\frac{151}{308}\right)$	$e\left(\frac{57}{308}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{89}{308}\right)$	$e\left(\frac{9}{77}\right)$
$\chi_{2001}(41,\cdot)$	2001.bg	44	yes	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2001}(43,\cdot)$	2001.bu	308	no	$1$	$1$	$e\left(\frac{283}{308}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{34}{77}\right)$	$e\left(\frac{137}{154}\right)$	$e\left(\frac{233}{308}\right)$	$e\left(\frac{111}{308}\right)$	$e\left(\frac{201}{308}\right)$	$e\left(\frac{83}{154}\right)$	$e\left(\frac{249}{308}\right)$	$e\left(\frac{52}{77}\right)$
$\chi_{2001}(44,\cdot)$	2001.bs	308	yes	$-1$	$1$	$e\left(\frac{199}{308}\right)$	$e\left(\frac{45}{154}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{289}{308}\right)$	$e\left(\frac{293}{308}\right)$	$e\left(\frac{285}{308}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{137}{308}\right)$	$e\left(\frac{45}{77}\right)$
$\chi_{2001}(47,\cdot)$	2001.bc	28	no	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{2001}(49,\cdot)$	2001.bk	77	no	$1$	$1$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{48}{77}\right)$	$e\left(\frac{45}{77}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{69}{77}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{19}{77}\right)$
$\chi_{2001}(50,\cdot)$	2001.bv	308	yes	$1$	$1$	$e\left(\frac{145}{308}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{127}{308}\right)$	$e\left(\frac{157}{308}\right)$	$e\left(\frac{97}{308}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{65}{308}\right)$	$e\left(\frac{68}{77}\right)$
$\chi_{2001}(52,\cdot)$	2001.bk	77	no	$1$	$1$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{41}{77}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{4}{77}\right)$	$e\left(\frac{68}{77}\right)$	$e\left(\frac{17}{77}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{31}{77}\right)$

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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	$2001$
Structure	\(C_{2}\times C_{2}\times C_{308}\)
Order	$1232$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2001}(1,\cdot)\)	2001.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2001}(2,\cdot)\)	2001.bv	308	yes	\(1\)	\(1\)	\(e\left(\frac{221}{308}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{47}{308}\right)\)	\(e\left(\frac{29}{308}\right)\)	\(e\left(\frac{65}{308}\right)\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{269}{308}\right)\)	\(e\left(\frac{67}{77}\right)\)
\(\chi_{2001}(4,\cdot)\)	2001.bo	154	no	\(1\)	\(1\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{57}{77}\right)\)
\(\chi_{2001}(5,\cdot)\)	2001.br	154	yes	\(1\)	\(1\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{39}{77}\right)\)
\(\chi_{2001}(7,\cdot)\)	2001.bp	154	no	\(-1\)	\(1\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)
\(\chi_{2001}(8,\cdot)\)	2001.bv	308	yes	\(1\)	\(1\)	\(e\left(\frac{47}{308}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{141}{308}\right)\)	\(e\left(\frac{87}{308}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{191}{308}\right)\)	\(e\left(\frac{47}{77}\right)\)
\(\chi_{2001}(10,\cdot)\)	2001.bu	308	no	\(1\)	\(1\)	\(e\left(\frac{29}{308}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{69}{154}\right)\)	\(e\left(\frac{87}{308}\right)\)	\(e\left(\frac{93}{308}\right)\)	\(e\left(\frac{235}{308}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{167}{308}\right)\)	\(e\left(\frac{29}{77}\right)\)
\(\chi_{2001}(11,\cdot)\)	2001.bs	308	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{308}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{235}{308}\right)\)	\(e\left(\frac{155}{308}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{65}{77}\right)\)
\(\chi_{2001}(13,\cdot)\)	2001.bo	154	no	\(1\)	\(1\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{37}{77}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{51}{77}\right)\)
\(\chi_{2001}(14,\cdot)\)	2001.bs	308	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{308}\right)\)	\(e\left(\frac{115}{154}\right)\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{191}{308}\right)\)	\(e\left(\frac{167}{308}\right)\)	\(e\left(\frac{215}{308}\right)\)	\(e\left(\frac{111}{154}\right)\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{38}{77}\right)\)
\(\chi_{2001}(16,\cdot)\)	2001.bk	77	no	\(1\)	\(1\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{37}{77}\right)\)
\(\chi_{2001}(17,\cdot)\)	2001.bj	44	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{2001}(19,\cdot)\)	2001.bu	308	no	\(1\)	\(1\)	\(e\left(\frac{211}{308}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{17}{308}\right)\)	\(e\left(\frac{135}{308}\right)\)	\(e\left(\frac{53}{308}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{153}{308}\right)\)	\(e\left(\frac{57}{77}\right)\)
\(\chi_{2001}(20,\cdot)\)	2001.bn	154	yes	\(1\)	\(1\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)
\(\chi_{2001}(22,\cdot)\)	2001.u	14	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2001}(25,\cdot)\)	2001.bk	77	no	\(1\)	\(1\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{51}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{20}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{43}{77}\right)\)	\(e\left(\frac{26}{77}\right)\)	\(e\left(\frac{1}{77}\right)\)
\(\chi_{2001}(26,\cdot)\)	2001.bv	308	yes	\(1\)	\(1\)	\(e\left(\frac{195}{308}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{12}{77}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{277}{308}\right)\)	\(e\left(\frac{243}{308}\right)\)	\(e\left(\frac{3}{308}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{183}{308}\right)\)	\(e\left(\frac{41}{77}\right)\)
\(\chi_{2001}(28,\cdot)\)	2001.bb	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2001}(31,\cdot)\)	2001.bt	308	no	\(-1\)	\(1\)	\(e\left(\frac{179}{308}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{229}{308}\right)\)	\(e\left(\frac{197}{308}\right)\)	\(e\left(\frac{107}{308}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{59}{308}\right)\)	\(e\left(\frac{25}{77}\right)\)
\(\chi_{2001}(32,\cdot)\)	2001.bv	308	yes	\(1\)	\(1\)	\(e\left(\frac{181}{308}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{60}{77}\right)\)	\(e\left(\frac{235}{308}\right)\)	\(e\left(\frac{145}{308}\right)\)	\(e\left(\frac{17}{308}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{113}{308}\right)\)	\(e\left(\frac{27}{77}\right)\)
\(\chi_{2001}(34,\cdot)\)	2001.bl	154	no	\(-1\)	\(1\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{23}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)
\(\chi_{2001}(35,\cdot)\)	2001.bq	154	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{46}{77}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{29}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)
\(\chi_{2001}(37,\cdot)\)	2001.bu	308	no	\(1\)	\(1\)	\(e\left(\frac{5}{308}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{65}{154}\right)\)	\(e\left(\frac{15}{308}\right)\)	\(e\left(\frac{101}{308}\right)\)	\(e\left(\frac{83}{308}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{135}{308}\right)\)	\(e\left(\frac{5}{77}\right)\)
\(\chi_{2001}(38,\cdot)\)	2001.br	154	yes	\(1\)	\(1\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{16}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{19}{77}\right)\)	\(e\left(\frac{57}{154}\right)\)	\(e\left(\frac{47}{77}\right)\)
\(\chi_{2001}(40,\cdot)\)	2001.bu	308	no	\(1\)	\(1\)	\(e\left(\frac{163}{308}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{181}{308}\right)\)	\(e\left(\frac{151}{308}\right)\)	\(e\left(\frac{57}{308}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{89}{308}\right)\)	\(e\left(\frac{9}{77}\right)\)
\(\chi_{2001}(41,\cdot)\)	2001.bg	44	yes	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2001}(43,\cdot)\)	2001.bu	308	no	\(1\)	\(1\)	\(e\left(\frac{283}{308}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{34}{77}\right)\)	\(e\left(\frac{137}{154}\right)\)	\(e\left(\frac{233}{308}\right)\)	\(e\left(\frac{111}{308}\right)\)	\(e\left(\frac{201}{308}\right)\)	\(e\left(\frac{83}{154}\right)\)	\(e\left(\frac{249}{308}\right)\)	\(e\left(\frac{52}{77}\right)\)
\(\chi_{2001}(44,\cdot)\)	2001.bs	308	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{308}\right)\)	\(e\left(\frac{45}{154}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{289}{308}\right)\)	\(e\left(\frac{293}{308}\right)\)	\(e\left(\frac{285}{308}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{137}{308}\right)\)	\(e\left(\frac{45}{77}\right)\)
\(\chi_{2001}(47,\cdot)\)	2001.bc	28	no	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{2001}(49,\cdot)\)	2001.bk	77	no	\(1\)	\(1\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{48}{77}\right)\)	\(e\left(\frac{45}{77}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{69}{77}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{19}{77}\right)\)
\(\chi_{2001}(50,\cdot)\)	2001.bv	308	yes	\(1\)	\(1\)	\(e\left(\frac{145}{308}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{127}{308}\right)\)	\(e\left(\frac{157}{308}\right)\)	\(e\left(\frac{97}{308}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{65}{308}\right)\)	\(e\left(\frac{68}{77}\right)\)
\(\chi_{2001}(52,\cdot)\)	2001.bk	77	no	\(1\)	\(1\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{68}{77}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{31}{77}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 1232 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.